Subgroups — C₂₃×#61663 #19209289

Order 5888.

2064 conjugacy classes of subgroups.

The subgroup lattice has 1178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3551	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3500	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3323	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3322	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3301	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3300	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3282	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3280	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3277	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3275	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3211	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3202	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3200	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3198	C₂	1	2	yes	maximal, complemented
15	C₂₃×#3102	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3013	C₂	1	2	yes	maximal, complemented
17	C₂₃×#3009	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3008	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2979	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₂₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₂₃×#137	C₂²	1	2	yes	complemented
24	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×#135	C₂²	1	2	yes	complemented
26	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
27	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
28	C₂₃×#563	—	2	1	no	—
29	C₂₃×#560	—	2	1	no	—
30	C₂₃×#555	—	2	1	no	—
31	C₂₃×#553	C₂²	1	2	yes	complemented
32	C₂₃×#552	C₂²	1	2	yes	complemented
33	C₂₃×#551	—	2	1	no	—
34	C₂₃×#548	C₂²	1	2	yes	—
35	C₂₃×#548	C₂²	1	2	yes	complemented
36	C₂₃×#548	C₂²	1	2	yes	complemented
37	C₂₃×#546	—	2	2	no	—
38	C₂₃×#546	—	2	2	no	—
39	C₂₃×#546	C₂²	1	2	yes	—
40	C₂₃×#546	C₂²	1	2	yes	complemented
41	C₂₃×#546	C₂²	1	2	yes	complemented
42	C₂₃×#540	—	2	2	no	—
43	C₂₃×#538	—	2	2	no	—
44	C₂₃×#537	C₂²	1	2	yes	complemented
45	C₂₃×#536	—	2	1	no	—
46	C₂₃×#536	C₂²	1	1	yes	characteristic
47	C₂₃×#536	C₂²	1	1	yes	characteristic
48	C₂₃×#535	—	2	1	no	—
49	C₂₃×#535	C₂²	1	1	yes	characteristic
50	C₂₃×#535	C₂²	1	1	yes	characteristic, complemented
51	C₂₃×#532	—	2	1	no	—
52	C₂₃×#532	C₂²	1	1	yes	characteristic
53	C₂₃×#529	C₂²	1	2	yes	complemented
54	C₂×C₂₃×#124	—	2	1	no	—
55	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic, complemented
56	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic, complemented
57	C₂₃×#495	C₂²	1	2	yes	complemented
58	C₂₃×#495	C₂²	1	2	yes	complemented
59	C₂₃×#488	C₂²	1	2	yes	complemented
60	C₂₃×#488	C₂²	1	2	yes	complemented
61	C₂₃×#485	C₂²	1	2	yes	complemented
62	C₂₃×#485	C₂²	1	2	yes	complemented
63	C₂₃×#485	C₂²	1	2	yes	complemented
64	C₂₃×#482	C₂²	1	2	yes	complemented
65	C₂₃×#481	C₂²	1	2	yes	complemented
66	C₂₃×#480	C₂²	1	2	yes	complemented
67	C₂₃×#479	C₂²	1	2	yes	complemented
68	C₂₃×#478	C₂²	1	2	yes	complemented
69	C₂₃×#470	C₂²	1	2	yes	complemented
70	C₂₃×#469	C₂²	1	2	yes	complemented
71	C₂₃×#468	C₂²	1	2	yes	complemented
72	C₂₃×#468	C₂²	1	2	yes	complemented
73	C₂₃×#467	C₂²	1	2	yes	complemented
74	C₂₃×#466	C₂²	1	2	yes	complemented
75	C₂₃×#465	C₂²	1	2	yes	complemented
76	C₂₃×#465	C₂²	1	2	yes	complemented
77	C₂₃×#464	C₂²	1	2	yes	complemented
78	C₂₃×#464	C₂²	1	2	yes	complemented
79	C₂₃×#464	C₂²	1	2	yes	complemented
80	C₂₃×#463	C₂²	1	2	yes	complemented
81	C₂₃×#463	C₂²	1	2	yes	complemented
82	C₂₃×#463	C₂²	1	2	yes	complemented
83	C₂₃×#452	C₂²	1	2	yes	—
84	C₂₃×#452	C₂²	1	2	yes	complemented
85	C₂₃×#452	C₂²	1	2	yes	complemented
86	C₂₃×#451	C₂²	1	2	yes	complemented
87	C₂₃×#451	C₂²	1	2	yes	complemented
88	C₂₃×#451	C₂²	1	2	yes	complemented
89	C₂₃×#450	C₂²	1	2	yes	—
90	C₂₃×#450	C₂²	1	2	yes	complemented
91	C₂₃×#450	C₂²	1	2	yes	complemented
92	C₂₃×#449	C₂²	1	2	yes	—
93	C₂₃×#449	C₂²	1	2	yes	—
94	C₂₃×#449	C₂²	1	2	yes	complemented
95	C₂₃×#449	C₂²	1	2	yes	complemented
96	C₂₃×#449	C₂²	1	2	yes	complemented
97	C₂₃×#448	C₂²	1	2	yes	complemented
98	C₂₃×#448	C₂²	1	2	yes	complemented
99	C₂₃×#447	C₂²	1	2	yes	—
100	C₂₃×#447	C₂²	1	2	yes	—
101	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
102	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
103	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
104	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
105	C₂₃×#436	C₂²	1	2	yes	complemented
106	C₂₃×#436	C₂²	1	2	yes	complemented
107	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
108	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
109	C₂₃×#431	C₂²	1	2	yes	complemented
110	C₂₃×#418	C₂²	1	1	yes	characteristic
111	C₂₃×#418	C₂²	1	1	yes	characteristic, complemented
112	C₂₃×#417	C₂²	1	2	yes	complemented
113	C₂₃×#416	C₂²	1	1	yes	characteristic
114	C₂₃×#416	C₂²	1	1	yes	characteristic, complemented
115	C₂×C₂₃×#103	C₂²	1	2	yes	complemented
116	C₂₃×#408	C₂²	1	1	yes	characteristic
117	C₂₃×#408	C₂²	1	1	yes	characteristic
118	C₂₃×#408	C₂²	1	2	yes	complemented
119	C₂₃×2₋¹⁺⁴	—	4	2	no	—
120	C₂₃×2₋¹⁺⁴	—	4	2	no	—
121	C₂₃×H(5,𝔽₂)	—	4	2	no	—
122	C₂₃×H(5,𝔽₂)	—	4	2	no	—
123	C₂×#41×C₂₃	—	2	1	no	—
124	C₂×#41×C₂₃	—	2	1	no	—
125	C₂×#41×C₂₃	—	2	2	no	—
126	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
127	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
128	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
129	C₂×#41×C₂₃	C₂³	1	2	yes	—
130	C₂×#41×C₂₃	C₂³	1	2	yes	—
131	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
132	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
133	C₂²×Q₈×C₂₃	—	2	1	no	—
134	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
135	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
136	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
137	C₂²×D₄×C₂₃	—	2	1	no	—
138	C₂²×D₄×C₂₃	—	2	1	no	—
139	C₂²×D₄×C₂₃	—	2	1	no	—
140	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
141	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
142	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
143	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
144	C₂₃×#137	—	4	4	no	—
145	C₂₃×#137	—	4	2	no	—
146	C₂₃×AGL(1,ℤ/8)	—	4	2	no	—
147	C₂₃×#135	—	4	4	no	—
148	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
149	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
150	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₂₃	—	4	2	no	—
152	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
158	C₂×D₈×C₂₃	—	4	2	no	—
159	C₂×D₈×C₂₃	C₂³	1	2	yes	—
160	C₂×D₈×C₂₃	C₂³	1	2	yes	—
161	C₂×D₈×C₂₃	C₂³	1	2	yes	—
162	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
163	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
164	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
165	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
166	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
167	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
168	C₂₃×C₄⋊Q₈	—	2	1	no	—
169	C₂₃×C₄⋊Q₈	—	2	1	no	—
170	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
171	C₂₃×#127	—	2	1	no	—
172	C₂₃×#127	—	2	1	no	—
173	C₂₃×#127	D₄	1	1	yes	characteristic
174	C₂₃×#126	—	2	2	no	—
175	C₂₃×#126	—	2	2	no	—
176	C₂₃×#126	—	2	2	no	—
177	C₂₃×#125	—	2	2	no	—
178	C₂₃×#125	C₂³	1	2	yes	—
179	C₂₃×#124	—	2	1	no	—
180	C₂₃×#124	—	2	1	no	—
181	C₂₃×#124	—	2	1	no	—
182	C₂₃×#124	—	2	1	no	—
183	C₂₃×#124	—	2	2	no	—
184	C₂₃×#124	—	2	2	no	—
185	C₂₃×#124	—	2	2	no	—
186	C₂₃×#124	—	2	1	no	—
187	C₂₃×#124	—	2	1	no	—
188	C₂₃×#124	D₄	1	1	yes	characteristic
189	C₂₃×#124	D₄	1	1	yes	characteristic
190	C₂₃×#124	C₂³	1	2	yes	—
191	C₂₃×#124	C₂³	1	2	yes	—
192	C₂₃×#124	C₂³	1	2	yes	—
193	C₂₃×#123	—	2	1	no	—
194	C₂₃×#123	—	2	2	no	—
195	C₂₃×#123	—	2	1	no	—
196	C₂₃×#123	—	2	1	no	—
197	C₂₃×#123	—	2	1	no	—
198	C₂₃×#123	—	2	2	no	—
199	C₂₃×#123	—	2	2	no	—
200	C₂₃×#123	—	2	2	no	—
201	C₂₃×#123	—	2	2	no	—
202	C₂₃×#123	—	2	2	no	—
203	C₂₃×C₂²⋊Q₈	—	2	2	no	—
204	C₂₃×C₂²⋊Q₈	—	2	2	no	—
205	C₂₃×C₂²⋊Q₈	—	2	2	no	—
206	C₂₃×C₂²⋊Q₈	—	2	2	no	—
207	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
208	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
209	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
210	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
211	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
212	C₂₃×#121	—	2	2	no	—
213	C₂₃×#121	—	2	2	no	—
214	C₂₃×#121	—	2	2	no	—
215	C₂₃×#121	—	2	2	no	—
216	C₂₃×#121	—	2	2	no	—
217	C₂₃×#121	—	2	2	no	—
218	C₂₃×#121	—	2	2	no	—
219	C₂₃×#121	—	2	2	no	—
220	C₂₃×#121	—	2	2	no	—
221	C₂₃×#121	—	2	2	no	—
222	C₂₃×#121	D₄	1	2	yes	—
223	C₂₃×#121	D₄	1	2	yes	—
224	C₂₃×#121	C₂³	1	2	yes	—
225	C₂₃×#121	C₂³	1	2	yes	—
226	C₂₃×#121	C₂³	1	2	yes	—
227	C₂₃×#121	C₂³	1	2	yes	—
228	C₂₃×#121	C₂³	1	2	yes	—
229	C₂₃×#120	—	2	1	no	—
230	C₂₃×#120	—	2	2	no	—
231	C₂₃×#120	—	2	2	no	—
232	C₂₃×#120	—	2	2	no	—
233	C₂₃×#120	—	2	1	no	—
234	C₂₃×#120	—	2	2	no	—
235	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
236	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
237	C₄×D₄×C₂₃	—	2	2	no	—
238	C₄×D₄×C₂₃	—	2	2	no	—
239	C₄×D₄×C₂₃	—	2	2	no	—
240	C₄×D₄×C₂₃	—	2	2	no	—
241	C₄×D₄×C₂₃	—	2	2	no	—
242	C₄×D₄×C₂₃	—	2	2	no	—
243	C₄×D₄×C₂₃	C₂³	1	2	yes	—
244	C₄×D₄×C₂₃	C₂³	1	2	yes	—
245	C₄×D₄×C₂₃	C₂³	1	2	yes	—
246	C₄×D₄×C₂₃	C₂³	1	2	yes	—
247	C₂₃×#117	—	2	2	no	—
248	C₂₃×#117	—	2	2	no	—
249	C₂₃×#117	—	2	1	no	—
250	C₂₃×#117	C₂³	1	1	yes	characteristic
251	C₂₃×#117	C₂³	1	1	yes	characteristic
252	C₂₃×#117	C₂³	1	1	yes	characteristic
253	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
254	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
255	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
256	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
257	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
258	C₂×C₄²×C₂₃	—	2	1	no	—
259	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
260	C₂₃×#107	C₂³	1	2	yes	—
261	C₂₃×#107	C₂³	1	2	yes	—
262	C₂₃×#106	C₂³	1	2	yes	—
263	C₂₃×#106	C₂³	1	2	yes	—
264	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
265	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
266	C₂₃×#103	C₂³	1	2	yes	—
267	C₂₃×#103	C₂³	1	2	yes	—
268	C₂₃×#103	C₂³	1	2	yes	—
269	C₂₃×#103	C₂³	1	2	yes	—
270	C₂₃×#103	C₂³	1	2	yes	—
271	C₂₃×#103	C₂³	1	2	yes	—
272	C₂₃×#103	C₂³	1	2	yes	—
273	C₂₃×#103	C₂³	1	2	yes	—
274	C₂₃×#102	C₂³	1	2	yes	—
275	C₂₃×#102	C₂³	1	2	yes	—
276	C₂₃×#102	C₂³	1	2	yes	—
277	C₂₃×#102	C₂³	1	2	yes	—
278	C₂₃×#102	C₂³	1	2	yes	—
279	C₂₃×#102	C₂³	1	2	yes	—
280	C₂₃×#102	C₂³	1	2	yes	—
281	C₂₃×#102	C₂³	1	2	yes	—
282	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
283	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
284	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
285	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
286	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
287	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
288	C₄×C₈×C₂₃	C₂³	1	2	yes	—
289	C₄×C₈×C₂₃	C₂³	1	2	yes	—
290	C₂⁴×C₂₃	—	2	1	no	—
291	C₂⁴×C₂₃	—	2	1	no	—
292	C₂⁴×C₂₃	—	2	1	no	—
293	C₂⁴×C₂₃	—	2	1	no	—
294	#41×C₂₃	—	2	2	no	—
295	#41×C₂₃	—	2	2	no	—
296	#41×C₂₃	—	2	2	no	—
297	#41×C₂₃	—	2	2	no	—
298	#41×C₂₃	—	2	4	no	—
299	#41×C₂₃	—	4	1	no	—
300	#41×C₂₃	—	4	1	no	—
301	#41×C₂₃	—	4	1	no	—
302	#41×C₂₃	—	4	1	no	—
303	#41×C₂₃	—	4	1	no	—
304	#41×C₂₃	—	4	1	no	—
305	#41×C₂₃	—	4	2	no	—
306	#41×C₂₃	—	4	4	no	—
307	#41×C₂₃	—	4	4	no	—
308	#41×C₂₃	—	4	2	no	—
309	#41×C₂₃	—	4	2	no	—
310	#41×C₂₃	—	4	8	no	—
311	C₂×Q₈×C₂₃	—	2	2	no	—
312	C₂×Q₈×C₂₃	—	2	1	no	—
313	C₂×Q₈×C₂₃	—	2	1	no	—
314	C₂×Q₈×C₂₃	—	2	4	no	—
315	C₂×Q₈×C₂₃	—	4	2	no	—
316	C₂×Q₈×C₂₃	—	4	1	no	—
317	C₂×Q₈×C₂₃	—	4	1	no	—
318	C₂×Q₈×C₂₃	—	4	4	no	—
319	C₂×Q₈×C₂₃	—	4	1	no	—
320	C₂×Q₈×C₂₃	—	4	1	no	—
321	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
322	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
323	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
324	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
325	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
326	C₂×D₄×C₂₃	—	2	1	no	—
327	C₂×D₄×C₂₃	—	2	2	no	—
328	C₂×D₄×C₂₃	—	2	2	no	—
329	C₂×D₄×C₂₃	—	2	2	no	—
330	C₂×D₄×C₂₃	—	2	1	no	—
331	C₂×D₄×C₂₃	—	2	1	no	—
332	C₂×D₄×C₂₃	—	2	2	no	—
333	C₂×D₄×C₂₃	—	2	2	no	—
334	C₂×D₄×C₂₃	—	2	2	no	—
335	C₂×D₄×C₂₃	—	2	2	no	—
336	C₂×D₄×C₂₃	—	2	2	no	—
337	C₂×D₄×C₂₃	—	2	2	no	—
338	C₂×D₄×C₂₃	—	2	1	no	—
339	C₂×D₄×C₂₃	—	2	1	no	—
340	C₂×D₄×C₂₃	—	2	1	no	—
341	C₂×D₄×C₂₃	—	2	1	no	—
342	C₂×D₄×C₂₃	—	4	1	no	—
343	C₂×D₄×C₂₃	—	4	1	no	—
344	C₂×D₄×C₂₃	—	4	1	no	—
345	C₂×D₄×C₂₃	—	4	1	no	—
346	C₂×D₄×C₂₃	—	4	1	no	—
347	C₂×D₄×C₂₃	—	4	1	no	—
348	C₂×D₄×C₂₃	—	4	4	no	—
349	C₂×D₄×C₂₃	—	4	4	no	—
350	C₂×D₄×C₂₃	—	4	4	no	—
351	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
352	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
353	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
354	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
355	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
356	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
357	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
358	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
359	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
360	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
361	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
362	C₂²×C₄×C₂₃	—	2	1	no	—
363	C₂²×C₄×C₂₃	—	2	1	no	—
364	C₂²×C₄×C₂₃	—	2	2	no	—
365	C₂²×C₄×C₂₃	—	2	2	no	—
366	C₂²×C₄×C₂₃	—	2	1	no	—
367	C₂²×C₄×C₂₃	—	2	2	no	—
368	C₂²×C₄×C₂₃	—	2	1	no	—
369	C₂²×C₄×C₂₃	—	2	1	no	—
370	C₂²×C₄×C₂₃	—	2	2	no	—
371	C₂²×C₄×C₂₃	—	2	2	no	—
372	C₂²×C₄×C₂₃	—	2	2	no	—
373	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
374	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
375	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
376	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
377	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
378	Q₁₆×C₂₃	—	2	4	no	—
379	Q₁₆×C₂₃	—	4	2	no	—
380	Q₁₆×C₂₃	—	4	2	no	—
381	SD₁₆×C₂₃	—	2	4	no	—
382	SD₁₆×C₂₃	—	2	4	no	—
383	SD₁₆×C₂₃	—	4	2	no	—
384	SD₁₆×C₂₃	—	4	2	no	—
385	SD₁₆×C₂₃	—	4	2	no	—
386	SD₁₆×C₂₃	—	4	2	no	—
387	D₈×C₂₃	—	2	4	no	—
388	D₈×C₂₃	—	4	2	no	—
389	D₈×C₂₃	—	4	2	no	—
390	M₁₆×C₂₃	—	4	1	no	—
391	M₁₆×C₂₃	—	4	2	no	—
392	M₁₆×C₂₃	—	4	1	no	—
393	C₂×C₈×C₂₃	—	4	1	no	—
394	C₂×C₈×C₂₃	—	4	1	no	—
395	C₂×C₈×C₂₃	—	4	2	no	—
396	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
397	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
398	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
399	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
400	C₄⋊C₄×C₂₃	—	2	2	no	—
401	C₄⋊C₄×C₂₃	—	2	2	no	—
402	C₄⋊C₄×C₂₃	—	2	2	no	—
403	C₄⋊C₄×C₂₃	—	2	2	no	—
404	C₄⋊C₄×C₂₃	—	2	2	no	—
405	C₄⋊C₄×C₂₃	—	2	2	no	—
406	C₄⋊C₄×C₂₃	—	2	2	no	—
407	C₄⋊C₄×C₂₃	—	2	2	no	—
408	C₄⋊C₄×C₂₃	—	2	2	no	—
409	C₄⋊C₄×C₂₃	—	2	2	no	—
410	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
411	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
412	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
413	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
414	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
415	C₂²⋊C₄×C₂₃	—	2	2	no	—
416	C₂²⋊C₄×C₂₃	—	2	2	no	—
417	C₂²⋊C₄×C₂₃	—	2	2	no	—
418	C₂²⋊C₄×C₂₃	—	2	2	no	—
419	C₂²⋊C₄×C₂₃	—	2	1	no	—
420	C₂²⋊C₄×C₂₃	—	2	1	no	—
421	C₂²⋊C₄×C₂₃	—	2	1	no	—
422	C₂²⋊C₄×C₂₃	—	2	2	no	—
423	C₂²⋊C₄×C₂₃	—	2	2	no	—
424	C₂²⋊C₄×C₂₃	—	2	2	no	—
425	C₂²⋊C₄×C₂₃	—	2	2	no	—
426	C₂²⋊C₄×C₂₃	—	2	2	no	—
427	C₂²⋊C₄×C₂₃	—	2	2	no	—
428	C₂²⋊C₄×C₂₃	—	2	2	no	—
429	C₂²⋊C₄×C₂₃	—	2	2	no	—
430	C₂²⋊C₄×C₂₃	—	2	2	no	—
431	C₂²⋊C₄×C₂₃	—	2	2	no	—
432	C₂²⋊C₄×C₂₃	—	2	2	no	—
433	C₂²⋊C₄×C₂₃	—	2	2	no	—
434	C₂²⋊C₄×C₂₃	—	2	2	no	—
435	C₂²⋊C₄×C₂₃	—	2	2	no	—
436	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
437	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
438	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
440	C₄²×C₂₃	—	2	1	no	—
441	C₄²×C₂₃	—	2	2	no	—
442	C₄²×C₂₃	—	2	1	no	—
443	C₄²×C₂₃	—	2	2	no	—
444	C₄²×C₂₃	—	2	1	no	—
445	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
446	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
447	C₄²×C₂₃	C₂⁴	1	2	yes	—
448	#61663	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
449	C₂³×C₂₃	—	2	1	no	—
450	C₂³×C₂₃	—	2	2	no	—
451	C₂³×C₂₃	—	2	1	no	—
452	C₂³×C₂₃	—	2	1	no	—
453	C₂³×C₂₃	—	4	2	no	—
454	C₂³×C₂₃	—	4	2	no	—
455	C₂³×C₂₃	—	4	2	no	—
456	C₂³×C₂₃	—	8	1	no	—
457	C₂³×C₂₃	—	8	2	no	—
458	C₂³×C₂₃	—	8	2	no	—
459	C₂³×C₂₃	—	8	2	no	—
460	C₂³×C₂₃	—	8	2	no	—
461	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
462	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
463	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
464	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
465	Q₈×C₂₃	—	2	1	no	—
466	Q₈×C₂₃	—	2	2	no	—
467	Q₈×C₂₃	—	2	2	no	—
468	Q₈×C₂₃	—	2	2	no	—
469	Q₈×C₂₃	—	2	2	no	—
470	Q₈×C₂₃	—	4	1	no	—
471	Q₈×C₂₃	—	4	1	no	—
472	Q₈×C₂₃	—	4	4	no	—
473	Q₈×C₂₃	—	4	2	no	—
474	Q₈×C₂₃	—	8	1	no	—
475	Q₈×C₂₃	H(5,𝔽₂)	1	2	yes	—
476	D₄×C₂₃	—	2	4	no	—
477	D₄×C₂₃	—	2	1	no	—
478	D₄×C₂₃	—	2	2	no	—
479	D₄×C₂₃	—	2	1	no	—
480	D₄×C₂₃	—	2	1	no	—
481	D₄×C₂₃	—	2	2	no	—
482	D₄×C₂₃	—	2	1	no	—
483	D₄×C₂₃	—	2	1	no	—
484	D₄×C₂₃	—	4	1	no	—
485	D₄×C₂₃	—	4	1	no	—
486	D₄×C₂₃	—	4	1	no	—
487	D₄×C₂₃	—	4	2	no	—
488	D₄×C₂₃	—	4	2	no	—
489	D₄×C₂₃	—	4	1	no	—
490	D₄×C₂₃	—	4	2	no	—
491	D₄×C₂₃	—	4	2	no	—
492	D₄×C₂₃	—	4	2	no	—
493	D₄×C₂₃	—	4	2	no	—
494	D₄×C₂₃	—	4	2	no	—
495	D₄×C₂₃	—	4	2	no	—
496	D₄×C₂₃	—	4	4	no	—
497	D₄×C₂₃	—	8	1	no	—
498	D₄×C₂₃	—	8	2	no	—
499	D₄×C₂₃	—	8	2	no	—
500	D₄×C₂₃	—	8	2	no	—
501	D₄×C₂₃	—	8	2	no	—
502	D₄×C₂₃	—	8	2	no	—
503	D₄×C₂₃	—	8	2	no	—
504	D₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
505	C₂×C₄×C₂₃	—	2	4	no	—
506	C₂×C₄×C₂₃	—	2	1	no	—
507	C₂×C₄×C₂₃	—	2	1	no	—
508	C₂×C₄×C₂₃	—	2	1	no	—
509	C₂×C₄×C₂₃	—	2	2	no	—
510	C₂×C₄×C₂₃	—	2	1	no	—
511	C₂×C₄×C₂₃	—	2	1	no	—
512	C₂×C₄×C₂₃	—	2	2	no	—
513	C₂×C₄×C₂₃	—	2	1	no	—
514	C₂×C₄×C₂₃	—	2	1	no	—
515	C₂×C₄×C₂₃	—	2	2	no	—
516	C₂×C₄×C₂₃	—	2	2	no	—
517	C₂×C₄×C₂₃	—	2	2	no	—
518	C₂×C₄×C₂₃	—	2	2	no	—
519	C₂×C₄×C₂₃	—	2	2	no	—
520	C₂×C₄×C₂₃	—	4	2	no	—
521	C₂×C₄×C₂₃	—	4	2	no	—
522	C₂×C₄×C₂₃	—	4	2	no	—
523	C₂×C₄×C₂₃	—	4	4	no	—
524	C₂×C₄×C₂₃	—	4	4	no	—
525	C₂×C₄×C₂₃	—	4	2	no	—
526	C₂×C₄×C₂₃	—	8	2	no	—
527	C₂×C₄×C₂₃	—	8	2	no	—
528	C₂×C₄×C₂₃	—	8	2	no	—
529	C₂×C₄×C₂₃	—	8	2	no	—
530	C₂×C₄×C₂₃	—	8	1	no	—
531	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
532	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
533	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
534	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
535	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
536	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
537	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
538	C₈×C₂₃	—	2	2	no	—
539	C₈×C₂₃	—	2	2	no	—
540	C₈×C₂₃	—	2	2	no	—
541	C₈×C₂₃	—	2	2	no	—
542	#3551	C₂×C₂₃	1	1	yes	characteristic, complemented
543	#3500	C₂×C₂₃	1	1	yes	characteristic, complemented
544	#3323	C₂×C₂₃	1	2	yes	complemented
545	#3322	C₂×C₂₃	1	2	yes	complemented
546	#3301	C₂×C₂₃	1	2	yes	complemented
547	#3300	C₂×C₂₃	1	2	yes	complemented
548	#3282	C₂×C₂₃	1	2	yes	complemented
549	#3280	C₂×C₂₃	1	2	yes	complemented
550	#3277	C₂×C₂₃	1	2	yes	complemented
551	#3275	C₂×C₂₃	1	2	yes	complemented
552	#3211	C₂×C₂₃	1	2	yes	complemented
553	#3202	C₂×C₂₃	1	1	yes	characteristic, complemented
554	#3200	C₂×C₂₃	1	1	yes	characteristic, complemented
555	#3198	C₂×C₂₃	1	2	yes	complemented
556	#3102	C₂×C₂₃	1	2	yes	complemented
557	#3013	C₂×C₂₃	1	2	yes	complemented
558	#3009	C₂×C₂₃	1	1	yes	characteristic, complemented
559	#3008	C₂×C₂₃	1	1	yes	characteristic, complemented
560	#2979	C₂×C₂₃	1	1	yes	characteristic, complemented
561	C₂²×C₂₃	—	2	2	no	—
562	C₂²×C₂₃	—	2	2	no	—
563	C₂²×C₂₃	—	2	2	no	—
564	C₂²×C₂₃	—	2	2	no	—
565	C₂²×C₂₃	—	2	2	no	—
566	C₂²×C₂₃	—	2	1	no	—
567	C₂²×C₂₃	—	2	2	no	—
568	C₂²×C₂₃	—	2	2	no	—
569	C₂²×C₂₃	—	2	1	no	—
570	C₂²×C₂₃	—	2	1	no	—
571	C₂²×C₂₃	—	4	2	no	—
572	C₂²×C₂₃	—	4	2	no	—
573	C₂²×C₂₃	—	4	2	no	—
574	C₂²×C₂₃	—	4	2	no	—
575	C₂²×C₂₃	—	4	2	no	—
576	C₂²×C₂₃	—	4	1	no	—
577	C₂²×C₂₃	—	4	1	no	—
578	C₂²×C₂₃	—	4	2	no	—
579	C₂²×C₂₃	—	16	2	no	—
580	C₂²×C₂₃	—	16	2	no	—
581	C₂²×C₂₃	—	16	2	no	—
582	C₂²×C₂₃	—	16	2	no	—
583	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
584	C₄×C₂₃	—	2	2	no	—
585	C₄×C₂₃	—	2	2	no	—
586	C₄×C₂₃	—	2	1	no	—
587	C₄×C₂₃	—	2	2	no	—
588	C₄×C₂₃	—	2	2	no	—
589	C₄×C₂₃	—	2	1	no	—
590	C₄×C₂₃	—	2	1	no	—
591	C₄×C₂₃	—	4	2	no	—
592	C₄×C₂₃	—	4	2	no	—
593	C₄×C₂₃	—	4	2	no	—
594	C₄×C₂₃	—	4	2	no	—
595	C₄×C₂₃	—	4	2	no	—
596	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
597	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
598	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	1	yes	characteristic, complemented
599	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	1	yes	characteristic
600	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic, complemented
601	C₂×#137	C₂²×C₂₃	1	2	yes	complemented
602	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic
603	C₂×#135	C₂²×C₂₃	1	2	yes	complemented
604	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
605	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
606	#563	—	2	1	no	—
607	#560	—	2	1	no	—
608	#555	—	2	1	no	—
609	#553	C₂²×C₂₃	1	2	yes	complemented
610	#552	C₂²×C₂₃	1	2	yes	complemented
611	#551	—	2	1	no	—
612	#548	C₂²×C₂₃	1	2	yes	—
613	#548	C₂²×C₂₃	1	2	yes	complemented
614	#548	C₂²×C₂₃	1	2	yes	complemented
615	#546	—	2	2	no	—
616	#546	—	2	2	no	—
617	#546	C₂²×C₂₃	1	2	yes	—
618	#546	C₂²×C₂₃	1	2	yes	complemented
619	#546	C₂²×C₂₃	1	2	yes	complemented
620	#540	—	2	2	no	—
621	#538	—	2	2	no	—
622	#537	C₂²×C₂₃	1	2	yes	complemented
623	#536	—	2	1	no	—
624	#536	C₂²×C₂₃	1	1	yes	characteristic
625	#536	C₂²×C₂₃	1	1	yes	characteristic
626	#535	—	2	1	no	—
627	#535	C₂²×C₂₃	1	1	yes	characteristic
628	#535	C₂²×C₂₃	1	1	yes	characteristic, complemented
629	#532	—	2	1	no	—
630	#532	C₂²×C₂₃	1	1	yes	characteristic
631	#529	C₂²×C₂₃	1	2	yes	complemented
632	C₂×#124	—	2	1	no	—
633	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic, complemented
634	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic, complemented
635	#495	C₂²×C₂₃	1	2	yes	complemented
636	#495	C₂²×C₂₃	1	2	yes	complemented
637	#488	C₂²×C₂₃	1	2	yes	complemented
638	#488	C₂²×C₂₃	1	2	yes	complemented
639	#485	C₂²×C₂₃	1	2	yes	complemented
640	#485	C₂²×C₂₃	1	2	yes	complemented
641	#485	C₂²×C₂₃	1	2	yes	complemented
642	#482	C₂²×C₂₃	1	2	yes	complemented
643	#481	C₂²×C₂₃	1	2	yes	complemented
644	#480	C₂²×C₂₃	1	2	yes	complemented
645	#479	C₂²×C₂₃	1	2	yes	complemented
646	#478	C₂²×C₂₃	1	2	yes	complemented
647	#470	C₂²×C₂₃	1	2	yes	complemented
648	#469	C₂²×C₂₃	1	2	yes	complemented
649	#468	C₂²×C₂₃	1	2	yes	complemented
650	#468	C₂²×C₂₃	1	2	yes	complemented
651	#467	C₂²×C₂₃	1	2	yes	complemented
652	#466	C₂²×C₂₃	1	2	yes	complemented
653	#465	C₂²×C₂₃	1	2	yes	complemented
654	#465	C₂²×C₂₃	1	2	yes	complemented
655	#464	C₂²×C₂₃	1	2	yes	complemented
656	#464	C₂²×C₂₃	1	2	yes	complemented
657	#464	C₂²×C₂₃	1	2	yes	complemented
658	#463	C₂²×C₂₃	1	2	yes	complemented
659	#463	C₂²×C₂₃	1	2	yes	complemented
660	#463	C₂²×C₂₃	1	2	yes	complemented
661	#452	C₂²×C₂₃	1	2	yes	—
662	#452	C₂²×C₂₃	1	2	yes	complemented
663	#452	C₂²×C₂₃	1	2	yes	complemented
664	#451	C₂²×C₂₃	1	2	yes	complemented
665	#451	C₂²×C₂₃	1	2	yes	complemented
666	#451	C₂²×C₂₃	1	2	yes	complemented
667	#450	C₂²×C₂₃	1	2	yes	—
668	#450	C₂²×C₂₃	1	2	yes	complemented
669	#450	C₂²×C₂₃	1	2	yes	complemented
670	#449	C₂²×C₂₃	1	2	yes	—
671	#449	C₂²×C₂₃	1	2	yes	—
672	#449	C₂²×C₂₃	1	2	yes	complemented
673	#449	C₂²×C₂₃	1	2	yes	complemented
674	#449	C₂²×C₂₃	1	2	yes	complemented
675	#448	C₂²×C₂₃	1	2	yes	complemented
676	#448	C₂²×C₂₃	1	2	yes	complemented
677	#447	C₂²×C₂₃	1	2	yes	—
678	#447	C₂²×C₂₃	1	2	yes	—
679	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
680	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
681	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
682	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
683	#436	C₂²×C₂₃	1	2	yes	complemented
684	#436	C₂²×C₂₃	1	2	yes	complemented
685	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
686	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
687	#431	C₂²×C₂₃	1	2	yes	complemented
688	#418	C₂²×C₂₃	1	1	yes	characteristic
689	#418	C₂²×C₂₃	1	1	yes	characteristic, complemented
690	#417	C₂²×C₂₃	1	2	yes	complemented
691	#416	C₂²×C₂₃	1	1	yes	characteristic
692	#416	C₂²×C₂₃	1	1	yes	characteristic, complemented
693	C₂×#103	C₂²×C₂₃	1	2	yes	complemented
694	#408	C₂²×C₂₃	1	1	yes	characteristic
695	#408	C₂²×C₂₃	1	1	yes	characteristic
696	#408	C₂²×C₂₃	1	2	yes	complemented
697	C₂×C₂₃	—	4	2	no	—
698	C₂×C₂₃	—	4	1	no	—
699	C₂×C₂₃	—	4	1	no	—
700	C₂×C₂₃	—	4	1	no	—
701	C₂×C₂₃	—	4	2	no	—
702	C₂×C₂₃	—	8	2	no	—
703	C₂×C₂₃	—	8	1	no	—
704	C₂×C₂₃	—	8	1	no	—
705	C₂×C₂₃	#3484	1	1	yes	characteristic
706	C₂×C₂₃	#3584	1	2	yes	—
707	2₋¹⁺⁴	—	4	2	no	—
708	2₋¹⁺⁴	—	4	2	no	—
709	H(5,𝔽₂)	—	4	2	no	—
710	H(5,𝔽₂)	—	4	2	no	—
711	C₂×#41	—	2	1	no	—
712	C₂×#41	—	2	1	no	—
713	C₂×#41	—	2	2	no	—
714	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
715	C₂×#41	C₂³×C₂₃	1	2	yes	—
716	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
717	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
718	C₂×#41	C₂³×C₂₃	1	2	yes	—
719	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
720	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
721	C₂²×Q₈	—	2	1	no	—
722	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
723	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
724	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
725	C₂²×D₄	—	2	1	no	—
726	C₂²×D₄	—	2	1	no	—
727	C₂²×D₄	—	2	1	no	—
728	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
729	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
730	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
731	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
732	#137	—	4	4	no	—
733	#137	—	4	2	no	—
734	AGL(1,ℤ/8)	—	4	2	no	—
735	#135	—	4	4	no	—
736	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
737	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
738	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
739	C₂×SD₁₆	—	4	2	no	—
740	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
741	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
742	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
743	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
744	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
745	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
746	C₂×D₈	—	4	2	no	—
747	C₂×D₈	C₂³×C₂₃	1	2	yes	—
748	C₂×D₈	C₂³×C₂₃	1	2	yes	—
749	C₂×D₈	C₂³×C₂₃	1	2	yes	—
750	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
751	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
752	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
753	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
754	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
755	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
756	C₄⋊Q₈	—	2	1	no	—
757	C₄⋊Q₈	—	2	1	no	—
758	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
759	#127	—	2	1	no	—
760	#127	—	2	1	no	—
761	#127	D₄×C₂₃	1	1	yes	characteristic
762	#126	—	2	2	no	—
763	#126	—	2	2	no	—
764	#126	—	2	2	no	—
765	#125	—	2	2	no	—
766	#125	C₂³×C₂₃	1	2	yes	—
767	#124	—	2	1	no	—
768	#124	—	2	1	no	—
769	#124	—	2	1	no	—
770	#124	—	2	1	no	—
771	#124	—	2	2	no	—
772	#124	—	2	2	no	—
773	#124	—	2	2	no	—
774	#124	—	2	1	no	—
775	#124	—	2	1	no	—
776	#124	D₄×C₂₃	1	1	yes	characteristic
777	#124	D₄×C₂₃	1	1	yes	characteristic
778	#124	C₂³×C₂₃	1	2	yes	—
779	#124	C₂³×C₂₃	1	2	yes	—
780	#124	C₂³×C₂₃	1	2	yes	—
781	#123	—	2	1	no	—
782	#123	—	2	1	no	—
783	#123	—	2	1	no	—
784	#123	—	2	1	no	—
785	#123	—	2	2	no	—
786	#123	—	2	2	no	—
787	#123	—	2	2	no	—
788	#123	—	2	2	no	—
789	#123	—	2	2	no	—
790	#123	—	2	2	no	—
791	C₂²⋊Q₈	—	2	2	no	—
792	C₂²⋊Q₈	—	2	2	no	—
793	C₂²⋊Q₈	—	2	2	no	—
794	C₂²⋊Q₈	—	2	2	no	—
795	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
796	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
797	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
798	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
799	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
800	#121	—	2	2	no	—
801	#121	—	2	2	no	—
802	#121	—	2	2	no	—
803	#121	—	2	2	no	—
804	#121	—	2	2	no	—
805	#121	—	2	2	no	—
806	#121	—	2	2	no	—
807	#121	—	2	2	no	—
808	#121	—	2	2	no	—
809	#121	—	2	2	no	—
810	#121	D₄×C₂₃	1	2	yes	—
811	#121	D₄×C₂₃	1	2	yes	—
812	#121	C₂³×C₂₃	1	2	yes	—
813	#121	C₂³×C₂₃	1	2	yes	—
814	#121	C₂³×C₂₃	1	2	yes	—
815	#121	C₂³×C₂₃	1	2	yes	—
816	#121	C₂³×C₂₃	1	2	yes	—
817	#120	—	2	2	no	—
818	#120	—	2	2	no	—
819	#120	—	2	1	no	—
820	#120	—	2	1	no	—
821	#120	—	2	2	no	—
822	#120	—	2	2	no	—
823	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
824	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
825	C₄×D₄	—	2	2	no	—
826	C₄×D₄	—	2	2	no	—
827	C₄×D₄	—	2	2	no	—
828	C₄×D₄	—	2	2	no	—
829	C₄×D₄	—	2	2	no	—
830	C₄×D₄	—	2	2	no	—
831	C₄×D₄	C₂³×C₂₃	1	2	yes	—
832	C₄×D₄	C₂³×C₂₃	1	2	yes	—
833	C₄×D₄	C₂³×C₂₃	1	2	yes	—
834	C₄×D₄	C₂³×C₂₃	1	2	yes	—
835	#117	—	2	2	no	—
836	#117	—	2	1	no	—
837	#117	—	2	2	no	—
838	#117	C₂³×C₂₃	1	1	yes	characteristic
839	#117	C₂³×C₂₃	1	1	yes	characteristic
840	#117	C₂³×C₂₃	1	1	yes	characteristic
841	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
842	C₂×C₂²⋊C₄	—	2	2	no	—
843	C₂×C₂²⋊C₄	—	2	2	no	—
844	C₂×C₂²⋊C₄	—	2	2	no	—
845	C₂×C₂²⋊C₄	—	2	2	no	—
846	C₂×C₄²	—	2	1	no	—
847	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
848	#107	C₂³×C₂₃	1	2	yes	—
849	#107	C₂³×C₂₃	1	2	yes	—
850	#106	C₂³×C₂₃	1	2	yes	—
851	#106	C₂³×C₂₃	1	2	yes	—
852	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
853	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
854	#103	C₂³×C₂₃	1	2	yes	—
855	#103	C₂³×C₂₃	1	2	yes	—
856	#103	C₂³×C₂₃	1	2	yes	—
857	#103	C₂³×C₂₃	1	2	yes	—
858	#103	C₂³×C₂₃	1	2	yes	—
859	#103	C₂³×C₂₃	1	2	yes	—
860	#103	C₂³×C₂₃	1	2	yes	—
861	#103	C₂³×C₂₃	1	2	yes	—
862	#102	C₂³×C₂₃	1	2	yes	—
863	#102	C₂³×C₂₃	1	2	yes	—
864	#102	C₂³×C₂₃	1	2	yes	—
865	#102	C₂³×C₂₃	1	2	yes	—
866	#102	C₂³×C₂₃	1	2	yes	—
867	#102	C₂³×C₂₃	1	2	yes	—
868	#102	C₂³×C₂₃	1	2	yes	—
869	#102	C₂³×C₂₃	1	2	yes	—
870	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
871	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
872	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
873	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
874	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
875	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
876	C₄×C₈	C₂³×C₂₃	1	2	yes	—
877	C₄×C₈	C₂³×C₂₃	1	2	yes	—
878	C₂₃	#61663	1	1	yes	characteristic, direct product factor, Sylow
879	C₂⁴	—	2	1	no	—
880	C₂⁴	—	2	1	no	—
881	C₂⁴	—	2	1	no	—
882	C₂⁴	—	2	1	no	—
883	#41	—	2	2	no	—
884	#41	—	2	2	no	—
885	#41	—	2	2	no	—
886	#41	—	2	2	no	—
887	#41	—	2	4	no	—
888	#41	—	4	1	no	—
889	#41	—	4	1	no	—
890	#41	—	4	1	no	—
891	#41	—	4	1	no	—
892	#41	—	4	1	no	—
893	#41	—	4	1	no	—
894	#41	—	4	2	no	—
895	#41	—	4	4	no	—
896	#41	—	4	4	no	—
897	#41	—	4	2	no	—
898	#41	—	4	2	no	—
899	#41	—	4	8	no	—
900	C₂×Q₈	—	2	2	no	—
901	C₂×Q₈	—	2	1	no	—
902	C₂×Q₈	—	2	1	no	—
903	C₂×Q₈	—	2	4	no	—
904	C₂×Q₈	—	4	2	no	—
905	C₂×Q₈	—	4	1	no	—
906	C₂×Q₈	—	4	1	no	—
907	C₂×Q₈	—	4	4	no	—
908	C₂×Q₈	—	4	1	no	—
909	C₂×Q₈	—	4	1	no	—
910	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
911	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
912	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
913	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
914	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
915	C₂×D₄	—	2	1	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	1	no	—
920	C₂×D₄	—	2	1	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	2	no	—
927	C₂×D₄	—	2	1	no	—
928	C₂×D₄	—	2	1	no	—
929	C₂×D₄	—	2	1	no	—
930	C₂×D₄	—	2	1	no	—
931	C₂×D₄	—	4	1	no	—
932	C₂×D₄	—	4	1	no	—
933	C₂×D₄	—	4	1	no	—
934	C₂×D₄	—	4	1	no	—
935	C₂×D₄	—	4	1	no	—
936	C₂×D₄	—	4	1	no	—
937	C₂×D₄	—	4	4	no	—
938	C₂×D₄	—	4	4	no	—
939	C₂×D₄	—	4	4	no	—
940	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
941	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
942	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
943	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
944	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
945	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
946	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
947	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
948	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
949	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
950	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
951	C₂²×C₄	—	2	1	no	—
952	C₂²×C₄	—	2	1	no	—
953	C₂²×C₄	—	2	2	no	—
954	C₂²×C₄	—	2	2	no	—
955	C₂²×C₄	—	2	1	no	—
956	C₂²×C₄	—	2	2	no	—
957	C₂²×C₄	—	2	1	no	—
958	C₂²×C₄	—	2	1	no	—
959	C₂²×C₄	—	2	2	no	—
960	C₂²×C₄	—	2	2	no	—
961	C₂²×C₄	—	2	2	no	—
962	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
963	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
964	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
965	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
966	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
967	Q₁₆	—	2	4	no	—
968	Q₁₆	—	4	2	no	—
969	Q₁₆	—	4	2	no	—
970	SD₁₆	—	2	4	no	—
971	SD₁₆	—	2	4	no	—
972	SD₁₆	—	4	2	no	—
973	SD₁₆	—	4	2	no	—
974	SD₁₆	—	4	2	no	—
975	SD₁₆	—	4	2	no	—
976	D₈	—	2	4	no	—
977	D₈	—	4	2	no	—
978	D₈	—	4	2	no	—
979	M₁₆	—	4	1	no	—
980	M₁₆	—	4	2	no	—
981	M₁₆	—	4	1	no	—
982	C₂×C₈	—	4	1	no	—
983	C₂×C₈	—	4	1	no	—
984	C₂×C₈	—	4	2	no	—
985	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
986	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
987	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
988	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	2	no	—
991	C₄⋊C₄	—	2	2	no	—
992	C₄⋊C₄	—	2	2	no	—
993	C₄⋊C₄	—	2	2	no	—
994	C₄⋊C₄	—	2	2	no	—
995	C₄⋊C₄	—	2	2	no	—
996	C₄⋊C₄	—	2	2	no	—
997	C₄⋊C₄	—	2	2	no	—
998	C₄⋊C₄	—	2	2	no	—
999	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1000	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1001	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1002	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1003	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1026	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1027	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1028	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1029	C₄²	—	2	1	no	—
1030	C₄²	—	2	2	no	—
1031	C₄²	—	2	1	no	—
1032	C₄²	—	2	2	no	—
1033	C₄²	—	2	1	no	—
1034	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1035	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1036	C₄²	C₂⁴×C₂₃	1	2	yes	—
1037	C₂³	—	2	1	no	—
1038	C₂³	—	2	2	no	—
1039	C₂³	—	2	1	no	—
1040	C₂³	—	2	1	no	—
1041	C₂³	—	4	2	no	—
1042	C₂³	—	4	2	no	—
1043	C₂³	—	4	2	no	—
1044	C₂³	—	8	1	no	—
1045	C₂³	—	8	2	no	—
1046	C₂³	—	8	2	no	—
1047	C₂³	—	8	2	no	—
1048	C₂³	—	8	2	no	—
1049	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1050	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1051	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1052	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1053	Q₈	—	2	1	no	—
1054	Q₈	—	2	2	no	—
1055	Q₈	—	2	2	no	—
1056	Q₈	—	2	2	no	—
1057	Q₈	—	2	2	no	—
1058	Q₈	—	4	1	no	—
1059	Q₈	—	4	1	no	—
1060	Q₈	—	4	4	no	—
1061	Q₈	—	4	2	no	—
1062	Q₈	—	8	1	no	—
1063	Q₈	C₂₃×H(5,𝔽₂)	1	2	yes	—
1064	D₄	—	2	4	no	—
1065	D₄	—	2	1	no	—
1066	D₄	—	2	2	no	—
1067	D₄	—	2	1	no	—
1068	D₄	—	2	1	no	—
1069	D₄	—	2	2	no	—
1070	D₄	—	2	1	no	—
1071	D₄	—	2	1	no	—
1072	D₄	—	4	1	no	—
1073	D₄	—	4	1	no	—
1074	D₄	—	4	1	no	—
1075	D₄	—	4	1	no	—
1076	D₄	—	4	2	no	—
1077	D₄	—	4	2	no	—
1078	D₄	—	4	2	no	—
1079	D₄	—	4	2	no	—
1080	D₄	—	4	2	no	—
1081	D₄	—	4	2	no	—
1082	D₄	—	4	2	no	—
1083	D₄	—	4	2	no	—
1084	D₄	—	4	4	no	—
1085	D₄	—	8	1	no	—
1086	D₄	—	8	2	no	—
1087	D₄	—	8	2	no	—
1088	D₄	—	8	2	no	—
1089	D₄	—	8	2	no	—
1090	D₄	—	8	2	no	—
1091	D₄	—	8	2	no	—
1092	D₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1093	C₂×C₄	—	2	4	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	2	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	2	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	2	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	2	no	—
1106	C₂×C₄	—	2	2	no	—
1107	C₂×C₄	—	2	2	no	—
1108	C₂×C₄	—	4	2	no	—
1109	C₂×C₄	—	4	2	no	—
1110	C₂×C₄	—	4	2	no	—
1111	C₂×C₄	—	4	4	no	—
1112	C₂×C₄	—	4	4	no	—
1113	C₂×C₄	—	4	2	no	—
1114	C₂×C₄	—	8	2	no	—
1115	C₂×C₄	—	8	2	no	—
1116	C₂×C₄	—	8	2	no	—
1117	C₂×C₄	—	8	1	no	—
1118	C₂×C₄	—	8	2	no	—
1119	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1120	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1121	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1122	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1123	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1124	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1125	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1126	C₈	—	2	2	no	—
1127	C₈	—	2	2	no	—
1128	C₈	—	2	2	no	—
1129	C₈	—	2	2	no	—
1130	C₂²	—	2	1	no	—
1131	C₂²	—	2	2	no	—
1132	C₂²	—	2	2	no	—
1133	C₂²	—	2	1	no	—
1134	C₂²	—	2	1	no	—
1135	C₂²	—	2	2	no	—
1136	C₂²	—	2	2	no	—
1137	C₂²	—	2	2	no	—
1138	C₂²	—	2	2	no	—
1139	C₂²	—	2	2	no	—
1140	C₂²	—	4	2	no	—
1141	C₂²	—	4	1	no	—
1142	C₂²	—	4	1	no	—
1143	C₂²	—	4	2	no	—
1144	C₂²	—	4	2	no	—
1145	C₂²	—	4	2	no	—
1146	C₂²	—	4	2	no	—
1147	C₂²	—	4	2	no	—
1148	C₂²	—	16	2	no	—
1149	C₂²	—	16	2	no	—
1150	C₂²	—	16	2	no	—
1151	C₂²	—	16	2	no	—
1152	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1153	C₄	—	2	1	no	—
1154	C₄	—	2	2	no	—
1155	C₄	—	2	2	no	—
1156	C₄	—	2	1	no	—
1157	C₄	—	2	1	no	—
1158	C₄	—	2	2	no	—
1159	C₄	—	2	2	no	—
1160	C₄	—	4	2	no	—
1161	C₄	—	4	2	no	—
1162	C₄	—	4	2	no	—
1163	C₄	—	4	2	no	—
1164	C₄	—	4	2	no	—
1165	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1166	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1167	C₂	—	4	1	no	—
1168	C₂	—	4	1	no	—
1169	C₂	—	4	1	no	—
1170	C₂	—	4	2	no	—
1171	C₂	—	4	2	no	—
1172	C₂	—	8	1	no	—
1173	C₂	—	8	1	no	—
1174	C₂	—	8	2	no	—
1175	C₂	C₂₃×#3484	1	1	yes	characteristic
1176	C₂	C₂₃×#3584	1	2	yes	—

	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 ◁ C₂₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3551	C₂	semidirect
2. C₂₃×#3500	C₂	semidirect
3. C₂₃×#3323	C₂	semidirect
4. C₂₃×#3322	C₂	semidirect
5. C₂₃×#3301	C₂	semidirect
6. C₂₃×#3300	C₂	semidirect
7. C₂₃×#3282	C₂	semidirect
8. C₂₃×#3280	C₂	semidirect
9. C₂₃×#3277	C₂	semidirect
10. C₂₃×#3275	C₂	semidirect
11. C₂₃×#3211	C₂	semidirect
12. C₂₃×#3202	C₂	semidirect
13. C₂₃×#3200	C₂	semidirect
14. C₂₃×#3198	C₂	semidirect
15. C₂₃×#3102	C₂	semidirect
16. C₂₃×#3013	C₂	semidirect
17. C₂₃×#3009	C₂	semidirect
18. C₂₃×#3008	C₂	semidirect
19. C₂₃×#2979	C₂	semidirect
20. C₂×C₂₃×2₋¹⁺⁴	C₂²	semidirect
22. C₂×C₂₃×#137	C₂²	semidirect
23. C₂×C₂₃×#137	C₂²	semidirect
25. C₂×C₂₃×#135	C₂²	semidirect
26. C₂²×SD₁₆×C₂₃	C₂²	semidirect
31. C₂₃×#553	C₂²	semidirect
32. C₂₃×#552	C₂²	semidirect
35. C₂₃×#548	C₂²	semidirect
36. C₂₃×#548	C₂²	semidirect
40. C₂₃×#546	C₂²	semidirect
41. C₂₃×#546	C₂²	semidirect
44. C₂₃×#537	C₂²	semidirect
50. C₂₃×#535	C₂²	semidirect
53. C₂₃×#529	C₂²	semidirect
55. C₂×C₂₃×#124	C₂²	semidirect
56. C₄×#41×C₂₃	C₂²	semidirect
57. C₂₃×#495	C₂²	semidirect
58. C₂₃×#495	C₂²	semidirect
59. C₂₃×#488	C₂²	semidirect
60. C₂₃×#488	C₂²	semidirect
61. C₂₃×#485	C₂²	semidirect
62. C₂₃×#485	C₂²	semidirect
63. C₂₃×#485	C₂²	semidirect
64. C₂₃×#482	C₂²	semidirect
65. C₂₃×#481	C₂²	semidirect
66. C₂₃×#480	C₂²	semidirect
67. C₂₃×#479	C₂²	semidirect
68. C₂₃×#478	C₂²	semidirect
69. C₂₃×#470	C₂²	semidirect
70. C₂₃×#469	C₂²	semidirect
71. C₂₃×#468	C₂²	semidirect
72. C₂₃×#468	C₂²	semidirect
73. C₂₃×#467	C₂²	semidirect
74. C₂₃×#466	C₂²	semidirect
75. C₂₃×#465	C₂²	semidirect
76. C₂₃×#465	C₂²	semidirect
77. C₂₃×#464	C₂²	semidirect
78. C₂₃×#464	C₂²	semidirect
79. C₂₃×#464	C₂²	semidirect
80. C₂₃×#463	C₂²	semidirect
81. C₂₃×#463	C₂²	semidirect
82. C₂₃×#463	C₂²	semidirect
84. C₂₃×#452	C₂²	semidirect
85. C₂₃×#452	C₂²	semidirect
86. C₂₃×#451	C₂²	semidirect
87. C₂₃×#451	C₂²	semidirect
88. C₂₃×#451	C₂²	semidirect
90. C₂₃×#450	C₂²	semidirect
91. C₂₃×#450	C₂²	semidirect
94. C₂₃×#449	C₂²	semidirect
95. C₂₃×#449	C₂²	semidirect
96. C₂₃×#449	C₂²	semidirect
97. C₂₃×#448	C₂²	semidirect
98. C₂₃×#448	C₂²	semidirect
101. C₄×Q₁₆×C₂₃	C₂²	semidirect
102. C₄×SD₁₆×C₂₃	C₂²	semidirect
103. C₄×SD₁₆×C₂₃	C₂²	semidirect
104. C₄×D₈×C₂₃	C₂²	semidirect
105. C₂₃×#436	C₂²	semidirect
106. C₂₃×#436	C₂²	semidirect
107. C₈×D₄×C₂₃	C₂²	semidirect
108. C₈×D₄×C₂₃	C₂²	semidirect
109. C₂₃×#431	C₂²	semidirect
111. C₂₃×#418	C₂²	semidirect
112. C₂₃×#417	C₂²	semidirect
114. C₂₃×#416	C₂²	semidirect
115. C₂×C₂₃×#103	C₂²	semidirect
118. C₂₃×#408	C₂²	semidirect
448. #61663	C₂₃	direct (N × H)
542. #3551	C₂×C₂₃	semidirect
543. #3500	C₂×C₂₃	semidirect
544. #3323	C₂×C₂₃	semidirect
545. #3322	C₂×C₂₃	semidirect
546. #3301	C₂×C₂₃	semidirect
547. #3300	C₂×C₂₃	semidirect
548. #3282	C₂×C₂₃	semidirect
549. #3280	C₂×C₂₃	semidirect
550. #3277	C₂×C₂₃	semidirect
551. #3275	C₂×C₂₃	semidirect
552. #3211	C₂×C₂₃	semidirect
553. #3202	C₂×C₂₃	semidirect
554. #3200	C₂×C₂₃	semidirect
555. #3198	C₂×C₂₃	semidirect
556. #3102	C₂×C₂₃	semidirect
557. #3013	C₂×C₂₃	semidirect
558. #3009	C₂×C₂₃	semidirect
559. #3008	C₂×C₂₃	semidirect
560. #2979	C₂×C₂₃	semidirect
598. C₂×2₋¹⁺⁴	C₂²×C₂₃	semidirect
600. C₂×#137	C₂²×C₂₃	semidirect
601. C₂×#137	C₂²×C₂₃	semidirect
603. C₂×#135	C₂²×C₂₃	semidirect
604. C₂²×SD₁₆	C₂²×C₂₃	semidirect
609. #553	C₂²×C₂₃	semidirect
610. #552	C₂²×C₂₃	semidirect
613. #548	C₂²×C₂₃	semidirect
614. #548	C₂²×C₂₃	semidirect
618. #546	C₂²×C₂₃	semidirect
619. #546	C₂²×C₂₃	semidirect
622. #537	C₂²×C₂₃	semidirect
628. #535	C₂²×C₂₃	semidirect
631. #529	C₂²×C₂₃	semidirect
633. C₂×#124	C₂²×C₂₃	semidirect
634. C₄×#41	C₂²×C₂₃	semidirect
635. #495	C₂²×C₂₃	semidirect
636. #495	C₂²×C₂₃	semidirect
637. #488	C₂²×C₂₃	semidirect
638. #488	C₂²×C₂₃	semidirect
639. #485	C₂²×C₂₃	semidirect
640. #485	C₂²×C₂₃	semidirect
641. #485	C₂²×C₂₃	semidirect
642. #482	C₂²×C₂₃	semidirect
643. #481	C₂²×C₂₃	semidirect
644. #480	C₂²×C₂₃	semidirect
645. #479	C₂²×C₂₃	semidirect
646. #478	C₂²×C₂₃	semidirect
647. #470	C₂²×C₂₃	semidirect
648. #469	C₂²×C₂₃	semidirect
649. #468	C₂²×C₂₃	semidirect
650. #468	C₂²×C₂₃	semidirect
651. #467	C₂²×C₂₃	semidirect
652. #466	C₂²×C₂₃	semidirect
653. #465	C₂²×C₂₃	semidirect
654. #465	C₂²×C₂₃	semidirect
655. #464	C₂²×C₂₃	semidirect
656. #464	C₂²×C₂₃	semidirect
657. #464	C₂²×C₂₃	semidirect
658. #463	C₂²×C₂₃	semidirect
659. #463	C₂²×C₂₃	semidirect
660. #463	C₂²×C₂₃	semidirect
662. #452	C₂²×C₂₃	semidirect
663. #452	C₂²×C₂₃	semidirect
664. #451	C₂²×C₂₃	semidirect
665. #451	C₂²×C₂₃	semidirect
666. #451	C₂²×C₂₃	semidirect
668. #450	C₂²×C₂₃	semidirect
669. #450	C₂²×C₂₃	semidirect
672. #449	C₂²×C₂₃	semidirect
673. #449	C₂²×C₂₃	semidirect
674. #449	C₂²×C₂₃	semidirect
675. #448	C₂²×C₂₃	semidirect
676. #448	C₂²×C₂₃	semidirect
679. C₄×Q₁₆	C₂²×C₂₃	semidirect
680. C₄×SD₁₆	C₂²×C₂₃	semidirect
681. C₄×SD₁₆	C₂²×C₂₃	semidirect
682. C₄×D₈	C₂²×C₂₃	semidirect
683. #436	C₂²×C₂₃	semidirect
684. #436	C₂²×C₂₃	semidirect
685. C₈×D₄	C₂²×C₂₃	semidirect
686. C₈×D₄	C₂²×C₂₃	semidirect
687. #431	C₂²×C₂₃	semidirect
689. #418	C₂²×C₂₃	semidirect
690. #417	C₂²×C₂₃	semidirect
692. #416	C₂²×C₂₃	semidirect
693. C₂×#103	C₂²×C₂₃	semidirect
696. #408	C₂²×C₂₃	semidirect
878. C₂₃	#61663	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×#3551	2
C₂₃×#3500	2
C₂₃×#3323	2
C₂₃×#3322	2
C₂₃×#3301	2
C₂₃×#3300	2
C₂₃×#3282	2
C₂₃×#3280	2
C₂₃×#3277	2
C₂₃×#3275	2
C₂₃×#3211	2
C₂₃×#3202	2
C₂₃×#3200	2
C₂₃×#3198	2
C₂₃×#3102	2
C₂₃×#3013	2
C₂₃×#3009	2
C₂₃×#3008	2
C₂₃×#2979	2
#61663	23

Subgroups — C23×#61663 #19209289

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61663 #19209289