Subgroups — C₂₃×#60315 #19207941

Order 5888.

1816 conjugacy classes of subgroups.

The subgroup lattice has 1040 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×#2994	C₂	1	2	yes	maximal, complemented
3	C₂₃×#2993	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2992	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2981	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2979	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2978	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2978	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2977	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2976	C₂	1	2	yes	maximal, complemented
11	C₂₃×#2969	C₂	1	2	yes	maximal, complemented
12	C₂₃×#2968	C₂	1	2	yes	maximal, complemented
13	C₂₃×#2967	C₂	1	2	yes	maximal, complemented
14	C₂₃×#2935	C₂	1	2	yes	maximal, complemented
15	C₂₃×#2933	C₂	1	2	yes	maximal, complemented
16	C₂₃×#2932	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#2930	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#2929	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2929	C₂	1	2	yes	maximal, complemented
20	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×#131	C₂²	1	2	yes	—
22	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic, complemented
23	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
24	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
25	C₂₃×#563	C₄	1	2	yes	—
26	C₂₃×#563	C₄	1	1	yes	characteristic
27	C₂₃×#562	C₄	1	2	yes	—
28	C₂₃×#562	C₄	1	2	yes	—
29	C₂₃×#562	C₄	1	2	yes	—
30	C₂₃×H(3,𝔽₄)	C₄	1	1	yes	characteristic
31	C₂₃×#560	C₄	1	2	yes	—
32	C₂₃×#560	C₄	1	1	yes	characteristic
33	C₂₃×#560	C₄	1	2	yes	—
34	C₂₃×#560	C₄	1	1	yes	characteristic
35	C₂₃×#532	C₂²	1	1	yes	characteristic
36	C₂₃×#532	C₂²	1	2	yes	—
37	C₂₃×#529	C₂²	1	2	yes	—
38	C₂₃×#529	C₂²	1	2	yes	—
39	C₂₃×#529	C₂²	1	2	yes	—
40	C₂₃×#525	C₂²	1	1	yes	characteristic
41	C₂₃×#525	C₂²	1	2	yes	—
42	C₂₃×#525	C₂²	1	1	yes	characteristic
43	C₂₃×#525	C₂²	1	2	yes	—
44	C₂₃×#446	C₂²	1	2	yes	complemented
45	C₂₃×#446	C₂²	1	2	yes	complemented
46	C₂₃×#446	C₂²	1	2	yes	complemented
47	C₈×Q₈×C₂₃	C₂²	1	2	yes	complemented
48	C₂₃×#436	C₂²	1	2	yes	—
49	C₂₃×#436	C₂²	1	2	yes	—
50	C₂₃×#436	C₂²	1	2	yes	—
51	C₂₃×#436	C₂²	1	2	yes	complemented
52	C₂₃×#436	C₂²	1	2	yes	complemented
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×#435	C₂²	1	2	yes	—
58	C₂₃×#435	C₂²	1	2	yes	—
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	complemented
64	C₂₃×#435	C₂²	1	2	yes	complemented
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	C₈×D₄×C₂₃	C₂²	1	2	yes	—
76	C₈×D₄×C₂₃	C₂²	1	2	yes	—
77	C₈×D₄×C₂₃	C₂²	1	2	yes	—
78	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
79	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
80	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
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	C₂₃×#433	C₂²	1	2	yes	complemented
85	C₂₃×#433	C₂²	1	2	yes	complemented
86	C₂₃×#433	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×#432	C₂²	1	2	yes	complemented
91	C₂₃×#431	C₂²	1	2	yes	complemented
92	C₂₃×#431	C₂²	1	2	yes	complemented
93	C₂₃×#424	C₂²	1	2	yes	complemented
94	C₂₃×#424	C₂²	1	1	yes	characteristic, complemented
95	C₂₃×#424	C₂²	1	1	yes	characteristic, complemented
96	C₂₃×#424	C₂²	1	2	yes	complemented
97	C₂₃×#423	C₂²	1	1	yes	characteristic, complemented
98	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	complemented
99	C₂₃×#408	C₂²	1	2	yes	—
100	C₂₃×#408	C₂²	1	1	yes	characteristic
101	C₂₃×#408	C₂²	1	1	yes	characteristic
102	C₂₃×#408	C₂²	1	1	yes	characteristic
103	C₂₃×#408	C₂²	1	2	yes	—
104	C₂₃×#408	C₂²	1	2	yes	—
105	C₂₃×#408	C₂²	1	1	yes	characteristic, complemented
106	C₂₃×#408	C₂²	1	2	yes	complemented
107	C₂₃×#407	C₂²	1	2	yes	complemented
108	C₂₃×#407	C₂²	1	1	yes	characteristic, complemented
109	C₂₃×#407	C₂²	1	1	yes	characteristic, complemented
110	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
111	C₂₃×#405	C₂²	1	1	yes	characteristic, complemented
112	C₂₃×#405	C₂²	1	2	yes	complemented
113	C₂₃×#405	C₂²	1	1	yes	characteristic, complemented
114	C₂₃×#405	C₂²	1	2	yes	complemented
115	C₄×M₁₆×C₂₃	C₂²	1	2	yes	complemented
116	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic, complemented
117	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
118	C₂×#41×C₂₃	C₂³	1	2	yes	—
119	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
122	C₂₃×#131	—	4	2	no	—
123	C₂₃×#131	—	4	4	no	—
124	C₂₃×#131	—	4	2	no	—
125	C₂×M₁₆×C₂₃	—	4	2	no	—
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	1	yes	characteristic
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	1	yes	characteristic
134	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
135	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
136	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
137	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
138	C₂²×C₈×C₂₃	—	4	2	no	—
139	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
140	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
141	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
142	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
143	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
144	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
145	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
146	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
147	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
148	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
149	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
150	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
151	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
152	C₂₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
153	C₂₃×#127	C₂×C₄	1	1	yes	characteristic
154	C₂₃×#127	C₂×C₄	1	2	yes	—
155	C₂₃×#126	C₂×C₄	1	2	yes	—
156	C₂₃×#126	C₂×C₄	1	2	yes	—
157	C₂₃×#126	C₂×C₄	1	2	yes	—
158	C₂₃×#126	C₂×C₄	1	2	yes	—
159	C₂₃×#126	C₂×C₄	1	2	yes	—
160	C₂₃×#126	C₂×C₄	1	2	yes	—
161	C₂₃×#125	C₂×C₄	1	2	yes	—
162	C₂₃×#125	C₂×C₄	1	2	yes	—
163	C₂₃×#125	C₂×C₄	1	2	yes	—
164	C₂₃×#124	C₂×C₄	1	2	yes	—
165	C₂₃×#124	C₂×C₄	1	2	yes	—
166	C₂₃×#124	C₂×C₄	1	2	yes	—
167	C₂₃×#124	C₂×C₄	1	1	yes	characteristic
168	C₂₃×#124	C₂×C₄	1	2	yes	—
169	C₂₃×#124	C₂×C₄	1	1	yes	characteristic
170	C₂₃×#124	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	1	yes	characteristic
178	C₂₃×#123	C₂×C₄	1	2	yes	—
179	C₂₃×#123	C₂×C₄	1	1	yes	characteristic
180	C₂₃×#123	C₂×C₄	1	2	yes	—
181	C₂₃×#123	C₂×C₄	1	1	yes	characteristic
182	C₂₃×#123	C₂×C₄	1	2	yes	—
183	C₂₃×#123	C₂×C₄	1	1	yes	characteristic
184	C₂₃×#123	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×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
190	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
191	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
192	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
193	C₂₃×C₂²⋊Q₈	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×#121	C₂×C₄	1	2	yes	—
206	C₂₃×#121	C₂×C₄	1	2	yes	—
207	C₂₃×#121	C₂×C₄	1	2	yes	—
208	C₂₃×#121	C₂×C₄	1	2	yes	—
209	C₂₃×#120	C₂×C₄	1	1	yes	characteristic
210	C₂₃×#120	C₂×C₄	1	2	yes	—
211	C₂₃×#120	C₂×C₄	1	1	yes	characteristic
212	C₂₃×#120	C₂×C₄	1	2	yes	—
213	C₂₃×#120	C₂×C₄	1	1	yes	characteristic
214	C₂₃×#120	C₂×C₄	1	2	yes	—
215	C₂₃×#120	C₂×C₄	1	1	yes	characteristic
216	C₂₃×#120	C₂×C₄	1	2	yes	—
217	C₄×Q₈×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	C₄×D₄×C₂₃	C₂³	1	2	yes	—
224	C₄×D₄×C₂₃	C₂³	1	2	yes	—
225	C₄×D₄×C₂₃	C₂³	1	2	yes	—
226	C₄×D₄×C₂₃	C₂³	1	2	yes	—
227	C₂₃×#117	C₂³	1	1	yes	characteristic
228	C₂₃×#117	C₂³	1	2	yes	—
229	C₂₃×#117	C₂³	1	1	yes	characteristic
230	C₂₃×#117	C₂³	1	2	yes	—
231	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₂₃	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	2	yes	—
236	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
237	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
238	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
239	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
240	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
241	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
242	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
243	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
244	C₂₃×C₄⋊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×C₂²⋊C₈	C₂³	1	2	yes	—
261	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
262	C₂₃×C₂²⋊C₈	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	C₂₃×#97	C₂³	1	2	yes	—
267	C₂₃×#97	C₂³	1	2	yes	—
268	C₂₃×#97	C₂³	1	2	yes	—
269	C₄×C₈×C₂₃	C₂³	1	2	yes	—
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	C₄×C₈×C₂₃	C₂³	1	2	yes	—
275	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
276	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
277	#41×C₂₃	—	4	1	no	—
278	#41×C₂₃	—	4	2	no	—
279	#41×C₂₃	—	4	1	no	—
280	#41×C₂₃	—	4	2	no	—
281	#41×C₂₃	—	4	1	no	—
282	#41×C₂₃	—	4	1	no	—
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	2	yes	—
286	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
287	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
288	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
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	1	yes	characteristic
297	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
298	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
299	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
300	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
301	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
302	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
303	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
304	C₂²×C₄×C₂₃	—	4	1	no	—
305	C₂²×C₄×C₂₃	—	4	1	no	—
306	C₂²×C₄×C₂₃	—	4	1	no	—
307	C₂²×C₄×C₂₃	—	4	1	no	—
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	1	yes	characteristic
312	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
313	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
314	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
315	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
317	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
321	M₁₆×C₂₃	—	2	4	no	—
322	M₁₆×C₂₃	—	2	4	no	—
323	M₁₆×C₂₃	—	4	2	no	—
324	M₁₆×C₂₃	—	4	2	no	—
325	M₁₆×C₂₃	—	4	1	no	—
326	M₁₆×C₂₃	—	4	2	no	—
327	M₁₆×C₂₃	—	4	1	no	—
328	M₁₆×C₂₃	—	4	1	no	—
329	M₁₆×C₂₃	—	4	1	no	—
330	M₁₆×C₂₃	—	4	1	no	—
331	M₁₆×C₂₃	—	4	2	no	—
332	M₁₆×C₂₃	—	4	1	no	—
333	C₂×C₈×C₂₃	—	2	4	no	—
334	C₂×C₈×C₂₃	—	2	2	no	—
335	C₂×C₈×C₂₃	—	2	2	no	—
336	C₂×C₈×C₂₃	—	2	2	no	—
337	C₂×C₈×C₂₃	—	4	1	no	—
338	C₂×C₈×C₂₃	—	4	2	no	—
339	C₂×C₈×C₂₃	—	4	1	no	—
340	C₂×C₈×C₂₃	—	4	2	no	—
341	C₂×C₈×C₂₃	—	4	1	no	—
342	C₂×C₈×C₂₃	—	4	2	no	—
343	C₂×C₈×C₂₃	—	4	2	no	—
344	C₂×C₈×C₂₃	—	4	2	no	—
345	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
346	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
347	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
348	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
349	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
350	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
351	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
352	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
353	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
354	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
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	2	yes	—
360	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
361	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
362	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
363	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
364	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
365	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
366	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
367	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
368	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
369	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
370	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
371	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
372	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
373	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
374	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
375	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
376	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
377	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
378	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
379	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
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	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
392	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
393	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
394	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
395	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
396	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
397	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
398	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
399	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
400	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
401	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
402	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
403	C₄²×C₂₃	C₂⁴	1	2	yes	—
404	C₄²×C₂₃	C₂⁴	1	2	yes	—
405	C₄²×C₂₃	C₂⁴	1	2	yes	—
406	#60315	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
407	C₂³×C₂₃	—	4	1	no	—
408	C₂³×C₂₃	—	4	2	no	—
409	C₂³×C₂₃	—	4	1	no	—
410	C₂³×C₂₃	—	4	2	no	—
411	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
412	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
413	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
414	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
415	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
416	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
417	Q₈×C₂₃	—	4	2	no	—
418	Q₈×C₂₃	—	4	1	no	—
419	Q₈×C₂₃	—	4	2	no	—
420	Q₈×C₂₃	—	4	1	no	—
421	D₄×C₂₃	—	4	2	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	2	no	—
427	D₄×C₂₃	—	4	2	no	—
428	D₄×C₂₃	—	4	2	no	—
429	D₄×C₂₃	—	4	2	no	—
430	D₄×C₂₃	—	4	1	no	—
431	D₄×C₂₃	—	4	1	no	—
432	D₄×C₂₃	—	4	2	no	—
433	D₄×C₂₃	—	4	2	no	—
434	D₄×C₂₃	—	4	1	no	—
435	D₄×C₂₃	—	4	2	no	—
436	D₄×C₂₃	—	4	1	no	—
437	D₄×C₂₃	—	4	2	no	—
438	C₂×C₄×C₂₃	—	2	2	no	—
439	C₂×C₄×C₂₃	—	2	1	no	—
440	C₂×C₄×C₂₃	—	2	1	no	—
441	C₂×C₄×C₂₃	—	2	1	no	—
442	C₂×C₄×C₂₃	—	2	2	no	—
443	C₂×C₄×C₂₃	—	2	2	no	—
444	C₂×C₄×C₂₃	—	2	2	no	—
445	C₂×C₄×C₂₃	—	2	1	no	—
446	C₂×C₄×C₂₃	—	2	2	no	—
447	C₂×C₄×C₂₃	—	2	1	no	—
448	C₂×C₄×C₂₃	—	2	1	no	—
449	C₂×C₄×C₂₃	—	2	2	no	—
450	C₂×C₄×C₂₃	—	4	1	no	—
451	C₂×C₄×C₂₃	—	4	2	no	—
452	C₂×C₄×C₂₃	—	4	2	no	—
453	C₂×C₄×C₂₃	—	4	1	no	—
454	C₂×C₄×C₂₃	—	4	2	no	—
455	C₂×C₄×C₂₃	—	4	2	no	—
456	C₂×C₄×C₂₃	—	4	2	no	—
457	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
458	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
459	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
460	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
461	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
462	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
463	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
464	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
465	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
466	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
467	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
468	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
469	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
470	C₈×C₂₃	—	2	2	no	—
471	C₈×C₂₃	—	2	1	no	—
472	C₈×C₂₃	—	2	1	no	—
473	C₈×C₂₃	—	2	1	no	—
474	C₈×C₂₃	—	2	2	no	—
475	C₈×C₂₃	—	2	2	no	—
476	C₈×C₂₃	—	2	2	no	—
477	C₈×C₂₃	—	2	2	no	—
478	C₈×C₂₃	—	2	2	no	—
479	C₈×C₂₃	H(5,𝔽₂)	1	2	yes	—
480	#3529	C₂×C₂₃	1	1	yes	characteristic
481	#2994	C₂×C₂₃	1	2	yes	complemented
482	#2993	C₂×C₂₃	1	2	yes	complemented
483	#2992	C₂×C₂₃	1	2	yes	complemented
484	#2981	C₂×C₂₃	1	2	yes	complemented
485	#2979	C₂×C₂₃	1	1	yes	characteristic, complemented
486	#2978	C₂×C₂₃	1	1	yes	characteristic, complemented
487	#2978	C₂×C₂₃	1	2	yes	complemented
488	#2977	C₂×C₂₃	1	1	yes	characteristic, complemented
489	#2976	C₂×C₂₃	1	2	yes	complemented
490	#2969	C₂×C₂₃	1	2	yes	complemented
491	#2968	C₂×C₂₃	1	2	yes	complemented
492	#2967	C₂×C₂₃	1	2	yes	complemented
493	#2935	C₂×C₂₃	1	2	yes	complemented
494	#2933	C₂×C₂₃	1	2	yes	complemented
495	#2932	C₂×C₂₃	1	1	yes	characteristic, complemented
496	#2930	C₂×C₂₃	1	1	yes	characteristic, complemented
497	#2929	C₂×C₂₃	1	1	yes	characteristic, complemented
498	#2929	C₂×C₂₃	1	2	yes	complemented
499	C₂²×C₂₃	—	2	2	no	—
500	C₂²×C₂₃	—	2	1	no	—
501	C₂²×C₂₃	—	2	1	no	—
502	C₂²×C₂₃	—	2	2	no	—
503	C₂²×C₂₃	—	2	1	no	—
504	C₂²×C₂₃	—	2	2	no	—
505	C₂²×C₂₃	—	2	2	no	—
506	C₂²×C₂₃	—	2	2	no	—
507	C₂²×C₂₃	—	2	2	no	—
508	C₂²×C₂₃	—	2	2	no	—
509	C₂²×C₂₃	—	2	2	no	—
510	C₂²×C₂₃	—	2	2	no	—
511	C₂²×C₂₃	—	2	2	no	—
512	C₂²×C₂₃	—	2	2	no	—
513	C₂²×C₂₃	—	2	2	no	—
514	C₂²×C₂₃	—	4	4	no	—
515	C₂²×C₂₃	—	8	2	no	—
516	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
517	C₄×C₂₃	—	2	2	no	—
518	C₄×C₂₃	—	2	1	no	—
519	C₄×C₂₃	—	2	1	no	—
520	C₄×C₂₃	—	2	2	no	—
521	C₄×C₂₃	—	2	1	no	—
522	C₄×C₂₃	—	2	2	no	—
523	C₄×C₂₃	—	2	2	no	—
524	C₄×C₂₃	—	2	2	no	—
525	C₄×C₂₃	—	2	2	no	—
526	C₄×C₂₃	—	2	2	no	—
527	C₄×C₂₃	—	2	2	no	—
528	C₄×C₂₃	—	2	2	no	—
529	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
530	C₄×C₂₃	#585	1	1	yes	characteristic
531	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
532	C₂×#131	C₂²×C₂₃	1	2	yes	—
533	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic, complemented
534	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
535	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
536	#563	C₄×C₂₃	1	2	yes	—
537	#563	C₄×C₂₃	1	1	yes	characteristic
538	#562	C₄×C₂₃	1	2	yes	—
539	#562	C₄×C₂₃	1	2	yes	—
540	#562	C₄×C₂₃	1	2	yes	—
541	H(3,𝔽₄)	C₄×C₂₃	1	1	yes	characteristic
542	#560	C₄×C₂₃	1	2	yes	—
543	#560	C₄×C₂₃	1	1	yes	characteristic
544	#560	C₄×C₂₃	1	2	yes	—
545	#560	C₄×C₂₃	1	1	yes	characteristic
546	#532	C₂²×C₂₃	1	1	yes	characteristic
547	#532	C₂²×C₂₃	1	2	yes	—
548	#529	C₂²×C₂₃	1	2	yes	—
549	#529	C₂²×C₂₃	1	2	yes	—
550	#529	C₂²×C₂₃	1	2	yes	—
551	#525	C₂²×C₂₃	1	1	yes	characteristic
552	#525	C₂²×C₂₃	1	2	yes	—
553	#525	C₂²×C₂₃	1	1	yes	characteristic
554	#525	C₂²×C₂₃	1	2	yes	—
555	#446	C₂²×C₂₃	1	2	yes	complemented
556	#446	C₂²×C₂₃	1	2	yes	complemented
557	#446	C₂²×C₂₃	1	2	yes	complemented
558	C₈×Q₈	C₂²×C₂₃	1	2	yes	complemented
559	#436	C₂²×C₂₃	1	2	yes	—
560	#436	C₂²×C₂₃	1	2	yes	—
561	#436	C₂²×C₂₃	1	2	yes	—
562	#436	C₂²×C₂₃	1	2	yes	complemented
563	#436	C₂²×C₂₃	1	2	yes	complemented
564	#436	C₂²×C₂₃	1	2	yes	complemented
565	#436	C₂²×C₂₃	1	2	yes	complemented
566	#436	C₂²×C₂₃	1	2	yes	complemented
567	#436	C₂²×C₂₃	1	2	yes	complemented
568	#435	C₂²×C₂₃	1	2	yes	—
569	#435	C₂²×C₂₃	1	2	yes	—
570	#435	C₂²×C₂₃	1	2	yes	—
571	#435	C₂²×C₂₃	1	2	yes	—
572	#435	C₂²×C₂₃	1	2	yes	—
573	#435	C₂²×C₂₃	1	2	yes	—
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	#435	C₂²×C₂₃	1	2	yes	complemented
580	#435	C₂²×C₂₃	1	2	yes	complemented
581	#435	C₂²×C₂₃	1	2	yes	complemented
582	#435	C₂²×C₂₃	1	2	yes	complemented
583	#435	C₂²×C₂₃	1	2	yes	complemented
584	#435	C₂²×C₂₃	1	2	yes	complemented
585	#435	C₂²×C₂₃	1	2	yes	complemented
586	C₈×D₄	C₂²×C₂₃	1	2	yes	—
587	C₈×D₄	C₂²×C₂₃	1	2	yes	—
588	C₈×D₄	C₂²×C₂₃	1	2	yes	—
589	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
590	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
591	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
592	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
593	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
594	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
595	#433	C₂²×C₂₃	1	2	yes	complemented
596	#433	C₂²×C₂₃	1	2	yes	complemented
597	#433	C₂²×C₂₃	1	2	yes	complemented
598	#433	C₂²×C₂₃	1	2	yes	complemented
599	#433	C₂²×C₂₃	1	2	yes	complemented
600	#433	C₂²×C₂₃	1	2	yes	complemented
601	#432	C₂²×C₂₃	1	2	yes	complemented
602	#431	C₂²×C₂₃	1	2	yes	complemented
603	#431	C₂²×C₂₃	1	2	yes	complemented
604	#424	C₂²×C₂₃	1	2	yes	complemented
605	#424	C₂²×C₂₃	1	1	yes	characteristic, complemented
606	#424	C₂²×C₂₃	1	1	yes	characteristic, complemented
607	#424	C₂²×C₂₃	1	2	yes	complemented
608	#423	C₂²×C₂₃	1	1	yes	characteristic, complemented
609	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	complemented
610	#408	C₂²×C₂₃	1	2	yes	—
611	#408	C₂²×C₂₃	1	1	yes	characteristic
612	#408	C₂²×C₂₃	1	1	yes	characteristic
613	#408	C₂²×C₂₃	1	1	yes	characteristic
614	#408	C₂²×C₂₃	1	2	yes	—
615	#408	C₂²×C₂₃	1	2	yes	—
616	#408	C₂²×C₂₃	1	1	yes	characteristic, complemented
617	#408	C₂²×C₂₃	1	2	yes	complemented
618	#407	C₂²×C₂₃	1	2	yes	complemented
619	#407	C₂²×C₂₃	1	1	yes	characteristic, complemented
620	#407	C₂²×C₂₃	1	1	yes	characteristic, complemented
621	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	complemented
622	#405	C₂²×C₂₃	1	1	yes	characteristic, complemented
623	#405	C₂²×C₂₃	1	2	yes	complemented
624	#405	C₂²×C₂₃	1	1	yes	characteristic, complemented
625	#405	C₂²×C₂₃	1	2	yes	complemented
626	C₄×M₁₆	C₂²×C₂₃	1	2	yes	complemented
627	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic, complemented
628	C₂×C₂₃	—	4	1	no	—
629	C₂×C₂₃	—	4	2	no	—
630	C₂×C₂₃	—	4	2	no	—
631	C₂×C₂₃	—	4	1	no	—
632	C₂×C₂₃	—	4	1	no	—
633	C₂×C₂₃	—	4	2	no	—
634	C₂×C₂₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
635	C₂×C₂₃	#3573	1	2	yes	—
636	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
637	C₂×#41	C₂³×C₂₃	1	2	yes	—
638	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
639	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
640	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
641	#131	—	4	2	no	—
642	#131	—	4	4	no	—
643	#131	—	4	2	no	—
644	C₂×M₁₆	—	4	2	no	—
645	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
646	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
647	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
648	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
649	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
650	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
651	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
652	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
653	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
654	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
655	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
656	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
657	C₂²×C₈	—	4	2	no	—
658	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
659	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
660	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
661	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
662	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
663	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
664	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
665	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
666	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
667	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
668	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
669	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
670	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
671	C₄⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
672	#127	C₂×C₄×C₂₃	1	1	yes	characteristic
673	#127	C₂×C₄×C₂₃	1	2	yes	—
674	#126	C₂×C₄×C₂₃	1	2	yes	—
675	#126	C₂×C₄×C₂₃	1	2	yes	—
676	#126	C₂×C₄×C₂₃	1	2	yes	—
677	#126	C₂×C₄×C₂₃	1	2	yes	—
678	#126	C₂×C₄×C₂₃	1	2	yes	—
679	#126	C₂×C₄×C₂₃	1	2	yes	—
680	#125	C₂×C₄×C₂₃	1	2	yes	—
681	#125	C₂×C₄×C₂₃	1	2	yes	—
682	#125	C₂×C₄×C₂₃	1	2	yes	—
683	#124	C₂×C₄×C₂₃	1	2	yes	—
684	#124	C₂×C₄×C₂₃	1	2	yes	—
685	#124	C₂×C₄×C₂₃	1	2	yes	—
686	#124	C₂×C₄×C₂₃	1	1	yes	characteristic
687	#124	C₂×C₄×C₂₃	1	2	yes	—
688	#124	C₂×C₄×C₂₃	1	1	yes	characteristic
689	#124	C₂×C₄×C₂₃	1	2	yes	—
690	#123	C₂×C₄×C₂₃	1	1	yes	characteristic
691	#123	C₂×C₄×C₂₃	1	2	yes	—
692	#123	C₂×C₄×C₂₃	1	1	yes	characteristic
693	#123	C₂×C₄×C₂₃	1	2	yes	—
694	#123	C₂×C₄×C₂₃	1	1	yes	characteristic
695	#123	C₂×C₄×C₂₃	1	2	yes	—
696	#123	C₂×C₄×C₂₃	1	1	yes	characteristic
697	#123	C₂×C₄×C₂₃	1	2	yes	—
698	#123	C₂×C₄×C₂₃	1	2	yes	—
699	#123	C₂×C₄×C₂₃	1	2	yes	—
700	#123	C₂×C₄×C₂₃	1	2	yes	—
701	#123	C₂×C₄×C₂₃	1	2	yes	—
702	#123	C₂×C₄×C₂₃	1	2	yes	—
703	#123	C₂×C₄×C₂₃	1	2	yes	—
704	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
705	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
706	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
707	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
708	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
709	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
710	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
711	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
712	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
713	#121	C₂×C₄×C₂₃	1	2	yes	—
714	#121	C₂×C₄×C₂₃	1	2	yes	—
715	#121	C₂×C₄×C₂₃	1	2	yes	—
716	#121	C₂×C₄×C₂₃	1	2	yes	—
717	#121	C₂×C₄×C₂₃	1	2	yes	—
718	#121	C₂×C₄×C₂₃	1	2	yes	—
719	#121	C₂×C₄×C₂₃	1	2	yes	—
720	#121	C₂×C₄×C₂₃	1	2	yes	—
721	#121	C₂×C₄×C₂₃	1	2	yes	—
722	#121	C₂×C₄×C₂₃	1	2	yes	—
723	#121	C₂×C₄×C₂₃	1	2	yes	—
724	#121	C₂×C₄×C₂₃	1	2	yes	—
725	#121	C₂×C₄×C₂₃	1	2	yes	—
726	#121	C₂×C₄×C₂₃	1	2	yes	—
727	#121	C₂×C₄×C₂₃	1	2	yes	—
728	#120	C₂×C₄×C₂₃	1	1	yes	characteristic
729	#120	C₂×C₄×C₂₃	1	2	yes	—
730	#120	C₂×C₄×C₂₃	1	1	yes	characteristic
731	#120	C₂×C₄×C₂₃	1	2	yes	—
732	#120	C₂×C₄×C₂₃	1	1	yes	characteristic
733	#120	C₂×C₄×C₂₃	1	2	yes	—
734	#120	C₂×C₄×C₂₃	1	1	yes	characteristic
735	#120	C₂×C₄×C₂₃	1	2	yes	—
736	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
737	C₄×D₄	C₂³×C₂₃	1	2	yes	—
738	C₄×D₄	C₂³×C₂₃	1	2	yes	—
739	C₄×D₄	C₂³×C₂₃	1	2	yes	—
740	C₄×D₄	C₂³×C₂₃	1	2	yes	—
741	C₄×D₄	C₂³×C₂₃	1	2	yes	—
742	C₄×D₄	C₂³×C₂₃	1	2	yes	—
743	C₄×D₄	C₂³×C₂₃	1	2	yes	—
744	C₄×D₄	C₂³×C₂₃	1	2	yes	—
745	C₄×D₄	C₂³×C₂₃	1	2	yes	—
746	#117	C₂³×C₂₃	1	1	yes	characteristic
747	#117	C₂³×C₂₃	1	2	yes	—
748	#117	C₂³×C₂₃	1	1	yes	characteristic
749	#117	C₂³×C₂₃	1	2	yes	—
750	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
751	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
752	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
753	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
754	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
755	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
756	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
757	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
758	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
759	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
760	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
761	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
762	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
763	C₄⋊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	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
771	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
772	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
773	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
774	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
775	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
776	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
777	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
778	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
779	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
780	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
781	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
782	#97	C₂³×C₂₃	1	2	yes	—
783	#97	C₂³×C₂₃	1	2	yes	—
784	#97	C₂³×C₂₃	1	2	yes	—
785	#97	C₂³×C₂₃	1	2	yes	—
786	#97	C₂³×C₂₃	1	2	yes	—
787	#97	C₂³×C₂₃	1	2	yes	—
788	C₄×C₈	C₂³×C₂₃	1	2	yes	—
789	C₄×C₈	C₂³×C₂₃	1	2	yes	—
790	C₄×C₈	C₂³×C₂₃	1	2	yes	—
791	C₄×C₈	C₂³×C₂₃	1	2	yes	—
792	C₄×C₈	C₂³×C₂₃	1	2	yes	—
793	C₄×C₈	C₂³×C₂₃	1	2	yes	—
794	C₂₃	#60315	1	1	yes	characteristic, direct product factor, Sylow
795	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
796	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
797	#41	—	4	1	no	—
798	#41	—	4	2	no	—
799	#41	—	4	1	no	—
800	#41	—	4	2	no	—
801	#41	—	4	1	no	—
802	#41	—	4	1	no	—
803	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
804	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
805	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
806	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
807	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
808	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
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	2	yes	—
814	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
815	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
816	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
817	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
818	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
819	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
820	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
821	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
822	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
823	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
824	C₂²×C₄	—	4	1	no	—
825	C₂²×C₄	—	4	1	no	—
826	C₂²×C₄	—	4	1	no	—
827	C₂²×C₄	—	4	1	no	—
828	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
829	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
830	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
831	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
832	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
833	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
834	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
835	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
836	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
837	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
838	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
839	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
840	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
841	M₁₆	—	2	4	no	—
842	M₁₆	—	2	4	no	—
843	M₁₆	—	4	2	no	—
844	M₁₆	—	4	1	no	—
845	M₁₆	—	4	1	no	—
846	M₁₆	—	4	1	no	—
847	M₁₆	—	4	2	no	—
848	M₁₆	—	4	1	no	—
849	M₁₆	—	4	2	no	—
850	M₁₆	—	4	1	no	—
851	M₁₆	—	4	2	no	—
852	M₁₆	—	4	1	no	—
853	C₂×C₈	—	2	4	no	—
854	C₂×C₈	—	2	2	no	—
855	C₂×C₈	—	2	2	no	—
856	C₂×C₈	—	2	2	no	—
857	C₂×C₈	—	4	1	no	—
858	C₂×C₈	—	4	2	no	—
859	C₂×C₈	—	4	1	no	—
860	C₂×C₈	—	4	2	no	—
861	C₂×C₈	—	4	2	no	—
862	C₂×C₈	—	4	2	no	—
863	C₂×C₈	—	4	1	no	—
864	C₂×C₈	—	4	2	no	—
865	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
866	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
867	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
868	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
869	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
870	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
871	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
872	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
873	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
874	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
875	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
876	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
877	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
878	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
879	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
880	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
881	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
882	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
883	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
884	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
885	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
886	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
887	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
888	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
889	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
890	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
891	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
892	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
893	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
894	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
895	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
896	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
897	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
898	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
899	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
900	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
901	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
902	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
903	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
904	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
905	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
906	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
907	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
908	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
909	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
910	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
911	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
912	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
913	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
914	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
915	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
916	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
917	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
918	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
919	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
920	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
921	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
922	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
923	C₄²	C₂⁴×C₂₃	1	2	yes	—
924	C₄²	C₂⁴×C₂₃	1	2	yes	—
925	C₄²	C₂⁴×C₂₃	1	2	yes	—
926	C₂³	—	4	1	no	—
927	C₂³	—	4	2	no	—
928	C₂³	—	4	1	no	—
929	C₂³	—	4	2	no	—
930	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
931	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
932	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
933	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
934	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
935	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
936	Q₈	—	4	1	no	—
937	Q₈	—	4	2	no	—
938	Q₈	—	4	1	no	—
939	Q₈	—	4	2	no	—
940	D₄	—	4	1	no	—
941	D₄	—	4	1	no	—
942	D₄	—	4	2	no	—
943	D₄	—	4	2	no	—
944	D₄	—	4	1	no	—
945	D₄	—	4	2	no	—
946	D₄	—	4	1	no	—
947	D₄	—	4	2	no	—
948	D₄	—	4	2	no	—
949	D₄	—	4	2	no	—
950	D₄	—	4	2	no	—
951	D₄	—	4	2	no	—
952	D₄	—	4	2	no	—
953	D₄	—	4	2	no	—
954	D₄	—	4	2	no	—
955	D₄	—	4	2	no	—
956	D₄	—	4	2	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	1	no	—
960	C₂×C₄	—	2	1	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	1	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	4	1	no	—
970	C₂×C₄	—	4	2	no	—
971	C₂×C₄	—	4	2	no	—
972	C₂×C₄	—	4	1	no	—
973	C₂×C₄	—	4	2	no	—
974	C₂×C₄	—	4	2	no	—
975	C₂×C₄	—	4	2	no	—
976	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
977	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
978	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
979	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
980	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
981	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
982	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
983	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
984	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
985	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
986	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
987	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
988	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
989	C₈	—	2	2	no	—
990	C₈	—	2	1	no	—
991	C₈	—	2	1	no	—
992	C₈	—	2	1	no	—
993	C₈	—	2	2	no	—
994	C₈	—	2	2	no	—
995	C₈	—	2	2	no	—
996	C₈	—	2	2	no	—
997	C₈	—	2	2	no	—
998	C₈	C₂₃×H(5,𝔽₂)	1	2	yes	—
999	C₂²	—	2	2	no	—
1000	C₂²	—	2	1	no	—
1001	C₂²	—	2	1	no	—
1002	C₂²	—	2	2	no	—
1003	C₂²	—	2	1	no	—
1004	C₂²	—	2	2	no	—
1005	C₂²	—	2	2	no	—
1006	C₂²	—	2	2	no	—
1007	C₂²	—	2	2	no	—
1008	C₂²	—	2	2	no	—
1009	C₂²	—	2	2	no	—
1010	C₂²	—	2	2	no	—
1011	C₂²	—	2	2	no	—
1012	C₂²	—	2	2	no	—
1013	C₂²	—	2	2	no	—
1014	C₂²	—	4	4	no	—
1015	C₂²	—	8	2	no	—
1016	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
1017	C₄	—	2	2	no	—
1018	C₄	—	2	1	no	—
1019	C₄	—	2	1	no	—
1020	C₄	—	2	2	no	—
1021	C₄	—	2	1	no	—
1022	C₄	—	2	2	no	—
1023	C₄	—	2	2	no	—
1024	C₄	—	2	2	no	—
1025	C₄	—	2	2	no	—
1026	C₄	—	2	2	no	—
1027	C₄	—	2	2	no	—
1028	C₄	—	2	2	no	—
1029	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1030	C₄	C₂₃×#585	1	1	yes	characteristic
1031	C₂	—	4	2	no	—
1032	C₂	—	4	1	no	—
1033	C₂	—	4	1	no	—
1034	C₂	—	4	2	no	—
1035	C₂	—	4	1	no	—
1036	C₂	—	4	2	no	—
1037	C₂	C₄×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1038	C₂	C₂₃×#3573	1	2	yes	—

	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×#2994	C₂	semidirect
3. C₂₃×#2993	C₂	semidirect
4. C₂₃×#2992	C₂	semidirect
5. C₂₃×#2981	C₂	semidirect
6. C₂₃×#2979	C₂	semidirect
7. C₂₃×#2978	C₂	semidirect
8. C₂₃×#2978	C₂	semidirect
9. C₂₃×#2977	C₂	semidirect
10. C₂₃×#2976	C₂	semidirect
11. C₂₃×#2969	C₂	semidirect
12. C₂₃×#2968	C₂	semidirect
13. C₂₃×#2967	C₂	semidirect
14. C₂₃×#2935	C₂	semidirect
15. C₂₃×#2933	C₂	semidirect
16. C₂₃×#2932	C₂	semidirect
17. C₂₃×#2930	C₂	semidirect
18. C₂₃×#2929	C₂	semidirect
19. C₂₃×#2929	C₂	semidirect
22. C₂×C₂₃×#131	C₂²	semidirect
23. C₂²×M₁₆×C₂₃	C₂²	semidirect
24. C₂³×C₈×C₂₃	C₂²	semidirect
44. C₂₃×#446	C₂²	semidirect
45. C₂₃×#446	C₂²	semidirect
46. C₂₃×#446	C₂²	semidirect
47. C₈×Q₈×C₂₃	C₂²	semidirect
51. C₂₃×#436	C₂²	semidirect
52. C₂₃×#436	C₂²	semidirect
53. C₂₃×#436	C₂²	semidirect
54. C₂₃×#436	C₂²	semidirect
55. C₂₃×#436	C₂²	semidirect
56. C₂₃×#436	C₂²	semidirect
63. C₂₃×#435	C₂²	semidirect
64. C₂₃×#435	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
78. C₈×D₄×C₂₃	C₂²	semidirect
79. C₈×D₄×C₂₃	C₂²	semidirect
80. C₈×D₄×C₂₃	C₂²	semidirect
81. C₈×D₄×C₂₃	C₂²	semidirect
82. C₈×D₄×C₂₃	C₂²	semidirect
83. C₈×D₄×C₂₃	C₂²	semidirect
84. C₂₃×#433	C₂²	semidirect
85. C₂₃×#433	C₂²	semidirect
86. C₂₃×#433	C₂²	semidirect
87. C₂₃×#433	C₂²	semidirect
88. C₂₃×#433	C₂²	semidirect
89. C₂₃×#433	C₂²	semidirect
90. C₂₃×#432	C₂²	semidirect
91. C₂₃×#431	C₂²	semidirect
92. C₂₃×#431	C₂²	semidirect
93. C₂₃×#424	C₂²	semidirect
94. C₂₃×#424	C₂²	semidirect
95. C₂₃×#424	C₂²	semidirect
96. C₂₃×#424	C₂²	semidirect
97. C₂₃×#423	C₂²	semidirect
98. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
105. C₂₃×#408	C₂²	semidirect
106. C₂₃×#408	C₂²	semidirect
107. C₂₃×#407	C₂²	semidirect
108. C₂₃×#407	C₂²	semidirect
109. C₂₃×#407	C₂²	semidirect
110. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
111. C₂₃×#405	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×C₂₃×#97	C₂²	semidirect
406. #60315	C₂₃	direct (N × H)
481. #2994	C₂×C₂₃	semidirect
482. #2993	C₂×C₂₃	semidirect
483. #2992	C₂×C₂₃	semidirect
484. #2981	C₂×C₂₃	semidirect
485. #2979	C₂×C₂₃	semidirect
486. #2978	C₂×C₂₃	semidirect
487. #2978	C₂×C₂₃	semidirect
488. #2977	C₂×C₂₃	semidirect
489. #2976	C₂×C₂₃	semidirect
490. #2969	C₂×C₂₃	semidirect
491. #2968	C₂×C₂₃	semidirect
492. #2967	C₂×C₂₃	semidirect
493. #2935	C₂×C₂₃	semidirect
494. #2933	C₂×C₂₃	semidirect
495. #2932	C₂×C₂₃	semidirect
496. #2930	C₂×C₂₃	semidirect
497. #2929	C₂×C₂₃	semidirect
498. #2929	C₂×C₂₃	semidirect
533. C₂×#131	C₂²×C₂₃	semidirect
534. C₂²×M₁₆	C₂²×C₂₃	semidirect
535. C₂³×C₈	C₂²×C₂₃	semidirect
555. #446	C₂²×C₂₃	semidirect
556. #446	C₂²×C₂₃	semidirect
557. #446	C₂²×C₂₃	semidirect
558. C₈×Q₈	C₂²×C₂₃	semidirect
562. #436	C₂²×C₂₃	semidirect
563. #436	C₂²×C₂₃	semidirect
564. #436	C₂²×C₂₃	semidirect
565. #436	C₂²×C₂₃	semidirect
566. #436	C₂²×C₂₃	semidirect
567. #436	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
579. #435	C₂²×C₂₃	semidirect
580. #435	C₂²×C₂₃	semidirect
581. #435	C₂²×C₂₃	semidirect
582. #435	C₂²×C₂₃	semidirect
583. #435	C₂²×C₂₃	semidirect
584. #435	C₂²×C₂₃	semidirect
585. #435	C₂²×C₂₃	semidirect
589. C₈×D₄	C₂²×C₂₃	semidirect
590. C₈×D₄	C₂²×C₂₃	semidirect
591. C₈×D₄	C₂²×C₂₃	semidirect
592. C₈×D₄	C₂²×C₂₃	semidirect
593. C₈×D₄	C₂²×C₂₃	semidirect
594. C₈×D₄	C₂²×C₂₃	semidirect
595. #433	C₂²×C₂₃	semidirect
596. #433	C₂²×C₂₃	semidirect
597. #433	C₂²×C₂₃	semidirect
598. #433	C₂²×C₂₃	semidirect
599. #433	C₂²×C₂₃	semidirect
600. #433	C₂²×C₂₃	semidirect
601. #432	C₂²×C₂₃	semidirect
602. #431	C₂²×C₂₃	semidirect
603. #431	C₂²×C₂₃	semidirect
604. #424	C₂²×C₂₃	semidirect
605. #424	C₂²×C₂₃	semidirect
606. #424	C₂²×C₂₃	semidirect
607. #424	C₂²×C₂₃	semidirect
608. #423	C₂²×C₂₃	semidirect
609. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
616. #408	C₂²×C₂₃	semidirect
617. #408	C₂²×C₂₃	semidirect
618. #407	C₂²×C₂₃	semidirect
619. #407	C₂²×C₂₃	semidirect
620. #407	C₂²×C₂₃	semidirect
621. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
622. #405	C₂²×C₂₃	semidirect
623. #405	C₂²×C₂₃	semidirect
624. #405	C₂²×C₂₃	semidirect
625. #405	C₂²×C₂₃	semidirect
626. C₄×M₁₆	C₂²×C₂₃	semidirect
627. C₂×#97	C₂²×C₂₃	semidirect
794. C₂₃	#60315	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×#2994	2
C₂₃×#2993	2
C₂₃×#2992	2
C₂₃×#2981	2
C₂₃×#2979	2
C₂₃×#2978	2
C₂₃×#2977	2
C₂₃×#2976	2
C₂₃×#2969	2
C₂₃×#2968	2
C₂₃×#2967	2
C₂₃×#2935	2
C₂₃×#2933	2
C₂₃×#2932	2
C₂₃×#2930	2
C₂₃×#2929	2
#60315	23

Subgroups — C23×#60315 #19207941

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60315 #19207941