Subgroups — C₂₃×#60983 #19208609

Order 5888.

1668 conjugacy classes of subgroups.

The subgroup lattice has 1220 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3495	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#541	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3261	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3258	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3242	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3236	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#3232	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3223	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3218	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3209	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3196	C₂	1	1	yes	maximal, characteristic
12	C₂₃×#3195	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3190	C₂	1	1	yes	maximal, characteristic
14	C₂₃×#3189	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3178	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3177	C₂	1	2	yes	maximal, complemented
17	C₂₃×#3127	C₂	1	2	yes	maximal, complemented
18	C₂₃×#3120	C₂	1	2	yes	maximal, complemented
19	C₂₃×#3117	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#3113	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#3108	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₃×#3104	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₃×#2924	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂₃×#556	—	2	1	no	—
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×#551	—	2	1	no	—
31	C₂₃×#551	—	2	1	no	—
32	C₂₃×#544	C₂²	1	1	yes	characteristic
33	C₂₃×#542	C₂²	1	1	yes	characteristic
34	C₂₃×#542	C₂²	1	1	yes	characteristic
35	C₂₃×#541	—	2	1	no	—
36	C₂₃×#541	—	2	1	no	—
37	C₂₃×#541	—	2	1	no	—
38	C₂₃×#541	—	2	1	no	—
39	C₂₃×#541	C₂²	1	1	yes	characteristic
40	C₂₃×#541	C₂²	1	2	yes	—
41	C₂₃×#541	C₂²	1	2	yes	—
42	C₂₃×#541	C₂²	1	2	yes	—
43	C₂₃×#541	C₂²	1	2	yes	—
44	C₂₃×#541	C₂²	1	1	yes	characteristic
45	C₂₃×#536	C₂²	1	1	yes	characteristic
46	C₂₃×#533	C₂²	1	1	yes	characteristic
47	C₂₃×#533	C₂²	1	1	yes	characteristic
48	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
49	C₂₃×#529	C₂²	1	1	yes	characteristic
50	C₂₃×#529	C₂²	1	1	yes	characteristic
51	C₂×C₂₃×#126	—	2	1	no	—
52	C₂×C₂₃×#126	—	2	1	no	—
53	C₂×C₂₃×#125	—	2	1	no	—
54	C₂×C₂₃×#125	—	2	1	no	—
55	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
56	C₂₃×#525	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	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
60	C₂₃×#520	C₂²	1	1	yes	characteristic
61	C₂₃×#519	C₂²	1	1	yes	characteristic
62	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
63	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
64	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
65	C₂₃×#501	C₂²	1	2	yes	complemented
66	C₂₃×#499	C₂²	1	2	yes	complemented
67	C₂₃×#497	C₂²	1	2	yes	complemented
68	C₂₃×#494	C₂²	1	2	yes	complemented
69	C₂₃×#491	C₂²	1	2	yes	complemented
70	C₂₃×#491	C₂²	1	2	yes	complemented
71	C₂₃×#488	C₂²	1	2	yes	complemented
72	C₂₃×#487	C₂²	1	2	yes	complemented
73	C₂₃×#485	C₂²	1	2	yes	—
74	C₂₃×#485	C₂²	1	2	yes	—
75	C₂₃×#484	C₂²	1	1	yes	characteristic
76	C₂₃×#484	C₂²	1	1	yes	characteristic
77	C₂₃×#484	C₂²	1	2	yes	—
78	C₂₃×#484	C₂²	1	1	yes	characteristic
79	C₂₃×#483	C₂²	1	1	yes	characteristic
80	C₂₃×#483	C₂²	1	1	yes	characteristic
81	C₂₃×#483	C₂²	1	1	yes	characteristic
82	C₂₃×#483	C₂²	1	2	yes	—
83	C₂₃×#481	C₂²	1	1	yes	characteristic
84	C₂₃×#480	C₂²	1	1	yes	characteristic
85	C₂₃×#479	C₂²	1	2	yes	complemented
86	C₂₃×#479	C₂²	1	2	yes	complemented
87	C₂₃×#479	C₂²	1	2	yes	complemented
88	C₂₃×#479	C₂²	1	2	yes	complemented
89	C₂₃×#479	C₂²	1	2	yes	complemented
90	C₂₃×#478	C₂²	1	2	yes	complemented
91	C₂₃×#477	C₂²	1	2	yes	complemented
92	C₂₃×#475	C₂²	1	2	yes	complemented
93	C₂₃×#470	C₂²	1	2	yes	—
94	C₂₃×#470	C₂²	1	2	yes	—
95	C₂₃×#470	C₂²	1	2	yes	—
96	C₂₃×#468	C₂²	1	2	yes	—
97	C₂₃×#467	C₂²	1	2	yes	—
98	C₂₃×#467	C₂²	1	2	yes	—
99	C₂₃×#467	C₂²	1	2	yes	—
100	C₂₃×#465	C₂²	1	2	yes	—
101	C₂₃×#464	C₂²	1	2	yes	complemented
102	C₂₃×#464	C₂²	1	2	yes	complemented
103	C₂₃×#462	C₂²	1	2	yes	complemented
104	C₂₃×#462	C₂²	1	2	yes	complemented
105	C₂₃×#462	C₂²	1	2	yes	complemented
106	C₂₃×#462	C₂²	1	2	yes	complemented
107	C₂₃×#462	C₂²	1	2	yes	complemented
108	C₂₃×#461	C₂²	1	2	yes	complemented
109	C₂₃×#452	C₂²	1	2	yes	—
110	C₂₃×#452	C₂²	1	2	yes	—
111	C₂₃×#451	C₂²	1	1	yes	characteristic
112	C₂₃×#451	C₂²	1	1	yes	characteristic
113	C₂₃×#451	C₂²	1	2	yes	—
114	C₂₃×#451	C₂²	1	1	yes	characteristic
115	C₂₃×#451	C₂²	1	1	yes	characteristic
116	C₂₃×#451	C₂²	1	1	yes	characteristic
117	C₂₃×#451	C₂²	1	2	yes	—
118	C₂₃×#451	C₂²	1	1	yes	characteristic
119	C₂₃×#448	C₂²	1	1	yes	characteristic
120	C₂₃×#448	C₂²	1	1	yes	characteristic
121	C₂₃×#441	C₂²	1	2	yes	complemented
122	C₂₃×#441	C₂²	1	2	yes	complemented
123	C₂₃×#441	C₂²	1	2	yes	complemented
124	C₂₃×#440	C₂²	1	2	yes	complemented
125	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
126	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
127	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
128	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
129	C₂₃×#433	C₂²	1	2	yes	—
130	C₂₃×#433	C₂²	1	2	yes	—
131	C₂₃×#432	C₂²	1	1	yes	characteristic
132	C₂₃×#432	C₂²	1	1	yes	characteristic
133	C₂₃×#431	C₂²	1	1	yes	characteristic
134	C₂₃×#431	C₂²	1	1	yes	characteristic
135	C₂₃×#424	C₂²	1	2	yes	—
136	C₂₃×#407	C₂²	1	1	yes	characteristic
137	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
138	C₂₃×#405	C₂²	1	2	yes	—
139	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
140	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
141	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
142	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
144	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
145	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
146	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
147	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
149	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
152	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
153	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
154	C₂₃×C₄⋊Q₈	—	2	1	no	—
155	C₂₃×C₄⋊Q₈	—	2	1	no	—
156	C₂₃×C₄⋊Q₈	—	2	1	no	—
157	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
158	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
160	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₂₃×#126	—	2	1	no	—
164	C₂₃×#126	—	2	1	no	—
165	C₂₃×#126	—	2	1	no	—
166	C₂₃×#126	—	2	1	no	—
167	C₂₃×#126	—	2	1	no	—
168	C₂₃×#126	—	2	1	no	—
169	C₂₃×#126	—	2	2	no	—
170	C₂₃×#126	—	2	2	no	—
171	C₂₃×#126	—	2	2	no	—
172	C₂₃×#126	—	2	2	no	—
173	C₂₃×#126	—	2	2	no	—
174	C₂₃×#126	—	2	2	no	—
175	C₂₃×#126	—	2	2	no	—
176	C₂₃×#126	—	2	2	no	—
177	C₂₃×#126	—	2	1	no	—
178	C₂₃×#126	—	2	1	no	—
179	C₂₃×#125	—	2	1	no	—
180	C₂₃×#125	—	2	1	no	—
181	C₂₃×#125	—	2	1	no	—
182	C₂₃×#125	—	2	1	no	—
183	C₂₃×#125	—	2	1	no	—
184	C₂₃×#125	—	2	2	no	—
185	C₂₃×#125	—	2	2	no	—
186	C₂₃×#125	—	2	2	no	—
187	C₂₃×#125	—	2	2	no	—
188	C₂₃×#125	—	2	2	no	—
189	C₂₃×#125	—	2	2	no	—
190	C₂₃×#125	—	2	2	no	—
191	C₂₃×#125	—	2	2	no	—
192	C₂₃×#125	—	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	2	yes	—
197	C₂₃×#125	C₂³	1	1	yes	characteristic
198	C₂₃×#125	C₂³	1	2	yes	—
199	C₂₃×#125	C₂³	1	1	yes	characteristic
200	C₂₃×#124	—	2	1	no	—
201	C₂₃×#124	—	2	1	no	—
202	C₂₃×#124	C₂³	1	1	yes	characteristic
203	C₂₃×#124	C₂³	1	1	yes	characteristic
204	C₂₃×#123	—	2	1	no	—
205	C₂₃×#123	—	2	1	no	—
206	C₂₃×#123	—	2	1	no	—
207	C₂₃×#123	—	2	1	no	—
208	C₂₃×#123	—	2	1	no	—
209	C₂₃×#123	—	2	1	no	—
210	C₂₃×#123	—	2	1	no	—
211	C₂₃×C₂²⋊Q₈	—	2	1	no	—
212	C₂₃×C₂²⋊Q₈	—	2	1	no	—
213	C₂₃×C₂²⋊Q₈	—	2	1	no	—
214	C₂₃×C₂²⋊Q₈	—	2	1	no	—
215	C₂₃×C₂²⋊Q₈	—	2	1	no	—
216	C₂₃×C₂²⋊Q₈	—	2	1	no	—
217	C₂₃×C₂²⋊Q₈	—	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	C₂³	1	1	yes	characteristic
226	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
227	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
228	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
229	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
230	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
231	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
232	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
233	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
234	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
235	C₂₃×#121	C₂³	1	1	yes	characteristic
236	C₂₃×#121	C₂³	1	1	yes	characteristic
237	C₂₃×#120	—	2	1	no	—
238	C₄×Q₈×C₂₃	—	2	1	no	—
239	C₄×Q₈×C₂₃	—	2	1	no	—
240	C₄×Q₈×C₂₃	—	2	1	no	—
241	C₄×Q₈×C₂₃	—	2	1	no	—
242	C₄×Q₈×C₂₃	—	2	1	no	—
243	C₄×Q₈×C₂₃	—	2	1	no	—
244	C₄×Q₈×C₂₃	—	2	1	no	—
245	C₄×Q₈×C₂₃	—	2	1	no	—
246	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
247	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
248	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
249	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
250	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
251	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
252	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
253	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
254	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
255	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
256	C₄×D₄×C₂₃	—	2	1	no	—
257	C₄×D₄×C₂₃	—	2	1	no	—
258	C₄×D₄×C₂₃	—	2	1	no	—
259	C₄×D₄×C₂₃	—	2	1	no	—
260	C₄×D₄×C₂₃	—	2	1	no	—
261	C₄×D₄×C₂₃	—	2	1	no	—
262	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
263	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
264	C₂₃×#117	—	2	1	no	—
265	C₂₃×#117	—	2	1	no	—
266	C₂₃×#117	—	2	1	no	—
267	C₂₃×#117	—	2	1	no	—
268	C₂₃×#117	—	2	1	no	—
269	C₂₃×#117	—	2	1	no	—
270	C₂₃×#117	—	2	1	no	—
271	C₂₃×#117	D₄	1	1	yes	characteristic
272	C₂₃×#117	D₄	1	1	yes	characteristic
273	C₂₃×#117	D₄	1	1	yes	characteristic
274	C₂₃×#117	D₄	1	1	yes	characteristic
275	C₂₃×#117	C₂³	1	1	yes	characteristic
276	C₂₃×#117	C₂³	1	1	yes	characteristic
277	C₂₃×#117	C₂³	1	1	yes	characteristic
278	C₂₃×#117	C₂³	1	1	yes	characteristic
279	C₂₃×#117	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
285	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
286	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
287	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
288	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
289	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
290	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
291	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
292	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
293	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
294	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
295	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
296	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
297	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
298	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
299	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
300	C₂×C₄²×C₂₃	—	2	1	no	—
301	C₂×C₄²×C₂₃	—	2	1	no	—
302	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
303	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
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×#106	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×C₄⋊C₈	C₂³	1	2	yes	—
313	C₂₃×C₄⋊C₈	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×#103	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	2	yes	—
335	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
336	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
337	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
338	C₂₃×#97	C₂³	1	2	yes	—
339	C₂₃×#97	C₂³	1	2	yes	—
340	C₄×C₈×C₂₃	C₂³	1	2	yes	—
341	C₄×C₈×C₂₃	C₂³	1	2	yes	—
342	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
343	#41×C₂₃	—	4	2	no	—
344	C₂×Q₈×C₂₃	—	2	1	no	—
345	C₂×Q₈×C₂₃	—	2	1	no	—
346	C₂×Q₈×C₂₃	—	2	1	no	—
347	C₂×Q₈×C₂₃	—	2	1	no	—
348	C₂×Q₈×C₂₃	—	2	1	no	—
349	C₂×Q₈×C₂₃	—	4	2	no	—
350	C₂×Q₈×C₂₃	—	4	2	no	—
351	C₂×Q₈×C₂₃	—	4	2	no	—
352	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
353	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
354	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
355	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
356	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
357	C₂×D₄×C₂₃	—	2	1	no	—
358	C₂×D₄×C₂₃	—	2	1	no	—
359	C₂×D₄×C₂₃	—	2	1	no	—
360	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
361	C₂²×C₄×C₂₃	—	2	1	no	—
362	C₂²×C₄×C₂₃	—	2	1	no	—
363	C₂²×C₄×C₂₃	—	2	1	no	—
364	C₂²×C₄×C₂₃	—	2	1	no	—
365	C₂²×C₄×C₂₃	—	2	1	no	—
366	C₂²×C₄×C₂₃	—	2	1	no	—
367	C₂²×C₄×C₂₃	—	2	1	no	—
368	C₂²×C₄×C₂₃	—	2	1	no	—
369	C₂²×C₄×C₂₃	—	2	1	no	—
370	C₂²×C₄×C₂₃	—	4	2	no	—
371	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
372	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
373	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
374	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
375	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
376	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
377	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
378	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
380	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
381	Q₁₆×C₂₃	—	4	2	no	—
382	Q₁₆×C₂₃	—	4	2	no	—
383	Q₁₆×C₂₃	—	4	2	no	—
384	Q₁₆×C₂₃	—	4	2	no	—
385	Q₁₆×C₂₃	—	4	2	no	—
386	Q₁₆×C₂₃	—	4	2	no	—
387	SD₁₆×C₂₃	—	4	2	no	—
388	SD₁₆×C₂₃	—	4	2	no	—
389	M₁₆×C₂₃	—	4	2	no	—
390	C₂×C₈×C₂₃	—	4	2	no	—
391	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
392	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
393	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
394	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
395	C₄⋊C₄×C₂₃	—	2	1	no	—
396	C₄⋊C₄×C₂₃	—	2	1	no	—
397	C₄⋊C₄×C₂₃	—	2	1	no	—
398	C₄⋊C₄×C₂₃	—	2	1	no	—
399	C₄⋊C₄×C₂₃	—	2	1	no	—
400	C₄⋊C₄×C₂₃	—	2	2	no	—
401	C₄⋊C₄×C₂₃	—	2	2	no	—
402	C₄⋊C₄×C₂₃	—	2	2	no	—
403	C₄⋊C₄×C₂₃	—	2	2	no	—
404	C₄⋊C₄×C₂₃	—	2	1	no	—
405	C₄⋊C₄×C₂₃	—	2	1	no	—
406	C₄⋊C₄×C₂₃	—	2	2	no	—
407	C₄⋊C₄×C₂₃	—	2	2	no	—
408	C₄⋊C₄×C₂₃	—	2	2	no	—
409	C₄⋊C₄×C₂₃	—	2	2	no	—
410	C₄⋊C₄×C₂₃	—	2	2	no	—
411	C₄⋊C₄×C₂₃	—	2	2	no	—
412	C₄⋊C₄×C₂₃	—	2	2	no	—
413	C₄⋊C₄×C₂₃	—	2	2	no	—
414	C₄⋊C₄×C₂₃	—	2	2	no	—
415	C₄⋊C₄×C₂₃	—	2	2	no	—
416	C₄⋊C₄×C₂₃	—	2	2	no	—
417	C₄⋊C₄×C₂₃	—	2	2	no	—
418	C₄⋊C₄×C₂₃	—	2	1	no	—
419	C₄⋊C₄×C₂₃	—	2	1	no	—
420	C₄⋊C₄×C₂₃	—	2	1	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	1	no	—
427	C₄⋊C₄×C₂₃	—	2	1	no	—
428	C₄⋊C₄×C₂₃	—	2	1	no	—
429	C₄⋊C₄×C₂₃	—	2	1	no	—
430	C₄⋊C₄×C₂₃	—	2	1	no	—
431	C₄⋊C₄×C₂₃	—	2	1	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	C₂×D₄	1	1	yes	characteristic
437	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
438	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
439	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
440	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
441	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
442	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
443	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
444	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
445	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
446	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
447	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
448	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
449	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
450	C₂²⋊C₄×C₂₃	—	2	1	no	—
451	C₂²⋊C₄×C₂₃	—	2	1	no	—
452	C₂²⋊C₄×C₂₃	—	2	1	no	—
453	C₂²⋊C₄×C₂₃	—	2	1	no	—
454	C₂²⋊C₄×C₂₃	—	2	2	no	—
455	C₂²⋊C₄×C₂₃	—	2	2	no	—
456	C₂²⋊C₄×C₂₃	—	2	2	no	—
457	C₂²⋊C₄×C₂₃	—	2	2	no	—
458	C₂²⋊C₄×C₂₃	—	2	1	no	—
459	C₂²⋊C₄×C₂₃	—	2	1	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	1	no	—
467	C₂²⋊C₄×C₂₃	—	2	1	no	—
468	C₂²⋊C₄×C₂₃	—	2	1	no	—
469	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
470	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
471	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
472	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
473	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
474	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
475	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
476	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
477	C₄²×C₂₃	—	2	2	no	—
478	C₄²×C₂₃	—	2	2	no	—
479	C₄²×C₂₃	—	2	2	no	—
480	C₄²×C₂₃	—	2	2	no	—
481	C₄²×C₂₃	—	2	1	no	—
482	C₄²×C₂₃	—	2	1	no	—
483	C₄²×C₂₃	—	2	1	no	—
484	C₄²×C₂₃	—	2	1	no	—
485	C₄²×C₂₃	—	2	1	no	—
486	C₄²×C₂₃	—	2	1	no	—
487	C₄²×C₂₃	—	2	1	no	—
488	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
489	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
490	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
491	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
492	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
493	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
494	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
495	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
496	#60983	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
497	C₂³×C₂₃	—	2	2	no	—
498	C₂³×C₂₃	—	2	1	no	—
499	C₂³×C₂₃	—	4	1	no	—
500	C₂³×C₂₃	—	4	1	no	—
501	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
502	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
503	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
504	Q₈×C₂₃	—	2	2	no	—
505	Q₈×C₂₃	—	2	2	no	—
506	Q₈×C₂₃	—	2	2	no	—
507	Q₈×C₂₃	—	2	2	no	—
508	Q₈×C₂₃	—	2	2	no	—
509	Q₈×C₂₃	—	2	2	no	—
510	Q₈×C₂₃	—	2	2	no	—
511	Q₈×C₂₃	—	4	2	no	—
512	Q₈×C₂₃	—	4	2	no	—
513	Q₈×C₂₃	—	4	2	no	—
514	Q₈×C₂₃	—	8	1	no	—
515	Q₈×C₂₃	—	8	1	no	—
516	D₄×C₂₃	—	2	2	no	—
517	D₄×C₂₃	—	4	2	no	—
518	D₄×C₂₃	—	4	2	no	—
519	D₄×C₂₃	—	8	1	no	—
520	C₂×C₄×C₂₃	—	2	2	no	—
521	C₂×C₄×C₂₃	—	2	2	no	—
522	C₂×C₄×C₂₃	—	2	2	no	—
523	C₂×C₄×C₂₃	—	2	2	no	—
524	C₂×C₄×C₂₃	—	2	2	no	—
525	C₂×C₄×C₂₃	—	2	1	no	—
526	C₂×C₄×C₂₃	—	2	1	no	—
527	C₂×C₄×C₂₃	—	2	1	no	—
528	C₂×C₄×C₂₃	—	2	1	no	—
529	C₂×C₄×C₂₃	—	2	2	no	—
530	C₂×C₄×C₂₃	—	2	2	no	—
531	C₂×C₄×C₂₃	—	2	1	no	—
532	C₂×C₄×C₂₃	—	2	2	no	—
533	C₂×C₄×C₂₃	—	2	2	no	—
534	C₂×C₄×C₂₃	—	2	1	no	—
535	C₂×C₄×C₂₃	—	2	1	no	—
536	C₂×C₄×C₂₃	—	4	1	no	—
537	C₂×C₄×C₂₃	—	4	1	no	—
538	C₂×C₄×C₂₃	—	4	1	no	—
539	C₂×C₄×C₂₃	—	4	1	no	—
540	C₂×C₄×C₂₃	—	4	1	no	—
541	C₂×C₄×C₂₃	—	4	2	no	—
542	C₂×C₄×C₂₃	—	4	2	no	—
543	C₂×C₄×C₂₃	—	4	2	no	—
544	C₂×C₄×C₂₃	—	4	2	no	—
545	C₂×C₄×C₂₃	—	4	2	no	—
546	C₂×C₄×C₂₃	—	4	2	no	—
547	C₂×C₄×C₂₃	—	8	1	no	—
548	C₂×C₄×C₂₃	—	8	1	no	—
549	C₂×C₄×C₂₃	—	8	1	no	—
550	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
551	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
552	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
553	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
554	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
555	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
556	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
557	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
558	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
559	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
560	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
561	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
562	C₈×C₂₃	—	2	2	no	—
563	C₈×C₂₃	—	2	2	no	—
564	C₈×C₂₃	—	2	2	no	—
565	C₈×C₂₃	—	2	2	no	—
566	#3495	C₂×C₂₃	1	1	yes	characteristic
567	C₂×#541	C₂×C₂₃	1	1	yes	characteristic, complemented
568	#3261	C₂×C₂₃	1	2	yes	complemented
569	#3258	C₂×C₂₃	1	2	yes	complemented
570	#3242	C₂×C₂₃	1	2	yes	complemented
571	#3236	C₂×C₂₃	1	1	yes	characteristic, complemented
572	#3232	C₂×C₂₃	1	1	yes	characteristic, complemented
573	#3223	C₂×C₂₃	1	2	yes	complemented
574	#3218	C₂×C₂₃	1	1	yes	characteristic, complemented
575	#3209	C₂×C₂₃	1	1	yes	characteristic, complemented
576	#3196	C₂×C₂₃	1	1	yes	characteristic
577	#3195	C₂×C₂₃	1	1	yes	characteristic, complemented
578	#3190	C₂×C₂₃	1	1	yes	characteristic
579	#3189	C₂×C₂₃	1	1	yes	characteristic, complemented
580	#3178	C₂×C₂₃	1	2	yes	complemented
581	#3177	C₂×C₂₃	1	2	yes	complemented
582	#3127	C₂×C₂₃	1	2	yes	complemented
583	#3120	C₂×C₂₃	1	2	yes	complemented
584	#3117	C₂×C₂₃	1	1	yes	characteristic, complemented
585	#3113	C₂×C₂₃	1	1	yes	characteristic, complemented
586	#3108	C₂×C₂₃	1	1	yes	characteristic, complemented
587	#3104	C₂×C₂₃	1	1	yes	characteristic, complemented
588	#2924	C₂×C₂₃	1	1	yes	characteristic, complemented
589	C₂²×C₂₃	—	2	1	no	—
590	C₂²×C₂₃	—	2	1	no	—
591	C₂²×C₂₃	—	2	1	no	—
592	C₂²×C₂₃	—	2	1	no	—
593	C₂²×C₂₃	—	2	1	no	—
594	C₂²×C₂₃	—	2	1	no	—
595	C₂²×C₂₃	—	2	1	no	—
596	C₂²×C₂₃	—	2	1	no	—
597	C₂²×C₂₃	—	4	1	no	—
598	C₂²×C₂₃	—	4	1	no	—
599	C₂²×C₂₃	—	4	1	no	—
600	C₂²×C₂₃	—	8	2	no	—
601	C₂²×C₂₃	#578	1	2	yes	—
602	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
603	C₄×C₂₃	—	2	1	no	—
604	C₄×C₂₃	—	2	1	no	—
605	C₄×C₂₃	—	2	1	no	—
606	C₄×C₂₃	—	2	1	no	—
607	C₄×C₂₃	—	2	1	no	—
608	C₄×C₂₃	—	2	1	no	—
609	C₄×C₂₃	—	2	1	no	—
610	C₄×C₂₃	—	2	1	no	—
611	C₄×C₂₃	—	2	1	no	—
612	C₄×C₂₃	—	2	1	no	—
613	C₄×C₂₃	—	2	1	no	—
614	C₄×C₂₃	—	4	2	no	—
615	C₄×C₂₃	—	4	1	no	—
616	C₄×C₂₃	—	4	1	no	—
617	C₄×C₂₃	—	4	1	no	—
618	C₄×C₂₃	—	4	1	no	—
619	C₄×C₂₃	—	4	1	no	—
620	C₄×C₂₃	—	4	1	no	—
621	C₄×C₂₃	—	4	2	no	—
622	C₄×C₂₃	—	4	2	no	—
623	C₄×C₂₃	—	4	2	no	—
624	C₄×C₂₃	—	4	1	no	—
625	C₄×C₂₃	#585	1	2	yes	—
626	#556	—	2	1	no	—
627	#554	—	2	1	no	—
628	#552	—	2	1	no	—
629	#552	—	2	1	no	—
630	#552	—	2	1	no	—
631	#552	—	2	1	no	—
632	#551	—	2	1	no	—
633	#551	—	2	1	no	—
634	#544	C₂²×C₂₃	1	1	yes	characteristic
635	#542	C₂²×C₂₃	1	1	yes	characteristic
636	#542	C₂²×C₂₃	1	1	yes	characteristic
637	#541	—	2	1	no	—
638	#541	—	2	1	no	—
639	#541	—	2	1	no	—
640	#541	—	2	1	no	—
641	#541	C₂²×C₂₃	1	2	yes	—
642	#541	C₂²×C₂₃	1	1	yes	characteristic
643	#541	C₂²×C₂₃	1	2	yes	—
644	#541	C₂²×C₂₃	1	2	yes	—
645	#541	C₂²×C₂₃	1	2	yes	—
646	#541	C₂²×C₂₃	1	1	yes	characteristic
647	#536	C₂²×C₂₃	1	1	yes	characteristic
648	#533	C₂²×C₂₃	1	1	yes	characteristic
649	#533	C₂²×C₂₃	1	1	yes	characteristic
650	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
651	#529	C₂²×C₂₃	1	1	yes	characteristic
652	#529	C₂²×C₂₃	1	1	yes	characteristic
653	C₂×#126	—	2	1	no	—
654	C₂×#126	—	2	1	no	—
655	C₂×#125	—	2	1	no	—
656	C₂×#125	—	2	1	no	—
657	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
658	#525	C₂²×C₂₃	1	1	yes	characteristic
659	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
660	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
661	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
662	#520	C₂²×C₂₃	1	1	yes	characteristic
663	#519	C₂²×C₂₃	1	1	yes	characteristic
664	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
665	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
666	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
667	#501	C₂²×C₂₃	1	2	yes	complemented
668	#499	C₂²×C₂₃	1	2	yes	complemented
669	#497	C₂²×C₂₃	1	2	yes	complemented
670	#494	C₂²×C₂₃	1	2	yes	complemented
671	#491	C₂²×C₂₃	1	2	yes	complemented
672	#491	C₂²×C₂₃	1	2	yes	complemented
673	#488	C₂²×C₂₃	1	2	yes	complemented
674	#487	C₂²×C₂₃	1	2	yes	complemented
675	#485	C₂²×C₂₃	1	2	yes	—
676	#485	C₂²×C₂₃	1	2	yes	—
677	#484	C₂²×C₂₃	1	1	yes	characteristic
678	#484	C₂²×C₂₃	1	1	yes	characteristic
679	#484	C₂²×C₂₃	1	1	yes	characteristic
680	#484	C₂²×C₂₃	1	2	yes	—
681	#483	C₂²×C₂₃	1	1	yes	characteristic
682	#483	C₂²×C₂₃	1	1	yes	characteristic
683	#483	C₂²×C₂₃	1	1	yes	characteristic
684	#483	C₂²×C₂₃	1	2	yes	—
685	#481	C₂²×C₂₃	1	1	yes	characteristic
686	#480	C₂²×C₂₃	1	1	yes	characteristic
687	#479	C₂²×C₂₃	1	2	yes	complemented
688	#479	C₂²×C₂₃	1	2	yes	complemented
689	#479	C₂²×C₂₃	1	2	yes	complemented
690	#479	C₂²×C₂₃	1	2	yes	complemented
691	#479	C₂²×C₂₃	1	2	yes	complemented
692	#478	C₂²×C₂₃	1	2	yes	complemented
693	#477	C₂²×C₂₃	1	2	yes	complemented
694	#475	C₂²×C₂₃	1	2	yes	complemented
695	#470	C₂²×C₂₃	1	2	yes	—
696	#470	C₂²×C₂₃	1	2	yes	—
697	#470	C₂²×C₂₃	1	2	yes	—
698	#468	C₂²×C₂₃	1	2	yes	—
699	#467	C₂²×C₂₃	1	2	yes	—
700	#467	C₂²×C₂₃	1	2	yes	—
701	#467	C₂²×C₂₃	1	2	yes	—
702	#465	C₂²×C₂₃	1	2	yes	—
703	#464	C₂²×C₂₃	1	2	yes	complemented
704	#464	C₂²×C₂₃	1	2	yes	complemented
705	#462	C₂²×C₂₃	1	2	yes	complemented
706	#462	C₂²×C₂₃	1	2	yes	complemented
707	#462	C₂²×C₂₃	1	2	yes	complemented
708	#462	C₂²×C₂₃	1	2	yes	complemented
709	#462	C₂²×C₂₃	1	2	yes	complemented
710	#461	C₂²×C₂₃	1	2	yes	complemented
711	#452	C₂²×C₂₃	1	2	yes	—
712	#452	C₂²×C₂₃	1	2	yes	—
713	#451	C₂²×C₂₃	1	1	yes	characteristic
714	#451	C₂²×C₂₃	1	1	yes	characteristic
715	#451	C₂²×C₂₃	1	1	yes	characteristic
716	#451	C₂²×C₂₃	1	1	yes	characteristic
717	#451	C₂²×C₂₃	1	1	yes	characteristic
718	#451	C₂²×C₂₃	1	1	yes	characteristic
719	#451	C₂²×C₂₃	1	2	yes	—
720	#451	C₂²×C₂₃	1	2	yes	—
721	#448	C₂²×C₂₃	1	1	yes	characteristic
722	#448	C₂²×C₂₃	1	1	yes	characteristic
723	#441	C₂²×C₂₃	1	2	yes	complemented
724	#441	C₂²×C₂₃	1	2	yes	complemented
725	#441	C₂²×C₂₃	1	2	yes	complemented
726	#440	C₂²×C₂₃	1	2	yes	complemented
727	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
728	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
729	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
730	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
731	#433	C₂²×C₂₃	1	2	yes	—
732	#433	C₂²×C₂₃	1	2	yes	—
733	#432	C₂²×C₂₃	1	1	yes	characteristic
734	#432	C₂²×C₂₃	1	1	yes	characteristic
735	#431	C₂²×C₂₃	1	1	yes	characteristic
736	#431	C₂²×C₂₃	1	1	yes	characteristic
737	#424	C₂²×C₂₃	1	2	yes	—
738	#407	C₂²×C₂₃	1	1	yes	characteristic
739	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
740	#405	C₂²×C₂₃	1	2	yes	—
741	C₂×C₂₃	—	2	2	no	—
742	C₂×C₂₃	—	4	1	no	—
743	C₂×C₂₃	—	4	1	no	—
744	C₂×C₂₃	—	8	1	no	—
745	C₂×C₂₃	#3449	1	1	yes	characteristic
746	C₂×C₂₃	C₂×#578	1	1	yes	characteristic
747	C₂×C₂₃	#3586	1	1	yes	characteristic
748	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
749	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
750	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
751	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
752	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
753	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
754	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
755	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
756	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
757	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
758	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
759	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
760	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
761	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
762	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
763	C₄⋊Q₈	—	2	1	no	—
764	C₄⋊Q₈	—	2	1	no	—
765	C₄⋊Q₈	—	2	1	no	—
766	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
767	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
768	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
769	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
770	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
771	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
772	#126	—	2	1	no	—
773	#126	—	2	1	no	—
774	#126	—	2	2	no	—
775	#126	—	2	2	no	—
776	#126	—	2	2	no	—
777	#126	—	2	2	no	—
778	#126	—	2	2	no	—
779	#126	—	2	2	no	—
780	#126	—	2	2	no	—
781	#126	—	2	2	no	—
782	#126	—	2	1	no	—
783	#126	—	2	1	no	—
784	#126	—	2	1	no	—
785	#126	—	2	1	no	—
786	#126	—	2	1	no	—
787	#126	—	2	1	no	—
788	#125	—	2	2	no	—
789	#125	—	2	2	no	—
790	#125	—	2	2	no	—
791	#125	—	2	2	no	—
792	#125	—	2	2	no	—
793	#125	—	2	2	no	—
794	#125	—	2	2	no	—
795	#125	—	2	2	no	—
796	#125	—	2	1	no	—
797	#125	—	2	1	no	—
798	#125	—	2	1	no	—
799	#125	—	2	1	no	—
800	#125	—	2	1	no	—
801	#125	—	2	1	no	—
802	#125	—	2	1	no	—
803	#125	—	2	1	no	—
804	#125	—	2	1	no	—
805	#125	C₂³×C₂₃	1	2	yes	—
806	#125	C₂³×C₂₃	1	2	yes	—
807	#125	C₂³×C₂₃	1	1	yes	characteristic
808	#125	C₂³×C₂₃	1	1	yes	characteristic
809	#124	—	2	1	no	—
810	#124	—	2	1	no	—
811	#124	C₂³×C₂₃	1	1	yes	characteristic
812	#124	C₂³×C₂₃	1	1	yes	characteristic
813	#123	—	2	1	no	—
814	#123	—	2	1	no	—
815	#123	—	2	1	no	—
816	#123	—	2	1	no	—
817	#123	—	2	1	no	—
818	#123	—	2	1	no	—
819	#123	—	2	1	no	—
820	C₂²⋊Q₈	—	2	1	no	—
821	C₂²⋊Q₈	—	2	1	no	—
822	C₂²⋊Q₈	—	2	1	no	—
823	C₂²⋊Q₈	—	2	1	no	—
824	C₂²⋊Q₈	—	2	1	no	—
825	C₂²⋊Q₈	—	2	1	no	—
826	C₂²⋊Q₈	—	2	1	no	—
827	C₂²⋊Q₈	—	2	1	no	—
828	C₂²⋊Q₈	—	2	1	no	—
829	C₂²⋊Q₈	—	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	C₂³×C₂₃	1	1	yes	characteristic
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	2	yes	—
839	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
840	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
841	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
842	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
843	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
844	#121	C₂³×C₂₃	1	1	yes	characteristic
845	#121	C₂³×C₂₃	1	1	yes	characteristic
846	#120	—	2	1	no	—
847	C₄×Q₈	—	2	1	no	—
848	C₄×Q₈	—	2	1	no	—
849	C₄×Q₈	—	2	1	no	—
850	C₄×Q₈	—	2	1	no	—
851	C₄×Q₈	—	2	1	no	—
852	C₄×Q₈	—	2	1	no	—
853	C₄×Q₈	—	2	1	no	—
854	C₄×Q₈	—	2	1	no	—
855	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
856	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
857	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
858	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
859	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
860	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
861	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
862	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
863	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
864	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
865	C₄×D₄	—	2	1	no	—
866	C₄×D₄	—	2	1	no	—
867	C₄×D₄	—	2	1	no	—
868	C₄×D₄	—	2	1	no	—
869	C₄×D₄	—	2	1	no	—
870	C₄×D₄	—	2	1	no	—
871	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
872	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
873	#117	—	2	1	no	—
874	#117	—	2	1	no	—
875	#117	—	2	1	no	—
876	#117	—	2	1	no	—
877	#117	—	2	1	no	—
878	#117	—	2	1	no	—
879	#117	—	2	1	no	—
880	#117	D₄×C₂₃	1	1	yes	characteristic
881	#117	D₄×C₂₃	1	1	yes	characteristic
882	#117	D₄×C₂₃	1	1	yes	characteristic
883	#117	D₄×C₂₃	1	1	yes	characteristic
884	#117	C₂³×C₂₃	1	1	yes	characteristic
885	#117	C₂³×C₂₃	1	1	yes	characteristic
886	#117	C₂³×C₂₃	1	1	yes	characteristic
887	#117	C₂³×C₂₃	1	1	yes	characteristic
888	#117	C₂³×C₂₃	1	1	yes	characteristic
889	C₂×C₄⋊C₄	—	2	1	no	—
890	C₂×C₄⋊C₄	—	2	1	no	—
891	C₂×C₄⋊C₄	—	2	1	no	—
892	C₂×C₄⋊C₄	—	2	1	no	—
893	C₂×C₄⋊C₄	—	2	1	no	—
894	C₂×C₄⋊C₄	—	2	1	no	—
895	C₂×C₄⋊C₄	—	2	1	no	—
896	C₂×C₄⋊C₄	—	2	1	no	—
897	C₂×C₄⋊C₄	—	2	1	no	—
898	C₂×C₄⋊C₄	—	2	1	no	—
899	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
900	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
901	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
902	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
903	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
904	C₂×C₂²⋊C₄	—	2	1	no	—
905	C₂×C₂²⋊C₄	—	2	1	no	—
906	C₂×C₂²⋊C₄	—	2	1	no	—
907	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
908	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
909	C₂×C₄²	—	2	1	no	—
910	C₂×C₄²	—	2	1	no	—
911	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
912	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
913	#107	C₂³×C₂₃	1	2	yes	—
914	#107	C₂³×C₂₃	1	2	yes	—
915	#107	C₂³×C₂₃	1	2	yes	—
916	#107	C₂³×C₂₃	1	2	yes	—
917	#106	C₂³×C₂₃	1	2	yes	—
918	#106	C₂³×C₂₃	1	2	yes	—
919	#106	C₂³×C₂₃	1	2	yes	—
920	#106	C₂³×C₂₃	1	2	yes	—
921	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
922	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
923	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
924	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
925	#103	C₂³×C₂₃	1	2	yes	—
926	#103	C₂³×C₂₃	1	2	yes	—
927	#103	C₂³×C₂₃	1	2	yes	—
928	#103	C₂³×C₂₃	1	2	yes	—
929	#103	C₂³×C₂₃	1	2	yes	—
930	#103	C₂³×C₂₃	1	2	yes	—
931	#103	C₂³×C₂₃	1	2	yes	—
932	#103	C₂³×C₂₃	1	2	yes	—
933	#103	C₂³×C₂₃	1	2	yes	—
934	#103	C₂³×C₂₃	1	2	yes	—
935	#103	C₂³×C₂₃	1	2	yes	—
936	#103	C₂³×C₂₃	1	2	yes	—
937	#103	C₂³×C₂₃	1	2	yes	—
938	#103	C₂³×C₂₃	1	2	yes	—
939	#102	C₂³×C₂₃	1	2	yes	—
940	#102	C₂³×C₂₃	1	2	yes	—
941	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
942	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
943	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
944	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
945	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
946	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
947	#97	C₂³×C₂₃	1	2	yes	—
948	#97	C₂³×C₂₃	1	2	yes	—
949	C₄×C₈	C₂³×C₂₃	1	2	yes	—
950	C₄×C₈	C₂³×C₂₃	1	2	yes	—
951	C₂₃	#60983	1	1	yes	characteristic, direct product factor, Sylow
952	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
953	#41	—	4	2	no	—
954	C₂×Q₈	—	2	1	no	—
955	C₂×Q₈	—	2	1	no	—
956	C₂×Q₈	—	2	1	no	—
957	C₂×Q₈	—	2	1	no	—
958	C₂×Q₈	—	2	1	no	—
959	C₂×Q₈	—	4	2	no	—
960	C₂×Q₈	—	4	2	no	—
961	C₂×Q₈	—	4	2	no	—
962	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
963	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
964	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
965	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
966	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
967	C₂×D₄	—	2	1	no	—
968	C₂×D₄	—	2	1	no	—
969	C₂×D₄	—	2	1	no	—
970	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
971	C₂²×C₄	—	2	1	no	—
972	C₂²×C₄	—	2	1	no	—
973	C₂²×C₄	—	2	1	no	—
974	C₂²×C₄	—	2	1	no	—
975	C₂²×C₄	—	2	1	no	—
976	C₂²×C₄	—	2	1	no	—
977	C₂²×C₄	—	2	1	no	—
978	C₂²×C₄	—	2	1	no	—
979	C₂²×C₄	—	2	1	no	—
980	C₂²×C₄	—	4	2	no	—
981	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
982	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
983	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
984	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
985	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
986	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
987	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
988	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
989	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
990	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
991	Q₁₆	—	4	2	no	—
992	Q₁₆	—	4	2	no	—
993	Q₁₆	—	4	2	no	—
994	Q₁₆	—	4	2	no	—
995	Q₁₆	—	4	2	no	—
996	Q₁₆	—	4	2	no	—
997	SD₁₆	—	4	2	no	—
998	SD₁₆	—	4	2	no	—
999	M₁₆	—	4	2	no	—
1000	C₂×C₈	—	4	2	no	—
1001	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1002	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1003	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1004	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1005	C₄⋊C₄	—	2	1	no	—
1006	C₄⋊C₄	—	2	1	no	—
1007	C₄⋊C₄	—	2	1	no	—
1008	C₄⋊C₄	—	2	1	no	—
1009	C₄⋊C₄	—	2	1	no	—
1010	C₄⋊C₄	—	2	2	no	—
1011	C₄⋊C₄	—	2	2	no	—
1012	C₄⋊C₄	—	2	2	no	—
1013	C₄⋊C₄	—	2	2	no	—
1014	C₄⋊C₄	—	2	1	no	—
1015	C₄⋊C₄	—	2	1	no	—
1016	C₄⋊C₄	—	2	2	no	—
1017	C₄⋊C₄	—	2	2	no	—
1018	C₄⋊C₄	—	2	2	no	—
1019	C₄⋊C₄	—	2	2	no	—
1020	C₄⋊C₄	—	2	2	no	—
1021	C₄⋊C₄	—	2	2	no	—
1022	C₄⋊C₄	—	2	2	no	—
1023	C₄⋊C₄	—	2	2	no	—
1024	C₄⋊C₄	—	2	2	no	—
1025	C₄⋊C₄	—	2	2	no	—
1026	C₄⋊C₄	—	2	2	no	—
1027	C₄⋊C₄	—	2	2	no	—
1028	C₄⋊C₄	—	2	1	no	—
1029	C₄⋊C₄	—	2	1	no	—
1030	C₄⋊C₄	—	2	1	no	—
1031	C₄⋊C₄	—	2	1	no	—
1032	C₄⋊C₄	—	2	1	no	—
1033	C₄⋊C₄	—	2	1	no	—
1034	C₄⋊C₄	—	2	1	no	—
1035	C₄⋊C₄	—	2	1	no	—
1036	C₄⋊C₄	—	2	1	no	—
1037	C₄⋊C₄	—	2	1	no	—
1038	C₄⋊C₄	—	2	1	no	—
1039	C₄⋊C₄	—	2	1	no	—
1040	C₄⋊C₄	—	2	1	no	—
1041	C₄⋊C₄	—	2	1	no	—
1042	C₄⋊C₄	—	2	1	no	—
1043	C₄⋊C₄	—	2	1	no	—
1044	C₄⋊C₄	—	2	1	no	—
1045	C₄⋊C₄	—	2	1	no	—
1046	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1047	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1048	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1049	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1050	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1051	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1052	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1053	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1054	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1055	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1056	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1057	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1058	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1059	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1060	C₂²⋊C₄	—	2	1	no	—
1061	C₂²⋊C₄	—	2	1	no	—
1062	C₂²⋊C₄	—	2	1	no	—
1063	C₂²⋊C₄	—	2	1	no	—
1064	C₂²⋊C₄	—	2	2	no	—
1065	C₂²⋊C₄	—	2	2	no	—
1066	C₂²⋊C₄	—	2	2	no	—
1067	C₂²⋊C₄	—	2	2	no	—
1068	C₂²⋊C₄	—	2	1	no	—
1069	C₂²⋊C₄	—	2	1	no	—
1070	C₂²⋊C₄	—	2	1	no	—
1071	C₂²⋊C₄	—	2	1	no	—
1072	C₂²⋊C₄	—	2	1	no	—
1073	C₂²⋊C₄	—	2	1	no	—
1074	C₂²⋊C₄	—	2	1	no	—
1075	C₂²⋊C₄	—	2	1	no	—
1076	C₂²⋊C₄	—	2	1	no	—
1077	C₂²⋊C₄	—	2	1	no	—
1078	C₂²⋊C₄	—	2	1	no	—
1079	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1080	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1081	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1082	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1083	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1084	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1085	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1086	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1087	C₄²	—	2	2	no	—
1088	C₄²	—	2	2	no	—
1089	C₄²	—	2	2	no	—
1090	C₄²	—	2	2	no	—
1091	C₄²	—	2	1	no	—
1092	C₄²	—	2	1	no	—
1093	C₄²	—	2	1	no	—
1094	C₄²	—	2	1	no	—
1095	C₄²	—	2	1	no	—
1096	C₄²	—	2	1	no	—
1097	C₄²	—	2	1	no	—
1098	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1099	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1100	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1101	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1102	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1103	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1104	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1105	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1106	C₂³	—	2	2	no	—
1107	C₂³	—	2	1	no	—
1108	C₂³	—	4	1	no	—
1109	C₂³	—	4	1	no	—
1110	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1111	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1112	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1113	Q₈	—	2	2	no	—
1114	Q₈	—	2	2	no	—
1115	Q₈	—	2	2	no	—
1116	Q₈	—	2	2	no	—
1117	Q₈	—	2	2	no	—
1118	Q₈	—	2	2	no	—
1119	Q₈	—	2	2	no	—
1120	Q₈	—	4	2	no	—
1121	Q₈	—	4	2	no	—
1122	Q₈	—	4	2	no	—
1123	Q₈	—	8	1	no	—
1124	Q₈	—	8	1	no	—
1125	D₄	—	2	2	no	—
1126	D₄	—	4	2	no	—
1127	D₄	—	4	2	no	—
1128	D₄	—	8	1	no	—
1129	C₂×C₄	—	2	2	no	—
1130	C₂×C₄	—	2	2	no	—
1131	C₂×C₄	—	2	2	no	—
1132	C₂×C₄	—	2	2	no	—
1133	C₂×C₄	—	2	2	no	—
1134	C₂×C₄	—	2	1	no	—
1135	C₂×C₄	—	2	1	no	—
1136	C₂×C₄	—	2	1	no	—
1137	C₂×C₄	—	2	1	no	—
1138	C₂×C₄	—	2	2	no	—
1139	C₂×C₄	—	2	2	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	2	no	—
1142	C₂×C₄	—	2	2	no	—
1143	C₂×C₄	—	2	1	no	—
1144	C₂×C₄	—	2	1	no	—
1145	C₂×C₄	—	4	1	no	—
1146	C₂×C₄	—	4	1	no	—
1147	C₂×C₄	—	4	1	no	—
1148	C₂×C₄	—	4	1	no	—
1149	C₂×C₄	—	4	1	no	—
1150	C₂×C₄	—	4	2	no	—
1151	C₂×C₄	—	4	2	no	—
1152	C₂×C₄	—	4	2	no	—
1153	C₂×C₄	—	4	2	no	—
1154	C₂×C₄	—	4	2	no	—
1155	C₂×C₄	—	4	2	no	—
1156	C₂×C₄	—	8	1	no	—
1157	C₂×C₄	—	8	1	no	—
1158	C₂×C₄	—	8	1	no	—
1159	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1160	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1161	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1162	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1163	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1164	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1165	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1166	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1167	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1168	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1169	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1170	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1171	C₈	—	2	2	no	—
1172	C₈	—	2	2	no	—
1173	C₈	—	2	2	no	—
1174	C₈	—	2	2	no	—
1175	C₂²	—	2	1	no	—
1176	C₂²	—	2	1	no	—
1177	C₂²	—	2	1	no	—
1178	C₂²	—	2	1	no	—
1179	C₂²	—	2	1	no	—
1180	C₂²	—	2	1	no	—
1181	C₂²	—	2	1	no	—
1182	C₂²	—	2	1	no	—
1183	C₂²	—	4	1	no	—
1184	C₂²	—	4	1	no	—
1185	C₂²	—	4	1	no	—
1186	C₂²	—	8	2	no	—
1187	C₂²	C₂₃×#578	1	2	yes	—
1188	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1189	C₄	—	2	1	no	—
1190	C₄	—	2	1	no	—
1191	C₄	—	2	1	no	—
1192	C₄	—	2	1	no	—
1193	C₄	—	2	1	no	—
1194	C₄	—	2	1	no	—
1195	C₄	—	2	1	no	—
1196	C₄	—	2	1	no	—
1197	C₄	—	2	1	no	—
1198	C₄	—	2	1	no	—
1199	C₄	—	2	1	no	—
1200	C₄	—	4	1	no	—
1201	C₄	—	4	1	no	—
1202	C₄	—	4	1	no	—
1203	C₄	—	4	2	no	—
1204	C₄	—	4	2	no	—
1205	C₄	—	4	2	no	—
1206	C₄	—	4	1	no	—
1207	C₄	—	4	2	no	—
1208	C₄	—	4	1	no	—
1209	C₄	—	4	1	no	—
1210	C₄	—	4	1	no	—
1211	C₄	C₂₃×#585	1	2	yes	—
1212	C₂	—	2	2	no	—
1213	C₂	—	4	1	no	—
1214	C₂	—	4	1	no	—
1215	C₂	—	8	1	no	—
1216	C₂	C₂₃×#3449	1	1	yes	characteristic
1217	C₂	C₂×C₂₃×#578	1	1	yes	characteristic
1218	C₂	C₂₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#525	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₂₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₃×#541	C₂	semidirect
3. C₂₃×#3261	C₂	semidirect
4. C₂₃×#3258	C₂	semidirect
5. C₂₃×#3242	C₂	semidirect
6. C₂₃×#3236	C₂	semidirect
7. C₂₃×#3232	C₂	semidirect
8. C₂₃×#3223	C₂	semidirect
9. C₂₃×#3218	C₂	semidirect
10. C₂₃×#3209	C₂	semidirect
12. C₂₃×#3195	C₂	semidirect
14. C₂₃×#3189	C₂	semidirect
15. C₂₃×#3178	C₂	semidirect
16. C₂₃×#3177	C₂	semidirect
17. C₂₃×#3127	C₂	semidirect
18. C₂₃×#3120	C₂	semidirect
19. C₂₃×#3117	C₂	semidirect
20. C₂₃×#3113	C₂	semidirect
21. C₂₃×#3108	C₂	semidirect
22. C₂₃×#3104	C₂	semidirect
23. C₂₃×#2924	C₂	semidirect
65. C₂₃×#501	C₂²	semidirect
66. C₂₃×#499	C₂²	semidirect
67. C₂₃×#497	C₂²	semidirect
68. C₂₃×#494	C₂²	semidirect
69. C₂₃×#491	C₂²	semidirect
70. C₂₃×#491	C₂²	semidirect
71. C₂₃×#488	C₂²	semidirect
72. C₂₃×#487	C₂²	semidirect
85. C₂₃×#479	C₂²	semidirect
86. C₂₃×#479	C₂²	semidirect
87. C₂₃×#479	C₂²	semidirect
88. C₂₃×#479	C₂²	semidirect
89. C₂₃×#479	C₂²	semidirect
90. C₂₃×#478	C₂²	semidirect
91. C₂₃×#477	C₂²	semidirect
92. C₂₃×#475	C₂²	semidirect
101. C₂₃×#464	C₂²	semidirect
102. C₂₃×#464	C₂²	semidirect
103. C₂₃×#462	C₂²	semidirect
104. C₂₃×#462	C₂²	semidirect
105. C₂₃×#462	C₂²	semidirect
106. C₂₃×#462	C₂²	semidirect
107. C₂₃×#462	C₂²	semidirect
108. C₂₃×#461	C₂²	semidirect
121. C₂₃×#441	C₂²	semidirect
122. C₂₃×#441	C₂²	semidirect
123. C₂₃×#441	C₂²	semidirect
124. C₂₃×#440	C₂²	semidirect
125. C₄×Q₁₆×C₂₃	C₂²	semidirect
126. C₄×Q₁₆×C₂₃	C₂²	semidirect
127. C₄×Q₁₆×C₂₃	C₂²	semidirect
128. C₄×SD₁₆×C₂₃	C₂²	semidirect
496. #60983	C₂₃	direct (N × H)
567. C₂×#541	C₂×C₂₃	semidirect
568. #3261	C₂×C₂₃	semidirect
569. #3258	C₂×C₂₃	semidirect
570. #3242	C₂×C₂₃	semidirect
571. #3236	C₂×C₂₃	semidirect
572. #3232	C₂×C₂₃	semidirect
573. #3223	C₂×C₂₃	semidirect
574. #3218	C₂×C₂₃	semidirect
575. #3209	C₂×C₂₃	semidirect
577. #3195	C₂×C₂₃	semidirect
579. #3189	C₂×C₂₃	semidirect
580. #3178	C₂×C₂₃	semidirect
581. #3177	C₂×C₂₃	semidirect
582. #3127	C₂×C₂₃	semidirect
583. #3120	C₂×C₂₃	semidirect
584. #3117	C₂×C₂₃	semidirect
585. #3113	C₂×C₂₃	semidirect
586. #3108	C₂×C₂₃	semidirect
587. #3104	C₂×C₂₃	semidirect
588. #2924	C₂×C₂₃	semidirect
667. #501	C₂²×C₂₃	semidirect
668. #499	C₂²×C₂₃	semidirect
669. #497	C₂²×C₂₃	semidirect
670. #494	C₂²×C₂₃	semidirect
671. #491	C₂²×C₂₃	semidirect
672. #491	C₂²×C₂₃	semidirect
673. #488	C₂²×C₂₃	semidirect
674. #487	C₂²×C₂₃	semidirect
687. #479	C₂²×C₂₃	semidirect
688. #479	C₂²×C₂₃	semidirect
689. #479	C₂²×C₂₃	semidirect
690. #479	C₂²×C₂₃	semidirect
691. #479	C₂²×C₂₃	semidirect
692. #478	C₂²×C₂₃	semidirect
693. #477	C₂²×C₂₃	semidirect
694. #475	C₂²×C₂₃	semidirect
703. #464	C₂²×C₂₃	semidirect
704. #464	C₂²×C₂₃	semidirect
705. #462	C₂²×C₂₃	semidirect
706. #462	C₂²×C₂₃	semidirect
707. #462	C₂²×C₂₃	semidirect
708. #462	C₂²×C₂₃	semidirect
709. #462	C₂²×C₂₃	semidirect
710. #461	C₂²×C₂₃	semidirect
723. #441	C₂²×C₂₃	semidirect
724. #441	C₂²×C₂₃	semidirect
725. #441	C₂²×C₂₃	semidirect
726. #440	C₂²×C₂₃	semidirect
727. C₄×Q₁₆	C₂²×C₂₃	semidirect
728. C₄×Q₁₆	C₂²×C₂₃	semidirect
729. C₄×Q₁₆	C₂²×C₂₃	semidirect
730. C₄×SD₁₆	C₂²×C₂₃	semidirect
951. C₂₃	#60983	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×#3495	2
C₂×C₂₃×#541	2
C₂₃×#3261	2
C₂₃×#3258	2
C₂₃×#3242	2
C₂₃×#3236	2
C₂₃×#3232	2
C₂₃×#3223	2
C₂₃×#3218	2
C₂₃×#3209	2
C₂₃×#3196	2
C₂₃×#3195	2
C₂₃×#3190	2
C₂₃×#3189	2
C₂₃×#3178	2
C₂₃×#3177	2
C₂₃×#3127	2
C₂₃×#3120	2
C₂₃×#3117	2
C₂₃×#3113	2
C₂₃×#3108	2
C₂₃×#3104	2
C₂₃×#2924	2
#60983	23

Subgroups — C23×#60983 #19208609

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60983 #19208609