Subgroups — C₂₃×#61596 #19209222

Order 5888.

2168 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3520	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#550	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3332	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3317	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3304	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3284	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3278	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3271	C₂	1	4	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	2	yes	maximal, complemented
12	C₂₃×#3187	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3113	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3108	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3007	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3002	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2974	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₂₃	C₂²	1	2	yes	—
19	C₂×C₂₃×#137	C₂²	1	4	yes	complemented
20	C₂×C₂₃×#135	C₂²	1	4	yes	complemented
21	C₂₃×#556	C₂²	1	1	yes	characteristic, complemented
22	C₂₃×#554	—	2	1	no	—
23	C₂₃×#552	C₂²	1	2	yes	complemented
24	C₂₃×#551	—	2	2	no	—
25	C₂₃×#550	—	2	1	no	—
26	C₂₃×#550	—	2	2	no	—
27	C₂₃×#550	—	2	1	no	—
28	C₂₃×#550	C₂²	1	4	yes	—
29	C₂₃×#550	C₂²	1	2	yes	—
30	C₂₃×#550	C₂²	1	2	yes	—
31	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
32	C₂₃×#548	C₂²	1	2	yes	complemented
33	C₂₃×#547	C₂²	1	1	yes	characteristic, complemented
34	C₂₃×#547	C₂²	1	1	yes	characteristic, complemented
35	C₂₃×#546	—	2	1	no	—
36	C₂₃×#542	—	2	1	no	—
37	C₂₃×#539	—	2	2	no	—
38	C₂₃×#533	C₂²	1	1	yes	characteristic
39	C₂×C₂₃×#127	—	2	1	no	—
40	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
41	C₂₃×#529	C₂²	1	1	yes	characteristic
42	C₂₃×#525	C₂²	1	2	yes	—
43	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
44	C₂×C₂₃×#121	—	2	2	no	—
45	C₂×C₂₃×#121	C₂²	1	2	yes	—
46	C₂₃×#520	—	2	1	no	—
47	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₂₃	—	2	1	no	—
49	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
50	C₂₃×#496	C₂²	1	2	yes	complemented
51	C₂₃×#492	C₂²	1	2	yes	complemented
52	C₂₃×#490	C₂²	1	2	yes	complemented
53	C₂₃×#486	C₂²	1	2	yes	complemented
54	C₂₃×#483	C₂²	1	1	yes	characteristic
55	C₂₃×#483	C₂²	1	2	yes	—
56	C₂₃×#482	C₂²	1	4	yes	complemented
57	C₂₃×#481	C₂²	1	4	yes	complemented
58	C₂₃×#480	C₂²	1	1	yes	characteristic
59	C₂₃×#479	C₂²	1	2	yes	complemented
60	C₂₃×#475	C₂²	1	2	yes	complemented
61	C₂₃×#469	C₂²	1	4	yes	complemented
62	C₂₃×#468	C₂²	1	4	yes	complemented
63	C₂₃×#465	C₂²	1	4	yes	complemented
64	C₂₃×#465	C₂²	1	4	yes	complemented
65	C₂₃×#464	C₂²	1	2	yes	complemented
66	C₂₃×#462	C₂²	1	2	yes	complemented
67	C₂₃×#460	C₂²	1	4	yes	complemented
68	C₂₃×#460	C₂²	1	2	yes	complemented
69	C₂₃×#459	C₂²	1	2	yes	complemented
70	C₂₃×#452	C₂²	1	4	yes	complemented
71	C₂₃×#452	C₂²	1	4	yes	complemented
72	C₂₃×#452	C₂²	1	4	yes	complemented
73	C₂₃×#451	C₂²	1	2	yes	—
74	C₂₃×#451	C₂²	1	1	yes	characteristic
75	C₂₃×#450	C₂²	1	2	yes	—
76	C₂₃×#450	C₂²	1	2	yes	—
77	C₂₃×#450	C₂²	1	2	yes	—
78	C₂₃×#449	C₂²	1	4	yes	complemented
79	C₂₃×#449	C₂²	1	4	yes	complemented
80	C₂₃×#448	C₂²	1	1	yes	characteristic
81	C₂₃×#448	C₂²	1	4	yes	complemented
82	C₂₃×#447	C₂²	1	2	yes	—
83	C₂₃×#441	C₂²	1	4	yes	complemented
84	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
85	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
86	C₂₃×#436	C₂²	1	2	yes	complemented
87	C₂₃×#435	C₂²	1	4	yes	complemented
88	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
89	C₂₃×#432	C₂²	1	1	yes	characteristic
90	C₂₃×#431	C₂²	1	1	yes	characteristic
91	C₂₃×#417	C₂²	1	4	yes	complemented
92	C₂₃×#416	C₂²	1	4	yes	complemented
93	C₂₃×#407	C₂²	1	2	yes	—
94	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
95	C₂×#41×C₂₃	—	2	1	no	—
96	C₂×#41×C₂₃	—	2	2	no	—
97	C₂×#41×C₂₃	—	2	2	no	—
98	C₂×#41×C₂₃	—	4	8	no	—
99	C₂×#41×C₂₃	C₂³	1	4	yes	—
100	C₂×#41×C₂₃	C₂³	1	4	yes	—
101	C₂×#41×C₂₃	C₂³	1	2	yes	—
102	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
103	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
104	C₂²×D₄×C₂₃	—	2	2	no	—
105	C₂²×D₄×C₂₃	—	2	2	no	—
106	C₂²×D₄×C₂₃	—	2	1	no	—
107	C₂²×D₄×C₂₃	—	2	1	no	—
108	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
109	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
110	C₂³×C₄×C₂₃	—	2	2	no	—
111	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
112	C₂₃×#137	—	4	8	no	—
113	C₂₃×#135	—	4	8	no	—
114	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
115	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
116	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
117	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
118	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
119	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
120	C₂×D₈×C₂₃	C₂³	1	4	yes	—
121	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
122	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
123	C₂₃×C₄⋊Q₈	—	2	1	no	—
124	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
125	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
126	C₂₃×#127	—	2	2	no	—
127	C₂₃×#127	—	2	2	no	—
128	C₂₃×#127	—	2	4	no	—
129	C₂₃×#127	—	2	1	no	—
130	C₂₃×#127	—	2	1	no	—
131	C₂₃×#127	C₂³	1	2	yes	—
132	C₂₃×#127	C₂³	1	2	yes	—
133	C₂₃×#126	—	2	2	no	—
134	C₂₃×#126	—	2	2	no	—
135	C₂₃×#126	—	2	1	no	—
136	C₂₃×#125	—	2	2	no	—
137	C₂₃×#125	—	2	1	no	—
138	C₂₃×#125	C₂³	1	1	yes	characteristic
139	C₂₃×#124	—	2	1	no	—
140	C₂₃×#124	—	2	2	no	—
141	C₂₃×#124	C₂³	1	1	yes	characteristic
142	C₂₃×#123	—	2	2	no	—
143	C₂₃×#123	—	2	1	no	—
144	C₂₃×#123	—	2	2	no	—
145	C₂₃×#123	—	2	2	no	—
146	C₂₃×#123	—	2	2	no	—
147	C₂₃×C₂²⋊Q₈	—	2	2	no	—
148	C₂₃×C₂²⋊Q₈	—	2	1	no	—
149	C₂₃×C₂²⋊Q₈	—	2	2	no	—
150	C₂₃×C₂²⋊Q₈	—	2	1	no	—
151	C₂₃×C₂²⋊Q₈	—	2	2	no	—
152	C₂₃×C₂²⋊Q₈	—	2	2	no	—
153	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
154	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
155	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
156	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
157	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
158	C₂₃×#121	—	2	1	no	—
159	C₂₃×#121	—	2	2	no	—
160	C₂₃×#121	—	2	2	no	—
161	C₂₃×#121	—	2	2	no	—
162	C₂₃×#121	—	2	4	no	—
163	C₂₃×#121	—	2	4	no	—
164	C₂₃×#121	—	2	4	no	—
165	C₂₃×#121	—	2	4	no	—
166	C₂₃×#121	C₂³	1	2	yes	—
167	C₂₃×#121	C₂³	1	4	yes	—
168	C₂₃×#121	C₂³	1	4	yes	—
169	C₂₃×#121	C₂³	1	1	yes	characteristic
170	C₂₃×#120	—	2	2	no	—
171	C₄×Q₈×C₂₃	—	2	1	no	—
172	C₄×Q₈×C₂₃	—	2	1	no	—
173	C₄×Q₈×C₂₃	—	2	1	no	—
174	C₄×Q₈×C₂₃	—	2	1	no	—
175	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
176	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
177	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
178	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
179	C₄×D₄×C₂₃	—	2	1	no	—
180	C₄×D₄×C₂₃	—	2	2	no	—
181	C₄×D₄×C₂₃	—	2	1	no	—
182	C₄×D₄×C₂₃	—	2	2	no	—
183	C₄×D₄×C₂₃	—	2	2	no	—
184	C₄×D₄×C₂₃	—	2	4	no	—
185	C₄×D₄×C₂₃	—	2	2	no	—
186	C₄×D₄×C₂₃	—	2	2	no	—
187	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
188	C₄×D₄×C₂₃	D₄	1	2	yes	—
189	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
190	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
191	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
192	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
193	C₄×D₄×C₂₃	C₂³	1	2	yes	—
194	C₂₃×#117	—	2	1	no	—
195	C₂₃×#117	—	2	2	no	—
196	C₂₃×#117	—	2	1	no	—
197	C₂₃×#117	C₂³	1	2	yes	—
198	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
199	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
200	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
201	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
202	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
203	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
205	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
206	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
207	C₂×C₄²×C₂₃	—	2	1	no	—
208	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
209	C₂₃×#107	C₂³	1	2	yes	—
210	C₂₃×#106	C₂³	1	2	yes	—
211	C₂₃×#106	C₂³	1	4	yes	—
212	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
213	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
214	C₂₃×#103	C₂³	1	2	yes	—
215	C₂₃×#103	C₂³	1	4	yes	—
216	C₂₃×#103	C₂³	1	2	yes	—
217	C₂₃×#103	C₂³	1	2	yes	—
218	C₂₃×#103	C₂³	1	4	yes	—
219	C₂₃×#102	C₂³	1	4	yes	—
220	C₂₃×#102	C₂³	1	4	yes	—
221	C₂₃×#102	C₂³	1	4	yes	—
222	C₂₃×#102	C₂³	1	4	yes	—
223	C₂₃×#102	C₂³	1	2	yes	—
224	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
225	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
226	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
227	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
228	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
229	C₂₃×#97	C₂³	1	2	yes	—
230	C₄×C₈×C₂₃	C₂³	1	2	yes	—
231	C₂⁴×C₂₃	—	2	2	no	—
232	C₂⁴×C₂₃	C₂×D₄	1	2	yes	—
233	#41×C₂₃	—	2	8	no	—
234	#41×C₂₃	—	2	8	no	—
235	#41×C₂₃	—	4	4	no	—
236	#41×C₂₃	—	4	4	no	—
237	#41×C₂₃	—	4	4	no	—
238	#41×C₂₃	—	4	4	no	—
239	#41×C₂₃	—	4	8	no	—
240	#41×C₂₃	—	4	8	no	—
241	C₂×Q₈×C₂₃	—	2	4	no	—
242	C₂×Q₈×C₂₃	—	2	1	no	—
243	C₂×Q₈×C₂₃	—	2	1	no	—
244	C₂×Q₈×C₂₃	—	2	2	no	—
245	C₂×Q₈×C₂₃	—	4	4	no	—
246	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
247	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
248	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
249	C₂×D₄×C₂₃	—	2	1	no	—
250	C₂×D₄×C₂₃	—	2	2	no	—
251	C₂×D₄×C₂₃	—	2	4	no	—
252	C₂×D₄×C₂₃	—	2	4	no	—
253	C₂×D₄×C₂₃	—	2	2	no	—
254	C₂×D₄×C₂₃	—	2	4	no	—
255	C₂×D₄×C₂₃	—	2	4	no	—
256	C₂×D₄×C₂₃	—	2	2	no	—
257	C₂×D₄×C₂₃	—	2	2	no	—
258	C₂×D₄×C₂₃	—	2	2	no	—
259	C₂×D₄×C₂₃	—	2	2	no	—
260	C₂×D₄×C₂₃	—	2	2	no	—
261	C₂×D₄×C₂₃	—	4	2	no	—
262	C₂×D₄×C₂₃	—	4	4	no	—
263	C₂×D₄×C₂₃	—	4	4	no	—
264	C₂×D₄×C₂₃	—	4	8	no	—
265	C₂×D₄×C₂₃	—	8	2	no	—
266	C₂×D₄×C₂₃	—	8	4	no	—
267	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
268	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
269	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
270	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
271	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₂₃	—	2	1	no	—
273	C₂²×C₄×C₂₃	—	2	1	no	—
274	C₂²×C₄×C₂₃	—	2	2	no	—
275	C₂²×C₄×C₂₃	—	2	2	no	—
276	C₂²×C₄×C₂₃	—	2	1	no	—
277	C₂²×C₄×C₂₃	—	2	4	no	—
278	C₂²×C₄×C₂₃	—	2	4	no	—
279	C₂²×C₄×C₂₃	—	2	2	no	—
280	C₂²×C₄×C₂₃	—	4	4	no	—
281	C₂²×C₄×C₂₃	—	4	8	no	—
282	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
283	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
284	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
285	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
286	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
287	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
290	Q₁₆×C₂₃	—	2	8	no	—
291	Q₁₆×C₂₃	—	2	4	no	—
292	SD₁₆×C₂₃	—	2	4	no	—
293	SD₁₆×C₂₃	—	4	4	no	—
294	SD₁₆×C₂₃	—	4	4	no	—
295	SD₁₆×C₂₃	—	4	4	no	—
296	D₈×C₂₃	—	4	4	no	—
297	M₁₆×C₂₃	—	4	4	no	—
298	C₂×C₈×C₂₃	—	4	4	no	—
299	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
300	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
301	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
302	C₄⋊C₄×C₂₃	—	2	1	no	—
303	C₄⋊C₄×C₂₃	—	2	2	no	—
304	C₄⋊C₄×C₂₃	—	2	1	no	—
305	C₄⋊C₄×C₂₃	—	2	2	no	—
306	C₄⋊C₄×C₂₃	—	2	2	no	—
307	C₄⋊C₄×C₂₃	—	2	2	no	—
308	C₄⋊C₄×C₂₃	—	2	2	no	—
309	C₄⋊C₄×C₂₃	—	2	1	no	—
310	C₄⋊C₄×C₂₃	—	2	2	no	—
311	C₄⋊C₄×C₂₃	—	2	1	no	—
312	C₄⋊C₄×C₂₃	—	2	1	no	—
313	C₄⋊C₄×C₂₃	—	2	1	no	—
314	C₄⋊C₄×C₂₃	—	2	2	no	—
315	C₄⋊C₄×C₂₃	—	2	1	no	—
316	C₄⋊C₄×C₂₃	—	2	2	no	—
317	C₄⋊C₄×C₂₃	—	2	1	no	—
318	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
319	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
320	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
321	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
322	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
323	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
324	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
325	C₂²⋊C₄×C₂₃	—	2	1	no	—
326	C₂²⋊C₄×C₂₃	—	2	2	no	—
327	C₂²⋊C₄×C₂₃	—	2	2	no	—
328	C₂²⋊C₄×C₂₃	—	2	2	no	—
329	C₂²⋊C₄×C₂₃	—	2	2	no	—
330	C₂²⋊C₄×C₂₃	—	2	2	no	—
331	C₂²⋊C₄×C₂₃	—	2	4	no	—
332	C₂²⋊C₄×C₂₃	—	2	4	no	—
333	C₂²⋊C₄×C₂₃	—	2	1	no	—
334	C₂²⋊C₄×C₂₃	—	2	1	no	—
335	C₂²⋊C₄×C₂₃	—	2	1	no	—
336	C₂²⋊C₄×C₂₃	—	2	2	no	—
337	C₂²⋊C₄×C₂₃	—	2	1	no	—
338	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
339	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
340	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
341	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
342	C₄²×C₂₃	—	2	2	no	—
343	C₄²×C₂₃	—	2	2	no	—
344	C₄²×C₂₃	—	2	2	no	—
345	C₄²×C₂₃	—	2	2	no	—
346	C₄²×C₂₃	—	2	1	no	—
347	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
348	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
349	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
350	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
351	#61596	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
352	C₂³×C₂₃	—	2	4	no	—
353	C₂³×C₂₃	—	2	1	no	—
354	C₂³×C₂₃	—	2	4	no	—
355	C₂³×C₂₃	—	4	2	no	—
356	C₂³×C₂₃	—	4	2	no	—
357	C₂³×C₂₃	—	4	4	no	—
358	C₂³×C₂₃	—	4	4	no	—
359	C₂³×C₂₃	—	4	4	no	—
360	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
361	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
362	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
363	Q₈×C₂₃	—	2	4	no	—
364	Q₈×C₂₃	—	2	2	no	—
365	Q₈×C₂₃	—	2	2	no	—
366	Q₈×C₂₃	—	2	4	no	—
367	Q₈×C₂₃	—	4	2	no	—
368	Q₈×C₂₃	—	8	2	no	—
369	Q₈×C₂₃	H(5,𝔽₂)	1	4	yes	—
370	D₄×C₂₃	—	2	2	no	—
371	D₄×C₂₃	—	2	2	no	—
372	D₄×C₂₃	—	2	2	no	—
373	D₄×C₂₃	—	2	4	no	—
374	D₄×C₂₃	—	2	4	no	—
375	D₄×C₂₃	—	4	2	no	—
376	D₄×C₂₃	—	4	8	no	—
377	D₄×C₂₃	—	4	8	no	—
378	D₄×C₂₃	—	4	4	no	—
379	D₄×C₂₃	—	4	4	no	—
380	D₄×C₂₃	—	4	4	no	—
381	D₄×C₂₃	—	4	2	no	—
382	D₄×C₂₃	—	4	4	no	—
383	D₄×C₂₃	—	8	2	no	—
384	D₄×C₂₃	—	8	2	no	—
385	D₄×C₂₃	—	8	4	no	—
386	D₄×C₂₃	—	8	4	no	—
387	D₄×C₂₃	—	8	2	no	—
388	C₂×C₄×C₂₃	—	2	4	no	—
389	C₂×C₄×C₂₃	—	2	2	no	—
390	C₂×C₄×C₂₃	—	2	2	no	—
391	C₂×C₄×C₂₃	—	2	2	no	—
392	C₂×C₄×C₂₃	—	2	4	no	—
393	C₂×C₄×C₂₃	—	2	4	no	—
394	C₂×C₄×C₂₃	—	2	2	no	—
395	C₂×C₄×C₂₃	—	2	1	no	—
396	C₂×C₄×C₂₃	—	2	2	no	—
397	C₂×C₄×C₂₃	—	2	2	no	—
398	C₂×C₄×C₂₃	—	2	1	no	—
399	C₂×C₄×C₂₃	—	2	2	no	—
400	C₂×C₄×C₂₃	—	2	1	no	—
401	C₂×C₄×C₂₃	—	4	2	no	—
402	C₂×C₄×C₂₃	—	4	2	no	—
403	C₂×C₄×C₂₃	—	4	2	no	—
404	C₂×C₄×C₂₃	—	4	8	no	—
405	C₂×C₄×C₂₃	—	4	8	no	—
406	C₂×C₄×C₂₃	—	4	4	no	—
407	C₂×C₄×C₂₃	—	4	2	no	—
408	C₂×C₄×C₂₃	—	4	2	no	—
409	C₂×C₄×C₂₃	—	8	2	no	—
410	C₂×C₄×C₂₃	—	8	2	no	—
411	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
412	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
413	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
414	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
415	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
416	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
417	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
418	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
419	C₈×C₂₃	—	2	2	no	—
420	C₈×C₂₃	—	2	4	no	—
421	C₈×C₂₃	—	2	2	no	—
422	#3520	C₂×C₂₃	1	1	yes	characteristic, complemented
423	C₂×#550	C₂×C₂₃	1	1	yes	characteristic, complemented
424	#3332	C₂×C₂₃	1	2	yes	complemented
425	#3317	C₂×C₂₃	1	4	yes	complemented
426	#3304	C₂×C₂₃	1	2	yes	complemented
427	#3284	C₂×C₂₃	1	2	yes	complemented
428	#3278	C₂×C₂₃	1	2	yes	complemented
429	#3271	C₂×C₂₃	1	4	yes	complemented
430	#3217	C₂×C₂₃	1	1	yes	characteristic, complemented
431	#3208	C₂×C₂₃	1	1	yes	characteristic, complemented
432	#3194	C₂×C₂₃	1	2	yes	complemented
433	#3187	C₂×C₂₃	1	2	yes	complemented
434	#3113	C₂×C₂₃	1	1	yes	characteristic, complemented
435	#3108	C₂×C₂₃	1	1	yes	characteristic, complemented
436	#3007	C₂×C₂₃	1	2	yes	complemented
437	#3002	C₂×C₂₃	1	2	yes	complemented
438	#2974	C₂×C₂₃	1	1	yes	characteristic, complemented
439	C₂²×C₂₃	—	2	1	no	—
440	C₂²×C₂₃	—	2	1	no	—
441	C₂²×C₂₃	—	2	2	no	—
442	C₂²×C₂₃	—	2	2	no	—
443	C₂²×C₂₃	—	2	2	no	—
444	C₂²×C₂₃	—	2	2	no	—
445	C₂²×C₂₃	—	2	2	no	—
446	C₂²×C₂₃	—	2	2	no	—
447	C₂²×C₂₃	—	4	4	no	—
448	C₂²×C₂₃	—	4	1	no	—
449	C₂²×C₂₃	—	4	1	no	—
450	C₂²×C₂₃	—	4	4	no	—
451	C₂²×C₂₃	—	4	1	no	—
452	C₂²×C₂₃	—	4	4	no	—
453	C₂²×C₂₃	—	8	4	no	—
454	C₂²×C₂₃	—	8	8	no	—
455	C₂²×C₂₃	#577	1	2	yes	—
456	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
457	C₄×C₂₃	—	2	4	no	—
458	C₄×C₂₃	—	2	2	no	—
459	C₄×C₂₃	—	2	2	no	—
460	C₄×C₂₃	—	2	1	no	—
461	C₄×C₂₃	—	2	1	no	—
462	C₄×C₂₃	—	2	1	no	—
463	C₄×C₂₃	—	2	1	no	—
464	C₄×C₂₃	—	4	2	no	—
465	C₄×C₂₃	—	4	1	no	—
466	C₄×C₂₃	—	4	1	no	—
467	C₄×C₂₃	—	4	2	no	—
468	C₄×C₂₃	—	4	2	no	—
469	C₄×C₂₃	—	4	1	no	—
470	C₄×C₂₃	#575	1	2	yes	—
471	C₄×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
472	C₂²×#41	C₂²×C₂₃	1	2	yes	—
473	C₂×#137	C₂²×C₂₃	1	4	yes	complemented
474	C₂×#135	C₂²×C₂₃	1	4	yes	complemented
475	#556	C₂²×C₂₃	1	1	yes	characteristic, complemented
476	#554	—	2	1	no	—
477	#552	C₂²×C₂₃	1	2	yes	complemented
478	#551	—	2	2	no	—
479	#550	—	2	1	no	—
480	#550	—	2	2	no	—
481	#550	—	2	1	no	—
482	#550	C₂²×C₂₃	1	2	yes	—
483	#550	C₂²×C₂₃	1	4	yes	—
484	#550	C₂²×C₂₃	1	2	yes	—
485	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
486	#548	C₂²×C₂₃	1	2	yes	complemented
487	#547	C₂²×C₂₃	1	1	yes	characteristic, complemented
488	#547	C₂²×C₂₃	1	1	yes	characteristic, complemented
489	#546	—	2	1	no	—
490	#542	—	2	1	no	—
491	#539	—	2	2	no	—
492	#533	C₂²×C₂₃	1	1	yes	characteristic
493	C₂×#127	—	2	1	no	—
494	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
495	#529	C₂²×C₂₃	1	1	yes	characteristic
496	#525	C₂²×C₂₃	1	2	yes	—
497	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
498	C₂×#121	—	2	2	no	—
499	C₂×#121	C₂²×C₂₃	1	2	yes	—
500	#520	—	2	1	no	—
501	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
502	C₂×C₄×D₄	—	2	1	no	—
503	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
504	#496	C₂²×C₂₃	1	2	yes	complemented
505	#492	C₂²×C₂₃	1	2	yes	complemented
506	#490	C₂²×C₂₃	1	2	yes	complemented
507	#486	C₂²×C₂₃	1	2	yes	complemented
508	#483	C₂²×C₂₃	1	1	yes	characteristic
509	#483	C₂²×C₂₃	1	2	yes	—
510	#482	C₂²×C₂₃	1	4	yes	complemented
511	#481	C₂²×C₂₃	1	4	yes	complemented
512	#480	C₂²×C₂₃	1	1	yes	characteristic
513	#479	C₂²×C₂₃	1	2	yes	complemented
514	#475	C₂²×C₂₃	1	2	yes	complemented
515	#469	C₂²×C₂₃	1	4	yes	complemented
516	#468	C₂²×C₂₃	1	4	yes	complemented
517	#465	C₂²×C₂₃	1	4	yes	complemented
518	#465	C₂²×C₂₃	1	4	yes	complemented
519	#464	C₂²×C₂₃	1	2	yes	complemented
520	#462	C₂²×C₂₃	1	2	yes	complemented
521	#460	C₂²×C₂₃	1	4	yes	complemented
522	#460	C₂²×C₂₃	1	2	yes	complemented
523	#459	C₂²×C₂₃	1	2	yes	complemented
524	#452	C₂²×C₂₃	1	4	yes	complemented
525	#452	C₂²×C₂₃	1	4	yes	complemented
526	#452	C₂²×C₂₃	1	4	yes	complemented
527	#451	C₂²×C₂₃	1	1	yes	characteristic
528	#451	C₂²×C₂₃	1	2	yes	—
529	#450	C₂²×C₂₃	1	2	yes	—
530	#450	C₂²×C₂₃	1	2	yes	—
531	#450	C₂²×C₂₃	1	2	yes	—
532	#449	C₂²×C₂₃	1	4	yes	complemented
533	#449	C₂²×C₂₃	1	4	yes	complemented
534	#448	C₂²×C₂₃	1	1	yes	characteristic
535	#448	C₂²×C₂₃	1	4	yes	complemented
536	#447	C₂²×C₂₃	1	2	yes	—
537	#441	C₂²×C₂₃	1	4	yes	complemented
538	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
539	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
540	#436	C₂²×C₂₃	1	2	yes	complemented
541	#435	C₂²×C₂₃	1	4	yes	complemented
542	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
543	#432	C₂²×C₂₃	1	1	yes	characteristic
544	#431	C₂²×C₂₃	1	1	yes	characteristic
545	#417	C₂²×C₂₃	1	4	yes	complemented
546	#416	C₂²×C₂₃	1	4	yes	complemented
547	#407	C₂²×C₂₃	1	2	yes	—
548	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
549	C₂×C₂₃	—	2	2	no	—
550	C₂×C₂₃	—	4	2	no	—
551	C₂×C₂₃	—	4	2	no	—
552	C₂×C₂₃	—	8	1	no	—
553	C₂×C₂₃	—	8	4	no	—
554	C₂×C₂₃	#3484	1	1	yes	characteristic
555	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
556	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
557	C₂×#41	—	2	1	no	—
558	C₂×#41	—	2	2	no	—
559	C₂×#41	—	2	2	no	—
560	C₂×#41	—	4	8	no	—
561	C₂×#41	C₂³×C₂₃	1	4	yes	—
562	C₂×#41	C₂³×C₂₃	1	4	yes	—
563	C₂×#41	C₂³×C₂₃	1	2	yes	—
564	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
565	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
566	C₂²×D₄	—	2	2	no	—
567	C₂²×D₄	—	2	2	no	—
568	C₂²×D₄	—	2	1	no	—
569	C₂²×D₄	—	2	1	no	—
570	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
571	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
572	C₂³×C₄	—	2	2	no	—
573	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
574	#137	—	4	8	no	—
575	#135	—	4	8	no	—
576	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
577	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
578	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
579	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
580	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
581	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
582	C₂×D₈	C₂³×C₂₃	1	4	yes	—
583	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
584	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
585	C₄⋊Q₈	—	2	1	no	—
586	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
587	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
588	#127	—	2	2	no	—
589	#127	—	2	2	no	—
590	#127	—	2	4	no	—
591	#127	—	2	1	no	—
592	#127	—	2	1	no	—
593	#127	C₂³×C₂₃	1	2	yes	—
594	#127	C₂³×C₂₃	1	2	yes	—
595	#126	—	2	2	no	—
596	#126	—	2	2	no	—
597	#126	—	2	1	no	—
598	#125	—	2	2	no	—
599	#125	—	2	1	no	—
600	#125	C₂³×C₂₃	1	1	yes	characteristic
601	#124	—	2	1	no	—
602	#124	—	2	2	no	—
603	#124	C₂³×C₂₃	1	1	yes	characteristic
604	#123	—	2	2	no	—
605	#123	—	2	2	no	—
606	#123	—	2	1	no	—
607	#123	—	2	2	no	—
608	#123	—	2	2	no	—
609	C₂²⋊Q₈	—	2	2	no	—
610	C₂²⋊Q₈	—	2	2	no	—
611	C₂²⋊Q₈	—	2	1	no	—
612	C₂²⋊Q₈	—	2	2	no	—
613	C₂²⋊Q₈	—	2	1	no	—
614	C₂²⋊Q₈	—	2	2	no	—
615	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
616	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
617	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
618	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
619	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
620	#121	—	2	2	no	—
621	#121	—	2	1	no	—
622	#121	—	2	2	no	—
623	#121	—	2	2	no	—
624	#121	—	2	4	no	—
625	#121	—	2	4	no	—
626	#121	—	2	4	no	—
627	#121	—	2	4	no	—
628	#121	C₂³×C₂₃	1	4	yes	—
629	#121	C₂³×C₂₃	1	4	yes	—
630	#121	C₂³×C₂₃	1	1	yes	characteristic
631	#121	C₂³×C₂₃	1	2	yes	—
632	#120	—	2	2	no	—
633	C₄×Q₈	—	2	1	no	—
634	C₄×Q₈	—	2	1	no	—
635	C₄×Q₈	—	2	1	no	—
636	C₄×Q₈	—	2	1	no	—
637	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
638	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
639	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
640	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
641	C₄×D₄	—	2	1	no	—
642	C₄×D₄	—	2	2	no	—
643	C₄×D₄	—	2	2	no	—
644	C₄×D₄	—	2	1	no	—
645	C₄×D₄	—	2	2	no	—
646	C₄×D₄	—	2	4	no	—
647	C₄×D₄	—	2	2	no	—
648	C₄×D₄	—	2	2	no	—
649	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
650	C₄×D₄	D₄×C₂₃	1	2	yes	—
651	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
652	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
653	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
654	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
655	C₄×D₄	C₂³×C₂₃	1	2	yes	—
656	#117	—	2	1	no	—
657	#117	—	2	2	no	—
658	#117	—	2	1	no	—
659	#117	C₂³×C₂₃	1	2	yes	—
660	C₂×C₄⋊C₄	—	2	1	no	—
661	C₂×C₄⋊C₄	—	2	2	no	—
662	C₂×C₄⋊C₄	—	2	1	no	—
663	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
664	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
665	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
666	C₂×C₂²⋊C₄	—	2	2	no	—
667	C₂×C₂²⋊C₄	—	2	2	no	—
668	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
669	C₂×C₄²	—	2	1	no	—
670	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
671	#107	C₂³×C₂₃	1	2	yes	—
672	#106	C₂³×C₂₃	1	2	yes	—
673	#106	C₂³×C₂₃	1	4	yes	—
674	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
675	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
676	#103	C₂³×C₂₃	1	2	yes	—
677	#103	C₂³×C₂₃	1	4	yes	—
678	#103	C₂³×C₂₃	1	2	yes	—
679	#103	C₂³×C₂₃	1	2	yes	—
680	#103	C₂³×C₂₃	1	4	yes	—
681	#102	C₂³×C₂₃	1	4	yes	—
682	#102	C₂³×C₂₃	1	4	yes	—
683	#102	C₂³×C₂₃	1	4	yes	—
684	#102	C₂³×C₂₃	1	4	yes	—
685	#102	C₂³×C₂₃	1	2	yes	—
686	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
687	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
688	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
689	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
690	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
691	#97	C₂³×C₂₃	1	2	yes	—
692	C₄×C₈	C₂³×C₂₃	1	2	yes	—
693	C₂₃	#61596	1	1	yes	characteristic, direct product factor, Sylow
694	C₂⁴	—	2	2	no	—
695	C₂⁴	C₂×D₄×C₂₃	1	2	yes	—
696	#41	—	2	8	no	—
697	#41	—	2	8	no	—
698	#41	—	4	4	no	—
699	#41	—	4	4	no	—
700	#41	—	4	4	no	—
701	#41	—	4	4	no	—
702	#41	—	4	8	no	—
703	#41	—	4	8	no	—
704	C₂×Q₈	—	2	4	no	—
705	C₂×Q₈	—	2	1	no	—
706	C₂×Q₈	—	2	1	no	—
707	C₂×Q₈	—	2	2	no	—
708	C₂×Q₈	—	4	4	no	—
709	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
710	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
711	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
712	C₂×D₄	—	2	1	no	—
713	C₂×D₄	—	2	2	no	—
714	C₂×D₄	—	2	4	no	—
715	C₂×D₄	—	2	4	no	—
716	C₂×D₄	—	2	2	no	—
717	C₂×D₄	—	2	4	no	—
718	C₂×D₄	—	2	4	no	—
719	C₂×D₄	—	2	2	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	2	2	no	—
722	C₂×D₄	—	2	2	no	—
723	C₂×D₄	—	2	2	no	—
724	C₂×D₄	—	4	2	no	—
725	C₂×D₄	—	4	4	no	—
726	C₂×D₄	—	4	8	no	—
727	C₂×D₄	—	4	4	no	—
728	C₂×D₄	—	8	2	no	—
729	C₂×D₄	—	8	4	no	—
730	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
731	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
732	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
733	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
734	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
735	C₂²×C₄	—	2	1	no	—
736	C₂²×C₄	—	2	1	no	—
737	C₂²×C₄	—	2	2	no	—
738	C₂²×C₄	—	2	2	no	—
739	C₂²×C₄	—	2	1	no	—
740	C₂²×C₄	—	2	4	no	—
741	C₂²×C₄	—	2	4	no	—
742	C₂²×C₄	—	2	2	no	—
743	C₂²×C₄	—	4	4	no	—
744	C₂²×C₄	—	4	8	no	—
745	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
746	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
747	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
748	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
749	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
750	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
751	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
752	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
753	Q₁₆	—	2	8	no	—
754	Q₁₆	—	2	4	no	—
755	SD₁₆	—	2	4	no	—
756	SD₁₆	—	4	4	no	—
757	SD₁₆	—	4	4	no	—
758	SD₁₆	—	4	4	no	—
759	D₈	—	4	4	no	—
760	M₁₆	—	4	4	no	—
761	C₂×C₈	—	4	4	no	—
762	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
763	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
764	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
765	C₄⋊C₄	—	2	1	no	—
766	C₄⋊C₄	—	2	2	no	—
767	C₄⋊C₄	—	2	1	no	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	—	2	1	no	—
773	C₄⋊C₄	—	2	2	no	—
774	C₄⋊C₄	—	2	1	no	—
775	C₄⋊C₄	—	2	1	no	—
776	C₄⋊C₄	—	2	1	no	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	1	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	2	1	no	—
781	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
782	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
783	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
784	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
785	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
786	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
787	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
788	C₂²⋊C₄	—	2	1	no	—
789	C₂²⋊C₄	—	2	2	no	—
790	C₂²⋊C₄	—	2	2	no	—
791	C₂²⋊C₄	—	2	2	no	—
792	C₂²⋊C₄	—	2	2	no	—
793	C₂²⋊C₄	—	2	2	no	—
794	C₂²⋊C₄	—	2	4	no	—
795	C₂²⋊C₄	—	2	4	no	—
796	C₂²⋊C₄	—	2	1	no	—
797	C₂²⋊C₄	—	2	1	no	—
798	C₂²⋊C₄	—	2	1	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	1	no	—
801	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
802	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
803	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
804	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
805	C₄²	—	2	2	no	—
806	C₄²	—	2	2	no	—
807	C₄²	—	2	2	no	—
808	C₄²	—	2	2	no	—
809	C₄²	—	2	1	no	—
810	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
811	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
812	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
813	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
814	C₂³	—	2	4	no	—
815	C₂³	—	2	1	no	—
816	C₂³	—	2	4	no	—
817	C₂³	—	4	2	no	—
818	C₂³	—	4	2	no	—
819	C₂³	—	4	4	no	—
820	C₂³	—	4	4	no	—
821	C₂³	—	4	4	no	—
822	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
823	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
824	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
825	Q₈	—	2	4	no	—
826	Q₈	—	2	2	no	—
827	Q₈	—	2	2	no	—
828	Q₈	—	2	4	no	—
829	Q₈	—	4	2	no	—
830	Q₈	—	8	2	no	—
831	Q₈	C₂₃×H(5,𝔽₂)	1	4	yes	—
832	D₄	—	2	2	no	—
833	D₄	—	2	2	no	—
834	D₄	—	2	2	no	—
835	D₄	—	2	4	no	—
836	D₄	—	2	4	no	—
837	D₄	—	4	2	no	—
838	D₄	—	4	8	no	—
839	D₄	—	4	8	no	—
840	D₄	—	4	4	no	—
841	D₄	—	4	4	no	—
842	D₄	—	4	4	no	—
843	D₄	—	4	2	no	—
844	D₄	—	4	4	no	—
845	D₄	—	8	2	no	—
846	D₄	—	8	2	no	—
847	D₄	—	8	4	no	—
848	D₄	—	8	4	no	—
849	D₄	—	8	2	no	—
850	C₂×C₄	—	2	4	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	4	no	—
855	C₂×C₄	—	2	4	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	4	2	no	—
864	C₂×C₄	—	4	2	no	—
865	C₂×C₄	—	4	2	no	—
866	C₂×C₄	—	4	8	no	—
867	C₂×C₄	—	4	8	no	—
868	C₂×C₄	—	4	4	no	—
869	C₂×C₄	—	4	2	no	—
870	C₂×C₄	—	4	2	no	—
871	C₂×C₄	—	8	2	no	—
872	C₂×C₄	—	8	2	no	—
873	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
874	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
875	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
876	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
877	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
878	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
879	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
880	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
881	C₈	—	2	2	no	—
882	C₈	—	2	4	no	—
883	C₈	—	2	2	no	—
884	C₂²	—	2	1	no	—
885	C₂²	—	2	1	no	—
886	C₂²	—	2	2	no	—
887	C₂²	—	2	2	no	—
888	C₂²	—	2	2	no	—
889	C₂²	—	2	2	no	—
890	C₂²	—	2	2	no	—
891	C₂²	—	2	2	no	—
892	C₂²	—	4	4	no	—
893	C₂²	—	4	1	no	—
894	C₂²	—	4	1	no	—
895	C₂²	—	4	4	no	—
896	C₂²	—	4	1	no	—
897	C₂²	—	4	4	no	—
898	C₂²	—	8	4	no	—
899	C₂²	—	8	8	no	—
900	C₂²	C₂₃×#577	1	2	yes	—
901	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
902	C₄	—	2	4	no	—
903	C₄	—	2	2	no	—
904	C₄	—	2	2	no	—
905	C₄	—	2	1	no	—
906	C₄	—	2	1	no	—
907	C₄	—	2	1	no	—
908	C₄	—	2	1	no	—
909	C₄	—	4	2	no	—
910	C₄	—	4	1	no	—
911	C₄	—	4	1	no	—
912	C₄	—	4	2	no	—
913	C₄	—	4	2	no	—
914	C₄	—	4	1	no	—
915	C₄	C₂₃×#575	1	2	yes	—
916	C₄	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
917	C₂	—	2	2	no	—
918	C₂	—	4	2	no	—
919	C₂	—	4	2	no	—
920	C₂	—	8	4	no	—
921	C₂	—	8	1	no	—
922	C₂	C₂₃×#3484	1	1	yes	characteristic
923	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
924	C₂	C₂×C₂₃×#577	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3520	C₂	semidirect
2. C₂×C₂₃×#550	C₂	semidirect
3. C₂₃×#3332	C₂	semidirect
4. C₂₃×#3317	C₂	semidirect
5. C₂₃×#3304	C₂	semidirect
6. C₂₃×#3284	C₂	semidirect
7. C₂₃×#3278	C₂	semidirect
8. C₂₃×#3271	C₂	semidirect
9. C₂₃×#3217	C₂	semidirect
10. C₂₃×#3208	C₂	semidirect
11. C₂₃×#3194	C₂	semidirect
12. C₂₃×#3187	C₂	semidirect
13. C₂₃×#3113	C₂	semidirect
14. C₂₃×#3108	C₂	semidirect
15. C₂₃×#3007	C₂	semidirect
16. C₂₃×#3002	C₂	semidirect
17. C₂₃×#2974	C₂	semidirect
19. C₂×C₂₃×#137	C₂²	semidirect
20. C₂×C₂₃×#135	C₂²	semidirect
21. C₂₃×#556	C₂²	semidirect
23. C₂₃×#552	C₂²	semidirect
31. D₄×Q₈×C₂₃	C₂²	semidirect
32. C₂₃×#548	C₂²	semidirect
33. C₂₃×#547	C₂²	semidirect
34. C₂₃×#547	C₂²	semidirect
50. C₂₃×#496	C₂²	semidirect
51. C₂₃×#492	C₂²	semidirect
52. C₂₃×#490	C₂²	semidirect
53. C₂₃×#486	C₂²	semidirect
56. C₂₃×#482	C₂²	semidirect
57. C₂₃×#481	C₂²	semidirect
59. C₂₃×#479	C₂²	semidirect
60. C₂₃×#475	C₂²	semidirect
61. C₂₃×#469	C₂²	semidirect
62. C₂₃×#468	C₂²	semidirect
63. C₂₃×#465	C₂²	semidirect
64. C₂₃×#465	C₂²	semidirect
65. C₂₃×#464	C₂²	semidirect
66. C₂₃×#462	C₂²	semidirect
67. C₂₃×#460	C₂²	semidirect
68. C₂₃×#460	C₂²	semidirect
69. C₂₃×#459	C₂²	semidirect
70. C₂₃×#452	C₂²	semidirect
71. C₂₃×#452	C₂²	semidirect
72. C₂₃×#452	C₂²	semidirect
78. C₂₃×#449	C₂²	semidirect
79. C₂₃×#449	C₂²	semidirect
81. C₂₃×#448	C₂²	semidirect
83. C₂₃×#441	C₂²	semidirect
84. C₄×Q₁₆×C₂₃	C₂²	semidirect
85. C₄×SD₁₆×C₂₃	C₂²	semidirect
86. C₂₃×#436	C₂²	semidirect
87. C₂₃×#435	C₂²	semidirect
88. C₈×D₄×C₂₃	C₂²	semidirect
91. C₂₃×#417	C₂²	semidirect
92. C₂₃×#416	C₂²	semidirect
351. #61596	C₂₃	direct (N × H)
422. #3520	C₂×C₂₃	semidirect
423. C₂×#550	C₂×C₂₃	semidirect
424. #3332	C₂×C₂₃	semidirect
425. #3317	C₂×C₂₃	semidirect
426. #3304	C₂×C₂₃	semidirect
427. #3284	C₂×C₂₃	semidirect
428. #3278	C₂×C₂₃	semidirect
429. #3271	C₂×C₂₃	semidirect
430. #3217	C₂×C₂₃	semidirect
431. #3208	C₂×C₂₃	semidirect
432. #3194	C₂×C₂₃	semidirect
433. #3187	C₂×C₂₃	semidirect
434. #3113	C₂×C₂₃	semidirect
435. #3108	C₂×C₂₃	semidirect
436. #3007	C₂×C₂₃	semidirect
437. #3002	C₂×C₂₃	semidirect
438. #2974	C₂×C₂₃	semidirect
473. C₂×#137	C₂²×C₂₃	semidirect
474. C₂×#135	C₂²×C₂₃	semidirect
475. #556	C₂²×C₂₃	semidirect
477. #552	C₂²×C₂₃	semidirect
485. D₄×Q₈	C₂²×C₂₃	semidirect
486. #548	C₂²×C₂₃	semidirect
487. #547	C₂²×C₂₃	semidirect
488. #547	C₂²×C₂₃	semidirect
504. #496	C₂²×C₂₃	semidirect
505. #492	C₂²×C₂₃	semidirect
506. #490	C₂²×C₂₃	semidirect
507. #486	C₂²×C₂₃	semidirect
510. #482	C₂²×C₂₃	semidirect
511. #481	C₂²×C₂₃	semidirect
513. #479	C₂²×C₂₃	semidirect
514. #475	C₂²×C₂₃	semidirect
515. #469	C₂²×C₂₃	semidirect
516. #468	C₂²×C₂₃	semidirect
517. #465	C₂²×C₂₃	semidirect
518. #465	C₂²×C₂₃	semidirect
519. #464	C₂²×C₂₃	semidirect
520. #462	C₂²×C₂₃	semidirect
521. #460	C₂²×C₂₃	semidirect
522. #460	C₂²×C₂₃	semidirect
523. #459	C₂²×C₂₃	semidirect
524. #452	C₂²×C₂₃	semidirect
525. #452	C₂²×C₂₃	semidirect
526. #452	C₂²×C₂₃	semidirect
532. #449	C₂²×C₂₃	semidirect
533. #449	C₂²×C₂₃	semidirect
535. #448	C₂²×C₂₃	semidirect
537. #441	C₂²×C₂₃	semidirect
538. C₄×Q₁₆	C₂²×C₂₃	semidirect
539. C₄×SD₁₆	C₂²×C₂₃	semidirect
540. #436	C₂²×C₂₃	semidirect
541. #435	C₂²×C₂₃	semidirect
542. C₈×D₄	C₂²×C₂₃	semidirect
545. #417	C₂²×C₂₃	semidirect
546. #416	C₂²×C₂₃	semidirect
693. C₂₃	#61596	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×#550	2
C₂₃×#3332	2
C₂₃×#3317	2
C₂₃×#3304	2
C₂₃×#3284	2
C₂₃×#3278	2
C₂₃×#3271	2
C₂₃×#3217	2
C₂₃×#3208	2
C₂₃×#3194	2
C₂₃×#3187	2
C₂₃×#3113	2
C₂₃×#3108	2
C₂₃×#3007	2
C₂₃×#3002	2
C₂₃×#2974	2
#61596	23

Subgroups — C23×#61596 #19209222

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61596 #19209222