Subgroups — C₂₃×#62822 #19210448

Order 5888.

7274 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3560	C₂	1	8	yes	maximal, complemented
2	C₂₃×#3559	C₂	1	4	yes	maximal, complemented
3	C₂₃×#3558	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3545	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3544	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3543	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3522	C₂	1	4	yes	maximal, complemented
8	C₂₃×#3519	C₂	1	4	yes	maximal, complemented
9	C₂₃×#3513	C₂	1	8	yes	maximal, complemented
10	C₂₃×#3505	C₂	1	4	yes	maximal, complemented
11	C₂₃×#3496	C₂	1	4	yes	maximal, complemented
12	C₂₃×#3494	C₂	1	8	yes	maximal, complemented
13	C₂₃×#3485	C₂	1	4	yes	maximal, complemented
14	C₂×C₂₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂₃×#529	C₂	1	2	yes	maximal, complemented
16	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	4	yes	complemented
17	C₂²×#41×C₂₃	C₂²	1	2	yes	complemented
18	C₂₃×#563	C₂²	1	8	yes	complemented
19	C₂₃×#563	C₂²	1	4	yes	complemented
20	C₂₃×#562	C₂²	1	8	yes	complemented
21	C₂₃×H(3,𝔽₄)	C₂²	1	4	yes	complemented
22	C₂₃×#560	C₂²	1	8	yes	complemented
23	C₂₃×#559	C₂²	1	8	yes	complemented
24	C₂₃×#559	C₂²	1	2	yes	complemented
25	Q₈²×C₂₃	C₂²	1	2	yes	complemented
26	C₂₃×#555	C₂²	1	8	yes	complemented
27	C₂₃×#555	C₂²	1	2	yes	complemented
28	C₂₃×#554	C₂²	1	8	yes	complemented
29	C₂₃×#554	C₂²	1	4	yes	complemented
30	C₂₃×#553	C₂²	1	16	yes	complemented
31	C₂₃×#553	C₂²	1	16	yes	complemented
32	C₂₃×#553	C₂²	1	8	yes	complemented
33	C₂₃×#553	C₂²	1	8	yes	complemented
34	C₂₃×#552	C₂²	1	8	yes	complemented
35	C₂₃×#551	C₂²	1	8	yes	complemented
36	C₂₃×#551	C₂²	1	16	yes	complemented
37	C₂₃×#551	C₂²	1	16	yes	complemented
38	C₂₃×#550	C₂²	1	4	yes	complemented
39	C₂₃×#548	C₂²	1	8	yes	complemented
40	C₂₃×#547	C₂²	1	16	yes	complemented
41	C₂₃×#547	C₂²	1	16	yes	complemented
42	C₂₃×#547	C₂²	1	8	yes	complemented
43	C₂₃×#547	C₂²	1	8	yes	complemented
44	C₂₃×#546	C₂²	1	16	yes	complemented
45	C₂₃×#546	C₂²	1	16	yes	complemented
46	C₂₃×#546	C₂²	1	16	yes	complemented
47	C₂₃×#546	C₂²	1	16	yes	complemented
48	C₂₃×#546	C₂²	1	8	yes	complemented
49	C₂₃×#546	C₂²	1	8	yes	complemented
50	D₄²×C₂₃	C₂²	1	8	yes	complemented
51	D₄²×C₂₃	C₂²	1	8	yes	complemented
52	D₄²×C₂₃	C₂²	1	2	yes	complemented
53	C₂₃×#544	C₂²	1	8	yes	complemented
54	C₂₃×#542	C₂²	1	8	yes	complemented
55	C₂₃×#542	C₂²	1	8	yes	complemented
56	C₂₃×#542	C₂²	1	16	yes	complemented
57	C₂₃×#540	C₂²	1	8	yes	complemented
58	C₂₃×#540	C₂²	1	8	yes	complemented
59	C₂₃×#539	C₂²	1	8	yes	complemented
60	C₂₃×#539	C₂²	1	16	yes	complemented
61	C₂₃×#538	C₂²	1	8	yes	complemented
62	C₂₃×#538	C₂²	1	16	yes	complemented
63	C₂₃×#538	C₂²	1	16	yes	complemented
64	C₂₃×#537	C₂²	1	8	yes	complemented
65	C₂₃×#536	C₂²	1	8	yes	complemented
66	C₂₃×#535	C₂²	1	8	yes	complemented
67	C₂₃×#534	C₂²	1	8	yes	complemented
68	C₂₃×#534	C₂²	1	8	yes	complemented
69	C₂₃×#534	C₂²	1	8	yes	complemented
70	C₂₃×#532	C₂²	1	4	yes	complemented
71	C₂₃×#532	C₂²	1	4	yes	complemented
72	C₂₃×#532	C₂²	1	4	yes	complemented
73	C₂₃×#532	C₂²	1	4	yes	complemented
74	C₂₃×#532	C₂²	1	8	yes	complemented
75	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
76	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic, complemented
77	C₂₃×#529	C₂²	1	4	yes	complemented
78	C₂₃×#529	C₂²	1	4	yes	complemented
79	C₂₃×#529	C₂²	1	4	yes	complemented
80	C₂₃×#529	C₂²	1	4	yes	complemented
81	C₂₃×#529	C₂²	1	4	yes	complemented
82	C₂₃×#529	C₂²	1	4	yes	complemented
83	C₂₃×#529	C₂²	1	4	yes	complemented
84	C₂₃×#529	C₂²	1	4	yes	complemented
85	C₂₃×#529	C₂²	1	8	yes	complemented
86	C₂×C₂₃×#126	C₂²	1	4	yes	complemented
87	C₂×C₂₃×#125	C₂²	1	2	yes	complemented
88	C₂×C₂₃×#124	C₂²	1	2	yes	complemented
89	C₂×C₂₃×#124	C₂²	1	2	yes	complemented
90	C₂₃×#525	C₂²	1	8	yes	complemented
91	C₂₃×#525	C₂²	1	8	yes	complemented
92	C₂×C₂₃×#123	C₂²	1	4	yes	complemented
93	C₂×C₂₃×#123	C₂²	1	8	yes	complemented
94	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
95	C₂×C₂₃×#121	C₂²	1	2	yes	—
96	C₂×C₂₃×#121	C₂²	1	4	yes	complemented
97	C₂×C₂₃×#121	C₂²	1	8	yes	complemented
98	C₂₃×#520	C₂²	1	8	yes	complemented
99	C₂₃×#518	C₂²	1	4	yes	complemented
100	C₂₃×#518	C₂²	1	8	yes	complemented
101	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	complemented
102	C₂×C₄×D₄×C₂₃	C₂²	1	4	yes	complemented
103	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
104	C₂×C₄×D₄×C₂₃	C₂²	1	4	yes	complemented
105	C₂×C₂₃×#117	C₂²	1	4	yes	complemented
106	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic, complemented
107	C₂₃×H(5,𝔽₂)	—	4	16	no	—
108	C₂×#41×C₂₃	—	4	8	no	—
109	C₂×#41×C₂₃	C₂³	1	16	yes	—
110	C₂×#41×C₂₃	C₂³	1	8	yes	—
111	C₂×#41×C₂₃	C₂³	1	8	yes	—
112	C₂×#41×C₂₃	C₂³	1	8	yes	—
113	C₂×#41×C₂₃	C₂³	1	8	yes	—
114	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
115	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
116	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
117	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
118	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
119	C₂²×D₄×C₂₃	C₂³	1	16	yes	—
120	C₂²×D₄×C₂₃	C₂³	1	8	yes	—
121	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
122	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
123	C₂²×D₄×C₂₃	C₂³	1	8	yes	—
124	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
126	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
127	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
128	C₂₃×C₄⋊Q₈	C₂³	1	8	yes	—
129	C₂₃×C₄⋊Q₈	C₂³	1	8	yes	—
130	C₂₃×C₄⋊Q₈	C₂³	1	8	yes	—
131	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
132	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
133	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
134	C₂₃×#127	C₂³	1	2	yes	—
135	C₂₃×#127	C₂³	1	8	yes	—
136	C₂₃×#127	C₂³	1	2	yes	—
137	C₂₃×#127	C₂³	1	4	yes	—
138	C₂₃×#126	C₂³	1	8	yes	—
139	C₂₃×#126	C₂³	1	16	yes	—
140	C₂₃×#126	C₂³	1	16	yes	—
141	C₂₃×#126	C₂³	1	16	yes	—
142	C₂₃×#126	C₂³	1	8	yes	—
143	C₂₃×#126	C₂³	1	8	yes	—
144	C₂₃×#126	C₂³	1	8	yes	—
145	C₂₃×#125	C₂³	1	16	yes	—
146	C₂₃×#125	C₂³	1	8	yes	—
147	C₂₃×#125	C₂³	1	4	yes	—
148	C₂₃×#125	C₂³	1	4	yes	—
149	C₂₃×#125	C₂³	1	4	yes	—
150	C₂₃×#125	C₂³	1	4	yes	—
151	C₂₃×#124	C₂³	1	16	yes	—
152	C₂₃×#124	C₂³	1	8	yes	—
153	C₂₃×#124	C₂³	1	4	yes	—
154	C₂₃×#124	C₂³	1	16	yes	—
155	C₂₃×#124	C₂³	1	8	yes	—
156	C₂₃×#124	C₂³	1	8	yes	—
157	C₂₃×#124	C₂³	1	4	yes	—
158	C₂₃×#124	C₂³	1	4	yes	—
159	C₂₃×#124	C₂³	1	4	yes	—
160	C₂₃×#124	C₂³	1	4	yes	—
161	C₂₃×#124	C₂³	1	4	yes	—
162	C₂₃×#124	C₂³	1	8	yes	—
163	C₂₃×#123	C₂³	1	16	yes	—
164	C₂₃×#123	C₂³	1	8	yes	—
165	C₂₃×#123	C₂³	1	8	yes	—
166	C₂₃×#123	C₂³	1	8	yes	—
167	C₂₃×#123	C₂³	1	8	yes	—
168	C₂₃×#123	C₂³	1	16	yes	—
169	C₂₃×#123	C₂³	1	16	yes	—
170	C₂₃×#123	C₂³	1	16	yes	—
171	C₂₃×#123	C₂³	1	16	yes	—
172	C₂₃×#123	C₂³	1	16	yes	—
173	C₂₃×#123	C₂³	1	16	yes	—
174	C₂₃×#123	C₂³	1	16	yes	—
175	C₂₃×#123	C₂³	1	16	yes	—
176	C₂₃×#123	C₂³	1	8	yes	—
177	C₂₃×#123	C₂³	1	8	yes	—
178	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	—
179	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	—
180	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	—
181	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	—
182	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	—
183	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	—
184	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
185	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
186	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
187	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
188	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
189	C₂₃×#121	C₂³	1	4	yes	—
190	C₂₃×#121	C₂³	1	8	yes	—
191	C₂₃×#121	C₂³	1	16	yes	—
192	C₂₃×#121	C₂³	1	8	yes	—
193	C₂₃×#121	C₂³	1	16	yes	—
194	C₂₃×#121	C₂³	1	16	yes	—
195	C₂₃×#121	C₂³	1	16	yes	—
196	C₂₃×#121	C₂³	1	8	yes	—
197	C₂₃×#121	C₂³	1	16	yes	—
198	C₂₃×#121	C₂³	1	8	yes	—
199	C₂₃×#121	C₂³	1	8	yes	—
200	C₂₃×#121	C₂³	1	16	yes	—
201	C₂₃×#121	C₂³	1	16	yes	—
202	C₂₃×#121	C₂³	1	16	yes	—
203	C₂₃×#121	C₂³	1	16	yes	—
204	C₂₃×#121	C₂³	1	4	yes	—
205	C₂₃×#121	C₂³	1	4	yes	—
206	C₂₃×#121	C₂³	1	4	yes	—
207	C₂₃×#121	C₂³	1	8	yes	—
208	C₂₃×#121	C₂³	1	8	yes	—
209	C₂₃×#120	C₂³	1	16	yes	—
210	C₂₃×#120	C₂³	1	8	yes	—
211	C₂₃×#120	C₂³	1	16	yes	—
212	C₂₃×#120	C₂³	1	8	yes	—
213	C₂₃×#120	C₂³	1	16	yes	—
214	C₂₃×#120	C₂³	1	16	yes	—
215	C₄×Q₈×C₂₃	C₂³	1	8	yes	—
216	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
217	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
218	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
219	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
220	C₄×D₄×C₂₃	C₂³	1	8	yes	—
221	C₄×D₄×C₂₃	C₂³	1	16	yes	—
222	C₄×D₄×C₂₃	C₂³	1	16	yes	—
223	C₄×D₄×C₂₃	C₂³	1	8	yes	—
224	C₄×D₄×C₂₃	C₂³	1	16	yes	—
225	C₄×D₄×C₂₃	C₂³	1	16	yes	—
226	C₄×D₄×C₂₃	C₂³	1	8	yes	—
227	C₄×D₄×C₂₃	C₂³	1	8	yes	—
228	C₄×D₄×C₂₃	C₂³	1	8	yes	—
229	C₄×D₄×C₂₃	C₂³	1	4	yes	—
230	C₄×D₄×C₂₃	C₂³	1	8	yes	—
231	C₄×D₄×C₂₃	C₂³	1	8	yes	—
232	C₄×D₄×C₂₃	C₂³	1	16	yes	—
233	C₄×D₄×C₂₃	C₂³	1	16	yes	—
234	C₄×D₄×C₂₃	C₂³	1	4	yes	—
235	C₄×D₄×C₂₃	C₂³	1	8	yes	—
236	C₄×D₄×C₂₃	C₂³	1	8	yes	—
237	C₄×D₄×C₂₃	C₂³	1	4	yes	—
238	C₄×D₄×C₂₃	C₂³	1	8	yes	—
239	C₄×D₄×C₂₃	C₂³	1	4	yes	—
240	C₄×D₄×C₂₃	C₂³	1	8	yes	—
241	C₂₃×#117	C₂³	1	8	yes	—
242	C₂₃×#117	C₂³	1	8	yes	—
243	C₂₃×#117	C₂³	1	16	yes	—
244	C₂₃×#117	C₂³	1	8	yes	—
245	C₂₃×#117	C₂³	1	8	yes	—
246	C₂₃×#117	C₂³	1	8	yes	—
247	C₂₃×#117	C₂³	1	8	yes	—
248	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
249	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
250	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
251	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
252	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
253	C₂×C₄⋊C₄×C₂₃	C₂³	1	16	yes	—
254	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
255	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
257	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
258	C₂×C₂²⋊C₄×C₂₃	C₂³	1	16	yes	—
259	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
260	C₂×C₂²⋊C₄×C₂₃	C₂³	1	16	yes	—
261	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
262	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
263	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
264	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
265	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
266	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
267	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
268	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
269	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
270	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
271	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
272	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
273	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
274	C₂⁴×C₂₃	C₂⁴	1	4	yes	—
275	C₂⁴×C₂₃	C₂⁴	1	4	yes	—
276	C₂⁴×C₂₃	C₂⁴	1	8	yes	—
277	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
278	#41×C₂₃	—	4	16	no	—
279	#41×C₂₃	—	4	16	no	—
280	#41×C₂₃	—	4	16	no	—
281	#41×C₂₃	—	4	32	no	—
282	#41×C₂₃	—	4	16	no	—
283	C₂×Q₈×C₂₃	—	4	4	no	—
284	C₂×Q₈×C₂₃	—	4	4	no	—
285	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
286	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
287	C₂×Q₈×C₂₃	C₂⁴	1	8	yes	—
288	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
289	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
290	C₂×D₄×C₂₃	—	2	16	no	—
291	C₂×D₄×C₂₃	—	2	16	no	—
292	C₂×D₄×C₂₃	—	4	8	no	—
293	C₂×D₄×C₂₃	—	4	4	no	—
294	C₂×D₄×C₂₃	—	4	16	no	—
295	C₂×D₄×C₂₃	—	4	4	no	—
296	C₂×D₄×C₂₃	—	4	16	no	—
297	C₂×D₄×C₂₃	—	4	32	no	—
298	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
299	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
300	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
301	C₂×D₄×C₂₃	C₂⁴	1	16	yes	—
302	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
303	C₂×D₄×C₂₃	C₂⁴	1	16	yes	—
304	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
305	C₂×D₄×C₂₃	C₂⁴	1	16	yes	—
306	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
307	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
308	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
309	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
310	C₂×D₄×C₂₃	C₂⁴	1	16	yes	—
311	C₂²×C₄×C₂₃	—	2	4	no	—
312	C₂²×C₄×C₂₃	—	4	4	no	—
313	C₂²×C₄×C₂₃	—	4	8	no	—
314	C₂²×C₄×C₂₃	—	4	8	no	—
315	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
317	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
319	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
323	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
324	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
325	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
326	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
327	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
328	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
329	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
330	C₂²×C₄×C₂₃	C₂⁴	1	16	yes	—
331	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
332	C₂²×C₄×C₂₃	C₂⁴	1	16	yes	—
333	C₂²×C₄×C₂₃	C₂⁴	1	16	yes	—
334	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
335	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
336	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
337	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
338	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
339	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
340	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
341	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
342	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
343	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
344	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
345	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
346	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
347	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
348	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
349	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
350	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
351	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
352	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
353	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
354	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
355	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
356	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
357	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
358	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
359	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
360	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
361	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
362	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
363	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
364	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
365	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
366	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
367	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
368	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
369	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
370	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
371	C₄²×C₂₃	C₂⁴	1	2	yes	—
372	C₄²×C₂₃	C₂⁴	1	2	yes	—
373	C₄²×C₂₃	C₂⁴	1	2	yes	—
374	C₄²×C₂₃	C₂⁴	1	2	yes	—
375	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
376	C₄²×C₂₃	C₂⁴	1	2	yes	—
377	C₄²×C₂₃	C₂⁴	1	2	yes	—
378	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
379	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
380	C₄²×C₂₃	C₂⁴	1	8	yes	—
381	C₄²×C₂₃	C₂⁴	1	8	yes	—
382	C₄²×C₂₃	C₂⁴	1	8	yes	—
383	C₄²×C₂₃	C₂⁴	1	8	yes	—
384	#62822	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
385	C₂³×C₂₃	—	2	8	no	—
386	C₂³×C₂₃	—	2	8	no	—
387	C₂³×C₂₃	—	4	2	no	—
388	C₂³×C₂₃	—	4	4	no	—
389	C₂³×C₂₃	—	4	4	no	—
390	C₂³×C₂₃	—	4	8	no	—
391	C₂³×C₂₃	—	4	8	no	—
392	C₂³×C₂₃	—	4	16	no	—
393	C₂³×C₂₃	H(5,𝔽₂)	1	4	yes	—
394	C₂³×C₂₃	C₂⁵	1	8	yes	—
395	C₂³×C₂₃	C₂⁵	1	8	yes	—
396	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
397	C₂³×C₂₃	C₂⁵	1	2	yes	—
398	Q₈×C₂₃	—	2	8	no	—
399	Q₈×C₂₃	—	4	4	no	—
400	Q₈×C₂₃	—	4	4	no	—
401	Q₈×C₂₃	—	4	4	no	—
402	Q₈×C₂₃	—	4	8	no	—
403	D₄×C₂₃	—	2	16	no	—
404	D₄×C₂₃	—	2	16	no	—
405	D₄×C₂₃	—	2	32	no	—
406	D₄×C₂₃	—	2	8	no	—
407	D₄×C₂₃	—	2	16	no	—
408	D₄×C₂₃	—	4	16	no	—
409	D₄×C₂₃	—	4	8	no	—
410	D₄×C₂₃	—	4	16	no	—
411	D₄×C₂₃	—	4	8	no	—
412	D₄×C₂₃	—	4	4	no	—
413	D₄×C₂₃	—	4	4	no	—
414	D₄×C₂₃	—	4	4	no	—
415	D₄×C₂₃	—	4	16	no	—
416	C₂×C₄×C₂₃	—	2	2	no	—
417	C₂×C₄×C₂₃	—	2	2	no	—
418	C₂×C₄×C₂₃	—	2	4	no	—
419	C₂×C₄×C₂₃	—	2	4	no	—
420	C₂×C₄×C₂₃	—	2	8	no	—
421	C₂×C₄×C₂₃	—	2	8	no	—
422	C₂×C₄×C₂₃	—	2	4	no	—
423	C₂×C₄×C₂₃	—	2	4	no	—
424	C₂×C₄×C₂₃	—	2	4	no	—
425	C₂×C₄×C₂₃	—	2	16	no	—
426	C₂×C₄×C₂₃	—	4	8	no	—
427	C₂×C₄×C₂₃	—	4	2	no	—
428	C₂×C₄×C₂₃	—	4	2	no	—
429	C₂×C₄×C₂₃	—	4	4	no	—
430	C₂×C₄×C₂₃	—	4	2	no	—
431	C₂×C₄×C₂₃	—	4	16	no	—
432	C₂×C₄×C₂₃	—	4	8	no	—
433	C₂×C₄×C₂₃	—	4	16	no	—
434	C₂×C₄×C₂₃	—	4	4	no	—
435	C₂×C₄×C₂₃	—	4	16	no	—
436	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
437	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
438	C₂×C₄×C₂₃	C₂⁵	1	8	yes	—
439	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
440	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
441	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
442	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
443	C₂×C₄×C₂₃	C₂⁵	1	8	yes	—
444	C₂×C₄×C₂₃	C₂⁵	1	8	yes	—
445	C₂×C₄×C₂₃	C₂⁵	1	8	yes	—
446	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
447	#3560	C₂×C₂₃	1	8	yes	complemented
448	#3559	C₂×C₂₃	1	4	yes	complemented
449	#3558	C₂×C₂₃	1	4	yes	complemented
450	#3545	C₂×C₂₃	1	4	yes	complemented
451	#3544	C₂×C₂₃	1	2	yes	complemented
452	#3543	C₂×C₂₃	1	2	yes	complemented
453	#3522	C₂×C₂₃	1	4	yes	complemented
454	#3519	C₂×C₂₃	1	4	yes	complemented
455	#3513	C₂×C₂₃	1	8	yes	complemented
456	#3505	C₂×C₂₃	1	4	yes	complemented
457	#3496	C₂×C₂₃	1	4	yes	complemented
458	#3494	C₂×C₂₃	1	8	yes	complemented
459	#3485	C₂×C₂₃	1	4	yes	complemented
460	C₂×#532	C₂×C₂₃	1	1	yes	characteristic, complemented
461	C₂×#529	C₂×C₂₃	1	2	yes	complemented
462	C₂²×C₂₃	—	2	2	no	—
463	C₂²×C₂₃	—	2	2	no	—
464	C₂²×C₂₃	—	2	2	no	—
465	C₂²×C₂₃	—	2	8	no	—
466	C₂²×C₂₃	—	2	8	no	—
467	C₂²×C₂₃	—	2	8	no	—
468	C₂²×C₂₃	—	2	16	no	—
469	C₂²×C₂₃	—	2	8	no	—
470	C₂²×C₂₃	—	4	4	no	—
471	C₂²×C₂₃	—	8	8	no	—
472	C₂²×C₂₃	—	8	8	no	—
473	C₂²×C₂₃	—	16	8	no	—
474	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
475	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	4	yes	—
476	C₂²×C₂₃	C₂⁶	1	1	yes	characteristic
477	C₄×C₂₃	—	2	2	no	—
478	C₄×C₂₃	—	2	1	no	—
479	C₄×C₂₃	—	2	1	no	—
480	C₄×C₂₃	—	2	8	no	—
481	C₄×C₂₃	—	2	8	no	—
482	C₄×C₂₃	—	2	2	no	—
483	C₄×C₂₃	—	2	8	no	—
484	C₄×C₂₃	—	2	2	no	—
485	C₄×C₂₃	—	2	2	no	—
486	C₄×C₂₃	—	2	8	no	—
487	C₄×C₂₃	#585	1	4	yes	—
488	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	4	yes	complemented
489	C₂²×#41	C₂²×C₂₃	1	2	yes	complemented
490	#563	C₂²×C₂₃	1	8	yes	complemented
491	#563	C₂²×C₂₃	1	4	yes	complemented
492	#562	C₂²×C₂₃	1	8	yes	complemented
493	H(3,𝔽₄)	C₂²×C₂₃	1	4	yes	complemented
494	#560	C₂²×C₂₃	1	8	yes	complemented
495	#559	C₂²×C₂₃	1	8	yes	complemented
496	#559	C₂²×C₂₃	1	2	yes	complemented
497	Q₈²	C₂²×C₂₃	1	2	yes	complemented
498	#555	C₂²×C₂₃	1	8	yes	complemented
499	#555	C₂²×C₂₃	1	2	yes	complemented
500	#554	C₂²×C₂₃	1	8	yes	complemented
501	#554	C₂²×C₂₃	1	4	yes	complemented
502	#553	C₂²×C₂₃	1	16	yes	complemented
503	#553	C₂²×C₂₃	1	16	yes	complemented
504	#553	C₂²×C₂₃	1	8	yes	complemented
505	#553	C₂²×C₂₃	1	8	yes	complemented
506	#552	C₂²×C₂₃	1	8	yes	complemented
507	#551	C₂²×C₂₃	1	8	yes	complemented
508	#551	C₂²×C₂₃	1	16	yes	complemented
509	#551	C₂²×C₂₃	1	16	yes	complemented
510	#550	C₂²×C₂₃	1	4	yes	complemented
511	#548	C₂²×C₂₃	1	8	yes	complemented
512	#547	C₂²×C₂₃	1	16	yes	complemented
513	#547	C₂²×C₂₃	1	16	yes	complemented
514	#547	C₂²×C₂₃	1	8	yes	complemented
515	#547	C₂²×C₂₃	1	8	yes	complemented
516	#546	C₂²×C₂₃	1	16	yes	complemented
517	#546	C₂²×C₂₃	1	16	yes	complemented
518	#546	C₂²×C₂₃	1	16	yes	complemented
519	#546	C₂²×C₂₃	1	16	yes	complemented
520	#546	C₂²×C₂₃	1	8	yes	complemented
521	#546	C₂²×C₂₃	1	8	yes	complemented
522	D₄²	C₂²×C₂₃	1	8	yes	complemented
523	D₄²	C₂²×C₂₃	1	8	yes	complemented
524	D₄²	C₂²×C₂₃	1	2	yes	complemented
525	#544	C₂²×C₂₃	1	8	yes	complemented
526	#542	C₂²×C₂₃	1	8	yes	complemented
527	#542	C₂²×C₂₃	1	8	yes	complemented
528	#542	C₂²×C₂₃	1	16	yes	complemented
529	#540	C₂²×C₂₃	1	8	yes	complemented
530	#540	C₂²×C₂₃	1	8	yes	complemented
531	#539	C₂²×C₂₃	1	8	yes	complemented
532	#539	C₂²×C₂₃	1	16	yes	complemented
533	#538	C₂²×C₂₃	1	8	yes	complemented
534	#538	C₂²×C₂₃	1	16	yes	complemented
535	#538	C₂²×C₂₃	1	16	yes	complemented
536	#537	C₂²×C₂₃	1	8	yes	complemented
537	#536	C₂²×C₂₃	1	8	yes	complemented
538	#535	C₂²×C₂₃	1	8	yes	complemented
539	#534	C₂²×C₂₃	1	8	yes	complemented
540	#534	C₂²×C₂₃	1	8	yes	complemented
541	#534	C₂²×C₂₃	1	8	yes	complemented
542	#532	C₂²×C₂₃	1	4	yes	complemented
543	#532	C₂²×C₂₃	1	4	yes	complemented
544	#532	C₂²×C₂₃	1	4	yes	complemented
545	#532	C₂²×C₂₃	1	4	yes	complemented
546	#532	C₂²×C₂₃	1	8	yes	complemented
547	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
548	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic, complemented
549	#529	C₂²×C₂₃	1	4	yes	complemented
550	#529	C₂²×C₂₃	1	4	yes	complemented
551	#529	C₂²×C₂₃	1	4	yes	complemented
552	#529	C₂²×C₂₃	1	4	yes	complemented
553	#529	C₂²×C₂₃	1	4	yes	complemented
554	#529	C₂²×C₂₃	1	4	yes	complemented
555	#529	C₂²×C₂₃	1	4	yes	complemented
556	#529	C₂²×C₂₃	1	4	yes	complemented
557	#529	C₂²×C₂₃	1	8	yes	complemented
558	C₂×#126	C₂²×C₂₃	1	4	yes	complemented
559	C₂×#125	C₂²×C₂₃	1	2	yes	complemented
560	C₂×#124	C₂²×C₂₃	1	2	yes	complemented
561	C₂×#124	C₂²×C₂₃	1	2	yes	complemented
562	#525	C₂²×C₂₃	1	8	yes	complemented
563	#525	C₂²×C₂₃	1	8	yes	complemented
564	C₂×#123	C₂²×C₂₃	1	4	yes	complemented
565	C₂×#123	C₂²×C₂₃	1	8	yes	complemented
566	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	complemented
567	C₂×#121	C₂²×C₂₃	1	2	yes	—
568	C₂×#121	C₂²×C₂₃	1	4	yes	complemented
569	C₂×#121	C₂²×C₂₃	1	8	yes	complemented
570	#520	C₂²×C₂₃	1	8	yes	complemented
571	#518	C₂²×C₂₃	1	4	yes	complemented
572	#518	C₂²×C₂₃	1	8	yes	complemented
573	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	complemented
574	C₂×C₄×D₄	C₂²×C₂₃	1	4	yes	complemented
575	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	complemented
576	C₂×C₄×D₄	C₂²×C₂₃	1	4	yes	complemented
577	C₂×#117	C₂²×C₂₃	1	4	yes	complemented
578	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic, complemented
579	C₂×C₂₃	—	2	2	no	—
580	C₂×C₂₃	—	2	4	no	—
581	C₂×C₂₃	—	4	8	no	—
582	C₂×C₂₃	—	4	8	no	—
583	C₂×C₂₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
584	C₂×C₂₃	C₂×#585	1	2	yes	—
585	H(5,𝔽₂)	—	4	16	no	—
586	C₂×#41	—	4	8	no	—
587	C₂×#41	C₂³×C₂₃	1	8	yes	—
588	C₂×#41	C₂³×C₂₃	1	8	yes	—
589	C₂×#41	C₂³×C₂₃	1	8	yes	—
590	C₂×#41	C₂³×C₂₃	1	8	yes	—
591	C₂×#41	C₂³×C₂₃	1	16	yes	—
592	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
593	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
594	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
595	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
596	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
597	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
598	C₂²×D₄	C₂³×C₂₃	1	8	yes	—
599	C₂²×D₄	C₂³×C₂₃	1	16	yes	—
600	C₂²×D₄	C₂³×C₂₃	1	8	yes	—
601	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
602	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
603	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
604	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
605	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
606	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
607	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
608	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
609	C₄⋊Q₈	C₂³×C₂₃	1	8	yes	—
610	C₄⋊Q₈	C₂³×C₂₃	1	8	yes	—
611	C₄⋊Q₈	C₂³×C₂₃	1	8	yes	—
612	#127	C₂³×C₂₃	1	4	yes	—
613	#127	C₂³×C₂₃	1	2	yes	—
614	#127	C₂³×C₂₃	1	2	yes	—
615	#127	C₂³×C₂₃	1	8	yes	—
616	#126	C₂³×C₂₃	1	8	yes	—
617	#126	C₂³×C₂₃	1	8	yes	—
618	#126	C₂³×C₂₃	1	8	yes	—
619	#126	C₂³×C₂₃	1	8	yes	—
620	#126	C₂³×C₂₃	1	16	yes	—
621	#126	C₂³×C₂₃	1	16	yes	—
622	#126	C₂³×C₂₃	1	16	yes	—
623	#125	C₂³×C₂₃	1	4	yes	—
624	#125	C₂³×C₂₃	1	4	yes	—
625	#125	C₂³×C₂₃	1	4	yes	—
626	#125	C₂³×C₂₃	1	4	yes	—
627	#125	C₂³×C₂₃	1	8	yes	—
628	#125	C₂³×C₂₃	1	16	yes	—
629	#124	C₂³×C₂₃	1	4	yes	—
630	#124	C₂³×C₂₃	1	4	yes	—
631	#124	C₂³×C₂₃	1	4	yes	—
632	#124	C₂³×C₂₃	1	4	yes	—
633	#124	C₂³×C₂₃	1	8	yes	—
634	#124	C₂³×C₂₃	1	4	yes	—
635	#124	C₂³×C₂₃	1	4	yes	—
636	#124	C₂³×C₂₃	1	8	yes	—
637	#124	C₂³×C₂₃	1	16	yes	—
638	#124	C₂³×C₂₃	1	8	yes	—
639	#124	C₂³×C₂₃	1	8	yes	—
640	#124	C₂³×C₂₃	1	16	yes	—
641	#123	C₂³×C₂₃	1	8	yes	—
642	#123	C₂³×C₂₃	1	8	yes	—
643	#123	C₂³×C₂₃	1	8	yes	—
644	#123	C₂³×C₂₃	1	8	yes	—
645	#123	C₂³×C₂₃	1	16	yes	—
646	#123	C₂³×C₂₃	1	16	yes	—
647	#123	C₂³×C₂₃	1	16	yes	—
648	#123	C₂³×C₂₃	1	16	yes	—
649	#123	C₂³×C₂₃	1	16	yes	—
650	#123	C₂³×C₂₃	1	16	yes	—
651	#123	C₂³×C₂₃	1	16	yes	—
652	#123	C₂³×C₂₃	1	8	yes	—
653	#123	C₂³×C₂₃	1	8	yes	—
654	#123	C₂³×C₂₃	1	16	yes	—
655	#123	C₂³×C₂₃	1	16	yes	—
656	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
657	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
658	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
659	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
660	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	—
661	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
662	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	—
663	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	—
664	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	—
665	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	—
666	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	—
667	#121	C₂³×C₂₃	1	4	yes	—
668	#121	C₂³×C₂₃	1	4	yes	—
669	#121	C₂³×C₂₃	1	4	yes	—
670	#121	C₂³×C₂₃	1	4	yes	—
671	#121	C₂³×C₂₃	1	8	yes	—
672	#121	C₂³×C₂₃	1	8	yes	—
673	#121	C₂³×C₂₃	1	8	yes	—
674	#121	C₂³×C₂₃	1	8	yes	—
675	#121	C₂³×C₂₃	1	16	yes	—
676	#121	C₂³×C₂₃	1	16	yes	—
677	#121	C₂³×C₂₃	1	8	yes	—
678	#121	C₂³×C₂₃	1	8	yes	—
679	#121	C₂³×C₂₃	1	16	yes	—
680	#121	C₂³×C₂₃	1	8	yes	—
681	#121	C₂³×C₂₃	1	16	yes	—
682	#121	C₂³×C₂₃	1	16	yes	—
683	#121	C₂³×C₂₃	1	16	yes	—
684	#121	C₂³×C₂₃	1	16	yes	—
685	#121	C₂³×C₂₃	1	16	yes	—
686	#121	C₂³×C₂₃	1	16	yes	—
687	#120	C₂³×C₂₃	1	16	yes	—
688	#120	C₂³×C₂₃	1	16	yes	—
689	#120	C₂³×C₂₃	1	8	yes	—
690	#120	C₂³×C₂₃	1	16	yes	—
691	#120	C₂³×C₂₃	1	8	yes	—
692	#120	C₂³×C₂₃	1	16	yes	—
693	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
694	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
695	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
696	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
697	C₄×Q₈	C₂³×C₂₃	1	8	yes	—
698	C₄×D₄	C₂³×C₂₃	1	4	yes	—
699	C₄×D₄	C₂³×C₂₃	1	8	yes	—
700	C₄×D₄	C₂³×C₂₃	1	4	yes	—
701	C₄×D₄	C₂³×C₂₃	1	8	yes	—
702	C₄×D₄	C₂³×C₂₃	1	8	yes	—
703	C₄×D₄	C₂³×C₂₃	1	4	yes	—
704	C₄×D₄	C₂³×C₂₃	1	8	yes	—
705	C₄×D₄	C₂³×C₂₃	1	4	yes	—
706	C₄×D₄	C₂³×C₂₃	1	8	yes	—
707	C₄×D₄	C₂³×C₂₃	1	8	yes	—
708	C₄×D₄	C₂³×C₂₃	1	8	yes	—
709	C₄×D₄	C₂³×C₂₃	1	8	yes	—
710	C₄×D₄	C₂³×C₂₃	1	16	yes	—
711	C₄×D₄	C₂³×C₂₃	1	16	yes	—
712	C₄×D₄	C₂³×C₂₃	1	16	yes	—
713	C₄×D₄	C₂³×C₂₃	1	16	yes	—
714	C₄×D₄	C₂³×C₂₃	1	8	yes	—
715	C₄×D₄	C₂³×C₂₃	1	8	yes	—
716	C₄×D₄	C₂³×C₂₃	1	16	yes	—
717	C₄×D₄	C₂³×C₂₃	1	8	yes	—
718	C₄×D₄	C₂³×C₂₃	1	16	yes	—
719	#117	C₂³×C₂₃	1	8	yes	—
720	#117	C₂³×C₂₃	1	8	yes	—
721	#117	C₂³×C₂₃	1	8	yes	—
722	#117	C₂³×C₂₃	1	8	yes	—
723	#117	C₂³×C₂₃	1	8	yes	—
724	#117	C₂³×C₂₃	1	8	yes	—
725	#117	C₂³×C₂₃	1	16	yes	—
726	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
727	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
728	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
729	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
730	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
731	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
732	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
733	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
734	C₂×C₄⋊C₄	C₂³×C₂₃	1	16	yes	—
735	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
736	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
737	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
738	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
739	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
740	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
741	C₂×C₂²⋊C₄	C₂³×C₂₃	1	16	yes	—
742	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
743	C₂×C₂²⋊C₄	C₂³×C₂₃	1	16	yes	—
744	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
745	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
746	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
747	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
748	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
749	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
750	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
751	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
752	C₂₃	#62822	1	1	yes	characteristic, direct product factor, Sylow
753	C₂⁴	C₂⁴×C₂₃	1	4	yes	—
754	C₂⁴	C₂⁴×C₂₃	1	4	yes	—
755	C₂⁴	C₂⁴×C₂₃	1	8	yes	—
756	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
757	#41	—	4	16	no	—
758	#41	—	4	16	no	—
759	#41	—	4	16	no	—
760	#41	—	4	32	no	—
761	#41	—	4	16	no	—
762	C₂×Q₈	—	4	4	no	—
763	C₂×Q₈	—	4	4	no	—
764	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
765	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
766	C₂×Q₈	C₂⁴×C₂₃	1	8	yes	—
767	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
768	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
769	C₂×D₄	—	2	16	no	—
770	C₂×D₄	—	2	16	no	—
771	C₂×D₄	—	4	8	no	—
772	C₂×D₄	—	4	4	no	—
773	C₂×D₄	—	4	16	no	—
774	C₂×D₄	—	4	4	no	—
775	C₂×D₄	—	4	16	no	—
776	C₂×D₄	—	4	32	no	—
777	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
778	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
779	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
780	C₂×D₄	C₂⁴×C₂₃	1	16	yes	—
781	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
782	C₂×D₄	C₂⁴×C₂₃	1	16	yes	—
783	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
784	C₂×D₄	C₂⁴×C₂₃	1	16	yes	—
785	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
786	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
787	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
788	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
789	C₂×D₄	C₂⁴×C₂₃	1	16	yes	—
790	C₂²×C₄	—	2	4	no	—
791	C₂²×C₄	—	4	4	no	—
792	C₂²×C₄	—	4	8	no	—
793	C₂²×C₄	—	4	8	no	—
794	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
795	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
796	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
797	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
798	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
799	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
800	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
801	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
802	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
803	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
804	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
805	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
806	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
807	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
808	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
809	C₂²×C₄	C₂⁴×C₂₃	1	16	yes	—
810	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
811	C₂²×C₄	C₂⁴×C₂₃	1	16	yes	—
812	C₂²×C₄	C₂⁴×C₂₃	1	16	yes	—
813	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
814	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
815	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
816	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
817	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
818	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
819	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
820	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
821	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
822	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
823	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
824	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
825	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
826	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
827	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
828	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
829	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
830	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
831	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
832	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
833	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
834	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
835	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
836	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
837	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
838	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
839	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
840	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
841	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
842	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
843	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
844	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
845	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
846	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
847	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
848	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
849	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
850	C₄²	C₂⁴×C₂₃	1	2	yes	—
851	C₄²	C₂⁴×C₂₃	1	2	yes	—
852	C₄²	C₂⁴×C₂₃	1	2	yes	—
853	C₄²	C₂⁴×C₂₃	1	2	yes	—
854	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
855	C₄²	C₂⁴×C₂₃	1	2	yes	—
856	C₄²	C₂⁴×C₂₃	1	2	yes	—
857	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
858	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
859	C₄²	C₂⁴×C₂₃	1	8	yes	—
860	C₄²	C₂⁴×C₂₃	1	8	yes	—
861	C₄²	C₂⁴×C₂₃	1	8	yes	—
862	C₄²	C₂⁴×C₂₃	1	8	yes	—
863	C₂³	—	2	8	no	—
864	C₂³	—	2	8	no	—
865	C₂³	—	4	2	no	—
866	C₂³	—	4	4	no	—
867	C₂³	—	4	4	no	—
868	C₂³	—	4	8	no	—
869	C₂³	—	4	8	no	—
870	C₂³	—	4	16	no	—
871	C₂³	C₂₃×H(5,𝔽₂)	1	4	yes	—
872	C₂³	C₂⁵×C₂₃	1	8	yes	—
873	C₂³	C₂⁵×C₂₃	1	8	yes	—
874	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
875	C₂³	C₂⁵×C₂₃	1	2	yes	—
876	Q₈	—	2	8	no	—
877	Q₈	—	4	4	no	—
878	Q₈	—	4	4	no	—
879	Q₈	—	4	4	no	—
880	Q₈	—	4	8	no	—
881	D₄	—	2	16	no	—
882	D₄	—	2	16	no	—
883	D₄	—	2	32	no	—
884	D₄	—	2	8	no	—
885	D₄	—	2	16	no	—
886	D₄	—	4	16	no	—
887	D₄	—	4	8	no	—
888	D₄	—	4	4	no	—
889	D₄	—	4	4	no	—
890	D₄	—	4	16	no	—
891	D₄	—	4	8	no	—
892	D₄	—	4	4	no	—
893	D₄	—	4	16	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	4	no	—
897	C₂×C₄	—	2	4	no	—
898	C₂×C₄	—	2	8	no	—
899	C₂×C₄	—	2	8	no	—
900	C₂×C₄	—	2	4	no	—
901	C₂×C₄	—	2	4	no	—
902	C₂×C₄	—	2	4	no	—
903	C₂×C₄	—	2	16	no	—
904	C₂×C₄	—	4	16	no	—
905	C₂×C₄	—	4	8	no	—
906	C₂×C₄	—	4	2	no	—
907	C₂×C₄	—	4	2	no	—
908	C₂×C₄	—	4	4	no	—
909	C₂×C₄	—	4	2	no	—
910	C₂×C₄	—	4	8	no	—
911	C₂×C₄	—	4	16	no	—
912	C₂×C₄	—	4	4	no	—
913	C₂×C₄	—	4	16	no	—
914	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
915	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
916	C₂×C₄	C₂⁵×C₂₃	1	8	yes	—
917	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
918	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
919	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
920	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
921	C₂×C₄	C₂⁵×C₂₃	1	8	yes	—
922	C₂×C₄	C₂⁵×C₂₃	1	8	yes	—
923	C₂×C₄	C₂⁵×C₂₃	1	8	yes	—
924	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
925	C₂²	—	2	2	no	—
926	C₂²	—	2	2	no	—
927	C₂²	—	2	2	no	—
928	C₂²	—	2	8	no	—
929	C₂²	—	2	8	no	—
930	C₂²	—	2	8	no	—
931	C₂²	—	2	16	no	—
932	C₂²	—	2	8	no	—
933	C₂²	—	4	4	no	—
934	C₂²	—	8	8	no	—
935	C₂²	—	8	8	no	—
936	C₂²	—	16	8	no	—
937	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
938	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	4	yes	—
939	C₂²	C₂⁶×C₂₃	1	1	yes	characteristic
940	C₄	—	2	2	no	—
941	C₄	—	2	1	no	—
942	C₄	—	2	1	no	—
943	C₄	—	2	8	no	—
944	C₄	—	2	8	no	—
945	C₄	—	2	2	no	—
946	C₄	—	2	8	no	—
947	C₄	—	2	2	no	—
948	C₄	—	2	2	no	—
949	C₄	—	2	8	no	—
950	C₄	C₂₃×#585	1	4	yes	—
951	C₂	—	2	2	no	—
952	C₂	—	2	4	no	—
953	C₂	—	4	8	no	—
954	C₂	—	4	8	no	—
955	C₂	C₂²×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
956	C₂	C₂×C₂₃×#585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₂₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3560	C₂	semidirect
2. C₂₃×#3559	C₂	semidirect
3. C₂₃×#3558	C₂	semidirect
4. C₂₃×#3545	C₂	semidirect
5. C₂₃×#3544	C₂	semidirect
6. C₂₃×#3543	C₂	semidirect
7. C₂₃×#3522	C₂	semidirect
8. C₂₃×#3519	C₂	semidirect
9. C₂₃×#3513	C₂	semidirect
10. C₂₃×#3505	C₂	semidirect
11. C₂₃×#3496	C₂	semidirect
12. C₂₃×#3494	C₂	semidirect
13. C₂₃×#3485	C₂	semidirect
14. C₂×C₂₃×#532	C₂	semidirect
15. C₂×C₂₃×#529	C₂	semidirect
16. C₂×C₂₃×H(5,𝔽₂)	C₂²	semidirect
17. C₂²×#41×C₂₃	C₂²	semidirect
18. C₂₃×#563	C₂²	semidirect
19. C₂₃×#563	C₂²	semidirect
20. C₂₃×#562	C₂²	semidirect
21. C₂₃×H(3,𝔽₄)	C₂²	semidirect
22. C₂₃×#560	C₂²	semidirect
23. C₂₃×#559	C₂²	semidirect
24. C₂₃×#559	C₂²	semidirect
25. Q₈²×C₂₃	C₂²	semidirect
26. C₂₃×#555	C₂²	semidirect
27. C₂₃×#555	C₂²	semidirect
28. C₂₃×#554	C₂²	semidirect
29. C₂₃×#554	C₂²	semidirect
30. C₂₃×#553	C₂²	semidirect
31. C₂₃×#553	C₂²	semidirect
32. C₂₃×#553	C₂²	semidirect
33. C₂₃×#553	C₂²	semidirect
34. C₂₃×#552	C₂²	semidirect
35. C₂₃×#551	C₂²	semidirect
36. C₂₃×#551	C₂²	semidirect
37. C₂₃×#551	C₂²	semidirect
38. C₂₃×#550	C₂²	semidirect
39. C₂₃×#548	C₂²	semidirect
40. C₂₃×#547	C₂²	semidirect
41. C₂₃×#547	C₂²	semidirect
42. C₂₃×#547	C₂²	semidirect
43. C₂₃×#547	C₂²	semidirect
44. C₂₃×#546	C₂²	semidirect
45. C₂₃×#546	C₂²	semidirect
46. C₂₃×#546	C₂²	semidirect
47. C₂₃×#546	C₂²	semidirect
48. C₂₃×#546	C₂²	semidirect
49. C₂₃×#546	C₂²	semidirect
50. D₄²×C₂₃	C₂²	semidirect
51. D₄²×C₂₃	C₂²	semidirect
52. D₄²×C₂₃	C₂²	semidirect
53. C₂₃×#544	C₂²	semidirect
54. C₂₃×#542	C₂²	semidirect
55. C₂₃×#542	C₂²	semidirect
56. C₂₃×#542	C₂²	semidirect
57. C₂₃×#540	C₂²	semidirect
58. C₂₃×#540	C₂²	semidirect
59. C₂₃×#539	C₂²	semidirect
60. C₂₃×#539	C₂²	semidirect
61. C₂₃×#538	C₂²	semidirect
62. C₂₃×#538	C₂²	semidirect
63. C₂₃×#538	C₂²	semidirect
64. C₂₃×#537	C₂²	semidirect
65. C₂₃×#536	C₂²	semidirect
66. C₂₃×#535	C₂²	semidirect
67. C₂₃×#534	C₂²	semidirect
68. C₂₃×#534	C₂²	semidirect
69. C₂₃×#534	C₂²	semidirect
70. C₂₃×#532	C₂²	semidirect
71. C₂₃×#532	C₂²	semidirect
72. C₂₃×#532	C₂²	semidirect
73. C₂₃×#532	C₂²	semidirect
74. C₂₃×#532	C₂²	semidirect
75. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
76. C₂×C₂₃×#127	C₂²	semidirect
77. C₂₃×#529	C₂²	semidirect
78. C₂₃×#529	C₂²	semidirect
79. C₂₃×#529	C₂²	semidirect
80. C₂₃×#529	C₂²	semidirect
81. C₂₃×#529	C₂²	semidirect
82. C₂₃×#529	C₂²	semidirect
83. C₂₃×#529	C₂²	semidirect
84. C₂₃×#529	C₂²	semidirect
85. C₂₃×#529	C₂²	semidirect
86. C₂×C₂₃×#126	C₂²	semidirect
87. C₂×C₂₃×#125	C₂²	semidirect
88. C₂×C₂₃×#124	C₂²	semidirect
89. C₂×C₂₃×#124	C₂²	semidirect
90. C₂₃×#525	C₂²	semidirect
91. C₂₃×#525	C₂²	semidirect
92. C₂×C₂₃×#123	C₂²	semidirect
93. C₂×C₂₃×#123	C₂²	semidirect
94. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
96. C₂×C₂₃×#121	C₂²	semidirect
97. C₂×C₂₃×#121	C₂²	semidirect
98. C₂₃×#520	C₂²	semidirect
99. C₂₃×#518	C₂²	semidirect
100. C₂₃×#518	C₂²	semidirect
101. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
102. C₂×C₄×D₄×C₂₃	C₂²	semidirect
103. C₂×C₄×D₄×C₂₃	C₂²	semidirect
104. C₂×C₄×D₄×C₂₃	C₂²	semidirect
105. C₂×C₂₃×#117	C₂²	semidirect
106. C₂²×C₄²×C₂₃	C₂²	semidirect
384. #62822	C₂₃	direct (N × H)
447. #3560	C₂×C₂₃	semidirect
448. #3559	C₂×C₂₃	semidirect
449. #3558	C₂×C₂₃	semidirect
450. #3545	C₂×C₂₃	semidirect
451. #3544	C₂×C₂₃	semidirect
452. #3543	C₂×C₂₃	semidirect
453. #3522	C₂×C₂₃	semidirect
454. #3519	C₂×C₂₃	semidirect
455. #3513	C₂×C₂₃	semidirect
456. #3505	C₂×C₂₃	semidirect
457. #3496	C₂×C₂₃	semidirect
458. #3494	C₂×C₂₃	semidirect
459. #3485	C₂×C₂₃	semidirect
460. C₂×#532	C₂×C₂₃	semidirect
461. C₂×#529	C₂×C₂₃	semidirect
488. C₂×H(5,𝔽₂)	C₂²×C₂₃	semidirect
489. C₂²×#41	C₂²×C₂₃	semidirect
490. #563	C₂²×C₂₃	semidirect
491. #563	C₂²×C₂₃	semidirect
492. #562	C₂²×C₂₃	semidirect
493. H(3,𝔽₄)	C₂²×C₂₃	semidirect
494. #560	C₂²×C₂₃	semidirect
495. #559	C₂²×C₂₃	semidirect
496. #559	C₂²×C₂₃	semidirect
497. Q₈²	C₂²×C₂₃	semidirect
498. #555	C₂²×C₂₃	semidirect
499. #555	C₂²×C₂₃	semidirect
500. #554	C₂²×C₂₃	semidirect
501. #554	C₂²×C₂₃	semidirect
502. #553	C₂²×C₂₃	semidirect
503. #553	C₂²×C₂₃	semidirect
504. #553	C₂²×C₂₃	semidirect
505. #553	C₂²×C₂₃	semidirect
506. #552	C₂²×C₂₃	semidirect
507. #551	C₂²×C₂₃	semidirect
508. #551	C₂²×C₂₃	semidirect
509. #551	C₂²×C₂₃	semidirect
510. #550	C₂²×C₂₃	semidirect
511. #548	C₂²×C₂₃	semidirect
512. #547	C₂²×C₂₃	semidirect
513. #547	C₂²×C₂₃	semidirect
514. #547	C₂²×C₂₃	semidirect
515. #547	C₂²×C₂₃	semidirect
516. #546	C₂²×C₂₃	semidirect
517. #546	C₂²×C₂₃	semidirect
518. #546	C₂²×C₂₃	semidirect
519. #546	C₂²×C₂₃	semidirect
520. #546	C₂²×C₂₃	semidirect
521. #546	C₂²×C₂₃	semidirect
522. D₄²	C₂²×C₂₃	semidirect
523. D₄²	C₂²×C₂₃	semidirect
524. D₄²	C₂²×C₂₃	semidirect
525. #544	C₂²×C₂₃	semidirect
526. #542	C₂²×C₂₃	semidirect
527. #542	C₂²×C₂₃	semidirect
528. #542	C₂²×C₂₃	semidirect
529. #540	C₂²×C₂₃	semidirect
530. #540	C₂²×C₂₃	semidirect
531. #539	C₂²×C₂₃	semidirect
532. #539	C₂²×C₂₃	semidirect
533. #538	C₂²×C₂₃	semidirect
534. #538	C₂²×C₂₃	semidirect
535. #538	C₂²×C₂₃	semidirect
536. #537	C₂²×C₂₃	semidirect
537. #536	C₂²×C₂₃	semidirect
538. #535	C₂²×C₂₃	semidirect
539. #534	C₂²×C₂₃	semidirect
540. #534	C₂²×C₂₃	semidirect
541. #534	C₂²×C₂₃	semidirect
542. #532	C₂²×C₂₃	semidirect
543. #532	C₂²×C₂₃	semidirect
544. #532	C₂²×C₂₃	semidirect
545. #532	C₂²×C₂₃	semidirect
546. #532	C₂²×C₂₃	semidirect
547. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
548. C₂×#127	C₂²×C₂₃	semidirect
549. #529	C₂²×C₂₃	semidirect
550. #529	C₂²×C₂₃	semidirect
551. #529	C₂²×C₂₃	semidirect
552. #529	C₂²×C₂₃	semidirect
553. #529	C₂²×C₂₃	semidirect
554. #529	C₂²×C₂₃	semidirect
555. #529	C₂²×C₂₃	semidirect
556. #529	C₂²×C₂₃	semidirect
557. #529	C₂²×C₂₃	semidirect
558. C₂×#126	C₂²×C₂₃	semidirect
559. C₂×#125	C₂²×C₂₃	semidirect
560. C₂×#124	C₂²×C₂₃	semidirect
561. C₂×#124	C₂²×C₂₃	semidirect
562. #525	C₂²×C₂₃	semidirect
563. #525	C₂²×C₂₃	semidirect
564. C₂×#123	C₂²×C₂₃	semidirect
565. C₂×#123	C₂²×C₂₃	semidirect
566. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
568. C₂×#121	C₂²×C₂₃	semidirect
569. C₂×#121	C₂²×C₂₃	semidirect
570. #520	C₂²×C₂₃	semidirect
571. #518	C₂²×C₂₃	semidirect
572. #518	C₂²×C₂₃	semidirect
573. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
574. C₂×C₄×D₄	C₂²×C₂₃	semidirect
575. C₂×C₄×D₄	C₂²×C₂₃	semidirect
576. C₂×C₄×D₄	C₂²×C₂₃	semidirect
577. C₂×#117	C₂²×C₂₃	semidirect
578. C₂²×C₄²	C₂²×C₂₃	semidirect
752. C₂₃	#62822	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×#3560	2
C₂₃×#3559	2
C₂₃×#3558	2
C₂₃×#3545	2
C₂₃×#3544	2
C₂₃×#3543	2
C₂₃×#3522	2
C₂₃×#3519	2
C₂₃×#3513	2
C₂₃×#3505	2
C₂₃×#3496	2
C₂₃×#3494	2
C₂₃×#3485	2
C₂×C₂₃×#532	2
C₂×C₂₃×#529	2
#62822	23

Subgroups — C23×#62822 #19210448

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#62822 #19210448