Subgroups — C₂₃×#60239 #19207865

Order 5888.

2186 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#41×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2981	C₂	1	2	yes	maximal, complemented
3	C₂₃×#2979	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2977	C₂	1	4	yes	maximal, complemented
5	C₂₃×#2976	C₂	1	4	yes	maximal, complemented
6	C₂₃×#2974	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2972	C₂	1	2	yes	maximal, complemented
8	C₂₃×#2935	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×M₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2933	C₂	1	2	yes	maximal, complemented
11	C₂₃×#2931	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#2929	C₂	1	2	yes	maximal, complemented
13	C₂×C₈×D₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#2925	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2922	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#2880	C₂	1	2	yes	maximal, complemented
17	C₂×C₂₃×#408	C₂	1	2	yes	maximal, complemented
18	C₂²×#41×C₂₃	C₂²	1	2	yes	—
19	C₂×C₂₃×#131	C₂²	1	2	yes	complemented
20	C₂×C₂₃×#131	C₂²	1	2	yes	complemented
21	C₂²×M₁₆×C₂₃	C₂²	1	2	yes	complemented
22	C₂³×C₈×C₂₃	C₂²	1	2	yes	complemented
23	C₂₃×#550	C₄	1	1	yes	characteristic
24	D₄×Q₈×C₂₃	C₄	1	1	yes	characteristic
25	C₂₃×#548	C₄	1	2	yes	—
26	C₂₃×#547	C₄	1	2	yes	—
27	C₂₃×#547	C₄	1	1	yes	characteristic
28	C₂₃×#546	C₄	1	4	yes	—
29	C₂₃×#546	C₄	1	2	yes	—
30	D₄²×C₂₃	C₄	1	1	yes	characteristic
31	D₄²×C₂₃	C₄	1	2	yes	—
32	C₂₃×#532	C₂²	1	1	yes	characteristic
33	C₂₃×#532	C₂²	1	2	yes	—
34	C₂₃×#525	C₂²	1	2	yes	—
35	C₂₃×#525	C₂²	1	4	yes	—
36	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
39	C₂₃×#436	C₂²	1	2	yes	complemented
40	C₂₃×#436	C₂²	1	2	yes	complemented
41	C₂₃×#436	C₂²	1	4	yes	complemented
42	C₂₃×#436	C₂²	1	2	yes	complemented
43	C₂₃×#436	C₂²	1	2	yes	complemented
44	C₂₃×#435	C₂²	1	4	yes	complemented
45	C₂₃×#435	C₂²	1	4	yes	complemented
46	C₂₃×#435	C₂²	1	4	yes	complemented
47	C₂₃×#435	C₂²	1	4	yes	complemented
48	C₂₃×#435	C₂²	1	4	yes	complemented
49	C₂₃×#435	C₂²	1	4	yes	complemented
50	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
51	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
52	C₈×D₄×C₂₃	C₂²	1	2	yes	—
53	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
54	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
55	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
56	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
57	C₈×D₄×C₂₃	C₂²	1	4	yes	complemented
58	C₈×D₄×C₂₃	C₂²	1	4	yes	complemented
59	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
60	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
61	C₈×D₄×C₂₃	C₂²	1	4	yes	complemented
62	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
63	C₂₃×#433	C₂²	1	2	yes	complemented
64	C₂₃×#433	C₂²	1	2	yes	complemented
65	C₂₃×#433	C₂²	1	4	yes	complemented
66	C₂₃×#432	C₂²	1	2	yes	complemented
67	C₂₃×#431	C₂²	1	2	yes	complemented
68	C₂₃×#431	C₂²	1	2	yes	complemented
69	C₂₃×#431	C₂²	1	2	yes	complemented
70	C₂₃×#424	C₂²	1	1	yes	characteristic, complemented
71	C₂₃×#424	C₂²	1	1	yes	characteristic, complemented
72	C₂₃×#423	C₂²	1	1	yes	characteristic, complemented
73	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
74	C₂₃×#408	C₂²	1	1	yes	characteristic
75	C₂₃×#408	C₂²	1	1	yes	characteristic
76	C₂₃×#408	C₂²	1	2	yes	—
77	C₂₃×#408	C₂²	1	2	yes	complemented
78	C₂₃×#408	C₂²	1	2	yes	complemented
79	C₂₃×#408	C₂²	1	4	yes	complemented
80	C₂₃×#408	C₂²	1	4	yes	complemented
81	C₂₃×#408	C₂²	1	4	yes	complemented
82	C₂₃×#408	C₂²	1	4	yes	complemented
83	C₂₃×#407	C₂²	1	2	yes	complemented
84	C₂₃×#407	C₂²	1	4	yes	complemented
85	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
86	C₂×C₂₃×C₂²⋊C₈	C₂²	1	4	yes	complemented
87	C₂×C₂₃×C₂²⋊C₈	C₂²	1	4	yes	complemented
88	C₂×C₂₃×C₂²⋊C₈	C₂²	1	4	yes	complemented
89	C₂₃×#405	C₂²	1	2	yes	complemented
90	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
91	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
92	C₂×#41×C₂₃	—	4	4	no	—
93	C₂×#41×C₂₃	—	4	4	no	—
94	C₂×#41×C₂₃	C₂×C₄	1	4	yes	—
95	C₂×#41×C₂₃	C₂×C₄	1	2	yes	—
96	C₂×#41×C₂₃	C₂×C₄	1	2	yes	—
97	C₂×#41×C₂₃	C₂³	1	2	yes	—
98	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
99	C₂×#41×C₂₃	C₂³	1	4	yes	—
100	C₂²×Q₈×C₂₃	C₂×C₄	1	2	yes	—
101	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
102	C₂²×D₄×C₂₃	C₂×C₄	1	2	yes	—
103	C₂²×D₄×C₂₃	C₂×C₄	1	2	yes	—
104	C₂²×D₄×C₂₃	C₂×C₄	1	4	yes	—
105	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
106	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
107	C₂₃×#131	—	4	4	no	—
108	C₂₃×#131	—	4	4	no	—
109	C₂×M₁₆×C₂₃	—	4	4	no	—
110	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
111	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
112	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
113	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
114	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
115	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
116	C₂²×C₈×C₂₃	—	4	4	no	—
117	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
118	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
119	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
121	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
122	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
123	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
124	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
125	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
126	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
127	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
128	C₂₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
129	C₂₃×#127	C₂×C₄	1	1	yes	characteristic
130	C₂₃×#127	C₂×C₄	1	2	yes	—
131	C₂₃×#124	C₂×C₄	1	2	yes	—
132	C₂₃×#124	C₂×C₄	1	4	yes	—
133	C₂₃×#123	C₂×C₄	1	4	yes	—
134	C₂₃×#123	C₂×C₄	1	4	yes	—
135	C₂₃×#123	C₂×C₄	1	4	yes	—
136	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
137	C₂₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
138	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
139	C₂₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
140	C₂₃×#121	C₂×C₄	1	2	yes	—
141	C₂₃×#121	C₂×C₄	1	2	yes	—
142	C₂₃×#121	C₂×C₄	1	2	yes	—
143	C₂₃×#121	C₂×C₄	1	2	yes	—
144	C₂₃×#121	C₂×C₄	1	4	yes	—
145	C₂₃×#121	C₂×C₄	1	2	yes	—
146	C₂₃×#121	C₂×C₄	1	4	yes	—
147	C₂₃×#121	C₂×C₄	1	2	yes	—
148	C₂₃×#121	C₂×C₄	1	4	yes	—
149	C₂₃×#120	C₂×C₄	1	4	yes	—
150	C₂₃×#120	C₂×C₄	1	4	yes	—
151	C₂₃×#120	C₂×C₄	1	4	yes	—
152	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
153	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
154	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
155	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
156	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
157	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
158	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
159	C₄×D₄×C₂₃	C₂×C₄	1	4	yes	—
160	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
161	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
162	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
163	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
164	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
165	C₄×D₄×C₂₃	C₂³	1	2	yes	—
166	C₄×D₄×C₂₃	C₂³	1	4	yes	—
167	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
168	C₄×D₄×C₂₃	C₂³	1	2	yes	—
169	C₄×D₄×C₂₃	C₂³	1	4	yes	—
170	C₄×D₄×C₂₃	C₂³	1	2	yes	—
171	C₂₃×#117	C₂³	1	1	yes	characteristic
172	C₂₃×#117	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
175	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
176	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	4	yes	—
177	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
179	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
180	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
181	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
182	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
183	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
184	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
185	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
186	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
187	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
188	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
189	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
190	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
191	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
192	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
193	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
194	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
195	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
196	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
197	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
198	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
199	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
200	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
201	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
202	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
203	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
204	C₂₃×#97	C₂³	1	2	yes	—
205	C₂₃×#97	C₂³	1	4	yes	—
206	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
207	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
208	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
209	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
210	C₄×C₈×C₂₃	C₂³	1	2	yes	—
211	C₄×C₈×C₂₃	C₂³	1	4	yes	—
212	C₂⁴×C₂₃	C₂²×C₄	1	2	yes	—
213	C₂⁴×C₂₃	C₂²×C₄	1	4	yes	—
214	#41×C₂₃	—	2	4	no	—
215	#41×C₂₃	—	2	4	no	—
216	#41×C₂₃	—	2	2	no	—
217	#41×C₂₃	—	2	2	no	—
218	#41×C₂₃	—	4	4	no	—
219	#41×C₂₃	—	4	4	no	—
220	#41×C₂₃	—	4	8	no	—
221	#41×C₂₃	—	4	4	no	—
222	#41×C₂₃	—	4	4	no	—
223	C₂×Q₈×C₂₃	—	4	4	no	—
224	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
225	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
226	C₂×Q₈×C₂₃	C₂²×C₄	1	4	yes	—
227	C₂×D₄×C₂₃	—	2	4	no	—
228	C₂×D₄×C₂₃	—	2	8	no	—
229	C₂×D₄×C₂₃	—	4	4	no	—
230	C₂×D₄×C₂₃	—	4	8	no	—
231	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
232	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
233	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
234	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
235	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
236	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
237	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
238	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
239	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
240	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
241	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
242	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
243	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
244	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
245	C₂²×C₄×C₂₃	—	2	4	no	—
246	C₂²×C₄×C₂₃	—	2	4	no	—
247	C₂²×C₄×C₂₃	—	4	4	no	—
248	C₂²×C₄×C₂₃	—	4	4	no	—
249	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
250	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
251	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
252	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
253	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
254	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
255	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
256	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
257	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
258	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
259	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
263	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
264	M₁₆×C₂₃	—	2	2	no	—
265	M₁₆×C₂₃	—	2	4	no	—
266	M₁₆×C₂₃	—	2	2	no	—
267	M₁₆×C₂₃	—	4	4	no	—
268	M₁₆×C₂₃	—	4	4	no	—
269	M₁₆×C₂₃	—	4	4	no	—
270	C₂×C₈×C₂₃	—	2	2	no	—
271	C₂×C₈×C₂₃	—	2	4	no	—
272	C₂×C₈×C₂₃	—	2	2	no	—
273	C₂×C₈×C₂₃	—	4	2	no	—
274	C₂×C₈×C₂₃	—	4	2	no	—
275	C₂×C₈×C₂₃	—	4	2	no	—
276	C₂×C₈×C₂₃	—	4	2	no	—
277	C₂×C₈×C₂₃	—	4	4	no	—
278	C₂×C₈×C₂₃	—	4	4	no	—
279	C₂×C₈×C₂₃	—	4	4	no	—
280	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
281	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
282	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
283	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
284	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
285	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
286	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
287	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
288	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
289	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
290	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
291	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
292	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
293	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
294	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
295	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
296	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
297	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
298	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
299	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
300	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
301	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
302	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
303	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
304	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
305	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
306	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
307	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
308	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
309	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
310	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
311	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
312	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
313	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
314	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
315	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
316	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
317	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
318	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
319	C₄²×C₂₃	C₂⁴	1	2	yes	—
320	#60239	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
321	C₂³×C₂₃	—	2	4	no	—
322	C₂³×C₂₃	—	2	4	no	—
323	C₂³×C₂₃	—	2	8	no	—
324	C₂³×C₂₃	—	4	2	no	—
325	C₂³×C₂₃	—	4	4	no	—
326	C₂³×C₂₃	—	4	4	no	—
327	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
328	C₂³×C₂₃	C₂³×C₄	1	4	yes	—
329	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
330	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
331	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
332	Q₈×C₂₃	—	2	2	no	—
333	Q₈×C₂₃	—	2	4	no	—
334	Q₈×C₂₃	—	4	4	no	—
335	D₄×C₂₃	—	2	4	no	—
336	D₄×C₂₃	—	2	8	no	—
337	D₄×C₂₃	—	2	4	no	—
338	D₄×C₂₃	—	2	8	no	—
339	D₄×C₂₃	—	2	2	no	—
340	D₄×C₂₃	—	2	4	no	—
341	D₄×C₂₃	—	2	2	no	—
342	D₄×C₂₃	—	2	4	no	—
343	D₄×C₂₃	—	4	4	no	—
344	D₄×C₂₃	—	4	4	no	—
345	D₄×C₂₃	—	4	4	no	—
346	D₄×C₂₃	—	4	4	no	—
347	D₄×C₂₃	—	4	2	no	—
348	D₄×C₂₃	#131	1	4	yes	complemented
349	C₂×C₄×C₂₃	—	2	4	no	—
350	C₂×C₄×C₂₃	—	2	4	no	—
351	C₂×C₄×C₂₃	—	2	4	no	—
352	C₂×C₄×C₂₃	—	2	2	no	—
353	C₂×C₄×C₂₃	—	2	4	no	—
354	C₂×C₄×C₂₃	—	2	2	no	—
355	C₂×C₄×C₂₃	—	2	2	no	—
356	C₂×C₄×C₂₃	—	2	2	no	—
357	C₂×C₄×C₂₃	—	2	4	no	—
358	C₂×C₄×C₂₃	—	2	4	no	—
359	C₂×C₄×C₂₃	—	2	2	no	—
360	C₂×C₄×C₂₃	—	2	2	no	—
361	C₂×C₄×C₂₃	—	2	2	no	—
362	C₂×C₄×C₂₃	—	4	4	no	—
363	C₂×C₄×C₂₃	—	4	4	no	—
364	C₂×C₄×C₂₃	—	4	4	no	—
365	C₂×C₄×C₂₃	—	4	1	no	—
366	C₂×C₄×C₂₃	—	4	2	no	—
367	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
368	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
369	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
370	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
371	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
372	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
373	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
374	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
375	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
376	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
377	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
378	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
379	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
380	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
381	C₈×C₂₃	—	2	1	no	—
382	C₈×C₂₃	—	2	1	no	—
383	C₈×C₂₃	—	2	2	no	—
384	C₈×C₂₃	—	2	1	no	—
385	C₈×C₂₃	—	2	2	no	—
386	C₈×C₂₃	—	2	1	no	—
387	C₈×C₂₃	—	2	2	no	—
388	C₈×C₂₃	—	2	4	no	—
389	C₈×C₂₃	—	2	2	no	—
390	D₄×#41	C₂×C₂₃	1	1	yes	characteristic
391	#2981	C₂×C₂₃	1	2	yes	complemented
392	#2979	C₂×C₂₃	1	2	yes	complemented
393	#2977	C₂×C₂₃	1	4	yes	complemented
394	#2976	C₂×C₂₃	1	4	yes	complemented
395	#2974	C₂×C₂₃	1	2	yes	complemented
396	#2972	C₂×C₂₃	1	2	yes	complemented
397	#2935	C₂×C₂₃	1	1	yes	characteristic, complemented
398	D₄×M₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
399	#2933	C₂×C₂₃	1	2	yes	complemented
400	#2931	C₂×C₂₃	1	1	yes	characteristic, complemented
401	#2929	C₂×C₂₃	1	2	yes	complemented
402	C₂×C₈×D₄	C₂×C₂₃	1	1	yes	characteristic, complemented
403	#2925	C₂×C₂₃	1	1	yes	characteristic, complemented
404	#2922	C₂×C₂₃	1	1	yes	characteristic, complemented
405	#2880	C₂×C₂₃	1	2	yes	complemented
406	C₂×#408	C₂×C₂₃	1	2	yes	complemented
407	C₂²×C₂₃	—	2	2	no	—
408	C₂²×C₂₃	—	2	1	no	—
409	C₂²×C₂₃	—	2	1	no	—
410	C₂²×C₂₃	—	2	2	no	—
411	C₂²×C₂₃	—	2	2	no	—
412	C₂²×C₂₃	—	2	2	no	—
413	C₂²×C₂₃	—	2	4	no	—
414	C₂²×C₂₃	—	2	2	no	—
415	C₂²×C₂₃	—	2	2	no	—
416	C₂²×C₂₃	—	2	4	no	—
417	C₂²×C₂₃	—	2	2	no	—
418	C₂²×C₂₃	—	2	2	no	—
419	C₂²×C₂₃	—	2	4	no	—
420	C₂²×C₂₃	—	4	8	no	—
421	C₂²×C₂₃	—	8	8	no	—
422	C₂²×C₂₃	#518	1	2	yes	—
423	C₂²×C₂₃	C₂×#131	1	4	yes	—
424	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
425	C₄×C₂₃	—	2	2	no	—
426	C₄×C₂₃	—	2	2	no	—
427	C₄×C₂₃	—	2	2	no	—
428	C₄×C₂₃	—	2	4	no	—
429	C₄×C₂₃	—	2	1	no	—
430	C₄×C₂₃	—	2	2	no	—
431	C₄×C₂₃	—	2	1	no	—
432	C₄×C₂₃	—	2	1	no	—
433	C₄×C₂₃	—	2	2	no	—
434	C₄×C₂₃	#518	1	2	yes	—
435	C₄×C₂₃	C₂×#131	1	2	yes	—
436	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
437	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
438	C₂²×#41	C₂²×C₂₃	1	2	yes	—
439	C₂×#131	C₂²×C₂₃	1	2	yes	complemented
440	C₂×#131	C₂²×C₂₃	1	2	yes	complemented
441	C₂²×M₁₆	C₂²×C₂₃	1	2	yes	complemented
442	C₂³×C₈	C₂²×C₂₃	1	2	yes	complemented
443	#550	C₄×C₂₃	1	1	yes	characteristic
444	D₄×Q₈	C₄×C₂₃	1	1	yes	characteristic
445	#548	C₄×C₂₃	1	2	yes	—
446	#547	C₄×C₂₃	1	2	yes	—
447	#547	C₄×C₂₃	1	1	yes	characteristic
448	#546	C₄×C₂₃	1	4	yes	—
449	#546	C₄×C₂₃	1	2	yes	—
450	D₄²	C₄×C₂₃	1	1	yes	characteristic
451	D₄²	C₄×C₂₃	1	2	yes	—
452	#532	C₂²×C₂₃	1	1	yes	characteristic
453	#532	C₂²×C₂₃	1	2	yes	—
454	#525	C₂²×C₂₃	1	2	yes	—
455	#525	C₂²×C₂₃	1	4	yes	—
456	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
457	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
458	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
459	#436	C₂²×C₂₃	1	2	yes	complemented
460	#436	C₂²×C₂₃	1	2	yes	complemented
461	#436	C₂²×C₂₃	1	4	yes	complemented
462	#436	C₂²×C₂₃	1	2	yes	complemented
463	#436	C₂²×C₂₃	1	2	yes	complemented
464	#435	C₂²×C₂₃	1	4	yes	complemented
465	#435	C₂²×C₂₃	1	4	yes	complemented
466	#435	C₂²×C₂₃	1	4	yes	complemented
467	#435	C₂²×C₂₃	1	4	yes	complemented
468	#435	C₂²×C₂₃	1	4	yes	complemented
469	#435	C₂²×C₂₃	1	4	yes	complemented
470	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
471	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
472	C₈×D₄	C₂²×C₂₃	1	2	yes	—
473	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
474	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
475	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
476	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
477	C₈×D₄	C₂²×C₂₃	1	4	yes	complemented
478	C₈×D₄	C₂²×C₂₃	1	4	yes	complemented
479	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
480	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
481	C₈×D₄	C₂²×C₂₃	1	4	yes	complemented
482	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
483	#433	C₂²×C₂₃	1	2	yes	complemented
484	#433	C₂²×C₂₃	1	2	yes	complemented
485	#433	C₂²×C₂₃	1	4	yes	complemented
486	#432	C₂²×C₂₃	1	2	yes	complemented
487	#431	C₂²×C₂₃	1	2	yes	complemented
488	#431	C₂²×C₂₃	1	2	yes	complemented
489	#431	C₂²×C₂₃	1	2	yes	complemented
490	#424	C₂²×C₂₃	1	1	yes	characteristic, complemented
491	#424	C₂²×C₂₃	1	1	yes	characteristic, complemented
492	#423	C₂²×C₂₃	1	1	yes	characteristic, complemented
493	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
494	#408	C₂²×C₂₃	1	1	yes	characteristic
495	#408	C₂²×C₂₃	1	2	yes	—
496	#408	C₂²×C₂₃	1	1	yes	characteristic
497	#408	C₂²×C₂₃	1	2	yes	complemented
498	#408	C₂²×C₂₃	1	2	yes	complemented
499	#408	C₂²×C₂₃	1	4	yes	complemented
500	#408	C₂²×C₂₃	1	4	yes	complemented
501	#408	C₂²×C₂₃	1	4	yes	complemented
502	#408	C₂²×C₂₃	1	4	yes	complemented
503	#407	C₂²×C₂₃	1	2	yes	complemented
504	#407	C₂²×C₂₃	1	4	yes	complemented
505	C₂×C₂²⋊C₈	C₂²×C₂₃	1	4	yes	complemented
506	C₂×C₂²⋊C₈	C₂²×C₂₃	1	4	yes	complemented
507	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	complemented
508	C₂×C₂²⋊C₈	C₂²×C₂₃	1	4	yes	complemented
509	#405	C₂²×C₂₃	1	2	yes	complemented
510	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
511	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
512	C₂×C₂₃	—	2	2	no	—
513	C₂×C₂₃	—	2	4	no	—
514	C₂×C₂₃	—	4	2	no	—
515	C₂×C₂₃	—	4	4	no	—
516	C₂×C₂₃	—	4	2	no	—
517	C₂×C₂₃	C₂×#518	1	1	yes	characteristic
518	C₂×C₂₃	C₂²×#131	1	1	yes	characteristic
519	C₂×C₂₃	#3573	1	1	yes	characteristic
520	C₂×#41	—	4	4	no	—
521	C₂×#41	—	4	4	no	—
522	C₂×#41	C₂×C₄×C₂₃	1	4	yes	—
523	C₂×#41	C₂×C₄×C₂₃	1	2	yes	—
524	C₂×#41	C₂×C₄×C₂₃	1	2	yes	—
525	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
526	C₂×#41	C₂³×C₂₃	1	2	yes	—
527	C₂×#41	C₂³×C₂₃	1	4	yes	—
528	C₂²×Q₈	C₂×C₄×C₂₃	1	2	yes	—
529	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
530	C₂²×D₄	C₂×C₄×C₂₃	1	2	yes	—
531	C₂²×D₄	C₂×C₄×C₂₃	1	2	yes	—
532	C₂²×D₄	C₂×C₄×C₂₃	1	4	yes	—
533	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
534	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
535	#131	—	4	4	no	—
536	#131	—	4	4	no	—
537	C₂×M₁₆	—	4	4	no	—
538	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
539	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
540	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
541	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
542	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
543	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
544	C₂²×C₈	—	4	4	no	—
545	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
546	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
547	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
548	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
549	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
550	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
551	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
552	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
553	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
554	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
555	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
556	C₄⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
557	#127	C₂×C₄×C₂₃	1	1	yes	characteristic
558	#127	C₂×C₄×C₂₃	1	2	yes	—
559	#124	C₂×C₄×C₂₃	1	2	yes	—
560	#124	C₂×C₄×C₂₃	1	4	yes	—
561	#123	C₂×C₄×C₂₃	1	4	yes	—
562	#123	C₂×C₄×C₂₃	1	4	yes	—
563	#123	C₂×C₄×C₂₃	1	4	yes	—
564	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
565	C₂²⋊Q₈	C₂×C₄×C₂₃	1	4	yes	—
566	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
567	C₂²⋊Q₈	C₂×C₄×C₂₃	1	4	yes	—
568	#121	C₂×C₄×C₂₃	1	2	yes	—
569	#121	C₂×C₄×C₂₃	1	4	yes	—
570	#121	C₂×C₄×C₂₃	1	2	yes	—
571	#121	C₂×C₄×C₂₃	1	4	yes	—
572	#121	C₂×C₄×C₂₃	1	2	yes	—
573	#121	C₂×C₄×C₂₃	1	2	yes	—
574	#121	C₂×C₄×C₂₃	1	2	yes	—
575	#121	C₂×C₄×C₂₃	1	2	yes	—
576	#121	C₂×C₄×C₂₃	1	4	yes	—
577	#120	C₂×C₄×C₂₃	1	4	yes	—
578	#120	C₂×C₄×C₂₃	1	4	yes	—
579	#120	C₂×C₄×C₂₃	1	4	yes	—
580	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
581	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
582	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
583	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
584	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
585	C₄×D₄	C₂×C₄×C₂₃	1	4	yes	—
586	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
587	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
588	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
589	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
590	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
591	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
592	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
593	C₄×D₄	C₂³×C₂₃	1	2	yes	—
594	C₄×D₄	C₂³×C₂₃	1	4	yes	—
595	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
596	C₄×D₄	C₂³×C₂₃	1	2	yes	—
597	C₄×D₄	C₂³×C₂₃	1	4	yes	—
598	C₄×D₄	C₂³×C₂₃	1	2	yes	—
599	#117	C₂³×C₂₃	1	1	yes	characteristic
600	#117	C₂³×C₂₃	1	2	yes	—
601	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
603	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	4	yes	—
605	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
606	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
607	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
608	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
609	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
610	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
611	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
612	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
613	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
614	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
615	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
616	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
617	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
618	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
619	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
620	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
621	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
622	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
623	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
624	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
625	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
626	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
627	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
628	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
629	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
630	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
631	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
632	#97	C₂³×C₂₃	1	2	yes	—
633	#97	C₂³×C₂₃	1	4	yes	—
634	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
635	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
636	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
637	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
638	C₄×C₈	C₂³×C₂₃	1	2	yes	—
639	C₄×C₈	C₂³×C₂₃	1	4	yes	—
640	C₂₃	#60239	1	1	yes	characteristic, direct product factor, Sylow
641	C₂⁴	C₂²×C₄×C₂₃	1	2	yes	—
642	C₂⁴	C₂²×C₄×C₂₃	1	4	yes	—
643	#41	—	2	4	no	—
644	#41	—	2	4	no	—
645	#41	—	2	2	no	—
646	#41	—	2	2	no	—
647	#41	—	4	4	no	—
648	#41	—	4	4	no	—
649	#41	—	4	8	no	—
650	#41	—	4	4	no	—
651	#41	—	4	4	no	—
652	C₂×Q₈	—	4	4	no	—
653	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
654	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
655	C₂×Q₈	C₂²×C₄×C₂₃	1	4	yes	—
656	C₂×D₄	—	2	4	no	—
657	C₂×D₄	—	2	8	no	—
658	C₂×D₄	—	4	4	no	—
659	C₂×D₄	—	4	8	no	—
660	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
661	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
662	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
663	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
664	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
665	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
666	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
667	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
668	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
669	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
670	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
671	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
672	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
673	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
674	C₂²×C₄	—	2	4	no	—
675	C₂²×C₄	—	2	4	no	—
676	C₂²×C₄	—	4	4	no	—
677	C₂²×C₄	—	4	4	no	—
678	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
679	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
680	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
681	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
682	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
683	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
684	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
685	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
686	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
687	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
688	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
689	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
690	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
691	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
692	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
693	M₁₆	—	2	2	no	—
694	M₁₆	—	2	4	no	—
695	M₁₆	—	2	2	no	—
696	M₁₆	—	4	4	no	—
697	M₁₆	—	4	4	no	—
698	M₁₆	—	4	4	no	—
699	C₂×C₈	—	2	2	no	—
700	C₂×C₈	—	2	4	no	—
701	C₂×C₈	—	2	2	no	—
702	C₂×C₈	—	4	2	no	—
703	C₂×C₈	—	4	2	no	—
704	C₂×C₈	—	4	2	no	—
705	C₂×C₈	—	4	2	no	—
706	C₂×C₈	—	4	4	no	—
707	C₂×C₈	—	4	4	no	—
708	C₂×C₈	—	4	4	no	—
709	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
710	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
711	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
712	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
713	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
714	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
715	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
716	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
717	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
718	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
719	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
720	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
721	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
722	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
723	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
724	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
725	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
726	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
727	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
728	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
729	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
730	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
731	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
732	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
733	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
734	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
735	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
736	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
737	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
738	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
739	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
740	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
741	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
742	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
743	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
744	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
745	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
746	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
747	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
748	C₄²	C₂⁴×C₂₃	1	2	yes	—
749	C₂³	—	2	4	no	—
750	C₂³	—	2	4	no	—
751	C₂³	—	2	8	no	—
752	C₂³	—	4	2	no	—
753	C₂³	—	4	4	no	—
754	C₂³	—	4	4	no	—
755	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
756	C₂³	C₂³×C₄×C₂₃	1	4	yes	—
757	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
758	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
759	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
760	Q₈	—	2	2	no	—
761	Q₈	—	2	4	no	—
762	Q₈	—	4	4	no	—
763	D₄	—	2	4	no	—
764	D₄	—	2	8	no	—
765	D₄	—	2	4	no	—
766	D₄	—	2	8	no	—
767	D₄	—	2	2	no	—
768	D₄	—	2	4	no	—
769	D₄	—	2	2	no	—
770	D₄	—	2	4	no	—
771	D₄	—	4	4	no	—
772	D₄	—	4	4	no	—
773	D₄	—	4	4	no	—
774	D₄	—	4	4	no	—
775	D₄	—	4	2	no	—
776	D₄	C₂₃×#131	1	4	yes	complemented
777	C₂×C₄	—	2	4	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	4	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	4	no	—
784	C₂×C₄	—	2	4	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	4	no	—
789	C₂×C₄	—	2	4	no	—
790	C₂×C₄	—	4	4	no	—
791	C₂×C₄	—	4	4	no	—
792	C₂×C₄	—	4	4	no	—
793	C₂×C₄	—	4	1	no	—
794	C₂×C₄	—	4	2	no	—
795	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
796	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
797	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
798	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
799	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
800	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
801	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
802	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
803	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
804	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
805	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
806	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
807	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
808	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
809	C₈	—	2	1	no	—
810	C₈	—	2	1	no	—
811	C₈	—	2	2	no	—
812	C₈	—	2	1	no	—
813	C₈	—	2	2	no	—
814	C₈	—	2	1	no	—
815	C₈	—	2	2	no	—
816	C₈	—	2	4	no	—
817	C₈	—	2	2	no	—
818	C₂²	—	2	2	no	—
819	C₂²	—	2	1	no	—
820	C₂²	—	2	1	no	—
821	C₂²	—	2	2	no	—
822	C₂²	—	2	2	no	—
823	C₂²	—	2	2	no	—
824	C₂²	—	2	4	no	—
825	C₂²	—	2	2	no	—
826	C₂²	—	2	2	no	—
827	C₂²	—	2	4	no	—
828	C₂²	—	2	2	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	2	4	no	—
831	C₂²	—	4	8	no	—
832	C₂²	—	8	8	no	—
833	C₂²	C₂₃×#518	1	2	yes	—
834	C₂²	C₂×C₂₃×#131	1	4	yes	—
835	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
836	C₄	—	2	2	no	—
837	C₄	—	2	2	no	—
838	C₄	—	2	2	no	—
839	C₄	—	2	4	no	—
840	C₄	—	2	1	no	—
841	C₄	—	2	2	no	—
842	C₄	—	2	1	no	—
843	C₄	—	2	1	no	—
844	C₄	—	2	2	no	—
845	C₄	C₂₃×#518	1	2	yes	—
846	C₄	C₂×C₂₃×#131	1	2	yes	—
847	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
848	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
849	C₂	—	2	2	no	—
850	C₂	—	2	4	no	—
851	C₂	—	4	2	no	—
852	C₂	—	4	2	no	—
853	C₂	—	4	4	no	—
854	C₂	C₂×C₂₃×#518	1	1	yes	characteristic
855	C₂	C₂²×C₂₃×#131	1	1	yes	characteristic
856	C₂	C₂₃×#3573	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₂₃
Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
socle	C₂²×C₂₃	C₂⁴×C₄
prime radical	D₄×#41×C₂₃	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#2981	C₂	semidirect
3. C₂₃×#2979	C₂	semidirect
4. C₂₃×#2977	C₂	semidirect
5. C₂₃×#2976	C₂	semidirect
6. C₂₃×#2974	C₂	semidirect
7. C₂₃×#2972	C₂	semidirect
8. C₂₃×#2935	C₂	semidirect
9. D₄×M₁₆×C₂₃	C₂	semidirect
10. C₂₃×#2933	C₂	semidirect
11. C₂₃×#2931	C₂	semidirect
12. C₂₃×#2929	C₂	semidirect
13. C₂×C₈×D₄×C₂₃	C₂	semidirect
14. C₂₃×#2925	C₂	semidirect
15. C₂₃×#2922	C₂	semidirect
16. C₂₃×#2880	C₂	semidirect
17. C₂×C₂₃×#408	C₂	semidirect
19. C₂×C₂₃×#131	C₂²	semidirect
20. C₂×C₂₃×#131	C₂²	semidirect
21. C₂²×M₁₆×C₂₃	C₂²	semidirect
22. C₂³×C₈×C₂₃	C₂²	semidirect
39. C₂₃×#436	C₂²	semidirect
40. C₂₃×#436	C₂²	semidirect
41. C₂₃×#436	C₂²	semidirect
42. C₂₃×#436	C₂²	semidirect
43. C₂₃×#436	C₂²	semidirect
44. C₂₃×#435	C₂²	semidirect
45. C₂₃×#435	C₂²	semidirect
46. C₂₃×#435	C₂²	semidirect
47. C₂₃×#435	C₂²	semidirect
48. C₂₃×#435	C₂²	semidirect
49. C₂₃×#435	C₂²	semidirect
53. C₈×D₄×C₂₃	C₂²	semidirect
54. C₈×D₄×C₂₃	C₂²	semidirect
55. C₈×D₄×C₂₃	C₂²	semidirect
56. C₈×D₄×C₂₃	C₂²	semidirect
57. C₈×D₄×C₂₃	C₂²	semidirect
58. C₈×D₄×C₂₃	C₂²	semidirect
59. C₈×D₄×C₂₃	C₂²	semidirect
60. C₈×D₄×C₂₃	C₂²	semidirect
61. C₈×D₄×C₂₃	C₂²	semidirect
62. C₈×D₄×C₂₃	C₂²	semidirect
63. C₂₃×#433	C₂²	semidirect
64. C₂₃×#433	C₂²	semidirect
65. C₂₃×#433	C₂²	semidirect
66. C₂₃×#432	C₂²	semidirect
67. C₂₃×#431	C₂²	semidirect
68. C₂₃×#431	C₂²	semidirect
69. C₂₃×#431	C₂²	semidirect
70. C₂₃×#424	C₂²	semidirect
71. C₂₃×#424	C₂²	semidirect
72. C₂₃×#423	C₂²	semidirect
73. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
77. C₂₃×#408	C₂²	semidirect
78. C₂₃×#408	C₂²	semidirect
79. C₂₃×#408	C₂²	semidirect
80. C₂₃×#408	C₂²	semidirect
81. C₂₃×#408	C₂²	semidirect
82. C₂₃×#408	C₂²	semidirect
83. C₂₃×#407	C₂²	semidirect
84. C₂₃×#407	C₂²	semidirect
85. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
86. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
87. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
88. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
89. C₂₃×#405	C₂²	semidirect
90. C₄×M₁₆×C₂₃	C₂²	semidirect
91. C₂×C₄×C₈×C₂₃	C₂²	semidirect
320. #60239	C₂₃	direct (N × H)
348. D₄×C₂₃	#131	semidirect
391. #2981	C₂×C₂₃	semidirect
392. #2979	C₂×C₂₃	semidirect
393. #2977	C₂×C₂₃	semidirect
394. #2976	C₂×C₂₃	semidirect
395. #2974	C₂×C₂₃	semidirect
396. #2972	C₂×C₂₃	semidirect
397. #2935	C₂×C₂₃	semidirect
398. D₄×M₁₆	C₂×C₂₃	semidirect
399. #2933	C₂×C₂₃	semidirect
400. #2931	C₂×C₂₃	semidirect
401. #2929	C₂×C₂₃	semidirect
402. C₂×C₈×D₄	C₂×C₂₃	semidirect
403. #2925	C₂×C₂₃	semidirect
404. #2922	C₂×C₂₃	semidirect
405. #2880	C₂×C₂₃	semidirect
406. C₂×#408	C₂×C₂₃	semidirect
439. C₂×#131	C₂²×C₂₃	semidirect
440. C₂×#131	C₂²×C₂₃	semidirect
441. C₂²×M₁₆	C₂²×C₂₃	semidirect
442. C₂³×C₈	C₂²×C₂₃	semidirect
459. #436	C₂²×C₂₃	semidirect
460. #436	C₂²×C₂₃	semidirect
461. #436	C₂²×C₂₃	semidirect
462. #436	C₂²×C₂₃	semidirect
463. #436	C₂²×C₂₃	semidirect
464. #435	C₂²×C₂₃	semidirect
465. #435	C₂²×C₂₃	semidirect
466. #435	C₂²×C₂₃	semidirect
467. #435	C₂²×C₂₃	semidirect
468. #435	C₂²×C₂₃	semidirect
469. #435	C₂²×C₂₃	semidirect
473. C₈×D₄	C₂²×C₂₃	semidirect
474. C₈×D₄	C₂²×C₂₃	semidirect
475. C₈×D₄	C₂²×C₂₃	semidirect
476. C₈×D₄	C₂²×C₂₃	semidirect
477. C₈×D₄	C₂²×C₂₃	semidirect
478. C₈×D₄	C₂²×C₂₃	semidirect
479. C₈×D₄	C₂²×C₂₃	semidirect
480. C₈×D₄	C₂²×C₂₃	semidirect
481. C₈×D₄	C₂²×C₂₃	semidirect
482. C₈×D₄	C₂²×C₂₃	semidirect
483. #433	C₂²×C₂₃	semidirect
484. #433	C₂²×C₂₃	semidirect
485. #433	C₂²×C₂₃	semidirect
486. #432	C₂²×C₂₃	semidirect
487. #431	C₂²×C₂₃	semidirect
488. #431	C₂²×C₂₃	semidirect
489. #431	C₂²×C₂₃	semidirect
490. #424	C₂²×C₂₃	semidirect
491. #424	C₂²×C₂₃	semidirect
492. #423	C₂²×C₂₃	semidirect
493. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
497. #408	C₂²×C₂₃	semidirect
498. #408	C₂²×C₂₃	semidirect
499. #408	C₂²×C₂₃	semidirect
500. #408	C₂²×C₂₃	semidirect
501. #408	C₂²×C₂₃	semidirect
502. #408	C₂²×C₂₃	semidirect
503. #407	C₂²×C₂₃	semidirect
504. #407	C₂²×C₂₃	semidirect
505. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
506. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
507. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
508. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
509. #405	C₂²×C₂₃	semidirect
510. C₄×M₁₆	C₂²×C₂₃	semidirect
511. C₂×C₄×C₈	C₂²×C₂₃	semidirect
640. C₂₃	#60239	direct (N × H)
776. D₄	C₂₃×#131	semidirect

Maximal subgroups

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

subgroup	index
D₄×#41×C₂₃	2
C₂₃×#2981	2
C₂₃×#2979	2
C₂₃×#2977	2
C₂₃×#2976	2
C₂₃×#2974	2
C₂₃×#2972	2
C₂₃×#2935	2
D₄×M₁₆×C₂₃	2
C₂₃×#2933	2
C₂₃×#2931	2
C₂₃×#2929	2
C₂×C₈×D₄×C₂₃	2
C₂₃×#2925	2
C₂₃×#2922	2
C₂₃×#2880	2
C₂×C₂₃×#408	2
#60239	23

Subgroups — C23×#60239 #19207865

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60239 #19207865