Subgroups — C₂₃×#61670 #19209296

Order 5888.

2102 conjugacy classes of subgroups.

The subgroup lattice has 1120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3496	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3319	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3315	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3314	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3310	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3269	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3267	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3266	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3265	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3219	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3216	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3203	C₂	1	2	yes	maximal, complemented
14	C₂₃×#3201	C₂	1	2	yes	maximal, complemented
15	C₂₃×#3114	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3110	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3012	C₂	1	2	yes	maximal, complemented
18	C₂₃×#3009	C₂	1	2	yes	maximal, complemented
19	C₂₃×#2980	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	2	yes	—
21	C₂×C₂₃×#137	C₂²	1	2	yes	complemented
22	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
23	C₂×C₂₃×#135	C₂²	1	2	yes	complemented
24	C₂²×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
25	C₂₃×#562	—	2	2	no	—
26	C₂₃×#555	—	2	1	no	—
27	C₂₃×#555	C₂²	1	1	yes	characteristic, complemented
28	C₂₃×#554	C₂²	1	1	yes	characteristic, complemented
29	C₂₃×#553	—	2	1	no	—
30	C₂₃×#552	C₂²	1	2	yes	complemented
31	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
32	C₂₃×#548	C₂²	1	2	yes	complemented
33	C₂₃×#547	—	2	1	no	—
34	C₂₃×#547	C₂²	1	2	yes	—
35	C₂₃×#547	C₂²	1	1	yes	characteristic, complemented
36	C₂₃×#546	—	2	2	no	—
37	C₂₃×#546	C₂²	1	2	yes	—
38	C₂₃×#546	C₂²	1	2	yes	—
39	D₄²×C₂₃	—	2	1	no	—
40	D₄²×C₂₃	C₂²	1	2	yes	—
41	C₂₃×#544	—	2	1	no	—
42	C₂₃×#542	—	2	2	no	—
43	C₂₃×#540	—	2	1	no	—
44	C₂₃×#537	C₂²	1	2	yes	—
45	C₂₃×#537	C₂²	1	2	yes	complemented
46	C₂₃×#536	C₂²	1	2	yes	complemented
47	C₂₃×#534	—	2	1	no	—
48	C₂₃×#534	—	2	1	no	—
49	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
50	C₂₃×#532	C₂²	1	1	yes	characteristic
51	C₂₃×#532	C₂²	1	1	yes	characteristic
52	C₂₃×#529	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₂₃×#121	—	2	2	no	—
54	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
55	C₂₃×#497	C₂²	1	2	yes	complemented
56	C₂₃×#497	C₂²	1	1	yes	characteristic, complemented
57	C₂₃×#496	C₂²	1	1	yes	characteristic, complemented
58	C₂₃×#491	C₂²	1	1	yes	characteristic, complemented
59	C₂₃×#490	C₂²	1	1	yes	characteristic, complemented
60	C₂₃×#489	C₂²	1	2	yes	complemented
61	C₂₃×#485	C₂²	1	2	yes	complemented
62	C₂₃×#484	C₂²	1	2	yes	complemented
63	C₂₃×#484	C₂²	1	2	yes	complemented
64	C₂₃×#483	C₂²	1	1	yes	characteristic, complemented
65	C₂₃×#482	C₂²	1	2	yes	complemented
66	C₂₃×#480	C₂²	1	1	yes	characteristic, complemented
67	C₂₃×#480	C₂²	1	2	yes	complemented
68	C₂₃×#478	C₂²	1	2	yes	complemented
69	C₂₃×#474	C₂²	1	2	yes	complemented
70	C₂₃×#470	C₂²	1	2	yes	complemented
71	C₂₃×#468	C₂²	1	2	yes	complemented
72	C₂₃×#468	C₂²	1	2	yes	complemented
73	C₂₃×#468	C₂²	1	2	yes	complemented
74	C₂₃×#467	C₂²	1	2	yes	complemented
75	C₂₃×#467	C₂²	1	2	yes	complemented
76	C₂₃×#466	C₂²	1	2	yes	complemented
77	C₂₃×#465	C₂²	1	2	yes	complemented
78	C₂₃×#464	C₂²	1	2	yes	complemented
79	C₂₃×#463	C₂²	1	2	yes	complemented
80	C₂₃×#463	C₂²	1	2	yes	complemented
81	C₂₃×#462	C₂²	1	2	yes	complemented
82	C₂₃×#461	C₂²	1	2	yes	complemented
83	C₂₃×#460	C₂²	1	2	yes	complemented
84	C₂₃×#452	C₂²	1	2	yes	complemented
85	C₂₃×#452	C₂²	1	2	yes	complemented
86	C₂₃×#452	C₂²	1	2	yes	complemented
87	C₂₃×#452	C₂²	1	2	yes	complemented
88	C₂₃×#452	C₂²	1	2	yes	complemented
89	C₂₃×#452	C₂²	1	2	yes	complemented
90	C₂₃×#452	C₂²	1	2	yes	complemented
91	C₂₃×#451	C₂²	1	2	yes	complemented
92	C₂₃×#450	C₂²	1	1	yes	characteristic
93	C₂₃×#450	C₂²	1	2	yes	—
94	C₂₃×#450	C₂²	1	2	yes	complemented
95	C₂₃×#450	C₂²	1	2	yes	complemented
96	C₂₃×#450	C₂²	1	2	yes	complemented
97	C₂₃×#449	C₂²	1	2	yes	complemented
98	C₂₃×#449	C₂²	1	2	yes	complemented
99	C₂₃×#449	C₂²	1	2	yes	complemented
100	C₂₃×#448	C₂²	1	2	yes	complemented
101	C₂₃×#447	C₂²	1	1	yes	characteristic
102	C₂₃×#447	C₂²	1	2	yes	complemented
103	C₂₃×#442	C₂²	1	2	yes	complemented
104	C₂₃×#440	C₂²	1	2	yes	complemented
105	C₂₃×#440	C₂²	1	2	yes	complemented
106	C₂₃×#440	C₂²	1	2	yes	complemented
107	C₂₃×#435	C₂²	1	2	yes	complemented
108	C₂₃×#435	C₂²	1	2	yes	complemented
109	C₂₃×#435	C₂²	1	2	yes	complemented
110	C₂₃×#435	C₂²	1	2	yes	complemented
111	C₂₃×#432	C₂²	1	1	yes	characteristic, complemented
112	C₂₃×#432	C₂²	1	1	yes	characteristic, complemented
113	C₂₃×#418	C₂²	1	2	yes	complemented
114	C₂₃×#417	C₂²	1	2	yes	complemented
115	C₂₃×#416	C₂²	1	2	yes	complemented
116	C₂×C₂₃×#102	C₂²	1	2	yes	complemented
117	C₂₃×#408	C₂²	1	2	yes	complemented
118	C₂₃×#408	C₂²	1	2	yes	complemented
119	C₂₃×H(5,𝔽₂)	—	4	4	no	—
120	C₂₃×H(5,𝔽₂)	—	4	4	no	—
121	C₂×#41×C₂₃	—	2	2	no	—
122	C₂×#41×C₂₃	C₂³	1	2	yes	—
123	C₂×#41×C₂₃	C₂³	1	2	yes	—
124	C₂×#41×C₂₃	C₂³	1	2	yes	—
125	C₂×#41×C₂₃	C₂³	1	2	yes	—
126	C₂×#41×C₂₃	C₂³	1	2	yes	—
127	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
128	C₂²×D₄×C₂₃	—	2	2	no	—
129	C₂²×D₄×C₂₃	—	2	2	no	—
130	C₂²×D₄×C₂₃	—	2	2	no	—
131	C₂²×D₄×C₂₃	—	2	2	no	—
132	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
134	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
135	C₂³×C₄×C₂₃	—	2	1	no	—
136	C₂₃×#137	—	4	4	no	—
137	C₂₃×AGL(1,ℤ/8)	—	4	4	no	—
138	C₂₃×#135	—	4	4	no	—
139	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
140	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
141	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
142	C₂×SD₁₆×C₂₃	—	4	4	no	—
143	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
144	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
147	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
150	C₂×D₈×C₂₃	C₂³	1	2	yes	—
151	C₂×D₈×C₂₃	C₂³	1	2	yes	—
152	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
153	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
154	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
155	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
156	C₂₃×C₄⋊Q₈	—	2	2	no	—
157	C₂₃×C₄⋊Q₈	—	2	1	no	—
158	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
159	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₂₃×#127	D₄	1	1	yes	characteristic
163	C₂₃×#127	C₂³	1	1	yes	characteristic
164	C₂₃×#126	—	2	2	no	—
165	C₂₃×#126	—	2	1	no	—
166	C₂₃×#125	—	2	2	no	—
167	C₂₃×#125	—	2	1	no	—
168	C₂₃×#125	—	2	1	no	—
169	C₂₃×#125	C₂³	1	1	yes	characteristic
170	C₂₃×#124	—	2	2	no	—
171	C₂₃×#124	—	2	2	no	—
172	C₂₃×#124	—	2	2	no	—
173	C₂₃×#124	D₄	1	2	yes	—
174	C₂₃×#124	C₂³	1	1	yes	characteristic
175	C₂₃×#124	C₂³	1	2	yes	—
176	C₂₃×#123	—	2	2	no	—
177	C₂₃×#123	—	2	2	no	—
178	C₂₃×#123	—	2	2	no	—
179	C₂₃×#123	—	2	1	no	—
180	C₂₃×#123	—	2	2	no	—
181	C₂₃×#123	—	2	2	no	—
182	C₂₃×#123	—	2	2	no	—
183	C₂₃×#123	—	2	2	no	—
184	C₂₃×#123	—	2	2	no	—
185	C₂₃×C₂²⋊Q₈	—	2	2	no	—
186	C₂₃×C₂²⋊Q₈	—	2	2	no	—
187	C₂₃×C₂²⋊Q₈	—	2	1	no	—
188	C₂₃×C₂²⋊Q₈	—	2	2	no	—
189	C₂₃×C₂²⋊Q₈	—	2	2	no	—
190	C₂₃×C₂²⋊Q₈	—	2	2	no	—
191	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
192	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
193	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
194	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
195	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
197	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
198	C₂₃×#121	—	2	2	no	—
199	C₂₃×#121	—	2	1	no	—
200	C₂₃×#121	—	2	2	no	—
201	C₂₃×#121	—	2	1	no	—
202	C₂₃×#121	—	2	2	no	—
203	C₂₃×#121	—	2	2	no	—
204	C₂₃×#121	—	2	2	no	—
205	C₂₃×#121	—	2	2	no	—
206	C₂₃×#121	—	2	2	no	—
207	C₂₃×#121	—	2	2	no	—
208	C₂₃×#121	—	2	1	no	—
209	C₂₃×#121	—	2	1	no	—
210	C₂₃×#121	—	2	2	no	—
211	C₂₃×#121	—	2	2	no	—
212	C₂₃×#121	—	2	2	no	—
213	C₂₃×#121	D₄	1	1	yes	characteristic
214	C₂₃×#121	D₄	1	1	yes	characteristic
215	C₂₃×#121	D₄	1	2	yes	—
216	C₂₃×#121	C₂³	1	2	yes	—
217	C₂₃×#121	C₂³	1	1	yes	characteristic
218	C₂₃×#121	C₂³	1	2	yes	—
219	C₂₃×#121	C₂³	1	2	yes	—
220	C₂₃×#120	—	2	2	no	—
221	C₂₃×#120	—	2	2	no	—
222	C₂₃×#120	—	2	2	no	—
223	C₂₃×#120	—	2	2	no	—
224	C₄×Q₈×C₂₃	—	2	1	no	—
225	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
226	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
227	C₄×D₄×C₂₃	—	2	1	no	—
228	C₄×D₄×C₂₃	—	2	1	no	—
229	C₄×D₄×C₂₃	—	2	1	no	—
230	C₄×D₄×C₂₃	—	2	2	no	—
231	C₄×D₄×C₂₃	—	2	1	no	—
232	C₄×D₄×C₂₃	—	2	1	no	—
233	C₄×D₄×C₂₃	—	2	1	no	—
234	C₄×D₄×C₂₃	—	2	1	no	—
235	C₄×D₄×C₂₃	C₂³	1	2	yes	—
236	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₂₃	C₂³	1	2	yes	—
238	C₄×D₄×C₂₃	C₂³	1	2	yes	—
239	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
241	C₂₃×#117	—	2	1	no	—
242	C₂₃×#117	—	2	1	no	—
243	C₂₃×#117	—	2	2	no	—
244	C₂₃×#117	—	2	1	no	—
245	C₂₃×#117	C₂³	1	2	yes	—
246	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
247	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
248	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
249	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
250	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
251	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
252	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
253	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
254	C₂₃×#107	C₂³	1	2	yes	—
255	C₂₃×#107	C₂³	1	2	yes	—
256	C₂₃×#107	C₂³	1	2	yes	—
257	C₂₃×#106	C₂³	1	2	yes	—
258	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
259	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
260	C₂₃×#103	C₂³	1	2	yes	—
261	C₂₃×#103	C₂³	1	2	yes	—
262	C₂₃×#103	C₂³	1	2	yes	—
263	C₂₃×#103	C₂³	1	2	yes	—
264	C₂₃×#103	C₂³	1	2	yes	—
265	C₂₃×#103	C₂³	1	2	yes	—
266	C₂₃×#103	C₂³	1	2	yes	—
267	C₂₃×#102	C₂³	1	2	yes	—
268	C₂₃×#102	C₂³	1	2	yes	—
269	C₂₃×#102	C₂³	1	2	yes	—
270	C₂₃×#102	C₂³	1	2	yes	—
271	C₂₃×#102	C₂³	1	2	yes	—
272	C₂₃×#102	C₂³	1	2	yes	—
273	C₂₃×#102	C₂³	1	2	yes	—
274	C₂₃×#102	C₂³	1	2	yes	—
275	C₂₃×#102	C₂³	1	2	yes	—
276	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
277	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
278	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
279	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
280	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
281	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
282	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
283	C₂₃×#97	C₂³	1	1	yes	characteristic
284	C₂₃×#97	C₂³	1	1	yes	characteristic
285	C₂₃×#97	C₂³	1	2	yes	—
286	C₂⁴×C₂₃	—	2	1	no	—
287	C₂⁴×C₂₃	—	2	2	no	—
288	C₂⁴×C₂₃	—	2	2	no	—
289	#41×C₂₃	—	2	4	no	—
290	#41×C₂₃	—	2	4	no	—
291	#41×C₂₃	—	4	2	no	—
292	#41×C₂₃	—	4	2	no	—
293	#41×C₂₃	—	4	2	no	—
294	#41×C₂₃	—	4	2	no	—
295	#41×C₂₃	—	4	2	no	—
296	#41×C₂₃	—	4	2	no	—
297	#41×C₂₃	—	4	2	no	—
298	#41×C₂₃	—	4	2	no	—
299	#41×C₂₃	—	4	8	no	—
300	C₂×Q₈×C₂₃	—	2	1	no	—
301	C₂×Q₈×C₂₃	—	2	2	no	—
302	C₂×Q₈×C₂₃	—	4	2	no	—
303	C₂×Q₈×C₂₃	—	4	2	no	—
304	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
305	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
306	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
307	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
308	C₂×D₄×C₂₃	—	2	4	no	—
309	C₂×D₄×C₂₃	—	2	4	no	—
310	C₂×D₄×C₂₃	—	2	4	no	—
311	C₂×D₄×C₂₃	—	2	2	no	—
312	C₂×D₄×C₂₃	—	2	2	no	—
313	C₂×D₄×C₂₃	—	2	2	no	—
314	C₂×D₄×C₂₃	—	2	1	no	—
315	C₂×D₄×C₂₃	—	2	2	no	—
316	C₂×D₄×C₂₃	—	2	2	no	—
317	C₂×D₄×C₂₃	—	2	2	no	—
318	C₂×D₄×C₂₃	—	2	2	no	—
319	C₂×D₄×C₂₃	—	2	1	no	—
320	C₂×D₄×C₂₃	—	2	1	no	—
321	C₂×D₄×C₂₃	—	2	2	no	—
322	C₂×D₄×C₂₃	—	2	2	no	—
323	C₂×D₄×C₂₃	—	2	1	no	—
324	C₂×D₄×C₂₃	—	4	2	no	—
325	C₂×D₄×C₂₃	—	4	2	no	—
326	C₂×D₄×C₂₃	—	4	8	no	—
327	C₂×D₄×C₂₃	—	4	8	no	—
328	C₂×D₄×C₂₃	—	4	8	no	—
329	C₂×D₄×C₂₃	—	8	4	no	—
330	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
331	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
332	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
333	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
334	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
335	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
336	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
337	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
338	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
339	C₂²×C₄×C₂₃	—	2	1	no	—
340	C₂²×C₄×C₂₃	—	2	2	no	—
341	C₂²×C₄×C₂₃	—	2	2	no	—
342	C₂²×C₄×C₂₃	—	2	2	no	—
343	C₂²×C₄×C₂₃	—	2	2	no	—
344	C₂²×C₄×C₂₃	—	2	1	no	—
345	C₂²×C₄×C₂₃	—	2	2	no	—
346	C₂²×C₄×C₂₃	—	2	2	no	—
347	C₂²×C₄×C₂₃	—	2	2	no	—
348	C₂²×C₄×C₂₃	—	2	2	no	—
349	C₂²×C₄×C₂₃	—	8	2	no	—
350	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
351	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
352	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
353	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
354	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
355	Q₁₆×C₂₃	—	4	2	no	—
356	Q₁₆×C₂₃	—	4	2	no	—
357	Q₁₆×C₂₃	—	4	2	no	—
358	SD₁₆×C₂₃	—	2	4	no	—
359	SD₁₆×C₂₃	—	2	4	no	—
360	SD₁₆×C₂₃	—	2	4	no	—
361	SD₁₆×C₂₃	—	4	2	no	—
362	SD₁₆×C₂₃	—	4	2	no	—
363	SD₁₆×C₂₃	—	4	2	no	—
364	SD₁₆×C₂₃	—	4	2	no	—
365	D₈×C₂₃	—	2	4	no	—
366	D₈×C₂₃	—	4	2	no	—
367	M₁₆×C₂₃	—	4	2	no	—
368	M₁₆×C₂₃	—	4	2	no	—
369	C₂×C₈×C₂₃	—	4	2	no	—
370	C₂×C₈×C₂₃	—	4	2	no	—
371	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
372	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
373	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
374	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
375	C₄⋊C₄×C₂₃	—	2	1	no	—
376	C₄⋊C₄×C₂₃	—	2	1	no	—
377	C₄⋊C₄×C₂₃	—	2	2	no	—
378	C₄⋊C₄×C₂₃	—	2	2	no	—
379	C₄⋊C₄×C₂₃	—	2	2	no	—
380	C₄⋊C₄×C₂₃	—	2	1	no	—
381	C₄⋊C₄×C₂₃	—	2	2	no	—
382	C₄⋊C₄×C₂₃	—	2	1	no	—
383	C₄⋊C₄×C₂₃	—	2	1	no	—
384	C₄⋊C₄×C₂₃	—	2	2	no	—
385	C₄⋊C₄×C₂₃	—	2	1	no	—
386	C₄⋊C₄×C₂₃	—	2	1	no	—
387	C₄⋊C₄×C₂₃	—	2	1	no	—
388	C₄⋊C₄×C₂₃	—	2	2	no	—
389	C₄⋊C₄×C₂₃	—	2	2	no	—
390	C₄⋊C₄×C₂₃	—	2	1	no	—
391	C₄⋊C₄×C₂₃	—	2	2	no	—
392	C₄⋊C₄×C₂₃	—	2	1	no	—
393	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
394	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
395	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
396	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
397	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
398	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
399	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
400	C₂²⋊C₄×C₂₃	—	2	2	no	—
401	C₂²⋊C₄×C₂₃	—	2	2	no	—
402	C₂²⋊C₄×C₂₃	—	2	2	no	—
403	C₂²⋊C₄×C₂₃	—	2	2	no	—
404	C₂²⋊C₄×C₂₃	—	2	2	no	—
405	C₂²⋊C₄×C₂₃	—	2	2	no	—
406	C₂²⋊C₄×C₂₃	—	2	2	no	—
407	C₂²⋊C₄×C₂₃	—	2	1	no	—
408	C₂²⋊C₄×C₂₃	—	2	2	no	—
409	C₂²⋊C₄×C₂₃	—	2	2	no	—
410	C₂²⋊C₄×C₂₃	—	2	2	no	—
411	C₂²⋊C₄×C₂₃	—	2	2	no	—
412	C₂²⋊C₄×C₂₃	—	2	2	no	—
413	C₂²⋊C₄×C₂₃	—	2	1	no	—
414	C₂²⋊C₄×C₂₃	—	2	1	no	—
415	C₂²⋊C₄×C₂₃	—	2	2	no	—
416	C₂²⋊C₄×C₂₃	—	2	1	no	—
417	C₂²⋊C₄×C₂₃	—	2	2	no	—
418	C₂²⋊C₄×C₂₃	—	2	1	no	—
419	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
420	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
421	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
422	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
423	C₄²×C₂₃	—	2	2	no	—
424	C₄²×C₂₃	—	2	2	no	—
425	C₄²×C₂₃	—	2	1	no	—
426	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
427	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
428	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
429	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
430	#61670	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
431	C₂³×C₂₃	—	2	4	no	—
432	C₂³×C₂₃	—	2	2	no	—
433	C₂³×C₂₃	—	2	1	no	—
434	C₂³×C₂₃	—	2	2	no	—
435	C₂³×C₂₃	—	4	4	no	—
436	C₂³×C₂₃	—	4	4	no	—
437	C₂³×C₂₃	—	8	1	no	—
438	C₂³×C₂₃	—	8	1	no	—
439	C₂³×C₂₃	—	8	2	no	—
440	C₂³×C₂₃	—	8	2	no	—
441	C₂³×C₂₃	—	8	2	no	—
442	C₂³×C₂₃	—	8	2	no	—
443	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
444	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
445	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
446	Q₈×C₂₃	—	2	2	no	—
447	Q₈×C₂₃	—	2	2	no	—
448	Q₈×C₂₃	—	2	2	no	—
449	Q₈×C₂₃	—	2	2	no	—
450	Q₈×C₂₃	—	2	2	no	—
451	Q₈×C₂₃	—	4	2	no	—
452	Q₈×C₂₃	—	8	1	no	—
453	Q₈×C₂₃	—	8	2	no	—
454	D₄×C₂₃	—	2	4	no	—
455	D₄×C₂₃	—	2	2	no	—
456	D₄×C₂₃	—	2	2	no	—
457	D₄×C₂₃	—	2	2	no	—
458	D₄×C₂₃	—	2	2	no	—
459	D₄×C₂₃	—	4	2	no	—
460	D₄×C₂₃	—	4	2	no	—
461	D₄×C₂₃	—	4	2	no	—
462	D₄×C₂₃	—	4	2	no	—
463	D₄×C₂₃	—	4	1	no	—
464	D₄×C₂₃	—	4	1	no	—
465	D₄×C₂₃	—	4	4	no	—
466	D₄×C₂₃	—	4	4	no	—
467	D₄×C₂₃	—	4	2	no	—
468	D₄×C₂₃	—	4	4	no	—
469	D₄×C₂₃	—	4	4	no	—
470	D₄×C₂₃	—	4	4	no	—
471	D₄×C₂₃	—	8	1	no	—
472	D₄×C₂₃	—	8	1	no	—
473	D₄×C₂₃	—	8	2	no	—
474	D₄×C₂₃	—	8	2	no	—
475	D₄×C₂₃	—	8	2	no	—
476	D₄×C₂₃	—	8	2	no	—
477	D₄×C₂₃	H(5,𝔽₂)	1	4	yes	—
478	C₂×C₄×C₂₃	—	2	2	no	—
479	C₂×C₄×C₂₃	—	2	2	no	—
480	C₂×C₄×C₂₃	—	2	2	no	—
481	C₂×C₄×C₂₃	—	2	2	no	—
482	C₂×C₄×C₂₃	—	2	2	no	—
483	C₂×C₄×C₂₃	—	2	1	no	—
484	C₂×C₄×C₂₃	—	2	2	no	—
485	C₂×C₄×C₂₃	—	2	1	no	—
486	C₂×C₄×C₂₃	—	2	1	no	—
487	C₂×C₄×C₂₃	—	2	2	no	—
488	C₂×C₄×C₂₃	—	2	2	no	—
489	C₂×C₄×C₂₃	—	2	2	no	—
490	C₂×C₄×C₂₃	—	4	1	no	—
491	C₂×C₄×C₂₃	—	4	1	no	—
492	C₂×C₄×C₂₃	—	4	4	no	—
493	C₂×C₄×C₂₃	—	4	4	no	—
494	C₂×C₄×C₂₃	—	4	2	no	—
495	C₂×C₄×C₂₃	—	4	4	no	—
496	C₂×C₄×C₂₃	—	4	4	no	—
497	C₂×C₄×C₂₃	—	8	2	no	—
498	C₂×C₄×C₂₃	—	8	2	no	—
499	C₂×C₄×C₂₃	—	8	2	no	—
500	C₂×C₄×C₂₃	—	8	1	no	—
501	C₂×C₄×C₂₃	—	8	2	no	—
502	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
503	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
504	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
505	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
509	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
510	C₈×C₂₃	—	2	2	no	—
511	C₈×C₂₃	—	2	2	no	—
512	C₈×C₂₃	—	2	2	no	—
513	C₈×C₂₃	—	2	2	no	—
514	#3547	C₂×C₂₃	1	1	yes	characteristic, complemented
515	#3496	C₂×C₂₃	1	1	yes	characteristic, complemented
516	#3319	C₂×C₂₃	1	2	yes	complemented
517	#3315	C₂×C₂₃	1	2	yes	complemented
518	#3314	C₂×C₂₃	1	2	yes	complemented
519	#3310	C₂×C₂₃	1	2	yes	complemented
520	#3269	C₂×C₂₃	1	2	yes	complemented
521	#3267	C₂×C₂₃	1	2	yes	complemented
522	#3266	C₂×C₂₃	1	2	yes	complemented
523	#3265	C₂×C₂₃	1	2	yes	complemented
524	#3219	C₂×C₂₃	1	1	yes	characteristic, complemented
525	#3216	C₂×C₂₃	1	1	yes	characteristic, complemented
526	#3203	C₂×C₂₃	1	2	yes	complemented
527	#3201	C₂×C₂₃	1	2	yes	complemented
528	#3114	C₂×C₂₃	1	1	yes	characteristic, complemented
529	#3110	C₂×C₂₃	1	1	yes	characteristic, complemented
530	#3012	C₂×C₂₃	1	2	yes	complemented
531	#3009	C₂×C₂₃	1	2	yes	complemented
532	#2980	C₂×C₂₃	1	1	yes	characteristic, complemented
533	C₂²×C₂₃	—	2	1	no	—
534	C₂²×C₂₃	—	2	2	no	—
535	C₂²×C₂₃	—	2	2	no	—
536	C₂²×C₂₃	—	2	1	no	—
537	C₂²×C₂₃	—	2	2	no	—
538	C₂²×C₂₃	—	2	2	no	—
539	C₂²×C₂₃	—	2	2	no	—
540	C₂²×C₂₃	—	2	1	no	—
541	C₂²×C₂₃	—	2	2	no	—
542	C₂²×C₂₃	—	2	4	no	—
543	C₂²×C₂₃	—	4	2	no	—
544	C₂²×C₂₃	—	4	2	no	—
545	C₂²×C₂₃	—	4	2	no	—
546	C₂²×C₂₃	—	4	1	no	—
547	C₂²×C₂₃	—	4	1	no	—
548	C₂²×C₂₃	—	4	2	no	—
549	C₂²×C₂₃	—	4	2	no	—
550	C₂²×C₂₃	—	4	1	no	—
551	C₂²×C₂₃	—	8	4	no	—
552	C₂²×C₂₃	—	16	4	no	—
553	C₂²×C₂₃	—	16	4	no	—
554	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
555	C₄×C₂₃	—	2	1	no	—
556	C₄×C₂₃	—	2	1	no	—
557	C₄×C₂₃	—	2	1	no	—
558	C₄×C₂₃	—	2	1	no	—
559	C₄×C₂₃	—	2	1	no	—
560	C₄×C₂₃	—	2	2	no	—
561	C₄×C₂₃	—	2	2	no	—
562	C₄×C₂₃	—	4	2	no	—
563	C₄×C₂₃	—	4	1	no	—
564	C₄×C₂₃	—	4	2	no	—
565	C₄×C₂₃	—	4	1	no	—
566	C₄×C₂₃	—	4	2	no	—
567	C₄×C₂₃	—	4	2	no	—
568	C₄×C₂₃	—	4	1	no	—
569	C₄×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
570	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	2	yes	—
571	C₂×#137	C₂²×C₂₃	1	2	yes	complemented
572	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	complemented
573	C₂×#135	C₂²×C₂₃	1	2	yes	complemented
574	C₂²×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
575	#562	—	2	2	no	—
576	#555	—	2	1	no	—
577	#555	C₂²×C₂₃	1	1	yes	characteristic, complemented
578	#554	C₂²×C₂₃	1	1	yes	characteristic, complemented
579	#553	—	2	1	no	—
580	#552	C₂²×C₂₃	1	2	yes	complemented
581	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
582	#548	C₂²×C₂₃	1	2	yes	complemented
583	#547	—	2	1	no	—
584	#547	C₂²×C₂₃	1	2	yes	—
585	#547	C₂²×C₂₃	1	1	yes	characteristic, complemented
586	#546	—	2	2	no	—
587	#546	C₂²×C₂₃	1	2	yes	—
588	#546	C₂²×C₂₃	1	2	yes	—
589	D₄²	—	2	1	no	—
590	D₄²	C₂²×C₂₃	1	2	yes	—
591	#544	—	2	1	no	—
592	#542	—	2	2	no	—
593	#540	—	2	1	no	—
594	#537	C₂²×C₂₃	1	2	yes	—
595	#537	C₂²×C₂₃	1	2	yes	complemented
596	#536	C₂²×C₂₃	1	2	yes	complemented
597	#534	—	2	1	no	—
598	#534	—	2	1	no	—
599	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
600	#532	C₂²×C₂₃	1	1	yes	characteristic
601	#532	C₂²×C₂₃	1	1	yes	characteristic
602	#529	C₂²×C₂₃	1	1	yes	characteristic, complemented
603	C₂×#121	—	2	2	no	—
604	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
605	#497	C₂²×C₂₃	1	2	yes	complemented
606	#497	C₂²×C₂₃	1	1	yes	characteristic, complemented
607	#496	C₂²×C₂₃	1	1	yes	characteristic, complemented
608	#491	C₂²×C₂₃	1	1	yes	characteristic, complemented
609	#490	C₂²×C₂₃	1	1	yes	characteristic, complemented
610	#489	C₂²×C₂₃	1	2	yes	complemented
611	#485	C₂²×C₂₃	1	2	yes	complemented
612	#484	C₂²×C₂₃	1	2	yes	complemented
613	#484	C₂²×C₂₃	1	2	yes	complemented
614	#483	C₂²×C₂₃	1	1	yes	characteristic, complemented
615	#482	C₂²×C₂₃	1	2	yes	complemented
616	#480	C₂²×C₂₃	1	1	yes	characteristic, complemented
617	#480	C₂²×C₂₃	1	2	yes	complemented
618	#478	C₂²×C₂₃	1	2	yes	complemented
619	#474	C₂²×C₂₃	1	2	yes	complemented
620	#470	C₂²×C₂₃	1	2	yes	complemented
621	#468	C₂²×C₂₃	1	2	yes	complemented
622	#468	C₂²×C₂₃	1	2	yes	complemented
623	#468	C₂²×C₂₃	1	2	yes	complemented
624	#467	C₂²×C₂₃	1	2	yes	complemented
625	#467	C₂²×C₂₃	1	2	yes	complemented
626	#466	C₂²×C₂₃	1	2	yes	complemented
627	#465	C₂²×C₂₃	1	2	yes	complemented
628	#464	C₂²×C₂₃	1	2	yes	complemented
629	#463	C₂²×C₂₃	1	2	yes	complemented
630	#463	C₂²×C₂₃	1	2	yes	complemented
631	#462	C₂²×C₂₃	1	2	yes	complemented
632	#461	C₂²×C₂₃	1	2	yes	complemented
633	#460	C₂²×C₂₃	1	2	yes	complemented
634	#452	C₂²×C₂₃	1	2	yes	complemented
635	#452	C₂²×C₂₃	1	2	yes	complemented
636	#452	C₂²×C₂₃	1	2	yes	complemented
637	#452	C₂²×C₂₃	1	2	yes	complemented
638	#452	C₂²×C₂₃	1	2	yes	complemented
639	#452	C₂²×C₂₃	1	2	yes	complemented
640	#452	C₂²×C₂₃	1	2	yes	complemented
641	#451	C₂²×C₂₃	1	2	yes	complemented
642	#450	C₂²×C₂₃	1	2	yes	—
643	#450	C₂²×C₂₃	1	1	yes	characteristic
644	#450	C₂²×C₂₃	1	2	yes	complemented
645	#450	C₂²×C₂₃	1	2	yes	complemented
646	#450	C₂²×C₂₃	1	2	yes	complemented
647	#449	C₂²×C₂₃	1	2	yes	complemented
648	#449	C₂²×C₂₃	1	2	yes	complemented
649	#449	C₂²×C₂₃	1	2	yes	complemented
650	#448	C₂²×C₂₃	1	2	yes	complemented
651	#447	C₂²×C₂₃	1	1	yes	characteristic
652	#447	C₂²×C₂₃	1	2	yes	complemented
653	#442	C₂²×C₂₃	1	2	yes	complemented
654	#440	C₂²×C₂₃	1	2	yes	complemented
655	#440	C₂²×C₂₃	1	2	yes	complemented
656	#440	C₂²×C₂₃	1	2	yes	complemented
657	#435	C₂²×C₂₃	1	2	yes	complemented
658	#435	C₂²×C₂₃	1	2	yes	complemented
659	#435	C₂²×C₂₃	1	2	yes	complemented
660	#435	C₂²×C₂₃	1	2	yes	complemented
661	#432	C₂²×C₂₃	1	1	yes	characteristic, complemented
662	#432	C₂²×C₂₃	1	1	yes	characteristic, complemented
663	#418	C₂²×C₂₃	1	2	yes	complemented
664	#417	C₂²×C₂₃	1	2	yes	complemented
665	#416	C₂²×C₂₃	1	2	yes	complemented
666	C₂×#102	C₂²×C₂₃	1	2	yes	complemented
667	#408	C₂²×C₂₃	1	2	yes	complemented
668	#408	C₂²×C₂₃	1	2	yes	complemented
669	C₂×C₂₃	—	4	1	no	—
670	C₂×C₂₃	—	4	2	no	—
671	C₂×C₂₃	—	4	2	no	—
672	C₂×C₂₃	—	4	4	no	—
673	C₂×C₂₃	—	8	1	no	—
674	C₂×C₂₃	—	8	2	no	—
675	C₂×C₂₃	#3484	1	1	yes	characteristic
676	C₂×C₂₃	#3585	1	1	yes	characteristic
677	C₂×C₂₃	#3586	1	1	yes	characteristic
678	H(5,𝔽₂)	—	4	4	no	—
679	H(5,𝔽₂)	—	4	4	no	—
680	C₂×#41	—	2	2	no	—
681	C₂×#41	C₂³×C₂₃	1	2	yes	—
682	C₂×#41	C₂³×C₂₃	1	2	yes	—
683	C₂×#41	C₂³×C₂₃	1	2	yes	—
684	C₂×#41	C₂³×C₂₃	1	2	yes	—
685	C₂×#41	C₂³×C₂₃	1	2	yes	—
686	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
687	C₂²×D₄	—	2	2	no	—
688	C₂²×D₄	—	2	2	no	—
689	C₂²×D₄	—	2	2	no	—
690	C₂²×D₄	—	2	2	no	—
691	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
692	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
693	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
694	C₂³×C₄	—	2	1	no	—
695	#137	—	4	4	no	—
696	AGL(1,ℤ/8)	—	4	4	no	—
697	#135	—	4	4	no	—
698	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
699	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
700	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
701	C₂×SD₁₆	—	4	4	no	—
702	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
703	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
704	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
705	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
706	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
707	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
708	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
709	C₂×D₈	C₂³×C₂₃	1	2	yes	—
710	C₂×D₈	C₂³×C₂₃	1	2	yes	—
711	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
712	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
713	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
714	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
715	C₄⋊Q₈	—	2	2	no	—
716	C₄⋊Q₈	—	2	1	no	—
717	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
718	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
719	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
720	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
721	#127	D₄×C₂₃	1	1	yes	characteristic
722	#127	C₂³×C₂₃	1	1	yes	characteristic
723	#126	—	2	2	no	—
724	#126	—	2	1	no	—
725	#125	—	2	2	no	—
726	#125	—	2	1	no	—
727	#125	—	2	1	no	—
728	#125	C₂³×C₂₃	1	1	yes	characteristic
729	#124	—	2	2	no	—
730	#124	—	2	2	no	—
731	#124	—	2	2	no	—
732	#124	D₄×C₂₃	1	2	yes	—
733	#124	C₂³×C₂₃	1	1	yes	characteristic
734	#124	C₂³×C₂₃	1	2	yes	—
735	#123	—	2	2	no	—
736	#123	—	2	2	no	—
737	#123	—	2	2	no	—
738	#123	—	2	1	no	—
739	#123	—	2	2	no	—
740	#123	—	2	2	no	—
741	#123	—	2	2	no	—
742	#123	—	2	2	no	—
743	#123	—	2	2	no	—
744	C₂²⋊Q₈	—	2	2	no	—
745	C₂²⋊Q₈	—	2	2	no	—
746	C₂²⋊Q₈	—	2	1	no	—
747	C₂²⋊Q₈	—	2	2	no	—
748	C₂²⋊Q₈	—	2	2	no	—
749	C₂²⋊Q₈	—	2	2	no	—
750	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
751	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
752	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
753	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
754	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
755	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
756	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
757	#121	—	2	2	no	—
758	#121	—	2	2	no	—
759	#121	—	2	2	no	—
760	#121	—	2	2	no	—
761	#121	—	2	2	no	—
762	#121	—	2	2	no	—
763	#121	—	2	2	no	—
764	#121	—	2	1	no	—
765	#121	—	2	2	no	—
766	#121	—	2	1	no	—
767	#121	—	2	1	no	—
768	#121	—	2	1	no	—
769	#121	—	2	2	no	—
770	#121	—	2	2	no	—
771	#121	—	2	2	no	—
772	#121	D₄×C₂₃	1	2	yes	—
773	#121	D₄×C₂₃	1	1	yes	characteristic
774	#121	D₄×C₂₃	1	1	yes	characteristic
775	#121	C₂³×C₂₃	1	1	yes	characteristic
776	#121	C₂³×C₂₃	1	2	yes	—
777	#121	C₂³×C₂₃	1	2	yes	—
778	#121	C₂³×C₂₃	1	2	yes	—
779	#120	—	2	2	no	—
780	#120	—	2	2	no	—
781	#120	—	2	2	no	—
782	#120	—	2	2	no	—
783	C₄×Q₈	—	2	1	no	—
784	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
785	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
786	C₄×D₄	—	2	1	no	—
787	C₄×D₄	—	2	1	no	—
788	C₄×D₄	—	2	1	no	—
789	C₄×D₄	—	2	2	no	—
790	C₄×D₄	—	2	1	no	—
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	—	2	1	no	—
794	C₄×D₄	C₂³×C₂₃	1	2	yes	—
795	C₄×D₄	C₂³×C₂₃	1	2	yes	—
796	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
797	C₄×D₄	C₂³×C₂₃	1	2	yes	—
798	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
799	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
800	#117	—	2	1	no	—
801	#117	—	2	1	no	—
802	#117	—	2	2	no	—
803	#117	—	2	1	no	—
804	#117	C₂³×C₂₃	1	2	yes	—
805	C₂×C₄⋊C₄	—	2	2	no	—
806	C₂×C₄⋊C₄	—	2	1	no	—
807	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
808	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
809	C₂×C₂²⋊C₄	—	2	1	no	—
810	C₂×C₂²⋊C₄	—	2	2	no	—
811	C₂×C₂²⋊C₄	—	2	2	no	—
812	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
813	#107	C₂³×C₂₃	1	2	yes	—
814	#107	C₂³×C₂₃	1	2	yes	—
815	#107	C₂³×C₂₃	1	2	yes	—
816	#106	C₂³×C₂₃	1	2	yes	—
817	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
818	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
819	#103	C₂³×C₂₃	1	2	yes	—
820	#103	C₂³×C₂₃	1	2	yes	—
821	#103	C₂³×C₂₃	1	2	yes	—
822	#103	C₂³×C₂₃	1	2	yes	—
823	#103	C₂³×C₂₃	1	2	yes	—
824	#103	C₂³×C₂₃	1	2	yes	—
825	#103	C₂³×C₂₃	1	2	yes	—
826	#102	C₂³×C₂₃	1	2	yes	—
827	#102	C₂³×C₂₃	1	2	yes	—
828	#102	C₂³×C₂₃	1	2	yes	—
829	#102	C₂³×C₂₃	1	2	yes	—
830	#102	C₂³×C₂₃	1	2	yes	—
831	#102	C₂³×C₂₃	1	2	yes	—
832	#102	C₂³×C₂₃	1	2	yes	—
833	#102	C₂³×C₂₃	1	2	yes	—
834	#102	C₂³×C₂₃	1	2	yes	—
835	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
836	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
837	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
838	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
839	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
840	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
841	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
842	#97	C₂³×C₂₃	1	1	yes	characteristic
843	#97	C₂³×C₂₃	1	1	yes	characteristic
844	#97	C₂³×C₂₃	1	2	yes	—
845	C₂₃	#61670	1	1	yes	characteristic, direct product factor, Sylow
846	C₂⁴	—	2	1	no	—
847	C₂⁴	—	2	2	no	—
848	C₂⁴	—	2	2	no	—
849	#41	—	2	4	no	—
850	#41	—	2	4	no	—
851	#41	—	4	2	no	—
852	#41	—	4	2	no	—
853	#41	—	4	2	no	—
854	#41	—	4	2	no	—
855	#41	—	4	2	no	—
856	#41	—	4	2	no	—
857	#41	—	4	2	no	—
858	#41	—	4	2	no	—
859	#41	—	4	8	no	—
860	C₂×Q₈	—	2	1	no	—
861	C₂×Q₈	—	2	2	no	—
862	C₂×Q₈	—	4	2	no	—
863	C₂×Q₈	—	4	2	no	—
864	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
865	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
866	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
867	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
868	C₂×D₄	—	2	4	no	—
869	C₂×D₄	—	2	4	no	—
870	C₂×D₄	—	2	4	no	—
871	C₂×D₄	—	2	2	no	—
872	C₂×D₄	—	2	2	no	—
873	C₂×D₄	—	2	2	no	—
874	C₂×D₄	—	2	1	no	—
875	C₂×D₄	—	2	2	no	—
876	C₂×D₄	—	2	2	no	—
877	C₂×D₄	—	2	2	no	—
878	C₂×D₄	—	2	2	no	—
879	C₂×D₄	—	2	1	no	—
880	C₂×D₄	—	2	1	no	—
881	C₂×D₄	—	2	2	no	—
882	C₂×D₄	—	2	2	no	—
883	C₂×D₄	—	2	1	no	—
884	C₂×D₄	—	4	2	no	—
885	C₂×D₄	—	4	2	no	—
886	C₂×D₄	—	4	8	no	—
887	C₂×D₄	—	4	8	no	—
888	C₂×D₄	—	4	8	no	—
889	C₂×D₄	—	8	4	no	—
890	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
891	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
892	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
893	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
894	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
895	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
896	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
897	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
898	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
899	C₂²×C₄	—	2	1	no	—
900	C₂²×C₄	—	2	2	no	—
901	C₂²×C₄	—	2	2	no	—
902	C₂²×C₄	—	2	2	no	—
903	C₂²×C₄	—	2	2	no	—
904	C₂²×C₄	—	2	1	no	—
905	C₂²×C₄	—	2	2	no	—
906	C₂²×C₄	—	2	2	no	—
907	C₂²×C₄	—	2	2	no	—
908	C₂²×C₄	—	2	2	no	—
909	C₂²×C₄	—	8	2	no	—
910	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
911	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
912	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
913	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
914	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
915	Q₁₆	—	4	2	no	—
916	Q₁₆	—	4	2	no	—
917	Q₁₆	—	4	2	no	—
918	SD₁₆	—	2	4	no	—
919	SD₁₆	—	2	4	no	—
920	SD₁₆	—	2	4	no	—
921	SD₁₆	—	4	2	no	—
922	SD₁₆	—	4	2	no	—
923	SD₁₆	—	4	2	no	—
924	SD₁₆	—	4	2	no	—
925	D₈	—	2	4	no	—
926	D₈	—	4	2	no	—
927	M₁₆	—	4	2	no	—
928	M₁₆	—	4	2	no	—
929	C₂×C₈	—	4	2	no	—
930	C₂×C₈	—	4	2	no	—
931	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
932	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
933	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
934	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
935	C₄⋊C₄	—	2	1	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
954	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
955	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
956	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
957	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
958	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
959	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
960	C₂²⋊C₄	—	2	2	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	2	no	—
963	C₂²⋊C₄	—	2	2	no	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	2	no	—
967	C₂²⋊C₄	—	2	1	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	2	1	no	—
974	C₂²⋊C₄	—	2	1	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	1	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	1	no	—
979	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
980	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
981	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
982	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
983	C₄²	—	2	2	no	—
984	C₄²	—	2	2	no	—
985	C₄²	—	2	1	no	—
986	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
987	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
988	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
989	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
990	C₂³	—	2	4	no	—
991	C₂³	—	2	2	no	—
992	C₂³	—	2	1	no	—
993	C₂³	—	2	2	no	—
994	C₂³	—	4	4	no	—
995	C₂³	—	4	4	no	—
996	C₂³	—	8	1	no	—
997	C₂³	—	8	1	no	—
998	C₂³	—	8	2	no	—
999	C₂³	—	8	2	no	—
1000	C₂³	—	8	2	no	—
1001	C₂³	—	8	2	no	—
1002	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1003	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1004	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1005	Q₈	—	2	2	no	—
1006	Q₈	—	2	2	no	—
1007	Q₈	—	2	2	no	—
1008	Q₈	—	2	2	no	—
1009	Q₈	—	2	2	no	—
1010	Q₈	—	4	2	no	—
1011	Q₈	—	8	2	no	—
1012	Q₈	—	8	1	no	—
1013	D₄	—	2	4	no	—
1014	D₄	—	2	2	no	—
1015	D₄	—	2	2	no	—
1016	D₄	—	2	2	no	—
1017	D₄	—	2	2	no	—
1018	D₄	—	4	2	no	—
1019	D₄	—	4	2	no	—
1020	D₄	—	4	2	no	—
1021	D₄	—	4	2	no	—
1022	D₄	—	4	1	no	—
1023	D₄	—	4	1	no	—
1024	D₄	—	4	4	no	—
1025	D₄	—	4	4	no	—
1026	D₄	—	4	2	no	—
1027	D₄	—	4	4	no	—
1028	D₄	—	4	4	no	—
1029	D₄	—	4	4	no	—
1030	D₄	—	8	1	no	—
1031	D₄	—	8	2	no	—
1032	D₄	—	8	2	no	—
1033	D₄	—	8	2	no	—
1034	D₄	—	8	1	no	—
1035	D₄	—	8	2	no	—
1036	D₄	C₂₃×H(5,𝔽₂)	1	4	yes	—
1037	C₂×C₄	—	2	2	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	2	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	2	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	2	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	4	1	no	—
1050	C₂×C₄	—	4	1	no	—
1051	C₂×C₄	—	4	4	no	—
1052	C₂×C₄	—	4	4	no	—
1053	C₂×C₄	—	4	4	no	—
1054	C₂×C₄	—	4	4	no	—
1055	C₂×C₄	—	4	2	no	—
1056	C₂×C₄	—	8	2	no	—
1057	C₂×C₄	—	8	2	no	—
1058	C₂×C₄	—	8	1	no	—
1059	C₂×C₄	—	8	2	no	—
1060	C₂×C₄	—	8	2	no	—
1061	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1062	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1063	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1064	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1065	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1066	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1067	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1068	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1069	C₈	—	2	2	no	—
1070	C₈	—	2	2	no	—
1071	C₈	—	2	2	no	—
1072	C₈	—	2	2	no	—
1073	C₂²	—	2	2	no	—
1074	C₂²	—	2	1	no	—
1075	C₂²	—	2	2	no	—
1076	C₂²	—	2	4	no	—
1077	C₂²	—	2	1	no	—
1078	C₂²	—	2	2	no	—
1079	C₂²	—	2	2	no	—
1080	C₂²	—	2	1	no	—
1081	C₂²	—	2	2	no	—
1082	C₂²	—	2	2	no	—
1083	C₂²	—	4	2	no	—
1084	C₂²	—	4	2	no	—
1085	C₂²	—	4	2	no	—
1086	C₂²	—	4	1	no	—
1087	C₂²	—	4	2	no	—
1088	C₂²	—	4	1	no	—
1089	C₂²	—	4	1	no	—
1090	C₂²	—	4	2	no	—
1091	C₂²	—	8	4	no	—
1092	C₂²	—	16	4	no	—
1093	C₂²	—	16	4	no	—
1094	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1095	C₄	—	2	1	no	—
1096	C₄	—	2	2	no	—
1097	C₄	—	2	2	no	—
1098	C₄	—	2	1	no	—
1099	C₄	—	2	1	no	—
1100	C₄	—	2	1	no	—
1101	C₄	—	2	1	no	—
1102	C₄	—	4	2	no	—
1103	C₄	—	4	2	no	—
1104	C₄	—	4	1	no	—
1105	C₄	—	4	2	no	—
1106	C₄	—	4	1	no	—
1107	C₄	—	4	2	no	—
1108	C₄	—	4	1	no	—
1109	C₄	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
1110	C₂	—	4	1	no	—
1111	C₂	—	4	2	no	—
1112	C₂	—	4	2	no	—
1113	C₂	—	4	4	no	—
1114	C₂	—	8	2	no	—
1115	C₂	—	8	1	no	—
1116	C₂	C₂₃×#3484	1	1	yes	characteristic
1117	C₂	C₂₃×#3585	1	1	yes	characteristic
1118	C₂	C₂₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3547	C₂	semidirect
2. C₂₃×#3496	C₂	semidirect
3. C₂₃×#3319	C₂	semidirect
4. C₂₃×#3315	C₂	semidirect
5. C₂₃×#3314	C₂	semidirect
6. C₂₃×#3310	C₂	semidirect
7. C₂₃×#3269	C₂	semidirect
8. C₂₃×#3267	C₂	semidirect
9. C₂₃×#3266	C₂	semidirect
10. C₂₃×#3265	C₂	semidirect
11. C₂₃×#3219	C₂	semidirect
12. C₂₃×#3216	C₂	semidirect
13. C₂₃×#3203	C₂	semidirect
14. C₂₃×#3201	C₂	semidirect
15. C₂₃×#3114	C₂	semidirect
16. C₂₃×#3110	C₂	semidirect
17. C₂₃×#3012	C₂	semidirect
18. C₂₃×#3009	C₂	semidirect
19. C₂₃×#2980	C₂	semidirect
21. C₂×C₂₃×#137	C₂²	semidirect
22. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
23. C₂×C₂₃×#135	C₂²	semidirect
24. C₂²×SD₁₆×C₂₃	C₂²	semidirect
27. C₂₃×#555	C₂²	semidirect
28. C₂₃×#554	C₂²	semidirect
30. C₂₃×#552	C₂²	semidirect
31. D₄×Q₈×C₂₃	C₂²	semidirect
32. C₂₃×#548	C₂²	semidirect
35. C₂₃×#547	C₂²	semidirect
45. C₂₃×#537	C₂²	semidirect
46. C₂₃×#536	C₂²	semidirect
49. C₂₃×#533	C₂²	semidirect
52. C₂₃×#529	C₂²	semidirect
55. C₂₃×#497	C₂²	semidirect
56. C₂₃×#497	C₂²	semidirect
57. C₂₃×#496	C₂²	semidirect
58. C₂₃×#491	C₂²	semidirect
59. C₂₃×#490	C₂²	semidirect
60. C₂₃×#489	C₂²	semidirect
61. C₂₃×#485	C₂²	semidirect
62. C₂₃×#484	C₂²	semidirect
63. C₂₃×#484	C₂²	semidirect
64. C₂₃×#483	C₂²	semidirect
65. C₂₃×#482	C₂²	semidirect
66. C₂₃×#480	C₂²	semidirect
67. C₂₃×#480	C₂²	semidirect
68. C₂₃×#478	C₂²	semidirect
69. C₂₃×#474	C₂²	semidirect
70. C₂₃×#470	C₂²	semidirect
71. C₂₃×#468	C₂²	semidirect
72. C₂₃×#468	C₂²	semidirect
73. C₂₃×#468	C₂²	semidirect
74. C₂₃×#467	C₂²	semidirect
75. C₂₃×#467	C₂²	semidirect
76. C₂₃×#466	C₂²	semidirect
77. C₂₃×#465	C₂²	semidirect
78. C₂₃×#464	C₂²	semidirect
79. C₂₃×#463	C₂²	semidirect
80. C₂₃×#463	C₂²	semidirect
81. C₂₃×#462	C₂²	semidirect
82. C₂₃×#461	C₂²	semidirect
83. C₂₃×#460	C₂²	semidirect
84. C₂₃×#452	C₂²	semidirect
85. C₂₃×#452	C₂²	semidirect
86. C₂₃×#452	C₂²	semidirect
87. C₂₃×#452	C₂²	semidirect
88. C₂₃×#452	C₂²	semidirect
89. C₂₃×#452	C₂²	semidirect
90. C₂₃×#452	C₂²	semidirect
91. C₂₃×#451	C₂²	semidirect
94. C₂₃×#450	C₂²	semidirect
95. C₂₃×#450	C₂²	semidirect
96. C₂₃×#450	C₂²	semidirect
97. C₂₃×#449	C₂²	semidirect
98. C₂₃×#449	C₂²	semidirect
99. C₂₃×#449	C₂²	semidirect
100. C₂₃×#448	C₂²	semidirect
102. C₂₃×#447	C₂²	semidirect
103. C₂₃×#442	C₂²	semidirect
104. C₂₃×#440	C₂²	semidirect
105. C₂₃×#440	C₂²	semidirect
106. C₂₃×#440	C₂²	semidirect
107. C₂₃×#435	C₂²	semidirect
108. C₂₃×#435	C₂²	semidirect
109. C₂₃×#435	C₂²	semidirect
110. C₂₃×#435	C₂²	semidirect
111. C₂₃×#432	C₂²	semidirect
112. C₂₃×#432	C₂²	semidirect
113. C₂₃×#418	C₂²	semidirect
114. C₂₃×#417	C₂²	semidirect
115. C₂₃×#416	C₂²	semidirect
116. C₂×C₂₃×#102	C₂²	semidirect
117. C₂₃×#408	C₂²	semidirect
118. C₂₃×#408	C₂²	semidirect
430. #61670	C₂₃	direct (N × H)
514. #3547	C₂×C₂₃	semidirect
515. #3496	C₂×C₂₃	semidirect
516. #3319	C₂×C₂₃	semidirect
517. #3315	C₂×C₂₃	semidirect
518. #3314	C₂×C₂₃	semidirect
519. #3310	C₂×C₂₃	semidirect
520. #3269	C₂×C₂₃	semidirect
521. #3267	C₂×C₂₃	semidirect
522. #3266	C₂×C₂₃	semidirect
523. #3265	C₂×C₂₃	semidirect
524. #3219	C₂×C₂₃	semidirect
525. #3216	C₂×C₂₃	semidirect
526. #3203	C₂×C₂₃	semidirect
527. #3201	C₂×C₂₃	semidirect
528. #3114	C₂×C₂₃	semidirect
529. #3110	C₂×C₂₃	semidirect
530. #3012	C₂×C₂₃	semidirect
531. #3009	C₂×C₂₃	semidirect
532. #2980	C₂×C₂₃	semidirect
571. C₂×#137	C₂²×C₂₃	semidirect
572. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
573. C₂×#135	C₂²×C₂₃	semidirect
574. C₂²×SD₁₆	C₂²×C₂₃	semidirect
577. #555	C₂²×C₂₃	semidirect
578. #554	C₂²×C₂₃	semidirect
580. #552	C₂²×C₂₃	semidirect
581. D₄×Q₈	C₂²×C₂₃	semidirect
582. #548	C₂²×C₂₃	semidirect
585. #547	C₂²×C₂₃	semidirect
595. #537	C₂²×C₂₃	semidirect
596. #536	C₂²×C₂₃	semidirect
599. #533	C₂²×C₂₃	semidirect
602. #529	C₂²×C₂₃	semidirect
605. #497	C₂²×C₂₃	semidirect
606. #497	C₂²×C₂₃	semidirect
607. #496	C₂²×C₂₃	semidirect
608. #491	C₂²×C₂₃	semidirect
609. #490	C₂²×C₂₃	semidirect
610. #489	C₂²×C₂₃	semidirect
611. #485	C₂²×C₂₃	semidirect
612. #484	C₂²×C₂₃	semidirect
613. #484	C₂²×C₂₃	semidirect
614. #483	C₂²×C₂₃	semidirect
615. #482	C₂²×C₂₃	semidirect
616. #480	C₂²×C₂₃	semidirect
617. #480	C₂²×C₂₃	semidirect
618. #478	C₂²×C₂₃	semidirect
619. #474	C₂²×C₂₃	semidirect
620. #470	C₂²×C₂₃	semidirect
621. #468	C₂²×C₂₃	semidirect
622. #468	C₂²×C₂₃	semidirect
623. #468	C₂²×C₂₃	semidirect
624. #467	C₂²×C₂₃	semidirect
625. #467	C₂²×C₂₃	semidirect
626. #466	C₂²×C₂₃	semidirect
627. #465	C₂²×C₂₃	semidirect
628. #464	C₂²×C₂₃	semidirect
629. #463	C₂²×C₂₃	semidirect
630. #463	C₂²×C₂₃	semidirect
631. #462	C₂²×C₂₃	semidirect
632. #461	C₂²×C₂₃	semidirect
633. #460	C₂²×C₂₃	semidirect
634. #452	C₂²×C₂₃	semidirect
635. #452	C₂²×C₂₃	semidirect
636. #452	C₂²×C₂₃	semidirect
637. #452	C₂²×C₂₃	semidirect
638. #452	C₂²×C₂₃	semidirect
639. #452	C₂²×C₂₃	semidirect
640. #452	C₂²×C₂₃	semidirect
641. #451	C₂²×C₂₃	semidirect
644. #450	C₂²×C₂₃	semidirect
645. #450	C₂²×C₂₃	semidirect
646. #450	C₂²×C₂₃	semidirect
647. #449	C₂²×C₂₃	semidirect
648. #449	C₂²×C₂₃	semidirect
649. #449	C₂²×C₂₃	semidirect
650. #448	C₂²×C₂₃	semidirect
652. #447	C₂²×C₂₃	semidirect
653. #442	C₂²×C₂₃	semidirect
654. #440	C₂²×C₂₃	semidirect
655. #440	C₂²×C₂₃	semidirect
656. #440	C₂²×C₂₃	semidirect
657. #435	C₂²×C₂₃	semidirect
658. #435	C₂²×C₂₃	semidirect
659. #435	C₂²×C₂₃	semidirect
660. #435	C₂²×C₂₃	semidirect
661. #432	C₂²×C₂₃	semidirect
662. #432	C₂²×C₂₃	semidirect
663. #418	C₂²×C₂₃	semidirect
664. #417	C₂²×C₂₃	semidirect
665. #416	C₂²×C₂₃	semidirect
666. C₂×#102	C₂²×C₂₃	semidirect
667. #408	C₂²×C₂₃	semidirect
668. #408	C₂²×C₂₃	semidirect
845. C₂₃	#61670	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×#3547	2
C₂₃×#3496	2
C₂₃×#3319	2
C₂₃×#3315	2
C₂₃×#3314	2
C₂₃×#3310	2
C₂₃×#3269	2
C₂₃×#3267	2
C₂₃×#3266	2
C₂₃×#3265	2
C₂₃×#3219	2
C₂₃×#3216	2
C₂₃×#3203	2
C₂₃×#3201	2
C₂₃×#3114	2
C₂₃×#3110	2
C₂₃×#3012	2
C₂₃×#3009	2
C₂₃×#2980	2
#61670	23

Subgroups — C23×#61670 #19209296

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61670 #19209296