Subgroups — C₂₃×#61726 #19209352

Order 5888.

1860 conjugacy classes of subgroups.

The subgroup lattice has 890 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
2	C₂×C₂₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3357	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3346	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3338	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3333	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3314	C₂	1	4	yes	maximal, complemented
8	C₂₃×#3295	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3238	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3226	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3193	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3190	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×#3092	C₂	1	2	yes	maximal, complemented
16	C₂×C₂₃×#480	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2974	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#555	C₂²	1	1	yes	characteristic
19	C₂₃×#554	—	2	1	no	—
20	C₂₃×#554	—	2	2	no	—
21	C₂₃×#554	—	2	1	no	—
22	C₂₃×#554	C₂²	1	2	yes	—
23	C₂₃×#554	C₂²	1	1	yes	characteristic
24	C₂₃×#554	C₂²	1	4	yes	complemented
25	C₂₃×#554	C₂²	1	2	yes	complemented
26	C₂₃×#553	—	2	1	no	—
27	C₂₃×#553	C₂²	1	2	yes	—
28	C₂₃×#550	C₂²	1	1	yes	characteristic
29	C₂₃×#546	—	2	2	no	—
30	C₂₃×#546	C₂²	1	2	yes	—
31	D₄²×C₂₃	—	2	1	no	—
32	D₄²×C₂₃	C₂²	1	1	yes	characteristic
33	C₂₃×#540	—	2	1	no	—
34	C₂₃×#538	—	2	2	no	—
35	C₂₃×#532	C₂²	1	1	yes	characteristic
36	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₂₃×#529	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×#125	—	2	1	no	—
39	C₂₃×#525	C₂²	1	2	yes	—
40	C₂×C₂₃×C₂²⋊Q₈	—	2	2	no	—
41	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
42	C₂×C₂₃×#121	C₂²	1	2	yes	—
43	C₂₃×#518	—	2	1	no	—
44	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₄×D₄×C₂₃	—	2	1	no	—
46	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
47	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
48	C₂₃×#501	C₂²	1	2	yes	complemented
49	C₂₃×#500	C₂²	1	2	yes	complemented
50	C₂₃×#489	C₂²	1	2	yes	complemented
51	C₂₃×#486	C₂²	1	2	yes	complemented
52	C₂₃×#485	C₂²	1	4	yes	complemented
53	C₂₃×#484	C₂²	1	4	yes	complemented
54	C₂₃×#484	C₂²	1	4	yes	complemented
55	C₂₃×#483	C₂²	1	2	yes	complemented
56	C₂₃×#483	C₂²	1	1	yes	characteristic, complemented
57	C₂₃×#481	C₂²	1	4	yes	complemented
58	C₂₃×#480	C₂²	1	2	yes	—
59	C₂₃×#480	C₂²	1	1	yes	characteristic
60	C₂₃×#480	C₂²	1	2	yes	complemented
61	C₂₃×#480	C₂²	1	2	yes	complemented
62	C₂₃×#480	C₂²	1	4	yes	complemented
63	C₂₃×#480	C₂²	1	4	yes	complemented
64	C₂₃×#480	C₂²	1	2	yes	complemented
65	C₂₃×#479	C₂²	1	2	yes	complemented
66	C₂₃×#477	C₂²	1	2	yes	complemented
67	C₂₃×#477	C₂²	1	2	yes	complemented
68	C₂₃×#476	C₂²	1	2	yes	complemented
69	C₂₃×#474	C₂²	1	4	yes	complemented
70	C₂₃×#468	C₂²	1	4	yes	complemented
71	C₂₃×#468	C₂²	1	4	yes	complemented
72	C₂₃×#467	C₂²	1	4	yes	complemented
73	C₂₃×#465	C₂²	1	4	yes	complemented
74	C₂₃×#464	C₂²	1	2	yes	complemented
75	C₂₃×#460	C₂²	1	2	yes	complemented
76	C₂₃×#452	C₂²	1	4	yes	complemented
77	C₂₃×#451	C₂²	1	1	yes	characteristic, complemented
78	C₂₃×#450	C₂²	1	4	yes	complemented
79	C₂₃×#448	C₂²	1	1	yes	characteristic
80	C₂₃×#448	C₂²	1	2	yes	complemented
81	C₂₃×#440	C₂²	1	4	yes	complemented
82	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
83	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
84	C₂₃×#436	C₂²	1	2	yes	complemented
85	C₂₃×#435	C₂²	1	4	yes	complemented
86	C₈×D₄×C₂₃	C₂²	1	2	yes	—
87	C₂₃×#432	C₂²	1	1	yes	characteristic, complemented
88	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
89	C₂₃×#428	C₂²	1	4	yes	complemented
90	C₂×C₂₃×#107	C₂²	1	4	yes	complemented
91	C₂₃×#417	C₂²	1	4	yes	complemented
92	C₂×C₂₃×#102	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	1	no	—
96	C₂×#41×C₂₃	C₂³	1	2	yes	—
97	C₂²×Q₈×C₂₃	—	2	1	no	—
98	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
99	C₂²×D₄×C₂₃	—	2	2	no	—
100	C₂²×D₄×C₂₃	—	2	1	no	—
101	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
102	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
103	C₂³×C₄×C₂₃	—	2	2	no	—
104	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
105	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
106	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
107	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
108	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
109	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
110	C₂₃×C₄⋊Q₈	—	2	1	no	—
111	C₂₃×C₄⋊Q₈	—	2	1	no	—
112	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
113	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
115	C₂₃×#127	—	2	1	no	—
116	C₂₃×#127	C₂³	1	1	yes	characteristic
117	C₂₃×#126	—	2	2	no	—
118	C₂₃×#126	—	2	1	no	—
119	C₂₃×#125	—	2	1	no	—
120	C₂₃×#125	—	2	2	no	—
121	C₂₃×#125	—	2	2	no	—
122	C₂₃×#125	—	2	4	no	—
123	C₂₃×#125	C₂³	1	1	yes	characteristic
124	C₂₃×#124	—	2	2	no	—
125	C₂₃×#124	—	2	1	no	—
126	C₂₃×#124	C₂³	1	1	yes	characteristic
127	C₂₃×#123	—	2	2	no	—
128	C₂₃×#123	—	2	1	no	—
129	C₂₃×#123	—	2	2	no	—
130	C₂₃×#123	—	2	2	no	—
131	C₂₃×C₂²⋊Q₈	—	2	2	no	—
132	C₂₃×C₂²⋊Q₈	—	2	2	no	—
133	C₂₃×C₂²⋊Q₈	—	2	4	no	—
134	C₂₃×C₂²⋊Q₈	—	2	4	no	—
135	C₂₃×C₂²⋊Q₈	—	2	4	no	—
136	C₂₃×C₂²⋊Q₈	—	2	4	no	—
137	C₂₃×C₂²⋊Q₈	—	2	2	no	—
138	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
139	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
140	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
141	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
142	C₂₃×#121	—	2	2	no	—
143	C₂₃×#121	—	2	1	no	—
144	C₂₃×#121	—	2	2	no	—
145	C₂₃×#121	—	2	1	no	—
146	C₂₃×#121	—	2	2	no	—
147	C₂₃×#121	—	2	1	no	—
148	C₂₃×#121	—	2	2	no	—
149	C₂₃×#121	—	2	2	no	—
150	C₂₃×#121	C₂³	1	2	yes	—
151	C₂₃×#121	C₂³	1	2	yes	—
152	C₂₃×#121	C₂³	1	2	yes	—
153	C₂₃×#121	C₂³	1	1	yes	characteristic
154	C₂₃×#121	C₂³	1	2	yes	—
155	C₂₃×#120	—	2	2	no	—
156	C₂₃×#120	—	2	2	no	—
157	C₂₃×#120	—	2	2	no	—
158	C₄×Q₈×C₂₃	—	2	1	no	—
159	C₄×Q₈×C₂₃	—	2	1	no	—
160	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
161	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
162	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
163	C₄×D₄×C₂₃	—	2	2	no	—
164	C₄×D₄×C₂₃	—	2	4	no	—
165	C₄×D₄×C₂₃	—	2	2	no	—
166	C₄×D₄×C₂₃	—	2	1	no	—
167	C₄×D₄×C₂₃	—	2	2	no	—
168	C₄×D₄×C₂₃	—	2	1	no	—
169	C₄×D₄×C₂₃	—	2	2	no	—
170	C₄×D₄×C₂₃	—	2	1	no	—
171	C₄×D₄×C₂₃	—	2	2	no	—
172	C₄×D₄×C₂₃	—	2	1	no	—
173	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
174	C₄×D₄×C₂₃	D₄	1	2	yes	—
175	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
176	C₄×D₄×C₂₃	C₂³	1	2	yes	—
177	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
178	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
179	C₄×D₄×C₂₃	C₂³	1	2	yes	—
180	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
181	C₂₃×#117	—	2	1	no	—
182	C₂₃×#117	—	2	1	no	—
183	C₂₃×#117	C₂³	1	2	yes	—
184	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
185	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
186	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
187	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
188	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
189	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
190	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
191	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
192	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
193	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
194	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
195	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
197	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
198	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
199	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
200	C₂×C₄²×C₂₃	—	2	1	no	—
201	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
202	C₂₃×#107	C₂³	1	2	yes	—
203	C₂₃×#107	C₂³	1	4	yes	—
204	C₂₃×#107	C₂³	1	4	yes	—
205	C₂₃×#107	C₂³	1	4	yes	—
206	C₂₃×#107	C₂³	1	4	yes	—
207	C₂₃×#106	C₂³	1	2	yes	—
208	C₂₃×#106	C₂³	1	4	yes	—
209	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
210	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
211	C₂₃×#103	C₂³	1	2	yes	—
212	C₂₃×#103	C₂³	1	4	yes	—
213	C₂₃×#103	C₂³	1	2	yes	—
214	C₂₃×#103	C₂³	1	2	yes	—
215	C₂₃×#103	C₂³	1	4	yes	—
216	C₂₃×#102	C₂³	1	2	yes	—
217	C₂₃×#102	C₂³	1	4	yes	—
218	C₂₃×#102	C₂³	1	4	yes	—
219	C₂₃×#102	C₂³	1	4	yes	—
220	C₂₃×#102	C₂³	1	4	yes	—
221	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
222	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
223	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
224	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
225	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
226	C₂₃×#97	C₂³	1	2	yes	—
227	C₄×C₈×C₂₃	C₂³	1	2	yes	—
228	C₂⁴×C₂₃	—	2	2	no	—
229	C₂⁴×C₂₃	C₂×D₄	1	2	yes	—
230	#41×C₂₃	—	4	4	no	—
231	#41×C₂₃	—	8	2	no	—
232	C₂×Q₈×C₂₃	—	2	1	no	—
233	C₂×Q₈×C₂₃	—	2	2	no	—
234	C₂×Q₈×C₂₃	—	2	2	no	—
235	C₂×Q₈×C₂₃	—	2	1	no	—
236	C₂×Q₈×C₂₃	—	4	2	no	—
237	C₂×Q₈×C₂₃	—	8	2	no	—
238	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
239	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
240	C₂×D₄×C₂₃	—	2	4	no	—
241	C₂×D₄×C₂₃	—	2	2	no	—
242	C₂×D₄×C₂₃	—	2	2	no	—
243	C₂×D₄×C₂₃	—	2	1	no	—
244	C₂×D₄×C₂₃	—	2	2	no	—
245	C₂×D₄×C₂₃	—	2	2	no	—
246	C₂×D₄×C₂₃	—	2	2	no	—
247	C₂×D₄×C₂₃	—	2	1	no	—
248	C₂×D₄×C₂₃	—	2	1	no	—
249	C₂×D₄×C₂₃	—	2	2	no	—
250	C₂×D₄×C₂₃	—	4	4	no	—
251	C₂×D₄×C₂₃	—	4	4	no	—
252	C₂×D₄×C₂₃	—	8	4	no	—
253	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
254	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
255	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
256	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
257	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₂₃	—	2	1	no	—
259	C₂²×C₄×C₂₃	—	2	1	no	—
260	C₂²×C₄×C₂₃	—	2	2	no	—
261	C₂²×C₄×C₂₃	—	2	2	no	—
262	C₂²×C₄×C₂₃	—	2	4	no	—
263	C₂²×C₄×C₂₃	—	2	4	no	—
264	C₂²×C₄×C₂₃	—	2	1	no	—
265	C₂²×C₄×C₂₃	—	2	2	no	—
266	C₂²×C₄×C₂₃	—	2	2	no	—
267	C₂²×C₄×C₂₃	—	4	4	no	—
268	C₂²×C₄×C₂₃	—	8	4	no	—
269	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
271	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
272	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
273	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
274	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
277	Q₁₆×C₂₃	—	4	2	no	—
278	SD₁₆×C₂₃	—	4	4	no	—
279	SD₁₆×C₂₃	—	4	2	no	—
280	M₁₆×C₂₃	—	4	4	no	—
281	C₂×C₈×C₂₃	—	4	4	no	—
282	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
283	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
284	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
285	C₄⋊C₄×C₂₃	—	2	1	no	—
286	C₄⋊C₄×C₂₃	—	2	4	no	—
287	C₄⋊C₄×C₂₃	—	2	4	no	—
288	C₄⋊C₄×C₂₃	—	2	2	no	—
289	C₄⋊C₄×C₂₃	—	2	2	no	—
290	C₄⋊C₄×C₂₃	—	2	2	no	—
291	C₄⋊C₄×C₂₃	—	2	2	no	—
292	C₄⋊C₄×C₂₃	—	2	2	no	—
293	C₄⋊C₄×C₂₃	—	2	4	no	—
294	C₄⋊C₄×C₂₃	—	2	4	no	—
295	C₄⋊C₄×C₂₃	—	2	2	no	—
296	C₄⋊C₄×C₂₃	—	2	1	no	—
297	C₄⋊C₄×C₂₃	—	2	1	no	—
298	C₄⋊C₄×C₂₃	—	2	1	no	—
299	C₄⋊C₄×C₂₃	—	2	1	no	—
300	C₄⋊C₄×C₂₃	—	2	2	no	—
301	C₄⋊C₄×C₂₃	—	2	1	no	—
302	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
303	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
304	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
305	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
306	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
307	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
308	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
309	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
310	C₂²⋊C₄×C₂₃	—	2	2	no	—
311	C₂²⋊C₄×C₂₃	—	2	4	no	—
312	C₂²⋊C₄×C₂₃	—	2	4	no	—
313	C₂²⋊C₄×C₂₃	—	2	2	no	—
314	C₂²⋊C₄×C₂₃	—	2	1	no	—
315	C₂²⋊C₄×C₂₃	—	2	1	no	—
316	C₂²⋊C₄×C₂₃	—	2	1	no	—
317	C₂²⋊C₄×C₂₃	—	2	2	no	—
318	C₂²⋊C₄×C₂₃	—	2	2	no	—
319	C₂²⋊C₄×C₂₃	—	2	2	no	—
320	C₂²⋊C₄×C₂₃	—	2	1	no	—
321	C₂²⋊C₄×C₂₃	—	2	2	no	—
322	C₂²⋊C₄×C₂₃	—	2	1	no	—
323	C₂²⋊C₄×C₂₃	—	2	2	no	—
324	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
325	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
326	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
327	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
328	C₄²×C₂₃	—	2	2	no	—
329	C₄²×C₂₃	—	2	2	no	—
330	C₄²×C₂₃	—	2	2	no	—
331	C₄²×C₂₃	—	2	1	no	—
332	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
333	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
334	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
335	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
336	#61726	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
337	C₂³×C₂₃	—	2	4	no	—
338	C₂³×C₂₃	—	2	4	no	—
339	C₂³×C₂₃	—	2	1	no	—
340	C₂³×C₂₃	—	2	2	no	—
341	C₂³×C₂₃	—	4	2	no	—
342	C₂³×C₂₃	—	4	4	no	—
343	C₂³×C₂₃	—	8	2	no	—
344	C₂³×C₂₃	—	8	2	no	—
345	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
346	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
347	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
348	Q₈×C₂₃	—	2	2	no	—
349	Q₈×C₂₃	—	2	2	no	—
350	Q₈×C₂₃	—	2	2	no	—
351	Q₈×C₂₃	—	4	2	no	—
352	Q₈×C₂₃	—	8	2	no	—
353	Q₈×C₂₃	—	8	2	no	—
354	Q₈×C₂₃	—	8	1	no	—
355	D₄×C₂₃	—	2	4	no	—
356	D₄×C₂₃	—	2	2	no	—
357	D₄×C₂₃	—	2	2	no	—
358	D₄×C₂₃	—	2	4	no	—
359	D₄×C₂₃	—	4	4	no	—
360	D₄×C₂₃	—	4	2	no	—
361	D₄×C₂₃	—	4	4	no	—
362	D₄×C₂₃	—	4	2	no	—
363	D₄×C₂₃	—	8	2	no	—
364	D₄×C₂₃	—	8	1	no	—
365	D₄×C₂₃	—	8	2	no	—
366	D₄×C₂₃	—	8	2	no	—
367	D₄×C₂₃	—	8	2	no	—
368	D₄×C₂₃	#137	1	4	yes	—
369	C₂×C₄×C₂₃	—	2	2	no	—
370	C₂×C₄×C₂₃	—	2	2	no	—
371	C₂×C₄×C₂₃	—	2	4	no	—
372	C₂×C₄×C₂₃	—	2	4	no	—
373	C₂×C₄×C₂₃	—	2	2	no	—
374	C₂×C₄×C₂₃	—	2	1	no	—
375	C₂×C₄×C₂₃	—	2	2	no	—
376	C₂×C₄×C₂₃	—	2	2	no	—
377	C₂×C₄×C₂₃	—	2	1	no	—
378	C₂×C₄×C₂₃	—	2	2	no	—
379	C₂×C₄×C₂₃	—	2	1	no	—
380	C₂×C₄×C₂₃	—	2	4	no	—
381	C₂×C₄×C₂₃	—	4	2	no	—
382	C₂×C₄×C₂₃	—	4	2	no	—
383	C₂×C₄×C₂₃	—	4	2	no	—
384	C₂×C₄×C₂₃	—	4	2	no	—
385	C₂×C₄×C₂₃	—	4	2	no	—
386	C₂×C₄×C₂₃	—	4	4	no	—
387	C₂×C₄×C₂₃	—	4	2	no	—
388	C₂×C₄×C₂₃	—	8	2	no	—
389	C₂×C₄×C₂₃	—	8	2	no	—
390	C₂×C₄×C₂₃	—	8	4	no	—
391	C₂×C₄×C₂₃	—	8	4	no	—
392	C₂×C₄×C₂₃	—	8	2	no	—
393	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
395	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
399	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
401	C₈×C₂₃	—	2	2	no	—
402	C₈×C₂₃	—	2	4	no	—
403	C₈×C₂₃	—	2	2	no	—
404	#3519	C₂×C₂₃	1	1	yes	characteristic
405	C₂×#554	C₂×C₂₃	1	1	yes	characteristic, complemented
406	#3357	C₂×C₂₃	1	2	yes	complemented
407	#3346	C₂×C₂₃	1	4	yes	complemented
408	#3338	C₂×C₂₃	1	2	yes	complemented
409	#3333	C₂×C₂₃	1	2	yes	complemented
410	#3314	C₂×C₂₃	1	4	yes	complemented
411	#3295	C₂×C₂₃	1	2	yes	complemented
412	#3238	C₂×C₂₃	1	1	yes	characteristic, complemented
413	#3226	C₂×C₂₃	1	1	yes	characteristic, complemented
414	#3193	C₂×C₂₃	1	2	yes	complemented
415	#3190	C₂×C₂₃	1	2	yes	complemented
416	#3112	C₂×C₂₃	1	1	yes	characteristic, complemented
417	#3108	C₂×C₂₃	1	1	yes	characteristic, complemented
418	#3092	C₂×C₂₃	1	2	yes	complemented
419	C₂×#480	C₂×C₂₃	1	2	yes	complemented
420	#2974	C₂×C₂₃	1	1	yes	characteristic, complemented
421	C₂²×C₂₃	—	2	1	no	—
422	C₂²×C₂₃	—	2	2	no	—
423	C₂²×C₂₃	—	2	1	no	—
424	C₂²×C₂₃	—	2	2	no	—
425	C₂²×C₂₃	—	2	2	no	—
426	C₂²×C₂₃	—	2	2	no	—
427	C₂²×C₂₃	—	2	2	no	—
428	C₂²×C₂₃	—	4	8	no	—
429	C₂²×C₂₃	—	4	2	no	—
430	C₂²×C₂₃	—	4	1	no	—
431	C₂²×C₂₃	—	4	1	no	—
432	C₂²×C₂₃	—	4	2	no	—
433	C₂²×C₂₃	—	4	2	no	—
434	C₂²×C₂₃	—	4	1	no	—
435	C₂²×C₂₃	—	16	4	no	—
436	C₂²×C₂₃	C₂×#137	1	4	yes	—
437	C₂²×C₂₃	#576	1	2	yes	—
438	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
439	C₄×C₂₃	—	2	1	no	—
440	C₄×C₂₃	—	2	2	no	—
441	C₄×C₂₃	—	2	2	no	—
442	C₄×C₂₃	—	2	1	no	—
443	C₄×C₂₃	—	2	1	no	—
444	C₄×C₂₃	—	2	1	no	—
445	C₄×C₂₃	—	4	2	no	—
446	C₄×C₂₃	—	4	1	no	—
447	C₄×C₂₃	—	4	1	no	—
448	C₄×C₂₃	—	4	2	no	—
449	C₄×C₂₃	—	4	4	no	—
450	C₄×C₂₃	—	4	1	no	—
451	C₄×C₂₃	—	4	2	no	—
452	C₄×C₂₃	C₂×#137	1	2	yes	—
453	C₄×C₂₃	#585	1	2	yes	—
454	#555	C₂²×C₂₃	1	1	yes	characteristic
455	#554	—	2	1	no	—
456	#554	—	2	2	no	—
457	#554	—	2	1	no	—
458	#554	C₂²×C₂₃	1	1	yes	characteristic
459	#554	C₂²×C₂₃	1	2	yes	—
460	#554	C₂²×C₂₃	1	2	yes	complemented
461	#554	C₂²×C₂₃	1	4	yes	complemented
462	#553	—	2	1	no	—
463	#553	C₂²×C₂₃	1	2	yes	—
464	#550	C₂²×C₂₃	1	1	yes	characteristic
465	#546	—	2	2	no	—
466	#546	C₂²×C₂₃	1	2	yes	—
467	D₄²	—	2	1	no	—
468	D₄²	C₂²×C₂₃	1	1	yes	characteristic
469	#540	—	2	1	no	—
470	#538	—	2	2	no	—
471	#532	C₂²×C₂₃	1	1	yes	characteristic
472	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
473	#529	C₂²×C₂₃	1	1	yes	characteristic
474	C₂×#125	—	2	1	no	—
475	#525	C₂²×C₂₃	1	2	yes	—
476	C₂×C₂²⋊Q₈	—	2	2	no	—
477	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	complemented
478	C₂×#121	C₂²×C₂₃	1	2	yes	—
479	#518	—	2	1	no	—
480	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
481	C₂×C₄×D₄	—	2	1	no	—
482	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
483	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
484	#501	C₂²×C₂₃	1	2	yes	complemented
485	#500	C₂²×C₂₃	1	2	yes	complemented
486	#489	C₂²×C₂₃	1	2	yes	complemented
487	#486	C₂²×C₂₃	1	2	yes	complemented
488	#485	C₂²×C₂₃	1	4	yes	complemented
489	#484	C₂²×C₂₃	1	4	yes	complemented
490	#484	C₂²×C₂₃	1	4	yes	complemented
491	#483	C₂²×C₂₃	1	1	yes	characteristic, complemented
492	#483	C₂²×C₂₃	1	2	yes	complemented
493	#481	C₂²×C₂₃	1	4	yes	complemented
494	#480	C₂²×C₂₃	1	1	yes	characteristic
495	#480	C₂²×C₂₃	1	2	yes	—
496	#480	C₂²×C₂₃	1	4	yes	complemented
497	#480	C₂²×C₂₃	1	2	yes	complemented
498	#480	C₂²×C₂₃	1	4	yes	complemented
499	#480	C₂²×C₂₃	1	2	yes	complemented
500	#480	C₂²×C₂₃	1	2	yes	complemented
501	#479	C₂²×C₂₃	1	2	yes	complemented
502	#477	C₂²×C₂₃	1	2	yes	complemented
503	#477	C₂²×C₂₃	1	2	yes	complemented
504	#476	C₂²×C₂₃	1	2	yes	complemented
505	#474	C₂²×C₂₃	1	4	yes	complemented
506	#468	C₂²×C₂₃	1	4	yes	complemented
507	#468	C₂²×C₂₃	1	4	yes	complemented
508	#467	C₂²×C₂₃	1	4	yes	complemented
509	#465	C₂²×C₂₃	1	4	yes	complemented
510	#464	C₂²×C₂₃	1	2	yes	complemented
511	#460	C₂²×C₂₃	1	2	yes	complemented
512	#452	C₂²×C₂₃	1	4	yes	complemented
513	#451	C₂²×C₂₃	1	1	yes	characteristic, complemented
514	#450	C₂²×C₂₃	1	4	yes	complemented
515	#448	C₂²×C₂₃	1	1	yes	characteristic
516	#448	C₂²×C₂₃	1	2	yes	complemented
517	#440	C₂²×C₂₃	1	4	yes	complemented
518	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
519	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
520	#436	C₂²×C₂₃	1	2	yes	complemented
521	#435	C₂²×C₂₃	1	4	yes	complemented
522	C₈×D₄	C₂²×C₂₃	1	2	yes	—
523	#432	C₂²×C₂₃	1	1	yes	characteristic, complemented
524	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
525	#428	C₂²×C₂₃	1	4	yes	complemented
526	C₂×#107	C₂²×C₂₃	1	4	yes	complemented
527	#417	C₂²×C₂₃	1	4	yes	complemented
528	C₂×#102	C₂²×C₂₃	1	4	yes	complemented
529	#407	C₂²×C₂₃	1	2	yes	complemented
530	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	complemented
531	C₂×C₂₃	—	2	2	no	—
532	C₂×C₂₃	—	2	4	no	—
533	C₂×C₂₃	—	4	2	no	—
534	C₂×C₂₃	—	8	2	no	—
535	C₂×C₂₃	—	8	1	no	—
536	C₂×C₂₃	#3485	1	1	yes	characteristic
537	C₂×C₂₃	C₂²×#137	1	1	yes	characteristic
538	C₂×C₂₃	C₂×#576	1	1	yes	characteristic
539	C₂×#41	—	2	1	no	—
540	C₂×#41	C₂³×C₂₃	1	2	yes	—
541	C₂²×Q₈	—	2	1	no	—
542	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
543	C₂²×D₄	—	2	2	no	—
544	C₂²×D₄	—	2	1	no	—
545	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
546	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
547	C₂³×C₄	—	2	2	no	—
548	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
549	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
550	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
551	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
552	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
553	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
554	C₄⋊Q₈	—	2	1	no	—
555	C₄⋊Q₈	—	2	1	no	—
556	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
557	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
558	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
559	#127	—	2	1	no	—
560	#127	C₂³×C₂₃	1	1	yes	characteristic
561	#126	—	2	2	no	—
562	#126	—	2	1	no	—
563	#125	—	2	2	no	—
564	#125	—	2	2	no	—
565	#125	—	2	4	no	—
566	#125	—	2	1	no	—
567	#125	C₂³×C₂₃	1	1	yes	characteristic
568	#124	—	2	2	no	—
569	#124	—	2	1	no	—
570	#124	C₂³×C₂₃	1	1	yes	characteristic
571	#123	—	2	2	no	—
572	#123	—	2	1	no	—
573	#123	—	2	2	no	—
574	#123	—	2	2	no	—
575	C₂²⋊Q₈	—	2	2	no	—
576	C₂²⋊Q₈	—	2	2	no	—
577	C₂²⋊Q₈	—	2	4	no	—
578	C₂²⋊Q₈	—	2	4	no	—
579	C₂²⋊Q₈	—	2	4	no	—
580	C₂²⋊Q₈	—	2	4	no	—
581	C₂²⋊Q₈	—	2	2	no	—
582	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
583	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
584	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
585	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
586	#121	—	2	2	no	—
587	#121	—	2	1	no	—
588	#121	—	2	2	no	—
589	#121	—	2	2	no	—
590	#121	—	2	1	no	—
591	#121	—	2	1	no	—
592	#121	—	2	2	no	—
593	#121	—	2	2	no	—
594	#121	C₂³×C₂₃	1	1	yes	characteristic
595	#121	C₂³×C₂₃	1	2	yes	—
596	#121	C₂³×C₂₃	1	2	yes	—
597	#121	C₂³×C₂₃	1	2	yes	—
598	#121	C₂³×C₂₃	1	2	yes	—
599	#120	—	2	2	no	—
600	#120	—	2	2	no	—
601	#120	—	2	2	no	—
602	C₄×Q₈	—	2	1	no	—
603	C₄×Q₈	—	2	1	no	—
604	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
605	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
606	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
607	C₄×D₄	—	2	2	no	—
608	C₄×D₄	—	2	4	no	—
609	C₄×D₄	—	2	2	no	—
610	C₄×D₄	—	2	1	no	—
611	C₄×D₄	—	2	2	no	—
612	C₄×D₄	—	2	2	no	—
613	C₄×D₄	—	2	1	no	—
614	C₄×D₄	—	2	1	no	—
615	C₄×D₄	—	2	2	no	—
616	C₄×D₄	—	2	1	no	—
617	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
618	C₄×D₄	D₄×C₂₃	1	2	yes	—
619	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
620	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
621	C₄×D₄	C₂³×C₂₃	1	2	yes	—
622	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
623	C₄×D₄	C₂³×C₂₃	1	2	yes	—
624	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
625	#117	—	2	1	no	—
626	#117	—	2	1	no	—
627	#117	C₂³×C₂₃	1	2	yes	—
628	C₂×C₄⋊C₄	—	2	2	no	—
629	C₂×C₄⋊C₄	—	2	2	no	—
630	C₂×C₄⋊C₄	—	2	2	no	—
631	C₂×C₄⋊C₄	—	2	1	no	—
632	C₂×C₄⋊C₄	—	2	1	no	—
633	C₂×C₄⋊C₄	—	2	2	no	—
634	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
635	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
636	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
637	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
638	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
639	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
640	C₂×C₂²⋊C₄	—	2	2	no	—
641	C₂×C₂²⋊C₄	—	2	2	no	—
642	C₂×C₂²⋊C₄	—	2	2	no	—
643	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
644	C₂×C₄²	—	2	1	no	—
645	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
646	#107	C₂³×C₂₃	1	2	yes	—
647	#107	C₂³×C₂₃	1	4	yes	—
648	#107	C₂³×C₂₃	1	4	yes	—
649	#107	C₂³×C₂₃	1	4	yes	—
650	#107	C₂³×C₂₃	1	4	yes	—
651	#106	C₂³×C₂₃	1	2	yes	—
652	#106	C₂³×C₂₃	1	4	yes	—
653	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
654	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
655	#103	C₂³×C₂₃	1	2	yes	—
656	#103	C₂³×C₂₃	1	4	yes	—
657	#103	C₂³×C₂₃	1	2	yes	—
658	#103	C₂³×C₂₃	1	2	yes	—
659	#103	C₂³×C₂₃	1	4	yes	—
660	#102	C₂³×C₂₃	1	2	yes	—
661	#102	C₂³×C₂₃	1	4	yes	—
662	#102	C₂³×C₂₃	1	4	yes	—
663	#102	C₂³×C₂₃	1	4	yes	—
664	#102	C₂³×C₂₃	1	4	yes	—
665	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
666	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
667	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
668	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
669	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
670	#97	C₂³×C₂₃	1	2	yes	—
671	C₄×C₈	C₂³×C₂₃	1	2	yes	—
672	C₂₃	#61726	1	1	yes	characteristic, direct product factor, Sylow
673	C₂⁴	—	2	2	no	—
674	C₂⁴	C₂×D₄×C₂₃	1	2	yes	—
675	#41	—	4	4	no	—
676	#41	—	8	2	no	—
677	C₂×Q₈	—	2	1	no	—
678	C₂×Q₈	—	2	2	no	—
679	C₂×Q₈	—	2	2	no	—
680	C₂×Q₈	—	2	1	no	—
681	C₂×Q₈	—	4	2	no	—
682	C₂×Q₈	—	8	2	no	—
683	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
684	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
685	C₂×D₄	—	2	4	no	—
686	C₂×D₄	—	2	2	no	—
687	C₂×D₄	—	2	2	no	—
688	C₂×D₄	—	2	1	no	—
689	C₂×D₄	—	2	2	no	—
690	C₂×D₄	—	2	2	no	—
691	C₂×D₄	—	2	2	no	—
692	C₂×D₄	—	2	1	no	—
693	C₂×D₄	—	2	1	no	—
694	C₂×D₄	—	2	2	no	—
695	C₂×D₄	—	4	4	no	—
696	C₂×D₄	—	4	4	no	—
697	C₂×D₄	—	8	4	no	—
698	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
699	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
700	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
701	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
702	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
703	C₂²×C₄	—	2	1	no	—
704	C₂²×C₄	—	2	1	no	—
705	C₂²×C₄	—	2	2	no	—
706	C₂²×C₄	—	2	2	no	—
707	C₂²×C₄	—	2	4	no	—
708	C₂²×C₄	—	2	4	no	—
709	C₂²×C₄	—	2	1	no	—
710	C₂²×C₄	—	2	2	no	—
711	C₂²×C₄	—	2	2	no	—
712	C₂²×C₄	—	4	4	no	—
713	C₂²×C₄	—	8	4	no	—
714	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
715	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
716	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
717	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
718	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
719	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
720	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
721	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
722	Q₁₆	—	4	2	no	—
723	SD₁₆	—	4	4	no	—
724	SD₁₆	—	4	2	no	—
725	M₁₆	—	4	4	no	—
726	C₂×C₈	—	4	4	no	—
727	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
728	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
729	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	4	no	—
732	C₄⋊C₄	—	2	4	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	4	no	—
739	C₄⋊C₄	—	2	4	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	1	no	—
742	C₄⋊C₄	—	2	1	no	—
743	C₄⋊C₄	—	2	1	no	—
744	C₄⋊C₄	—	2	1	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	1	no	—
747	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
748	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
749	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
750	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
751	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
752	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
753	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
754	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	4	no	—
757	C₂²⋊C₄	—	2	4	no	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	—	2	1	no	—
760	C₂²⋊C₄	—	2	1	no	—
761	C₂²⋊C₄	—	2	1	no	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₂²⋊C₄	—	2	2	no	—
765	C₂²⋊C₄	—	2	1	no	—
766	C₂²⋊C₄	—	2	2	no	—
767	C₂²⋊C₄	—	2	1	no	—
768	C₂²⋊C₄	—	2	2	no	—
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	C₂×D₄×C₂₃	1	2	yes	—
773	C₄²	—	2	2	no	—
774	C₄²	—	2	2	no	—
775	C₄²	—	2	2	no	—
776	C₄²	—	2	1	no	—
777	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
778	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
779	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
780	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
781	C₂³	—	2	4	no	—
782	C₂³	—	2	4	no	—
783	C₂³	—	2	1	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	4	2	no	—
786	C₂³	—	4	4	no	—
787	C₂³	—	8	2	no	—
788	C₂³	—	8	2	no	—
789	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
790	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
791	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
792	Q₈	—	2	2	no	—
793	Q₈	—	2	2	no	—
794	Q₈	—	2	2	no	—
795	Q₈	—	4	2	no	—
796	Q₈	—	8	2	no	—
797	Q₈	—	8	2	no	—
798	Q₈	—	8	1	no	—
799	D₄	—	2	4	no	—
800	D₄	—	2	2	no	—
801	D₄	—	2	2	no	—
802	D₄	—	2	4	no	—
803	D₄	—	4	4	no	—
804	D₄	—	4	2	no	—
805	D₄	—	4	4	no	—
806	D₄	—	4	2	no	—
807	D₄	—	8	2	no	—
808	D₄	—	8	1	no	—
809	D₄	—	8	2	no	—
810	D₄	—	8	2	no	—
811	D₄	—	8	2	no	—
812	D₄	C₂₃×#137	1	4	yes	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	4	no	—
816	C₂×C₄	—	2	4	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	4	no	—
825	C₂×C₄	—	4	2	no	—
826	C₂×C₄	—	4	2	no	—
827	C₂×C₄	—	4	2	no	—
828	C₂×C₄	—	4	2	no	—
829	C₂×C₄	—	4	2	no	—
830	C₂×C₄	—	4	4	no	—
831	C₂×C₄	—	4	2	no	—
832	C₂×C₄	—	8	2	no	—
833	C₂×C₄	—	8	2	no	—
834	C₂×C₄	—	8	4	no	—
835	C₂×C₄	—	8	4	no	—
836	C₂×C₄	—	8	2	no	—
837	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
838	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
839	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
840	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
841	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
842	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
843	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
844	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
845	C₈	—	2	2	no	—
846	C₈	—	2	4	no	—
847	C₈	—	2	2	no	—
848	C₂²	—	2	1	no	—
849	C₂²	—	2	2	no	—
850	C₂²	—	2	1	no	—
851	C₂²	—	2	2	no	—
852	C₂²	—	2	2	no	—
853	C₂²	—	2	2	no	—
854	C₂²	—	2	2	no	—
855	C₂²	—	4	8	no	—
856	C₂²	—	4	2	no	—
857	C₂²	—	4	1	no	—
858	C₂²	—	4	1	no	—
859	C₂²	—	4	2	no	—
860	C₂²	—	4	2	no	—
861	C₂²	—	4	1	no	—
862	C₂²	—	16	4	no	—
863	C₂²	C₂×C₂₃×#137	1	4	yes	—
864	C₂²	C₂₃×#576	1	2	yes	—
865	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
866	C₄	—	2	1	no	—
867	C₄	—	2	2	no	—
868	C₄	—	2	2	no	—
869	C₄	—	2	1	no	—
870	C₄	—	2	1	no	—
871	C₄	—	2	1	no	—
872	C₄	—	4	2	no	—
873	C₄	—	4	1	no	—
874	C₄	—	4	1	no	—
875	C₄	—	4	2	no	—
876	C₄	—	4	4	no	—
877	C₄	—	4	1	no	—
878	C₄	—	4	2	no	—
879	C₄	C₂×C₂₃×#137	1	2	yes	—
880	C₄	C₂₃×#585	1	2	yes	—
881	C₂	—	2	2	no	—
882	C₂	—	2	4	no	—
883	C₂	—	4	2	no	—
884	C₂	—	8	1	no	—
885	C₂	—	8	2	no	—
886	C₂	C₂₃×#3485	1	1	yes	characteristic
887	C₂	C₂²×C₂₃×#137	1	1	yes	characteristic
888	C₂	C₂×C₂₃×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#3519	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄×D₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₃×#554	C₂	semidirect
3. C₂₃×#3357	C₂	semidirect
4. C₂₃×#3346	C₂	semidirect
5. C₂₃×#3338	C₂	semidirect
6. C₂₃×#3333	C₂	semidirect
7. C₂₃×#3314	C₂	semidirect
8. C₂₃×#3295	C₂	semidirect
9. C₂₃×#3238	C₂	semidirect
10. C₂₃×#3226	C₂	semidirect
11. C₂₃×#3193	C₂	semidirect
12. C₂₃×#3190	C₂	semidirect
13. C₂₃×#3112	C₂	semidirect
14. C₂₃×#3108	C₂	semidirect
15. C₂₃×#3092	C₂	semidirect
16. C₂×C₂₃×#480	C₂	semidirect
17. C₂₃×#2974	C₂	semidirect
24. C₂₃×#554	C₂²	semidirect
25. C₂₃×#554	C₂²	semidirect
36. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
41. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
44. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
47. C₂²×C₄⋊C₄×C₂₃	C₂²	semidirect
48. C₂₃×#501	C₂²	semidirect
49. C₂₃×#500	C₂²	semidirect
50. C₂₃×#489	C₂²	semidirect
51. C₂₃×#486	C₂²	semidirect
52. C₂₃×#485	C₂²	semidirect
53. C₂₃×#484	C₂²	semidirect
54. C₂₃×#484	C₂²	semidirect
55. C₂₃×#483	C₂²	semidirect
56. C₂₃×#483	C₂²	semidirect
57. C₂₃×#481	C₂²	semidirect
60. C₂₃×#480	C₂²	semidirect
61. C₂₃×#480	C₂²	semidirect
62. C₂₃×#480	C₂²	semidirect
63. C₂₃×#480	C₂²	semidirect
64. C₂₃×#480	C₂²	semidirect
65. C₂₃×#479	C₂²	semidirect
66. C₂₃×#477	C₂²	semidirect
67. C₂₃×#477	C₂²	semidirect
68. C₂₃×#476	C₂²	semidirect
69. C₂₃×#474	C₂²	semidirect
70. C₂₃×#468	C₂²	semidirect
71. C₂₃×#468	C₂²	semidirect
72. C₂₃×#467	C₂²	semidirect
73. C₂₃×#465	C₂²	semidirect
74. C₂₃×#464	C₂²	semidirect
75. C₂₃×#460	C₂²	semidirect
76. C₂₃×#452	C₂²	semidirect
77. C₂₃×#451	C₂²	semidirect
78. C₂₃×#450	C₂²	semidirect
80. C₂₃×#448	C₂²	semidirect
81. C₂₃×#440	C₂²	semidirect
82. C₄×Q₁₆×C₂₃	C₂²	semidirect
83. C₄×SD₁₆×C₂₃	C₂²	semidirect
84. C₂₃×#436	C₂²	semidirect
85. C₂₃×#435	C₂²	semidirect
87. C₂₃×#432	C₂²	semidirect
88. C₂₃×#431	C₂²	semidirect
89. C₂₃×#428	C₂²	semidirect
90. C₂×C₂₃×#107	C₂²	semidirect
91. C₂₃×#417	C₂²	semidirect
92. C₂×C₂₃×#102	C₂²	semidirect
93. C₂₃×#407	C₂²	semidirect
94. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
336. #61726	C₂₃	direct (N × H)
405. C₂×#554	C₂×C₂₃	semidirect
406. #3357	C₂×C₂₃	semidirect
407. #3346	C₂×C₂₃	semidirect
408. #3338	C₂×C₂₃	semidirect
409. #3333	C₂×C₂₃	semidirect
410. #3314	C₂×C₂₃	semidirect
411. #3295	C₂×C₂₃	semidirect
412. #3238	C₂×C₂₃	semidirect
413. #3226	C₂×C₂₃	semidirect
414. #3193	C₂×C₂₃	semidirect
415. #3190	C₂×C₂₃	semidirect
416. #3112	C₂×C₂₃	semidirect
417. #3108	C₂×C₂₃	semidirect
418. #3092	C₂×C₂₃	semidirect
419. C₂×#480	C₂×C₂₃	semidirect
420. #2974	C₂×C₂₃	semidirect
460. #554	C₂²×C₂₃	semidirect
461. #554	C₂²×C₂₃	semidirect
472. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
477. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
480. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
483. C₂²×C₄⋊C₄	C₂²×C₂₃	semidirect
484. #501	C₂²×C₂₃	semidirect
485. #500	C₂²×C₂₃	semidirect
486. #489	C₂²×C₂₃	semidirect
487. #486	C₂²×C₂₃	semidirect
488. #485	C₂²×C₂₃	semidirect
489. #484	C₂²×C₂₃	semidirect
490. #484	C₂²×C₂₃	semidirect
491. #483	C₂²×C₂₃	semidirect
492. #483	C₂²×C₂₃	semidirect
493. #481	C₂²×C₂₃	semidirect
496. #480	C₂²×C₂₃	semidirect
497. #480	C₂²×C₂₃	semidirect
498. #480	C₂²×C₂₃	semidirect
499. #480	C₂²×C₂₃	semidirect
500. #480	C₂²×C₂₃	semidirect
501. #479	C₂²×C₂₃	semidirect
502. #477	C₂²×C₂₃	semidirect
503. #477	C₂²×C₂₃	semidirect
504. #476	C₂²×C₂₃	semidirect
505. #474	C₂²×C₂₃	semidirect
506. #468	C₂²×C₂₃	semidirect
507. #468	C₂²×C₂₃	semidirect
508. #467	C₂²×C₂₃	semidirect
509. #465	C₂²×C₂₃	semidirect
510. #464	C₂²×C₂₃	semidirect
511. #460	C₂²×C₂₃	semidirect
512. #452	C₂²×C₂₃	semidirect
513. #451	C₂²×C₂₃	semidirect
514. #450	C₂²×C₂₃	semidirect
516. #448	C₂²×C₂₃	semidirect
517. #440	C₂²×C₂₃	semidirect
518. C₄×Q₁₆	C₂²×C₂₃	semidirect
519. C₄×SD₁₆	C₂²×C₂₃	semidirect
520. #436	C₂²×C₂₃	semidirect
521. #435	C₂²×C₂₃	semidirect
523. #432	C₂²×C₂₃	semidirect
524. #431	C₂²×C₂₃	semidirect
525. #428	C₂²×C₂₃	semidirect
526. C₂×#107	C₂²×C₂₃	semidirect
527. #417	C₂²×C₂₃	semidirect
528. C₂×#102	C₂²×C₂₃	semidirect
529. #407	C₂²×C₂₃	semidirect
530. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
672. C₂₃	#61726	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×#554	2
C₂₃×#3357	2
C₂₃×#3346	2
C₂₃×#3338	2
C₂₃×#3333	2
C₂₃×#3314	2
C₂₃×#3295	2
C₂₃×#3238	2
C₂₃×#3226	2
C₂₃×#3193	2
C₂₃×#3190	2
C₂₃×#3112	2
C₂₃×#3108	2
C₂₃×#3092	2
C₂×C₂₃×#480	2
C₂₃×#2974	2
#61726	23

Subgroups — C23×#61726 #19209352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61726 #19209352