Subgroups — C₂₃×#61738 #19209364

Order 5888.

1758 conjugacy classes of subgroups.

The subgroup lattice has 1266 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
2	C₂×C₂₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3352	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3349	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3343	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3336	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3327	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3315	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3312	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3300	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3236	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3232	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3196	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3195	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3190	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3189	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×#3095	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#3092	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#3091	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₂₃×#484	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₃×#2974	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂₃×#556	C₂²	1	1	yes	characteristic
25	C₂₃×#554	—	2	1	no	—
26	C₂₃×#552	—	2	1	no	—
27	C₂₃×#552	—	2	1	no	—
28	C₂₃×#552	—	2	1	no	—
29	C₂₃×#552	—	2	1	no	—
30	C₂₃×#552	C₂²	1	2	yes	—
31	C₂₃×#552	C₂²	1	2	yes	—
32	C₂₃×#552	C₂²	1	2	yes	—
33	C₂₃×#552	C₂²	1	2	yes	—
34	C₂₃×#552	C₂²	1	1	yes	characteristic
35	C₂₃×#552	C₂²	1	1	yes	characteristic
36	C₂₃×#551	—	2	1	no	—
37	C₂₃×#551	—	2	1	no	—
38	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
39	C₂₃×#548	C₂²	1	1	yes	characteristic
40	C₂₃×#548	C₂²	1	1	yes	characteristic
41	C₂₃×#547	C₂²	1	1	yes	characteristic
42	C₂₃×#547	C₂²	1	1	yes	characteristic
43	C₂₃×#546	—	2	1	no	—
44	C₂₃×#542	—	2	1	no	—
45	C₂₃×#539	—	2	1	no	—
46	C₂₃×#539	—	2	1	no	—
47	C₂₃×#533	C₂²	1	1	yes	characteristic
48	C₂₃×#529	C₂²	1	1	yes	characteristic
49	C₂×C₂₃×#126	—	2	1	no	—
50	C₂×C₂₃×#125	—	2	1	no	—
51	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
52	C₂₃×#525	C₂²	1	1	yes	characteristic
53	C₂₃×#525	C₂²	1	1	yes	characteristic
54	C₂×C₂₃×#123	—	2	1	no	—
55	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
56	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
57	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
58	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
59	C₂₃×#520	—	2	1	no	—
60	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
61	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
62	C₂×C₂₃×#117	—	2	1	no	—
63	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
64	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
65	C₂₃×#501	C₂²	1	2	yes	complemented
66	C₂₃×#499	C₂²	1	2	yes	complemented
67	C₂₃×#491	C₂²	1	2	yes	complemented
68	C₂₃×#488	C₂²	1	2	yes	complemented
69	C₂₃×#485	C₂²	1	2	yes	complemented
70	C₂₃×#485	C₂²	1	2	yes	complemented
71	C₂₃×#485	C₂²	1	2	yes	complemented
72	C₂₃×#485	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	1	yes	characteristic
78	C₂₃×#484	C₂²	1	1	yes	characteristic
79	C₂₃×#484	C₂²	1	1	yes	characteristic
80	C₂₃×#484	C₂²	1	2	yes	complemented
81	C₂₃×#484	C₂²	1	2	yes	complemented
82	C₂₃×#484	C₂²	1	2	yes	complemented
83	C₂₃×#483	C₂²	1	1	yes	characteristic
84	C₂₃×#483	C₂²	1	1	yes	characteristic
85	C₂₃×#483	C₂²	1	1	yes	characteristic
86	C₂₃×#483	C₂²	1	2	yes	complemented
87	C₂₃×#483	C₂²	1	2	yes	complemented
88	C₂₃×#482	C₂²	1	2	yes	complemented
89	C₂₃×#481	C₂²	1	1	yes	characteristic
90	C₂₃×#481	C₂²	1	1	yes	characteristic
91	C₂₃×#480	C₂²	1	1	yes	characteristic
92	C₂₃×#480	C₂²	1	2	yes	complemented
93	C₂₃×#479	C₂²	1	2	yes	complemented
94	C₂₃×#479	C₂²	1	2	yes	complemented
95	C₂₃×#479	C₂²	1	2	yes	complemented
96	C₂₃×#479	C₂²	1	2	yes	complemented
97	C₂₃×#478	C₂²	1	2	yes	complemented
98	C₂₃×#477	C₂²	1	2	yes	complemented
99	C₂₃×#470	C₂²	1	2	yes	complemented
100	C₂₃×#470	C₂²	1	2	yes	complemented
101	C₂₃×#470	C₂²	1	2	yes	complemented
102	C₂₃×#468	C₂²	1	2	yes	complemented
103	C₂₃×#467	C₂²	1	2	yes	complemented
104	C₂₃×#467	C₂²	1	2	yes	complemented
105	C₂₃×#467	C₂²	1	2	yes	complemented
106	C₂₃×#465	C₂²	1	2	yes	complemented
107	C₂₃×#464	C₂²	1	2	yes	complemented
108	C₂₃×#462	C₂²	1	2	yes	complemented
109	C₂₃×#452	C₂²	1	2	yes	complemented
110	C₂₃×#452	C₂²	1	2	yes	complemented
111	C₂₃×#451	C₂²	1	1	yes	characteristic
112	C₂₃×#451	C₂²	1	1	yes	characteristic
113	C₂₃×#451	C₂²	1	1	yes	characteristic
114	C₂₃×#451	C₂²	1	2	yes	complemented
115	C₂₃×#451	C₂²	1	2	yes	complemented
116	C₂₃×#448	C₂²	1	1	yes	characteristic
117	C₂₃×#441	C₂²	1	2	yes	complemented
118	C₂₃×#440	C₂²	1	2	yes	complemented
119	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
120	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
121	C₂₃×#436	C₂²	1	2	yes	—
122	C₂₃×#435	C₂²	1	2	yes	—
123	C₂₃×#435	C₂²	1	2	yes	—
124	C₈×D₄×C₂₃	C₂²	1	2	yes	—
125	C₂₃×#432	C₂²	1	1	yes	characteristic
126	C₂₃×#431	C₂²	1	1	yes	characteristic
127	C₂₃×#428	C₂²	1	2	yes	complemented
128	C₂₃×#428	C₂²	1	2	yes	complemented
129	C₂₃×#427	C₂²	1	2	yes	complemented
130	C₂×C₂₃×#107	C₂²	1	2	yes	complemented
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	C₂³	1	1	yes	characteristic
141	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
142	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
143	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
144	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
145	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
146	C₂³×C₄×C₂₃	—	2	1	no	—
147	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
148	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
149	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
150	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
151	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
153	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
154	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
155	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
156	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
157	C₂₃×C₄⋊Q₈	—	2	1	no	—
158	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₂₃×#126	—	2	1	no	—
161	C₂₃×#126	—	2	1	no	—
162	C₂₃×#126	—	2	1	no	—
163	C₂₃×#126	—	2	1	no	—
164	C₂₃×#126	—	2	2	no	—
165	C₂₃×#126	—	2	2	no	—
166	C₂₃×#126	—	2	2	no	—
167	C₂₃×#126	—	2	2	no	—
168	C₂₃×#126	—	2	1	no	—
169	C₂₃×#125	—	2	2	no	—
170	C₂₃×#125	—	2	2	no	—
171	C₂₃×#125	—	2	2	no	—
172	C₂₃×#125	—	2	2	no	—
173	C₂₃×#125	—	2	1	no	—
174	C₂₃×#125	—	2	1	no	—
175	C₂₃×#125	—	2	1	no	—
176	C₂₃×#125	—	2	1	no	—
177	C₂₃×#125	—	2	1	no	—
178	C₂₃×#125	C₂³	1	2	yes	—
179	C₂₃×#125	C₂³	1	2	yes	—
180	C₂₃×#125	C₂³	1	1	yes	characteristic
181	C₂₃×#124	—	2	1	no	—
182	C₂₃×#124	—	2	1	no	—
183	C₂₃×#124	—	2	1	no	—
184	C₂₃×#124	C₂³	1	1	yes	characteristic
185	C₂₃×#123	—	2	2	no	—
186	C₂₃×#123	—	2	2	no	—
187	C₂₃×#123	—	2	2	no	—
188	C₂₃×#123	—	2	2	no	—
189	C₂₃×#123	—	2	1	no	—
190	C₂₃×#123	—	2	1	no	—
191	C₂₃×#123	—	2	1	no	—
192	C₂₃×#123	—	2	1	no	—
193	C₂₃×#123	—	2	1	no	—
194	C₂₃×#123	—	2	1	no	—
195	C₂₃×#123	—	2	1	no	—
196	C₂₃×#123	—	2	1	no	—
197	C₂₃×#123	—	2	1	no	—
198	C₂₃×C₂²⋊Q₈	—	2	1	no	—
199	C₂₃×C₂²⋊Q₈	—	2	1	no	—
200	C₂₃×C₂²⋊Q₈	—	2	1	no	—
201	C₂₃×C₂²⋊Q₈	—	2	1	no	—
202	C₂₃×C₂²⋊Q₈	—	2	1	no	—
203	C₂₃×C₂²⋊Q₈	—	2	1	no	—
204	C₂₃×C₂²⋊Q₈	—	2	1	no	—
205	C₂₃×C₂²⋊Q₈	—	2	1	no	—
206	C₂₃×C₂²⋊Q₈	—	2	1	no	—
207	C₂₃×C₂²⋊Q₈	—	2	1	no	—
208	C₂₃×C₂²⋊Q₈	—	2	1	no	—
209	C₂₃×C₂²⋊Q₈	—	2	1	no	—
210	C₂₃×C₂²⋊Q₈	—	2	1	no	—
211	C₂₃×C₂²⋊Q₈	—	2	1	no	—
212	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
213	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
214	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
215	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
216	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
217	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
218	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
219	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
220	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
221	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
222	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
223	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
224	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
225	C₂₃×#121	—	2	1	no	—
226	C₂₃×#121	—	2	1	no	—
227	C₂₃×#121	—	2	1	no	—
228	C₂₃×#121	C₂³	1	1	yes	characteristic
229	C₂₃×#121	C₂³	1	1	yes	characteristic
230	C₂₃×#121	C₂³	1	1	yes	characteristic
231	C₂₃×#120	—	2	1	no	—
232	C₂₃×#120	—	2	1	no	—
233	C₄×Q₈×C₂₃	—	2	1	no	—
234	C₄×Q₈×C₂₃	—	2	1	no	—
235	C₄×Q₈×C₂₃	—	2	1	no	—
236	C₄×Q₈×C₂₃	—	2	1	no	—
237	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
238	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
239	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
240	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
241	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
242	C₄×D₄×C₂₃	—	2	1	no	—
243	C₄×D₄×C₂₃	—	2	1	no	—
244	C₄×D₄×C₂₃	—	2	1	no	—
245	C₄×D₄×C₂₃	—	2	1	no	—
246	C₄×D₄×C₂₃	—	2	1	no	—
247	C₄×D₄×C₂₃	—	2	1	no	—
248	C₄×D₄×C₂₃	—	2	1	no	—
249	C₄×D₄×C₂₃	—	2	1	no	—
250	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
251	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
252	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
253	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
254	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
256	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
257	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
259	C₂₃×#117	—	2	1	no	—
260	C₂₃×#117	—	2	1	no	—
261	C₂₃×#117	—	2	1	no	—
262	C₂₃×#117	—	2	1	no	—
263	C₂₃×#117	—	2	1	no	—
264	C₂₃×#117	—	2	2	no	—
265	C₂₃×#117	—	2	2	no	—
266	C₂₃×#117	—	2	2	no	—
267	C₂₃×#117	—	2	2	no	—
268	C₂₃×#117	—	2	1	no	—
269	C₂₃×#117	C₂³	1	2	yes	—
270	C₂₃×#117	C₂³	1	2	yes	—
271	C₂₃×#117	C₂³	1	1	yes	characteristic
272	C₂₃×#117	C₂³	1	1	yes	characteristic
273	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
274	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
275	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
276	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
277	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
278	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
279	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
280	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
281	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
282	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
283	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
284	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
285	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
286	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
287	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
288	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
289	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
290	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
291	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
292	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
293	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
294	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
295	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
296	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
297	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
298	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
299	C₂×C₄²×C₂₃	—	2	1	no	—
300	C₂×C₄²×C₂₃	—	2	1	no	—
301	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
302	C₂₃×#107	C₂³	1	2	yes	—
303	C₂₃×#107	C₂³	1	2	yes	—
304	C₂₃×#107	C₂³	1	2	yes	—
305	C₂₃×#107	C₂³	1	2	yes	—
306	C₂₃×#107	C₂³	1	2	yes	—
307	C₂₃×#107	C₂³	1	2	yes	—
308	C₂₃×#107	C₂³	1	2	yes	—
309	C₂₃×#106	C₂³	1	2	yes	—
310	C₂₃×#106	C₂³	1	2	yes	—
311	C₂₃×#106	C₂³	1	2	yes	—
312	C₂₃×#106	C₂³	1	2	yes	—
313	C₂₃×#106	C₂³	1	2	yes	—
314	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
315	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
316	C₂₃×#103	C₂³	1	2	yes	—
317	C₂₃×#103	C₂³	1	2	yes	—
318	C₂₃×#103	C₂³	1	2	yes	—
319	C₂₃×#103	C₂³	1	2	yes	—
320	C₂₃×#103	C₂³	1	2	yes	—
321	C₂₃×#103	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×#102	C₂³	1	2	yes	—
330	C₂₃×#102	C₂³	1	2	yes	—
331	C₂₃×#102	C₂³	1	2	yes	—
332	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
333	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
334	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
335	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
336	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
337	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
338	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
339	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
340	C₂₃×#97	C₂³	1	2	yes	—
341	C₄×C₈×C₂₃	C₂³	1	2	yes	—
342	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
343	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
344	#41×C₂₃	—	4	2	no	—
345	#41×C₂₃	—	4	2	no	—
346	#41×C₂₃	—	4	4	no	—
347	C₂×Q₈×C₂₃	—	2	1	no	—
348	C₂×Q₈×C₂₃	—	2	1	no	—
349	C₂×Q₈×C₂₃	—	2	1	no	—
350	C₂×Q₈×C₂₃	—	2	1	no	—
351	C₂×Q₈×C₂₃	—	4	2	no	—
352	C₂×Q₈×C₂₃	—	4	2	no	—
353	C₂×Q₈×C₂₃	—	4	2	no	—
354	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
355	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
356	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
357	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
358	C₂×D₄×C₂₃	—	2	1	no	—
359	C₂×D₄×C₂₃	—	2	1	no	—
360	C₂×D₄×C₂₃	—	2	1	no	—
361	C₂×D₄×C₂₃	—	2	1	no	—
362	C₂×D₄×C₂₃	—	2	1	no	—
363	C₂×D₄×C₂₃	—	4	2	no	—
364	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
365	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
366	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
367	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
368	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
369	C₂²×C₄×C₂₃	—	2	1	no	—
370	C₂²×C₄×C₂₃	—	2	1	no	—
371	C₂²×C₄×C₂₃	—	2	1	no	—
372	C₂²×C₄×C₂₃	—	2	1	no	—
373	C₂²×C₄×C₂₃	—	2	1	no	—
374	C₂²×C₄×C₂₃	—	2	1	no	—
375	C₂²×C₄×C₂₃	—	2	2	no	—
376	C₂²×C₄×C₂₃	—	2	2	no	—
377	C₂²×C₄×C₂₃	—	2	1	no	—
378	C₂²×C₄×C₂₃	—	2	1	no	—
379	C₂²×C₄×C₂₃	—	2	1	no	—
380	C₂²×C₄×C₂₃	—	2	1	no	—
381	C₂²×C₄×C₂₃	—	2	1	no	—
382	C₂²×C₄×C₂₃	—	4	2	no	—
383	C₂²×C₄×C₂₃	—	4	2	no	—
384	C₂²×C₄×C₂₃	—	4	4	no	—
385	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
386	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
387	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
388	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
389	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
390	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
391	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
392	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
393	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
394	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
395	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
396	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
397	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
398	Q₁₆×C₂₃	—	4	2	no	—
399	Q₁₆×C₂₃	—	4	2	no	—
400	Q₁₆×C₂₃	—	4	2	no	—
401	SD₁₆×C₂₃	—	4	2	no	—
402	M₁₆×C₂₃	—	4	2	no	—
403	M₁₆×C₂₃	—	4	2	no	—
404	C₂×C₈×C₂₃	—	4	2	no	—
405	C₂×C₈×C₂₃	—	4	2	no	—
406	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
407	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
408	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
409	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
410	C₄⋊C₄×C₂₃	—	2	1	no	—
411	C₄⋊C₄×C₂₃	—	2	1	no	—
412	C₄⋊C₄×C₂₃	—	2	2	no	—
413	C₄⋊C₄×C₂₃	—	2	2	no	—
414	C₄⋊C₄×C₂₃	—	2	1	no	—
415	C₄⋊C₄×C₂₃	—	2	1	no	—
416	C₄⋊C₄×C₂₃	—	2	1	no	—
417	C₄⋊C₄×C₂₃	—	2	2	no	—
418	C₄⋊C₄×C₂₃	—	2	2	no	—
419	C₄⋊C₄×C₂₃	—	2	2	no	—
420	C₄⋊C₄×C₂₃	—	2	2	no	—
421	C₄⋊C₄×C₂₃	—	2	1	no	—
422	C₄⋊C₄×C₂₃	—	2	1	no	—
423	C₄⋊C₄×C₂₃	—	2	1	no	—
424	C₄⋊C₄×C₂₃	—	2	1	no	—
425	C₄⋊C₄×C₂₃	—	2	1	no	—
426	C₄⋊C₄×C₂₃	—	2	2	no	—
427	C₄⋊C₄×C₂₃	—	2	2	no	—
428	C₄⋊C₄×C₂₃	—	2	2	no	—
429	C₄⋊C₄×C₂₃	—	2	2	no	—
430	C₄⋊C₄×C₂₃	—	2	2	no	—
431	C₄⋊C₄×C₂₃	—	2	2	no	—
432	C₄⋊C₄×C₂₃	—	2	1	no	—
433	C₄⋊C₄×C₂₃	—	2	1	no	—
434	C₄⋊C₄×C₂₃	—	2	1	no	—
435	C₄⋊C₄×C₂₃	—	2	1	no	—
436	C₄⋊C₄×C₂₃	—	2	1	no	—
437	C₄⋊C₄×C₂₃	—	2	1	no	—
438	C₄⋊C₄×C₂₃	—	2	1	no	—
439	C₄⋊C₄×C₂₃	—	2	1	no	—
440	C₄⋊C₄×C₂₃	—	2	1	no	—
441	C₄⋊C₄×C₂₃	—	2	1	no	—
442	C₄⋊C₄×C₂₃	—	2	1	no	—
443	C₄⋊C₄×C₂₃	—	2	1	no	—
444	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
445	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
446	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
447	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
448	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
449	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
450	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
451	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
452	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
453	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
454	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
455	C₂²⋊C₄×C₂₃	—	2	1	no	—
456	C₂²⋊C₄×C₂₃	—	2	2	no	—
457	C₂²⋊C₄×C₂₃	—	2	2	no	—
458	C₂²⋊C₄×C₂₃	—	2	2	no	—
459	C₂²⋊C₄×C₂₃	—	2	2	no	—
460	C₂²⋊C₄×C₂₃	—	2	1	no	—
461	C₂²⋊C₄×C₂₃	—	2	1	no	—
462	C₂²⋊C₄×C₂₃	—	2	1	no	—
463	C₂²⋊C₄×C₂₃	—	2	1	no	—
464	C₂²⋊C₄×C₂₃	—	2	1	no	—
465	C₂²⋊C₄×C₂₃	—	2	1	no	—
466	C₂²⋊C₄×C₂₃	—	2	2	no	—
467	C₂²⋊C₄×C₂₃	—	2	2	no	—
468	C₂²⋊C₄×C₂₃	—	2	1	no	—
469	C₂²⋊C₄×C₂₃	—	2	1	no	—
470	C₂²⋊C₄×C₂₃	—	2	1	no	—
471	C₂²⋊C₄×C₂₃	—	2	1	no	—
472	C₂²⋊C₄×C₂₃	—	2	1	no	—
473	C₂²⋊C₄×C₂₃	—	2	1	no	—
474	C₂²⋊C₄×C₂₃	—	2	1	no	—
475	C₂²⋊C₄×C₂₃	—	2	1	no	—
476	C₂²⋊C₄×C₂₃	—	2	1	no	—
477	C₂²⋊C₄×C₂₃	—	2	1	no	—
478	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
479	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
480	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
481	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
482	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
483	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
484	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
485	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
486	C₄²×C₂₃	—	2	2	no	—
487	C₄²×C₂₃	—	2	2	no	—
488	C₄²×C₂₃	—	2	2	no	—
489	C₄²×C₂₃	—	2	2	no	—
490	C₄²×C₂₃	—	2	1	no	—
491	C₄²×C₂₃	—	2	1	no	—
492	C₄²×C₂₃	—	2	1	no	—
493	C₄²×C₂₃	—	2	1	no	—
494	C₄²×C₂₃	—	2	1	no	—
495	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
496	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
497	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
498	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
499	#61738	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
500	C₂³×C₂₃	—	2	2	no	—
501	C₂³×C₂₃	—	2	2	no	—
502	C₂³×C₂₃	—	2	2	no	—
503	C₂³×C₂₃	—	2	1	no	—
504	C₂³×C₂₃	—	4	1	no	—
505	C₂³×C₂₃	—	4	1	no	—
506	C₂³×C₂₃	—	4	1	no	—
507	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
508	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
509	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
510	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
511	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
512	Q₈×C₂₃	—	2	2	no	—
513	Q₈×C₂₃	—	2	2	no	—
514	Q₈×C₂₃	—	2	2	no	—
515	Q₈×C₂₃	—	2	2	no	—
516	Q₈×C₂₃	—	2	2	no	—
517	Q₈×C₂₃	—	4	2	no	—
518	Q₈×C₂₃	—	4	2	no	—
519	Q₈×C₂₃	—	8	1	no	—
520	Q₈×C₂₃	—	8	1	no	—
521	D₄×C₂₃	—	2	2	no	—
522	D₄×C₂₃	—	2	2	no	—
523	D₄×C₂₃	—	2	2	no	—
524	D₄×C₂₃	—	4	1	no	—
525	D₄×C₂₃	—	4	1	no	—
526	D₄×C₂₃	—	4	2	no	—
527	D₄×C₂₃	—	4	2	no	—
528	D₄×C₂₃	—	4	2	no	—
529	D₄×C₂₃	—	8	1	no	—
530	D₄×C₂₃	—	8	1	no	—
531	C₂×C₄×C₂₃	—	2	2	no	—
532	C₂×C₄×C₂₃	—	2	2	no	—
533	C₂×C₄×C₂₃	—	2	2	no	—
534	C₂×C₄×C₂₃	—	2	2	no	—
535	C₂×C₄×C₂₃	—	2	2	no	—
536	C₂×C₄×C₂₃	—	2	2	no	—
537	C₂×C₄×C₂₃	—	2	2	no	—
538	C₂×C₄×C₂₃	—	2	1	no	—
539	C₂×C₄×C₂₃	—	2	2	no	—
540	C₂×C₄×C₂₃	—	2	2	no	—
541	C₂×C₄×C₂₃	—	2	1	no	—
542	C₂×C₄×C₂₃	—	2	1	no	—
543	C₂×C₄×C₂₃	—	2	1	no	—
544	C₂×C₄×C₂₃	—	2	1	no	—
545	C₂×C₄×C₂₃	—	2	1	no	—
546	C₂×C₄×C₂₃	—	2	1	no	—
547	C₂×C₄×C₂₃	—	2	2	no	—
548	C₂×C₄×C₂₃	—	4	1	no	—
549	C₂×C₄×C₂₃	—	4	1	no	—
550	C₂×C₄×C₂₃	—	4	1	no	—
551	C₂×C₄×C₂₃	—	4	1	no	—
552	C₂×C₄×C₂₃	—	4	1	no	—
553	C₂×C₄×C₂₃	—	4	1	no	—
554	C₂×C₄×C₂₃	—	4	1	no	—
555	C₂×C₄×C₂₃	—	4	2	no	—
556	C₂×C₄×C₂₃	—	4	2	no	—
557	C₂×C₄×C₂₃	—	4	2	no	—
558	C₂×C₄×C₂₃	—	4	4	no	—
559	C₂×C₄×C₂₃	—	4	2	no	—
560	C₂×C₄×C₂₃	—	4	2	no	—
561	C₂×C₄×C₂₃	—	4	4	no	—
562	C₂×C₄×C₂₃	—	4	2	no	—
563	C₂×C₄×C₂₃	—	4	2	no	—
564	C₂×C₄×C₂₃	—	8	1	no	—
565	C₂×C₄×C₂₃	—	8	1	no	—
566	C₂×C₄×C₂₃	—	8	1	no	—
567	C₂×C₄×C₂₃	—	8	1	no	—
568	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
569	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
570	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
571	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
572	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
573	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
574	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
575	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
576	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
577	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
578	C₈×C₂₃	—	2	2	no	—
579	C₈×C₂₃	—	2	2	no	—
580	C₈×C₂₃	—	2	2	no	—
581	C₈×C₂₃	—	2	2	no	—
582	#3520	C₂×C₂₃	1	1	yes	characteristic
583	C₂×#552	C₂×C₂₃	1	1	yes	characteristic, complemented
584	#3352	C₂×C₂₃	1	2	yes	complemented
585	#3349	C₂×C₂₃	1	2	yes	complemented
586	#3343	C₂×C₂₃	1	2	yes	complemented
587	#3336	C₂×C₂₃	1	2	yes	complemented
588	#3327	C₂×C₂₃	1	2	yes	complemented
589	#3315	C₂×C₂₃	1	2	yes	complemented
590	#3312	C₂×C₂₃	1	2	yes	complemented
591	#3300	C₂×C₂₃	1	2	yes	complemented
592	#3236	C₂×C₂₃	1	1	yes	characteristic, complemented
593	#3232	C₂×C₂₃	1	1	yes	characteristic, complemented
594	#3196	C₂×C₂₃	1	1	yes	characteristic, complemented
595	#3195	C₂×C₂₃	1	1	yes	characteristic, complemented
596	#3190	C₂×C₂₃	1	1	yes	characteristic, complemented
597	#3189	C₂×C₂₃	1	1	yes	characteristic, complemented
598	#3117	C₂×C₂₃	1	1	yes	characteristic, complemented
599	#3104	C₂×C₂₃	1	1	yes	characteristic, complemented
600	#3095	C₂×C₂₃	1	1	yes	characteristic, complemented
601	#3092	C₂×C₂₃	1	1	yes	characteristic, complemented
602	#3091	C₂×C₂₃	1	1	yes	characteristic, complemented
603	C₂×#484	C₂×C₂₃	1	1	yes	characteristic, complemented
604	#2974	C₂×C₂₃	1	1	yes	characteristic, complemented
605	C₂²×C₂₃	—	2	1	no	—
606	C₂²×C₂₃	—	2	1	no	—
607	C₂²×C₂₃	—	2	1	no	—
608	C₂²×C₂₃	—	2	1	no	—
609	C₂²×C₂₃	—	2	1	no	—
610	C₂²×C₂₃	—	2	1	no	—
611	C₂²×C₂₃	—	2	1	no	—
612	C₂²×C₂₃	—	2	1	no	—
613	C₂²×C₂₃	—	2	1	no	—
614	C₂²×C₂₃	—	2	1	no	—
615	C₂²×C₂₃	—	2	1	no	—
616	C₂²×C₂₃	—	2	1	no	—
617	C₂²×C₂₃	—	2	1	no	—
618	C₂²×C₂₃	—	4	4	no	—
619	C₂²×C₂₃	—	4	1	no	—
620	C₂²×C₂₃	—	4	1	no	—
621	C₂²×C₂₃	—	4	1	no	—
622	C₂²×C₂₃	—	8	2	no	—
623	C₂²×C₂₃	#575	1	2	yes	—
624	C₂²×C₂₃	#578	1	2	yes	—
625	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
626	C₄×C₂₃	—	2	1	no	—
627	C₄×C₂₃	—	2	1	no	—
628	C₄×C₂₃	—	2	1	no	—
629	C₄×C₂₃	—	2	1	no	—
630	C₄×C₂₃	—	2	1	no	—
631	C₄×C₂₃	—	2	1	no	—
632	C₄×C₂₃	—	2	1	no	—
633	C₄×C₂₃	—	2	1	no	—
634	C₄×C₂₃	—	2	1	no	—
635	C₄×C₂₃	—	4	2	no	—
636	C₄×C₂₃	—	4	1	no	—
637	C₄×C₂₃	—	4	1	no	—
638	C₄×C₂₃	—	4	1	no	—
639	C₄×C₂₃	—	4	2	no	—
640	C₄×C₂₃	—	4	1	no	—
641	C₄×C₂₃	—	4	2	no	—
642	C₄×C₂₃	—	4	1	no	—
643	C₄×C₂₃	—	4	1	no	—
644	C₄×C₂₃	—	4	2	no	—
645	C₄×C₂₃	—	4	1	no	—
646	C₄×C₂₃	#585	1	2	yes	—
647	#556	C₂²×C₂₃	1	1	yes	characteristic
648	#554	—	2	1	no	—
649	#552	—	2	1	no	—
650	#552	—	2	1	no	—
651	#552	—	2	1	no	—
652	#552	—	2	1	no	—
653	#552	C₂²×C₂₃	1	1	yes	characteristic
654	#552	C₂²×C₂₃	1	2	yes	—
655	#552	C₂²×C₂₃	1	2	yes	—
656	#552	C₂²×C₂₃	1	2	yes	—
657	#552	C₂²×C₂₃	1	1	yes	characteristic
658	#552	C₂²×C₂₃	1	2	yes	—
659	#551	—	2	1	no	—
660	#551	—	2	1	no	—
661	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
662	#548	C₂²×C₂₃	1	1	yes	characteristic
663	#548	C₂²×C₂₃	1	1	yes	characteristic
664	#547	C₂²×C₂₃	1	1	yes	characteristic
665	#547	C₂²×C₂₃	1	1	yes	characteristic
666	#546	—	2	1	no	—
667	#542	—	2	1	no	—
668	#539	—	2	1	no	—
669	#539	—	2	1	no	—
670	#533	C₂²×C₂₃	1	1	yes	characteristic
671	#529	C₂²×C₂₃	1	1	yes	characteristic
672	C₂×#126	—	2	1	no	—
673	C₂×#125	—	2	1	no	—
674	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
675	#525	C₂²×C₂₃	1	1	yes	characteristic
676	#525	C₂²×C₂₃	1	1	yes	characteristic
677	C₂×#123	—	2	1	no	—
678	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
679	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
680	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
681	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
682	#520	—	2	1	no	—
683	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
684	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
685	C₂×#117	—	2	1	no	—
686	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
687	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
688	#501	C₂²×C₂₃	1	2	yes	complemented
689	#499	C₂²×C₂₃	1	2	yes	complemented
690	#491	C₂²×C₂₃	1	2	yes	complemented
691	#488	C₂²×C₂₃	1	2	yes	complemented
692	#485	C₂²×C₂₃	1	2	yes	complemented
693	#485	C₂²×C₂₃	1	2	yes	complemented
694	#485	C₂²×C₂₃	1	2	yes	complemented
695	#485	C₂²×C₂₃	1	2	yes	complemented
696	#485	C₂²×C₂₃	1	2	yes	complemented
697	#484	C₂²×C₂₃	1	1	yes	characteristic
698	#484	C₂²×C₂₃	1	1	yes	characteristic
699	#484	C₂²×C₂₃	1	1	yes	characteristic
700	#484	C₂²×C₂₃	1	1	yes	characteristic
701	#484	C₂²×C₂₃	1	1	yes	characteristic
702	#484	C₂²×C₂₃	1	1	yes	characteristic
703	#484	C₂²×C₂₃	1	2	yes	complemented
704	#484	C₂²×C₂₃	1	2	yes	complemented
705	#484	C₂²×C₂₃	1	2	yes	complemented
706	#483	C₂²×C₂₃	1	1	yes	characteristic
707	#483	C₂²×C₂₃	1	1	yes	characteristic
708	#483	C₂²×C₂₃	1	1	yes	characteristic
709	#483	C₂²×C₂₃	1	2	yes	complemented
710	#483	C₂²×C₂₃	1	2	yes	complemented
711	#482	C₂²×C₂₃	1	2	yes	complemented
712	#481	C₂²×C₂₃	1	1	yes	characteristic
713	#481	C₂²×C₂₃	1	1	yes	characteristic
714	#480	C₂²×C₂₃	1	1	yes	characteristic
715	#480	C₂²×C₂₃	1	2	yes	complemented
716	#479	C₂²×C₂₃	1	2	yes	complemented
717	#479	C₂²×C₂₃	1	2	yes	complemented
718	#479	C₂²×C₂₃	1	2	yes	complemented
719	#479	C₂²×C₂₃	1	2	yes	complemented
720	#478	C₂²×C₂₃	1	2	yes	complemented
721	#477	C₂²×C₂₃	1	2	yes	complemented
722	#470	C₂²×C₂₃	1	2	yes	complemented
723	#470	C₂²×C₂₃	1	2	yes	complemented
724	#470	C₂²×C₂₃	1	2	yes	complemented
725	#468	C₂²×C₂₃	1	2	yes	complemented
726	#467	C₂²×C₂₃	1	2	yes	complemented
727	#467	C₂²×C₂₃	1	2	yes	complemented
728	#467	C₂²×C₂₃	1	2	yes	complemented
729	#465	C₂²×C₂₃	1	2	yes	complemented
730	#464	C₂²×C₂₃	1	2	yes	complemented
731	#462	C₂²×C₂₃	1	2	yes	complemented
732	#452	C₂²×C₂₃	1	2	yes	complemented
733	#452	C₂²×C₂₃	1	2	yes	complemented
734	#451	C₂²×C₂₃	1	1	yes	characteristic
735	#451	C₂²×C₂₃	1	1	yes	characteristic
736	#451	C₂²×C₂₃	1	1	yes	characteristic
737	#451	C₂²×C₂₃	1	2	yes	complemented
738	#451	C₂²×C₂₃	1	2	yes	complemented
739	#448	C₂²×C₂₃	1	1	yes	characteristic
740	#441	C₂²×C₂₃	1	2	yes	complemented
741	#440	C₂²×C₂₃	1	2	yes	complemented
742	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
743	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
744	#436	C₂²×C₂₃	1	2	yes	—
745	#435	C₂²×C₂₃	1	2	yes	—
746	#435	C₂²×C₂₃	1	2	yes	—
747	C₈×D₄	C₂²×C₂₃	1	2	yes	—
748	#432	C₂²×C₂₃	1	1	yes	characteristic
749	#431	C₂²×C₂₃	1	1	yes	characteristic
750	#428	C₂²×C₂₃	1	2	yes	complemented
751	#428	C₂²×C₂₃	1	2	yes	complemented
752	#427	C₂²×C₂₃	1	2	yes	complemented
753	C₂×#107	C₂²×C₂₃	1	2	yes	complemented
754	#419	C₂²×C₂₃	1	2	yes	complemented
755	#417	C₂²×C₂₃	1	2	yes	complemented
756	#416	C₂²×C₂₃	1	2	yes	complemented
757	C₂×#103	C₂²×C₂₃	1	2	yes	complemented
758	#407	C₂²×C₂₃	1	1	yes	characteristic
759	#407	C₂²×C₂₃	1	1	yes	characteristic
760	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
761	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
762	C₂×C₂₃	—	2	2	no	—
763	C₂×C₂₃	—	2	2	no	—
764	C₂×C₂₃	—	4	1	no	—
765	C₂×C₂₃	—	4	1	no	—
766	C₂×C₂₃	—	4	1	no	—
767	C₂×C₂₃	—	8	1	no	—
768	C₂×C₂₃	#3485	1	1	yes	characteristic
769	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
770	C₂×C₂₃	C₂×#578	1	1	yes	characteristic
771	C₂×#41	—	2	1	no	—
772	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
773	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
774	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
775	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
776	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
777	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
778	C₂³×C₄	—	2	1	no	—
779	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
780	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
781	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
782	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
783	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
784	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
785	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
786	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
787	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
788	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
789	C₄⋊Q₈	—	2	1	no	—
790	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
791	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
792	#126	—	2	2	no	—
793	#126	—	2	2	no	—
794	#126	—	2	2	no	—
795	#126	—	2	2	no	—
796	#126	—	2	1	no	—
797	#126	—	2	1	no	—
798	#126	—	2	1	no	—
799	#126	—	2	1	no	—
800	#126	—	2	1	no	—
801	#125	—	2	2	no	—
802	#125	—	2	2	no	—
803	#125	—	2	2	no	—
804	#125	—	2	2	no	—
805	#125	—	2	1	no	—
806	#125	—	2	1	no	—
807	#125	—	2	1	no	—
808	#125	—	2	1	no	—
809	#125	—	2	1	no	—
810	#125	C₂³×C₂₃	1	2	yes	—
811	#125	C₂³×C₂₃	1	2	yes	—
812	#125	C₂³×C₂₃	1	1	yes	characteristic
813	#124	—	2	1	no	—
814	#124	—	2	1	no	—
815	#124	—	2	1	no	—
816	#124	C₂³×C₂₃	1	1	yes	characteristic
817	#123	—	2	2	no	—
818	#123	—	2	2	no	—
819	#123	—	2	2	no	—
820	#123	—	2	2	no	—
821	#123	—	2	1	no	—
822	#123	—	2	1	no	—
823	#123	—	2	1	no	—
824	#123	—	2	1	no	—
825	#123	—	2	1	no	—
826	#123	—	2	1	no	—
827	#123	—	2	1	no	—
828	#123	—	2	1	no	—
829	#123	—	2	1	no	—
830	C₂²⋊Q₈	—	2	1	no	—
831	C₂²⋊Q₈	—	2	1	no	—
832	C₂²⋊Q₈	—	2	1	no	—
833	C₂²⋊Q₈	—	2	1	no	—
834	C₂²⋊Q₈	—	2	1	no	—
835	C₂²⋊Q₈	—	2	1	no	—
836	C₂²⋊Q₈	—	2	1	no	—
837	C₂²⋊Q₈	—	2	1	no	—
838	C₂²⋊Q₈	—	2	1	no	—
839	C₂²⋊Q₈	—	2	1	no	—
840	C₂²⋊Q₈	—	2	1	no	—
841	C₂²⋊Q₈	—	2	1	no	—
842	C₂²⋊Q₈	—	2	1	no	—
843	C₂²⋊Q₈	—	2	1	no	—
844	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
845	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
846	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
847	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
848	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
849	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
850	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
851	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
852	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
853	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
854	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
855	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
856	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
857	#121	—	2	1	no	—
858	#121	—	2	1	no	—
859	#121	—	2	1	no	—
860	#121	C₂³×C₂₃	1	1	yes	characteristic
861	#121	C₂³×C₂₃	1	1	yes	characteristic
862	#121	C₂³×C₂₃	1	1	yes	characteristic
863	#120	—	2	1	no	—
864	#120	—	2	1	no	—
865	C₄×Q₈	—	2	1	no	—
866	C₄×Q₈	—	2	1	no	—
867	C₄×Q₈	—	2	1	no	—
868	C₄×Q₈	—	2	1	no	—
869	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
870	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
871	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
872	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
873	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
874	C₄×D₄	—	2	1	no	—
875	C₄×D₄	—	2	1	no	—
876	C₄×D₄	—	2	1	no	—
877	C₄×D₄	—	2	1	no	—
878	C₄×D₄	—	2	1	no	—
879	C₄×D₄	—	2	1	no	—
880	C₄×D₄	—	2	1	no	—
881	C₄×D₄	—	2	1	no	—
882	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
883	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
884	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
885	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
886	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
887	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
888	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
889	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
890	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
891	#117	—	2	1	no	—
892	#117	—	2	1	no	—
893	#117	—	2	1	no	—
894	#117	—	2	2	no	—
895	#117	—	2	2	no	—
896	#117	—	2	2	no	—
897	#117	—	2	2	no	—
898	#117	—	2	1	no	—
899	#117	—	2	1	no	—
900	#117	—	2	1	no	—
901	#117	C₂³×C₂₃	1	2	yes	—
902	#117	C₂³×C₂₃	1	2	yes	—
903	#117	C₂³×C₂₃	1	1	yes	characteristic
904	#117	C₂³×C₂₃	1	1	yes	characteristic
905	C₂×C₄⋊C₄	—	2	1	no	—
906	C₂×C₄⋊C₄	—	2	1	no	—
907	C₂×C₄⋊C₄	—	2	1	no	—
908	C₂×C₄⋊C₄	—	2	1	no	—
909	C₂×C₄⋊C₄	—	2	1	no	—
910	C₂×C₄⋊C₄	—	2	1	no	—
911	C₂×C₄⋊C₄	—	2	1	no	—
912	C₂×C₄⋊C₄	—	2	1	no	—
913	C₂×C₄⋊C₄	—	2	1	no	—
914	C₂×C₄⋊C₄	—	2	1	no	—
915	C₂×C₄⋊C₄	—	2	1	no	—
916	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
917	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
918	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
919	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
920	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
921	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
922	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
923	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
924	C₂×C₂²⋊C₄	—	2	1	no	—
925	C₂×C₂²⋊C₄	—	2	1	no	—
926	C₂×C₂²⋊C₄	—	2	1	no	—
927	C₂×C₂²⋊C₄	—	2	1	no	—
928	C₂×C₂²⋊C₄	—	2	1	no	—
929	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
930	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
931	C₂×C₄²	—	2	1	no	—
932	C₂×C₄²	—	2	1	no	—
933	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
934	#107	C₂³×C₂₃	1	2	yes	—
935	#107	C₂³×C₂₃	1	2	yes	—
936	#107	C₂³×C₂₃	1	2	yes	—
937	#107	C₂³×C₂₃	1	2	yes	—
938	#107	C₂³×C₂₃	1	2	yes	—
939	#107	C₂³×C₂₃	1	2	yes	—
940	#107	C₂³×C₂₃	1	2	yes	—
941	#106	C₂³×C₂₃	1	2	yes	—
942	#106	C₂³×C₂₃	1	2	yes	—
943	#106	C₂³×C₂₃	1	2	yes	—
944	#106	C₂³×C₂₃	1	2	yes	—
945	#106	C₂³×C₂₃	1	2	yes	—
946	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
947	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
948	#103	C₂³×C₂₃	1	2	yes	—
949	#103	C₂³×C₂₃	1	2	yes	—
950	#103	C₂³×C₂₃	1	2	yes	—
951	#103	C₂³×C₂₃	1	2	yes	—
952	#103	C₂³×C₂₃	1	2	yes	—
953	#103	C₂³×C₂₃	1	2	yes	—
954	#103	C₂³×C₂₃	1	2	yes	—
955	#103	C₂³×C₂₃	1	2	yes	—
956	#103	C₂³×C₂₃	1	2	yes	—
957	#103	C₂³×C₂₃	1	2	yes	—
958	#103	C₂³×C₂₃	1	2	yes	—
959	#103	C₂³×C₂₃	1	2	yes	—
960	#103	C₂³×C₂₃	1	2	yes	—
961	#102	C₂³×C₂₃	1	2	yes	—
962	#102	C₂³×C₂₃	1	2	yes	—
963	#102	C₂³×C₂₃	1	2	yes	—
964	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
965	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
966	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
967	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
968	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
969	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
970	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
971	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
972	#97	C₂³×C₂₃	1	2	yes	—
973	C₄×C₈	C₂³×C₂₃	1	2	yes	—
974	C₂₃	#61738	1	1	yes	characteristic, direct product factor, Sylow
975	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
976	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
977	#41	—	4	2	no	—
978	#41	—	4	2	no	—
979	#41	—	4	4	no	—
980	C₂×Q₈	—	2	1	no	—
981	C₂×Q₈	—	2	1	no	—
982	C₂×Q₈	—	2	1	no	—
983	C₂×Q₈	—	2	1	no	—
984	C₂×Q₈	—	4	2	no	—
985	C₂×Q₈	—	4	2	no	—
986	C₂×Q₈	—	4	2	no	—
987	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
988	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
989	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
990	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
991	C₂×D₄	—	2	1	no	—
992	C₂×D₄	—	2	1	no	—
993	C₂×D₄	—	2	1	no	—
994	C₂×D₄	—	2	1	no	—
995	C₂×D₄	—	2	1	no	—
996	C₂×D₄	—	4	2	no	—
997	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
998	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
999	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1000	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1001	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1002	C₂²×C₄	—	2	1	no	—
1003	C₂²×C₄	—	2	1	no	—
1004	C₂²×C₄	—	2	1	no	—
1005	C₂²×C₄	—	2	1	no	—
1006	C₂²×C₄	—	2	1	no	—
1007	C₂²×C₄	—	2	1	no	—
1008	C₂²×C₄	—	2	2	no	—
1009	C₂²×C₄	—	2	2	no	—
1010	C₂²×C₄	—	2	1	no	—
1011	C₂²×C₄	—	2	1	no	—
1012	C₂²×C₄	—	2	1	no	—
1013	C₂²×C₄	—	2	1	no	—
1014	C₂²×C₄	—	2	1	no	—
1015	C₂²×C₄	—	4	2	no	—
1016	C₂²×C₄	—	4	2	no	—
1017	C₂²×C₄	—	4	4	no	—
1018	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1019	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1020	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1021	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1022	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1023	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1024	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1025	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1026	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1027	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1028	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1029	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1030	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1031	Q₁₆	—	4	2	no	—
1032	Q₁₆	—	4	2	no	—
1033	Q₁₆	—	4	2	no	—
1034	SD₁₆	—	4	2	no	—
1035	M₁₆	—	4	2	no	—
1036	M₁₆	—	4	2	no	—
1037	C₂×C₈	—	4	2	no	—
1038	C₂×C₈	—	4	2	no	—
1039	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1040	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1041	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1042	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1043	C₄⋊C₄	—	2	1	no	—
1044	C₄⋊C₄	—	2	1	no	—
1045	C₄⋊C₄	—	2	2	no	—
1046	C₄⋊C₄	—	2	2	no	—
1047	C₄⋊C₄	—	2	1	no	—
1048	C₄⋊C₄	—	2	1	no	—
1049	C₄⋊C₄	—	2	1	no	—
1050	C₄⋊C₄	—	2	2	no	—
1051	C₄⋊C₄	—	2	2	no	—
1052	C₄⋊C₄	—	2	2	no	—
1053	C₄⋊C₄	—	2	2	no	—
1054	C₄⋊C₄	—	2	1	no	—
1055	C₄⋊C₄	—	2	1	no	—
1056	C₄⋊C₄	—	2	1	no	—
1057	C₄⋊C₄	—	2	1	no	—
1058	C₄⋊C₄	—	2	1	no	—
1059	C₄⋊C₄	—	2	2	no	—
1060	C₄⋊C₄	—	2	2	no	—
1061	C₄⋊C₄	—	2	2	no	—
1062	C₄⋊C₄	—	2	2	no	—
1063	C₄⋊C₄	—	2	2	no	—
1064	C₄⋊C₄	—	2	2	no	—
1065	C₄⋊C₄	—	2	1	no	—
1066	C₄⋊C₄	—	2	1	no	—
1067	C₄⋊C₄	—	2	1	no	—
1068	C₄⋊C₄	—	2	1	no	—
1069	C₄⋊C₄	—	2	1	no	—
1070	C₄⋊C₄	—	2	1	no	—
1071	C₄⋊C₄	—	2	1	no	—
1072	C₄⋊C₄	—	2	1	no	—
1073	C₄⋊C₄	—	2	1	no	—
1074	C₄⋊C₄	—	2	1	no	—
1075	C₄⋊C₄	—	2	1	no	—
1076	C₄⋊C₄	—	2	1	no	—
1077	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1078	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1079	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1080	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1081	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1082	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1083	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1084	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1085	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1086	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1087	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1088	C₂²⋊C₄	—	2	1	no	—
1089	C₂²⋊C₄	—	2	2	no	—
1090	C₂²⋊C₄	—	2	2	no	—
1091	C₂²⋊C₄	—	2	2	no	—
1092	C₂²⋊C₄	—	2	2	no	—
1093	C₂²⋊C₄	—	2	1	no	—
1094	C₂²⋊C₄	—	2	1	no	—
1095	C₂²⋊C₄	—	2	1	no	—
1096	C₂²⋊C₄	—	2	1	no	—
1097	C₂²⋊C₄	—	2	1	no	—
1098	C₂²⋊C₄	—	2	1	no	—
1099	C₂²⋊C₄	—	2	2	no	—
1100	C₂²⋊C₄	—	2	2	no	—
1101	C₂²⋊C₄	—	2	1	no	—
1102	C₂²⋊C₄	—	2	1	no	—
1103	C₂²⋊C₄	—	2	1	no	—
1104	C₂²⋊C₄	—	2	1	no	—
1105	C₂²⋊C₄	—	2	1	no	—
1106	C₂²⋊C₄	—	2	1	no	—
1107	C₂²⋊C₄	—	2	1	no	—
1108	C₂²⋊C₄	—	2	1	no	—
1109	C₂²⋊C₄	—	2	1	no	—
1110	C₂²⋊C₄	—	2	1	no	—
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	C₂×D₄×C₂₃	1	1	yes	characteristic
1115	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1116	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1117	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1118	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1119	C₄²	—	2	2	no	—
1120	C₄²	—	2	2	no	—
1121	C₄²	—	2	2	no	—
1122	C₄²	—	2	2	no	—
1123	C₄²	—	2	1	no	—
1124	C₄²	—	2	1	no	—
1125	C₄²	—	2	1	no	—
1126	C₄²	—	2	1	no	—
1127	C₄²	—	2	1	no	—
1128	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1129	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1130	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1131	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1132	C₂³	—	2	2	no	—
1133	C₂³	—	2	2	no	—
1134	C₂³	—	2	2	no	—
1135	C₂³	—	2	1	no	—
1136	C₂³	—	4	1	no	—
1137	C₂³	—	4	1	no	—
1138	C₂³	—	4	1	no	—
1139	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1140	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1141	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1142	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1143	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1144	Q₈	—	2	2	no	—
1145	Q₈	—	2	2	no	—
1146	Q₈	—	2	2	no	—
1147	Q₈	—	2	2	no	—
1148	Q₈	—	2	2	no	—
1149	Q₈	—	4	2	no	—
1150	Q₈	—	4	2	no	—
1151	Q₈	—	8	1	no	—
1152	Q₈	—	8	1	no	—
1153	D₄	—	2	2	no	—
1154	D₄	—	2	2	no	—
1155	D₄	—	2	2	no	—
1156	D₄	—	4	1	no	—
1157	D₄	—	4	1	no	—
1158	D₄	—	4	2	no	—
1159	D₄	—	4	2	no	—
1160	D₄	—	4	2	no	—
1161	D₄	—	8	1	no	—
1162	D₄	—	8	1	no	—
1163	C₂×C₄	—	2	2	no	—
1164	C₂×C₄	—	2	2	no	—
1165	C₂×C₄	—	2	2	no	—
1166	C₂×C₄	—	2	2	no	—
1167	C₂×C₄	—	2	2	no	—
1168	C₂×C₄	—	2	2	no	—
1169	C₂×C₄	—	2	2	no	—
1170	C₂×C₄	—	2	1	no	—
1171	C₂×C₄	—	2	2	no	—
1172	C₂×C₄	—	2	2	no	—
1173	C₂×C₄	—	2	1	no	—
1174	C₂×C₄	—	2	1	no	—
1175	C₂×C₄	—	2	1	no	—
1176	C₂×C₄	—	2	1	no	—
1177	C₂×C₄	—	2	1	no	—
1178	C₂×C₄	—	2	1	no	—
1179	C₂×C₄	—	2	2	no	—
1180	C₂×C₄	—	4	1	no	—
1181	C₂×C₄	—	4	1	no	—
1182	C₂×C₄	—	4	1	no	—
1183	C₂×C₄	—	4	1	no	—
1184	C₂×C₄	—	4	1	no	—
1185	C₂×C₄	—	4	1	no	—
1186	C₂×C₄	—	4	1	no	—
1187	C₂×C₄	—	4	2	no	—
1188	C₂×C₄	—	4	2	no	—
1189	C₂×C₄	—	4	2	no	—
1190	C₂×C₄	—	4	4	no	—
1191	C₂×C₄	—	4	2	no	—
1192	C₂×C₄	—	4	2	no	—
1193	C₂×C₄	—	4	4	no	—
1194	C₂×C₄	—	4	2	no	—
1195	C₂×C₄	—	4	2	no	—
1196	C₂×C₄	—	8	1	no	—
1197	C₂×C₄	—	8	1	no	—
1198	C₂×C₄	—	8	1	no	—
1199	C₂×C₄	—	8	1	no	—
1200	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1201	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1202	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1203	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1204	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1205	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1206	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1207	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1208	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1209	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1210	C₈	—	2	2	no	—
1211	C₈	—	2	2	no	—
1212	C₈	—	2	2	no	—
1213	C₈	—	2	2	no	—
1214	C₂²	—	2	1	no	—
1215	C₂²	—	2	1	no	—
1216	C₂²	—	2	1	no	—
1217	C₂²	—	2	1	no	—
1218	C₂²	—	2	1	no	—
1219	C₂²	—	2	1	no	—
1220	C₂²	—	2	1	no	—
1221	C₂²	—	2	1	no	—
1222	C₂²	—	2	1	no	—
1223	C₂²	—	2	1	no	—
1224	C₂²	—	2	1	no	—
1225	C₂²	—	2	1	no	—
1226	C₂²	—	2	1	no	—
1227	C₂²	—	4	4	no	—
1228	C₂²	—	4	1	no	—
1229	C₂²	—	4	1	no	—
1230	C₂²	—	4	1	no	—
1231	C₂²	—	8	2	no	—
1232	C₂²	C₂₃×#575	1	2	yes	—
1233	C₂²	C₂₃×#578	1	2	yes	—
1234	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1235	C₄	—	2	1	no	—
1236	C₄	—	2	1	no	—
1237	C₄	—	2	1	no	—
1238	C₄	—	2	1	no	—
1239	C₄	—	2	1	no	—
1240	C₄	—	2	1	no	—
1241	C₄	—	2	1	no	—
1242	C₄	—	2	1	no	—
1243	C₄	—	2	1	no	—
1244	C₄	—	4	2	no	—
1245	C₄	—	4	1	no	—
1246	C₄	—	4	1	no	—
1247	C₄	—	4	1	no	—
1248	C₄	—	4	2	no	—
1249	C₄	—	4	1	no	—
1250	C₄	—	4	2	no	—
1251	C₄	—	4	1	no	—
1252	C₄	—	4	1	no	—
1253	C₄	—	4	2	no	—
1254	C₄	—	4	1	no	—
1255	C₄	C₂₃×#585	1	2	yes	—
1256	C₂	—	2	2	no	—
1257	C₂	—	2	2	no	—
1258	C₂	—	4	1	no	—
1259	C₂	—	4	1	no	—
1260	C₂	—	4	1	no	—
1261	C₂	—	8	1	no	—
1262	C₂	C₂₃×#3485	1	1	yes	characteristic
1263	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
1264	C₂	C₂×C₂₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#3520	C₂
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
2. C₂×C₂₃×#552	C₂	semidirect
3. C₂₃×#3352	C₂	semidirect
4. C₂₃×#3349	C₂	semidirect
5. C₂₃×#3343	C₂	semidirect
6. C₂₃×#3336	C₂	semidirect
7. C₂₃×#3327	C₂	semidirect
8. C₂₃×#3315	C₂	semidirect
9. C₂₃×#3312	C₂	semidirect
10. C₂₃×#3300	C₂	semidirect
11. C₂₃×#3236	C₂	semidirect
12. C₂₃×#3232	C₂	semidirect
13. C₂₃×#3196	C₂	semidirect
14. C₂₃×#3195	C₂	semidirect
15. C₂₃×#3190	C₂	semidirect
16. C₂₃×#3189	C₂	semidirect
17. C₂₃×#3117	C₂	semidirect
18. C₂₃×#3104	C₂	semidirect
19. C₂₃×#3095	C₂	semidirect
20. C₂₃×#3092	C₂	semidirect
21. C₂₃×#3091	C₂	semidirect
22. C₂×C₂₃×#484	C₂	semidirect
23. C₂₃×#2974	C₂	semidirect
65. C₂₃×#501	C₂²	semidirect
66. C₂₃×#499	C₂²	semidirect
67. C₂₃×#491	C₂²	semidirect
68. C₂₃×#488	C₂²	semidirect
69. C₂₃×#485	C₂²	semidirect
70. C₂₃×#485	C₂²	semidirect
71. C₂₃×#485	C₂²	semidirect
72. C₂₃×#485	C₂²	semidirect
73. C₂₃×#485	C₂²	semidirect
80. C₂₃×#484	C₂²	semidirect
81. C₂₃×#484	C₂²	semidirect
82. C₂₃×#484	C₂²	semidirect
86. C₂₃×#483	C₂²	semidirect
87. C₂₃×#483	C₂²	semidirect
88. C₂₃×#482	C₂²	semidirect
92. C₂₃×#480	C₂²	semidirect
93. C₂₃×#479	C₂²	semidirect
94. C₂₃×#479	C₂²	semidirect
95. C₂₃×#479	C₂²	semidirect
96. C₂₃×#479	C₂²	semidirect
97. C₂₃×#478	C₂²	semidirect
98. C₂₃×#477	C₂²	semidirect
99. C₂₃×#470	C₂²	semidirect
100. C₂₃×#470	C₂²	semidirect
101. C₂₃×#470	C₂²	semidirect
102. C₂₃×#468	C₂²	semidirect
103. C₂₃×#467	C₂²	semidirect
104. C₂₃×#467	C₂²	semidirect
105. C₂₃×#467	C₂²	semidirect
106. C₂₃×#465	C₂²	semidirect
107. C₂₃×#464	C₂²	semidirect
108. C₂₃×#462	C₂²	semidirect
109. C₂₃×#452	C₂²	semidirect
110. C₂₃×#452	C₂²	semidirect
114. C₂₃×#451	C₂²	semidirect
115. C₂₃×#451	C₂²	semidirect
117. C₂₃×#441	C₂²	semidirect
118. C₂₃×#440	C₂²	semidirect
119. C₄×Q₁₆×C₂₃	C₂²	semidirect
120. C₄×Q₁₆×C₂₃	C₂²	semidirect
127. C₂₃×#428	C₂²	semidirect
128. C₂₃×#428	C₂²	semidirect
129. C₂₃×#427	C₂²	semidirect
130. C₂×C₂₃×#107	C₂²	semidirect
131. C₂₃×#419	C₂²	semidirect
132. C₂₃×#417	C₂²	semidirect
133. C₂₃×#416	C₂²	semidirect
134. C₂×C₂₃×#103	C₂²	semidirect
499. #61738	C₂₃	direct (N × H)
583. C₂×#552	C₂×C₂₃	semidirect
584. #3352	C₂×C₂₃	semidirect
585. #3349	C₂×C₂₃	semidirect
586. #3343	C₂×C₂₃	semidirect
587. #3336	C₂×C₂₃	semidirect
588. #3327	C₂×C₂₃	semidirect
589. #3315	C₂×C₂₃	semidirect
590. #3312	C₂×C₂₃	semidirect
591. #3300	C₂×C₂₃	semidirect
592. #3236	C₂×C₂₃	semidirect
593. #3232	C₂×C₂₃	semidirect
594. #3196	C₂×C₂₃	semidirect
595. #3195	C₂×C₂₃	semidirect
596. #3190	C₂×C₂₃	semidirect
597. #3189	C₂×C₂₃	semidirect
598. #3117	C₂×C₂₃	semidirect
599. #3104	C₂×C₂₃	semidirect
600. #3095	C₂×C₂₃	semidirect
601. #3092	C₂×C₂₃	semidirect
602. #3091	C₂×C₂₃	semidirect
603. C₂×#484	C₂×C₂₃	semidirect
604. #2974	C₂×C₂₃	semidirect
688. #501	C₂²×C₂₃	semidirect
689. #499	C₂²×C₂₃	semidirect
690. #491	C₂²×C₂₃	semidirect
691. #488	C₂²×C₂₃	semidirect
692. #485	C₂²×C₂₃	semidirect
693. #485	C₂²×C₂₃	semidirect
694. #485	C₂²×C₂₃	semidirect
695. #485	C₂²×C₂₃	semidirect
696. #485	C₂²×C₂₃	semidirect
703. #484	C₂²×C₂₃	semidirect
704. #484	C₂²×C₂₃	semidirect
705. #484	C₂²×C₂₃	semidirect
709. #483	C₂²×C₂₃	semidirect
710. #483	C₂²×C₂₃	semidirect
711. #482	C₂²×C₂₃	semidirect
715. #480	C₂²×C₂₃	semidirect
716. #479	C₂²×C₂₃	semidirect
717. #479	C₂²×C₂₃	semidirect
718. #479	C₂²×C₂₃	semidirect
719. #479	C₂²×C₂₃	semidirect
720. #478	C₂²×C₂₃	semidirect
721. #477	C₂²×C₂₃	semidirect
722. #470	C₂²×C₂₃	semidirect
723. #470	C₂²×C₂₃	semidirect
724. #470	C₂²×C₂₃	semidirect
725. #468	C₂²×C₂₃	semidirect
726. #467	C₂²×C₂₃	semidirect
727. #467	C₂²×C₂₃	semidirect
728. #467	C₂²×C₂₃	semidirect
729. #465	C₂²×C₂₃	semidirect
730. #464	C₂²×C₂₃	semidirect
731. #462	C₂²×C₂₃	semidirect
732. #452	C₂²×C₂₃	semidirect
733. #452	C₂²×C₂₃	semidirect
737. #451	C₂²×C₂₃	semidirect
738. #451	C₂²×C₂₃	semidirect
740. #441	C₂²×C₂₃	semidirect
741. #440	C₂²×C₂₃	semidirect
742. C₄×Q₁₆	C₂²×C₂₃	semidirect
743. C₄×Q₁₆	C₂²×C₂₃	semidirect
750. #428	C₂²×C₂₃	semidirect
751. #428	C₂²×C₂₃	semidirect
752. #427	C₂²×C₂₃	semidirect
753. C₂×#107	C₂²×C₂₃	semidirect
754. #419	C₂²×C₂₃	semidirect
755. #417	C₂²×C₂₃	semidirect
756. #416	C₂²×C₂₃	semidirect
757. C₂×#103	C₂²×C₂₃	semidirect
974. C₂₃	#61738	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×#552	2
C₂₃×#3352	2
C₂₃×#3349	2
C₂₃×#3343	2
C₂₃×#3336	2
C₂₃×#3327	2
C₂₃×#3315	2
C₂₃×#3312	2
C₂₃×#3300	2
C₂₃×#3236	2
C₂₃×#3232	2
C₂₃×#3196	2
C₂₃×#3195	2
C₂₃×#3190	2
C₂₃×#3189	2
C₂₃×#3117	2
C₂₃×#3104	2
C₂₃×#3095	2
C₂₃×#3092	2
C₂₃×#3091	2
C₂×C₂₃×#484	2
C₂₃×#2974	2
#61738	23

Subgroups — C23×#61738 #19209364

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61738 #19209364