Subgroups — C₂₃×#60596 #19208222

Order 5888.

2130 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₂₃×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3124	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3118	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3115	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3110	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3107	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3100	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3098	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3079	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂₃×#474	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3036	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3012	C₂	1	2	yes	maximal, complemented
15	C₂₃×#2951	C₂	1	2	yes	maximal, complemented
16	C₂₃×#2946	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2925	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
20	C₂×C₂₃×#135	C₂²	1	2	yes	—
21	C₂₃×#556	—	2	1	no	—
22	C₂₃×#555	—	2	1	no	—
23	C₂₃×#554	—	2	1	no	—
24	C₂₃×#553	—	2	2	no	—
25	C₂₃×#548	—	2	2	no	—
26	C₂₃×#547	—	2	1	no	—
27	C₂₃×#542	C₂²	1	4	yes	complemented
28	C₂₃×#537	C₂²	1	2	yes	—
29	C₂₃×#533	C₂²	1	2	yes	complemented
30	C₂₃×#532	C₂²	1	1	yes	characteristic, complemented
31	C₂₃×#532	C₂²	1	2	yes	complemented
32	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₂₃×#520	—	2	1	no	—
34	C₂₃×#520	C₂²	1	1	yes	characteristic
35	C₂₃×#520	C₂²	1	2	yes	—
36	C₂₃×#520	C₂²	1	1	yes	characteristic
37	C₂₃×#520	C₂²	1	2	yes	complemented
38	C₂₃×#518	—	2	2	no	—
39	C₂₃×#518	—	2	1	no	—
40	C₂₃×#518	C₂²	1	1	yes	characteristic
41	C₂₃×#518	C₂²	1	2	yes	—
42	C₄×#41×C₂₃	—	2	1	no	—
43	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
44	C₄×#41×C₂₃	C₂²	1	2	yes	—
45	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₂₃	—	2	1	no	—
47	C₂×C₄×D₄×C₂₃	—	2	2	no	—
48	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
50	C₂₃×#485	C₂²	1	4	yes	complemented
51	C₂₃×#484	C₂²	1	4	yes	complemented
52	C₂₃×#482	C₂²	1	4	yes	complemented
53	C₂₃×#480	C₂²	1	4	yes	complemented
54	C₂₃×#477	C₂²	1	2	yes	complemented
55	C₂₃×#476	C₂²	1	2	yes	complemented
56	C₂₃×#475	C₂²	1	2	yes	complemented
57	C₂₃×#474	C₂²	1	2	yes	complemented
58	C₂₃×#474	C₂²	1	2	yes	complemented
59	C₂₃×#474	C₂²	1	4	yes	complemented
60	C₂₃×#474	C₂²	1	2	yes	complemented
61	C₂₃×#464	C₂²	1	2	yes	complemented
62	C₂₃×#463	C₂²	1	2	yes	complemented
63	C₂₃×#463	C₂²	1	4	yes	complemented
64	C₂₃×#462	C₂²	1	1	yes	characteristic, complemented
65	C₂₃×#461	C₂²	1	1	yes	characteristic, complemented
66	C₂₃×#461	C₂²	1	2	yes	complemented
67	C₂₃×#460	C₂²	1	1	yes	characteristic, complemented
68	C₂₃×#459	C₂²	1	1	yes	characteristic, complemented
69	C₂₃×#459	C₂²	1	2	yes	complemented
70	C₂₃×#452	C₂²	1	4	yes	—
71	C₂₃×#450	C₂²	1	4	yes	—
72	C₂₃×#449	C₂²	1	4	yes	—
73	C₂₃×#447	C₂²	1	4	yes	—
74	C₂₃×#442	C₂²	1	4	yes	complemented
75	C₂₃×#440	C₂²	1	4	yes	complemented
76	C₂₃×#440	C₂²	1	4	yes	complemented
77	C₂₃×#440	C₂²	1	4	yes	complemented
78	C₄×Q₁₆×C₂₃	C₂²	1	4	yes	complemented
79	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	complemented
80	C₄×D₈×C₂₃	C₂²	1	4	yes	complemented
81	C₄×D₈×C₂₃	C₂²	1	4	yes	complemented
82	C₂₃×#433	C₂²	1	4	yes	complemented
83	C₂₃×#432	C₂²	1	2	yes	complemented
84	C₂₃×#431	C₂²	1	2	yes	complemented
85	C₂₃×#428	C₂²	1	2	yes	complemented
86	C₂×C₂₃×#107	C₂²	1	2	yes	complemented
87	C₂₃×#423	C₂²	1	1	yes	characteristic, complemented
88	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
89	C₂₃×#417	C₂²	1	2	yes	—
90	C₂₃×#417	C₂²	1	2	yes	complemented
91	C₂₃×#416	C₂²	1	2	yes	complemented
92	C₂×C₂₃×#102	C₂²	1	2	yes	—
93	C₂₃×#408	C₂²	1	2	yes	—
94	C₂₃×#405	C₂²	1	2	yes	complemented
95	C₂₃×H(5,𝔽₂)	—	2	4	no	—
96	C₂₃×H(5,𝔽₂)	—	2	4	no	—
97	C₂×#41×C₂₃	—	2	1	no	—
98	C₂×#41×C₂₃	—	2	2	no	—
99	C₂×#41×C₂₃	C₂³	1	2	yes	—
100	C₂×#41×C₂₃	C₂³	1	2	yes	—
101	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
102	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
103	C₂²×Q₈×C₂₃	—	2	1	no	—
104	C₂²×D₄×C₂₃	—	2	2	no	—
105	C₂²×D₄×C₂₃	—	2	1	no	—
106	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
107	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₂₃	—	2	1	no	—
109	C₂³×C₄×C₂₃	—	2	2	no	—
110	C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
111	C₂₃×#135	—	2	8	no	—
112	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
113	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
114	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
115	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
116	C₂×D₈×C₂₃	C₂³	1	2	yes	—
117	C₂×D₈×C₂₃	C₂³	1	4	yes	—
118	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
119	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
120	C₂₃×C₄⋊Q₈	—	2	1	no	—
121	C₂₃×C₄⋊Q₈	—	2	1	no	—
122	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
123	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
124	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
125	C₂₃×#127	C₂³	1	1	yes	characteristic
126	C₂₃×#126	—	2	4	no	—
127	C₂₃×#125	—	2	2	no	—
128	C₂₃×#124	—	2	4	no	—
129	C₂₃×#124	—	2	2	no	—
130	C₂₃×#124	C₂³	1	2	yes	—
131	C₂₃×#123	—	2	4	no	—
132	C₂₃×C₂²⋊Q₈	—	2	2	no	—
133	C₂₃×C₂²⋊Q₈	—	2	2	no	—
134	C₂₃×C₂²⋊Q₈	—	2	4	no	—
135	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
136	C₂₃×#121	—	2	2	no	—
137	C₂₃×#121	—	2	4	no	—
138	C₂₃×#121	—	2	1	no	—
139	C₂₃×#121	—	2	1	no	—
140	C₂₃×#121	—	2	2	no	—
141	C₂₃×#121	C₂³	1	4	yes	—
142	C₄×Q₈×C₂₃	—	2	1	no	—
143	C₄×Q₈×C₂₃	—	2	2	no	—
144	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
145	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
146	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
147	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
148	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
149	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
150	C₄×D₄×C₂₃	—	2	2	no	—
151	C₄×D₄×C₂₃	—	2	1	no	—
152	C₄×D₄×C₂₃	—	2	1	no	—
153	C₄×D₄×C₂₃	—	2	2	no	—
154	C₄×D₄×C₂₃	—	2	1	no	—
155	C₄×D₄×C₂₃	—	2	2	no	—
156	C₄×D₄×C₂₃	—	2	1	no	—
157	C₄×D₄×C₂₃	—	2	2	no	—
158	C₄×D₄×C₂₃	—	2	1	no	—
159	C₄×D₄×C₂₃	—	2	2	no	—
160	C₄×D₄×C₂₃	—	2	4	no	—
161	C₄×D₄×C₂₃	—	2	2	no	—
162	C₄×D₄×C₂₃	—	2	2	no	—
163	C₄×D₄×C₂₃	—	2	2	no	—
164	C₄×D₄×C₂₃	—	2	1	no	—
165	C₄×D₄×C₂₃	—	2	2	no	—
166	C₄×D₄×C₂₃	—	2	1	no	—
167	C₄×D₄×C₂₃	—	2	1	no	—
168	C₄×D₄×C₂₃	—	2	2	no	—
169	C₄×D₄×C₂₃	—	2	2	no	—
170	C₄×D₄×C₂₃	—	2	1	no	—
171	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
172	C₄×D₄×C₂₃	D₄	1	2	yes	—
173	C₄×D₄×C₂₃	D₄	1	2	yes	—
174	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
175	C₄×D₄×C₂₃	C₂³	1	2	yes	—
176	C₄×D₄×C₂₃	C₂³	1	2	yes	—
177	C₄×D₄×C₂₃	C₂³	1	4	yes	—
178	C₄×D₄×C₂₃	C₂³	1	2	yes	—
179	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
180	C₄×D₄×C₂₃	C₂³	1	2	yes	—
181	C₄×D₄×C₂₃	C₂³	1	2	yes	—
182	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
183	C₂₃×#117	—	2	2	no	—
184	C₂₃×#117	—	2	2	no	—
185	C₂₃×#117	—	2	1	no	—
186	C₂₃×#117	—	2	2	no	—
187	C₂₃×#117	—	2	2	no	—
188	C₂₃×#117	—	2	1	no	—
189	C₂₃×#117	C₂³	1	1	yes	characteristic
190	C₂₃×#117	C₂³	1	2	yes	—
191	C₂₃×#117	C₂³	1	1	yes	characteristic
192	C₂₃×#117	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
194	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
195	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
196	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
197	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
198	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
199	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
201	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
202	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
203	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
204	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
205	C₂×C₄²×C₂₃	—	2	1	no	—
206	C₂×C₄²×C₂₃	—	2	2	no	—
207	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
209	C₂₃×#107	C₂³	1	4	yes	—
210	C₂₃×#107	C₂³	1	4	yes	—
211	C₂₃×#107	C₂³	1	4	yes	—
212	C₂₃×#106	C₂³	1	4	yes	—
213	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
214	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
215	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
216	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
217	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
218	C₂₃×#103	C₂³	1	2	yes	—
219	C₂₃×#103	C₂³	1	2	yes	—
220	C₂₃×#103	C₂³	1	4	yes	—
221	C₂₃×#103	C₂³	1	4	yes	—
222	C₂₃×#102	C₂³	1	4	yes	—
223	C₂₃×#102	C₂³	1	4	yes	—
224	C₂₃×#102	C₂³	1	2	yes	—
225	C₂₃×#102	C₂³	1	2	yes	—
226	C₂₃×#102	C₂³	1	4	yes	—
227	C₂₃×#102	C₂³	1	4	yes	—
228	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
229	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
230	C₂₃×#97	C₂³	1	4	yes	—
231	C₄×C₈×C₂₃	C₂³	1	4	yes	—
232	C₂⁴×C₂₃	—	2	2	no	—
233	C₂⁴×C₂₃	—	2	1	no	—
234	#41×C₂₃	—	2	8	no	—
235	#41×C₂₃	—	2	4	no	—
236	#41×C₂₃	—	2	4	no	—
237	#41×C₂₃	—	2	2	no	—
238	#41×C₂₃	—	2	2	no	—
239	#41×C₂₃	—	2	2	no	—
240	#41×C₂₃	—	2	4	no	—
241	#41×C₂₃	—	2	4	no	—
242	#41×C₂₃	—	8	4	no	—
243	#41×C₂₃	#41	1	4	yes	complemented
244	C₂×Q₈×C₂₃	—	2	2	no	—
245	C₂×Q₈×C₂₃	—	2	2	no	—
246	C₂×Q₈×C₂₃	—	8	2	no	—
247	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
248	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
249	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
250	C₂×D₄×C₂₃	—	2	16	no	—
251	C₂×D₄×C₂₃	—	2	8	no	—
252	C₂×D₄×C₂₃	—	2	2	no	—
253	C₂×D₄×C₂₃	—	2	1	no	—
254	C₂×D₄×C₂₃	—	2	4	no	—
255	C₂×D₄×C₂₃	—	2	4	no	—
256	C₂×D₄×C₂₃	—	2	2	no	—
257	C₂×D₄×C₂₃	—	2	4	no	—
258	C₂×D₄×C₂₃	—	2	2	no	—
259	C₂×D₄×C₂₃	—	2	1	no	—
260	C₂×D₄×C₂₃	—	2	1	no	—
261	C₂×D₄×C₂₃	—	2	1	no	—
262	C₂×D₄×C₂₃	—	2	2	no	—
263	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
264	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
265	C₂×D₄×C₂₃	#41	1	4	yes	complemented
266	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
267	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
268	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₂₃	—	2	2	no	—
270	C₂²×C₄×C₂₃	—	2	1	no	—
271	C₂²×C₄×C₂₃	—	2	2	no	—
272	C₂²×C₄×C₂₃	—	2	1	no	—
273	C₂²×C₄×C₂₃	—	2	2	no	—
274	C₂²×C₄×C₂₃	—	2	1	no	—
275	C₂²×C₄×C₂₃	—	2	2	no	—
276	C₂²×C₄×C₂₃	—	2	2	no	—
277	C₂²×C₄×C₂₃	—	2	2	no	—
278	C₂²×C₄×C₂₃	—	2	1	no	—
279	C₂²×C₄×C₂₃	—	2	2	no	—
280	C₂²×C₄×C₂₃	—	2	2	no	—
281	C₂²×C₄×C₂₃	—	2	2	no	—
282	C₂²×C₄×C₂₃	—	2	4	no	—
283	C₂²×C₄×C₂₃	—	8	2	no	—
284	C₂²×C₄×C₂₃	—	8	4	no	—
285	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
286	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
287	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
288	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
289	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
291	Q₁₆×C₂₃	—	2	4	no	—
292	SD₁₆×C₂₃	—	2	4	no	—
293	SD₁₆×C₂₃	—	2	4	no	—
294	SD₁₆×C₂₃	—	2	8	no	—
295	D₈×C₂₃	—	2	4	no	—
296	D₈×C₂₃	—	2	8	no	—
297	M₁₆×C₂₃	—	2	4	no	—
298	C₂×C₈×C₂₃	—	2	4	no	—
299	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
300	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
301	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
302	C₄⋊C₄×C₂₃	—	2	1	no	—
303	C₄⋊C₄×C₂₃	—	2	2	no	—
304	C₄⋊C₄×C₂₃	—	2	2	no	—
305	C₄⋊C₄×C₂₃	—	2	1	no	—
306	C₄⋊C₄×C₂₃	—	2	2	no	—
307	C₄⋊C₄×C₂₃	—	2	2	no	—
308	C₄⋊C₄×C₂₃	—	2	4	no	—
309	C₄⋊C₄×C₂₃	—	2	2	no	—
310	C₄⋊C₄×C₂₃	—	2	1	no	—
311	C₄⋊C₄×C₂₃	—	2	1	no	—
312	C₄⋊C₄×C₂₃	—	2	1	no	—
313	C₄⋊C₄×C₂₃	—	2	4	no	—
314	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
315	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
316	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
317	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
318	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
319	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
320	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
321	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
322	C₂²⋊C₄×C₂₃	—	2	2	no	—
323	C₂²⋊C₄×C₂₃	—	2	1	no	—
324	C₂²⋊C₄×C₂₃	—	2	4	no	—
325	C₂²⋊C₄×C₂₃	—	2	1	no	—
326	C₂²⋊C₄×C₂₃	—	2	2	no	—
327	C₂²⋊C₄×C₂₃	—	2	2	no	—
328	C₂²⋊C₄×C₂₃	—	2	2	no	—
329	C₂²⋊C₄×C₂₃	—	2	2	no	—
330	C₂²⋊C₄×C₂₃	—	2	2	no	—
331	C₂²⋊C₄×C₂₃	—	2	1	no	—
332	C₂²⋊C₄×C₂₃	—	2	4	no	—
333	C₂²⋊C₄×C₂₃	—	2	4	no	—
334	C₂²⋊C₄×C₂₃	—	2	2	no	—
335	C₂²⋊C₄×C₂₃	—	2	2	no	—
336	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
337	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
338	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
339	C₄²×C₂₃	—	2	1	no	—
340	C₄²×C₂₃	—	2	2	no	—
341	C₄²×C₂₃	—	2	1	no	—
342	C₄²×C₂₃	—	2	2	no	—
343	C₄²×C₂₃	—	2	1	no	—
344	C₄²×C₂₃	—	2	4	no	—
345	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
346	C₄²×C₂₃	C₂×D₄	1	2	yes	—
347	C₄²×C₂₃	C₂×D₄	1	2	yes	—
348	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
349	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
350	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
351	C₄²×C₂₃	C₂⁴	1	2	yes	—
352	#60596	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
353	C₂³×C₂₃	—	2	8	no	—
354	C₂³×C₂₃	—	2	2	no	—
355	C₂³×C₂₃	—	2	1	no	—
356	C₂³×C₂₃	—	2	4	no	—
357	C₂³×C₂₃	—	2	2	no	—
358	C₂³×C₂₃	—	8	1	no	—
359	C₂³×C₂₃	—	8	2	no	—
360	C₂³×C₂₃	—	8	1	no	—
361	C₂³×C₂₃	—	8	2	no	—
362	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
363	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
364	Q₈×C₂₃	—	2	2	no	—
365	Q₈×C₂₃	—	2	1	no	—
366	Q₈×C₂₃	—	2	2	no	—
367	Q₈×C₂₃	—	2	2	no	—
368	Q₈×C₂₃	—	4	4	no	—
369	Q₈×C₂₃	—	8	2	no	—
370	Q₈×C₂₃	C₂×#41	1	2	yes	—
371	D₄×C₂₃	—	2	8	no	—
372	D₄×C₂₃	—	2	8	no	—
373	D₄×C₂₃	—	2	4	no	—
374	D₄×C₂₃	—	2	4	no	—
375	D₄×C₂₃	—	2	2	no	—
376	D₄×C₂₃	—	2	4	no	—
377	D₄×C₂₃	—	2	2	no	—
378	D₄×C₂₃	—	2	1	no	—
379	D₄×C₂₃	—	2	2	no	—
380	D₄×C₂₃	—	2	2	no	—
381	D₄×C₂₃	—	4	2	no	—
382	D₄×C₂₃	—	4	4	no	—
383	D₄×C₂₃	—	4	2	no	—
384	D₄×C₂₃	—	8	4	no	—
385	D₄×C₂₃	C₂×#41	1	2	yes	—
386	D₄×C₂₃	C₂×#41	1	4	yes	—
387	C₂×C₄×C₂₃	—	2	8	no	—
388	C₂×C₄×C₂₃	—	2	1	no	—
389	C₂×C₄×C₂₃	—	2	4	no	—
390	C₂×C₄×C₂₃	—	2	2	no	—
391	C₂×C₄×C₂₃	—	2	4	no	—
392	C₂×C₄×C₂₃	—	2	2	no	—
393	C₂×C₄×C₂₃	—	2	2	no	—
394	C₂×C₄×C₂₃	—	2	1	no	—
395	C₂×C₄×C₂₃	—	2	2	no	—
396	C₂×C₄×C₂₃	—	2	2	no	—
397	C₂×C₄×C₂₃	—	2	1	no	—
398	C₂×C₄×C₂₃	—	2	4	no	—
399	C₂×C₄×C₂₃	—	4	1	no	—
400	C₂×C₄×C₂₃	—	4	2	no	—
401	C₂×C₄×C₂₃	—	4	4	no	—
402	C₂×C₄×C₂₃	—	4	4	no	—
403	C₂×C₄×C₂₃	—	4	2	no	—
404	C₂×C₄×C₂₃	—	8	2	no	—
405	C₂×C₄×C₂₃	—	8	1	no	—
406	C₂×C₄×C₂₃	—	8	2	no	—
407	C₂×C₄×C₂₃	—	8	2	no	—
408	C₂×C₄×C₂₃	—	8	2	no	—
409	C₂×C₄×C₂₃	—	8	4	no	—
410	C₂×C₄×C₂₃	—	8	1	no	—
411	C₂×C₄×C₂₃	—	8	2	no	—
412	C₂×C₄×C₂₃	—	8	2	no	—
413	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
414	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
415	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
416	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
417	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
418	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
419	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
420	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
421	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
422	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
423	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
424	C₈×C₂₃	—	2	2	no	—
425	C₈×C₂₃	—	2	2	no	—
426	C₈×C₂₃	—	2	4	no	—
427	#3511	C₂×C₂₃	1	1	yes	characteristic, complemented
428	C₄×H(5,𝔽₂)	C₂×C₂₃	1	1	yes	characteristic, complemented
429	#3124	C₂×C₂₃	1	4	yes	complemented
430	#3118	C₂×C₂₃	1	4	yes	complemented
431	#3115	C₂×C₂₃	1	2	yes	complemented
432	#3110	C₂×C₂₃	1	2	yes	complemented
433	#3107	C₂×C₂₃	1	2	yes	complemented
434	#3100	C₂×C₂₃	1	2	yes	complemented
435	#3098	C₂×C₂₃	1	2	yes	complemented
436	#3079	C₂×C₂₃	1	1	yes	characteristic, complemented
437	C₂×#474	C₂×C₂₃	1	1	yes	characteristic, complemented
438	#3036	C₂×C₂₃	1	1	yes	characteristic, complemented
439	#3035	C₂×C₂₃	1	1	yes	characteristic, complemented
440	#3012	C₂×C₂₃	1	2	yes	complemented
441	#2951	C₂×C₂₃	1	2	yes	complemented
442	#2946	C₂×C₂₃	1	2	yes	complemented
443	#2925	C₂×C₂₃	1	1	yes	characteristic, complemented
444	C₂²×C₂₃	—	2	1	no	—
445	C₂²×C₂₃	—	2	1	no	—
446	C₂²×C₂₃	—	2	2	no	—
447	C₂²×C₂₃	—	2	2	no	—
448	C₂²×C₂₃	—	2	4	no	—
449	C₂²×C₂₃	—	2	2	no	—
450	C₂²×C₂₃	—	2	2	no	—
451	C₂²×C₂₃	—	4	2	no	—
452	C₂²×C₂₃	—	4	1	no	—
453	C₂²×C₂₃	—	4	2	no	—
454	C₂²×C₂₃	—	4	1	no	—
455	C₂²×C₂₃	—	4	2	no	—
456	C₂²×C₂₃	—	4	2	no	—
457	C₂²×C₂₃	—	4	2	no	—
458	C₂²×C₂₃	—	8	4	no	—
459	C₂²×C₂₃	—	8	8	no	—
460	C₂²×C₂₃	#525	1	2	yes	—
461	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
462	C₄×C₂₃	—	2	1	no	—
463	C₄×C₂₃	—	2	2	no	—
464	C₄×C₂₃	—	2	1	no	—
465	C₄×C₂₃	—	2	2	no	—
466	C₄×C₂₃	—	2	2	no	—
467	C₄×C₂₃	—	2	2	no	—
468	C₄×C₂₃	—	2	1	no	—
469	C₄×C₂₃	—	4	1	no	—
470	C₄×C₂₃	—	4	2	no	—
471	C₄×C₂₃	—	4	1	no	—
472	C₄×C₂₃	—	4	2	no	—
473	C₄×C₂₃	—	4	4	no	—
474	C₄×C₂₃	#525	1	2	yes	—
475	C₄×C₂₃	#576	1	2	yes	—
476	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
477	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
478	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	1	yes	characteristic
479	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	—
480	C₂×#135	C₂²×C₂₃	1	2	yes	—
481	#556	—	2	1	no	—
482	#555	—	2	1	no	—
483	#554	—	2	1	no	—
484	#553	—	2	2	no	—
485	#548	—	2	2	no	—
486	#547	—	2	1	no	—
487	#542	C₂²×C₂₃	1	4	yes	complemented
488	#537	C₂²×C₂₃	1	2	yes	—
489	#533	C₂²×C₂₃	1	2	yes	complemented
490	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
491	#532	C₂²×C₂₃	1	2	yes	complemented
492	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
493	#520	—	2	1	no	—
494	#520	C₂²×C₂₃	1	2	yes	—
495	#520	C₂²×C₂₃	1	1	yes	characteristic
496	#520	C₂²×C₂₃	1	1	yes	characteristic
497	#520	C₂²×C₂₃	1	2	yes	complemented
498	#518	—	2	2	no	—
499	#518	—	2	1	no	—
500	#518	C₂²×C₂₃	1	2	yes	—
501	#518	C₂²×C₂₃	1	1	yes	characteristic
502	C₄×#41	—	2	1	no	—
503	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
504	C₄×#41	C₂²×C₂₃	1	2	yes	—
505	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
506	C₂×C₄×D₄	—	2	1	no	—
507	C₂×C₄×D₄	—	2	2	no	—
508	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
509	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
510	#485	C₂²×C₂₃	1	4	yes	complemented
511	#484	C₂²×C₂₃	1	4	yes	complemented
512	#482	C₂²×C₂₃	1	4	yes	complemented
513	#480	C₂²×C₂₃	1	4	yes	complemented
514	#477	C₂²×C₂₃	1	2	yes	complemented
515	#476	C₂²×C₂₃	1	2	yes	complemented
516	#475	C₂²×C₂₃	1	2	yes	complemented
517	#474	C₂²×C₂₃	1	2	yes	complemented
518	#474	C₂²×C₂₃	1	2	yes	complemented
519	#474	C₂²×C₂₃	1	2	yes	complemented
520	#474	C₂²×C₂₃	1	4	yes	complemented
521	#464	C₂²×C₂₃	1	2	yes	complemented
522	#463	C₂²×C₂₃	1	2	yes	complemented
523	#463	C₂²×C₂₃	1	4	yes	complemented
524	#462	C₂²×C₂₃	1	1	yes	characteristic, complemented
525	#461	C₂²×C₂₃	1	2	yes	complemented
526	#461	C₂²×C₂₃	1	1	yes	characteristic, complemented
527	#460	C₂²×C₂₃	1	1	yes	characteristic, complemented
528	#459	C₂²×C₂₃	1	1	yes	characteristic, complemented
529	#459	C₂²×C₂₃	1	2	yes	complemented
530	#452	C₂²×C₂₃	1	4	yes	—
531	#450	C₂²×C₂₃	1	4	yes	—
532	#449	C₂²×C₂₃	1	4	yes	—
533	#447	C₂²×C₂₃	1	4	yes	—
534	#442	C₂²×C₂₃	1	4	yes	complemented
535	#440	C₂²×C₂₃	1	4	yes	complemented
536	#440	C₂²×C₂₃	1	4	yes	complemented
537	#440	C₂²×C₂₃	1	4	yes	complemented
538	C₄×Q₁₆	C₂²×C₂₃	1	4	yes	complemented
539	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
540	C₄×D₈	C₂²×C₂₃	1	4	yes	complemented
541	C₄×D₈	C₂²×C₂₃	1	4	yes	complemented
542	#433	C₂²×C₂₃	1	4	yes	complemented
543	#432	C₂²×C₂₃	1	2	yes	complemented
544	#431	C₂²×C₂₃	1	2	yes	complemented
545	#428	C₂²×C₂₃	1	2	yes	complemented
546	C₂×#107	C₂²×C₂₃	1	2	yes	complemented
547	#423	C₂²×C₂₃	1	1	yes	characteristic, complemented
548	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
549	#417	C₂²×C₂₃	1	2	yes	—
550	#417	C₂²×C₂₃	1	2	yes	complemented
551	#416	C₂²×C₂₃	1	2	yes	complemented
552	C₂×#102	C₂²×C₂₃	1	2	yes	—
553	#408	C₂²×C₂₃	1	2	yes	—
554	#405	C₂²×C₂₃	1	2	yes	complemented
555	C₂×C₂₃	—	2	2	no	—
556	C₂×C₂₃	—	4	2	no	—
557	C₂×C₂₃	—	4	4	no	—
558	C₂×C₂₃	—	4	2	no	—
559	C₂×C₂₃	—	8	2	no	—
560	C₂×C₂₃	C₂×#525	1	1	yes	characteristic
561	C₂×C₂₃	C₂×#576	1	1	yes	characteristic
562	C₂×C₂₃	#3586	1	1	yes	characteristic
563	H(5,𝔽₂)	—	2	4	no	—
564	H(5,𝔽₂)	—	2	4	no	—
565	C₂×#41	—	2	1	no	—
566	C₂×#41	—	2	2	no	—
567	C₂×#41	C₂³×C₂₃	1	2	yes	—
568	C₂×#41	C₂³×C₂₃	1	2	yes	—
569	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
570	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
571	C₂²×Q₈	—	2	1	no	—
572	C₂²×D₄	—	2	2	no	—
573	C₂²×D₄	—	2	1	no	—
574	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
575	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
576	C₂³×C₄	—	2	1	no	—
577	C₂³×C₄	—	2	2	no	—
578	AGL(1,ℤ/8)	—	2	8	no	—
579	#135	—	2	8	no	—
580	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
581	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
582	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
583	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
584	C₂×D₈	C₂³×C₂₃	1	2	yes	—
585	C₂×D₈	C₂³×C₂₃	1	4	yes	—
586	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
587	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
588	C₄⋊Q₈	—	2	1	no	—
589	C₄⋊Q₈	—	2	1	no	—
590	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
591	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
592	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
593	#127	C₂³×C₂₃	1	1	yes	characteristic
594	#126	—	2	4	no	—
595	#125	—	2	2	no	—
596	#124	—	2	4	no	—
597	#124	—	2	2	no	—
598	#124	C₂³×C₂₃	1	2	yes	—
599	#123	—	2	4	no	—
600	C₂²⋊Q₈	—	2	2	no	—
601	C₂²⋊Q₈	—	2	2	no	—
602	C₂²⋊Q₈	—	2	4	no	—
603	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
604	#121	—	2	2	no	—
605	#121	—	2	4	no	—
606	#121	—	2	1	no	—
607	#121	—	2	1	no	—
608	#121	—	2	2	no	—
609	#121	C₂³×C₂₃	1	4	yes	—
610	C₄×Q₈	—	2	1	no	—
611	C₄×Q₈	—	2	2	no	—
612	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
613	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
614	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
615	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
616	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
617	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
618	C₄×D₄	—	2	2	no	—
619	C₄×D₄	—	2	1	no	—
620	C₄×D₄	—	2	1	no	—
621	C₄×D₄	—	2	2	no	—
622	C₄×D₄	—	2	1	no	—
623	C₄×D₄	—	2	2	no	—
624	C₄×D₄	—	2	1	no	—
625	C₄×D₄	—	2	2	no	—
626	C₄×D₄	—	2	1	no	—
627	C₄×D₄	—	2	2	no	—
628	C₄×D₄	—	2	2	no	—
629	C₄×D₄	—	2	2	no	—
630	C₄×D₄	—	2	2	no	—
631	C₄×D₄	—	2	4	no	—
632	C₄×D₄	—	2	1	no	—
633	C₄×D₄	—	2	2	no	—
634	C₄×D₄	—	2	2	no	—
635	C₄×D₄	—	2	1	no	—
636	C₄×D₄	—	2	1	no	—
637	C₄×D₄	—	2	2	no	—
638	C₄×D₄	—	2	1	no	—
639	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
640	C₄×D₄	D₄×C₂₃	1	2	yes	—
641	C₄×D₄	D₄×C₂₃	1	2	yes	—
642	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
643	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
644	C₄×D₄	C₂³×C₂₃	1	2	yes	—
645	C₄×D₄	C₂³×C₂₃	1	2	yes	—
646	C₄×D₄	C₂³×C₂₃	1	2	yes	—
647	C₄×D₄	C₂³×C₂₃	1	2	yes	—
648	C₄×D₄	C₂³×C₂₃	1	2	yes	—
649	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
650	C₄×D₄	C₂³×C₂₃	1	4	yes	—
651	#117	—	2	2	no	—
652	#117	—	2	1	no	—
653	#117	—	2	2	no	—
654	#117	—	2	2	no	—
655	#117	—	2	2	no	—
656	#117	—	2	1	no	—
657	#117	C₂³×C₂₃	1	1	yes	characteristic
658	#117	C₂³×C₂₃	1	2	yes	—
659	#117	C₂³×C₂₃	1	1	yes	characteristic
660	#117	C₂³×C₂₃	1	2	yes	—
661	C₂×C₄⋊C₄	—	2	1	no	—
662	C₂×C₄⋊C₄	—	2	1	no	—
663	C₂×C₄⋊C₄	—	2	2	no	—
664	C₂×C₄⋊C₄	—	2	2	no	—
665	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
666	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
667	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
668	C₂×C₂²⋊C₄	—	2	1	no	—
669	C₂×C₂²⋊C₄	—	2	2	no	—
670	C₂×C₂²⋊C₄	—	2	2	no	—
671	C₂×C₂²⋊C₄	—	2	2	no	—
672	C₂×C₂²⋊C₄	—	2	2	no	—
673	C₂×C₄²	—	2	1	no	—
674	C₂×C₄²	—	2	2	no	—
675	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
676	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
677	#107	C₂³×C₂₃	1	4	yes	—
678	#107	C₂³×C₂₃	1	4	yes	—
679	#107	C₂³×C₂₃	1	4	yes	—
680	#106	C₂³×C₂₃	1	4	yes	—
681	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
682	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
683	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
684	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
685	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
686	#103	C₂³×C₂₃	1	2	yes	—
687	#103	C₂³×C₂₃	1	2	yes	—
688	#103	C₂³×C₂₃	1	4	yes	—
689	#103	C₂³×C₂₃	1	4	yes	—
690	#102	C₂³×C₂₃	1	4	yes	—
691	#102	C₂³×C₂₃	1	4	yes	—
692	#102	C₂³×C₂₃	1	2	yes	—
693	#102	C₂³×C₂₃	1	2	yes	—
694	#102	C₂³×C₂₃	1	4	yes	—
695	#102	C₂³×C₂₃	1	4	yes	—
696	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
697	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
698	#97	C₂³×C₂₃	1	4	yes	—
699	C₄×C₈	C₂³×C₂₃	1	4	yes	—
700	C₂₃	#60596	1	1	yes	characteristic, direct product factor, Sylow
701	C₂⁴	—	2	2	no	—
702	C₂⁴	—	2	1	no	—
703	#41	—	2	8	no	—
704	#41	—	2	4	no	—
705	#41	—	2	4	no	—
706	#41	—	2	2	no	—
707	#41	—	2	2	no	—
708	#41	—	2	2	no	—
709	#41	—	2	4	no	—
710	#41	—	2	4	no	—
711	#41	—	8	4	no	—
712	#41	#41×C₂₃	1	4	yes	complemented
713	C₂×Q₈	—	2	2	no	—
714	C₂×Q₈	—	2	2	no	—
715	C₂×Q₈	—	8	2	no	—
716	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
717	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
718	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
719	C₂×D₄	—	2	16	no	—
720	C₂×D₄	—	2	8	no	—
721	C₂×D₄	—	2	2	no	—
722	C₂×D₄	—	2	1	no	—
723	C₂×D₄	—	2	4	no	—
724	C₂×D₄	—	2	4	no	—
725	C₂×D₄	—	2	2	no	—
726	C₂×D₄	—	2	4	no	—
727	C₂×D₄	—	2	2	no	—
728	C₂×D₄	—	2	1	no	—
729	C₂×D₄	—	2	1	no	—
730	C₂×D₄	—	2	1	no	—
731	C₂×D₄	—	2	2	no	—
732	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
733	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
734	C₂×D₄	#41×C₂₃	1	4	yes	complemented
735	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
736	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
737	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
738	C₂²×C₄	—	2	2	no	—
739	C₂²×C₄	—	2	1	no	—
740	C₂²×C₄	—	2	2	no	—
741	C₂²×C₄	—	2	1	no	—
742	C₂²×C₄	—	2	2	no	—
743	C₂²×C₄	—	2	1	no	—
744	C₂²×C₄	—	2	2	no	—
745	C₂²×C₄	—	2	2	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	1	no	—
748	C₂²×C₄	—	2	2	no	—
749	C₂²×C₄	—	2	2	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	4	no	—
752	C₂²×C₄	—	8	2	no	—
753	C₂²×C₄	—	8	4	no	—
754	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
755	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
756	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
757	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
758	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
759	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
760	Q₁₆	—	2	4	no	—
761	SD₁₆	—	2	4	no	—
762	SD₁₆	—	2	4	no	—
763	SD₁₆	—	2	8	no	—
764	D₈	—	2	4	no	—
765	D₈	—	2	8	no	—
766	M₁₆	—	2	4	no	—
767	C₂×C₈	—	2	4	no	—
768	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
769	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
770	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
771	C₄⋊C₄	—	2	1	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	—	2	2	no	—
774	C₄⋊C₄	—	2	1	no	—
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	—	2	4	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	2	1	no	—
780	C₄⋊C₄	—	2	1	no	—
781	C₄⋊C₄	—	2	1	no	—
782	C₄⋊C₄	—	2	4	no	—
783	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
784	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
785	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
786	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
787	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
788	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
789	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
790	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
791	C₂²⋊C₄	—	2	2	no	—
792	C₂²⋊C₄	—	2	1	no	—
793	C₂²⋊C₄	—	2	4	no	—
794	C₂²⋊C₄	—	2	1	no	—
795	C₂²⋊C₄	—	2	2	no	—
796	C₂²⋊C₄	—	2	2	no	—
797	C₂²⋊C₄	—	2	2	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	1	no	—
801	C₂²⋊C₄	—	2	4	no	—
802	C₂²⋊C₄	—	2	4	no	—
803	C₂²⋊C₄	—	2	2	no	—
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
806	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
807	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
808	C₄²	—	2	1	no	—
809	C₄²	—	2	2	no	—
810	C₄²	—	2	1	no	—
811	C₄²	—	2	2	no	—
812	C₄²	—	2	1	no	—
813	C₄²	—	2	4	no	—
814	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
815	C₄²	C₂×D₄×C₂₃	1	2	yes	—
816	C₄²	C₂×D₄×C₂₃	1	2	yes	—
817	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
818	C₄²	C₂⁴×C₂₃	1	2	yes	—
819	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
820	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
821	C₂³	—	2	8	no	—
822	C₂³	—	2	2	no	—
823	C₂³	—	2	1	no	—
824	C₂³	—	2	4	no	—
825	C₂³	—	2	2	no	—
826	C₂³	—	8	1	no	—
827	C₂³	—	8	2	no	—
828	C₂³	—	8	1	no	—
829	C₂³	—	8	2	no	—
830	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
831	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
832	Q₈	—	2	1	no	—
833	Q₈	—	2	2	no	—
834	Q₈	—	2	2	no	—
835	Q₈	—	2	2	no	—
836	Q₈	—	4	4	no	—
837	Q₈	—	8	2	no	—
838	Q₈	C₂×#41×C₂₃	1	2	yes	—
839	D₄	—	2	8	no	—
840	D₄	—	2	8	no	—
841	D₄	—	2	4	no	—
842	D₄	—	2	4	no	—
843	D₄	—	2	2	no	—
844	D₄	—	2	1	no	—
845	D₄	—	2	2	no	—
846	D₄	—	2	2	no	—
847	D₄	—	2	2	no	—
848	D₄	—	2	4	no	—
849	D₄	—	4	2	no	—
850	D₄	—	4	4	no	—
851	D₄	—	4	2	no	—
852	D₄	—	8	4	no	—
853	D₄	C₂×#41×C₂₃	1	2	yes	—
854	D₄	C₂×#41×C₂₃	1	4	yes	—
855	C₂×C₄	—	2	8	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	4	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	4	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	4	no	—
867	C₂×C₄	—	4	1	no	—
868	C₂×C₄	—	4	2	no	—
869	C₂×C₄	—	4	4	no	—
870	C₂×C₄	—	4	2	no	—
871	C₂×C₄	—	4	4	no	—
872	C₂×C₄	—	8	2	no	—
873	C₂×C₄	—	8	2	no	—
874	C₂×C₄	—	8	2	no	—
875	C₂×C₄	—	8	4	no	—
876	C₂×C₄	—	8	2	no	—
877	C₂×C₄	—	8	1	no	—
878	C₂×C₄	—	8	1	no	—
879	C₂×C₄	—	8	2	no	—
880	C₂×C₄	—	8	2	no	—
881	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
882	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
883	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
884	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
885	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
886	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
887	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
888	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
889	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
890	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
891	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
892	C₈	—	2	2	no	—
893	C₈	—	2	2	no	—
894	C₈	—	2	4	no	—
895	C₂²	—	2	1	no	—
896	C₂²	—	2	1	no	—
897	C₂²	—	2	2	no	—
898	C₂²	—	2	4	no	—
899	C₂²	—	2	2	no	—
900	C₂²	—	2	2	no	—
901	C₂²	—	2	2	no	—
902	C₂²	—	4	2	no	—
903	C₂²	—	4	1	no	—
904	C₂²	—	4	2	no	—
905	C₂²	—	4	1	no	—
906	C₂²	—	4	2	no	—
907	C₂²	—	4	2	no	—
908	C₂²	—	4	2	no	—
909	C₂²	—	8	4	no	—
910	C₂²	—	8	8	no	—
911	C₂²	C₂₃×#525	1	2	yes	—
912	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
913	C₄	—	2	2	no	—
914	C₄	—	2	2	no	—
915	C₄	—	2	2	no	—
916	C₄	—	2	1	no	—
917	C₄	—	2	1	no	—
918	C₄	—	2	2	no	—
919	C₄	—	2	1	no	—
920	C₄	—	4	2	no	—
921	C₄	—	4	1	no	—
922	C₄	—	4	2	no	—
923	C₄	—	4	4	no	—
924	C₄	—	4	1	no	—
925	C₄	C₂₃×#525	1	2	yes	—
926	C₄	C₂₃×#576	1	2	yes	—
927	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
928	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
929	C₂	—	2	2	no	—
930	C₂	—	4	2	no	—
931	C₂	—	4	4	no	—
932	C₂	—	4	2	no	—
933	C₂	—	8	2	no	—
934	C₂	C₂×C₂₃×#525	1	1	yes	characteristic
935	C₂	C₂×C₂₃×#576	1	1	yes	characteristic
936	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 ◁ C₄×#41×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3511	C₂	semidirect
2. C₄×C₂₃×H(5,𝔽₂)	C₂	semidirect
3. C₂₃×#3124	C₂	semidirect
4. C₂₃×#3118	C₂	semidirect
5. C₂₃×#3115	C₂	semidirect
6. C₂₃×#3110	C₂	semidirect
7. C₂₃×#3107	C₂	semidirect
8. C₂₃×#3100	C₂	semidirect
9. C₂₃×#3098	C₂	semidirect
10. C₂₃×#3079	C₂	semidirect
11. C₂×C₂₃×#474	C₂	semidirect
12. C₂₃×#3036	C₂	semidirect
13. C₂₃×#3035	C₂	semidirect
14. C₂₃×#3012	C₂	semidirect
15. C₂₃×#2951	C₂	semidirect
16. C₂₃×#2946	C₂	semidirect
17. C₂₃×#2925	C₂	semidirect
27. C₂₃×#542	C₂²	semidirect
29. C₂₃×#533	C₂²	semidirect
30. C₂₃×#532	C₂²	semidirect
31. C₂₃×#532	C₂²	semidirect
32. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
37. C₂₃×#520	C₂²	semidirect
50. C₂₃×#485	C₂²	semidirect
51. C₂₃×#484	C₂²	semidirect
52. C₂₃×#482	C₂²	semidirect
53. C₂₃×#480	C₂²	semidirect
54. C₂₃×#477	C₂²	semidirect
55. C₂₃×#476	C₂²	semidirect
56. C₂₃×#475	C₂²	semidirect
57. C₂₃×#474	C₂²	semidirect
58. C₂₃×#474	C₂²	semidirect
59. C₂₃×#474	C₂²	semidirect
60. C₂₃×#474	C₂²	semidirect
61. C₂₃×#464	C₂²	semidirect
62. C₂₃×#463	C₂²	semidirect
63. C₂₃×#463	C₂²	semidirect
64. C₂₃×#462	C₂²	semidirect
65. C₂₃×#461	C₂²	semidirect
66. C₂₃×#461	C₂²	semidirect
67. C₂₃×#460	C₂²	semidirect
68. C₂₃×#459	C₂²	semidirect
69. C₂₃×#459	C₂²	semidirect
74. C₂₃×#442	C₂²	semidirect
75. C₂₃×#440	C₂²	semidirect
76. C₂₃×#440	C₂²	semidirect
77. C₂₃×#440	C₂²	semidirect
78. C₄×Q₁₆×C₂₃	C₂²	semidirect
79. C₄×SD₁₆×C₂₃	C₂²	semidirect
80. C₄×D₈×C₂₃	C₂²	semidirect
81. C₄×D₈×C₂₃	C₂²	semidirect
82. C₂₃×#433	C₂²	semidirect
83. C₂₃×#432	C₂²	semidirect
84. C₂₃×#431	C₂²	semidirect
85. C₂₃×#428	C₂²	semidirect
86. C₂×C₂₃×#107	C₂²	semidirect
87. C₂₃×#423	C₂²	semidirect
88. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
90. C₂₃×#417	C₂²	semidirect
91. C₂₃×#416	C₂²	semidirect
94. C₂₃×#405	C₂²	semidirect
243. #41×C₂₃	#41	semidirect
265. C₂×D₄×C₂₃	#41	semidirect
352. #60596	C₂₃	direct (N × H)
427. #3511	C₂×C₂₃	semidirect
428. C₄×H(5,𝔽₂)	C₂×C₂₃	semidirect
429. #3124	C₂×C₂₃	semidirect
430. #3118	C₂×C₂₃	semidirect
431. #3115	C₂×C₂₃	semidirect
432. #3110	C₂×C₂₃	semidirect
433. #3107	C₂×C₂₃	semidirect
434. #3100	C₂×C₂₃	semidirect
435. #3098	C₂×C₂₃	semidirect
436. #3079	C₂×C₂₃	semidirect
437. C₂×#474	C₂×C₂₃	semidirect
438. #3036	C₂×C₂₃	semidirect
439. #3035	C₂×C₂₃	semidirect
440. #3012	C₂×C₂₃	semidirect
441. #2951	C₂×C₂₃	semidirect
442. #2946	C₂×C₂₃	semidirect
443. #2925	C₂×C₂₃	semidirect
487. #542	C₂²×C₂₃	semidirect
489. #533	C₂²×C₂₃	semidirect
490. #532	C₂²×C₂₃	semidirect
491. #532	C₂²×C₂₃	semidirect
492. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
497. #520	C₂²×C₂₃	semidirect
510. #485	C₂²×C₂₃	semidirect
511. #484	C₂²×C₂₃	semidirect
512. #482	C₂²×C₂₃	semidirect
513. #480	C₂²×C₂₃	semidirect
514. #477	C₂²×C₂₃	semidirect
515. #476	C₂²×C₂₃	semidirect
516. #475	C₂²×C₂₃	semidirect
517. #474	C₂²×C₂₃	semidirect
518. #474	C₂²×C₂₃	semidirect
519. #474	C₂²×C₂₃	semidirect
520. #474	C₂²×C₂₃	semidirect
521. #464	C₂²×C₂₃	semidirect
522. #463	C₂²×C₂₃	semidirect
523. #463	C₂²×C₂₃	semidirect
524. #462	C₂²×C₂₃	semidirect
525. #461	C₂²×C₂₃	semidirect
526. #461	C₂²×C₂₃	semidirect
527. #460	C₂²×C₂₃	semidirect
528. #459	C₂²×C₂₃	semidirect
529. #459	C₂²×C₂₃	semidirect
534. #442	C₂²×C₂₃	semidirect
535. #440	C₂²×C₂₃	semidirect
536. #440	C₂²×C₂₃	semidirect
537. #440	C₂²×C₂₃	semidirect
538. C₄×Q₁₆	C₂²×C₂₃	semidirect
539. C₄×SD₁₆	C₂²×C₂₃	semidirect
540. C₄×D₈	C₂²×C₂₃	semidirect
541. C₄×D₈	C₂²×C₂₃	semidirect
542. #433	C₂²×C₂₃	semidirect
543. #432	C₂²×C₂₃	semidirect
544. #431	C₂²×C₂₃	semidirect
545. #428	C₂²×C₂₃	semidirect
546. C₂×#107	C₂²×C₂₃	semidirect
547. #423	C₂²×C₂₃	semidirect
548. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
550. #417	C₂²×C₂₃	semidirect
551. #416	C₂²×C₂₃	semidirect
554. #405	C₂²×C₂₃	semidirect
700. C₂₃	#60596	direct (N × H)
712. #41	#41×C₂₃	semidirect
734. C₂×D₄	#41×C₂₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₃×#3511	2
C₄×C₂₃×H(5,𝔽₂)	2
C₂₃×#3124	2
C₂₃×#3118	2
C₂₃×#3115	2
C₂₃×#3110	2
C₂₃×#3107	2
C₂₃×#3100	2
C₂₃×#3098	2
C₂₃×#3079	2
C₂×C₂₃×#474	2
C₂₃×#3036	2
C₂₃×#3035	2
C₂₃×#3012	2
C₂₃×#2951	2
C₂₃×#2946	2
C₂₃×#2925	2
#60596	23

Subgroups — C23×#60596 #19208222

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60596 #19208222