Subgroups — C₂₃×#60327 #19207953

Order 5888.

1812 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3529	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2995	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2995	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2994	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2992	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2981	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2980	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2977	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2976	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2976	C₂	1	2	yes	maximal, complemented
11	C₂₃×#2969	C₂	1	2	yes	maximal, complemented
12	C₂₃×#2967	C₂	1	2	yes	maximal, complemented
13	C₂₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2935	C₂	1	2	yes	maximal, complemented
16	C₂₃×#2933	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2933	C₂	1	2	yes	maximal, complemented
18	C₂₃×#2931	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2930	C₂	1	2	yes	maximal, complemented
20	C₂×C₂₃×#131	C₂²	1	2	yes	—
21	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic, complemented
23	C₂²×M₁₆×C₂₃	C₂²	1	2	yes	complemented
24	C₂₃×#563	C₄	1	1	yes	characteristic
25	C₂₃×#563	C₄	1	2	yes	—
26	C₂₃×#562	C₄	1	1	yes	characteristic
27	C₂₃×#562	C₄	1	2	yes	—
28	C₂₃×#562	C₄	1	2	yes	—
29	C₂₃×#562	C₄	1	1	yes	characteristic
30	C₂₃×H(3,𝔽₄)	C₄	1	1	yes	characteristic
31	C₂₃×#560	C₄	1	2	yes	—
32	C₂₃×#560	C₄	1	2	yes	—
33	C₂₃×#560	C₄	1	2	yes	—
34	C₂₃×#532	C₂²	1	1	yes	characteristic
35	C₂₃×#532	C₂²	1	2	yes	—
36	C₂₃×#529	C₂²	1	1	yes	characteristic
37	C₂₃×#529	C₂²	1	1	yes	characteristic
38	C₂₃×#529	C₂²	1	2	yes	—
39	C₂₃×#529	C₂²	1	2	yes	—
40	C₂₃×#525	C₂²	1	2	yes	—
41	C₂₃×#525	C₂²	1	2	yes	—
42	C₂₃×#525	C₂²	1	2	yes	—
43	C₂₃×#446	C₂²	1	1	yes	characteristic, complemented
44	C₂₃×#446	C₂²	1	1	yes	characteristic, complemented
45	C₂₃×#446	C₂²	1	2	yes	complemented
46	C₂₃×#446	C₂²	1	2	yes	complemented
47	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
48	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
49	C₂₃×#436	C₂²	1	1	yes	characteristic
50	C₂₃×#436	C₂²	1	2	yes	—
51	C₂₃×#436	C₂²	1	2	yes	—
52	C₂₃×#436	C₂²	1	1	yes	characteristic
53	C₂₃×#436	C₂²	1	2	yes	complemented
54	C₂₃×#436	C₂²	1	2	yes	complemented
55	C₂₃×#436	C₂²	1	2	yes	complemented
56	C₂₃×#436	C₂²	1	2	yes	complemented
57	C₂₃×#436	C₂²	1	2	yes	complemented
58	C₂₃×#436	C₂²	1	2	yes	complemented
59	C₂₃×#435	C₂²	1	2	yes	—
60	C₂₃×#435	C₂²	1	2	yes	—
61	C₂₃×#435	C₂²	1	2	yes	—
62	C₂₃×#435	C₂²	1	2	yes	—
63	C₂₃×#435	C₂²	1	2	yes	—
64	C₂₃×#435	C₂²	1	2	yes	—
65	C₂₃×#435	C₂²	1	2	yes	complemented
66	C₂₃×#435	C₂²	1	2	yes	complemented
67	C₂₃×#435	C₂²	1	2	yes	complemented
68	C₂₃×#435	C₂²	1	2	yes	complemented
69	C₂₃×#435	C₂²	1	2	yes	complemented
70	C₂₃×#435	C₂²	1	2	yes	complemented
71	C₂₃×#435	C₂²	1	2	yes	complemented
72	C₂₃×#435	C₂²	1	2	yes	complemented
73	C₂₃×#435	C₂²	1	2	yes	complemented
74	C₂₃×#435	C₂²	1	2	yes	complemented
75	C₂₃×#435	C₂²	1	2	yes	complemented
76	C₂₃×#435	C₂²	1	2	yes	complemented
77	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
78	C₈×D₄×C₂₃	C₂²	1	2	yes	—
79	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
80	C₈×D₄×C₂₃	C₂²	1	2	yes	—
81	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
82	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
83	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
84	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
85	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
86	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
87	C₂₃×#433	C₂²	1	2	yes	complemented
88	C₂₃×#433	C₂²	1	2	yes	complemented
89	C₂₃×#433	C₂²	1	2	yes	complemented
90	C₂₃×#433	C₂²	1	2	yes	complemented
91	C₂₃×#433	C₂²	1	2	yes	complemented
92	C₂₃×#433	C₂²	1	2	yes	complemented
93	C₂₃×#432	C₂²	1	1	yes	characteristic, complemented
94	C₂₃×#432	C₂²	1	1	yes	characteristic, complemented
95	C₂₃×#432	C₂²	1	2	yes	complemented
96	C₂₃×#431	C₂²	1	2	yes	complemented
97	C₂₃×#424	C₂²	1	2	yes	complemented
98	C₂₃×#424	C₂²	1	2	yes	complemented
99	C₂₃×#424	C₂²	1	2	yes	complemented
100	C₂₃×#423	C₂²	1	1	yes	characteristic, complemented
101	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	complemented
102	C₂₃×#408	C₂²	1	2	yes	—
103	C₂₃×#408	C₂²	1	1	yes	characteristic
104	C₂₃×#408	C₂²	1	2	yes	—
105	C₂₃×#408	C₂²	1	2	yes	—
106	C₂₃×#408	C₂²	1	2	yes	—
107	C₂₃×#408	C₂²	1	1	yes	characteristic, complemented
108	C₂₃×#408	C₂²	1	2	yes	complemented
109	C₂₃×#407	C₂²	1	2	yes	complemented
110	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
111	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
112	C₂₃×#405	C₂²	1	2	yes	complemented
113	C₂₃×#405	C₂²	1	2	yes	complemented
114	C₂₃×#405	C₂²	1	2	yes	complemented
115	C₄×M₁₆×C₂₃	C₂²	1	2	yes	complemented
116	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
117	C₂×#41×C₂₃	C₂³	1	2	yes	—
118	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
119	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
121	C₂₃×#131	—	4	4	no	—
122	C₂₃×#131	—	4	2	no	—
123	C₂₃×#131	—	4	2	no	—
124	C₂×M₁₆×C₂₃	—	4	4	no	—
125	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
126	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
127	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
128	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
129	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
130	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
131	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
132	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
133	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
134	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
135	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
136	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
137	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
138	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
139	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
140	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
141	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
142	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
143	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
144	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
145	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
146	C₂₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
147	C₂₃×#127	C₂×C₄	1	1	yes	characteristic
148	C₂₃×#127	C₂×C₄	1	2	yes	—
149	C₂₃×#126	C₂×C₄	1	2	yes	—
150	C₂₃×#126	C₂×C₄	1	2	yes	—
151	C₂₃×#126	C₂×C₄	1	2	yes	—
152	C₂₃×#126	C₂×C₄	1	2	yes	—
153	C₂₃×#126	C₂×C₄	1	2	yes	—
154	C₂₃×#126	C₂×C₄	1	2	yes	—
155	C₂₃×#125	C₂×C₄	1	1	yes	characteristic
156	C₂₃×#125	C₂×C₄	1	1	yes	characteristic
157	C₂₃×#125	C₂×C₄	1	2	yes	—
158	C₂₃×#125	C₂×C₄	1	2	yes	—
159	C₂₃×#124	C₂×C₄	1	1	yes	characteristic
160	C₂₃×#124	C₂×C₄	1	1	yes	characteristic
161	C₂₃×#124	C₂×C₄	1	2	yes	—
162	C₂₃×#124	C₂×C₄	1	2	yes	—
163	C₂₃×#124	C₂×C₄	1	1	yes	characteristic
164	C₂₃×#124	C₂×C₄	1	2	yes	—
165	C₂₃×#124	C₂×C₄	1	1	yes	characteristic
166	C₂₃×#124	C₂×C₄	1	2	yes	—
167	C₂₃×#123	C₂×C₄	1	2	yes	—
168	C₂₃×#123	C₂×C₄	1	2	yes	—
169	C₂₃×#123	C₂×C₄	1	2	yes	—
170	C₂₃×#123	C₂×C₄	1	2	yes	—
171	C₂₃×#123	C₂×C₄	1	2	yes	—
172	C₂₃×#123	C₂×C₄	1	2	yes	—
173	C₂₃×#123	C₂×C₄	1	2	yes	—
174	C₂₃×#123	C₂×C₄	1	2	yes	—
175	C₂₃×#123	C₂×C₄	1	2	yes	—
176	C₂₃×#123	C₂×C₄	1	2	yes	—
177	C₂₃×#123	C₂×C₄	1	2	yes	—
178	C₂₃×#123	C₂×C₄	1	2	yes	—
179	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
180	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
181	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
182	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
183	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
184	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
185	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
186	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
187	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
188	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
189	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
190	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
191	C₂₃×#121	C₂×C₄	1	2	yes	—
192	C₂₃×#121	C₂×C₄	1	2	yes	—
193	C₂₃×#121	C₂×C₄	1	2	yes	—
194	C₂₃×#121	C₂×C₄	1	2	yes	—
195	C₂₃×#121	C₂×C₄	1	2	yes	—
196	C₂₃×#121	C₂×C₄	1	2	yes	—
197	C₂₃×#121	C₂×C₄	1	2	yes	—
198	C₂₃×#121	C₂×C₄	1	2	yes	—
199	C₂₃×#121	C₂×C₄	1	2	yes	—
200	C₂₃×#121	C₂×C₄	1	2	yes	—
201	C₂₃×#121	C₂×C₄	1	2	yes	—
202	C₂₃×#121	C₂×C₄	1	2	yes	—
203	C₂₃×#121	C₂×C₄	1	2	yes	—
204	C₂₃×#121	C₂×C₄	1	2	yes	—
205	C₂₃×#120	C₂×C₄	1	2	yes	—
206	C₂₃×#120	C₂×C₄	1	2	yes	—
207	C₂₃×#120	C₂×C₄	1	2	yes	—
208	C₂₃×#120	C₂×C₄	1	2	yes	—
209	C₂₃×#120	C₂×C₄	1	2	yes	—
210	C₂₃×#120	C₂×C₄	1	2	yes	—
211	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
212	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
213	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
214	C₄×D₄×C₂₃	C₂³	1	2	yes	—
215	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
216	C₄×D₄×C₂₃	C₂³	1	2	yes	—
217	C₄×D₄×C₂₃	C₂³	1	2	yes	—
218	C₄×D₄×C₂₃	C₂³	1	2	yes	—
219	C₄×D₄×C₂₃	C₂³	1	2	yes	—
220	C₄×D₄×C₂₃	C₂³	1	2	yes	—
221	C₄×D₄×C₂₃	C₂³	1	2	yes	—
222	C₄×D₄×C₂₃	C₂³	1	2	yes	—
223	C₂₃×#117	C₂³	1	2	yes	—
224	C₂₃×#117	C₂³	1	2	yes	—
225	C₂₃×#117	C₂³	1	2	yes	—
226	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
228	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
229	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
230	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
231	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
232	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
233	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
234	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
235	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
236	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
237	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
238	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
239	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
240	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
241	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
242	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
243	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
244	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
245	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
246	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
247	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
248	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
249	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
250	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
251	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
252	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
253	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
254	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
255	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
256	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
257	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
258	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
259	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
260	C₂₃×#97	C₂³	1	2	yes	—
261	C₂₃×#97	C₂³	1	2	yes	—
262	C₂₃×#97	C₂³	1	2	yes	—
263	C₂₃×#97	C₂³	1	2	yes	—
264	C₂₃×#97	C₂³	1	2	yes	—
265	C₂₃×#97	C₂³	1	2	yes	—
266	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
267	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
268	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
269	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
270	C₄×C₈×C₂₃	C₂³	1	2	yes	—
271	C₄×C₈×C₂₃	C₂³	1	2	yes	—
272	C₄×C₈×C₂₃	C₂³	1	2	yes	—
273	C₄×C₈×C₂₃	C₂³	1	2	yes	—
274	C₂⁴×C₂₃	C₂²×C₄	1	2	yes	—
275	#41×C₂₃	—	4	2	no	—
276	#41×C₂₃	—	4	1	no	—
277	#41×C₂₃	—	4	1	no	—
278	#41×C₂₃	—	4	1	no	—
279	#41×C₂₃	—	4	2	no	—
280	#41×C₂₃	—	4	1	no	—
281	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
282	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
283	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
284	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
285	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
286	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
287	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
288	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
289	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
290	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
291	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
292	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
293	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
294	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
295	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
296	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
297	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
298	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
299	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
300	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
301	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
302	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
303	C₂²×C₄×C₂₃	—	4	2	no	—
304	C₂²×C₄×C₂₃	—	4	2	no	—
305	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
306	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
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	2	yes	—
311	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
312	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
314	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
315	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
317	M₁₆×C₂₃	—	2	4	no	—
318	M₁₆×C₂₃	—	2	4	no	—
319	M₁₆×C₂₃	—	2	4	no	—
320	M₁₆×C₂₃	—	4	2	no	—
321	M₁₆×C₂₃	—	4	2	no	—
322	M₁₆×C₂₃	—	4	2	no	—
323	M₁₆×C₂₃	—	4	2	no	—
324	M₁₆×C₂₃	—	4	2	no	—
325	M₁₆×C₂₃	—	4	1	no	—
326	M₁₆×C₂₃	—	4	1	no	—
327	C₂×C₈×C₂₃	—	2	4	no	—
328	C₂×C₈×C₂₃	—	2	2	no	—
329	C₂×C₈×C₂₃	—	4	2	no	—
330	C₂×C₈×C₂₃	—	4	1	no	—
331	C₂×C₈×C₂₃	—	4	2	no	—
332	C₂×C₈×C₂₃	—	4	2	no	—
333	C₂×C₈×C₂₃	—	4	2	no	—
334	C₂×C₈×C₂₃	—	4	2	no	—
335	C₂×C₈×C₂₃	—	4	2	no	—
336	C₂×C₈×C₂₃	—	4	2	no	—
337	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
338	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
339	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
340	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
341	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
342	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
343	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
344	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
345	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
346	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
347	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
348	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
349	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
350	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
351	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
352	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
353	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
354	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
355	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
356	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
357	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
358	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
359	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
360	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
361	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
362	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
363	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
364	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
365	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
366	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
367	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
368	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
369	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
370	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
371	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
372	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
373	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
374	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
375	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
376	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
377	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
378	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
379	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
380	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
381	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
382	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
383	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
384	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
385	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
386	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
387	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
388	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
389	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
390	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
391	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
392	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
393	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
394	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
395	C₄²×C₂₃	C₂⁴	1	2	yes	—
396	C₄²×C₂₃	C₂⁴	1	2	yes	—
397	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
398	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
399	#60327	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
400	C₂³×C₂₃	—	4	2	no	—
401	C₂³×C₂₃	—	4	2	no	—
402	C₂³×C₂₃	—	4	2	no	—
403	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
404	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
405	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
406	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
407	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
408	Q₈×C₂₃	—	4	1	no	—
409	Q₈×C₂₃	—	4	1	no	—
410	Q₈×C₂₃	—	4	2	no	—
411	Q₈×C₂₃	—	4	1	no	—
412	Q₈×C₂₃	—	4	1	no	—
413	D₄×C₂₃	—	4	2	no	—
414	D₄×C₂₃	—	4	2	no	—
415	D₄×C₂₃	—	4	2	no	—
416	D₄×C₂₃	—	4	2	no	—
417	D₄×C₂₃	—	4	2	no	—
418	D₄×C₂₃	—	4	2	no	—
419	D₄×C₂₃	—	4	1	no	—
420	D₄×C₂₃	—	4	2	no	—
421	D₄×C₂₃	—	4	1	no	—
422	D₄×C₂₃	—	4	2	no	—
423	D₄×C₂₃	—	4	2	no	—
424	D₄×C₂₃	—	4	2	no	—
425	D₄×C₂₃	—	4	2	no	—
426	D₄×C₂₃	—	4	1	no	—
427	D₄×C₂₃	—	4	2	no	—
428	D₄×C₂₃	—	4	1	no	—
429	D₄×C₂₃	—	4	2	no	—
430	C₂×C₄×C₂₃	—	2	2	no	—
431	C₂×C₄×C₂₃	—	2	1	no	—
432	C₂×C₄×C₂₃	—	2	2	no	—
433	C₂×C₄×C₂₃	—	2	2	no	—
434	C₂×C₄×C₂₃	—	2	2	no	—
435	C₂×C₄×C₂₃	—	2	2	no	—
436	C₂×C₄×C₂₃	—	2	2	no	—
437	C₂×C₄×C₂₃	—	2	1	no	—
438	C₂×C₄×C₂₃	—	2	2	no	—
439	C₂×C₄×C₂₃	—	2	2	no	—
440	C₂×C₄×C₂₃	—	4	2	no	—
441	C₂×C₄×C₂₃	—	4	2	no	—
442	C₂×C₄×C₂₃	—	4	2	no	—
443	C₂×C₄×C₂₃	—	4	1	no	—
444	C₂×C₄×C₂₃	—	4	1	no	—
445	C₂×C₄×C₂₃	—	4	2	no	—
446	C₂×C₄×C₂₃	—	4	2	no	—
447	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
448	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
449	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
450	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
451	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
452	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
453	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
454	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
455	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
456	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
457	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
458	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
459	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
460	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
461	C₈×C₂₃	—	2	1	no	—
462	C₈×C₂₃	—	2	2	no	—
463	C₈×C₂₃	—	2	2	no	—
464	C₈×C₂₃	—	2	2	no	—
465	C₈×C₂₃	—	2	2	no	—
466	C₈×C₂₃	—	2	1	no	—
467	C₈×C₂₃	—	2	2	no	—
468	C₈×C₂₃	—	2	1	no	—
469	C₈×C₂₃	—	2	2	no	—
470	C₈×C₂₃	H(5,𝔽₂)	1	2	yes	—
471	#3529	C₂×C₂₃	1	1	yes	characteristic
472	#2995	C₂×C₂₃	1	1	yes	characteristic, complemented
473	#2995	C₂×C₂₃	1	1	yes	characteristic, complemented
474	#2994	C₂×C₂₃	1	2	yes	complemented
475	#2992	C₂×C₂₃	1	2	yes	complemented
476	#2981	C₂×C₂₃	1	2	yes	complemented
477	#2980	C₂×C₂₃	1	1	yes	characteristic, complemented
478	#2977	C₂×C₂₃	1	2	yes	complemented
479	#2976	C₂×C₂₃	1	2	yes	complemented
480	#2976	C₂×C₂₃	1	2	yes	complemented
481	#2969	C₂×C₂₃	1	2	yes	complemented
482	#2967	C₂×C₂₃	1	2	yes	complemented
483	#2966	C₂×C₂₃	1	1	yes	characteristic, complemented
484	#2966	C₂×C₂₃	1	1	yes	characteristic, complemented
485	#2935	C₂×C₂₃	1	2	yes	complemented
486	#2933	C₂×C₂₃	1	2	yes	complemented
487	#2933	C₂×C₂₃	1	2	yes	complemented
488	#2931	C₂×C₂₃	1	1	yes	characteristic, complemented
489	#2930	C₂×C₂₃	1	2	yes	complemented
490	C₂²×C₂₃	—	2	2	no	—
491	C₂²×C₂₃	—	2	2	no	—
492	C₂²×C₂₃	—	2	2	no	—
493	C₂²×C₂₃	—	2	1	no	—
494	C₂²×C₂₃	—	2	2	no	—
495	C₂²×C₂₃	—	2	1	no	—
496	C₂²×C₂₃	—	2	1	no	—
497	C₂²×C₂₃	—	2	2	no	—
498	C₂²×C₂₃	—	2	2	no	—
499	C₂²×C₂₃	—	2	2	no	—
500	C₂²×C₂₃	—	2	2	no	—
501	C₂²×C₂₃	—	2	2	no	—
502	C₂²×C₂₃	—	2	2	no	—
503	C₂²×C₂₃	—	2	2	no	—
504	C₂²×C₂₃	—	2	2	no	—
505	C₂²×C₂₃	—	8	4	no	—
506	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
507	C₄×C₂₃	—	2	2	no	—
508	C₄×C₂₃	—	2	2	no	—
509	C₄×C₂₃	—	2	2	no	—
510	C₄×C₂₃	—	2	1	no	—
511	C₄×C₂₃	—	2	2	no	—
512	C₄×C₂₃	—	2	1	no	—
513	C₄×C₂₃	—	2	1	no	—
514	C₄×C₂₃	—	2	2	no	—
515	C₄×C₂₃	—	2	2	no	—
516	C₄×C₂₃	—	2	1	no	—
517	C₄×C₂₃	—	2	1	no	—
518	C₄×C₂₃	—	2	2	no	—
519	C₄×C₂₃	—	2	2	no	—
520	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
521	C₄×C₂₃	#585	1	1	yes	characteristic
522	C₂×#131	C₂²×C₂₃	1	2	yes	—
523	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
524	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic, complemented
525	C₂²×M₁₆	C₂²×C₂₃	1	2	yes	complemented
526	#563	C₄×C₂₃	1	1	yes	characteristic
527	#563	C₄×C₂₃	1	2	yes	—
528	#562	C₄×C₂₃	1	1	yes	characteristic
529	#562	C₄×C₂₃	1	2	yes	—
530	#562	C₄×C₂₃	1	2	yes	—
531	#562	C₄×C₂₃	1	1	yes	characteristic
532	H(3,𝔽₄)	C₄×C₂₃	1	1	yes	characteristic
533	#560	C₄×C₂₃	1	2	yes	—
534	#560	C₄×C₂₃	1	2	yes	—
535	#560	C₄×C₂₃	1	2	yes	—
536	#532	C₂²×C₂₃	1	1	yes	characteristic
537	#532	C₂²×C₂₃	1	2	yes	—
538	#529	C₂²×C₂₃	1	1	yes	characteristic
539	#529	C₂²×C₂₃	1	1	yes	characteristic
540	#529	C₂²×C₂₃	1	2	yes	—
541	#529	C₂²×C₂₃	1	2	yes	—
542	#525	C₂²×C₂₃	1	2	yes	—
543	#525	C₂²×C₂₃	1	2	yes	—
544	#525	C₂²×C₂₃	1	2	yes	—
545	#446	C₂²×C₂₃	1	1	yes	characteristic, complemented
546	#446	C₂²×C₂₃	1	1	yes	characteristic, complemented
547	#446	C₂²×C₂₃	1	2	yes	complemented
548	#446	C₂²×C₂₃	1	2	yes	complemented
549	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
550	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
551	#436	C₂²×C₂₃	1	1	yes	characteristic
552	#436	C₂²×C₂₃	1	2	yes	—
553	#436	C₂²×C₂₃	1	2	yes	—
554	#436	C₂²×C₂₃	1	1	yes	characteristic
555	#436	C₂²×C₂₃	1	2	yes	complemented
556	#436	C₂²×C₂₃	1	2	yes	complemented
557	#436	C₂²×C₂₃	1	2	yes	complemented
558	#436	C₂²×C₂₃	1	2	yes	complemented
559	#436	C₂²×C₂₃	1	2	yes	complemented
560	#436	C₂²×C₂₃	1	2	yes	complemented
561	#435	C₂²×C₂₃	1	2	yes	—
562	#435	C₂²×C₂₃	1	2	yes	—
563	#435	C₂²×C₂₃	1	2	yes	—
564	#435	C₂²×C₂₃	1	2	yes	—
565	#435	C₂²×C₂₃	1	2	yes	—
566	#435	C₂²×C₂₃	1	2	yes	—
567	#435	C₂²×C₂₃	1	2	yes	complemented
568	#435	C₂²×C₂₃	1	2	yes	complemented
569	#435	C₂²×C₂₃	1	2	yes	complemented
570	#435	C₂²×C₂₃	1	2	yes	complemented
571	#435	C₂²×C₂₃	1	2	yes	complemented
572	#435	C₂²×C₂₃	1	2	yes	complemented
573	#435	C₂²×C₂₃	1	2	yes	complemented
574	#435	C₂²×C₂₃	1	2	yes	complemented
575	#435	C₂²×C₂₃	1	2	yes	complemented
576	#435	C₂²×C₂₃	1	2	yes	complemented
577	#435	C₂²×C₂₃	1	2	yes	complemented
578	#435	C₂²×C₂₃	1	2	yes	complemented
579	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
580	C₈×D₄	C₂²×C₂₃	1	2	yes	—
581	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
582	C₈×D₄	C₂²×C₂₃	1	2	yes	—
583	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
584	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
585	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
586	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
587	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
588	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
589	#433	C₂²×C₂₃	1	2	yes	complemented
590	#433	C₂²×C₂₃	1	2	yes	complemented
591	#433	C₂²×C₂₃	1	2	yes	complemented
592	#433	C₂²×C₂₃	1	2	yes	complemented
593	#433	C₂²×C₂₃	1	2	yes	complemented
594	#433	C₂²×C₂₃	1	2	yes	complemented
595	#432	C₂²×C₂₃	1	1	yes	characteristic, complemented
596	#432	C₂²×C₂₃	1	1	yes	characteristic, complemented
597	#432	C₂²×C₂₃	1	2	yes	complemented
598	#431	C₂²×C₂₃	1	2	yes	complemented
599	#424	C₂²×C₂₃	1	2	yes	complemented
600	#424	C₂²×C₂₃	1	2	yes	complemented
601	#424	C₂²×C₂₃	1	2	yes	complemented
602	#423	C₂²×C₂₃	1	1	yes	characteristic, complemented
603	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	complemented
604	#408	C₂²×C₂₃	1	2	yes	—
605	#408	C₂²×C₂₃	1	1	yes	characteristic
606	#408	C₂²×C₂₃	1	2	yes	—
607	#408	C₂²×C₂₃	1	2	yes	—
608	#408	C₂²×C₂₃	1	2	yes	—
609	#408	C₂²×C₂₃	1	1	yes	characteristic, complemented
610	#408	C₂²×C₂₃	1	2	yes	complemented
611	#407	C₂²×C₂₃	1	2	yes	complemented
612	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	complemented
613	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	complemented
614	#405	C₂²×C₂₃	1	2	yes	complemented
615	#405	C₂²×C₂₃	1	2	yes	complemented
616	#405	C₂²×C₂₃	1	2	yes	complemented
617	C₄×M₁₆	C₂²×C₂₃	1	2	yes	complemented
618	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
619	C₂×C₂₃	—	4	1	no	—
620	C₂×C₂₃	—	4	2	no	—
621	C₂×C₂₃	—	4	2	no	—
622	C₂×C₂₃	—	4	2	no	—
623	C₂×C₂₃	—	4	2	no	—
624	C₂×C₂₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
625	C₂×C₂₃	#3573	1	1	yes	characteristic
626	C₂×C₂₃	#3573	1	1	yes	characteristic
627	C₂×#41	C₂³×C₂₃	1	2	yes	—
628	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
629	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
630	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
631	#131	—	4	4	no	—
632	#131	—	4	2	no	—
633	#131	—	4	2	no	—
634	C₂×M₁₆	—	4	4	no	—
635	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
636	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
637	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
638	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
639	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
640	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
641	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
642	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
643	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
644	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
645	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
646	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
647	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
648	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
649	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
650	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
651	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
652	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
653	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
654	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
655	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
656	C₄⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
657	#127	C₂×C₄×C₂₃	1	1	yes	characteristic
658	#127	C₂×C₄×C₂₃	1	2	yes	—
659	#126	C₂×C₄×C₂₃	1	2	yes	—
660	#126	C₂×C₄×C₂₃	1	2	yes	—
661	#126	C₂×C₄×C₂₃	1	2	yes	—
662	#126	C₂×C₄×C₂₃	1	2	yes	—
663	#126	C₂×C₄×C₂₃	1	2	yes	—
664	#126	C₂×C₄×C₂₃	1	2	yes	—
665	#125	C₂×C₄×C₂₃	1	1	yes	characteristic
666	#125	C₂×C₄×C₂₃	1	1	yes	characteristic
667	#125	C₂×C₄×C₂₃	1	2	yes	—
668	#125	C₂×C₄×C₂₃	1	2	yes	—
669	#124	C₂×C₄×C₂₃	1	1	yes	characteristic
670	#124	C₂×C₄×C₂₃	1	1	yes	characteristic
671	#124	C₂×C₄×C₂₃	1	2	yes	—
672	#124	C₂×C₄×C₂₃	1	2	yes	—
673	#124	C₂×C₄×C₂₃	1	1	yes	characteristic
674	#124	C₂×C₄×C₂₃	1	2	yes	—
675	#124	C₂×C₄×C₂₃	1	1	yes	characteristic
676	#124	C₂×C₄×C₂₃	1	2	yes	—
677	#123	C₂×C₄×C₂₃	1	2	yes	—
678	#123	C₂×C₄×C₂₃	1	2	yes	—
679	#123	C₂×C₄×C₂₃	1	2	yes	—
680	#123	C₂×C₄×C₂₃	1	2	yes	—
681	#123	C₂×C₄×C₂₃	1	2	yes	—
682	#123	C₂×C₄×C₂₃	1	2	yes	—
683	#123	C₂×C₄×C₂₃	1	2	yes	—
684	#123	C₂×C₄×C₂₃	1	2	yes	—
685	#123	C₂×C₄×C₂₃	1	2	yes	—
686	#123	C₂×C₄×C₂₃	1	2	yes	—
687	#123	C₂×C₄×C₂₃	1	2	yes	—
688	#123	C₂×C₄×C₂₃	1	2	yes	—
689	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
690	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
691	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
692	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
693	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
694	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
695	C₂²⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
696	C₂²⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
697	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
698	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
699	#121	C₂×C₄×C₂₃	1	2	yes	—
700	#121	C₂×C₄×C₂₃	1	2	yes	—
701	#121	C₂×C₄×C₂₃	1	2	yes	—
702	#121	C₂×C₄×C₂₃	1	2	yes	—
703	#121	C₂×C₄×C₂₃	1	2	yes	—
704	#121	C₂×C₄×C₂₃	1	2	yes	—
705	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
706	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
707	#121	C₂×C₄×C₂₃	1	2	yes	—
708	#121	C₂×C₄×C₂₃	1	2	yes	—
709	#121	C₂×C₄×C₂₃	1	2	yes	—
710	#121	C₂×C₄×C₂₃	1	2	yes	—
711	#121	C₂×C₄×C₂₃	1	2	yes	—
712	#121	C₂×C₄×C₂₃	1	2	yes	—
713	#121	C₂×C₄×C₂₃	1	2	yes	—
714	#121	C₂×C₄×C₂₃	1	2	yes	—
715	#120	C₂×C₄×C₂₃	1	2	yes	—
716	#120	C₂×C₄×C₂₃	1	2	yes	—
717	#120	C₂×C₄×C₂₃	1	2	yes	—
718	#120	C₂×C₄×C₂₃	1	2	yes	—
719	#120	C₂×C₄×C₂₃	1	2	yes	—
720	#120	C₂×C₄×C₂₃	1	2	yes	—
721	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
722	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
723	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
724	C₄×D₄	C₂³×C₂₃	1	2	yes	—
725	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
726	C₄×D₄	C₂³×C₂₃	1	2	yes	—
727	C₄×D₄	C₂³×C₂₃	1	2	yes	—
728	C₄×D₄	C₂³×C₂₃	1	2	yes	—
729	C₄×D₄	C₂³×C₂₃	1	2	yes	—
730	C₄×D₄	C₂³×C₂₃	1	2	yes	—
731	C₄×D₄	C₂³×C₂₃	1	2	yes	—
732	C₄×D₄	C₂³×C₂₃	1	2	yes	—
733	#117	C₂³×C₂₃	1	2	yes	—
734	#117	C₂³×C₂₃	1	2	yes	—
735	#117	C₂³×C₂₃	1	2	yes	—
736	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
737	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
738	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
739	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
740	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
741	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
742	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
743	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
744	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
745	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
746	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
747	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
748	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
749	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
750	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
751	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
752	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
753	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
754	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
755	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
756	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
757	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
758	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
759	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
760	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
761	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
762	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
763	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
764	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
765	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
766	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
767	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
768	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
769	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
770	#97	C₂³×C₂₃	1	2	yes	—
771	#97	C₂³×C₂₃	1	2	yes	—
772	#97	C₂³×C₂₃	1	2	yes	—
773	#97	C₂³×C₂₃	1	2	yes	—
774	#97	C₂³×C₂₃	1	2	yes	—
775	#97	C₂³×C₂₃	1	2	yes	—
776	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
777	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
778	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
779	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
780	C₄×C₈	C₂³×C₂₃	1	2	yes	—
781	C₄×C₈	C₂³×C₂₃	1	2	yes	—
782	C₄×C₈	C₂³×C₂₃	1	2	yes	—
783	C₄×C₈	C₂³×C₂₃	1	2	yes	—
784	C₂₃	#60327	1	1	yes	characteristic, direct product factor, Sylow
785	C₂⁴	C₂²×C₄×C₂₃	1	2	yes	—
786	#41	—	4	2	no	—
787	#41	—	4	1	no	—
788	#41	—	4	1	no	—
789	#41	—	4	1	no	—
790	#41	—	4	2	no	—
791	#41	—	4	1	no	—
792	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
793	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
794	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
795	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
796	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
797	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
798	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
799	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
800	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
801	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
802	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
803	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
804	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
805	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
806	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
807	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
808	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
809	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
810	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
811	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
812	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
813	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
814	C₂²×C₄	—	4	2	no	—
815	C₂²×C₄	—	4	2	no	—
816	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
817	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
818	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
819	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
820	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
821	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
822	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
823	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
824	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
825	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
826	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
827	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
828	M₁₆	—	2	4	no	—
829	M₁₆	—	2	4	no	—
830	M₁₆	—	2	4	no	—
831	M₁₆	—	4	2	no	—
832	M₁₆	—	4	2	no	—
833	M₁₆	—	4	2	no	—
834	M₁₆	—	4	1	no	—
835	M₁₆	—	4	1	no	—
836	M₁₆	—	4	2	no	—
837	M₁₆	—	4	2	no	—
838	C₂×C₈	—	2	4	no	—
839	C₂×C₈	—	2	2	no	—
840	C₂×C₈	—	4	2	no	—
841	C₂×C₈	—	4	2	no	—
842	C₂×C₈	—	4	2	no	—
843	C₂×C₈	—	4	2	no	—
844	C₂×C₈	—	4	2	no	—
845	C₂×C₈	—	4	2	no	—
846	C₂×C₈	—	4	1	no	—
847	C₂×C₈	—	4	2	no	—
848	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
849	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
850	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
851	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
852	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
853	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
854	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
855	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
856	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
857	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
858	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
859	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
860	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
861	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
862	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
863	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
864	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
865	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
866	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
867	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
868	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
869	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
870	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
871	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
872	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
873	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
874	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
875	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
876	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
877	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
878	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
879	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
880	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
881	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
882	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
883	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
884	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
885	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
886	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
887	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
888	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
889	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
890	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
891	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
892	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
893	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
894	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
895	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
896	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
897	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
898	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
899	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
900	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
901	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
902	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
903	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
904	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
905	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
906	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
907	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
908	C₄²	C₂⁴×C₂₃	1	2	yes	—
909	C₄²	C₂⁴×C₂₃	1	2	yes	—
910	C₂³	—	4	2	no	—
911	C₂³	—	4	2	no	—
912	C₂³	—	4	2	no	—
913	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
914	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
915	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
916	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
917	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
918	Q₈	—	4	2	no	—
919	Q₈	—	4	1	no	—
920	Q₈	—	4	1	no	—
921	Q₈	—	4	1	no	—
922	Q₈	—	4	1	no	—
923	D₄	—	4	2	no	—
924	D₄	—	4	2	no	—
925	D₄	—	4	2	no	—
926	D₄	—	4	1	no	—
927	D₄	—	4	2	no	—
928	D₄	—	4	1	no	—
929	D₄	—	4	2	no	—
930	D₄	—	4	2	no	—
931	D₄	—	4	2	no	—
932	D₄	—	4	2	no	—
933	D₄	—	4	2	no	—
934	D₄	—	4	2	no	—
935	D₄	—	4	2	no	—
936	D₄	—	4	1	no	—
937	D₄	—	4	2	no	—
938	D₄	—	4	1	no	—
939	D₄	—	4	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	2	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	2	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	4	2	no	—
951	C₂×C₄	—	4	2	no	—
952	C₂×C₄	—	4	2	no	—
953	C₂×C₄	—	4	1	no	—
954	C₂×C₄	—	4	1	no	—
955	C₂×C₄	—	4	2	no	—
956	C₂×C₄	—	4	2	no	—
957	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
958	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
959	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
960	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
961	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
962	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
963	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
964	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
965	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
966	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
967	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
968	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
969	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
970	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
971	C₈	—	2	1	no	—
972	C₈	—	2	2	no	—
973	C₈	—	2	2	no	—
974	C₈	—	2	2	no	—
975	C₈	—	2	2	no	—
976	C₈	—	2	1	no	—
977	C₈	—	2	2	no	—
978	C₈	—	2	1	no	—
979	C₈	—	2	2	no	—
980	C₈	C₂₃×H(5,𝔽₂)	1	2	yes	—
981	C₂²	—	2	2	no	—
982	C₂²	—	2	2	no	—
983	C₂²	—	2	2	no	—
984	C₂²	—	2	1	no	—
985	C₂²	—	2	2	no	—
986	C₂²	—	2	1	no	—
987	C₂²	—	2	1	no	—
988	C₂²	—	2	2	no	—
989	C₂²	—	2	2	no	—
990	C₂²	—	2	2	no	—
991	C₂²	—	2	2	no	—
992	C₂²	—	2	2	no	—
993	C₂²	—	2	2	no	—
994	C₂²	—	2	2	no	—
995	C₂²	—	2	2	no	—
996	C₂²	—	8	4	no	—
997	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
998	C₄	—	2	2	no	—
999	C₄	—	2	2	no	—
1000	C₄	—	2	2	no	—
1001	C₄	—	2	1	no	—
1002	C₄	—	2	2	no	—
1003	C₄	—	2	1	no	—
1004	C₄	—	2	1	no	—
1005	C₄	—	2	2	no	—
1006	C₄	—	2	2	no	—
1007	C₄	—	2	1	no	—
1008	C₄	—	2	1	no	—
1009	C₄	—	2	2	no	—
1010	C₄	—	2	2	no	—
1011	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1012	C₄	C₂₃×#585	1	1	yes	characteristic
1013	C₂	—	4	2	no	—
1014	C₂	—	4	2	no	—
1015	C₂	—	4	2	no	—
1016	C₂	—	4	1	no	—
1017	C₂	—	4	2	no	—
1018	C₂	C₄×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1019	C₂	C₂₃×#3573	1	1	yes	characteristic
1020	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	C₂₃×#3529	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×#2995	C₂	semidirect
3. C₂₃×#2995	C₂	semidirect
4. C₂₃×#2994	C₂	semidirect
5. C₂₃×#2992	C₂	semidirect
6. C₂₃×#2981	C₂	semidirect
7. C₂₃×#2980	C₂	semidirect
8. C₂₃×#2977	C₂	semidirect
9. C₂₃×#2976	C₂	semidirect
10. C₂₃×#2976	C₂	semidirect
11. C₂₃×#2969	C₂	semidirect
12. C₂₃×#2967	C₂	semidirect
13. C₂₃×#2966	C₂	semidirect
14. C₂₃×#2966	C₂	semidirect
15. C₂₃×#2935	C₂	semidirect
16. C₂₃×#2933	C₂	semidirect
17. C₂₃×#2933	C₂	semidirect
18. C₂₃×#2931	C₂	semidirect
19. C₂₃×#2930	C₂	semidirect
22. C₂×C₂₃×#131	C₂²	semidirect
23. C₂²×M₁₆×C₂₃	C₂²	semidirect
43. C₂₃×#446	C₂²	semidirect
44. C₂₃×#446	C₂²	semidirect
45. C₂₃×#446	C₂²	semidirect
46. C₂₃×#446	C₂²	semidirect
47. C₈×Q₈×C₂₃	C₂²	semidirect
48. C₈×Q₈×C₂₃	C₂²	semidirect
53. C₂₃×#436	C₂²	semidirect
54. C₂₃×#436	C₂²	semidirect
55. C₂₃×#436	C₂²	semidirect
56. C₂₃×#436	C₂²	semidirect
57. C₂₃×#436	C₂²	semidirect
58. C₂₃×#436	C₂²	semidirect
65. C₂₃×#435	C₂²	semidirect
66. C₂₃×#435	C₂²	semidirect
67. C₂₃×#435	C₂²	semidirect
68. C₂₃×#435	C₂²	semidirect
69. C₂₃×#435	C₂²	semidirect
70. C₂₃×#435	C₂²	semidirect
71. C₂₃×#435	C₂²	semidirect
72. C₂₃×#435	C₂²	semidirect
73. C₂₃×#435	C₂²	semidirect
74. C₂₃×#435	C₂²	semidirect
75. C₂₃×#435	C₂²	semidirect
76. C₂₃×#435	C₂²	semidirect
81. C₈×D₄×C₂₃	C₂²	semidirect
82. C₈×D₄×C₂₃	C₂²	semidirect
83. C₈×D₄×C₂₃	C₂²	semidirect
84. C₈×D₄×C₂₃	C₂²	semidirect
85. C₈×D₄×C₂₃	C₂²	semidirect
86. C₈×D₄×C₂₃	C₂²	semidirect
87. C₂₃×#433	C₂²	semidirect
88. C₂₃×#433	C₂²	semidirect
89. C₂₃×#433	C₂²	semidirect
90. C₂₃×#433	C₂²	semidirect
91. C₂₃×#433	C₂²	semidirect
92. C₂₃×#433	C₂²	semidirect
93. C₂₃×#432	C₂²	semidirect
94. C₂₃×#432	C₂²	semidirect
95. C₂₃×#432	C₂²	semidirect
96. C₂₃×#431	C₂²	semidirect
97. C₂₃×#424	C₂²	semidirect
98. C₂₃×#424	C₂²	semidirect
99. C₂₃×#424	C₂²	semidirect
100. C₂₃×#423	C₂²	semidirect
101. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
107. C₂₃×#408	C₂²	semidirect
108. C₂₃×#408	C₂²	semidirect
109. C₂₃×#407	C₂²	semidirect
110. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
111. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
112. C₂₃×#405	C₂²	semidirect
113. C₂₃×#405	C₂²	semidirect
114. C₂₃×#405	C₂²	semidirect
115. C₄×M₁₆×C₂₃	C₂²	semidirect
116. C₂×C₄×C₈×C₂₃	C₂²	semidirect
399. #60327	C₂₃	direct (N × H)
472. #2995	C₂×C₂₃	semidirect
473. #2995	C₂×C₂₃	semidirect
474. #2994	C₂×C₂₃	semidirect
475. #2992	C₂×C₂₃	semidirect
476. #2981	C₂×C₂₃	semidirect
477. #2980	C₂×C₂₃	semidirect
478. #2977	C₂×C₂₃	semidirect
479. #2976	C₂×C₂₃	semidirect
480. #2976	C₂×C₂₃	semidirect
481. #2969	C₂×C₂₃	semidirect
482. #2967	C₂×C₂₃	semidirect
483. #2966	C₂×C₂₃	semidirect
484. #2966	C₂×C₂₃	semidirect
485. #2935	C₂×C₂₃	semidirect
486. #2933	C₂×C₂₃	semidirect
487. #2933	C₂×C₂₃	semidirect
488. #2931	C₂×C₂₃	semidirect
489. #2930	C₂×C₂₃	semidirect
524. C₂×#131	C₂²×C₂₃	semidirect
525. C₂²×M₁₆	C₂²×C₂₃	semidirect
545. #446	C₂²×C₂₃	semidirect
546. #446	C₂²×C₂₃	semidirect
547. #446	C₂²×C₂₃	semidirect
548. #446	C₂²×C₂₃	semidirect
549. C₈×Q₈	C₂²×C₂₃	semidirect
550. C₈×Q₈	C₂²×C₂₃	semidirect
555. #436	C₂²×C₂₃	semidirect
556. #436	C₂²×C₂₃	semidirect
557. #436	C₂²×C₂₃	semidirect
558. #436	C₂²×C₂₃	semidirect
559. #436	C₂²×C₂₃	semidirect
560. #436	C₂²×C₂₃	semidirect
567. #435	C₂²×C₂₃	semidirect
568. #435	C₂²×C₂₃	semidirect
569. #435	C₂²×C₂₃	semidirect
570. #435	C₂²×C₂₃	semidirect
571. #435	C₂²×C₂₃	semidirect
572. #435	C₂²×C₂₃	semidirect
573. #435	C₂²×C₂₃	semidirect
574. #435	C₂²×C₂₃	semidirect
575. #435	C₂²×C₂₃	semidirect
576. #435	C₂²×C₂₃	semidirect
577. #435	C₂²×C₂₃	semidirect
578. #435	C₂²×C₂₃	semidirect
583. C₈×D₄	C₂²×C₂₃	semidirect
584. C₈×D₄	C₂²×C₂₃	semidirect
585. C₈×D₄	C₂²×C₂₃	semidirect
586. C₈×D₄	C₂²×C₂₃	semidirect
587. C₈×D₄	C₂²×C₂₃	semidirect
588. C₈×D₄	C₂²×C₂₃	semidirect
589. #433	C₂²×C₂₃	semidirect
590. #433	C₂²×C₂₃	semidirect
591. #433	C₂²×C₂₃	semidirect
592. #433	C₂²×C₂₃	semidirect
593. #433	C₂²×C₂₃	semidirect
594. #433	C₂²×C₂₃	semidirect
595. #432	C₂²×C₂₃	semidirect
596. #432	C₂²×C₂₃	semidirect
597. #432	C₂²×C₂₃	semidirect
598. #431	C₂²×C₂₃	semidirect
599. #424	C₂²×C₂₃	semidirect
600. #424	C₂²×C₂₃	semidirect
601. #424	C₂²×C₂₃	semidirect
602. #423	C₂²×C₂₃	semidirect
603. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
609. #408	C₂²×C₂₃	semidirect
610. #408	C₂²×C₂₃	semidirect
611. #407	C₂²×C₂₃	semidirect
612. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
613. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
614. #405	C₂²×C₂₃	semidirect
615. #405	C₂²×C₂₃	semidirect
616. #405	C₂²×C₂₃	semidirect
617. C₄×M₁₆	C₂²×C₂₃	semidirect
618. C₂×C₄×C₈	C₂²×C₂₃	semidirect
784. C₂₃	#60327	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×#3529	2
C₂₃×#2995	2
C₂₃×#2994	2
C₂₃×#2992	2
C₂₃×#2981	2
C₂₃×#2980	2
C₂₃×#2977	2
C₂₃×#2976	2
C₂₃×#2969	2
C₂₃×#2967	2
C₂₃×#2966	2
C₂₃×#2935	2
C₂₃×#2933	2
C₂₃×#2931	2
C₂₃×#2930	2
#60327	23

Subgroups — C23×#60327 #19207953

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60327 #19207953