Subgroups — C₂₃×#60823 #19208449

Order 5888.

2054 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3512	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3500	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3223	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3222	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3221	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3220	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3212	C₂	1	4	yes	maximal, complemented
8	C₂₃×#3211	C₂	1	4	yes	maximal, complemented
9	C₂₃×#3153	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3147	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3142	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₃×#488	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3046	C₂	1	2	yes	maximal, complemented
14	C₂₃×#3045	C₂	1	2	yes	maximal, complemented
15	C₂₃×#3013	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3012	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2922	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₂₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
20	C₂×C₂₃×#137	C₂²	1	2	yes	complemented
21	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
22	C₂×C₂₃×#135	C₂²	1	2	yes	—
23	C₂×C₂₃×#135	C₂²	1	2	yes	complemented
24	C₂₃×#553	—	2	4	no	—
25	C₂₃×#553	—	2	2	no	—
26	C₂₃×#552	—	2	2	no	—
27	C₂₃×#548	—	2	2	no	—
28	C₂₃×#546	—	2	4	no	—
29	C₂₃×#546	—	2	2	no	—
30	C₂₃×#541	C₂²	1	2	yes	complemented
31	C₂₃×#540	C₂²	1	2	yes	complemented
32	C₂₃×#537	C₂²	1	2	yes	—
33	C₂₃×#536	C₂²	1	2	yes	—
34	C₂₃×#536	C₂²	1	1	yes	characteristic
35	C₂₃×#535	C₂²	1	2	yes	—
36	C₂₃×#535	C₂²	1	1	yes	characteristic
37	C₂₃×#532	C₂²	1	2	yes	—
38	C₂₃×#532	C₂²	1	1	yes	characteristic
39	C₂₃×#532	C₂²	1	1	yes	characteristic, complemented
40	C₂₃×#529	C₂²	1	4	yes	complemented
41	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₂₃×#124	C₂²	1	2	yes	—
43	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
44	C₂₃×#520	C₂²	1	2	yes	complemented
45	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
46	C₂₃×#497	C₂²	1	2	yes	complemented
47	C₂₃×#496	C₂²	1	2	yes	complemented
48	C₂₃×#495	C₂²	1	2	yes	complemented
49	C₂₃×#495	C₂²	1	4	yes	complemented
50	C₂₃×#495	C₂²	1	2	yes	complemented
51	C₂₃×#494	C₂²	1	1	yes	characteristic, complemented
52	C₂₃×#493	C₂²	1	1	yes	characteristic, complemented
53	C₂₃×#492	C₂²	1	1	yes	characteristic, complemented
54	C₂₃×#492	C₂²	1	1	yes	characteristic, complemented
55	C₂₃×#491	C₂²	1	2	yes	complemented
56	C₂₃×#490	C₂²	1	2	yes	complemented
57	C₂₃×#488	C₂²	1	2	yes	complemented
58	C₂₃×#488	C₂²	1	4	yes	complemented
59	C₂₃×#488	C₂²	1	2	yes	complemented
60	C₂₃×#488	C₂²	1	2	yes	complemented
61	C₂₃×#488	C₂²	1	2	yes	complemented
62	C₂₃×#464	C₂²	1	4	yes	complemented
63	C₂₃×#464	C₂²	1	4	yes	complemented
64	C₂₃×#463	C₂²	1	4	yes	complemented
65	C₂₃×#463	C₂²	1	4	yes	complemented
66	C₂₃×#462	C₂²	1	4	yes	complemented
67	C₂₃×#461	C₂²	1	4	yes	complemented
68	C₂₃×#460	C₂²	1	4	yes	complemented
69	C₂₃×#459	C₂²	1	4	yes	complemented
70	C₂₃×#452	C₂²	1	4	yes	—
71	C₂₃×#452	C₂²	1	4	yes	complemented
72	C₂₃×#451	C₂²	1	4	yes	complemented
73	C₂₃×#450	C₂²	1	4	yes	—
74	C₂₃×#449	C₂²	1	4	yes	—
75	C₂₃×#449	C₂²	1	4	yes	complemented
76	C₂₃×#448	C₂²	1	4	yes	complemented
77	C₂₃×#447	C₂²	1	4	yes	—
78	C₂₃×#433	C₂²	1	2	yes	complemented
79	C₂₃×#433	C₂²	1	2	yes	complemented
80	C₂₃×#431	C₂²	1	4	yes	complemented
81	C₂₃×#424	C₂²	1	2	yes	complemented
82	C₂₃×#417	C₂²	1	2	yes	—
83	C₂₃×#417	C₂²	1	2	yes	complemented
84	C₂×C₂₃×#103	C₂²	1	2	yes	complemented
85	C₂×C₂₃×#102	C₂²	1	2	yes	—
86	C₂₃×#408	C₂²	1	2	yes	—
87	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
88	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
89	C₂₃×2₋¹⁺⁴	—	4	4	no	—
90	C₂₃×H(5,𝔽₂)	—	4	4	no	—
91	C₂×#41×C₂₃	—	2	1	no	—
92	C₂×#41×C₂₃	—	2	1	no	—
93	C₂×#41×C₂₃	—	2	2	no	—
94	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
95	C₂×#41×C₂₃	C₂³	1	2	yes	—
96	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
97	C₂×#41×C₂₃	C₂³	1	2	yes	—
98	C₂×#41×C₂₃	C₂³	1	2	yes	—
99	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
100	C₂²×Q₈×C₂₃	—	2	1	no	—
101	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
102	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
103	C₂²×D₄×C₂₃	—	2	2	no	—
104	C₂²×D₄×C₂₃	—	2	1	no	—
105	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
106	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
107	C₂₃×#137	—	4	4	no	—
108	C₂₃×AGL(1,ℤ/8)	—	4	4	no	—
109	C₂₃×#135	—	4	4	no	—
110	C₂₃×#135	—	4	4	no	—
111	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
112	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
113	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
114	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
115	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
116	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
117	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
118	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
119	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
120	C₂×D₈×C₂₃	C₂³	1	2	yes	—
121	C₂×D₈×C₂₃	C₂³	1	2	yes	—
122	C₂×D₈×C₂₃	C₂³	1	4	yes	—
123	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
124	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
125	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
126	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
127	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
128	C₂₃×#127	C₂³	1	2	yes	—
129	C₂₃×#127	C₂³	1	1	yes	characteristic
130	C₂₃×#127	C₂³	1	1	yes	characteristic
131	C₂₃×#126	—	2	4	no	—
132	C₂₃×#126	—	2	4	no	—
133	C₂₃×#125	—	2	4	no	—
134	C₂₃×#125	—	2	2	no	—
135	C₂₃×#125	C₂³	1	2	yes	—
136	C₂₃×#125	C₂³	1	2	yes	—
137	C₂₃×#124	—	2	4	no	—
138	C₂₃×#124	—	2	2	no	—
139	C₂₃×#124	C₂³	1	2	yes	—
140	C₂₃×#124	C₂³	1	2	yes	—
141	C₂₃×#124	C₂³	1	1	yes	characteristic
142	C₂₃×#124	C₂³	1	2	yes	—
143	C₂₃×#124	C₂³	1	1	yes	characteristic
144	C₂₃×#124	C₂³	1	2	yes	—
145	C₂₃×#124	C₂³	1	2	yes	—
146	C₂₃×#123	—	2	4	no	—
147	C₂₃×#123	—	2	4	no	—
148	C₂₃×#123	—	2	2	no	—
149	C₂₃×#123	—	2	4	no	—
150	C₂₃×C₂²⋊Q₈	—	2	2	no	—
151	C₂₃×C₂²⋊Q₈	—	2	2	no	—
152	C₂₃×C₂²⋊Q₈	—	2	4	no	—
153	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
154	C₂₃×#121	—	2	2	no	—
155	C₂₃×#121	—	2	4	no	—
156	C₂₃×#121	—	2	2	no	—
157	C₂₃×#121	—	2	2	no	—
158	C₂₃×#121	—	2	4	no	—
159	C₂₃×#121	—	2	2	no	—
160	C₂₃×#121	—	2	4	no	—
161	C₂₃×#121	—	2	4	no	—
162	C₂₃×#121	C₂³	1	4	yes	—
163	C₂₃×#120	—	2	2	no	—
164	C₂₃×#120	—	2	4	no	—
165	C₄×Q₈×C₂₃	D₄	1	2	yes	—
166	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
167	C₄×D₄×C₂₃	—	2	4	no	—
168	C₄×D₄×C₂₃	—	2	4	no	—
169	C₄×D₄×C₂₃	—	2	4	no	—
170	C₄×D₄×C₂₃	—	2	2	no	—
171	C₄×D₄×C₂₃	—	2	2	no	—
172	C₄×D₄×C₂₃	D₄	1	4	yes	—
173	C₄×D₄×C₂₃	D₄	1	2	yes	—
174	C₄×D₄×C₂₃	C₂³	1	4	yes	—
175	C₂₃×#117	—	2	2	no	—
176	C₂₃×#117	—	2	4	no	—
177	C₂₃×#117	C₂³	1	1	yes	characteristic
178	C₂₃×#117	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
180	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
181	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
183	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
184	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
186	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
187	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
188	C₂₃×#103	C₂³	1	4	yes	—
189	C₂₃×#103	C₂³	1	4	yes	—
190	C₂₃×#103	C₂³	1	4	yes	—
191	C₂₃×#103	C₂³	1	4	yes	—
192	C₂₃×#102	C₂³	1	4	yes	—
193	C₂₃×#102	C₂³	1	4	yes	—
194	C₂₃×#102	C₂³	1	4	yes	—
195	C₂₃×#102	C₂³	1	4	yes	—
196	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
197	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
198	C₂₃×#97	C₂³	1	2	yes	—
199	C₄×C₈×C₂₃	C₂³	1	2	yes	—
200	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
201	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
202	C₄×C₈×C₂₃	C₂³	1	2	yes	—
203	C₂⁴×C₂₃	—	2	2	no	—
204	C₂⁴×C₂₃	—	2	1	no	—
205	#41×C₂₃	—	2	4	no	—
206	#41×C₂₃	—	2	4	no	—
207	#41×C₂₃	—	2	4	no	—
208	#41×C₂₃	—	2	4	no	—
209	#41×C₂₃	—	2	4	no	—
210	#41×C₂₃	—	4	4	no	—
211	#41×C₂₃	—	4	4	no	—
212	#41×C₂₃	—	4	8	no	—
213	#41×C₂₃	—	4	4	no	—
214	#41×C₂₃	—	4	4	no	—
215	C₂×Q₈×C₂₃	—	2	2	no	—
216	C₂×Q₈×C₂₃	—	2	1	no	—
217	C₂×Q₈×C₂₃	—	2	4	no	—
218	C₂×Q₈×C₂₃	—	4	4	no	—
219	C₂×Q₈×C₂₃	—	4	4	no	—
220	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
221	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
222	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
223	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
224	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
225	C₂×D₄×C₂₃	—	2	2	no	—
226	C₂×D₄×C₂₃	—	2	2	no	—
227	C₂×D₄×C₂₃	—	2	1	no	—
228	C₂×D₄×C₂₃	—	2	2	no	—
229	C₂×D₄×C₂₃	—	2	1	no	—
230	C₂×D₄×C₂₃	—	2	4	no	—
231	C₂×D₄×C₂₃	—	2	2	no	—
232	C₂×D₄×C₂₃	—	2	1	no	—
233	C₂×D₄×C₂₃	—	2	4	no	—
234	C₂×D₄×C₂₃	—	2	2	no	—
235	C₂×D₄×C₂₃	—	2	2	no	—
236	C₂×D₄×C₂₃	—	2	4	no	—
237	C₂×D₄×C₂₃	—	4	4	no	—
238	C₂×D₄×C₂₃	—	4	8	no	—
239	C₂×D₄×C₂₃	—	4	4	no	—
240	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
241	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
242	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
243	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
244	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
245	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₂₃	—	2	2	no	—
247	C₂²×C₄×C₂₃	—	2	1	no	—
248	C₂²×C₄×C₂₃	—	2	2	no	—
249	C₂²×C₄×C₂₃	—	2	2	no	—
250	C₂²×C₄×C₂₃	—	2	2	no	—
251	C₂²×C₄×C₂₃	—	2	1	no	—
252	C₂²×C₄×C₂₃	—	2	2	no	—
253	C₂²×C₄×C₂₃	—	2	1	no	—
254	C₂²×C₄×C₂₃	—	2	4	no	—
255	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
256	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
257	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
259	Q₁₆×C₂₃	—	4	2	no	—
260	Q₁₆×C₂₃	—	4	2	no	—
261	Q₁₆×C₂₃	—	4	4	no	—
262	SD₁₆×C₂₃	—	4	2	no	—
263	SD₁₆×C₂₃	—	4	2	no	—
264	SD₁₆×C₂₃	—	4	2	no	—
265	SD₁₆×C₂₃	—	4	2	no	—
266	SD₁₆×C₂₃	—	4	4	no	—
267	SD₁₆×C₂₃	—	4	4	no	—
268	D₈×C₂₃	—	4	2	no	—
269	D₈×C₂₃	—	4	2	no	—
270	D₈×C₂₃	—	4	4	no	—
271	M₁₆×C₂₃	—	2	4	no	—
272	C₂×C₈×C₂₃	—	2	4	no	—
273	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
274	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
275	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
276	C₄⋊C₄×C₂₃	—	2	2	no	—
277	C₄⋊C₄×C₂₃	—	2	4	no	—
278	C₄⋊C₄×C₂₃	—	2	4	no	—
279	C₄⋊C₄×C₂₃	—	2	4	no	—
280	C₄⋊C₄×C₂₃	—	2	4	no	—
281	C₄⋊C₄×C₂₃	—	2	4	no	—
282	C₄⋊C₄×C₂₃	—	2	2	no	—
283	C₄⋊C₄×C₂₃	—	2	2	no	—
284	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
285	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
286	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
287	C₂²⋊C₄×C₂₃	—	2	4	no	—
288	C₂²⋊C₄×C₂₃	—	2	4	no	—
289	C₂²⋊C₄×C₂₃	—	2	2	no	—
290	C₂²⋊C₄×C₂₃	—	2	4	no	—
291	C₂²⋊C₄×C₂₃	—	2	4	no	—
292	C₂²⋊C₄×C₂₃	—	2	4	no	—
293	C₂²⋊C₄×C₂₃	—	2	2	no	—
294	C₂²⋊C₄×C₂₃	—	2	4	no	—
295	C₂²⋊C₄×C₂₃	—	2	4	no	—
296	C₂²⋊C₄×C₂₃	—	2	2	no	—
297	C₂²⋊C₄×C₂₃	—	2	2	no	—
298	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
299	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
300	C₄²×C₂₃	—	2	4	no	—
301	C₄²×C₂₃	C₂×D₄	1	4	yes	—
302	C₄²×C₂₃	C₂×D₄	1	2	yes	—
303	C₄²×C₂₃	C₂⁴	1	2	yes	—
304	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
305	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
306	#60823	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
307	C₂³×C₂₃	—	2	2	no	—
308	C₂³×C₂₃	—	2	2	no	—
309	C₂³×C₂₃	—	2	1	no	—
310	C₂³×C₂₃	—	2	1	no	—
311	C₂³×C₂₃	—	4	4	no	—
312	C₂³×C₂₃	—	4	2	no	—
313	C₂³×C₂₃	—	8	2	no	—
314	C₂³×C₂₃	—	8	4	no	—
315	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
316	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
317	Q₈×C₂₃	—	2	2	no	—
318	Q₈×C₂₃	—	2	2	no	—
319	Q₈×C₂₃	—	2	2	no	—
320	Q₈×C₂₃	—	2	4	no	—
321	Q₈×C₂₃	—	2	2	no	—
322	Q₈×C₂₃	—	2	2	no	—
323	Q₈×C₂₃	—	4	4	no	—
324	Q₈×C₂₃	—	4	2	no	—
325	D₄×C₂₃	—	2	4	no	—
326	D₄×C₂₃	—	2	2	no	—
327	D₄×C₂₃	—	2	2	no	—
328	D₄×C₂₃	—	2	2	no	—
329	D₄×C₂₃	—	2	4	no	—
330	D₄×C₂₃	—	2	2	no	—
331	D₄×C₂₃	—	2	2	no	—
332	D₄×C₂₃	—	4	4	no	—
333	D₄×C₂₃	—	4	4	no	—
334	D₄×C₂₃	—	4	4	no	—
335	D₄×C₂₃	—	4	2	no	—
336	D₄×C₂₃	—	4	4	no	—
337	D₄×C₂₃	—	4	2	no	—
338	D₄×C₂₃	—	4	2	no	—
339	D₄×C₂₃	—	8	4	no	—
340	D₄×C₂₃	—	8	2	no	—
341	D₄×C₂₃	—	8	2	no	—
342	D₄×C₂₃	—	8	4	no	—
343	C₂×C₄×C₂₃	—	2	4	no	—
344	C₂×C₄×C₂₃	—	2	2	no	—
345	C₂×C₄×C₂₃	—	2	4	no	—
346	C₂×C₄×C₂₃	—	2	2	no	—
347	C₂×C₄×C₂₃	—	2	1	no	—
348	C₂×C₄×C₂₃	—	2	1	no	—
349	C₂×C₄×C₂₃	—	4	4	no	—
350	C₂×C₄×C₂₃	—	4	2	no	—
351	C₂×C₄×C₂₃	—	4	4	no	—
352	C₂×C₄×C₂₃	—	4	4	no	—
353	C₂×C₄×C₂₃	—	4	4	no	—
354	C₂×C₄×C₂₃	—	4	2	no	—
355	C₂×C₄×C₂₃	—	4	2	no	—
356	C₂×C₄×C₂₃	—	4	2	no	—
357	C₂×C₄×C₂₃	—	4	4	no	—
358	C₂×C₄×C₂₃	—	8	4	no	—
359	C₂×C₄×C₂₃	—	8	2	no	—
360	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
361	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
362	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
363	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
364	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
365	C₂×C₄×C₂₃	H(5,𝔽₂)	1	4	yes	—
366	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
367	C₈×C₂₃	—	2	2	no	—
368	C₈×C₂₃	—	2	2	no	—
369	C₈×C₂₃	—	2	4	no	—
370	#3512	C₂×C₂₃	1	1	yes	characteristic, complemented
371	#3500	C₂×C₂₃	1	1	yes	characteristic, complemented
372	#3223	C₂×C₂₃	1	2	yes	complemented
373	#3222	C₂×C₂₃	1	2	yes	complemented
374	#3221	C₂×C₂₃	1	2	yes	complemented
375	#3220	C₂×C₂₃	1	2	yes	complemented
376	#3212	C₂×C₂₃	1	4	yes	complemented
377	#3211	C₂×C₂₃	1	4	yes	complemented
378	#3153	C₂×C₂₃	1	1	yes	characteristic, complemented
379	#3147	C₂×C₂₃	1	1	yes	characteristic, complemented
380	#3142	C₂×C₂₃	1	1	yes	characteristic, complemented
381	C₂×#488	C₂×C₂₃	1	1	yes	characteristic, complemented
382	#3046	C₂×C₂₃	1	2	yes	complemented
383	#3045	C₂×C₂₃	1	2	yes	complemented
384	#3013	C₂×C₂₃	1	2	yes	complemented
385	#3012	C₂×C₂₃	1	2	yes	complemented
386	#2922	C₂×C₂₃	1	1	yes	characteristic, complemented
387	C₂²×C₂₃	—	2	2	no	—
388	C₂²×C₂₃	—	2	4	no	—
389	C₂²×C₂₃	—	2	2	no	—
390	C₂²×C₂₃	—	4	2	no	—
391	C₂²×C₂₃	—	4	2	no	—
392	C₂²×C₂₃	—	4	2	no	—
393	C₂²×C₂₃	—	4	4	no	—
394	C₂²×C₂₃	—	4	2	no	—
395	C₂²×C₂₃	—	4	1	no	—
396	C₂²×C₂₃	—	4	2	no	—
397	C₂²×C₂₃	—	4	1	no	—
398	C₂²×C₂₃	—	4	2	no	—
399	C₂²×C₂₃	—	16	2	no	—
400	C₂²×C₂₃	—	16	4	no	—
401	C₂²×C₂₃	#535	1	2	yes	—
402	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
403	C₄×C₂₃	—	2	2	no	—
404	C₄×C₂₃	—	2	4	no	—
405	C₄×C₂₃	—	2	2	no	—
406	C₄×C₂₃	—	2	2	no	—
407	C₄×C₂₃	—	4	4	no	—
408	C₄×C₂₃	—	4	1	no	—
409	C₄×C₂₃	—	4	2	no	—
410	C₄×C₂₃	—	4	1	no	—
411	C₄×C₂₃	—	4	2	no	—
412	C₄×C₂₃	#535	1	2	yes	—
413	C₄×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
414	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	1	yes	characteristic
415	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	1	yes	characteristic
416	C₂×#137	C₂²×C₂₃	1	2	yes	complemented
417	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	—
418	C₂×#135	C₂²×C₂₃	1	2	yes	—
419	C₂×#135	C₂²×C₂₃	1	2	yes	complemented
420	#553	—	2	4	no	—
421	#553	—	2	2	no	—
422	#552	—	2	2	no	—
423	#548	—	2	2	no	—
424	#546	—	2	4	no	—
425	#546	—	2	2	no	—
426	#541	C₂²×C₂₃	1	2	yes	complemented
427	#540	C₂²×C₂₃	1	2	yes	complemented
428	#537	C₂²×C₂₃	1	2	yes	—
429	#536	C₂²×C₂₃	1	2	yes	—
430	#536	C₂²×C₂₃	1	1	yes	characteristic
431	#535	C₂²×C₂₃	1	2	yes	—
432	#535	C₂²×C₂₃	1	1	yes	characteristic
433	#532	C₂²×C₂₃	1	1	yes	characteristic
434	#532	C₂²×C₂₃	1	2	yes	—
435	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
436	#529	C₂²×C₂₃	1	4	yes	complemented
437	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic, complemented
438	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
439	C₂×#124	C₂²×C₂₃	1	2	yes	—
440	#520	C₂²×C₂₃	1	2	yes	complemented
441	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
442	#497	C₂²×C₂₃	1	2	yes	complemented
443	#496	C₂²×C₂₃	1	2	yes	complemented
444	#495	C₂²×C₂₃	1	2	yes	complemented
445	#495	C₂²×C₂₃	1	2	yes	complemented
446	#495	C₂²×C₂₃	1	4	yes	complemented
447	#494	C₂²×C₂₃	1	1	yes	characteristic, complemented
448	#493	C₂²×C₂₃	1	1	yes	characteristic, complemented
449	#492	C₂²×C₂₃	1	1	yes	characteristic, complemented
450	#492	C₂²×C₂₃	1	1	yes	characteristic, complemented
451	#491	C₂²×C₂₃	1	2	yes	complemented
452	#490	C₂²×C₂₃	1	2	yes	complemented
453	#488	C₂²×C₂₃	1	4	yes	complemented
454	#488	C₂²×C₂₃	1	2	yes	complemented
455	#488	C₂²×C₂₃	1	2	yes	complemented
456	#488	C₂²×C₂₃	1	2	yes	complemented
457	#488	C₂²×C₂₃	1	2	yes	complemented
458	#464	C₂²×C₂₃	1	4	yes	complemented
459	#464	C₂²×C₂₃	1	4	yes	complemented
460	#463	C₂²×C₂₃	1	4	yes	complemented
461	#463	C₂²×C₂₃	1	4	yes	complemented
462	#462	C₂²×C₂₃	1	4	yes	complemented
463	#461	C₂²×C₂₃	1	4	yes	complemented
464	#460	C₂²×C₂₃	1	4	yes	complemented
465	#459	C₂²×C₂₃	1	4	yes	complemented
466	#452	C₂²×C₂₃	1	4	yes	—
467	#452	C₂²×C₂₃	1	4	yes	complemented
468	#451	C₂²×C₂₃	1	4	yes	complemented
469	#450	C₂²×C₂₃	1	4	yes	—
470	#449	C₂²×C₂₃	1	4	yes	—
471	#449	C₂²×C₂₃	1	4	yes	complemented
472	#448	C₂²×C₂₃	1	4	yes	complemented
473	#447	C₂²×C₂₃	1	4	yes	—
474	#433	C₂²×C₂₃	1	2	yes	complemented
475	#433	C₂²×C₂₃	1	2	yes	complemented
476	#431	C₂²×C₂₃	1	4	yes	complemented
477	#424	C₂²×C₂₃	1	2	yes	complemented
478	#417	C₂²×C₂₃	1	2	yes	—
479	#417	C₂²×C₂₃	1	2	yes	complemented
480	C₂×#103	C₂²×C₂₃	1	2	yes	complemented
481	C₂×#102	C₂²×C₂₃	1	2	yes	—
482	#408	C₂²×C₂₃	1	2	yes	—
483	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
484	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
485	C₂×C₂₃	—	2	2	no	—
486	C₂×C₂₃	—	4	2	no	—
487	C₂×C₂₃	—	8	2	no	—
488	C₂×C₂₃	—	8	1	no	—
489	C₂×C₂₃	—	8	2	no	—
490	C₂×C₂₃	—	8	1	no	—
491	C₂×C₂₃	C₂×#535	1	1	yes	characteristic
492	C₂×C₂₃	#3584	1	2	yes	—
493	2₋¹⁺⁴	—	4	4	no	—
494	H(5,𝔽₂)	—	4	4	no	—
495	C₂×#41	—	2	1	no	—
496	C₂×#41	—	2	1	no	—
497	C₂×#41	—	2	2	no	—
498	C₂×#41	C₂³×C₂₃	1	2	yes	—
499	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
500	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
501	C₂×#41	C₂³×C₂₃	1	2	yes	—
502	C₂×#41	C₂³×C₂₃	1	2	yes	—
503	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
504	C₂²×Q₈	—	2	1	no	—
505	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
506	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
507	C₂²×D₄	—	2	2	no	—
508	C₂²×D₄	—	2	1	no	—
509	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
510	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
511	#137	—	4	4	no	—
512	AGL(1,ℤ/8)	—	4	4	no	—
513	#135	—	4	4	no	—
514	#135	—	4	4	no	—
515	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
516	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
517	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
518	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
519	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
520	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
521	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
522	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
523	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
524	C₂×D₈	C₂³×C₂₃	1	2	yes	—
525	C₂×D₈	C₂³×C₂₃	1	2	yes	—
526	C₂×D₈	C₂³×C₂₃	1	4	yes	—
527	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
528	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
529	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
530	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
531	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
532	#127	C₂³×C₂₃	1	2	yes	—
533	#127	C₂³×C₂₃	1	1	yes	characteristic
534	#127	C₂³×C₂₃	1	1	yes	characteristic
535	#126	—	2	4	no	—
536	#126	—	2	4	no	—
537	#125	—	2	4	no	—
538	#125	—	2	2	no	—
539	#125	C₂³×C₂₃	1	2	yes	—
540	#125	C₂³×C₂₃	1	2	yes	—
541	#124	—	2	4	no	—
542	#124	—	2	2	no	—
543	#124	C₂³×C₂₃	1	2	yes	—
544	#124	C₂³×C₂₃	1	1	yes	characteristic
545	#124	C₂³×C₂₃	1	2	yes	—
546	#124	C₂³×C₂₃	1	2	yes	—
547	#124	C₂³×C₂₃	1	2	yes	—
548	#124	C₂³×C₂₃	1	2	yes	—
549	#124	C₂³×C₂₃	1	1	yes	characteristic
550	#123	—	2	4	no	—
551	#123	—	2	4	no	—
552	#123	—	2	2	no	—
553	#123	—	2	4	no	—
554	C₂²⋊Q₈	—	2	2	no	—
555	C₂²⋊Q₈	—	2	2	no	—
556	C₂²⋊Q₈	—	2	4	no	—
557	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
558	#121	—	2	2	no	—
559	#121	—	2	4	no	—
560	#121	—	2	2	no	—
561	#121	—	2	4	no	—
562	#121	—	2	2	no	—
563	#121	—	2	2	no	—
564	#121	—	2	4	no	—
565	#121	—	2	4	no	—
566	#121	C₂³×C₂₃	1	4	yes	—
567	#120	—	2	2	no	—
568	#120	—	2	4	no	—
569	C₄×Q₈	D₄×C₂₃	1	2	yes	—
570	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
571	C₄×D₄	—	2	4	no	—
572	C₄×D₄	—	2	4	no	—
573	C₄×D₄	—	2	4	no	—
574	C₄×D₄	—	2	2	no	—
575	C₄×D₄	—	2	2	no	—
576	C₄×D₄	D₄×C₂₃	1	4	yes	—
577	C₄×D₄	D₄×C₂₃	1	2	yes	—
578	C₄×D₄	C₂³×C₂₃	1	4	yes	—
579	#117	—	2	2	no	—
580	#117	—	2	4	no	—
581	#117	C₂³×C₂₃	1	1	yes	characteristic
582	#117	C₂³×C₂₃	1	2	yes	—
583	C₂×C₄⋊C₄	—	2	2	no	—
584	C₂×C₄⋊C₄	—	2	2	no	—
585	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
586	C₂×C₂²⋊C₄	—	2	2	no	—
587	C₂×C₂²⋊C₄	—	2	4	no	—
588	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
589	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
590	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
591	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
592	#103	C₂³×C₂₃	1	4	yes	—
593	#103	C₂³×C₂₃	1	4	yes	—
594	#103	C₂³×C₂₃	1	4	yes	—
595	#103	C₂³×C₂₃	1	4	yes	—
596	#102	C₂³×C₂₃	1	4	yes	—
597	#102	C₂³×C₂₃	1	4	yes	—
598	#102	C₂³×C₂₃	1	4	yes	—
599	#102	C₂³×C₂₃	1	4	yes	—
600	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
601	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
602	#97	C₂³×C₂₃	1	2	yes	—
603	C₄×C₈	C₂³×C₂₃	1	2	yes	—
604	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
605	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
606	C₄×C₈	C₂³×C₂₃	1	2	yes	—
607	C₂₃	#60823	1	1	yes	characteristic, direct product factor, Sylow
608	C₂⁴	—	2	2	no	—
609	C₂⁴	—	2	1	no	—
610	#41	—	2	4	no	—
611	#41	—	2	4	no	—
612	#41	—	2	4	no	—
613	#41	—	2	4	no	—
614	#41	—	2	4	no	—
615	#41	—	4	4	no	—
616	#41	—	4	4	no	—
617	#41	—	4	8	no	—
618	#41	—	4	4	no	—
619	#41	—	4	4	no	—
620	C₂×Q₈	—	2	2	no	—
621	C₂×Q₈	—	2	1	no	—
622	C₂×Q₈	—	2	4	no	—
623	C₂×Q₈	—	4	4	no	—
624	C₂×Q₈	—	4	4	no	—
625	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
626	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
627	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
628	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
629	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
630	C₂×D₄	—	2	2	no	—
631	C₂×D₄	—	2	2	no	—
632	C₂×D₄	—	2	1	no	—
633	C₂×D₄	—	2	2	no	—
634	C₂×D₄	—	2	1	no	—
635	C₂×D₄	—	2	4	no	—
636	C₂×D₄	—	2	2	no	—
637	C₂×D₄	—	2	1	no	—
638	C₂×D₄	—	2	4	no	—
639	C₂×D₄	—	2	2	no	—
640	C₂×D₄	—	2	2	no	—
641	C₂×D₄	—	2	4	no	—
642	C₂×D₄	—	4	4	no	—
643	C₂×D₄	—	4	8	no	—
644	C₂×D₄	—	4	4	no	—
645	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
646	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
647	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
648	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
649	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
650	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
651	C₂²×C₄	—	2	2	no	—
652	C₂²×C₄	—	2	1	no	—
653	C₂²×C₄	—	2	2	no	—
654	C₂²×C₄	—	2	2	no	—
655	C₂²×C₄	—	2	2	no	—
656	C₂²×C₄	—	2	1	no	—
657	C₂²×C₄	—	2	2	no	—
658	C₂²×C₄	—	2	1	no	—
659	C₂²×C₄	—	2	4	no	—
660	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
661	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
662	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
663	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
664	Q₁₆	—	4	2	no	—
665	Q₁₆	—	4	2	no	—
666	Q₁₆	—	4	4	no	—
667	SD₁₆	—	4	2	no	—
668	SD₁₆	—	4	2	no	—
669	SD₁₆	—	4	2	no	—
670	SD₁₆	—	4	2	no	—
671	SD₁₆	—	4	4	no	—
672	SD₁₆	—	4	4	no	—
673	D₈	—	4	2	no	—
674	D₈	—	4	2	no	—
675	D₈	—	4	4	no	—
676	M₁₆	—	2	4	no	—
677	C₂×C₈	—	2	4	no	—
678	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
679	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
680	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	—	2	4	no	—
683	C₄⋊C₄	—	2	4	no	—
684	C₄⋊C₄	—	2	4	no	—
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	2	4	no	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	—	2	2	no	—
689	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
690	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
691	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	—	2	2	no	—
695	C₂²⋊C₄	—	2	4	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	4	no	—
698	C₂²⋊C₄	—	2	2	no	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	2	no	—
702	C₂²⋊C₄	—	2	2	no	—
703	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
704	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
705	C₄²	—	2	4	no	—
706	C₄²	C₂×D₄×C₂₃	1	4	yes	—
707	C₄²	C₂×D₄×C₂₃	1	2	yes	—
708	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
709	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
710	C₄²	C₂⁴×C₂₃	1	2	yes	—
711	C₂³	—	2	2	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	2	1	no	—
714	C₂³	—	2	1	no	—
715	C₂³	—	4	4	no	—
716	C₂³	—	4	2	no	—
717	C₂³	—	8	2	no	—
718	C₂³	—	8	4	no	—
719	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
720	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
721	Q₈	—	2	2	no	—
722	Q₈	—	2	2	no	—
723	Q₈	—	2	2	no	—
724	Q₈	—	2	4	no	—
725	Q₈	—	2	2	no	—
726	Q₈	—	2	2	no	—
727	Q₈	—	4	4	no	—
728	Q₈	—	4	2	no	—
729	D₄	—	2	4	no	—
730	D₄	—	2	2	no	—
731	D₄	—	2	2	no	—
732	D₄	—	2	4	no	—
733	D₄	—	2	2	no	—
734	D₄	—	2	2	no	—
735	D₄	—	2	2	no	—
736	D₄	—	4	4	no	—
737	D₄	—	4	4	no	—
738	D₄	—	4	4	no	—
739	D₄	—	4	2	no	—
740	D₄	—	4	2	no	—
741	D₄	—	4	4	no	—
742	D₄	—	4	2	no	—
743	D₄	—	8	4	no	—
744	D₄	—	8	2	no	—
745	D₄	—	8	2	no	—
746	D₄	—	8	4	no	—
747	C₂×C₄	—	2	4	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	4	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	4	4	no	—
754	C₂×C₄	—	4	2	no	—
755	C₂×C₄	—	4	4	no	—
756	C₂×C₄	—	4	4	no	—
757	C₂×C₄	—	4	4	no	—
758	C₂×C₄	—	4	2	no	—
759	C₂×C₄	—	4	2	no	—
760	C₂×C₄	—	4	2	no	—
761	C₂×C₄	—	4	4	no	—
762	C₂×C₄	—	8	4	no	—
763	C₂×C₄	—	8	2	no	—
764	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
765	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
766	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
767	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
768	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
769	C₂×C₄	C₂₃×H(5,𝔽₂)	1	4	yes	—
770	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
771	C₈	—	2	2	no	—
772	C₈	—	2	2	no	—
773	C₈	—	2	4	no	—
774	C₂²	—	2	2	no	—
775	C₂²	—	2	2	no	—
776	C₂²	—	2	4	no	—
777	C₂²	—	4	1	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	4	1	no	—
780	C₂²	—	4	2	no	—
781	C₂²	—	4	2	no	—
782	C₂²	—	4	2	no	—
783	C₂²	—	4	2	no	—
784	C₂²	—	4	4	no	—
785	C₂²	—	4	2	no	—
786	C₂²	—	16	2	no	—
787	C₂²	—	16	4	no	—
788	C₂²	C₂₃×#535	1	2	yes	—
789	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
790	C₄	—	2	2	no	—
791	C₄	—	2	2	no	—
792	C₄	—	2	4	no	—
793	C₄	—	2	2	no	—
794	C₄	—	4	1	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	1	no	—
797	C₄	—	4	2	no	—
798	C₄	—	4	4	no	—
799	C₄	C₂₃×#535	1	2	yes	—
800	C₄	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
801	C₂	—	2	2	no	—
802	C₂	—	4	2	no	—
803	C₂	—	8	2	no	—
804	C₂	—	8	1	no	—
805	C₂	—	8	1	no	—
806	C₂	—	8	2	no	—
807	C₂	C₂×C₂₃×#535	1	1	yes	characteristic
808	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 ◁ C₄×#41×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3512	C₂	semidirect
2. C₂₃×#3500	C₂	semidirect
3. C₂₃×#3223	C₂	semidirect
4. C₂₃×#3222	C₂	semidirect
5. C₂₃×#3221	C₂	semidirect
6. C₂₃×#3220	C₂	semidirect
7. C₂₃×#3212	C₂	semidirect
8. C₂₃×#3211	C₂	semidirect
9. C₂₃×#3153	C₂	semidirect
10. C₂₃×#3147	C₂	semidirect
11. C₂₃×#3142	C₂	semidirect
12. C₂×C₂₃×#488	C₂	semidirect
13. C₂₃×#3046	C₂	semidirect
14. C₂₃×#3045	C₂	semidirect
15. C₂₃×#3013	C₂	semidirect
16. C₂₃×#3012	C₂	semidirect
17. C₂₃×#2922	C₂	semidirect
20. C₂×C₂₃×#137	C₂²	semidirect
23. C₂×C₂₃×#135	C₂²	semidirect
30. C₂₃×#541	C₂²	semidirect
31. C₂₃×#540	C₂²	semidirect
39. C₂₃×#532	C₂²	semidirect
40. C₂₃×#529	C₂²	semidirect
41. C₂×C₂₃×#125	C₂²	semidirect
44. C₂₃×#520	C₂²	semidirect
46. C₂₃×#497	C₂²	semidirect
47. C₂₃×#496	C₂²	semidirect
48. C₂₃×#495	C₂²	semidirect
49. C₂₃×#495	C₂²	semidirect
50. C₂₃×#495	C₂²	semidirect
51. C₂₃×#494	C₂²	semidirect
52. C₂₃×#493	C₂²	semidirect
53. C₂₃×#492	C₂²	semidirect
54. C₂₃×#492	C₂²	semidirect
55. C₂₃×#491	C₂²	semidirect
56. C₂₃×#490	C₂²	semidirect
57. C₂₃×#488	C₂²	semidirect
58. C₂₃×#488	C₂²	semidirect
59. C₂₃×#488	C₂²	semidirect
60. C₂₃×#488	C₂²	semidirect
61. C₂₃×#488	C₂²	semidirect
62. C₂₃×#464	C₂²	semidirect
63. C₂₃×#464	C₂²	semidirect
64. C₂₃×#463	C₂²	semidirect
65. C₂₃×#463	C₂²	semidirect
66. C₂₃×#462	C₂²	semidirect
67. C₂₃×#461	C₂²	semidirect
68. C₂₃×#460	C₂²	semidirect
69. C₂₃×#459	C₂²	semidirect
71. C₂₃×#452	C₂²	semidirect
72. C₂₃×#451	C₂²	semidirect
75. C₂₃×#449	C₂²	semidirect
76. C₂₃×#448	C₂²	semidirect
78. C₂₃×#433	C₂²	semidirect
79. C₂₃×#433	C₂²	semidirect
80. C₂₃×#431	C₂²	semidirect
81. C₂₃×#424	C₂²	semidirect
83. C₂₃×#417	C₂²	semidirect
84. C₂×C₂₃×#103	C₂²	semidirect
87. C₄×M₁₆×C₂₃	C₂²	semidirect
88. C₂×C₄×C₈×C₂₃	C₂²	semidirect
306. #60823	C₂₃	direct (N × H)
370. #3512	C₂×C₂₃	semidirect
371. #3500	C₂×C₂₃	semidirect
372. #3223	C₂×C₂₃	semidirect
373. #3222	C₂×C₂₃	semidirect
374. #3221	C₂×C₂₃	semidirect
375. #3220	C₂×C₂₃	semidirect
376. #3212	C₂×C₂₃	semidirect
377. #3211	C₂×C₂₃	semidirect
378. #3153	C₂×C₂₃	semidirect
379. #3147	C₂×C₂₃	semidirect
380. #3142	C₂×C₂₃	semidirect
381. C₂×#488	C₂×C₂₃	semidirect
382. #3046	C₂×C₂₃	semidirect
383. #3045	C₂×C₂₃	semidirect
384. #3013	C₂×C₂₃	semidirect
385. #3012	C₂×C₂₃	semidirect
386. #2922	C₂×C₂₃	semidirect
416. C₂×#137	C₂²×C₂₃	semidirect
419. C₂×#135	C₂²×C₂₃	semidirect
426. #541	C₂²×C₂₃	semidirect
427. #540	C₂²×C₂₃	semidirect
435. #532	C₂²×C₂₃	semidirect
436. #529	C₂²×C₂₃	semidirect
437. C₂×#125	C₂²×C₂₃	semidirect
440. #520	C₂²×C₂₃	semidirect
442. #497	C₂²×C₂₃	semidirect
443. #496	C₂²×C₂₃	semidirect
444. #495	C₂²×C₂₃	semidirect
445. #495	C₂²×C₂₃	semidirect
446. #495	C₂²×C₂₃	semidirect
447. #494	C₂²×C₂₃	semidirect
448. #493	C₂²×C₂₃	semidirect
449. #492	C₂²×C₂₃	semidirect
450. #492	C₂²×C₂₃	semidirect
451. #491	C₂²×C₂₃	semidirect
452. #490	C₂²×C₂₃	semidirect
453. #488	C₂²×C₂₃	semidirect
454. #488	C₂²×C₂₃	semidirect
455. #488	C₂²×C₂₃	semidirect
456. #488	C₂²×C₂₃	semidirect
457. #488	C₂²×C₂₃	semidirect
458. #464	C₂²×C₂₃	semidirect
459. #464	C₂²×C₂₃	semidirect
460. #463	C₂²×C₂₃	semidirect
461. #463	C₂²×C₂₃	semidirect
462. #462	C₂²×C₂₃	semidirect
463. #461	C₂²×C₂₃	semidirect
464. #460	C₂²×C₂₃	semidirect
465. #459	C₂²×C₂₃	semidirect
467. #452	C₂²×C₂₃	semidirect
468. #451	C₂²×C₂₃	semidirect
471. #449	C₂²×C₂₃	semidirect
472. #448	C₂²×C₂₃	semidirect
474. #433	C₂²×C₂₃	semidirect
475. #433	C₂²×C₂₃	semidirect
476. #431	C₂²×C₂₃	semidirect
477. #424	C₂²×C₂₃	semidirect
479. #417	C₂²×C₂₃	semidirect
480. C₂×#103	C₂²×C₂₃	semidirect
483. C₄×M₁₆	C₂²×C₂₃	semidirect
484. C₂×C₄×C₈	C₂²×C₂₃	semidirect
607. C₂₃	#60823	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×#3512	2
C₂₃×#3500	2
C₂₃×#3223	2
C₂₃×#3222	2
C₂₃×#3221	2
C₂₃×#3220	2
C₂₃×#3212	2
C₂₃×#3211	2
C₂₃×#3153	2
C₂₃×#3147	2
C₂₃×#3142	2
C₂×C₂₃×#488	2
C₂₃×#3046	2
C₂₃×#3045	2
C₂₃×#3013	2
C₂₃×#3012	2
C₂₃×#2922	2
#60823	23

Subgroups — C23×#60823 #19208449

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60823 #19208449