Subgroups — C₂₃×#61605 #19209231

Order 5888.

2232 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3519	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#550	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3333	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3309	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3305	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3287	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3274	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3268	C₂	1	4	yes	maximal, complemented
9	C₂₃×#3217	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3205	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3194	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3186	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3112	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3108	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3006	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	complemented
19	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
20	C₂×C₂₃×#135	C₂²	1	4	yes	complemented
21	C₂₃×#555	C₂²	1	1	yes	characteristic, complemented
22	C₂₃×#554	C₂²	1	1	yes	characteristic, complemented
23	C₂₃×#553	—	2	1	no	—
24	C₂₃×#553	C₂²	1	2	yes	complemented
25	C₂₃×#550	—	2	1	no	—
26	C₂₃×#550	—	2	1	no	—
27	C₂₃×#550	—	2	2	no	—
28	C₂₃×#550	C₂²	1	2	yes	—
29	C₂₃×#550	C₂²	1	4	yes	complemented
30	C₂₃×#550	C₂²	1	2	yes	complemented
31	C₂₃×#550	C₂²	1	1	yes	characteristic, complemented
32	C₂₃×#546	—	2	2	no	—
33	C₂₃×#546	C₂²	1	2	yes	complemented
34	D₄²×C₂₃	—	2	1	no	—
35	D₄²×C₂₃	C₂²	1	1	yes	characteristic, complemented
36	C₂₃×#540	—	2	1	no	—
37	C₂₃×#538	—	2	2	no	—
38	C₂₃×#532	C₂²	1	1	yes	characteristic
39	C₂×C₂₃×#127	—	2	1	no	—
40	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic, complemented
41	C₂₃×#529	C₂²	1	1	yes	characteristic
42	C₂₃×#525	C₂²	1	2	yes	—
43	C₂×C₂₃×#121	—	2	2	no	—
44	C₂×C₂₃×#121	C₂²	1	2	yes	—
45	C₂×C₂₃×#121	C₂²	1	2	yes	complemented
46	C₂₃×#518	—	2	1	no	—
47	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
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×#493	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, complemented
55	C₂₃×#482	C₂²	1	4	yes	complemented
56	C₂₃×#480	C₂²	1	1	yes	characteristic
57	C₂₃×#480	C₂²	1	2	yes	complemented
58	C₂₃×#480	C₂²	1	4	yes	complemented
59	C₂₃×#479	C₂²	1	2	yes	complemented
60	C₂₃×#477	C₂²	1	2	yes	complemented
61	C₂₃×#469	C₂²	1	4	yes	complemented
62	C₂₃×#468	C₂²	1	4	yes	complemented
63	C₂₃×#466	C₂²	1	4	yes	complemented
64	C₂₃×#466	C₂²	1	4	yes	complemented
65	C₂₃×#464	C₂²	1	2	yes	complemented
66	C₂₃×#460	C₂²	1	2	yes	complemented
67	C₂₃×#460	C₂²	1	2	yes	complemented
68	C₂₃×#459	C₂²	1	4	yes	complemented
69	C₂₃×#459	C₂²	1	2	yes	complemented
70	C₂₃×#452	C₂²	1	4	yes	complemented
71	C₂₃×#451	C₂²	1	1	yes	characteristic, complemented
72	C₂₃×#450	C₂²	1	2	yes	complemented
73	C₂₃×#449	C₂²	1	4	yes	complemented
74	C₂₃×#449	C₂²	1	4	yes	complemented
75	C₂₃×#449	C₂²	1	4	yes	complemented
76	C₂₃×#449	C₂²	1	4	yes	complemented
77	C₂₃×#448	C₂²	1	1	yes	characteristic
78	C₂₃×#448	C₂²	1	2	yes	complemented
79	C₂₃×#447	C₂²	1	2	yes	—
80	C₂₃×#447	C₂²	1	2	yes	complemented
81	C₂₃×#447	C₂²	1	4	yes	complemented
82	C₂₃×#447	C₂²	1	2	yes	complemented
83	C₂₃×#440	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, complemented
90	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
91	C₂₃×#417	C₂²	1	4	yes	complemented
92	C₂₃×#416	C₂²	1	4	yes	complemented
93	C₂₃×#407	C₂²	1	2	yes	complemented
94	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
95	C₂×#41×C₂₃	—	2	2	no	—
96	C₂×#41×C₂₃	—	2	2	no	—
97	C₂×#41×C₂₃	—	2	1	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×D₄×C₂₃	—	2	2	no	—
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	—	2	1	no	—
109	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
110	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
111	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
112	C₂³×C₄×C₂₃	—	2	2	no	—
113	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
114	C₂₃×AGL(1,ℤ/8)	—	4	8	no	—
115	C₂₃×#135	—	4	8	no	—
116	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
117	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
118	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
119	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
120	C₂×D₈×C₂₃	C₂³	1	4	yes	—
121	C₂×D₈×C₂₃	C₂³	1	4	yes	—
122	C₂×D₈×C₂₃	C₂³	1	4	yes	—
123	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
124	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
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	—	2	1	no	—
132	C₂₃×#127	C₂³	1	2	yes	—
133	C₂₃×#127	C₂³	1	2	yes	—
134	C₂₃×#127	C₂³	1	1	yes	characteristic
135	C₂₃×#126	—	2	2	no	—
136	C₂₃×#126	—	2	1	no	—
137	C₂₃×#125	—	2	1	no	—
138	C₂₃×#125	C₂³	1	1	yes	characteristic
139	C₂₃×#124	—	2	2	no	—
140	C₂₃×#124	—	2	1	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×C₂²⋊Q₈	—	2	2	no	—
147	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
148	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
149	C₂₃×#121	—	2	2	no	—
150	C₂₃×#121	—	2	1	no	—
151	C₂₃×#121	—	2	2	no	—
152	C₂₃×#121	—	2	2	no	—
153	C₂₃×#121	—	2	2	no	—
154	C₂₃×#121	—	2	1	no	—
155	C₂₃×#121	—	2	2	no	—
156	C₂₃×#121	—	2	1	no	—
157	C₂₃×#121	—	2	4	no	—
158	C₂₃×#121	—	2	4	no	—
159	C₂₃×#121	—	2	4	no	—
160	C₂₃×#121	—	2	4	no	—
161	C₂₃×#121	—	2	2	no	—
162	C₂₃×#121	—	2	2	no	—
163	C₂₃×#121	C₂³	1	4	yes	—
164	C₂₃×#121	C₂³	1	4	yes	—
165	C₂₃×#121	C₂³	1	2	yes	—
166	C₂₃×#121	C₂³	1	2	yes	—
167	C₂₃×#121	C₂³	1	2	yes	—
168	C₂₃×#121	C₂³	1	1	yes	characteristic
169	C₂₃×#121	C₂³	1	2	yes	—
170	C₂₃×#120	—	2	2	no	—
171	C₂₃×#120	—	2	2	no	—
172	C₂₃×#120	—	2	2	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	2	yes	—
177	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
178	C₄×D₄×C₂₃	—	2	1	no	—
179	C₄×D₄×C₂₃	—	2	2	no	—
180	C₄×D₄×C₂₃	—	2	1	no	—
181	C₄×D₄×C₂₃	—	2	2	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	1	no	—
186	C₄×D₄×C₂₃	—	2	2	no	—
187	C₄×D₄×C₂₃	—	2	1	no	—
188	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
189	C₄×D₄×C₂₃	D₄	1	2	yes	—
190	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
191	C₄×D₄×C₂₃	C₂³	1	2	yes	—
192	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
193	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
194	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
195	C₄×D₄×C₂₃	C₂³	1	2	yes	—
196	C₂₃×#117	—	2	1	no	—
197	C₂₃×#117	—	2	1	no	—
198	C₂₃×#117	C₂³	1	2	yes	—
199	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
200	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
201	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
202	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
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×#107	C₂³	1	4	yes	—
211	C₂₃×#106	C₂³	1	2	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×#102	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	2	yes	—
223	C₂₃×#102	C₂³	1	4	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	—	2	2	no	—
233	C₂⁴×C₂₃	C₂×D₄	1	2	yes	—
234	#41×C₂₃	—	2	8	no	—
235	#41×C₂₃	—	2	8	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	#41×C₂₃	—	8	2	no	—
242	C₂×Q₈×C₂₃	—	2	4	no	—
243	C₂×Q₈×C₂₃	—	2	1	no	—
244	C₂×Q₈×C₂₃	—	2	1	no	—
245	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
246	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
247	C₂×D₄×C₂₃	—	2	2	no	—
248	C₂×D₄×C₂₃	—	2	2	no	—
249	C₂×D₄×C₂₃	—	2	1	no	—
250	C₂×D₄×C₂₃	—	2	4	no	—
251	C₂×D₄×C₂₃	—	2	4	no	—
252	C₂×D₄×C₂₃	—	2	2	no	—
253	C₂×D₄×C₂₃	—	2	2	no	—
254	C₂×D₄×C₂₃	—	2	2	no	—
255	C₂×D₄×C₂₃	—	2	4	no	—
256	C₂×D₄×C₂₃	—	2	4	no	—
257	C₂×D₄×C₂₃	—	2	1	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	—	2	1	no	—
262	C₂×D₄×C₂₃	—	2	2	no	—
263	C₂×D₄×C₂₃	—	2	2	no	—
264	C₂×D₄×C₂₃	—	2	2	no	—
265	C₂×D₄×C₂₃	—	4	2	no	—
266	C₂×D₄×C₂₃	—	4	4	no	—
267	C₂×D₄×C₂₃	—	4	4	no	—
268	C₂×D₄×C₂₃	—	4	4	no	—
269	C₂×D₄×C₂₃	—	4	8	no	—
270	C₂×D₄×C₂₃	—	4	4	no	—
271	C₂×D₄×C₂₃	—	8	2	no	—
272	C₂×D₄×C₂₃	—	8	4	no	—
273	C₂×D₄×C₂₃	—	8	4	no	—
274	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
275	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
276	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
277	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
278	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
279	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₂₃	—	2	1	no	—
281	C₂²×C₄×C₂₃	—	2	1	no	—
282	C₂²×C₄×C₂₃	—	2	2	no	—
283	C₂²×C₄×C₂₃	—	2	1	no	—
284	C₂²×C₄×C₂₃	—	2	4	no	—
285	C₂²×C₄×C₂₃	—	2	4	no	—
286	C₂²×C₄×C₂₃	—	2	2	no	—
287	C₂²×C₄×C₂₃	—	2	2	no	—
288	C₂²×C₄×C₂₃	—	4	4	no	—
289	C₂²×C₄×C₂₃	—	4	8	no	—
290	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
291	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
292	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
293	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
294	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
295	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
298	Q₁₆×C₂₃	—	2	4	no	—
299	SD₁₆×C₂₃	—	2	8	no	—
300	SD₁₆×C₂₃	—	2	4	no	—
301	SD₁₆×C₂₃	—	4	4	no	—
302	D₈×C₂₃	—	4	4	no	—
303	D₈×C₂₃	—	4	4	no	—
304	D₈×C₂₃	—	4	4	no	—
305	M₁₆×C₂₃	—	4	4	no	—
306	C₂×C₈×C₂₃	—	4	4	no	—
307	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
308	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
309	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
310	C₄⋊C₄×C₂₃	—	2	2	no	—
311	C₄⋊C₄×C₂₃	—	2	2	no	—
312	C₄⋊C₄×C₂₃	—	2	1	no	—
313	C₄⋊C₄×C₂₃	—	2	2	no	—
314	C₄⋊C₄×C₂₃	—	2	1	no	—
315	C₄⋊C₄×C₂₃	—	2	1	no	—
316	C₄⋊C₄×C₂₃	—	2	1	no	—
317	C₄⋊C₄×C₂₃	—	2	1	no	—
318	C₄⋊C₄×C₂₃	—	2	2	no	—
319	C₄⋊C₄×C₂₃	—	2	1	no	—
320	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
321	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
322	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
323	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
324	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
325	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
326	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
327	C₂²⋊C₄×C₂₃	—	2	2	no	—
328	C₂²⋊C₄×C₂₃	—	2	2	no	—
329	C₂²⋊C₄×C₂₃	—	2	1	no	—
330	C₂²⋊C₄×C₂₃	—	2	1	no	—
331	C₂²⋊C₄×C₂₃	—	2	1	no	—
332	C₂²⋊C₄×C₂₃	—	2	2	no	—
333	C₂²⋊C₄×C₂₃	—	2	4	no	—
334	C₂²⋊C₄×C₂₃	—	2	4	no	—
335	C₂²⋊C₄×C₂₃	—	2	2	no	—
336	C₂²⋊C₄×C₂₃	—	2	2	no	—
337	C₂²⋊C₄×C₂₃	—	2	1	no	—
338	C₂²⋊C₄×C₂₃	—	2	2	no	—
339	C₂²⋊C₄×C₂₃	—	2	1	no	—
340	C₂²⋊C₄×C₂₃	—	2	2	no	—
341	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
342	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
343	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
344	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
345	C₄²×C₂₃	—	2	2	no	—
346	C₄²×C₂₃	—	2	2	no	—
347	C₄²×C₂₃	—	2	2	no	—
348	C₄²×C₂₃	—	2	1	no	—
349	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
350	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
351	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
352	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
353	#61605	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
354	C₂³×C₂₃	—	2	4	no	—
355	C₂³×C₂₃	—	2	1	no	—
356	C₂³×C₂₃	—	2	2	no	—
357	C₂³×C₂₃	—	2	4	no	—
358	C₂³×C₂₃	—	4	2	no	—
359	C₂³×C₂₃	—	4	2	no	—
360	C₂³×C₂₃	—	4	4	no	—
361	C₂³×C₂₃	—	4	4	no	—
362	C₂³×C₂₃	—	4	4	no	—
363	C₂³×C₂₃	—	4	4	no	—
364	C₂³×C₂₃	—	8	2	no	—
365	C₂³×C₂₃	—	8	2	no	—
366	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
367	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
368	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
369	Q₈×C₂₃	—	2	4	no	—
370	Q₈×C₂₃	—	2	2	no	—
371	Q₈×C₂₃	—	2	2	no	—
372	Q₈×C₂₃	—	8	1	no	—
373	Q₈×C₂₃	H(5,𝔽₂)	1	4	yes	—
374	D₄×C₂₃	—	2	2	no	—
375	D₄×C₂₃	—	2	2	no	—
376	D₄×C₂₃	—	2	2	no	—
377	D₄×C₂₃	—	2	4	no	—
378	D₄×C₂₃	—	2	4	no	—
379	D₄×C₂₃	—	2	4	no	—
380	D₄×C₂₃	—	4	2	no	—
381	D₄×C₂₃	—	4	8	no	—
382	D₄×C₂₃	—	4	8	no	—
383	D₄×C₂₃	—	4	4	no	—
384	D₄×C₂₃	—	4	4	no	—
385	D₄×C₂₃	—	4	4	no	—
386	D₄×C₂₃	—	4	2	no	—
387	D₄×C₂₃	—	4	4	no	—
388	D₄×C₂₃	—	4	2	no	—
389	D₄×C₂₃	—	4	4	no	—
390	D₄×C₂₃	—	8	2	no	—
391	D₄×C₂₃	—	8	2	no	—
392	D₄×C₂₃	—	8	2	no	—
393	D₄×C₂₃	—	8	1	no	—
394	D₄×C₂₃	—	8	4	no	—
395	D₄×C₂₃	—	8	4	no	—
396	D₄×C₂₃	—	8	2	no	—
397	D₄×C₂₃	—	8	2	no	—
398	D₄×C₂₃	—	8	2	no	—
399	C₂×C₄×C₂₃	—	2	4	no	—
400	C₂×C₄×C₂₃	—	2	2	no	—
401	C₂×C₄×C₂₃	—	2	2	no	—
402	C₂×C₄×C₂₃	—	2	2	no	—
403	C₂×C₄×C₂₃	—	2	4	no	—
404	C₂×C₄×C₂₃	—	2	4	no	—
405	C₂×C₄×C₂₃	—	2	2	no	—
406	C₂×C₄×C₂₃	—	2	1	no	—
407	C₂×C₄×C₂₃	—	2	2	no	—
408	C₂×C₄×C₂₃	—	2	1	no	—
409	C₂×C₄×C₂₃	—	2	2	no	—
410	C₂×C₄×C₂₃	—	2	1	no	—
411	C₂×C₄×C₂₃	—	4	2	no	—
412	C₂×C₄×C₂₃	—	4	2	no	—
413	C₂×C₄×C₂₃	—	4	2	no	—
414	C₂×C₄×C₂₃	—	4	8	no	—
415	C₂×C₄×C₂₃	—	4	8	no	—
416	C₂×C₄×C₂₃	—	4	2	no	—
417	C₂×C₄×C₂₃	—	4	2	no	—
418	C₂×C₄×C₂₃	—	8	2	no	—
419	C₂×C₄×C₂₃	—	8	2	no	—
420	C₂×C₄×C₂₃	—	8	2	no	—
421	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
422	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
423	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
424	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
425	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
426	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
427	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
428	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
429	C₈×C₂₃	—	2	2	no	—
430	C₈×C₂₃	—	2	4	no	—
431	C₈×C₂₃	—	2	2	no	—
432	#3519	C₂×C₂₃	1	1	yes	characteristic, complemented
433	C₂×#550	C₂×C₂₃	1	1	yes	characteristic, complemented
434	#3333	C₂×C₂₃	1	2	yes	complemented
435	#3309	C₂×C₂₃	1	4	yes	complemented
436	#3305	C₂×C₂₃	1	2	yes	complemented
437	#3287	C₂×C₂₃	1	2	yes	complemented
438	#3274	C₂×C₂₃	1	2	yes	complemented
439	#3268	C₂×C₂₃	1	4	yes	complemented
440	#3217	C₂×C₂₃	1	1	yes	characteristic, complemented
441	#3205	C₂×C₂₃	1	1	yes	characteristic, complemented
442	#3194	C₂×C₂₃	1	2	yes	complemented
443	#3186	C₂×C₂₃	1	2	yes	complemented
444	#3112	C₂×C₂₃	1	1	yes	characteristic, complemented
445	#3108	C₂×C₂₃	1	1	yes	characteristic, complemented
446	#3006	C₂×C₂₃	1	2	yes	complemented
447	#3002	C₂×C₂₃	1	2	yes	complemented
448	#2974	C₂×C₂₃	1	1	yes	characteristic, complemented
449	C₂²×C₂₃	—	2	1	no	—
450	C₂²×C₂₃	—	2	1	no	—
451	C₂²×C₂₃	—	2	2	no	—
452	C₂²×C₂₃	—	2	2	no	—
453	C₂²×C₂₃	—	2	2	no	—
454	C₂²×C₂₃	—	2	2	no	—
455	C₂²×C₂₃	—	2	2	no	—
456	C₂²×C₂₃	—	2	2	no	—
457	C₂²×C₂₃	—	4	4	no	—
458	C₂²×C₂₃	—	4	2	no	—
459	C₂²×C₂₃	—	4	1	no	—
460	C₂²×C₂₃	—	4	1	no	—
461	C₂²×C₂₃	—	4	4	no	—
462	C₂²×C₂₃	—	4	2	no	—
463	C₂²×C₂₃	—	4	2	no	—
464	C₂²×C₂₃	—	4	1	no	—
465	C₂²×C₂₃	—	4	4	no	—
466	C₂²×C₂₃	—	8	4	no	—
467	C₂²×C₂₃	—	8	8	no	—
468	C₂²×C₂₃	—	16	4	no	—
469	C₂²×C₂₃	#576	1	2	yes	—
470	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
471	C₄×C₂₃	—	2	4	no	—
472	C₄×C₂₃	—	2	2	no	—
473	C₄×C₂₃	—	2	2	no	—
474	C₄×C₂₃	—	2	1	no	—
475	C₄×C₂₃	—	2	1	no	—
476	C₄×C₂₃	—	2	1	no	—
477	C₄×C₂₃	—	2	1	no	—
478	C₄×C₂₃	—	4	1	no	—
479	C₄×C₂₃	—	4	1	no	—
480	C₄×C₂₃	—	4	2	no	—
481	C₄×C₂₃	—	4	1	no	—
482	C₄×C₂₃	—	4	2	no	—
483	C₄×C₂₃	#575	1	2	yes	—
484	C₄×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
485	C₂²×#41	C₂²×C₂₃	1	2	yes	complemented
486	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	4	yes	complemented
487	C₂×#135	C₂²×C₂₃	1	4	yes	complemented
488	#555	C₂²×C₂₃	1	1	yes	characteristic, complemented
489	#554	C₂²×C₂₃	1	1	yes	characteristic, complemented
490	#553	—	2	1	no	—
491	#553	C₂²×C₂₃	1	2	yes	complemented
492	#550	—	2	1	no	—
493	#550	—	2	1	no	—
494	#550	—	2	2	no	—
495	#550	C₂²×C₂₃	1	2	yes	—
496	#550	C₂²×C₂₃	1	4	yes	complemented
497	#550	C₂²×C₂₃	1	2	yes	complemented
498	#550	C₂²×C₂₃	1	1	yes	characteristic, complemented
499	#546	—	2	2	no	—
500	#546	C₂²×C₂₃	1	2	yes	complemented
501	D₄²	—	2	1	no	—
502	D₄²	C₂²×C₂₃	1	1	yes	characteristic, complemented
503	#540	—	2	1	no	—
504	#538	—	2	2	no	—
505	#532	C₂²×C₂₃	1	1	yes	characteristic
506	C₂×#127	—	2	1	no	—
507	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic, complemented
508	#529	C₂²×C₂₃	1	1	yes	characteristic
509	#525	C₂²×C₂₃	1	2	yes	—
510	C₂×#121	—	2	2	no	—
511	C₂×#121	C₂²×C₂₃	1	2	yes	—
512	C₂×#121	C₂²×C₂₃	1	2	yes	complemented
513	#518	—	2	1	no	—
514	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
515	C₂×C₄×D₄	—	2	1	no	—
516	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
517	#496	C₂²×C₂₃	1	2	yes	complemented
518	#493	C₂²×C₂₃	1	2	yes	complemented
519	#490	C₂²×C₂₃	1	2	yes	complemented
520	#486	C₂²×C₂₃	1	2	yes	complemented
521	#483	C₂²×C₂₃	1	1	yes	characteristic, complemented
522	#482	C₂²×C₂₃	1	4	yes	complemented
523	#480	C₂²×C₂₃	1	1	yes	characteristic
524	#480	C₂²×C₂₃	1	4	yes	complemented
525	#480	C₂²×C₂₃	1	2	yes	complemented
526	#479	C₂²×C₂₃	1	2	yes	complemented
527	#477	C₂²×C₂₃	1	2	yes	complemented
528	#469	C₂²×C₂₃	1	4	yes	complemented
529	#468	C₂²×C₂₃	1	4	yes	complemented
530	#466	C₂²×C₂₃	1	4	yes	complemented
531	#466	C₂²×C₂₃	1	4	yes	complemented
532	#464	C₂²×C₂₃	1	2	yes	complemented
533	#460	C₂²×C₂₃	1	2	yes	complemented
534	#460	C₂²×C₂₃	1	2	yes	complemented
535	#459	C₂²×C₂₃	1	4	yes	complemented
536	#459	C₂²×C₂₃	1	2	yes	complemented
537	#452	C₂²×C₂₃	1	4	yes	complemented
538	#451	C₂²×C₂₃	1	1	yes	characteristic, complemented
539	#450	C₂²×C₂₃	1	2	yes	complemented
540	#449	C₂²×C₂₃	1	4	yes	complemented
541	#449	C₂²×C₂₃	1	4	yes	complemented
542	#449	C₂²×C₂₃	1	4	yes	complemented
543	#449	C₂²×C₂₃	1	4	yes	complemented
544	#448	C₂²×C₂₃	1	1	yes	characteristic
545	#448	C₂²×C₂₃	1	2	yes	complemented
546	#447	C₂²×C₂₃	1	2	yes	—
547	#447	C₂²×C₂₃	1	2	yes	complemented
548	#447	C₂²×C₂₃	1	4	yes	complemented
549	#447	C₂²×C₂₃	1	2	yes	complemented
550	#440	C₂²×C₂₃	1	4	yes	complemented
551	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
552	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
553	#436	C₂²×C₂₃	1	2	yes	complemented
554	#435	C₂²×C₂₃	1	4	yes	complemented
555	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
556	#432	C₂²×C₂₃	1	1	yes	characteristic, complemented
557	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
558	#417	C₂²×C₂₃	1	4	yes	complemented
559	#416	C₂²×C₂₃	1	4	yes	complemented
560	#407	C₂²×C₂₃	1	2	yes	complemented
561	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	complemented
562	C₂×C₂₃	—	2	2	no	—
563	C₂×C₂₃	—	4	2	no	—
564	C₂×C₂₃	—	4	2	no	—
565	C₂×C₂₃	—	8	4	no	—
566	C₂×C₂₃	—	8	2	no	—
567	C₂×C₂₃	—	8	1	no	—
568	C₂×C₂₃	#3484	1	1	yes	characteristic
569	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
570	C₂×C₂₃	C₂×#576	1	1	yes	characteristic
571	C₂×#41	—	2	2	no	—
572	C₂×#41	—	2	2	no	—
573	C₂×#41	—	2	1	no	—
574	C₂×#41	—	4	8	no	—
575	C₂×#41	C₂³×C₂₃	1	4	yes	—
576	C₂×#41	C₂³×C₂₃	1	4	yes	—
577	C₂×#41	C₂³×C₂₃	1	2	yes	—
578	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
579	C₂²×D₄	—	2	2	no	—
580	C₂²×D₄	—	2	2	no	—
581	C₂²×D₄	—	2	2	no	—
582	C₂²×D₄	—	2	1	no	—
583	C₂²×D₄	—	2	1	no	—
584	C₂²×D₄	—	2	1	no	—
585	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
586	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
587	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
588	C₂³×C₄	—	2	2	no	—
589	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
590	AGL(1,ℤ/8)	—	4	8	no	—
591	#135	—	4	8	no	—
592	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
593	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
594	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
595	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
596	C₂×D₈	C₂³×C₂₃	1	4	yes	—
597	C₂×D₈	C₂³×C₂₃	1	4	yes	—
598	C₂×D₈	C₂³×C₂₃	1	4	yes	—
599	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
600	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
601	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
602	#127	—	2	2	no	—
603	#127	—	2	2	no	—
604	#127	—	2	4	no	—
605	#127	—	2	1	no	—
606	#127	—	2	1	no	—
607	#127	—	2	1	no	—
608	#127	C₂³×C₂₃	1	2	yes	—
609	#127	C₂³×C₂₃	1	2	yes	—
610	#127	C₂³×C₂₃	1	1	yes	characteristic
611	#126	—	2	2	no	—
612	#126	—	2	1	no	—
613	#125	—	2	1	no	—
614	#125	C₂³×C₂₃	1	1	yes	characteristic
615	#124	—	2	2	no	—
616	#124	—	2	1	no	—
617	#124	C₂³×C₂₃	1	1	yes	characteristic
618	#123	—	2	2	no	—
619	#123	—	2	1	no	—
620	#123	—	2	2	no	—
621	#123	—	2	2	no	—
622	C₂²⋊Q₈	—	2	2	no	—
623	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
624	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
625	#121	—	2	2	no	—
626	#121	—	2	1	no	—
627	#121	—	2	2	no	—
628	#121	—	2	2	no	—
629	#121	—	2	2	no	—
630	#121	—	2	2	no	—
631	#121	—	2	1	no	—
632	#121	—	2	1	no	—
633	#121	—	2	4	no	—
634	#121	—	2	4	no	—
635	#121	—	2	4	no	—
636	#121	—	2	4	no	—
637	#121	—	2	2	no	—
638	#121	—	2	2	no	—
639	#121	C₂³×C₂₃	1	1	yes	characteristic
640	#121	C₂³×C₂₃	1	2	yes	—
641	#121	C₂³×C₂₃	1	2	yes	—
642	#121	C₂³×C₂₃	1	2	yes	—
643	#121	C₂³×C₂₃	1	4	yes	—
644	#121	C₂³×C₂₃	1	4	yes	—
645	#121	C₂³×C₂₃	1	2	yes	—
646	#120	—	2	2	no	—
647	#120	—	2	2	no	—
648	#120	—	2	2	no	—
649	C₄×Q₈	—	2	1	no	—
650	C₄×Q₈	—	2	1	no	—
651	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
652	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
653	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
654	C₄×D₄	—	2	1	no	—
655	C₄×D₄	—	2	2	no	—
656	C₄×D₄	—	2	2	no	—
657	C₄×D₄	—	2	1	no	—
658	C₄×D₄	—	2	2	no	—
659	C₄×D₄	—	2	2	no	—
660	C₄×D₄	—	2	4	no	—
661	C₄×D₄	—	2	1	no	—
662	C₄×D₄	—	2	2	no	—
663	C₄×D₄	—	2	1	no	—
664	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
665	C₄×D₄	D₄×C₂₃	1	2	yes	—
666	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
667	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
668	C₄×D₄	C₂³×C₂₃	1	2	yes	—
669	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
670	C₄×D₄	C₂³×C₂₃	1	2	yes	—
671	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
672	#117	—	2	1	no	—
673	#117	—	2	1	no	—
674	#117	C₂³×C₂₃	1	2	yes	—
675	C₂×C₄⋊C₄	—	2	1	no	—
676	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
677	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
678	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
679	C₂×C₂²⋊C₄	—	2	2	no	—
680	C₂×C₂²⋊C₄	—	2	2	no	—
681	C₂×C₂²⋊C₄	—	2	2	no	—
682	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
683	C₂×C₄²	—	2	1	no	—
684	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
685	#107	C₂³×C₂₃	1	2	yes	—
686	#107	C₂³×C₂₃	1	4	yes	—
687	#106	C₂³×C₂₃	1	2	yes	—
688	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
689	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
690	#103	C₂³×C₂₃	1	2	yes	—
691	#103	C₂³×C₂₃	1	4	yes	—
692	#103	C₂³×C₂₃	1	2	yes	—
693	#103	C₂³×C₂₃	1	2	yes	—
694	#102	C₂³×C₂₃	1	4	yes	—
695	#102	C₂³×C₂₃	1	4	yes	—
696	#102	C₂³×C₂₃	1	4	yes	—
697	#102	C₂³×C₂₃	1	4	yes	—
698	#102	C₂³×C₂₃	1	2	yes	—
699	#102	C₂³×C₂₃	1	4	yes	—
700	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
701	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
702	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
703	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
704	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
705	#97	C₂³×C₂₃	1	2	yes	—
706	C₄×C₈	C₂³×C₂₃	1	2	yes	—
707	C₂₃	#61605	1	1	yes	characteristic, direct product factor, Sylow
708	C₂⁴	—	2	2	no	—
709	C₂⁴	—	2	2	no	—
710	C₂⁴	C₂×D₄×C₂₃	1	2	yes	—
711	#41	—	2	8	no	—
712	#41	—	2	8	no	—
713	#41	—	4	4	no	—
714	#41	—	4	4	no	—
715	#41	—	4	4	no	—
716	#41	—	4	8	no	—
717	#41	—	4	8	no	—
718	#41	—	8	2	no	—
719	C₂×Q₈	—	2	4	no	—
720	C₂×Q₈	—	2	1	no	—
721	C₂×Q₈	—	2	1	no	—
722	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
723	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
724	C₂×D₄	—	2	2	no	—
725	C₂×D₄	—	2	2	no	—
726	C₂×D₄	—	2	1	no	—
727	C₂×D₄	—	2	4	no	—
728	C₂×D₄	—	2	4	no	—
729	C₂×D₄	—	2	2	no	—
730	C₂×D₄	—	2	2	no	—
731	C₂×D₄	—	2	2	no	—
732	C₂×D₄	—	2	4	no	—
733	C₂×D₄	—	2	4	no	—
734	C₂×D₄	—	2	1	no	—
735	C₂×D₄	—	2	2	no	—
736	C₂×D₄	—	2	2	no	—
737	C₂×D₄	—	2	2	no	—
738	C₂×D₄	—	2	1	no	—
739	C₂×D₄	—	2	2	no	—
740	C₂×D₄	—	2	2	no	—
741	C₂×D₄	—	2	2	no	—
742	C₂×D₄	—	4	2	no	—
743	C₂×D₄	—	4	4	no	—
744	C₂×D₄	—	4	4	no	—
745	C₂×D₄	—	4	8	no	—
746	C₂×D₄	—	4	4	no	—
747	C₂×D₄	—	4	4	no	—
748	C₂×D₄	—	8	2	no	—
749	C₂×D₄	—	8	4	no	—
750	C₂×D₄	—	8	4	no	—
751	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
752	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
753	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
754	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
755	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
756	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
757	C₂²×C₄	—	2	1	no	—
758	C₂²×C₄	—	2	1	no	—
759	C₂²×C₄	—	2	2	no	—
760	C₂²×C₄	—	2	1	no	—
761	C₂²×C₄	—	2	4	no	—
762	C₂²×C₄	—	2	4	no	—
763	C₂²×C₄	—	2	2	no	—
764	C₂²×C₄	—	2	2	no	—
765	C₂²×C₄	—	4	4	no	—
766	C₂²×C₄	—	4	8	no	—
767	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
768	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
769	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
770	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
771	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
772	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
773	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
774	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
775	Q₁₆	—	2	4	no	—
776	SD₁₆	—	2	8	no	—
777	SD₁₆	—	2	4	no	—
778	SD₁₆	—	4	4	no	—
779	D₈	—	4	4	no	—
780	D₈	—	4	4	no	—
781	D₈	—	4	4	no	—
782	M₁₆	—	4	4	no	—
783	C₂×C₈	—	4	4	no	—
784	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
785	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
786	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	1	no	—
790	C₄⋊C₄	—	2	2	no	—
791	C₄⋊C₄	—	2	1	no	—
792	C₄⋊C₄	—	2	1	no	—
793	C₄⋊C₄	—	2	1	no	—
794	C₄⋊C₄	—	2	1	no	—
795	C₄⋊C₄	—	2	2	no	—
796	C₄⋊C₄	—	2	1	no	—
797	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
798	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
799	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
800	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
801	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
802	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
803	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	—	2	2	no	—
806	C₂²⋊C₄	—	2	1	no	—
807	C₂²⋊C₄	—	2	1	no	—
808	C₂²⋊C₄	—	2	1	no	—
809	C₂²⋊C₄	—	2	2	no	—
810	C₂²⋊C₄	—	2	4	no	—
811	C₂²⋊C₄	—	2	4	no	—
812	C₂²⋊C₄	—	2	2	no	—
813	C₂²⋊C₄	—	2	2	no	—
814	C₂²⋊C₄	—	2	1	no	—
815	C₂²⋊C₄	—	2	2	no	—
816	C₂²⋊C₄	—	2	1	no	—
817	C₂²⋊C₄	—	2	2	no	—
818	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
819	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
820	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
821	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
822	C₄²	—	2	2	no	—
823	C₄²	—	2	2	no	—
824	C₄²	—	2	2	no	—
825	C₄²	—	2	1	no	—
826	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
827	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
828	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
829	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
830	C₂³	—	2	4	no	—
831	C₂³	—	2	1	no	—
832	C₂³	—	2	2	no	—
833	C₂³	—	2	4	no	—
834	C₂³	—	4	2	no	—
835	C₂³	—	4	2	no	—
836	C₂³	—	4	4	no	—
837	C₂³	—	4	4	no	—
838	C₂³	—	4	4	no	—
839	C₂³	—	4	4	no	—
840	C₂³	—	8	2	no	—
841	C₂³	—	8	2	no	—
842	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
843	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
844	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
845	Q₈	—	2	4	no	—
846	Q₈	—	2	2	no	—
847	Q₈	—	2	2	no	—
848	Q₈	—	8	1	no	—
849	Q₈	C₂₃×H(5,𝔽₂)	1	4	yes	—
850	D₄	—	2	2	no	—
851	D₄	—	2	2	no	—
852	D₄	—	2	2	no	—
853	D₄	—	2	4	no	—
854	D₄	—	2	4	no	—
855	D₄	—	2	4	no	—
856	D₄	—	4	2	no	—
857	D₄	—	4	8	no	—
858	D₄	—	4	8	no	—
859	D₄	—	4	4	no	—
860	D₄	—	4	4	no	—
861	D₄	—	4	4	no	—
862	D₄	—	4	2	no	—
863	D₄	—	4	4	no	—
864	D₄	—	4	2	no	—
865	D₄	—	4	4	no	—
866	D₄	—	8	2	no	—
867	D₄	—	8	2	no	—
868	D₄	—	8	2	no	—
869	D₄	—	8	1	no	—
870	D₄	—	8	4	no	—
871	D₄	—	8	4	no	—
872	D₄	—	8	2	no	—
873	D₄	—	8	2	no	—
874	D₄	—	8	2	no	—
875	C₂×C₄	—	2	4	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	4	no	—
880	C₂×C₄	—	2	4	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	4	2	no	—
888	C₂×C₄	—	4	2	no	—
889	C₂×C₄	—	4	2	no	—
890	C₂×C₄	—	4	8	no	—
891	C₂×C₄	—	4	8	no	—
892	C₂×C₄	—	4	2	no	—
893	C₂×C₄	—	4	2	no	—
894	C₂×C₄	—	8	2	no	—
895	C₂×C₄	—	8	2	no	—
896	C₂×C₄	—	8	2	no	—
897	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
898	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
899	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
900	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
901	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
902	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
903	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
904	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
905	C₈	—	2	2	no	—
906	C₈	—	2	4	no	—
907	C₈	—	2	2	no	—
908	C₂²	—	2	1	no	—
909	C₂²	—	2	1	no	—
910	C₂²	—	2	2	no	—
911	C₂²	—	2	2	no	—
912	C₂²	—	2	2	no	—
913	C₂²	—	2	2	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	2	2	no	—
916	C₂²	—	4	4	no	—
917	C₂²	—	4	2	no	—
918	C₂²	—	4	1	no	—
919	C₂²	—	4	1	no	—
920	C₂²	—	4	4	no	—
921	C₂²	—	4	2	no	—
922	C₂²	—	4	2	no	—
923	C₂²	—	4	1	no	—
924	C₂²	—	4	4	no	—
925	C₂²	—	8	4	no	—
926	C₂²	—	8	8	no	—
927	C₂²	—	16	4	no	—
928	C₂²	C₂₃×#576	1	2	yes	—
929	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
930	C₄	—	2	4	no	—
931	C₄	—	2	2	no	—
932	C₄	—	2	2	no	—
933	C₄	—	2	1	no	—
934	C₄	—	2	1	no	—
935	C₄	—	2	1	no	—
936	C₄	—	2	1	no	—
937	C₄	—	4	1	no	—
938	C₄	—	4	1	no	—
939	C₄	—	4	2	no	—
940	C₄	—	4	1	no	—
941	C₄	—	4	2	no	—
942	C₄	C₂₃×#575	1	2	yes	—
943	C₄	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
944	C₂	—	2	2	no	—
945	C₂	—	4	2	no	—
946	C₂	—	4	2	no	—
947	C₂	—	8	4	no	—
948	C₂	—	8	1	no	—
949	C₂	—	8	2	no	—
950	C₂	C₂₃×#3484	1	1	yes	characteristic
951	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
952	C₂	C₂×C₂₃×#576	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×#3519	C₂	semidirect
2. C₂×C₂₃×#550	C₂	semidirect
3. C₂₃×#3333	C₂	semidirect
4. C₂₃×#3309	C₂	semidirect
5. C₂₃×#3305	C₂	semidirect
6. C₂₃×#3287	C₂	semidirect
7. C₂₃×#3274	C₂	semidirect
8. C₂₃×#3268	C₂	semidirect
9. C₂₃×#3217	C₂	semidirect
10. C₂₃×#3205	C₂	semidirect
11. C₂₃×#3194	C₂	semidirect
12. C₂₃×#3186	C₂	semidirect
13. C₂₃×#3112	C₂	semidirect
14. C₂₃×#3108	C₂	semidirect
15. C₂₃×#3006	C₂	semidirect
16. C₂₃×#3002	C₂	semidirect
17. C₂₃×#2974	C₂	semidirect
18. C₂²×#41×C₂₃	C₂²	semidirect
19. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
20. C₂×C₂₃×#135	C₂²	semidirect
21. C₂₃×#555	C₂²	semidirect
22. C₂₃×#554	C₂²	semidirect
24. C₂₃×#553	C₂²	semidirect
29. C₂₃×#550	C₂²	semidirect
30. C₂₃×#550	C₂²	semidirect
31. C₂₃×#550	C₂²	semidirect
33. C₂₃×#546	C₂²	semidirect
35. D₄²×C₂₃	C₂²	semidirect
40. C₂×C₂₃×#127	C₂²	semidirect
45. C₂×C₂₃×#121	C₂²	semidirect
47. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
50. C₂₃×#496	C₂²	semidirect
51. C₂₃×#493	C₂²	semidirect
52. C₂₃×#490	C₂²	semidirect
53. C₂₃×#486	C₂²	semidirect
54. C₂₃×#483	C₂²	semidirect
55. C₂₃×#482	C₂²	semidirect
57. C₂₃×#480	C₂²	semidirect
58. C₂₃×#480	C₂²	semidirect
59. C₂₃×#479	C₂²	semidirect
60. C₂₃×#477	C₂²	semidirect
61. C₂₃×#469	C₂²	semidirect
62. C₂₃×#468	C₂²	semidirect
63. C₂₃×#466	C₂²	semidirect
64. C₂₃×#466	C₂²	semidirect
65. C₂₃×#464	C₂²	semidirect
66. C₂₃×#460	C₂²	semidirect
67. C₂₃×#460	C₂²	semidirect
68. C₂₃×#459	C₂²	semidirect
69. C₂₃×#459	C₂²	semidirect
70. C₂₃×#452	C₂²	semidirect
71. C₂₃×#451	C₂²	semidirect
72. C₂₃×#450	C₂²	semidirect
73. C₂₃×#449	C₂²	semidirect
74. C₂₃×#449	C₂²	semidirect
75. C₂₃×#449	C₂²	semidirect
76. C₂₃×#449	C₂²	semidirect
78. C₂₃×#448	C₂²	semidirect
80. C₂₃×#447	C₂²	semidirect
81. C₂₃×#447	C₂²	semidirect
82. C₂₃×#447	C₂²	semidirect
83. C₂₃×#440	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
89. C₂₃×#432	C₂²	semidirect
90. C₂₃×#431	C₂²	semidirect
91. C₂₃×#417	C₂²	semidirect
92. C₂₃×#416	C₂²	semidirect
93. C₂₃×#407	C₂²	semidirect
94. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
353. #61605	C₂₃	direct (N × H)
432. #3519	C₂×C₂₃	semidirect
433. C₂×#550	C₂×C₂₃	semidirect
434. #3333	C₂×C₂₃	semidirect
435. #3309	C₂×C₂₃	semidirect
436. #3305	C₂×C₂₃	semidirect
437. #3287	C₂×C₂₃	semidirect
438. #3274	C₂×C₂₃	semidirect
439. #3268	C₂×C₂₃	semidirect
440. #3217	C₂×C₂₃	semidirect
441. #3205	C₂×C₂₃	semidirect
442. #3194	C₂×C₂₃	semidirect
443. #3186	C₂×C₂₃	semidirect
444. #3112	C₂×C₂₃	semidirect
445. #3108	C₂×C₂₃	semidirect
446. #3006	C₂×C₂₃	semidirect
447. #3002	C₂×C₂₃	semidirect
448. #2974	C₂×C₂₃	semidirect
485. C₂²×#41	C₂²×C₂₃	semidirect
486. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
487. C₂×#135	C₂²×C₂₃	semidirect
488. #555	C₂²×C₂₃	semidirect
489. #554	C₂²×C₂₃	semidirect
491. #553	C₂²×C₂₃	semidirect
496. #550	C₂²×C₂₃	semidirect
497. #550	C₂²×C₂₃	semidirect
498. #550	C₂²×C₂₃	semidirect
500. #546	C₂²×C₂₃	semidirect
502. D₄²	C₂²×C₂₃	semidirect
507. C₂×#127	C₂²×C₂₃	semidirect
512. C₂×#121	C₂²×C₂₃	semidirect
514. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
517. #496	C₂²×C₂₃	semidirect
518. #493	C₂²×C₂₃	semidirect
519. #490	C₂²×C₂₃	semidirect
520. #486	C₂²×C₂₃	semidirect
521. #483	C₂²×C₂₃	semidirect
522. #482	C₂²×C₂₃	semidirect
524. #480	C₂²×C₂₃	semidirect
525. #480	C₂²×C₂₃	semidirect
526. #479	C₂²×C₂₃	semidirect
527. #477	C₂²×C₂₃	semidirect
528. #469	C₂²×C₂₃	semidirect
529. #468	C₂²×C₂₃	semidirect
530. #466	C₂²×C₂₃	semidirect
531. #466	C₂²×C₂₃	semidirect
532. #464	C₂²×C₂₃	semidirect
533. #460	C₂²×C₂₃	semidirect
534. #460	C₂²×C₂₃	semidirect
535. #459	C₂²×C₂₃	semidirect
536. #459	C₂²×C₂₃	semidirect
537. #452	C₂²×C₂₃	semidirect
538. #451	C₂²×C₂₃	semidirect
539. #450	C₂²×C₂₃	semidirect
540. #449	C₂²×C₂₃	semidirect
541. #449	C₂²×C₂₃	semidirect
542. #449	C₂²×C₂₃	semidirect
543. #449	C₂²×C₂₃	semidirect
545. #448	C₂²×C₂₃	semidirect
547. #447	C₂²×C₂₃	semidirect
548. #447	C₂²×C₂₃	semidirect
549. #447	C₂²×C₂₃	semidirect
550. #440	C₂²×C₂₃	semidirect
551. C₄×Q₁₆	C₂²×C₂₃	semidirect
552. C₄×SD₁₆	C₂²×C₂₃	semidirect
553. #436	C₂²×C₂₃	semidirect
554. #435	C₂²×C₂₃	semidirect
555. C₈×D₄	C₂²×C₂₃	semidirect
556. #432	C₂²×C₂₃	semidirect
557. #431	C₂²×C₂₃	semidirect
558. #417	C₂²×C₂₃	semidirect
559. #416	C₂²×C₂₃	semidirect
560. #407	C₂²×C₂₃	semidirect
561. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
707. C₂₃	#61605	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×#3519	2
C₂×C₂₃×#550	2
C₂₃×#3333	2
C₂₃×#3309	2
C₂₃×#3305	2
C₂₃×#3287	2
C₂₃×#3274	2
C₂₃×#3268	2
C₂₃×#3217	2
C₂₃×#3205	2
C₂₃×#3194	2
C₂₃×#3186	2
C₂₃×#3112	2
C₂₃×#3108	2
C₂₃×#3006	2
C₂₃×#3002	2
C₂₃×#2974	2
#61605	23

Subgroups — C23×#61605 #19209231

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61605 #19209231