Subgroups — C₂₃×#61603 #19209229

Order 5888.

2110 conjugacy classes of subgroups.

The subgroup lattice has 1370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3520	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#548	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3327	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3313	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3308	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3300	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3285	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3277	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3270	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3269	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3215	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3211	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3196	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3193	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3189	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3188	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3117	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3104	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#3007	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#3004	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#3002	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₂₃×#451	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₃×#2974	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
25	C₂³×Q₈×C₂₃	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×#137	C₂²	1	2	yes	complemented
27	C₂×C₂₃×#137	C₂²	1	2	yes	complemented
28	C₂×C₂₃×#135	C₂²	1	2	yes	complemented
29	C₂²×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
30	C₂₃×#556	C₂²	1	1	yes	characteristic, complemented
31	C₂₃×#554	—	2	1	no	—
32	C₂₃×#552	C₂²	1	1	yes	characteristic, complemented
33	C₂₃×#552	C₂²	1	1	yes	characteristic, complemented
34	C₂₃×#551	—	2	1	no	—
35	C₂₃×#551	—	2	1	no	—
36	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
37	C₂₃×#548	—	2	1	no	—
38	C₂₃×#548	—	2	1	no	—
39	C₂₃×#548	—	2	1	no	—
40	C₂₃×#548	—	2	1	no	—
41	C₂₃×#548	C₂²	1	2	yes	—
42	C₂₃×#548	C₂²	1	2	yes	—
43	C₂₃×#548	C₂²	1	2	yes	—
44	C₂₃×#548	C₂²	1	2	yes	—
45	C₂₃×#548	C₂²	1	1	yes	characteristic, complemented
46	C₂₃×#548	C₂²	1	1	yes	characteristic, complemented
47	C₂₃×#547	C₂²	1	1	yes	characteristic, complemented
48	C₂₃×#547	C₂²	1	1	yes	characteristic, complemented
49	C₂₃×#546	—	2	1	no	—
50	C₂₃×#542	—	2	1	no	—
51	C₂₃×#539	—	2	1	no	—
52	C₂₃×#539	—	2	1	no	—
53	C₂₃×#533	C₂²	1	1	yes	characteristic
54	C₂₃×#529	C₂²	1	1	yes	characteristic
55	C₂×C₂₃×#124	—	2	1	no	—
56	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
57	C₂₃×#525	C₂²	1	1	yes	characteristic
58	C₂₃×#525	C₂²	1	1	yes	characteristic
59	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
60	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
61	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
62	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
63	C₂×C₂₃×#121	—	2	1	no	—
64	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
65	C₂₃×#520	—	2	1	no	—
66	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
67	C₂×C₄×D₄×C₂₃	—	2	1	no	—
68	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
69	C₂₃×#497	C₂²	1	2	yes	complemented
70	C₂₃×#495	C₂²	1	2	yes	complemented
71	C₂₃×#489	C₂²	1	2	yes	complemented
72	C₂₃×#488	C₂²	1	2	yes	complemented
73	C₂₃×#485	C₂²	1	2	yes	complemented
74	C₂₃×#484	C₂²	1	1	yes	characteristic
75	C₂₃×#484	C₂²	1	1	yes	characteristic
76	C₂₃×#484	C₂²	1	1	yes	characteristic
77	C₂₃×#484	C₂²	1	2	yes	complemented
78	C₂₃×#482	C₂²	1	2	yes	complemented
79	C₂₃×#481	C₂²	1	1	yes	characteristic
80	C₂₃×#480	C₂²	1	2	yes	complemented
81	C₂₃×#479	C₂²	1	2	yes	complemented
82	C₂₃×#477	C₂²	1	2	yes	complemented
83	C₂₃×#470	C₂²	1	2	yes	complemented
84	C₂₃×#468	C₂²	1	2	yes	complemented
85	C₂₃×#468	C₂²	1	2	yes	complemented
86	C₂₃×#468	C₂²	1	2	yes	complemented
87	C₂₃×#467	C₂²	1	2	yes	complemented
88	C₂₃×#467	C₂²	1	2	yes	complemented
89	C₂₃×#466	C₂²	1	2	yes	complemented
90	C₂₃×#465	C₂²	1	2	yes	complemented
91	C₂₃×#464	C₂²	1	2	yes	complemented
92	C₂₃×#464	C₂²	1	2	yes	complemented
93	C₂₃×#464	C₂²	1	2	yes	complemented
94	C₂₃×#464	C₂²	1	2	yes	complemented
95	C₂₃×#463	C₂²	1	2	yes	complemented
96	C₂₃×#462	C₂²	1	2	yes	complemented
97	C₂₃×#452	C₂²	1	2	yes	complemented
98	C₂₃×#452	C₂²	1	2	yes	complemented
99	C₂₃×#452	C₂²	1	2	yes	complemented
100	C₂₃×#452	C₂²	1	2	yes	complemented
101	C₂₃×#451	C₂²	1	1	yes	characteristic
102	C₂₃×#451	C₂²	1	1	yes	characteristic
103	C₂₃×#451	C₂²	1	1	yes	characteristic
104	C₂₃×#451	C₂²	1	1	yes	characteristic
105	C₂₃×#451	C₂²	1	1	yes	characteristic
106	C₂₃×#451	C₂²	1	1	yes	characteristic
107	C₂₃×#451	C₂²	1	2	yes	complemented
108	C₂₃×#451	C₂²	1	2	yes	complemented
109	C₂₃×#451	C₂²	1	2	yes	complemented
110	C₂₃×#451	C₂²	1	2	yes	complemented
111	C₂₃×#450	C₂²	1	1	yes	characteristic
112	C₂₃×#450	C₂²	1	1	yes	characteristic
113	C₂₃×#450	C₂²	1	1	yes	characteristic
114	C₂₃×#449	C₂²	1	2	yes	complemented
115	C₂₃×#449	C₂²	1	2	yes	complemented
116	C₂₃×#448	C₂²	1	1	yes	characteristic
117	C₂₃×#448	C₂²	1	1	yes	characteristic
118	C₂₃×#448	C₂²	1	2	yes	complemented
119	C₂₃×#448	C₂²	1	2	yes	complemented
120	C₂₃×#447	C₂²	1	1	yes	characteristic
121	C₂₃×#441	C₂²	1	2	yes	complemented
122	C₂₃×#440	C₂²	1	2	yes	complemented
123	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
124	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
125	C₂₃×#436	C₂²	1	2	yes	complemented
126	C₂₃×#435	C₂²	1	2	yes	complemented
127	C₂₃×#435	C₂²	1	2	yes	complemented
128	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
129	C₂₃×#432	C₂²	1	1	yes	characteristic
130	C₂₃×#431	C₂²	1	1	yes	characteristic
131	C₂₃×#419	C₂²	1	2	yes	complemented
132	C₂₃×#417	C₂²	1	2	yes	complemented
133	C₂₃×#416	C₂²	1	2	yes	complemented
134	C₂×C₂₃×#103	C₂²	1	2	yes	complemented
135	C₂₃×#407	C₂²	1	1	yes	characteristic
136	C₂₃×#407	C₂²	1	1	yes	characteristic
137	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
138	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
139	C₂×#41×C₂₃	—	2	1	no	—
140	C₂×#41×C₂₃	—	2	1	no	—
141	C₂×#41×C₂₃	—	2	1	no	—
142	C₂×#41×C₂₃	—	4	4	no	—
143	C₂×#41×C₂₃	C₂³	1	2	yes	—
144	C₂×#41×C₂₃	C₂³	1	2	yes	—
145	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
146	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
147	C₂²×Q₈×C₂₃	—	2	1	no	—
148	C₂²×Q₈×C₂₃	—	2	1	no	—
149	C₂²×Q₈×C₂₃	—	2	1	no	—
150	C₂²×Q₈×C₂₃	—	4	4	no	—
151	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
152	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
153	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
154	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
155	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
156	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
157	C₂²×D₄×C₂₃	—	2	1	no	—
158	C₂²×D₄×C₂₃	—	2	1	no	—
159	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
160	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
161	C₂³×C₄×C₂₃	—	2	1	no	—
162	C₂³×C₄×C₂₃	—	2	1	no	—
163	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
164	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
165	C₂₃×#137	—	4	4	no	—
166	C₂₃×#137	—	4	4	no	—
167	C₂₃×#135	—	4	4	no	—
168	C₂×Q₁₆×C₂₃	—	4	4	no	—
169	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
170	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
171	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
172	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
173	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
174	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
175	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
176	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
177	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
178	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
179	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
180	C₂×D₈×C₂₃	C₂³	1	2	yes	—
181	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
182	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
183	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
184	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
185	C₂₃×C₄⋊Q₈	—	2	1	no	—
186	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
187	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
188	C₂₃×#126	—	2	1	no	—
189	C₂₃×#126	—	2	1	no	—
190	C₂₃×#126	—	2	1	no	—
191	C₂₃×#126	—	2	1	no	—
192	C₂₃×#126	—	2	1	no	—
193	C₂₃×#125	—	2	1	no	—
194	C₂₃×#125	—	2	1	no	—
195	C₂₃×#125	—	2	1	no	—
196	C₂₃×#125	C₂³	1	1	yes	characteristic
197	C₂₃×#124	—	2	1	no	—
198	C₂₃×#124	—	2	2	no	—
199	C₂₃×#124	—	2	2	no	—
200	C₂₃×#124	—	2	2	no	—
201	C₂₃×#124	—	2	2	no	—
202	C₂₃×#124	—	2	1	no	—
203	C₂₃×#124	—	2	1	no	—
204	C₂₃×#124	—	2	1	no	—
205	C₂₃×#124	—	2	1	no	—
206	C₂₃×#124	C₂³	1	2	yes	—
207	C₂₃×#124	C₂³	1	2	yes	—
208	C₂₃×#124	C₂³	1	1	yes	characteristic
209	C₂₃×#123	—	2	1	no	—
210	C₂₃×#123	—	2	1	no	—
211	C₂₃×#123	—	2	1	no	—
212	C₂₃×#123	—	2	1	no	—
213	C₂₃×#123	—	2	1	no	—
214	C₂₃×#123	—	2	1	no	—
215	C₂₃×#123	—	2	1	no	—
216	C₂₃×#123	—	2	1	no	—
217	C₂₃×#123	—	2	1	no	—
218	C₂₃×C₂²⋊Q₈	—	2	1	no	—
219	C₂₃×C₂²⋊Q₈	—	2	1	no	—
220	C₂₃×C₂²⋊Q₈	—	2	1	no	—
221	C₂₃×C₂²⋊Q₈	—	2	1	no	—
222	C₂₃×C₂²⋊Q₈	—	2	1	no	—
223	C₂₃×C₂²⋊Q₈	—	2	1	no	—
224	C₂₃×C₂²⋊Q₈	—	2	1	no	—
225	C₂₃×C₂²⋊Q₈	—	2	1	no	—
226	C₂₃×C₂²⋊Q₈	—	2	2	no	—
227	C₂₃×C₂²⋊Q₈	—	2	2	no	—
228	C₂₃×C₂²⋊Q₈	—	2	2	no	—
229	C₂₃×C₂²⋊Q₈	—	2	2	no	—
230	C₂₃×C₂²⋊Q₈	—	2	1	no	—
231	C₂₃×C₂²⋊Q₈	—	2	1	no	—
232	C₂₃×C₂²⋊Q₈	—	2	1	no	—
233	C₂₃×C₂²⋊Q₈	—	2	1	no	—
234	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
235	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
236	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
237	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
238	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
239	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
240	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
241	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
242	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
243	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
244	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
245	C₂₃×#121	—	2	1	no	—
246	C₂₃×#121	—	2	2	no	—
247	C₂₃×#121	—	2	2	no	—
248	C₂₃×#121	—	2	2	no	—
249	C₂₃×#121	—	2	2	no	—
250	C₂₃×#121	—	2	1	no	—
251	C₂₃×#121	—	2	1	no	—
252	C₂₃×#121	—	2	1	no	—
253	C₂₃×#121	—	2	1	no	—
254	C₂₃×#121	C₂³	1	1	yes	characteristic
255	C₂₃×#121	C₂³	1	1	yes	characteristic
256	C₂₃×#121	C₂³	1	2	yes	—
257	C₂₃×#121	C₂³	1	2	yes	—
258	C₂₃×#121	C₂³	1	1	yes	characteristic
259	C₂₃×#120	—	2	1	no	—
260	C₂₃×#120	—	2	1	no	—
261	C₄×Q₈×C₂₃	—	2	1	no	—
262	C₄×Q₈×C₂₃	—	2	1	no	—
263	C₄×Q₈×C₂₃	—	2	1	no	—
264	C₄×Q₈×C₂₃	—	2	1	no	—
265	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
266	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
267	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
268	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
269	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
270	C₄×D₄×C₂₃	—	2	1	no	—
271	C₄×D₄×C₂₃	—	2	1	no	—
272	C₄×D₄×C₂₃	—	2	1	no	—
273	C₄×D₄×C₂₃	—	2	1	no	—
274	C₄×D₄×C₂₃	—	2	1	no	—
275	C₄×D₄×C₂₃	—	2	1	no	—
276	C₄×D₄×C₂₃	—	2	2	no	—
277	C₄×D₄×C₂₃	—	2	2	no	—
278	C₄×D₄×C₂₃	—	2	2	no	—
279	C₄×D₄×C₂₃	—	2	2	no	—
280	C₄×D₄×C₂₃	—	2	1	no	—
281	C₄×D₄×C₂₃	—	2	1	no	—
282	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
283	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
284	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
285	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
286	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
287	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
288	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
289	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
290	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
291	C₂₃×#117	—	2	1	no	—
292	C₂₃×#117	—	2	1	no	—
293	C₂₃×#117	—	2	1	no	—
294	C₂₃×#117	—	2	1	no	—
295	C₂₃×#117	C₂³	1	1	yes	characteristic
296	C₂₃×#117	C₂³	1	1	yes	characteristic
297	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
298	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
299	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
300	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
301	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
302	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
303	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
304	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
305	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
306	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
307	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
308	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
309	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
310	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
311	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
312	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
313	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
314	C₂×C₄²×C₂₃	—	2	1	no	—
315	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
316	C₂₃×#107	C₂³	1	2	yes	—
317	C₂₃×#107	C₂³	1	2	yes	—
318	C₂₃×#107	C₂³	1	2	yes	—
319	C₂₃×#106	C₂³	1	2	yes	—
320	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
321	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
322	C₂₃×#103	C₂³	1	2	yes	—
323	C₂₃×#103	C₂³	1	2	yes	—
324	C₂₃×#103	C₂³	1	2	yes	—
325	C₂₃×#103	C₂³	1	2	yes	—
326	C₂₃×#103	C₂³	1	2	yes	—
327	C₂₃×#103	C₂³	1	2	yes	—
328	C₂₃×#103	C₂³	1	2	yes	—
329	C₂₃×#103	C₂³	1	2	yes	—
330	C₂₃×#103	C₂³	1	2	yes	—
331	C₂₃×#103	C₂³	1	2	yes	—
332	C₂₃×#103	C₂³	1	2	yes	—
333	C₂₃×#102	C₂³	1	2	yes	—
334	C₂₃×#102	C₂³	1	2	yes	—
335	C₂₃×#102	C₂³	1	2	yes	—
336	C₂₃×#102	C₂³	1	2	yes	—
337	C₂₃×#102	C₂³	1	2	yes	—
338	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
339	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
340	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
341	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
342	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
343	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
344	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
345	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
346	C₂₃×#97	C₂³	1	2	yes	—
347	C₄×C₈×C₂₃	C₂³	1	2	yes	—
348	C₂⁴×C₂₃	—	2	1	no	—
349	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
350	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
351	#41×C₂₃	—	2	4	no	—
352	#41×C₂₃	—	2	4	no	—
353	#41×C₂₃	—	4	2	no	—
354	#41×C₂₃	—	4	2	no	—
355	#41×C₂₃	—	4	2	no	—
356	#41×C₂₃	—	4	2	no	—
357	#41×C₂₃	—	4	4	no	—
358	#41×C₂₃	—	4	4	no	—
359	#41×C₂₃	—	4	4	no	—
360	C₂×Q₈×C₂₃	—	2	4	no	—
361	C₂×Q₈×C₂₃	—	2	1	no	—
362	C₂×Q₈×C₂₃	—	2	1	no	—
363	C₂×Q₈×C₂₃	—	2	2	no	—
364	C₂×Q₈×C₂₃	—	2	2	no	—
365	C₂×Q₈×C₂₃	—	2	1	no	—
366	C₂×Q₈×C₂₃	—	2	1	no	—
367	C₂×Q₈×C₂₃	—	2	1	no	—
368	C₂×Q₈×C₂₃	—	2	4	no	—
369	C₂×Q₈×C₂₃	—	2	4	no	—
370	C₂×Q₈×C₂₃	—	4	2	no	—
371	C₂×Q₈×C₂₃	—	4	2	no	—
372	C₂×Q₈×C₂₃	—	4	2	no	—
373	C₂×Q₈×C₂₃	—	4	4	no	—
374	C₂×Q₈×C₂₃	—	4	2	no	—
375	C₂×Q₈×C₂₃	—	4	2	no	—
376	C₂×Q₈×C₂₃	—	4	4	no	—
377	C₂×Q₈×C₂₃	—	4	4	no	—
378	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
379	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
380	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
381	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
382	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
383	C₂×D₄×C₂₃	—	2	1	no	—
384	C₂×D₄×C₂₃	—	2	1	no	—
385	C₂×D₄×C₂₃	—	2	1	no	—
386	C₂×D₄×C₂₃	—	2	2	no	—
387	C₂×D₄×C₂₃	—	2	2	no	—
388	C₂×D₄×C₂₃	—	2	2	no	—
389	C₂×D₄×C₂₃	—	2	2	no	—
390	C₂×D₄×C₂₃	—	2	1	no	—
391	C₂×D₄×C₂₃	—	2	1	no	—
392	C₂×D₄×C₂₃	—	2	1	no	—
393	C₂×D₄×C₂₃	—	4	2	no	—
394	C₂×D₄×C₂₃	—	4	4	no	—
395	C₂×D₄×C₂₃	—	4	2	no	—
396	C₂×D₄×C₂₃	—	4	4	no	—
397	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
398	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
399	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
400	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
401	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
402	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
403	C₂²×C₄×C₂₃	—	2	1	no	—
404	C₂²×C₄×C₂₃	—	2	1	no	—
405	C₂²×C₄×C₂₃	—	2	1	no	—
406	C₂²×C₄×C₂₃	—	2	1	no	—
407	C₂²×C₄×C₂₃	—	2	1	no	—
408	C₂²×C₄×C₂₃	—	2	2	no	—
409	C₂²×C₄×C₂₃	—	2	2	no	—
410	C₂²×C₄×C₂₃	—	2	1	no	—
411	C₂²×C₄×C₂₃	—	2	1	no	—
412	C₂²×C₄×C₂₃	—	2	1	no	—
413	C₂²×C₄×C₂₃	—	2	2	no	—
414	C₂²×C₄×C₂₃	—	2	2	no	—
415	C₂²×C₄×C₂₃	—	2	1	no	—
416	C₂²×C₄×C₂₃	—	2	1	no	—
417	C₂²×C₄×C₂₃	—	4	2	no	—
418	C₂²×C₄×C₂₃	—	4	2	no	—
419	C₂²×C₄×C₂₃	—	4	4	no	—
420	C₂²×C₄×C₂₃	—	4	4	no	—
421	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
422	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
423	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
424	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
425	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
426	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
427	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
428	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
429	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
430	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
431	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
432	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
433	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
434	Q₁₆×C₂₃	—	2	4	no	—
435	Q₁₆×C₂₃	—	2	4	no	—
436	Q₁₆×C₂₃	—	2	4	no	—
437	Q₁₆×C₂₃	—	4	2	no	—
438	Q₁₆×C₂₃	—	4	2	no	—
439	Q₁₆×C₂₃	—	4	2	no	—
440	SD₁₆×C₂₃	—	2	4	no	—
441	SD₁₆×C₂₃	—	4	2	no	—
442	SD₁₆×C₂₃	—	4	2	no	—
443	SD₁₆×C₂₃	—	4	2	no	—
444	SD₁₆×C₂₃	—	4	2	no	—
445	D₈×C₂₃	—	4	2	no	—
446	M₁₆×C₂₃	—	4	2	no	—
447	M₁₆×C₂₃	—	4	2	no	—
448	C₂×C₈×C₂₃	—	4	2	no	—
449	C₂×C₈×C₂₃	—	4	2	no	—
450	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
451	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
452	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
453	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
454	C₄⋊C₄×C₂₃	—	2	1	no	—
455	C₄⋊C₄×C₂₃	—	2	1	no	—
456	C₄⋊C₄×C₂₃	—	2	1	no	—
457	C₄⋊C₄×C₂₃	—	2	2	no	—
458	C₄⋊C₄×C₂₃	—	2	2	no	—
459	C₄⋊C₄×C₂₃	—	2	1	no	—
460	C₄⋊C₄×C₂₃	—	2	1	no	—
461	C₄⋊C₄×C₂₃	—	2	1	no	—
462	C₄⋊C₄×C₂₃	—	2	1	no	—
463	C₄⋊C₄×C₂₃	—	2	1	no	—
464	C₄⋊C₄×C₂₃	—	2	2	no	—
465	C₄⋊C₄×C₂₃	—	2	2	no	—
466	C₄⋊C₄×C₂₃	—	2	1	no	—
467	C₄⋊C₄×C₂₃	—	2	1	no	—
468	C₄⋊C₄×C₂₃	—	2	1	no	—
469	C₄⋊C₄×C₂₃	—	2	1	no	—
470	C₄⋊C₄×C₂₃	—	2	1	no	—
471	C₄⋊C₄×C₂₃	—	2	1	no	—
472	C₄⋊C₄×C₂₃	—	2	1	no	—
473	C₄⋊C₄×C₂₃	—	2	1	no	—
474	C₄⋊C₄×C₂₃	—	2	1	no	—
475	C₄⋊C₄×C₂₃	—	2	1	no	—
476	C₄⋊C₄×C₂₃	—	2	1	no	—
477	C₄⋊C₄×C₂₃	—	2	1	no	—
478	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
479	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
480	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
481	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
482	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
483	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
484	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
485	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
486	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
487	C₂²⋊C₄×C₂₃	—	2	1	no	—
488	C₂²⋊C₄×C₂₃	—	2	1	no	—
489	C₂²⋊C₄×C₂₃	—	2	1	no	—
490	C₂²⋊C₄×C₂₃	—	2	2	no	—
491	C₂²⋊C₄×C₂₃	—	2	2	no	—
492	C₂²⋊C₄×C₂₃	—	2	1	no	—
493	C₂²⋊C₄×C₂₃	—	2	1	no	—
494	C₂²⋊C₄×C₂₃	—	2	1	no	—
495	C₂²⋊C₄×C₂₃	—	2	1	no	—
496	C₂²⋊C₄×C₂₃	—	2	1	no	—
497	C₂²⋊C₄×C₂₃	—	2	1	no	—
498	C₂²⋊C₄×C₂₃	—	2	1	no	—
499	C₂²⋊C₄×C₂₃	—	2	1	no	—
500	C₂²⋊C₄×C₂₃	—	2	2	no	—
501	C₂²⋊C₄×C₂₃	—	2	2	no	—
502	C₂²⋊C₄×C₂₃	—	2	2	no	—
503	C₂²⋊C₄×C₂₃	—	2	2	no	—
504	C₂²⋊C₄×C₂₃	—	2	2	no	—
505	C₂²⋊C₄×C₂₃	—	2	2	no	—
506	C₂²⋊C₄×C₂₃	—	2	1	no	—
507	C₂²⋊C₄×C₂₃	—	2	1	no	—
508	C₂²⋊C₄×C₂₃	—	2	1	no	—
509	C₂²⋊C₄×C₂₃	—	2	1	no	—
510	C₂²⋊C₄×C₂₃	—	2	1	no	—
511	C₂²⋊C₄×C₂₃	—	2	1	no	—
512	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
513	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
514	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
515	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
516	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
517	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
518	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
519	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
520	C₄²×C₂₃	—	2	2	no	—
521	C₄²×C₂₃	—	2	2	no	—
522	C₄²×C₂₃	—	2	1	no	—
523	C₄²×C₂₃	—	2	1	no	—
524	C₄²×C₂₃	—	2	1	no	—
525	C₄²×C₂₃	—	2	1	no	—
526	C₄²×C₂₃	—	2	1	no	—
527	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
528	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
529	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
530	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
531	#61603	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
532	C₂³×C₂₃	—	2	2	no	—
533	C₂³×C₂₃	—	2	2	no	—
534	C₂³×C₂₃	—	2	2	no	—
535	C₂³×C₂₃	—	2	1	no	—
536	C₂³×C₂₃	—	2	2	no	—
537	C₂³×C₂₃	—	4	1	no	—
538	C₂³×C₂₃	—	4	1	no	—
539	C₂³×C₂₃	—	4	1	no	—
540	C₂³×C₂₃	—	4	2	no	—
541	C₂³×C₂₃	—	4	2	no	—
542	C₂³×C₂₃	—	4	2	no	—
543	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
544	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
545	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
546	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
547	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
548	Q₈×C₂₃	—	2	4	no	—
549	Q₈×C₂₃	—	2	2	no	—
550	Q₈×C₂₃	—	2	2	no	—
551	Q₈×C₂₃	—	2	2	no	—
552	Q₈×C₂₃	—	2	2	no	—
553	Q₈×C₂₃	—	2	2	no	—
554	Q₈×C₂₃	—	2	2	no	—
555	Q₈×C₂₃	—	4	4	no	—
556	Q₈×C₂₃	—	4	4	no	—
557	Q₈×C₂₃	—	4	2	no	—
558	Q₈×C₂₃	—	4	2	no	—
559	Q₈×C₂₃	—	8	1	no	—
560	Q₈×C₂₃	—	8	1	no	—
561	Q₈×C₂₃	H(5,𝔽₂)	1	4	yes	—
562	D₄×C₂₃	—	2	2	no	—
563	D₄×C₂₃	—	2	2	no	—
564	D₄×C₂₃	—	2	2	no	—
565	D₄×C₂₃	—	2	2	no	—
566	D₄×C₂₃	—	2	2	no	—
567	D₄×C₂₃	—	4	1	no	—
568	D₄×C₂₃	—	4	1	no	—
569	D₄×C₂₃	—	4	4	no	—
570	D₄×C₂₃	—	4	4	no	—
571	D₄×C₂₃	—	4	2	no	—
572	D₄×C₂₃	—	4	4	no	—
573	D₄×C₂₃	—	4	2	no	—
574	D₄×C₂₃	—	4	4	no	—
575	D₄×C₂₃	—	4	2	no	—
576	D₄×C₂₃	—	4	2	no	—
577	D₄×C₂₃	—	8	1	no	—
578	D₄×C₂₃	—	8	1	no	—
579	C₂×C₄×C₂₃	—	2	4	no	—
580	C₂×C₄×C₂₃	—	2	2	no	—
581	C₂×C₄×C₂₃	—	2	2	no	—
582	C₂×C₄×C₂₃	—	2	2	no	—
583	C₂×C₄×C₂₃	—	2	2	no	—
584	C₂×C₄×C₂₃	—	2	2	no	—
585	C₂×C₄×C₂₃	—	2	2	no	—
586	C₂×C₄×C₂₃	—	2	2	no	—
587	C₂×C₄×C₂₃	—	2	1	no	—
588	C₂×C₄×C₂₃	—	2	2	no	—
589	C₂×C₄×C₂₃	—	2	1	no	—
590	C₂×C₄×C₂₃	—	2	1	no	—
591	C₂×C₄×C₂₃	—	2	1	no	—
592	C₂×C₄×C₂₃	—	2	1	no	—
593	C₂×C₄×C₂₃	—	2	1	no	—
594	C₂×C₄×C₂₃	—	2	2	no	—
595	C₂×C₄×C₂₃	—	2	1	no	—
596	C₂×C₄×C₂₃	—	4	1	no	—
597	C₂×C₄×C₂₃	—	4	1	no	—
598	C₂×C₄×C₂₃	—	4	1	no	—
599	C₂×C₄×C₂₃	—	4	1	no	—
600	C₂×C₄×C₂₃	—	4	1	no	—
601	C₂×C₄×C₂₃	—	4	1	no	—
602	C₂×C₄×C₂₃	—	4	1	no	—
603	C₂×C₄×C₂₃	—	4	4	no	—
604	C₂×C₄×C₂₃	—	4	4	no	—
605	C₂×C₄×C₂₃	—	4	4	no	—
606	C₂×C₄×C₂₃	—	4	4	no	—
607	C₂×C₄×C₂₃	—	4	2	no	—
608	C₂×C₄×C₂₃	—	4	2	no	—
609	C₂×C₄×C₂₃	—	4	2	no	—
610	C₂×C₄×C₂₃	—	4	2	no	—
611	C₂×C₄×C₂₃	—	4	2	no	—
612	C₂×C₄×C₂₃	—	8	1	no	—
613	C₂×C₄×C₂₃	—	8	1	no	—
614	C₂×C₄×C₂₃	—	8	1	no	—
615	C₂×C₄×C₂₃	—	8	1	no	—
616	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
617	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
618	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
619	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
620	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
621	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
622	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
623	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
624	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
625	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
626	C₈×C₂₃	—	2	2	no	—
627	C₈×C₂₃	—	2	2	no	—
628	C₈×C₂₃	—	2	2	no	—
629	C₈×C₂₃	—	2	2	no	—
630	#3520	C₂×C₂₃	1	1	yes	characteristic, complemented
631	C₂×#548	C₂×C₂₃	1	1	yes	characteristic, complemented
632	#3327	C₂×C₂₃	1	2	yes	complemented
633	#3313	C₂×C₂₃	1	2	yes	complemented
634	#3308	C₂×C₂₃	1	2	yes	complemented
635	#3300	C₂×C₂₃	1	2	yes	complemented
636	#3285	C₂×C₂₃	1	2	yes	complemented
637	#3277	C₂×C₂₃	1	2	yes	complemented
638	#3270	C₂×C₂₃	1	2	yes	complemented
639	#3269	C₂×C₂₃	1	2	yes	complemented
640	#3215	C₂×C₂₃	1	1	yes	characteristic, complemented
641	#3211	C₂×C₂₃	1	1	yes	characteristic, complemented
642	#3196	C₂×C₂₃	1	1	yes	characteristic, complemented
643	#3193	C₂×C₂₃	1	1	yes	characteristic, complemented
644	#3189	C₂×C₂₃	1	1	yes	characteristic, complemented
645	#3188	C₂×C₂₃	1	1	yes	characteristic, complemented
646	#3117	C₂×C₂₃	1	1	yes	characteristic, complemented
647	#3104	C₂×C₂₃	1	1	yes	characteristic, complemented
648	#3007	C₂×C₂₃	1	1	yes	characteristic, complemented
649	#3004	C₂×C₂₃	1	1	yes	characteristic, complemented
650	#3002	C₂×C₂₃	1	1	yes	characteristic, complemented
651	C₂×#451	C₂×C₂₃	1	1	yes	characteristic, complemented
652	#2974	C₂×C₂₃	1	1	yes	characteristic, complemented
653	C₂²×C₂₃	—	2	1	no	—
654	C₂²×C₂₃	—	2	1	no	—
655	C₂²×C₂₃	—	2	1	no	—
656	C₂²×C₂₃	—	2	1	no	—
657	C₂²×C₂₃	—	2	1	no	—
658	C₂²×C₂₃	—	2	1	no	—
659	C₂²×C₂₃	—	2	1	no	—
660	C₂²×C₂₃	—	2	1	no	—
661	C₂²×C₂₃	—	2	1	no	—
662	C₂²×C₂₃	—	2	1	no	—
663	C₂²×C₂₃	—	2	1	no	—
664	C₂²×C₂₃	—	2	1	no	—
665	C₂²×C₂₃	—	2	1	no	—
666	C₂²×C₂₃	—	4	4	no	—
667	C₂²×C₂₃	—	4	2	no	—
668	C₂²×C₂₃	—	4	1	no	—
669	C₂²×C₂₃	—	4	1	no	—
670	C₂²×C₂₃	—	4	2	no	—
671	C₂²×C₂₃	—	4	1	no	—
672	C₂²×C₂₃	—	4	2	no	—
673	C₂²×C₂₃	—	8	2	no	—
674	C₂²×C₂₃	—	8	4	no	—
675	C₂²×C₂₃	#575	1	2	yes	—
676	C₂²×C₂₃	#578	1	2	yes	—
677	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
678	C₄×C₂₃	—	2	4	no	—
679	C₄×C₂₃	—	2	1	no	—
680	C₄×C₂₃	—	2	1	no	—
681	C₄×C₂₃	—	2	1	no	—
682	C₄×C₂₃	—	2	1	no	—
683	C₄×C₂₃	—	2	1	no	—
684	C₄×C₂₃	—	2	1	no	—
685	C₄×C₂₃	—	2	1	no	—
686	C₄×C₂₃	—	2	1	no	—
687	C₄×C₂₃	—	2	1	no	—
688	C₄×C₂₃	—	4	2	no	—
689	C₄×C₂₃	—	4	1	no	—
690	C₄×C₂₃	—	4	1	no	—
691	C₄×C₂₃	—	4	1	no	—
692	C₄×C₂₃	—	4	1	no	—
693	C₄×C₂₃	—	4	2	no	—
694	C₄×C₂₃	—	4	1	no	—
695	C₄×C₂₃	—	4	1	no	—
696	C₄×C₂₃	—	4	1	no	—
697	C₄×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
698	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
699	C₂³×Q₈	C₂²×C₂₃	1	1	yes	characteristic
700	C₂×#137	C₂²×C₂₃	1	2	yes	complemented
701	C₂×#137	C₂²×C₂₃	1	2	yes	complemented
702	C₂×#135	C₂²×C₂₃	1	2	yes	complemented
703	C₂²×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
704	#556	C₂²×C₂₃	1	1	yes	characteristic, complemented
705	#554	—	2	1	no	—
706	#552	C₂²×C₂₃	1	1	yes	characteristic, complemented
707	#552	C₂²×C₂₃	1	1	yes	characteristic, complemented
708	#551	—	2	1	no	—
709	#551	—	2	1	no	—
710	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
711	#548	—	2	1	no	—
712	#548	—	2	1	no	—
713	#548	—	2	1	no	—
714	#548	—	2	1	no	—
715	#548	C₂²×C₂₃	1	2	yes	—
716	#548	C₂²×C₂₃	1	2	yes	—
717	#548	C₂²×C₂₃	1	2	yes	—
718	#548	C₂²×C₂₃	1	2	yes	—
719	#548	C₂²×C₂₃	1	1	yes	characteristic, complemented
720	#548	C₂²×C₂₃	1	1	yes	characteristic, complemented
721	#547	C₂²×C₂₃	1	1	yes	characteristic, complemented
722	#547	C₂²×C₂₃	1	1	yes	characteristic, complemented
723	#546	—	2	1	no	—
724	#542	—	2	1	no	—
725	#539	—	2	1	no	—
726	#539	—	2	1	no	—
727	#533	C₂²×C₂₃	1	1	yes	characteristic
728	#529	C₂²×C₂₃	1	1	yes	characteristic
729	C₂×#124	—	2	1	no	—
730	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
731	#525	C₂²×C₂₃	1	1	yes	characteristic
732	#525	C₂²×C₂₃	1	1	yes	characteristic
733	C₂×C₂²⋊Q₈	—	2	1	no	—
734	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
735	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
736	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
737	C₂×#121	—	2	1	no	—
738	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
739	#520	—	2	1	no	—
740	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
741	C₂×C₄×D₄	—	2	1	no	—
742	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
743	#497	C₂²×C₂₃	1	2	yes	complemented
744	#495	C₂²×C₂₃	1	2	yes	complemented
745	#489	C₂²×C₂₃	1	2	yes	complemented
746	#488	C₂²×C₂₃	1	2	yes	complemented
747	#485	C₂²×C₂₃	1	2	yes	complemented
748	#484	C₂²×C₂₃	1	1	yes	characteristic
749	#484	C₂²×C₂₃	1	1	yes	characteristic
750	#484	C₂²×C₂₃	1	1	yes	characteristic
751	#484	C₂²×C₂₃	1	2	yes	complemented
752	#482	C₂²×C₂₃	1	2	yes	complemented
753	#481	C₂²×C₂₃	1	1	yes	characteristic
754	#480	C₂²×C₂₃	1	2	yes	complemented
755	#479	C₂²×C₂₃	1	2	yes	complemented
756	#477	C₂²×C₂₃	1	2	yes	complemented
757	#470	C₂²×C₂₃	1	2	yes	complemented
758	#468	C₂²×C₂₃	1	2	yes	complemented
759	#468	C₂²×C₂₃	1	2	yes	complemented
760	#468	C₂²×C₂₃	1	2	yes	complemented
761	#467	C₂²×C₂₃	1	2	yes	complemented
762	#467	C₂²×C₂₃	1	2	yes	complemented
763	#466	C₂²×C₂₃	1	2	yes	complemented
764	#465	C₂²×C₂₃	1	2	yes	complemented
765	#464	C₂²×C₂₃	1	2	yes	complemented
766	#464	C₂²×C₂₃	1	2	yes	complemented
767	#464	C₂²×C₂₃	1	2	yes	complemented
768	#464	C₂²×C₂₃	1	2	yes	complemented
769	#463	C₂²×C₂₃	1	2	yes	complemented
770	#462	C₂²×C₂₃	1	2	yes	complemented
771	#452	C₂²×C₂₃	1	2	yes	complemented
772	#452	C₂²×C₂₃	1	2	yes	complemented
773	#452	C₂²×C₂₃	1	2	yes	complemented
774	#452	C₂²×C₂₃	1	2	yes	complemented
775	#451	C₂²×C₂₃	1	1	yes	characteristic
776	#451	C₂²×C₂₃	1	1	yes	characteristic
777	#451	C₂²×C₂₃	1	1	yes	characteristic
778	#451	C₂²×C₂₃	1	1	yes	characteristic
779	#451	C₂²×C₂₃	1	1	yes	characteristic
780	#451	C₂²×C₂₃	1	1	yes	characteristic
781	#451	C₂²×C₂₃	1	2	yes	complemented
782	#451	C₂²×C₂₃	1	2	yes	complemented
783	#451	C₂²×C₂₃	1	2	yes	complemented
784	#451	C₂²×C₂₃	1	2	yes	complemented
785	#450	C₂²×C₂₃	1	1	yes	characteristic
786	#450	C₂²×C₂₃	1	1	yes	characteristic
787	#450	C₂²×C₂₃	1	1	yes	characteristic
788	#449	C₂²×C₂₃	1	2	yes	complemented
789	#449	C₂²×C₂₃	1	2	yes	complemented
790	#448	C₂²×C₂₃	1	1	yes	characteristic
791	#448	C₂²×C₂₃	1	1	yes	characteristic
792	#448	C₂²×C₂₃	1	2	yes	complemented
793	#448	C₂²×C₂₃	1	2	yes	complemented
794	#447	C₂²×C₂₃	1	1	yes	characteristic
795	#441	C₂²×C₂₃	1	2	yes	complemented
796	#440	C₂²×C₂₃	1	2	yes	complemented
797	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
798	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
799	#436	C₂²×C₂₃	1	2	yes	complemented
800	#435	C₂²×C₂₃	1	2	yes	complemented
801	#435	C₂²×C₂₃	1	2	yes	complemented
802	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
803	#432	C₂²×C₂₃	1	1	yes	characteristic
804	#431	C₂²×C₂₃	1	1	yes	characteristic
805	#419	C₂²×C₂₃	1	2	yes	complemented
806	#417	C₂²×C₂₃	1	2	yes	complemented
807	#416	C₂²×C₂₃	1	2	yes	complemented
808	C₂×#103	C₂²×C₂₃	1	2	yes	complemented
809	#407	C₂²×C₂₃	1	1	yes	characteristic
810	#407	C₂²×C₂₃	1	1	yes	characteristic
811	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
812	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
813	C₂×C₂₃	—	2	2	no	—
814	C₂×C₂₃	—	2	2	no	—
815	C₂×C₂₃	—	4	1	no	—
816	C₂×C₂₃	—	4	1	no	—
817	C₂×C₂₃	—	4	1	no	—
818	C₂×C₂₃	—	8	1	no	—
819	C₂×C₂₃	—	8	2	no	—
820	C₂×C₂₃	#3484	1	1	yes	characteristic
821	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
822	C₂×C₂₃	C₂×#578	1	1	yes	characteristic
823	C₂×#41	—	2	1	no	—
824	C₂×#41	—	2	1	no	—
825	C₂×#41	—	2	1	no	—
826	C₂×#41	—	4	4	no	—
827	C₂×#41	C₂³×C₂₃	1	2	yes	—
828	C₂×#41	C₂³×C₂₃	1	2	yes	—
829	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
830	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
831	C₂²×Q₈	—	2	1	no	—
832	C₂²×Q₈	—	2	1	no	—
833	C₂²×Q₈	—	2	1	no	—
834	C₂²×Q₈	—	4	4	no	—
835	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
836	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
837	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
838	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
839	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
840	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
841	C₂²×D₄	—	2	1	no	—
842	C₂²×D₄	—	2	1	no	—
843	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
844	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
845	C₂³×C₄	—	2	1	no	—
846	C₂³×C₄	—	2	1	no	—
847	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
848	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
849	#137	—	4	4	no	—
850	#137	—	4	4	no	—
851	#135	—	4	4	no	—
852	C₂×Q₁₆	—	4	4	no	—
853	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
854	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
855	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
856	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
857	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
858	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
859	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
860	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
861	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
862	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
863	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
864	C₂×D₈	C₂³×C₂₃	1	2	yes	—
865	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
866	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
867	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
868	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
869	C₄⋊Q₈	—	2	1	no	—
870	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
871	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
872	#126	—	2	1	no	—
873	#126	—	2	1	no	—
874	#126	—	2	1	no	—
875	#126	—	2	1	no	—
876	#126	—	2	1	no	—
877	#125	—	2	1	no	—
878	#125	—	2	1	no	—
879	#125	—	2	1	no	—
880	#125	C₂³×C₂₃	1	1	yes	characteristic
881	#124	—	2	1	no	—
882	#124	—	2	2	no	—
883	#124	—	2	2	no	—
884	#124	—	2	2	no	—
885	#124	—	2	2	no	—
886	#124	—	2	1	no	—
887	#124	—	2	1	no	—
888	#124	—	2	1	no	—
889	#124	—	2	1	no	—
890	#124	C₂³×C₂₃	1	2	yes	—
891	#124	C₂³×C₂₃	1	2	yes	—
892	#124	C₂³×C₂₃	1	1	yes	characteristic
893	#123	—	2	1	no	—
894	#123	—	2	1	no	—
895	#123	—	2	1	no	—
896	#123	—	2	1	no	—
897	#123	—	2	1	no	—
898	#123	—	2	1	no	—
899	#123	—	2	1	no	—
900	#123	—	2	1	no	—
901	#123	—	2	1	no	—
902	C₂²⋊Q₈	—	2	1	no	—
903	C₂²⋊Q₈	—	2	1	no	—
904	C₂²⋊Q₈	—	2	1	no	—
905	C₂²⋊Q₈	—	2	1	no	—
906	C₂²⋊Q₈	—	2	1	no	—
907	C₂²⋊Q₈	—	2	1	no	—
908	C₂²⋊Q₈	—	2	1	no	—
909	C₂²⋊Q₈	—	2	2	no	—
910	C₂²⋊Q₈	—	2	2	no	—
911	C₂²⋊Q₈	—	2	2	no	—
912	C₂²⋊Q₈	—	2	2	no	—
913	C₂²⋊Q₈	—	2	1	no	—
914	C₂²⋊Q₈	—	2	1	no	—
915	C₂²⋊Q₈	—	2	1	no	—
916	C₂²⋊Q₈	—	2	1	no	—
917	C₂²⋊Q₈	—	2	1	no	—
918	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
919	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
920	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
921	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
922	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
923	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
924	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
925	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
926	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
927	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
928	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
929	#121	—	2	2	no	—
930	#121	—	2	2	no	—
931	#121	—	2	2	no	—
932	#121	—	2	2	no	—
933	#121	—	2	1	no	—
934	#121	—	2	1	no	—
935	#121	—	2	1	no	—
936	#121	—	2	1	no	—
937	#121	—	2	1	no	—
938	#121	C₂³×C₂₃	1	2	yes	—
939	#121	C₂³×C₂₃	1	2	yes	—
940	#121	C₂³×C₂₃	1	1	yes	characteristic
941	#121	C₂³×C₂₃	1	1	yes	characteristic
942	#121	C₂³×C₂₃	1	1	yes	characteristic
943	#120	—	2	1	no	—
944	#120	—	2	1	no	—
945	C₄×Q₈	—	2	1	no	—
946	C₄×Q₈	—	2	1	no	—
947	C₄×Q₈	—	2	1	no	—
948	C₄×Q₈	—	2	1	no	—
949	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
950	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
951	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
952	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
953	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
954	C₄×D₄	—	2	1	no	—
955	C₄×D₄	—	2	1	no	—
956	C₄×D₄	—	2	1	no	—
957	C₄×D₄	—	2	1	no	—
958	C₄×D₄	—	2	1	no	—
959	C₄×D₄	—	2	1	no	—
960	C₄×D₄	—	2	2	no	—
961	C₄×D₄	—	2	2	no	—
962	C₄×D₄	—	2	2	no	—
963	C₄×D₄	—	2	2	no	—
964	C₄×D₄	—	2	1	no	—
965	C₄×D₄	—	2	1	no	—
966	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
967	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
968	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
969	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
970	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
971	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
972	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
973	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
974	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
975	#117	—	2	1	no	—
976	#117	—	2	1	no	—
977	#117	—	2	1	no	—
978	#117	—	2	1	no	—
979	#117	C₂³×C₂₃	1	1	yes	characteristic
980	#117	C₂³×C₂₃	1	1	yes	characteristic
981	C₂×C₄⋊C₄	—	2	1	no	—
982	C₂×C₄⋊C₄	—	2	1	no	—
983	C₂×C₄⋊C₄	—	2	1	no	—
984	C₂×C₄⋊C₄	—	2	1	no	—
985	C₂×C₄⋊C₄	—	2	1	no	—
986	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
987	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
988	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
989	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
990	C₂×C₂²⋊C₄	—	2	1	no	—
991	C₂×C₂²⋊C₄	—	2	1	no	—
992	C₂×C₂²⋊C₄	—	2	1	no	—
993	C₂×C₂²⋊C₄	—	2	1	no	—
994	C₂×C₂²⋊C₄	—	2	1	no	—
995	C₂×C₂²⋊C₄	—	2	1	no	—
996	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
997	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
998	C₂×C₄²	—	2	1	no	—
999	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1000	#107	C₂³×C₂₃	1	2	yes	—
1001	#107	C₂³×C₂₃	1	2	yes	—
1002	#107	C₂³×C₂₃	1	2	yes	—
1003	#106	C₂³×C₂₃	1	2	yes	—
1004	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
1005	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
1006	#103	C₂³×C₂₃	1	2	yes	—
1007	#103	C₂³×C₂₃	1	2	yes	—
1008	#103	C₂³×C₂₃	1	2	yes	—
1009	#103	C₂³×C₂₃	1	2	yes	—
1010	#103	C₂³×C₂₃	1	2	yes	—
1011	#103	C₂³×C₂₃	1	2	yes	—
1012	#103	C₂³×C₂₃	1	2	yes	—
1013	#103	C₂³×C₂₃	1	2	yes	—
1014	#103	C₂³×C₂₃	1	2	yes	—
1015	#103	C₂³×C₂₃	1	2	yes	—
1016	#103	C₂³×C₂₃	1	2	yes	—
1017	#102	C₂³×C₂₃	1	2	yes	—
1018	#102	C₂³×C₂₃	1	2	yes	—
1019	#102	C₂³×C₂₃	1	2	yes	—
1020	#102	C₂³×C₂₃	1	2	yes	—
1021	#102	C₂³×C₂₃	1	2	yes	—
1022	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1023	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1024	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1025	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
1026	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
1027	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1028	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
1029	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
1030	#97	C₂³×C₂₃	1	2	yes	—
1031	C₄×C₈	C₂³×C₂₃	1	2	yes	—
1032	C₂₃	#61603	1	1	yes	characteristic, direct product factor, Sylow
1033	C₂⁴	—	2	1	no	—
1034	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
1035	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
1036	#41	—	2	4	no	—
1037	#41	—	2	4	no	—
1038	#41	—	4	2	no	—
1039	#41	—	4	2	no	—
1040	#41	—	4	2	no	—
1041	#41	—	4	2	no	—
1042	#41	—	4	4	no	—
1043	#41	—	4	4	no	—
1044	#41	—	4	4	no	—
1045	C₂×Q₈	—	2	4	no	—
1046	C₂×Q₈	—	2	1	no	—
1047	C₂×Q₈	—	2	1	no	—
1048	C₂×Q₈	—	2	2	no	—
1049	C₂×Q₈	—	2	2	no	—
1050	C₂×Q₈	—	2	1	no	—
1051	C₂×Q₈	—	2	1	no	—
1052	C₂×Q₈	—	2	1	no	—
1053	C₂×Q₈	—	2	4	no	—
1054	C₂×Q₈	—	2	4	no	—
1055	C₂×Q₈	—	4	2	no	—
1056	C₂×Q₈	—	4	2	no	—
1057	C₂×Q₈	—	4	2	no	—
1058	C₂×Q₈	—	4	4	no	—
1059	C₂×Q₈	—	4	2	no	—
1060	C₂×Q₈	—	4	2	no	—
1061	C₂×Q₈	—	4	4	no	—
1062	C₂×Q₈	—	4	4	no	—
1063	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
1064	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
1065	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
1066	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
1067	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
1068	C₂×D₄	—	2	1	no	—
1069	C₂×D₄	—	2	1	no	—
1070	C₂×D₄	—	2	1	no	—
1071	C₂×D₄	—	2	2	no	—
1072	C₂×D₄	—	2	2	no	—
1073	C₂×D₄	—	2	2	no	—
1074	C₂×D₄	—	2	2	no	—
1075	C₂×D₄	—	2	1	no	—
1076	C₂×D₄	—	2	1	no	—
1077	C₂×D₄	—	2	1	no	—
1078	C₂×D₄	—	4	2	no	—
1079	C₂×D₄	—	4	4	no	—
1080	C₂×D₄	—	4	2	no	—
1081	C₂×D₄	—	4	4	no	—
1082	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1083	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1084	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1085	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1086	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
1087	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1088	C₂²×C₄	—	2	1	no	—
1089	C₂²×C₄	—	2	1	no	—
1090	C₂²×C₄	—	2	1	no	—
1091	C₂²×C₄	—	2	1	no	—
1092	C₂²×C₄	—	2	1	no	—
1093	C₂²×C₄	—	2	2	no	—
1094	C₂²×C₄	—	2	2	no	—
1095	C₂²×C₄	—	2	1	no	—
1096	C₂²×C₄	—	2	1	no	—
1097	C₂²×C₄	—	2	1	no	—
1098	C₂²×C₄	—	2	2	no	—
1099	C₂²×C₄	—	2	2	no	—
1100	C₂²×C₄	—	2	1	no	—
1101	C₂²×C₄	—	2	1	no	—
1102	C₂²×C₄	—	4	2	no	—
1103	C₂²×C₄	—	4	2	no	—
1104	C₂²×C₄	—	4	4	no	—
1105	C₂²×C₄	—	4	4	no	—
1106	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1107	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1108	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1109	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1110	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1111	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1112	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1113	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1114	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1115	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1116	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1117	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1118	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1119	Q₁₆	—	2	4	no	—
1120	Q₁₆	—	2	4	no	—
1121	Q₁₆	—	2	4	no	—
1122	Q₁₆	—	4	2	no	—
1123	Q₁₆	—	4	2	no	—
1124	Q₁₆	—	4	2	no	—
1125	SD₁₆	—	2	4	no	—
1126	SD₁₆	—	4	2	no	—
1127	SD₁₆	—	4	2	no	—
1128	SD₁₆	—	4	2	no	—
1129	SD₁₆	—	4	2	no	—
1130	D₈	—	4	2	no	—
1131	M₁₆	—	4	2	no	—
1132	M₁₆	—	4	2	no	—
1133	C₂×C₈	—	4	2	no	—
1134	C₂×C₈	—	4	2	no	—
1135	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1136	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1137	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1138	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1139	C₄⋊C₄	—	2	1	no	—
1140	C₄⋊C₄	—	2	1	no	—
1141	C₄⋊C₄	—	2	1	no	—
1142	C₄⋊C₄	—	2	2	no	—
1143	C₄⋊C₄	—	2	2	no	—
1144	C₄⋊C₄	—	2	1	no	—
1145	C₄⋊C₄	—	2	1	no	—
1146	C₄⋊C₄	—	2	1	no	—
1147	C₄⋊C₄	—	2	1	no	—
1148	C₄⋊C₄	—	2	1	no	—
1149	C₄⋊C₄	—	2	2	no	—
1150	C₄⋊C₄	—	2	2	no	—
1151	C₄⋊C₄	—	2	1	no	—
1152	C₄⋊C₄	—	2	1	no	—
1153	C₄⋊C₄	—	2	1	no	—
1154	C₄⋊C₄	—	2	1	no	—
1155	C₄⋊C₄	—	2	1	no	—
1156	C₄⋊C₄	—	2	1	no	—
1157	C₄⋊C₄	—	2	1	no	—
1158	C₄⋊C₄	—	2	1	no	—
1159	C₄⋊C₄	—	2	1	no	—
1160	C₄⋊C₄	—	2	1	no	—
1161	C₄⋊C₄	—	2	1	no	—
1162	C₄⋊C₄	—	2	1	no	—
1163	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1164	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1165	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1166	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1167	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1168	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1169	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1170	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1171	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1172	C₂²⋊C₄	—	2	1	no	—
1173	C₂²⋊C₄	—	2	1	no	—
1174	C₂²⋊C₄	—	2	1	no	—
1175	C₂²⋊C₄	—	2	2	no	—
1176	C₂²⋊C₄	—	2	2	no	—
1177	C₂²⋊C₄	—	2	1	no	—
1178	C₂²⋊C₄	—	2	1	no	—
1179	C₂²⋊C₄	—	2	1	no	—
1180	C₂²⋊C₄	—	2	1	no	—
1181	C₂²⋊C₄	—	2	1	no	—
1182	C₂²⋊C₄	—	2	1	no	—
1183	C₂²⋊C₄	—	2	1	no	—
1184	C₂²⋊C₄	—	2	1	no	—
1185	C₂²⋊C₄	—	2	2	no	—
1186	C₂²⋊C₄	—	2	2	no	—
1187	C₂²⋊C₄	—	2	2	no	—
1188	C₂²⋊C₄	—	2	2	no	—
1189	C₂²⋊C₄	—	2	2	no	—
1190	C₂²⋊C₄	—	2	2	no	—
1191	C₂²⋊C₄	—	2	1	no	—
1192	C₂²⋊C₄	—	2	1	no	—
1193	C₂²⋊C₄	—	2	1	no	—
1194	C₂²⋊C₄	—	2	1	no	—
1195	C₂²⋊C₄	—	2	1	no	—
1196	C₂²⋊C₄	—	2	1	no	—
1197	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1198	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1199	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1200	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1201	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1202	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1203	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1204	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1205	C₄²	—	2	2	no	—
1206	C₄²	—	2	2	no	—
1207	C₄²	—	2	1	no	—
1208	C₄²	—	2	1	no	—
1209	C₄²	—	2	1	no	—
1210	C₄²	—	2	1	no	—
1211	C₄²	—	2	1	no	—
1212	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1213	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1214	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1215	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1216	C₂³	—	2	2	no	—
1217	C₂³	—	2	2	no	—
1218	C₂³	—	2	2	no	—
1219	C₂³	—	2	1	no	—
1220	C₂³	—	2	2	no	—
1221	C₂³	—	4	1	no	—
1222	C₂³	—	4	1	no	—
1223	C₂³	—	4	1	no	—
1224	C₂³	—	4	2	no	—
1225	C₂³	—	4	2	no	—
1226	C₂³	—	4	2	no	—
1227	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1228	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1229	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1230	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1231	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1232	Q₈	—	2	4	no	—
1233	Q₈	—	2	2	no	—
1234	Q₈	—	2	2	no	—
1235	Q₈	—	2	2	no	—
1236	Q₈	—	2	2	no	—
1237	Q₈	—	2	2	no	—
1238	Q₈	—	2	2	no	—
1239	Q₈	—	4	4	no	—
1240	Q₈	—	4	4	no	—
1241	Q₈	—	4	2	no	—
1242	Q₈	—	4	2	no	—
1243	Q₈	—	8	1	no	—
1244	Q₈	—	8	1	no	—
1245	Q₈	C₂₃×H(5,𝔽₂)	1	4	yes	—
1246	D₄	—	2	2	no	—
1247	D₄	—	2	2	no	—
1248	D₄	—	2	2	no	—
1249	D₄	—	2	2	no	—
1250	D₄	—	2	2	no	—
1251	D₄	—	4	1	no	—
1252	D₄	—	4	1	no	—
1253	D₄	—	4	4	no	—
1254	D₄	—	4	4	no	—
1255	D₄	—	4	2	no	—
1256	D₄	—	4	4	no	—
1257	D₄	—	4	2	no	—
1258	D₄	—	4	4	no	—
1259	D₄	—	4	2	no	—
1260	D₄	—	4	2	no	—
1261	D₄	—	8	1	no	—
1262	D₄	—	8	1	no	—
1263	C₂×C₄	—	2	4	no	—
1264	C₂×C₄	—	2	2	no	—
1265	C₂×C₄	—	2	2	no	—
1266	C₂×C₄	—	2	2	no	—
1267	C₂×C₄	—	2	2	no	—
1268	C₂×C₄	—	2	2	no	—
1269	C₂×C₄	—	2	2	no	—
1270	C₂×C₄	—	2	2	no	—
1271	C₂×C₄	—	2	1	no	—
1272	C₂×C₄	—	2	2	no	—
1273	C₂×C₄	—	2	1	no	—
1274	C₂×C₄	—	2	1	no	—
1275	C₂×C₄	—	2	1	no	—
1276	C₂×C₄	—	2	1	no	—
1277	C₂×C₄	—	2	1	no	—
1278	C₂×C₄	—	2	2	no	—
1279	C₂×C₄	—	2	1	no	—
1280	C₂×C₄	—	4	1	no	—
1281	C₂×C₄	—	4	1	no	—
1282	C₂×C₄	—	4	1	no	—
1283	C₂×C₄	—	4	1	no	—
1284	C₂×C₄	—	4	1	no	—
1285	C₂×C₄	—	4	1	no	—
1286	C₂×C₄	—	4	1	no	—
1287	C₂×C₄	—	4	4	no	—
1288	C₂×C₄	—	4	4	no	—
1289	C₂×C₄	—	4	4	no	—
1290	C₂×C₄	—	4	4	no	—
1291	C₂×C₄	—	4	2	no	—
1292	C₂×C₄	—	4	2	no	—
1293	C₂×C₄	—	4	2	no	—
1294	C₂×C₄	—	4	2	no	—
1295	C₂×C₄	—	4	2	no	—
1296	C₂×C₄	—	8	1	no	—
1297	C₂×C₄	—	8	1	no	—
1298	C₂×C₄	—	8	1	no	—
1299	C₂×C₄	—	8	1	no	—
1300	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1301	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1302	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1303	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1304	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1305	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1306	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1307	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1308	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1309	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1310	C₈	—	2	2	no	—
1311	C₈	—	2	2	no	—
1312	C₈	—	2	2	no	—
1313	C₈	—	2	2	no	—
1314	C₂²	—	2	1	no	—
1315	C₂²	—	2	1	no	—
1316	C₂²	—	2	1	no	—
1317	C₂²	—	2	1	no	—
1318	C₂²	—	2	1	no	—
1319	C₂²	—	2	1	no	—
1320	C₂²	—	2	1	no	—
1321	C₂²	—	2	1	no	—
1322	C₂²	—	2	1	no	—
1323	C₂²	—	2	1	no	—
1324	C₂²	—	2	1	no	—
1325	C₂²	—	2	1	no	—
1326	C₂²	—	2	1	no	—
1327	C₂²	—	4	4	no	—
1328	C₂²	—	4	2	no	—
1329	C₂²	—	4	1	no	—
1330	C₂²	—	4	1	no	—
1331	C₂²	—	4	2	no	—
1332	C₂²	—	4	1	no	—
1333	C₂²	—	4	2	no	—
1334	C₂²	—	8	2	no	—
1335	C₂²	—	8	4	no	—
1336	C₂²	C₂₃×#575	1	2	yes	—
1337	C₂²	C₂₃×#578	1	2	yes	—
1338	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1339	C₄	—	2	4	no	—
1340	C₄	—	2	1	no	—
1341	C₄	—	2	1	no	—
1342	C₄	—	2	1	no	—
1343	C₄	—	2	1	no	—
1344	C₄	—	2	1	no	—
1345	C₄	—	2	1	no	—
1346	C₄	—	2	1	no	—
1347	C₄	—	2	1	no	—
1348	C₄	—	2	1	no	—
1349	C₄	—	4	2	no	—
1350	C₄	—	4	1	no	—
1351	C₄	—	4	1	no	—
1352	C₄	—	4	1	no	—
1353	C₄	—	4	1	no	—
1354	C₄	—	4	2	no	—
1355	C₄	—	4	1	no	—
1356	C₄	—	4	1	no	—
1357	C₄	—	4	1	no	—
1358	C₄	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
1359	C₂	—	2	2	no	—
1360	C₂	—	2	2	no	—
1361	C₂	—	4	1	no	—
1362	C₂	—	4	1	no	—
1363	C₂	—	4	1	no	—
1364	C₂	—	8	2	no	—
1365	C₂	—	8	1	no	—
1366	C₂	C₂₃×#3484	1	1	yes	characteristic
1367	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
1368	C₂	C₂×C₂₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄×D₄×C₂₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂₃×#3520	C₂	semidirect
2. C₂×C₂₃×#548	C₂	semidirect
3. C₂₃×#3327	C₂	semidirect
4. C₂₃×#3313	C₂	semidirect
5. C₂₃×#3308	C₂	semidirect
6. C₂₃×#3300	C₂	semidirect
7. C₂₃×#3285	C₂	semidirect
8. C₂₃×#3277	C₂	semidirect
9. C₂₃×#3270	C₂	semidirect
10. C₂₃×#3269	C₂	semidirect
11. C₂₃×#3215	C₂	semidirect
12. C₂₃×#3211	C₂	semidirect
13. C₂₃×#3196	C₂	semidirect
14. C₂₃×#3193	C₂	semidirect
15. C₂₃×#3189	C₂	semidirect
16. C₂₃×#3188	C₂	semidirect
17. C₂₃×#3117	C₂	semidirect
18. C₂₃×#3104	C₂	semidirect
19. C₂₃×#3007	C₂	semidirect
20. C₂₃×#3004	C₂	semidirect
21. C₂₃×#3002	C₂	semidirect
22. C₂×C₂₃×#451	C₂	semidirect
23. C₂₃×#2974	C₂	semidirect
26. C₂×C₂₃×#137	C₂²	semidirect
27. C₂×C₂₃×#137	C₂²	semidirect
28. C₂×C₂₃×#135	C₂²	semidirect
29. C₂²×Q₁₆×C₂₃	C₂²	semidirect
30. C₂₃×#556	C₂²	semidirect
32. C₂₃×#552	C₂²	semidirect
33. C₂₃×#552	C₂²	semidirect
36. D₄×Q₈×C₂₃	C₂²	semidirect
45. C₂₃×#548	C₂²	semidirect
46. C₂₃×#548	C₂²	semidirect
47. C₂₃×#547	C₂²	semidirect
48. C₂₃×#547	C₂²	semidirect
69. C₂₃×#497	C₂²	semidirect
70. C₂₃×#495	C₂²	semidirect
71. C₂₃×#489	C₂²	semidirect
72. C₂₃×#488	C₂²	semidirect
73. C₂₃×#485	C₂²	semidirect
77. C₂₃×#484	C₂²	semidirect
78. C₂₃×#482	C₂²	semidirect
80. C₂₃×#480	C₂²	semidirect
81. C₂₃×#479	C₂²	semidirect
82. C₂₃×#477	C₂²	semidirect
83. C₂₃×#470	C₂²	semidirect
84. C₂₃×#468	C₂²	semidirect
85. C₂₃×#468	C₂²	semidirect
86. C₂₃×#468	C₂²	semidirect
87. C₂₃×#467	C₂²	semidirect
88. C₂₃×#467	C₂²	semidirect
89. C₂₃×#466	C₂²	semidirect
90. C₂₃×#465	C₂²	semidirect
91. C₂₃×#464	C₂²	semidirect
92. C₂₃×#464	C₂²	semidirect
93. C₂₃×#464	C₂²	semidirect
94. C₂₃×#464	C₂²	semidirect
95. C₂₃×#463	C₂²	semidirect
96. C₂₃×#462	C₂²	semidirect
97. C₂₃×#452	C₂²	semidirect
98. C₂₃×#452	C₂²	semidirect
99. C₂₃×#452	C₂²	semidirect
100. C₂₃×#452	C₂²	semidirect
107. C₂₃×#451	C₂²	semidirect
108. C₂₃×#451	C₂²	semidirect
109. C₂₃×#451	C₂²	semidirect
110. C₂₃×#451	C₂²	semidirect
114. C₂₃×#449	C₂²	semidirect
115. C₂₃×#449	C₂²	semidirect
118. C₂₃×#448	C₂²	semidirect
119. C₂₃×#448	C₂²	semidirect
121. C₂₃×#441	C₂²	semidirect
122. C₂₃×#440	C₂²	semidirect
123. C₄×Q₁₆×C₂₃	C₂²	semidirect
124. C₄×Q₁₆×C₂₃	C₂²	semidirect
125. C₂₃×#436	C₂²	semidirect
126. C₂₃×#435	C₂²	semidirect
127. C₂₃×#435	C₂²	semidirect
128. C₈×D₄×C₂₃	C₂²	semidirect
131. C₂₃×#419	C₂²	semidirect
132. C₂₃×#417	C₂²	semidirect
133. C₂₃×#416	C₂²	semidirect
134. C₂×C₂₃×#103	C₂²	semidirect
531. #61603	C₂₃	direct (N × H)
630. #3520	C₂×C₂₃	semidirect
631. C₂×#548	C₂×C₂₃	semidirect
632. #3327	C₂×C₂₃	semidirect
633. #3313	C₂×C₂₃	semidirect
634. #3308	C₂×C₂₃	semidirect
635. #3300	C₂×C₂₃	semidirect
636. #3285	C₂×C₂₃	semidirect
637. #3277	C₂×C₂₃	semidirect
638. #3270	C₂×C₂₃	semidirect
639. #3269	C₂×C₂₃	semidirect
640. #3215	C₂×C₂₃	semidirect
641. #3211	C₂×C₂₃	semidirect
642. #3196	C₂×C₂₃	semidirect
643. #3193	C₂×C₂₃	semidirect
644. #3189	C₂×C₂₃	semidirect
645. #3188	C₂×C₂₃	semidirect
646. #3117	C₂×C₂₃	semidirect
647. #3104	C₂×C₂₃	semidirect
648. #3007	C₂×C₂₃	semidirect
649. #3004	C₂×C₂₃	semidirect
650. #3002	C₂×C₂₃	semidirect
651. C₂×#451	C₂×C₂₃	semidirect
652. #2974	C₂×C₂₃	semidirect
700. C₂×#137	C₂²×C₂₃	semidirect
701. C₂×#137	C₂²×C₂₃	semidirect
702. C₂×#135	C₂²×C₂₃	semidirect
703. C₂²×Q₁₆	C₂²×C₂₃	semidirect
704. #556	C₂²×C₂₃	semidirect
706. #552	C₂²×C₂₃	semidirect
707. #552	C₂²×C₂₃	semidirect
710. D₄×Q₈	C₂²×C₂₃	semidirect
719. #548	C₂²×C₂₃	semidirect
720. #548	C₂²×C₂₃	semidirect
721. #547	C₂²×C₂₃	semidirect
722. #547	C₂²×C₂₃	semidirect
743. #497	C₂²×C₂₃	semidirect
744. #495	C₂²×C₂₃	semidirect
745. #489	C₂²×C₂₃	semidirect
746. #488	C₂²×C₂₃	semidirect
747. #485	C₂²×C₂₃	semidirect
751. #484	C₂²×C₂₃	semidirect
752. #482	C₂²×C₂₃	semidirect
754. #480	C₂²×C₂₃	semidirect
755. #479	C₂²×C₂₃	semidirect
756. #477	C₂²×C₂₃	semidirect
757. #470	C₂²×C₂₃	semidirect
758. #468	C₂²×C₂₃	semidirect
759. #468	C₂²×C₂₃	semidirect
760. #468	C₂²×C₂₃	semidirect
761. #467	C₂²×C₂₃	semidirect
762. #467	C₂²×C₂₃	semidirect
763. #466	C₂²×C₂₃	semidirect
764. #465	C₂²×C₂₃	semidirect
765. #464	C₂²×C₂₃	semidirect
766. #464	C₂²×C₂₃	semidirect
767. #464	C₂²×C₂₃	semidirect
768. #464	C₂²×C₂₃	semidirect
769. #463	C₂²×C₂₃	semidirect
770. #462	C₂²×C₂₃	semidirect
771. #452	C₂²×C₂₃	semidirect
772. #452	C₂²×C₂₃	semidirect
773. #452	C₂²×C₂₃	semidirect
774. #452	C₂²×C₂₃	semidirect
781. #451	C₂²×C₂₃	semidirect
782. #451	C₂²×C₂₃	semidirect
783. #451	C₂²×C₂₃	semidirect
784. #451	C₂²×C₂₃	semidirect
788. #449	C₂²×C₂₃	semidirect
789. #449	C₂²×C₂₃	semidirect
792. #448	C₂²×C₂₃	semidirect
793. #448	C₂²×C₂₃	semidirect
795. #441	C₂²×C₂₃	semidirect
796. #440	C₂²×C₂₃	semidirect
797. C₄×Q₁₆	C₂²×C₂₃	semidirect
798. C₄×Q₁₆	C₂²×C₂₃	semidirect
799. #436	C₂²×C₂₃	semidirect
800. #435	C₂²×C₂₃	semidirect
801. #435	C₂²×C₂₃	semidirect
802. C₈×D₄	C₂²×C₂₃	semidirect
805. #419	C₂²×C₂₃	semidirect
806. #417	C₂²×C₂₃	semidirect
807. #416	C₂²×C₂₃	semidirect
808. C₂×#103	C₂²×C₂₃	semidirect
1032. C₂₃	#61603	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₃×#3520	2
C₂×C₂₃×#548	2
C₂₃×#3327	2
C₂₃×#3313	2
C₂₃×#3308	2
C₂₃×#3300	2
C₂₃×#3285	2
C₂₃×#3277	2
C₂₃×#3270	2
C₂₃×#3269	2
C₂₃×#3215	2
C₂₃×#3211	2
C₂₃×#3196	2
C₂₃×#3193	2
C₂₃×#3189	2
C₂₃×#3188	2
C₂₃×#3117	2
C₂₃×#3104	2
C₂₃×#3007	2
C₂₃×#3004	2
C₂₃×#3002	2
C₂×C₂₃×#451	2
C₂₃×#2974	2
#61603	23

Subgroups — C23×#61603 #19209229

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61603 #19209229