Subgroups — C₂₃×#60979 #19208605

Order 5888.

1796 conjugacy classes of subgroups.

The subgroup lattice has 1280 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, complemented
2	C₂×C₂₃×#540	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3260	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3257	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3241	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×#3221	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3217	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3208	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3194	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3193	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3188	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3187	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3179	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3174	C₂	1	2	yes	maximal, complemented
17	C₂₃×#3126	C₂	1	2	yes	maximal, complemented
18	C₂₃×#3119	C₂	1	2	yes	maximal, complemented
19	C₂₃×#3114	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#3110	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#3105	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₃×#3101	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, complemented
33	C₂₃×#542	C₂²	1	1	yes	characteristic, complemented
34	C₂₃×#542	C₂²	1	1	yes	characteristic, complemented
35	C₂₃×#541	C₂²	1	1	yes	characteristic, complemented
36	C₂₃×#541	C₂²	1	1	yes	characteristic, complemented
37	C₂₃×#540	—	2	1	no	—
38	C₂₃×#540	—	2	1	no	—
39	C₂₃×#540	—	2	1	no	—
40	C₂₃×#540	—	2	1	no	—
41	C₂₃×#540	C₂²	1	2	yes	—
42	C₂₃×#540	C₂²	1	2	yes	—
43	C₂₃×#540	C₂²	1	2	yes	—
44	C₂₃×#540	C₂²	1	2	yes	—
45	C₂₃×#536	C₂²	1	1	yes	characteristic, complemented
46	C₂₃×#533	C₂²	1	1	yes	characteristic
47	C₂₃×#533	C₂²	1	1	yes	characteristic
48	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
49	C₂₃×#529	C₂²	1	1	yes	characteristic
50	C₂₃×#529	C₂²	1	1	yes	characteristic
51	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
52	C₂₃×#525	C₂²	1	1	yes	characteristic
53	C₂×C₂₃×#123	—	2	1	no	—
54	C₂×C₂₃×#123	—	2	1	no	—
55	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
56	C₂×C₂₃×#121	—	2	1	no	—
57	C₂×C₂₃×#121	—	2	1	no	—
58	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
59	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
60	C₂₃×#520	C₂²	1	1	yes	characteristic, complemented
61	C₂₃×#519	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
63	C₂×C₄×D₄×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×#496	C₂²	1	2	yes	complemented
68	C₂₃×#492	C₂²	1	2	yes	complemented
69	C₂₃×#491	C₂²	1	2	yes	complemented
70	C₂₃×#490	C₂²	1	2	yes	complemented
71	C₂₃×#488	C₂²	1	2	yes	complemented
72	C₂₃×#486	C₂²	1	2	yes	complemented
73	C₂₃×#484	C₂²	1	1	yes	characteristic
74	C₂₃×#484	C₂²	1	1	yes	characteristic
75	C₂₃×#484	C₂²	1	1	yes	characteristic
76	C₂₃×#483	C₂²	1	1	yes	characteristic
77	C₂₃×#483	C₂²	1	1	yes	characteristic
78	C₂₃×#483	C₂²	1	1	yes	characteristic
79	C₂₃×#482	C₂²	1	2	yes	complemented
80	C₂₃×#482	C₂²	1	2	yes	complemented
81	C₂₃×#481	C₂²	1	1	yes	characteristic
82	C₂₃×#481	C₂²	1	2	yes	complemented
83	C₂₃×#480	C₂²	1	1	yes	characteristic
84	C₂₃×#480	C₂²	1	2	yes	complemented
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×#478	C₂²	1	2	yes	complemented
89	C₂₃×#478	C₂²	1	2	yes	complemented
90	C₂₃×#478	C₂²	1	2	yes	complemented
91	C₂₃×#476	C₂²	1	2	yes	complemented
92	C₂₃×#474	C₂²	1	2	yes	complemented
93	C₂₃×#469	C₂²	1	2	yes	complemented
94	C₂₃×#468	C₂²	1	2	yes	complemented
95	C₂₃×#468	C₂²	1	2	yes	complemented
96	C₂₃×#468	C₂²	1	2	yes	complemented
97	C₂₃×#466	C₂²	1	2	yes	complemented
98	C₂₃×#465	C₂²	1	2	yes	complemented
99	C₂₃×#465	C₂²	1	2	yes	complemented
100	C₂₃×#465	C₂²	1	2	yes	complemented
101	C₂₃×#463	C₂²	1	2	yes	complemented
102	C₂₃×#463	C₂²	1	2	yes	complemented
103	C₂₃×#461	C₂²	1	2	yes	complemented
104	C₂₃×#461	C₂²	1	2	yes	complemented
105	C₂₃×#460	C₂²	1	2	yes	complemented
106	C₂₃×#460	C₂²	1	2	yes	complemented
107	C₂₃×#460	C₂²	1	2	yes	complemented
108	C₂₃×#459	C₂²	1	2	yes	complemented
109	C₂₃×#450	C₂²	1	1	yes	characteristic
110	C₂₃×#450	C₂²	1	1	yes	characteristic
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×#450	C₂²	1	1	yes	characteristic
115	C₂₃×#449	C₂²	1	2	yes	complemented
116	C₂₃×#449	C₂²	1	2	yes	complemented
117	C₂₃×#448	C₂²	1	2	yes	complemented
118	C₂₃×#448	C₂²	1	2	yes	complemented
119	C₂₃×#447	C₂²	1	1	yes	characteristic
120	C₂₃×#447	C₂²	1	1	yes	characteristic
121	C₂₃×#442	C₂²	1	2	yes	complemented
122	C₂₃×#440	C₂²	1	2	yes	complemented
123	C₂₃×#440	C₂²	1	2	yes	complemented
124	C₂₃×#440	C₂²	1	2	yes	complemented
125	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
126	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
127	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
128	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
129	C₂₃×#433	C₂²	1	2	yes	complemented
130	C₂₃×#433	C₂²	1	2	yes	complemented
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	complemented
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	complemented
139	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
140	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
141	C₂²×D₄×C₂₃	—	2	1	no	—
142	C₂²×D₄×C₂₃	—	2	1	no	—
143	C₂²×D₄×C₂₃	—	2	1	no	—
144	C₂²×D₄×C₂₃	—	2	1	no	—
145	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
146	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
147	C₂³×C₄×C₂₃	—	2	1	no	—
148	C₂³×C₄×C₂₃	—	2	1	no	—
149	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
156	C₂×D₈×C₂₃	C₂³	1	2	yes	—
157	C₂×D₈×C₂₃	C₂³	1	2	yes	—
158	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
159	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
160	C₂₃×C₄⋊Q₈	—	2	1	no	—
161	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₂₃×#127	—	2	1	no	—
166	C₂₃×#127	—	2	1	no	—
167	C₂₃×#127	C₂³	1	2	yes	—
168	C₂₃×#127	C₂³	1	2	yes	—
169	C₂₃×#126	—	2	1	no	—
170	C₂₃×#126	—	2	1	no	—
171	C₂₃×#126	—	2	1	no	—
172	C₂₃×#126	—	2	1	no	—
173	C₂₃×#126	—	2	1	no	—
174	C₂₃×#126	—	2	1	no	—
175	C₂₃×#126	—	2	1	no	—
176	C₂₃×#126	—	2	1	no	—
177	C₂₃×#125	—	2	1	no	—
178	C₂₃×#125	—	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	1	no	—
185	C₂₃×#125	—	2	1	no	—
186	C₂₃×#125	C₂³	1	1	yes	characteristic
187	C₂₃×#125	C₂³	1	2	yes	—
188	C₂₃×#125	C₂³	1	2	yes	—
189	C₂₃×#125	C₂³	1	1	yes	characteristic
190	C₂₃×#124	—	2	1	no	—
191	C₂₃×#124	—	2	1	no	—
192	C₂₃×#124	C₂³	1	1	yes	characteristic
193	C₂₃×#124	C₂³	1	1	yes	characteristic
194	C₂₃×#123	—	2	1	no	—
195	C₂₃×#123	—	2	1	no	—
196	C₂₃×#123	—	2	1	no	—
197	C₂₃×#123	—	2	2	no	—
198	C₂₃×#123	—	2	2	no	—
199	C₂₃×#123	—	2	2	no	—
200	C₂₃×#123	—	2	2	no	—
201	C₂₃×#123	—	2	2	no	—
202	C₂₃×#123	—	2	2	no	—
203	C₂₃×#123	—	2	2	no	—
204	C₂₃×#123	—	2	2	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×C₂²⋊Q₈	—	2	1	no	—
210	C₂₃×C₂²⋊Q₈	—	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	C₂³	1	1	yes	characteristic
220	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
221	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
229	C₂₃×#121	—	2	2	no	—
230	C₂₃×#121	—	2	2	no	—
231	C₂₃×#121	—	2	2	no	—
232	C₂₃×#121	—	2	2	no	—
233	C₂₃×#121	—	2	2	no	—
234	C₂₃×#121	—	2	2	no	—
235	C₂₃×#121	—	2	2	no	—
236	C₂₃×#121	—	2	2	no	—
237	C₂₃×#121	C₂³	1	1	yes	characteristic
238	C₂₃×#121	C₂³	1	2	yes	—
239	C₂₃×#121	C₂³	1	2	yes	—
240	C₂₃×#121	C₂³	1	2	yes	—
241	C₂₃×#121	C₂³	1	2	yes	—
242	C₂₃×#121	C₂³	1	1	yes	characteristic
243	C₂₃×#120	—	2	1	no	—
244	C₄×Q₈×C₂₃	—	2	1	no	—
245	C₄×Q₈×C₂₃	—	2	1	no	—
246	C₄×Q₈×C₂₃	—	2	1	no	—
247	C₄×Q₈×C₂₃	—	2	1	no	—
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×D₄×C₂₃	—	2	1	no	—
255	C₄×D₄×C₂₃	—	2	1	no	—
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	—	2	1	no	—
263	C₄×D₄×C₂₃	—	2	1	no	—
264	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
265	C₄×D₄×C₂₃	C₂³	1	2	yes	—
266	C₄×D₄×C₂₃	C₂³	1	2	yes	—
267	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
268	C₄×D₄×C₂₃	C₂³	1	2	yes	—
269	C₄×D₄×C₂₃	C₂³	1	2	yes	—
270	C₂₃×#117	—	2	1	no	—
271	C₂₃×#117	—	2	1	no	—
272	C₂₃×#117	—	2	1	no	—
273	C₂₃×#117	—	2	1	no	—
274	C₂₃×#117	—	2	1	no	—
275	C₂₃×#117	—	2	1	no	—
276	C₂₃×#117	—	2	1	no	—
277	C₂₃×#117	D₄	1	1	yes	characteristic
278	C₂₃×#117	D₄	1	1	yes	characteristic
279	C₂₃×#117	D₄	1	1	yes	characteristic
280	C₂₃×#117	D₄	1	1	yes	characteristic
281	C₂₃×#117	C₂³	1	1	yes	characteristic
282	C₂₃×#117	C₂³	1	1	yes	characteristic
283	C₂₃×#117	C₂³	1	1	yes	characteristic
284	C₂₃×#117	C₂³	1	1	yes	characteristic
285	C₂₃×#117	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
299	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
300	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
301	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
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×#102	C₂³	1	2	yes	—
323	C₂₃×#102	C₂³	1	2	yes	—
324	C₂₃×#102	C₂³	1	2	yes	—
325	C₂₃×#102	C₂³	1	2	yes	—
326	C₂₃×#102	C₂³	1	2	yes	—
327	C₂₃×#102	C₂³	1	2	yes	—
328	C₂₃×#102	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	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	—	2	1	no	—
343	C₂⁴×C₂₃	—	2	1	no	—
344	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
345	#41×C₂₃	—	4	2	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	C₂⁴	1	1	yes	characteristic
351	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
352	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
353	C₂×D₄×C₂₃	—	2	1	no	—
354	C₂×D₄×C₂₃	—	2	1	no	—
355	C₂×D₄×C₂₃	—	2	1	no	—
356	C₂×D₄×C₂₃	—	2	2	no	—
357	C₂×D₄×C₂₃	—	2	2	no	—
358	C₂×D₄×C₂₃	—	2	2	no	—
359	C₂×D₄×C₂₃	—	2	2	no	—
360	C₂×D₄×C₂₃	—	2	1	no	—
361	C₂×D₄×C₂₃	—	2	1	no	—
362	C₂×D₄×C₂₃	—	2	2	no	—
363	C₂×D₄×C₂₃	—	2	2	no	—
364	C₂×D₄×C₂₃	—	2	2	no	—
365	C₂×D₄×C₂₃	—	2	2	no	—
366	C₂×D₄×C₂₃	—	4	2	no	—
367	C₂×D₄×C₂₃	—	4	2	no	—
368	C₂×D₄×C₂₃	—	8	2	no	—
369	C₂×D₄×C₂₃	—	8	2	no	—
370	C₂×D₄×C₂₃	—	8	2	no	—
371	C₂×D₄×C₂₃	—	8	2	no	—
372	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
373	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
374	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
375	C₂²×C₄×C₂₃	—	2	1	no	—
376	C₂²×C₄×C₂₃	—	2	1	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	—	2	2	no	—
383	C₂²×C₄×C₂₃	—	2	2	no	—
384	C₂²×C₄×C₂₃	—	2	2	no	—
385	C₂²×C₄×C₂₃	—	2	2	no	—
386	C₂²×C₄×C₂₃	—	4	2	no	—
387	C₂²×C₄×C₂₃	—	8	2	no	—
388	C₂²×C₄×C₂₃	—	8	2	no	—
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	C₂×D₄	1	1	yes	characteristic
394	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
395	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
396	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
397	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
398	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
399	SD₁₆×C₂₃	—	4	2	no	—
400	SD₁₆×C₂₃	—	4	2	no	—
401	SD₁₆×C₂₃	—	4	2	no	—
402	SD₁₆×C₂₃	—	4	2	no	—
403	SD₁₆×C₂₃	—	4	2	no	—
404	SD₁₆×C₂₃	—	4	2	no	—
405	D₈×C₂₃	—	4	2	no	—
406	D₈×C₂₃	—	4	2	no	—
407	M₁₆×C₂₃	—	4	2	no	—
408	C₂×C₈×C₂₃	—	4	2	no	—
409	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
410	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
411	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
412	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
413	C₄⋊C₄×C₂₃	—	2	1	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	1	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	2	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	—	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	C₂×D₄	1	1	yes	characteristic
443	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
449	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
450	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
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	2	yes	—
455	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
456	C₂²⋊C₄×C₂₃	—	2	1	no	—
457	C₂²⋊C₄×C₂₃	—	2	1	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	2	no	—
464	C₂²⋊C₄×C₂₃	—	2	2	no	—
465	C₂²⋊C₄×C₂₃	—	2	2	no	—
466	C₂²⋊C₄×C₂₃	—	2	2	no	—
467	C₂²⋊C₄×C₂₃	—	2	2	no	—
468	C₂²⋊C₄×C₂₃	—	2	2	no	—
469	C₂²⋊C₄×C₂₃	—	2	2	no	—
470	C₂²⋊C₄×C₂₃	—	2	2	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	—	2	1	no	—
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	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
487	C₄²×C₂₃	—	2	1	no	—
488	C₄²×C₂₃	—	2	1	no	—
489	C₄²×C₂₃	—	2	1	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	C₂×D₄	1	1	yes	characteristic
495	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
496	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
497	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
498	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
499	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
500	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
501	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
502	#60979	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
503	C₂³×C₂₃	—	2	2	no	—
504	C₂³×C₂₃	—	2	1	no	—
505	C₂³×C₂₃	—	2	2	no	—
506	C₂³×C₂₃	—	2	2	no	—
507	C₂³×C₂₃	—	4	1	no	—
508	C₂³×C₂₃	—	4	1	no	—
509	C₂³×C₂₃	—	4	2	no	—
510	C₂³×C₂₃	—	4	2	no	—
511	C₂³×C₂₃	—	4	2	no	—
512	C₂³×C₂₃	—	4	2	no	—
513	C₂³×C₂₃	—	4	2	no	—
514	C₂³×C₂₃	—	4	2	no	—
515	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
516	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
517	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
518	Q₈×C₂₃	—	2	2	no	—
519	Q₈×C₂₃	—	2	2	no	—
520	Q₈×C₂₃	—	2	2	no	—
521	Q₈×C₂₃	—	4	2	no	—
522	Q₈×C₂₃	—	8	1	no	—
523	Q₈×C₂₃	—	8	1	no	—
524	D₄×C₂₃	—	2	2	no	—
525	D₄×C₂₃	—	2	2	no	—
526	D₄×C₂₃	—	2	2	no	—
527	D₄×C₂₃	—	2	2	no	—
528	D₄×C₂₃	—	2	2	no	—
529	D₄×C₂₃	—	4	2	no	—
530	D₄×C₂₃	—	4	2	no	—
531	D₄×C₂₃	—	4	2	no	—
532	D₄×C₂₃	—	4	2	no	—
533	D₄×C₂₃	—	8	2	no	—
534	D₄×C₂₃	—	8	2	no	—
535	D₄×C₂₃	—	8	2	no	—
536	D₄×C₂₃	—	8	2	no	—
537	D₄×C₂₃	—	8	1	no	—
538	D₄×C₂₃	—	8	2	no	—
539	D₄×C₂₃	—	8	2	no	—
540	D₄×C₂₃	—	8	2	no	—
541	D₄×C₂₃	—	8	2	no	—
542	C₂×C₄×C₂₃	—	2	2	no	—
543	C₂×C₄×C₂₃	—	2	2	no	—
544	C₂×C₄×C₂₃	—	2	2	no	—
545	C₂×C₄×C₂₃	—	2	2	no	—
546	C₂×C₄×C₂₃	—	2	2	no	—
547	C₂×C₄×C₂₃	—	2	1	no	—
548	C₂×C₄×C₂₃	—	2	1	no	—
549	C₂×C₄×C₂₃	—	2	1	no	—
550	C₂×C₄×C₂₃	—	2	1	no	—
551	C₂×C₄×C₂₃	—	2	1	no	—
552	C₂×C₄×C₂₃	—	2	1	no	—
553	C₂×C₄×C₂₃	—	2	1	no	—
554	C₂×C₄×C₂₃	—	2	2	no	—
555	C₂×C₄×C₂₃	—	2	2	no	—
556	C₂×C₄×C₂₃	—	4	1	no	—
557	C₂×C₄×C₂₃	—	4	1	no	—
558	C₂×C₄×C₂₃	—	4	1	no	—
559	C₂×C₄×C₂₃	—	4	1	no	—
560	C₂×C₄×C₂₃	—	4	1	no	—
561	C₂×C₄×C₂₃	—	4	2	no	—
562	C₂×C₄×C₂₃	—	4	2	no	—
563	C₂×C₄×C₂₃	—	4	2	no	—
564	C₂×C₄×C₂₃	—	4	2	no	—
565	C₂×C₄×C₂₃	—	8	1	no	—
566	C₂×C₄×C₂₃	—	8	1	no	—
567	C₂×C₄×C₂₃	—	8	2	no	—
568	C₂×C₄×C₂₃	—	8	2	no	—
569	C₂×C₄×C₂₃	—	8	2	no	—
570	C₂×C₄×C₂₃	—	8	2	no	—
571	C₂×C₄×C₂₃	—	8	1	no	—
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	C₂²×D₄	1	1	yes	characteristic
578	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
579	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
580	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
581	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
582	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
583	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
584	C₈×C₂₃	—	2	2	no	—
585	C₈×C₂₃	—	2	2	no	—
586	C₈×C₂₃	—	2	2	no	—
587	C₈×C₂₃	—	2	2	no	—
588	#3495	C₂×C₂₃	1	1	yes	characteristic, complemented
589	C₂×#540	C₂×C₂₃	1	1	yes	characteristic, complemented
590	#3260	C₂×C₂₃	1	2	yes	complemented
591	#3257	C₂×C₂₃	1	2	yes	complemented
592	#3241	C₂×C₂₃	1	2	yes	complemented
593	#3236	C₂×C₂₃	1	1	yes	characteristic, complemented
594	#3232	C₂×C₂₃	1	1	yes	characteristic, complemented
595	#3221	C₂×C₂₃	1	2	yes	complemented
596	#3217	C₂×C₂₃	1	1	yes	characteristic, complemented
597	#3208	C₂×C₂₃	1	1	yes	characteristic, complemented
598	#3194	C₂×C₂₃	1	1	yes	characteristic, complemented
599	#3193	C₂×C₂₃	1	1	yes	characteristic, complemented
600	#3188	C₂×C₂₃	1	1	yes	characteristic, complemented
601	#3187	C₂×C₂₃	1	1	yes	characteristic, complemented
602	#3179	C₂×C₂₃	1	2	yes	complemented
603	#3174	C₂×C₂₃	1	2	yes	complemented
604	#3126	C₂×C₂₃	1	2	yes	complemented
605	#3119	C₂×C₂₃	1	2	yes	complemented
606	#3114	C₂×C₂₃	1	1	yes	characteristic, complemented
607	#3110	C₂×C₂₃	1	1	yes	characteristic, complemented
608	#3105	C₂×C₂₃	1	1	yes	characteristic, complemented
609	#3101	C₂×C₂₃	1	1	yes	characteristic, complemented
610	#2924	C₂×C₂₃	1	1	yes	characteristic, complemented
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	—	2	1	no	—
619	C₂²×C₂₃	—	4	2	no	—
620	C₂²×C₂₃	—	4	1	no	—
621	C₂²×C₂₃	—	4	2	no	—
622	C₂²×C₂₃	—	4	1	no	—
623	C₂²×C₂₃	—	4	2	no	—
624	C₂²×C₂₃	—	4	2	no	—
625	C₂²×C₂₃	—	4	2	no	—
626	C₂²×C₂₃	—	4	1	no	—
627	C₂²×C₂₃	—	4	2	no	—
628	C₂²×C₂₃	—	8	2	no	—
629	C₂²×C₂₃	—	8	4	no	—
630	C₂²×C₂₃	—	8	4	no	—
631	C₂²×C₂₃	#577	1	2	yes	—
632	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
633	C₄×C₂₃	—	2	1	no	—
634	C₄×C₂₃	—	2	1	no	—
635	C₄×C₂₃	—	2	1	no	—
636	C₄×C₂₃	—	2	1	no	—
637	C₄×C₂₃	—	2	1	no	—
638	C₄×C₂₃	—	2	1	no	—
639	C₄×C₂₃	—	2	1	no	—
640	C₄×C₂₃	—	2	1	no	—
641	C₄×C₂₃	—	2	1	no	—
642	C₄×C₂₃	—	2	1	no	—
643	C₄×C₂₃	—	2	1	no	—
644	C₄×C₂₃	—	4	2	no	—
645	C₄×C₂₃	—	4	1	no	—
646	C₄×C₂₃	—	4	1	no	—
647	C₄×C₂₃	—	4	1	no	—
648	C₄×C₂₃	—	4	1	no	—
649	C₄×C₂₃	—	4	1	no	—
650	C₄×C₂₃	—	4	1	no	—
651	C₄×C₂₃	—	4	2	no	—
652	C₄×C₂₃	—	4	1	no	—
653	C₄×C₂₃	#585	1	2	yes	—
654	#556	—	2	1	no	—
655	#554	—	2	1	no	—
656	#552	—	2	1	no	—
657	#552	—	2	1	no	—
658	#552	—	2	1	no	—
659	#552	—	2	1	no	—
660	#551	—	2	1	no	—
661	#551	—	2	1	no	—
662	#544	C₂²×C₂₃	1	1	yes	characteristic, complemented
663	#542	C₂²×C₂₃	1	1	yes	characteristic, complemented
664	#542	C₂²×C₂₃	1	1	yes	characteristic, complemented
665	#541	C₂²×C₂₃	1	1	yes	characteristic, complemented
666	#541	C₂²×C₂₃	1	1	yes	characteristic, complemented
667	#540	—	2	1	no	—
668	#540	—	2	1	no	—
669	#540	—	2	1	no	—
670	#540	—	2	1	no	—
671	#540	C₂²×C₂₃	1	2	yes	—
672	#540	C₂²×C₂₃	1	2	yes	—
673	#540	C₂²×C₂₃	1	2	yes	—
674	#540	C₂²×C₂₃	1	2	yes	—
675	#536	C₂²×C₂₃	1	1	yes	characteristic, complemented
676	#533	C₂²×C₂₃	1	1	yes	characteristic
677	#533	C₂²×C₂₃	1	1	yes	characteristic
678	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
679	#529	C₂²×C₂₃	1	1	yes	characteristic
680	#529	C₂²×C₂₃	1	1	yes	characteristic
681	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
682	#525	C₂²×C₂₃	1	1	yes	characteristic
683	C₂×#123	—	2	1	no	—
684	C₂×#123	—	2	1	no	—
685	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
686	C₂×#121	—	2	1	no	—
687	C₂×#121	—	2	1	no	—
688	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
689	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
690	#520	C₂²×C₂₃	1	1	yes	characteristic, complemented
691	#519	C₂²×C₂₃	1	1	yes	characteristic, complemented
692	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
693	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
694	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
695	#501	C₂²×C₂₃	1	2	yes	complemented
696	#499	C₂²×C₂₃	1	2	yes	complemented
697	#496	C₂²×C₂₃	1	2	yes	complemented
698	#492	C₂²×C₂₃	1	2	yes	complemented
699	#491	C₂²×C₂₃	1	2	yes	complemented
700	#490	C₂²×C₂₃	1	2	yes	complemented
701	#488	C₂²×C₂₃	1	2	yes	complemented
702	#486	C₂²×C₂₃	1	2	yes	complemented
703	#484	C₂²×C₂₃	1	1	yes	characteristic
704	#484	C₂²×C₂₃	1	1	yes	characteristic
705	#484	C₂²×C₂₃	1	1	yes	characteristic
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	#482	C₂²×C₂₃	1	2	yes	complemented
710	#482	C₂²×C₂₃	1	2	yes	complemented
711	#481	C₂²×C₂₃	1	1	yes	characteristic
712	#481	C₂²×C₂₃	1	2	yes	complemented
713	#480	C₂²×C₂₃	1	1	yes	characteristic
714	#480	C₂²×C₂₃	1	2	yes	complemented
715	#479	C₂²×C₂₃	1	2	yes	complemented
716	#479	C₂²×C₂₃	1	2	yes	complemented
717	#479	C₂²×C₂₃	1	2	yes	complemented
718	#478	C₂²×C₂₃	1	2	yes	complemented
719	#478	C₂²×C₂₃	1	2	yes	complemented
720	#478	C₂²×C₂₃	1	2	yes	complemented
721	#476	C₂²×C₂₃	1	2	yes	complemented
722	#474	C₂²×C₂₃	1	2	yes	complemented
723	#469	C₂²×C₂₃	1	2	yes	complemented
724	#468	C₂²×C₂₃	1	2	yes	complemented
725	#468	C₂²×C₂₃	1	2	yes	complemented
726	#468	C₂²×C₂₃	1	2	yes	complemented
727	#466	C₂²×C₂₃	1	2	yes	complemented
728	#465	C₂²×C₂₃	1	2	yes	complemented
729	#465	C₂²×C₂₃	1	2	yes	complemented
730	#465	C₂²×C₂₃	1	2	yes	complemented
731	#463	C₂²×C₂₃	1	2	yes	complemented
732	#463	C₂²×C₂₃	1	2	yes	complemented
733	#461	C₂²×C₂₃	1	2	yes	complemented
734	#461	C₂²×C₂₃	1	2	yes	complemented
735	#460	C₂²×C₂₃	1	2	yes	complemented
736	#460	C₂²×C₂₃	1	2	yes	complemented
737	#460	C₂²×C₂₃	1	2	yes	complemented
738	#459	C₂²×C₂₃	1	2	yes	complemented
739	#450	C₂²×C₂₃	1	1	yes	characteristic
740	#450	C₂²×C₂₃	1	1	yes	characteristic
741	#450	C₂²×C₂₃	1	1	yes	characteristic
742	#450	C₂²×C₂₃	1	1	yes	characteristic
743	#450	C₂²×C₂₃	1	1	yes	characteristic
744	#450	C₂²×C₂₃	1	1	yes	characteristic
745	#449	C₂²×C₂₃	1	2	yes	complemented
746	#449	C₂²×C₂₃	1	2	yes	complemented
747	#448	C₂²×C₂₃	1	2	yes	complemented
748	#448	C₂²×C₂₃	1	2	yes	complemented
749	#447	C₂²×C₂₃	1	1	yes	characteristic
750	#447	C₂²×C₂₃	1	1	yes	characteristic
751	#442	C₂²×C₂₃	1	2	yes	complemented
752	#440	C₂²×C₂₃	1	2	yes	complemented
753	#440	C₂²×C₂₃	1	2	yes	complemented
754	#440	C₂²×C₂₃	1	2	yes	complemented
755	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
756	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
757	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
758	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
759	#433	C₂²×C₂₃	1	2	yes	complemented
760	#433	C₂²×C₂₃	1	2	yes	complemented
761	#432	C₂²×C₂₃	1	1	yes	characteristic
762	#432	C₂²×C₂₃	1	1	yes	characteristic
763	#431	C₂²×C₂₃	1	1	yes	characteristic
764	#431	C₂²×C₂₃	1	1	yes	characteristic
765	#424	C₂²×C₂₃	1	2	yes	complemented
766	#407	C₂²×C₂₃	1	1	yes	characteristic
767	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
768	#405	C₂²×C₂₃	1	2	yes	complemented
769	C₂×C₂₃	—	2	2	no	—
770	C₂×C₂₃	—	4	1	no	—
771	C₂×C₂₃	—	4	1	no	—
772	C₂×C₂₃	—	8	1	no	—
773	C₂×C₂₃	—	8	2	no	—
774	C₂×C₂₃	—	8	2	no	—
775	C₂×C₂₃	#3449	1	1	yes	characteristic
776	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
777	C₂×C₂₃	#3585	1	1	yes	characteristic
778	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
779	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
780	C₂²×D₄	—	2	1	no	—
781	C₂²×D₄	—	2	1	no	—
782	C₂²×D₄	—	2	1	no	—
783	C₂²×D₄	—	2	1	no	—
784	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
785	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
786	C₂³×C₄	—	2	1	no	—
787	C₂³×C₄	—	2	1	no	—
788	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
789	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
790	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
791	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
792	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
793	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
794	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
795	C₂×D₈	C₂³×C₂₃	1	2	yes	—
796	C₂×D₈	C₂³×C₂₃	1	2	yes	—
797	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
798	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
799	C₄⋊Q₈	—	2	1	no	—
800	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
801	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
802	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
803	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
804	#127	—	2	1	no	—
805	#127	—	2	1	no	—
806	#127	C₂³×C₂₃	1	2	yes	—
807	#127	C₂³×C₂₃	1	2	yes	—
808	#126	—	2	1	no	—
809	#126	—	2	1	no	—
810	#126	—	2	1	no	—
811	#126	—	2	1	no	—
812	#126	—	2	1	no	—
813	#126	—	2	1	no	—
814	#126	—	2	1	no	—
815	#126	—	2	1	no	—
816	#125	—	2	1	no	—
817	#125	—	2	1	no	—
818	#125	—	2	1	no	—
819	#125	—	2	1	no	—
820	#125	—	2	1	no	—
821	#125	—	2	1	no	—
822	#125	—	2	1	no	—
823	#125	—	2	1	no	—
824	#125	—	2	1	no	—
825	#125	C₂³×C₂₃	1	2	yes	—
826	#125	C₂³×C₂₃	1	2	yes	—
827	#125	C₂³×C₂₃	1	1	yes	characteristic
828	#125	C₂³×C₂₃	1	1	yes	characteristic
829	#124	—	2	1	no	—
830	#124	—	2	1	no	—
831	#124	C₂³×C₂₃	1	1	yes	characteristic
832	#124	C₂³×C₂₃	1	1	yes	characteristic
833	#123	—	2	1	no	—
834	#123	—	2	1	no	—
835	#123	—	2	1	no	—
836	#123	—	2	2	no	—
837	#123	—	2	2	no	—
838	#123	—	2	2	no	—
839	#123	—	2	2	no	—
840	#123	—	2	2	no	—
841	#123	—	2	2	no	—
842	#123	—	2	2	no	—
843	#123	—	2	2	no	—
844	#123	—	2	1	no	—
845	#123	—	2	1	no	—
846	#123	—	2	1	no	—
847	#123	—	2	1	no	—
848	C₂²⋊Q₈	—	2	1	no	—
849	C₂²⋊Q₈	—	2	1	no	—
850	C₂²⋊Q₈	—	2	1	no	—
851	C₂²⋊Q₈	—	2	1	no	—
852	C₂²⋊Q₈	—	2	1	no	—
853	C₂²⋊Q₈	—	2	1	no	—
854	C₂²⋊Q₈	—	2	1	no	—
855	C₂²⋊Q₈	—	2	1	no	—
856	C₂²⋊Q₈	—	2	1	no	—
857	C₂²⋊Q₈	—	2	1	no	—
858	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
859	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
860	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
861	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
862	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
863	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
864	#121	—	2	1	no	—
865	#121	—	2	1	no	—
866	#121	—	2	1	no	—
867	#121	—	2	1	no	—
868	#121	—	2	2	no	—
869	#121	—	2	2	no	—
870	#121	—	2	2	no	—
871	#121	—	2	2	no	—
872	#121	—	2	2	no	—
873	#121	—	2	2	no	—
874	#121	—	2	2	no	—
875	#121	—	2	2	no	—
876	#121	C₂³×C₂₃	1	2	yes	—
877	#121	C₂³×C₂₃	1	2	yes	—
878	#121	C₂³×C₂₃	1	2	yes	—
879	#121	C₂³×C₂₃	1	2	yes	—
880	#121	C₂³×C₂₃	1	1	yes	characteristic
881	#121	C₂³×C₂₃	1	1	yes	characteristic
882	#120	—	2	1	no	—
883	C₄×Q₈	—	2	1	no	—
884	C₄×Q₈	—	2	1	no	—
885	C₄×Q₈	—	2	1	no	—
886	C₄×Q₈	—	2	1	no	—
887	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
888	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
889	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
890	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
891	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
892	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
893	C₄×D₄	—	2	1	no	—
894	C₄×D₄	—	2	1	no	—
895	C₄×D₄	—	2	1	no	—
896	C₄×D₄	—	2	1	no	—
897	C₄×D₄	—	2	1	no	—
898	C₄×D₄	—	2	1	no	—
899	C₄×D₄	—	2	1	no	—
900	C₄×D₄	—	2	1	no	—
901	C₄×D₄	—	2	1	no	—
902	C₄×D₄	—	2	1	no	—
903	C₄×D₄	C₂³×C₂₃	1	2	yes	—
904	C₄×D₄	C₂³×C₂₃	1	2	yes	—
905	C₄×D₄	C₂³×C₂₃	1	2	yes	—
906	C₄×D₄	C₂³×C₂₃	1	2	yes	—
907	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
908	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
909	#117	—	2	1	no	—
910	#117	—	2	1	no	—
911	#117	—	2	1	no	—
912	#117	—	2	1	no	—
913	#117	—	2	1	no	—
914	#117	—	2	1	no	—
915	#117	—	2	1	no	—
916	#117	D₄×C₂₃	1	1	yes	characteristic
917	#117	D₄×C₂₃	1	1	yes	characteristic
918	#117	D₄×C₂₃	1	1	yes	characteristic
919	#117	D₄×C₂₃	1	1	yes	characteristic
920	#117	C₂³×C₂₃	1	1	yes	characteristic
921	#117	C₂³×C₂₃	1	1	yes	characteristic
922	#117	C₂³×C₂₃	1	1	yes	characteristic
923	#117	C₂³×C₂₃	1	1	yes	characteristic
924	#117	C₂³×C₂₃	1	1	yes	characteristic
925	C₂×C₄⋊C₄	—	2	1	no	—
926	C₂×C₄⋊C₄	—	2	1	no	—
927	C₂×C₄⋊C₄	—	2	1	no	—
928	C₂×C₄⋊C₄	—	2	1	no	—
929	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
930	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
931	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
932	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
933	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
934	C₂×C₂²⋊C₄	—	2	1	no	—
935	C₂×C₂²⋊C₄	—	2	1	no	—
936	C₂×C₂²⋊C₄	—	2	1	no	—
937	C₂×C₂²⋊C₄	—	2	1	no	—
938	C₂×C₂²⋊C₄	—	2	1	no	—
939	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
940	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
941	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
942	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
943	#107	C₂³×C₂₃	1	2	yes	—
944	#107	C₂³×C₂₃	1	2	yes	—
945	#107	C₂³×C₂₃	1	2	yes	—
946	#107	C₂³×C₂₃	1	2	yes	—
947	#106	C₂³×C₂₃	1	2	yes	—
948	#106	C₂³×C₂₃	1	2	yes	—
949	#106	C₂³×C₂₃	1	2	yes	—
950	#106	C₂³×C₂₃	1	2	yes	—
951	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
952	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
953	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
954	C₄⋊C₈	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	#102	C₂³×C₂₃	1	2	yes	—
965	#102	C₂³×C₂₃	1	2	yes	—
966	#102	C₂³×C₂₃	1	2	yes	—
967	#102	C₂³×C₂₃	1	2	yes	—
968	#102	C₂³×C₂₃	1	2	yes	—
969	#102	C₂³×C₂₃	1	2	yes	—
970	#102	C₂³×C₂₃	1	2	yes	—
971	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
972	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
973	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
974	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
975	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
976	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
977	#97	C₂³×C₂₃	1	2	yes	—
978	#97	C₂³×C₂₃	1	2	yes	—
979	C₄×C₈	C₂³×C₂₃	1	2	yes	—
980	C₄×C₈	C₂³×C₂₃	1	2	yes	—
981	C₂₃	#60979	1	1	yes	characteristic, direct product factor, Sylow
982	C₂⁴	—	2	1	no	—
983	C₂⁴	—	2	1	no	—
984	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
985	#41	—	4	2	no	—
986	C₂×Q₈	—	2	1	no	—
987	C₂×Q₈	—	2	1	no	—
988	C₂×Q₈	—	2	1	no	—
989	C₂×Q₈	—	4	2	no	—
990	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
991	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
992	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
993	C₂×D₄	—	2	1	no	—
994	C₂×D₄	—	2	1	no	—
995	C₂×D₄	—	2	1	no	—
996	C₂×D₄	—	2	2	no	—
997	C₂×D₄	—	2	2	no	—
998	C₂×D₄	—	2	2	no	—
999	C₂×D₄	—	2	2	no	—
1000	C₂×D₄	—	2	1	no	—
1001	C₂×D₄	—	2	1	no	—
1002	C₂×D₄	—	2	2	no	—
1003	C₂×D₄	—	2	2	no	—
1004	C₂×D₄	—	2	2	no	—
1005	C₂×D₄	—	2	2	no	—
1006	C₂×D₄	—	4	2	no	—
1007	C₂×D₄	—	4	2	no	—
1008	C₂×D₄	—	8	2	no	—
1009	C₂×D₄	—	8	2	no	—
1010	C₂×D₄	—	8	2	no	—
1011	C₂×D₄	—	8	2	no	—
1012	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1013	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
1014	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
1015	C₂²×C₄	—	2	1	no	—
1016	C₂²×C₄	—	2	1	no	—
1017	C₂²×C₄	—	2	1	no	—
1018	C₂²×C₄	—	2	1	no	—
1019	C₂²×C₄	—	2	1	no	—
1020	C₂²×C₄	—	2	1	no	—
1021	C₂²×C₄	—	2	1	no	—
1022	C₂²×C₄	—	2	2	no	—
1023	C₂²×C₄	—	2	2	no	—
1024	C₂²×C₄	—	2	2	no	—
1025	C₂²×C₄	—	2	2	no	—
1026	C₂²×C₄	—	4	2	no	—
1027	C₂²×C₄	—	8	2	no	—
1028	C₂²×C₄	—	8	2	no	—
1029	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1030	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1031	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1032	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1033	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1034	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1035	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1036	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1037	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1038	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1039	SD₁₆	—	4	2	no	—
1040	SD₁₆	—	4	2	no	—
1041	SD₁₆	—	4	2	no	—
1042	SD₁₆	—	4	2	no	—
1043	SD₁₆	—	4	2	no	—
1044	SD₁₆	—	4	2	no	—
1045	D₈	—	4	2	no	—
1046	D₈	—	4	2	no	—
1047	M₁₆	—	4	2	no	—
1048	C₂×C₈	—	4	2	no	—
1049	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1050	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1051	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1052	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1053	C₄⋊C₄	—	2	1	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	2	no	—
1059	C₄⋊C₄	—	2	2	no	—
1060	C₄⋊C₄	—	2	2	no	—
1061	C₄⋊C₄	—	2	2	no	—
1062	C₄⋊C₄	—	2	1	no	—
1063	C₄⋊C₄	—	2	1	no	—
1064	C₄⋊C₄	—	2	1	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	—	2	1	no	—
1078	C₄⋊C₄	—	2	1	no	—
1079	C₄⋊C₄	—	2	1	no	—
1080	C₄⋊C₄	—	2	1	no	—
1081	C₄⋊C₄	—	2	1	no	—
1082	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1083	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1084	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1085	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1086	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1087	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1088	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1089	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1090	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1091	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1092	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1093	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1094	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1095	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1096	C₂²⋊C₄	—	2	1	no	—
1097	C₂²⋊C₄	—	2	1	no	—
1098	C₂²⋊C₄	—	2	1	no	—
1099	C₂²⋊C₄	—	2	1	no	—
1100	C₂²⋊C₄	—	2	1	no	—
1101	C₂²⋊C₄	—	2	1	no	—
1102	C₂²⋊C₄	—	2	1	no	—
1103	C₂²⋊C₄	—	2	2	no	—
1104	C₂²⋊C₄	—	2	2	no	—
1105	C₂²⋊C₄	—	2	2	no	—
1106	C₂²⋊C₄	—	2	2	no	—
1107	C₂²⋊C₄	—	2	2	no	—
1108	C₂²⋊C₄	—	2	2	no	—
1109	C₂²⋊C₄	—	2	2	no	—
1110	C₂²⋊C₄	—	2	2	no	—
1111	C₂²⋊C₄	—	2	1	no	—
1112	C₂²⋊C₄	—	2	1	no	—
1113	C₂²⋊C₄	—	2	1	no	—
1114	C₂²⋊C₄	—	2	1	no	—
1115	C₂²⋊C₄	—	2	1	no	—
1116	C₂²⋊C₄	—	2	1	no	—
1117	C₂²⋊C₄	—	2	1	no	—
1118	C₂²⋊C₄	—	2	1	no	—
1119	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1120	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1121	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1122	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1123	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1124	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1125	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1126	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1127	C₄²	—	2	1	no	—
1128	C₄²	—	2	1	no	—
1129	C₄²	—	2	1	no	—
1130	C₄²	—	2	1	no	—
1131	C₄²	—	2	1	no	—
1132	C₄²	—	2	1	no	—
1133	C₄²	—	2	1	no	—
1134	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1135	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1136	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1137	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1138	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1139	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1140	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1141	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1142	C₂³	—	2	2	no	—
1143	C₂³	—	2	1	no	—
1144	C₂³	—	2	2	no	—
1145	C₂³	—	2	2	no	—
1146	C₂³	—	4	1	no	—
1147	C₂³	—	4	1	no	—
1148	C₂³	—	4	2	no	—
1149	C₂³	—	4	2	no	—
1150	C₂³	—	4	2	no	—
1151	C₂³	—	4	2	no	—
1152	C₂³	—	4	2	no	—
1153	C₂³	—	4	2	no	—
1154	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1155	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1156	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1157	Q₈	—	2	2	no	—
1158	Q₈	—	2	2	no	—
1159	Q₈	—	2	2	no	—
1160	Q₈	—	4	2	no	—
1161	Q₈	—	8	1	no	—
1162	Q₈	—	8	1	no	—
1163	D₄	—	2	2	no	—
1164	D₄	—	2	2	no	—
1165	D₄	—	2	2	no	—
1166	D₄	—	2	2	no	—
1167	D₄	—	2	2	no	—
1168	D₄	—	4	2	no	—
1169	D₄	—	4	2	no	—
1170	D₄	—	4	2	no	—
1171	D₄	—	4	2	no	—
1172	D₄	—	8	2	no	—
1173	D₄	—	8	2	no	—
1174	D₄	—	8	2	no	—
1175	D₄	—	8	2	no	—
1176	D₄	—	8	2	no	—
1177	D₄	—	8	2	no	—
1178	D₄	—	8	2	no	—
1179	D₄	—	8	2	no	—
1180	D₄	—	8	1	no	—
1181	C₂×C₄	—	2	2	no	—
1182	C₂×C₄	—	2	2	no	—
1183	C₂×C₄	—	2	2	no	—
1184	C₂×C₄	—	2	2	no	—
1185	C₂×C₄	—	2	2	no	—
1186	C₂×C₄	—	2	1	no	—
1187	C₂×C₄	—	2	1	no	—
1188	C₂×C₄	—	2	1	no	—
1189	C₂×C₄	—	2	1	no	—
1190	C₂×C₄	—	2	1	no	—
1191	C₂×C₄	—	2	1	no	—
1192	C₂×C₄	—	2	1	no	—
1193	C₂×C₄	—	2	2	no	—
1194	C₂×C₄	—	2	2	no	—
1195	C₂×C₄	—	4	1	no	—
1196	C₂×C₄	—	4	1	no	—
1197	C₂×C₄	—	4	1	no	—
1198	C₂×C₄	—	4	1	no	—
1199	C₂×C₄	—	4	1	no	—
1200	C₂×C₄	—	4	2	no	—
1201	C₂×C₄	—	4	2	no	—
1202	C₂×C₄	—	4	2	no	—
1203	C₂×C₄	—	4	2	no	—
1204	C₂×C₄	—	8	2	no	—
1205	C₂×C₄	—	8	2	no	—
1206	C₂×C₄	—	8	2	no	—
1207	C₂×C₄	—	8	2	no	—
1208	C₂×C₄	—	8	1	no	—
1209	C₂×C₄	—	8	1	no	—
1210	C₂×C₄	—	8	1	no	—
1211	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1212	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1213	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1214	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1215	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1216	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1217	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1218	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1219	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1220	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1221	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1222	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1223	C₈	—	2	2	no	—
1224	C₈	—	2	2	no	—
1225	C₈	—	2	2	no	—
1226	C₈	—	2	2	no	—
1227	C₂²	—	2	1	no	—
1228	C₂²	—	2	1	no	—
1229	C₂²	—	2	1	no	—
1230	C₂²	—	2	1	no	—
1231	C₂²	—	2	1	no	—
1232	C₂²	—	2	1	no	—
1233	C₂²	—	2	1	no	—
1234	C₂²	—	2	1	no	—
1235	C₂²	—	4	1	no	—
1236	C₂²	—	4	2	no	—
1237	C₂²	—	4	2	no	—
1238	C₂²	—	4	2	no	—
1239	C₂²	—	4	1	no	—
1240	C₂²	—	4	2	no	—
1241	C₂²	—	4	2	no	—
1242	C₂²	—	4	1	no	—
1243	C₂²	—	4	2	no	—
1244	C₂²	—	8	2	no	—
1245	C₂²	—	8	4	no	—
1246	C₂²	—	8	4	no	—
1247	C₂²	C₂₃×#577	1	2	yes	—
1248	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1249	C₄	—	2	1	no	—
1250	C₄	—	2	1	no	—
1251	C₄	—	2	1	no	—
1252	C₄	—	2	1	no	—
1253	C₄	—	2	1	no	—
1254	C₄	—	2	1	no	—
1255	C₄	—	2	1	no	—
1256	C₄	—	2	1	no	—
1257	C₄	—	2	1	no	—
1258	C₄	—	2	1	no	—
1259	C₄	—	2	1	no	—
1260	C₄	—	4	1	no	—
1261	C₄	—	4	1	no	—
1262	C₄	—	4	1	no	—
1263	C₄	—	4	2	no	—
1264	C₄	—	4	1	no	—
1265	C₄	—	4	2	no	—
1266	C₄	—	4	1	no	—
1267	C₄	—	4	1	no	—
1268	C₄	—	4	1	no	—
1269	C₄	C₂₃×#585	1	2	yes	—
1270	C₂	—	2	2	no	—
1271	C₂	—	4	1	no	—
1272	C₂	—	4	1	no	—
1273	C₂	—	8	2	no	—
1274	C₂	—	8	2	no	—
1275	C₂	—	8	1	no	—
1276	C₂	C₂₃×#3449	1	1	yes	characteristic
1277	C₂	C₂×C₂₃×#577	1	1	yes	characteristic
1278	C₂	C₂₃×#3585	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×C₂₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3495	C₂	semidirect
2. C₂×C₂₃×#540	C₂	semidirect
3. C₂₃×#3260	C₂	semidirect
4. C₂₃×#3257	C₂	semidirect
5. C₂₃×#3241	C₂	semidirect
6. C₂₃×#3236	C₂	semidirect
7. C₂₃×#3232	C₂	semidirect
8. C₂₃×#3221	C₂	semidirect
9. C₂₃×#3217	C₂	semidirect
10. C₂₃×#3208	C₂	semidirect
11. C₂₃×#3194	C₂	semidirect
12. C₂₃×#3193	C₂	semidirect
13. C₂₃×#3188	C₂	semidirect
14. C₂₃×#3187	C₂	semidirect
15. C₂₃×#3179	C₂	semidirect
16. C₂₃×#3174	C₂	semidirect
17. C₂₃×#3126	C₂	semidirect
18. C₂₃×#3119	C₂	semidirect
19. C₂₃×#3114	C₂	semidirect
20. C₂₃×#3110	C₂	semidirect
21. C₂₃×#3105	C₂	semidirect
22. C₂₃×#3101	C₂	semidirect
23. C₂₃×#2924	C₂	semidirect
32. C₂₃×#544	C₂²	semidirect
33. C₂₃×#542	C₂²	semidirect
34. C₂₃×#542	C₂²	semidirect
35. C₂₃×#541	C₂²	semidirect
36. C₂₃×#541	C₂²	semidirect
45. C₂₃×#536	C₂²	semidirect
60. C₂₃×#520	C₂²	semidirect
61. C₂₃×#519	C₂²	semidirect
65. C₂₃×#501	C₂²	semidirect
66. C₂₃×#499	C₂²	semidirect
67. C₂₃×#496	C₂²	semidirect
68. C₂₃×#492	C₂²	semidirect
69. C₂₃×#491	C₂²	semidirect
70. C₂₃×#490	C₂²	semidirect
71. C₂₃×#488	C₂²	semidirect
72. C₂₃×#486	C₂²	semidirect
79. C₂₃×#482	C₂²	semidirect
80. C₂₃×#482	C₂²	semidirect
82. C₂₃×#481	C₂²	semidirect
84. C₂₃×#480	C₂²	semidirect
85. C₂₃×#479	C₂²	semidirect
86. C₂₃×#479	C₂²	semidirect
87. C₂₃×#479	C₂²	semidirect
88. C₂₃×#478	C₂²	semidirect
89. C₂₃×#478	C₂²	semidirect
90. C₂₃×#478	C₂²	semidirect
91. C₂₃×#476	C₂²	semidirect
92. C₂₃×#474	C₂²	semidirect
93. C₂₃×#469	C₂²	semidirect
94. C₂₃×#468	C₂²	semidirect
95. C₂₃×#468	C₂²	semidirect
96. C₂₃×#468	C₂²	semidirect
97. C₂₃×#466	C₂²	semidirect
98. C₂₃×#465	C₂²	semidirect
99. C₂₃×#465	C₂²	semidirect
100. C₂₃×#465	C₂²	semidirect
101. C₂₃×#463	C₂²	semidirect
102. C₂₃×#463	C₂²	semidirect
103. C₂₃×#461	C₂²	semidirect
104. C₂₃×#461	C₂²	semidirect
105. C₂₃×#460	C₂²	semidirect
106. C₂₃×#460	C₂²	semidirect
107. C₂₃×#460	C₂²	semidirect
108. C₂₃×#459	C₂²	semidirect
115. C₂₃×#449	C₂²	semidirect
116. C₂₃×#449	C₂²	semidirect
117. C₂₃×#448	C₂²	semidirect
118. C₂₃×#448	C₂²	semidirect
121. C₂₃×#442	C₂²	semidirect
122. C₂₃×#440	C₂²	semidirect
123. C₂₃×#440	C₂²	semidirect
124. C₂₃×#440	C₂²	semidirect
125. C₄×SD₁₆×C₂₃	C₂²	semidirect
126. C₄×SD₁₆×C₂₃	C₂²	semidirect
127. C₄×SD₁₆×C₂₃	C₂²	semidirect
128. C₄×D₈×C₂₃	C₂²	semidirect
129. C₂₃×#433	C₂²	semidirect
130. C₂₃×#433	C₂²	semidirect
135. C₂₃×#424	C₂²	semidirect
138. C₂₃×#405	C₂²	semidirect
502. #60979	C₂₃	direct (N × H)
588. #3495	C₂×C₂₃	semidirect
589. C₂×#540	C₂×C₂₃	semidirect
590. #3260	C₂×C₂₃	semidirect
591. #3257	C₂×C₂₃	semidirect
592. #3241	C₂×C₂₃	semidirect
593. #3236	C₂×C₂₃	semidirect
594. #3232	C₂×C₂₃	semidirect
595. #3221	C₂×C₂₃	semidirect
596. #3217	C₂×C₂₃	semidirect
597. #3208	C₂×C₂₃	semidirect
598. #3194	C₂×C₂₃	semidirect
599. #3193	C₂×C₂₃	semidirect
600. #3188	C₂×C₂₃	semidirect
601. #3187	C₂×C₂₃	semidirect
602. #3179	C₂×C₂₃	semidirect
603. #3174	C₂×C₂₃	semidirect
604. #3126	C₂×C₂₃	semidirect
605. #3119	C₂×C₂₃	semidirect
606. #3114	C₂×C₂₃	semidirect
607. #3110	C₂×C₂₃	semidirect
608. #3105	C₂×C₂₃	semidirect
609. #3101	C₂×C₂₃	semidirect
610. #2924	C₂×C₂₃	semidirect
662. #544	C₂²×C₂₃	semidirect
663. #542	C₂²×C₂₃	semidirect
664. #542	C₂²×C₂₃	semidirect
665. #541	C₂²×C₂₃	semidirect
666. #541	C₂²×C₂₃	semidirect
675. #536	C₂²×C₂₃	semidirect
690. #520	C₂²×C₂₃	semidirect
691. #519	C₂²×C₂₃	semidirect
695. #501	C₂²×C₂₃	semidirect
696. #499	C₂²×C₂₃	semidirect
697. #496	C₂²×C₂₃	semidirect
698. #492	C₂²×C₂₃	semidirect
699. #491	C₂²×C₂₃	semidirect
700. #490	C₂²×C₂₃	semidirect
701. #488	C₂²×C₂₃	semidirect
702. #486	C₂²×C₂₃	semidirect
709. #482	C₂²×C₂₃	semidirect
710. #482	C₂²×C₂₃	semidirect
712. #481	C₂²×C₂₃	semidirect
714. #480	C₂²×C₂₃	semidirect
715. #479	C₂²×C₂₃	semidirect
716. #479	C₂²×C₂₃	semidirect
717. #479	C₂²×C₂₃	semidirect
718. #478	C₂²×C₂₃	semidirect
719. #478	C₂²×C₂₃	semidirect
720. #478	C₂²×C₂₃	semidirect
721. #476	C₂²×C₂₃	semidirect
722. #474	C₂²×C₂₃	semidirect
723. #469	C₂²×C₂₃	semidirect
724. #468	C₂²×C₂₃	semidirect
725. #468	C₂²×C₂₃	semidirect
726. #468	C₂²×C₂₃	semidirect
727. #466	C₂²×C₂₃	semidirect
728. #465	C₂²×C₂₃	semidirect
729. #465	C₂²×C₂₃	semidirect
730. #465	C₂²×C₂₃	semidirect
731. #463	C₂²×C₂₃	semidirect
732. #463	C₂²×C₂₃	semidirect
733. #461	C₂²×C₂₃	semidirect
734. #461	C₂²×C₂₃	semidirect
735. #460	C₂²×C₂₃	semidirect
736. #460	C₂²×C₂₃	semidirect
737. #460	C₂²×C₂₃	semidirect
738. #459	C₂²×C₂₃	semidirect
745. #449	C₂²×C₂₃	semidirect
746. #449	C₂²×C₂₃	semidirect
747. #448	C₂²×C₂₃	semidirect
748. #448	C₂²×C₂₃	semidirect
751. #442	C₂²×C₂₃	semidirect
752. #440	C₂²×C₂₃	semidirect
753. #440	C₂²×C₂₃	semidirect
754. #440	C₂²×C₂₃	semidirect
755. C₄×SD₁₆	C₂²×C₂₃	semidirect
756. C₄×SD₁₆	C₂²×C₂₃	semidirect
757. C₄×SD₁₆	C₂²×C₂₃	semidirect
758. C₄×D₈	C₂²×C₂₃	semidirect
759. #433	C₂²×C₂₃	semidirect
760. #433	C₂²×C₂₃	semidirect
765. #424	C₂²×C₂₃	semidirect
768. #405	C₂²×C₂₃	semidirect
981. C₂₃	#60979	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×#540	2
C₂₃×#3260	2
C₂₃×#3257	2
C₂₃×#3241	2
C₂₃×#3236	2
C₂₃×#3232	2
C₂₃×#3221	2
C₂₃×#3217	2
C₂₃×#3208	2
C₂₃×#3194	2
C₂₃×#3193	2
C₂₃×#3188	2
C₂₃×#3187	2
C₂₃×#3179	2
C₂₃×#3174	2
C₂₃×#3126	2
C₂₃×#3119	2
C₂₃×#3114	2
C₂₃×#3110	2
C₂₃×#3105	2
C₂₃×#3101	2
C₂₃×#2924	2
#60979	23

Subgroups — C23×#60979 #19208605

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60979 #19208605