Subgroups — C₂₃×#61063 #19208689

Order 5888.

2818 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#576	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#575	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3488	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3275	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3274	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3271	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3264	C₂	1	4	yes	maximal, complemented
8	C₂₃×#3155	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#3060	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₂₃×#469	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3045	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3012	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3006	C₂	1	2	yes	maximal, complemented
14	C₂₃×#2952	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2930	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	2	yes	complemented
17	C₂²×#41×C₂₃	C₂²	1	2	yes	complemented
18	C₂₃×#576	—	2	8	no	—
19	C₂₃×#575	—	2	8	no	—
20	C₂×C₂₃×#137	C₂²	1	2	yes	complemented
21	C₂×C₂₃×#137	C₂²	1	2	yes	complemented
22	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
23	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
24	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
25	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
26	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
27	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×#135	C₂²	1	2	yes	complemented
29	C₂×C₂₃×#135	C₂²	1	2	yes	complemented
30	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic, complemented
31	C₂²×D₈×C₂₃	C₂²	1	2	yes	complemented
32	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic, complemented
34	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
35	C₂₃×#550	C₂²	1	4	yes	complemented
36	C₂₃×#548	C₂²	1	4	yes	complemented
37	C₂₃×#546	—	2	4	no	—
38	C₂₃×#546	C₂²	1	4	yes	complemented
39	D₄²×C₂₃	—	2	4	no	—
40	D₄²×C₂₃	C₂²	1	4	yes	complemented
41	C₂₃×#537	—	2	2	no	—
42	C₂₃×#537	C₂²	1	2	yes	complemented
43	C₂₃×#535	—	2	2	no	—
44	C₂₃×#535	C₂²	1	2	yes	complemented
45	C₂₃×#525	—	2	2	no	—
46	C₂₃×#525	C₂²	1	1	yes	characteristic
47	C₂×C₂₃×#121	—	2	2	no	—
48	C₂×C₂₃×#121	C₂²	1	2	yes	complemented
49	C₂₃×#520	C₂²	1	2	yes	complemented
50	C₂₃×#496	C₂²	1	4	yes	complemented
51	C₂₃×#495	C₂²	1	2	yes	complemented
52	C₂₃×#493	C₂²	1	2	yes	complemented
53	C₂₃×#470	C₂²	1	2	yes	complemented
54	C₂₃×#469	C₂²	1	4	yes	complemented
55	C₂₃×#469	C₂²	1	2	yes	complemented
56	C₂₃×#469	C₂²	1	4	yes	complemented
57	C₂₃×#465	C₂²	1	4	yes	complemented
58	C₂₃×#464	C₂²	1	4	yes	complemented
59	C₂₃×#463	C₂²	1	4	yes	complemented
60	C₂₃×#460	C₂²	1	4	yes	complemented
61	C₂₃×#459	C₂²	1	4	yes	complemented
62	C₂₃×#452	C₂²	1	4	yes	complemented
63	C₂₃×#450	C₂²	1	4	yes	complemented
64	C₂₃×#449	C₂²	1	4	yes	complemented
65	C₂₃×#449	C₂²	1	4	yes	complemented
66	C₂₃×#449	C₂²	1	4	yes	complemented
67	C₂₃×#448	C₂²	1	4	yes	complemented
68	C₂₃×#447	C₂²	1	4	yes	complemented
69	C₂₃×#447	C₂²	1	4	yes	complemented
70	C₂₃×#442	C₂²	1	2	yes	complemented
71	C₂₃×#441	C₂²	1	2	yes	complemented
72	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	complemented
73	C₂₃×#436	C₂²	1	4	yes	complemented
74	C₂₃×#435	C₂²	1	4	yes	complemented
75	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic, complemented
76	C₂₃×#424	C₂²	1	1	yes	characteristic, complemented
77	C₂₃×#417	C₂²	1	2	yes	complemented
78	C₂₃×#417	C₂²	1	2	yes	complemented
79	C₂×C₂₃×#102	C₂²	1	2	yes	complemented
80	C₂₃×#408	C₂²	1	1	yes	characteristic, complemented
81	C₂₃×#407	C₂²	1	1	yes	characteristic, complemented
82	C₂₃×#405	C₂²	1	1	yes	characteristic, complemented
83	C₂₃×H(5,𝔽₂)	—	2	8	no	—
84	C₂₃×H(5,𝔽₂)	—	4	4	no	—
85	C₂×#41×C₂₃	—	2	2	no	—
86	C₂×#41×C₂₃	—	2	2	no	—
87	C₂×#41×C₂₃	—	2	2	no	—
88	C₂×#41×C₂₃	—	2	8	no	—
89	C₂×#41×C₂₃	—	4	4	no	—
90	C₂×#41×C₂₃	C₂³	1	2	yes	—
91	C₂×#41×C₂₃	C₂³	1	4	yes	—
92	C₂×#41×C₂₃	C₂³	1	2	yes	—
93	C₂×#41×C₂₃	C₂³	1	2	yes	—
94	C₂×#41×C₂₃	C₂³	1	2	yes	—
95	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
97	C₂²×D₄×C₂₃	—	2	2	no	—
98	C₂²×D₄×C₂₃	—	2	2	no	—
99	C₂²×D₄×C₂₃	—	2	2	no	—
100	C₂²×D₄×C₂₃	—	2	4	no	—
101	C₂²×D₄×C₂₃	—	2	4	no	—
102	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
103	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
104	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
105	C₂³×C₄×C₂₃	—	2	2	no	—
106	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
107	C₂₃×#137	—	2	8	no	—
108	C₂₃×#137	—	2	8	no	—
109	C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
110	C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
111	C₂₃×AGL(1,ℤ/8)	—	2	16	no	—
112	C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
113	C₂₃×AGL(1,ℤ/8)	—	4	4	no	—
114	C₂₃×#135	—	2	8	no	—
115	C₂₃×#135	—	2	8	no	—
116	C₂₃×#135	—	2	4	no	—
117	C₂₃×#135	D₄	1	8	yes	complemented
118	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
119	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
120	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
121	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
122	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
123	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
124	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
125	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
126	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
127	C₂×D₈×C₂₃	—	2	8	no	—
128	C₂×D₈×C₂₃	—	2	4	no	—
129	C₂×D₈×C₂₃	C₂³	1	2	yes	—
130	C₂×D₈×C₂₃	C₂³	1	4	yes	—
131	C₂×D₈×C₂₃	C₂³	1	2	yes	—
132	C₂×D₈×C₂₃	C₂³	1	2	yes	—
133	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
134	C₂×D₈×C₂₃	C₂³	1	4	yes	—
135	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
136	C₂₃×#131	—	2	4	no	—
137	C₂×M₁₆×C₂₃	—	2	4	no	—
138	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
139	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
140	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
141	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
142	C₂×M₁₆×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	C₂₃×#127	—	2	4	no	—
147	C₂₃×#127	C₂³	1	4	yes	—
148	C₂₃×#124	—	2	4	no	—
149	C₂₃×#124	C₂³	1	4	yes	—
150	C₂₃×#123	—	2	4	no	—
151	C₂₃×#123	D₄	1	2	yes	—
152	C₂₃×C₂²⋊Q₈	—	2	2	no	—
153	C₂₃×C₂²⋊Q₈	—	2	4	no	—
154	C₂₃×C₂²⋊Q₈	D₄	1	2	yes	—
155	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
156	C₂₃×#121	—	2	4	no	—
157	C₂₃×#121	—	2	2	no	—
158	C₂₃×#121	—	2	4	no	—
159	C₂₃×#121	—	2	2	no	—
160	C₂₃×#121	—	2	2	no	—
161	C₂₃×#121	—	2	2	no	—
162	C₂₃×#121	—	2	2	no	—
163	C₂₃×#121	—	2	4	no	—
164	C₂₃×#121	—	2	4	no	—
165	C₂₃×#121	—	2	4	no	—
166	C₂₃×#121	—	2	4	no	—
167	C₂₃×#121	D₄	1	2	yes	—
168	C₂₃×#121	C₂³	1	4	yes	—
169	C₂₃×#121	C₂³	1	4	yes	—
170	C₂₃×#121	C₂³	1	4	yes	—
171	C₂₃×#120	—	2	4	no	—
172	C₂₃×#120	—	2	4	no	—
173	C₂₃×#120	—	2	4	no	—
174	C₂₃×#120	—	2	4	no	—
175	C₂₃×#120	D₄	1	2	yes	—
176	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
177	C₄×D₄×C₂₃	—	2	4	no	—
178	C₄×D₄×C₂₃	—	2	4	no	—
179	C₄×D₄×C₂₃	—	2	4	no	—
180	C₄×D₄×C₂₃	C₂³	1	4	yes	—
181	C₄×D₄×C₂₃	C₂³	1	4	yes	—
182	C₂₃×#117	—	2	2	no	—
183	C₂₃×#117	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
185	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
187	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
188	C₂₃×#106	C₂³	1	2	yes	—
189	C₂₃×#106	C₂³	1	2	yes	—
190	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
191	C₂₃×#103	C₂³	1	4	yes	—
192	C₂₃×#103	C₂³	1	4	yes	—
193	C₂₃×#102	C₂³	1	4	yes	—
194	C₂₃×#102	C₂³	1	4	yes	—
195	C₂₃×#102	C₂³	1	4	yes	—
196	C₂₃×#102	C₂³	1	4	yes	—
197	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
198	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
199	C₂₃×#97	C₂³	1	2	yes	—
200	C₄×C₈×C₂₃	C₂³	1	2	yes	—
201	C₂⁴×C₂₃	—	2	2	no	—
202	C₂⁴×C₂₃	—	2	4	no	—
203	C₂⁴×C₂₃	—	2	2	no	—
204	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
205	#41×C₂₃	—	2	2	no	—
206	#41×C₂₃	—	2	4	no	—
207	#41×C₂₃	—	2	2	no	—
208	#41×C₂₃	—	2	8	no	—
209	#41×C₂₃	—	2	4	no	—
210	#41×C₂₃	—	2	4	no	—
211	#41×C₂₃	—	2	4	no	—
212	#41×C₂₃	—	2	4	no	—
213	#41×C₂₃	—	4	8	no	—
214	#41×C₂₃	—	4	2	no	—
215	#41×C₂₃	—	4	2	no	—
216	#41×C₂₃	—	4	4	no	—
217	#41×C₂₃	—	4	8	no	—
218	#41×C₂₃	—	4	8	no	—
219	#41×C₂₃	C₂×D₄	1	8	yes	complemented
220	C₂×Q₈×C₂₃	—	2	2	no	—
221	C₂×Q₈×C₂₃	—	2	4	no	—
222	C₂×Q₈×C₂₃	—	4	2	no	—
223	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
224	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
225	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
226	C₂×D₄×C₂₃	—	2	2	no	—
227	C₂×D₄×C₂₃	—	2	8	no	—
228	C₂×D₄×C₂₃	—	2	4	no	—
229	C₂×D₄×C₂₃	—	2	4	no	—
230	C₂×D₄×C₂₃	—	2	2	no	—
231	C₂×D₄×C₂₃	—	2	2	no	—
232	C₂×D₄×C₂₃	—	2	4	no	—
233	C₂×D₄×C₂₃	—	2	2	no	—
234	C₂×D₄×C₂₃	—	2	4	no	—
235	C₂×D₄×C₂₃	—	2	4	no	—
236	C₂×D₄×C₂₃	—	2	4	no	—
237	C₂×D₄×C₂₃	—	2	2	no	—
238	C₂×D₄×C₂₃	—	2	4	no	—
239	C₂×D₄×C₂₃	—	2	2	no	—
240	C₂×D₄×C₂₃	—	2	4	no	—
241	C₂×D₄×C₂₃	—	2	4	no	—
242	C₂×D₄×C₂₃	—	2	4	no	—
243	C₂×D₄×C₂₃	—	4	2	no	—
244	C₂×D₄×C₂₃	—	4	4	no	—
245	C₂×D₄×C₂₃	—	4	8	no	—
246	C₂×D₄×C₂₃	—	4	16	no	—
247	C₂×D₄×C₂₃	—	4	8	no	—
248	C₂×D₄×C₂₃	—	8	8	no	—
249	C₂×D₄×C₂₃	—	8	4	no	—
250	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
251	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
252	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
253	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
254	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
255	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₂₃	—	2	2	no	—
257	C₂²×C₄×C₂₃	—	2	2	no	—
258	C₂²×C₄×C₂₃	—	2	2	no	—
259	C₂²×C₄×C₂₃	—	2	2	no	—
260	C₂²×C₄×C₂₃	—	2	2	no	—
261	C₂²×C₄×C₂₃	—	2	2	no	—
262	C₂²×C₄×C₂₃	—	2	2	no	—
263	C₂²×C₄×C₂₃	—	2	4	no	—
264	C₂²×C₄×C₂₃	—	2	2	no	—
265	C₂²×C₄×C₂₃	—	2	4	no	—
266	C₂²×C₄×C₂₃	—	4	8	no	—
267	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
269	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
272	Q₁₆×C₂₃	—	2	4	no	—
273	Q₁₆×C₂₃	—	2	2	no	—
274	Q₁₆×C₂₃	C₂×D₄	1	4	yes	complemented
275	SD₁₆×C₂₃	—	2	8	no	—
276	SD₁₆×C₂₃	—	2	4	no	—
277	SD₁₆×C₂₃	—	2	4	no	—
278	SD₁₆×C₂₃	—	2	4	no	—
279	SD₁₆×C₂₃	—	4	4	no	—
280	SD₁₆×C₂₃	C₂×D₄	1	8	yes	complemented
281	D₈×C₂₃	—	2	8	no	—
282	D₈×C₂₃	—	2	4	no	—
283	D₈×C₂₃	—	2	4	no	—
284	D₈×C₂₃	—	2	4	no	—
285	D₈×C₂₃	—	2	2	no	—
286	D₈×C₂₃	—	4	4	no	—
287	D₈×C₂₃	C₂×D₄	1	4	yes	complemented
288	M₁₆×C₂₃	—	2	2	no	—
289	M₁₆×C₂₃	—	2	2	no	—
290	M₁₆×C₂₃	—	2	4	no	—
291	M₁₆×C₂₃	—	2	4	no	—
292	M₁₆×C₂₃	—	2	4	no	—
293	C₂×C₈×C₂₃	—	2	2	no	—
294	C₂×C₈×C₂₃	—	2	4	no	—
295	C₂×C₈×C₂₃	C₂×D₄	1	4	yes	complemented
296	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
297	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
298	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
299	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
300	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
301	C₄⋊C₄×C₂₃	—	2	2	no	—
302	C₄⋊C₄×C₂₃	—	2	4	no	—
303	C₄⋊C₄×C₂₃	—	2	4	no	—
304	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
305	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
306	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
307	C₂²⋊C₄×C₂₃	—	2	4	no	—
308	C₂²⋊C₄×C₂₃	—	2	4	no	—
309	C₂²⋊C₄×C₂₃	—	2	4	no	—
310	C₂²⋊C₄×C₂₃	—	2	4	no	—
311	C₂²⋊C₄×C₂₃	—	2	4	no	—
312	C₂²⋊C₄×C₂₃	—	2	4	no	—
313	C₂²⋊C₄×C₂₃	—	2	4	no	—
314	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
315	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
316	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
317	C₄²×C₂₃	—	2	4	no	—
318	C₄²×C₂₃	C₂⁴	1	2	yes	—
319	#61063	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
320	C₂³×C₂₃	—	2	2	no	—
321	C₂³×C₂₃	—	2	2	no	—
322	C₂³×C₂₃	—	2	4	no	—
323	C₂³×C₂₃	—	2	2	no	—
324	C₂³×C₂₃	—	4	2	no	—
325	C₂³×C₂₃	—	4	4	no	—
326	C₂³×C₂₃	—	4	8	no	—
327	C₂³×C₂₃	—	4	4	no	—
328	C₂³×C₂₃	—	4	4	no	—
329	C₂³×C₂₃	—	8	2	no	—
330	C₂³×C₂₃	—	8	2	no	—
331	C₂³×C₂₃	—	8	4	no	—
332	C₂³×C₂₃	—	8	2	no	—
333	C₂³×C₂₃	—	8	4	no	—
334	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
335	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
336	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
337	Q₈×C₂₃	—	2	2	no	—
338	Q₈×C₂₃	—	2	2	no	—
339	Q₈×C₂₃	—	2	2	no	—
340	Q₈×C₂₃	—	2	2	no	—
341	Q₈×C₂₃	—	4	4	no	—
342	Q₈×C₂₃	C₂²×D₄	1	4	yes	—
343	D₄×C₂₃	—	2	8	no	—
344	D₄×C₂₃	—	2	4	no	—
345	D₄×C₂₃	—	2	2	no	—
346	D₄×C₂₃	—	2	4	no	—
347	D₄×C₂₃	—	2	2	no	—
348	D₄×C₂₃	—	2	2	no	—
349	D₄×C₂₃	—	2	2	no	—
350	D₄×C₂₃	—	2	4	no	—
351	D₄×C₂₃	—	4	4	no	—
352	D₄×C₂₃	—	4	8	no	—
353	D₄×C₂₃	—	4	4	no	—
354	D₄×C₂₃	—	4	8	no	—
355	D₄×C₂₃	—	4	4	no	—
356	D₄×C₂₃	—	4	4	no	—
357	D₄×C₂₃	—	4	8	no	—
358	D₄×C₂₃	—	4	4	no	—
359	D₄×C₂₃	—	4	4	no	—
360	D₄×C₂₃	—	8	4	no	—
361	D₄×C₂₃	—	8	4	no	—
362	D₄×C₂₃	—	8	4	no	—
363	D₄×C₂₃	—	8	4	no	—
364	D₄×C₂₃	C₂²×D₄	1	4	yes	—
365	C₂×C₄×C₂₃	—	2	2	no	—
366	C₂×C₄×C₂₃	—	2	2	no	—
367	C₂×C₄×C₂₃	—	2	4	no	—
368	C₂×C₄×C₂₃	—	2	8	no	—
369	C₂×C₄×C₂₃	—	2	2	no	—
370	C₂×C₄×C₂₃	—	2	2	no	—
371	C₂×C₄×C₂₃	—	2	2	no	—
372	C₂×C₄×C₂₃	—	2	2	no	—
373	C₂×C₄×C₂₃	—	2	4	no	—
374	C₂×C₄×C₂₃	—	2	2	no	—
375	C₂×C₄×C₂₃	—	4	4	no	—
376	C₂×C₄×C₂₃	—	4	8	no	—
377	C₂×C₄×C₂₃	—	4	4	no	—
378	C₂×C₄×C₂₃	—	4	4	no	—
379	C₂×C₄×C₂₃	—	4	4	no	—
380	C₂×C₄×C₂₃	—	8	4	no	—
381	C₂×C₄×C₂₃	—	8	2	no	—
382	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
383	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
384	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
385	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
387	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
388	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
389	C₈×C₂₃	—	2	2	no	—
390	C₈×C₂₃	—	2	2	no	—
391	C₈×C₂₃	—	2	2	no	—
392	C₈×C₂₃	C₂²×D₄	1	2	yes	—
393	C₈×C₂₃	C₂²×D₄	1	2	yes	—
394	C₂×#576	C₂×C₂₃	1	1	yes	characteristic, complemented
395	C₂×#575	C₂×C₂₃	1	1	yes	characteristic, complemented
396	#3488	C₂×C₂₃	1	2	yes	complemented
397	#3275	C₂×C₂₃	1	4	yes	complemented
398	#3274	C₂×C₂₃	1	4	yes	complemented
399	#3271	C₂×C₂₃	1	4	yes	complemented
400	#3264	C₂×C₂₃	1	4	yes	complemented
401	#3155	C₂×C₂₃	1	1	yes	characteristic, complemented
402	#3060	C₂×C₂₃	1	1	yes	characteristic, complemented
403	C₂×#469	C₂×C₂₃	1	1	yes	characteristic, complemented
404	#3045	C₂×C₂₃	1	2	yes	complemented
405	#3012	C₂×C₂₃	1	2	yes	complemented
406	#3006	C₂×C₂₃	1	2	yes	complemented
407	#2952	C₂×C₂₃	1	1	yes	characteristic, complemented
408	#2930	C₂×C₂₃	1	1	yes	characteristic, complemented
409	C₂²×C₂₃	—	2	2	no	—
410	C₂²×C₂₃	—	2	2	no	—
411	C₂²×C₂₃	—	2	4	no	—
412	C₂²×C₂₃	—	2	2	no	—
413	C₂²×C₂₃	—	2	2	no	—
414	C₂²×C₂₃	—	2	4	no	—
415	C₂²×C₂₃	—	2	2	no	—
416	C₂²×C₂₃	—	4	2	no	—
417	C₂²×C₂₃	—	4	2	no	—
418	C₂²×C₂₃	—	4	4	no	—
419	C₂²×C₂₃	—	4	2	no	—
420	C₂²×C₂₃	—	4	2	no	—
421	C₂²×C₂₃	—	4	4	no	—
422	C₂²×C₂₃	—	4	2	no	—
423	C₂²×C₂₃	—	4	4	no	—
424	C₂²×C₂₃	—	8	2	no	—
425	C₂²×C₂₃	—	8	8	no	—
426	C₂²×C₂₃	—	16	4	no	—
427	C₂²×C₂₃	—	16	8	no	—
428	C₂²×C₂₃	D₄²	1	2	yes	—
429	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
430	C₄×C₂₃	—	2	4	no	—
431	C₄×C₂₃	—	2	2	no	—
432	C₄×C₂₃	—	2	4	no	—
433	C₄×C₂₃	—	2	2	no	—
434	C₄×C₂₃	—	4	4	no	—
435	C₄×C₂₃	—	4	2	no	—
436	C₄×C₂₃	D₄²	1	2	yes	—
437	C₄×C₂₃	C₂³×D₄	1	1	yes	characteristic
438	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
439	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	2	yes	complemented
440	C₂²×#41	C₂²×C₂₃	1	2	yes	complemented
441	#576	—	2	8	no	—
442	#575	—	2	8	no	—
443	C₂×#137	C₂²×C₂₃	1	2	yes	complemented
444	C₂×#137	C₂²×C₂₃	1	2	yes	complemented
445	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	complemented
446	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	complemented
447	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	complemented
448	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	4	yes	complemented
449	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	complemented
450	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic
451	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic, complemented
452	C₂×#135	C₂²×C₂₃	1	2	yes	complemented
453	C₂×#135	C₂²×C₂₃	1	2	yes	complemented
454	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
455	C₂²×D₈	C₂²×C₂₃	1	2	yes	complemented
456	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic, complemented
457	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
458	#550	C₂²×C₂₃	1	4	yes	complemented
459	#548	C₂²×C₂₃	1	4	yes	complemented
460	#546	—	2	4	no	—
461	#546	C₂²×C₂₃	1	4	yes	complemented
462	D₄²	—	2	4	no	—
463	D₄²	C₂²×C₂₃	1	4	yes	complemented
464	#537	—	2	2	no	—
465	#537	C₂²×C₂₃	1	2	yes	complemented
466	#535	—	2	2	no	—
467	#535	C₂²×C₂₃	1	2	yes	complemented
468	#525	—	2	2	no	—
469	#525	C₂²×C₂₃	1	1	yes	characteristic
470	C₂×#121	—	2	2	no	—
471	C₂×#121	C₂²×C₂₃	1	2	yes	complemented
472	#520	C₂²×C₂₃	1	2	yes	complemented
473	#496	C₂²×C₂₃	1	4	yes	complemented
474	#495	C₂²×C₂₃	1	2	yes	complemented
475	#493	C₂²×C₂₃	1	2	yes	complemented
476	#470	C₂²×C₂₃	1	2	yes	complemented
477	#469	C₂²×C₂₃	1	4	yes	complemented
478	#469	C₂²×C₂₃	1	2	yes	complemented
479	#469	C₂²×C₂₃	1	4	yes	complemented
480	#465	C₂²×C₂₃	1	4	yes	complemented
481	#464	C₂²×C₂₃	1	4	yes	complemented
482	#463	C₂²×C₂₃	1	4	yes	complemented
483	#460	C₂²×C₂₃	1	4	yes	complemented
484	#459	C₂²×C₂₃	1	4	yes	complemented
485	#452	C₂²×C₂₃	1	4	yes	complemented
486	#450	C₂²×C₂₃	1	4	yes	complemented
487	#449	C₂²×C₂₃	1	4	yes	complemented
488	#449	C₂²×C₂₃	1	4	yes	complemented
489	#449	C₂²×C₂₃	1	4	yes	complemented
490	#448	C₂²×C₂₃	1	4	yes	complemented
491	#447	C₂²×C₂₃	1	4	yes	complemented
492	#447	C₂²×C₂₃	1	4	yes	complemented
493	#442	C₂²×C₂₃	1	2	yes	complemented
494	#441	C₂²×C₂₃	1	2	yes	complemented
495	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
496	#436	C₂²×C₂₃	1	4	yes	complemented
497	#435	C₂²×C₂₃	1	4	yes	complemented
498	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic, complemented
499	#424	C₂²×C₂₃	1	1	yes	characteristic, complemented
500	#417	C₂²×C₂₃	1	2	yes	complemented
501	#417	C₂²×C₂₃	1	2	yes	complemented
502	C₂×#102	C₂²×C₂₃	1	2	yes	complemented
503	#408	C₂²×C₂₃	1	1	yes	characteristic, complemented
504	#407	C₂²×C₂₃	1	1	yes	characteristic, complemented
505	#405	C₂²×C₂₃	1	1	yes	characteristic, complemented
506	C₂×C₂₃	—	2	2	no	—
507	C₂×C₂₃	—	4	2	no	—
508	C₂×C₂₃	—	4	2	no	—
509	C₂×C₂₃	—	4	4	no	—
510	C₂×C₂₃	—	8	2	no	—
511	C₂×C₂₃	—	8	4	no	—
512	C₂×C₂₃	C₂×D₄²	1	1	yes	characteristic
513	C₂×C₂₃	#3585	1	2	yes	—
514	H(5,𝔽₂)	—	2	8	no	—
515	H(5,𝔽₂)	—	4	4	no	—
516	C₂×#41	—	2	2	no	—
517	C₂×#41	—	2	2	no	—
518	C₂×#41	—	2	2	no	—
519	C₂×#41	—	2	8	no	—
520	C₂×#41	—	4	4	no	—
521	C₂×#41	C₂³×C₂₃	1	2	yes	—
522	C₂×#41	C₂³×C₂₃	1	2	yes	—
523	C₂×#41	C₂³×C₂₃	1	4	yes	—
524	C₂×#41	C₂³×C₂₃	1	2	yes	—
525	C₂×#41	C₂³×C₂₃	1	2	yes	—
526	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
527	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
528	C₂²×D₄	—	2	2	no	—
529	C₂²×D₄	—	2	2	no	—
530	C₂²×D₄	—	2	2	no	—
531	C₂²×D₄	—	2	4	no	—
532	C₂²×D₄	—	2	4	no	—
533	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
534	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
535	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
536	C₂³×C₄	—	2	2	no	—
537	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
538	#137	—	2	8	no	—
539	#137	—	2	8	no	—
540	AGL(1,ℤ/8)	—	2	8	no	—
541	AGL(1,ℤ/8)	—	2	8	no	—
542	AGL(1,ℤ/8)	—	2	16	no	—
543	AGL(1,ℤ/8)	—	2	8	no	—
544	AGL(1,ℤ/8)	—	4	4	no	—
545	#135	—	2	8	no	—
546	#135	—	2	8	no	—
547	#135	—	2	4	no	—
548	#135	D₄×C₂₃	1	8	yes	complemented
549	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
550	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
551	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
552	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
553	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
554	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
555	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
556	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
557	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
558	C₂×D₈	—	2	8	no	—
559	C₂×D₈	—	2	4	no	—
560	C₂×D₈	C₂³×C₂₃	1	2	yes	—
561	C₂×D₈	C₂³×C₂₃	1	4	yes	—
562	C₂×D₈	C₂³×C₂₃	1	2	yes	—
563	C₂×D₈	C₂³×C₂₃	1	2	yes	—
564	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
565	C₂×D₈	C₂³×C₂₃	1	4	yes	—
566	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
567	#131	—	2	4	no	—
568	C₂×M₁₆	—	2	4	no	—
569	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
570	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
571	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
572	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
573	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
574	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
575	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
576	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
577	#127	—	2	4	no	—
578	#127	C₂³×C₂₃	1	4	yes	—
579	#124	—	2	4	no	—
580	#124	C₂³×C₂₃	1	4	yes	—
581	#123	—	2	4	no	—
582	#123	D₄×C₂₃	1	2	yes	—
583	C₂²⋊Q₈	—	2	2	no	—
584	C₂²⋊Q₈	—	2	4	no	—
585	C₂²⋊Q₈	D₄×C₂₃	1	2	yes	—
586	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
587	#121	—	2	2	no	—
588	#121	—	2	4	no	—
589	#121	—	2	4	no	—
590	#121	—	2	2	no	—
591	#121	—	2	2	no	—
592	#121	—	2	2	no	—
593	#121	—	2	2	no	—
594	#121	—	2	4	no	—
595	#121	—	2	4	no	—
596	#121	—	2	4	no	—
597	#121	—	2	4	no	—
598	#121	D₄×C₂₃	1	2	yes	—
599	#121	C₂³×C₂₃	1	4	yes	—
600	#121	C₂³×C₂₃	1	4	yes	—
601	#121	C₂³×C₂₃	1	4	yes	—
602	#120	—	2	4	no	—
603	#120	—	2	4	no	—
604	#120	—	2	4	no	—
605	#120	—	2	4	no	—
606	#120	D₄×C₂₃	1	2	yes	—
607	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
608	C₄×D₄	—	2	4	no	—
609	C₄×D₄	—	2	4	no	—
610	C₄×D₄	—	2	4	no	—
611	C₄×D₄	C₂³×C₂₃	1	4	yes	—
612	C₄×D₄	C₂³×C₂₃	1	4	yes	—
613	#117	—	2	2	no	—
614	#117	C₂³×C₂₃	1	1	yes	characteristic
615	C₂×C₄⋊C₄	—	2	2	no	—
616	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
617	C₂×C₂²⋊C₄	—	2	2	no	—
618	C₂×C₂²⋊C₄	—	2	4	no	—
619	#106	C₂³×C₂₃	1	2	yes	—
620	#106	C₂³×C₂₃	1	2	yes	—
621	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
622	#103	C₂³×C₂₃	1	4	yes	—
623	#103	C₂³×C₂₃	1	4	yes	—
624	#102	C₂³×C₂₃	1	4	yes	—
625	#102	C₂³×C₂₃	1	4	yes	—
626	#102	C₂³×C₂₃	1	4	yes	—
627	#102	C₂³×C₂₃	1	4	yes	—
628	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
629	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
630	#97	C₂³×C₂₃	1	2	yes	—
631	C₄×C₈	C₂³×C₂₃	1	2	yes	—
632	C₂₃	#61063	1	1	yes	characteristic, direct product factor, Sylow
633	C₂⁴	—	2	2	no	—
634	C₂⁴	—	2	4	no	—
635	C₂⁴	—	2	2	no	—
636	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
637	#41	—	2	2	no	—
638	#41	—	2	4	no	—
639	#41	—	2	2	no	—
640	#41	—	2	8	no	—
641	#41	—	2	4	no	—
642	#41	—	2	4	no	—
643	#41	—	2	4	no	—
644	#41	—	2	4	no	—
645	#41	—	4	8	no	—
646	#41	—	4	2	no	—
647	#41	—	4	2	no	—
648	#41	—	4	4	no	—
649	#41	—	4	8	no	—
650	#41	—	4	8	no	—
651	#41	C₂×D₄×C₂₃	1	8	yes	complemented
652	C₂×Q₈	—	2	2	no	—
653	C₂×Q₈	—	2	4	no	—
654	C₂×Q₈	—	4	2	no	—
655	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
656	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
657	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
658	C₂×D₄	—	2	2	no	—
659	C₂×D₄	—	2	8	no	—
660	C₂×D₄	—	2	4	no	—
661	C₂×D₄	—	2	4	no	—
662	C₂×D₄	—	2	2	no	—
663	C₂×D₄	—	2	2	no	—
664	C₂×D₄	—	2	4	no	—
665	C₂×D₄	—	2	2	no	—
666	C₂×D₄	—	2	4	no	—
667	C₂×D₄	—	2	4	no	—
668	C₂×D₄	—	2	4	no	—
669	C₂×D₄	—	2	2	no	—
670	C₂×D₄	—	2	4	no	—
671	C₂×D₄	—	2	2	no	—
672	C₂×D₄	—	2	4	no	—
673	C₂×D₄	—	2	4	no	—
674	C₂×D₄	—	2	4	no	—
675	C₂×D₄	—	4	2	no	—
676	C₂×D₄	—	4	4	no	—
677	C₂×D₄	—	4	8	no	—
678	C₂×D₄	—	4	16	no	—
679	C₂×D₄	—	4	8	no	—
680	C₂×D₄	—	8	8	no	—
681	C₂×D₄	—	8	4	no	—
682	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
683	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
684	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
685	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
686	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
687	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	2	2	no	—
693	C₂²×C₄	—	2	2	no	—
694	C₂²×C₄	—	2	2	no	—
695	C₂²×C₄	—	2	4	no	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	4	no	—
698	C₂²×C₄	—	4	8	no	—
699	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
700	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
701	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
702	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
703	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
704	Q₁₆	—	2	4	no	—
705	Q₁₆	—	2	2	no	—
706	Q₁₆	C₂×D₄×C₂₃	1	4	yes	complemented
707	SD₁₆	—	2	8	no	—
708	SD₁₆	—	2	4	no	—
709	SD₁₆	—	2	4	no	—
710	SD₁₆	—	2	4	no	—
711	SD₁₆	—	4	4	no	—
712	SD₁₆	C₂×D₄×C₂₃	1	8	yes	complemented
713	D₈	—	2	8	no	—
714	D₈	—	2	4	no	—
715	D₈	—	2	4	no	—
716	D₈	—	2	4	no	—
717	D₈	—	2	2	no	—
718	D₈	—	4	4	no	—
719	D₈	C₂×D₄×C₂₃	1	4	yes	complemented
720	M₁₆	—	2	2	no	—
721	M₁₆	—	2	2	no	—
722	M₁₆	—	2	4	no	—
723	M₁₆	—	2	4	no	—
724	M₁₆	—	2	4	no	—
725	C₂×C₈	—	2	2	no	—
726	C₂×C₈	—	2	4	no	—
727	C₂×C₈	C₂×D₄×C₂₃	1	4	yes	complemented
728	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
729	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
730	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
731	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
732	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	4	no	—
735	C₄⋊C₄	—	2	4	no	—
736	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
737	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
738	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
739	C₂²⋊C₄	—	2	4	no	—
740	C₂²⋊C₄	—	2	4	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	4	no	—
745	C₂²⋊C₄	—	2	4	no	—
746	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
747	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
748	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
749	C₄²	—	2	4	no	—
750	C₄²	C₂⁴×C₂₃	1	2	yes	—
751	C₂³	—	2	2	no	—
752	C₂³	—	2	2	no	—
753	C₂³	—	2	4	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	4	2	no	—
756	C₂³	—	4	4	no	—
757	C₂³	—	4	8	no	—
758	C₂³	—	4	4	no	—
759	C₂³	—	4	4	no	—
760	C₂³	—	8	2	no	—
761	C₂³	—	8	2	no	—
762	C₂³	—	8	4	no	—
763	C₂³	—	8	2	no	—
764	C₂³	—	8	4	no	—
765	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
766	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
767	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
768	Q₈	—	2	2	no	—
769	Q₈	—	2	2	no	—
770	Q₈	—	2	2	no	—
771	Q₈	—	2	2	no	—
772	Q₈	—	4	4	no	—
773	Q₈	C₂²×D₄×C₂₃	1	4	yes	—
774	D₄	—	2	8	no	—
775	D₄	—	2	4	no	—
776	D₄	—	2	4	no	—
777	D₄	—	2	2	no	—
778	D₄	—	2	2	no	—
779	D₄	—	2	2	no	—
780	D₄	—	2	4	no	—
781	D₄	—	2	2	no	—
782	D₄	—	4	4	no	—
783	D₄	—	4	8	no	—
784	D₄	—	4	4	no	—
785	D₄	—	4	8	no	—
786	D₄	—	4	4	no	—
787	D₄	—	4	4	no	—
788	D₄	—	4	8	no	—
789	D₄	—	4	4	no	—
790	D₄	—	4	4	no	—
791	D₄	—	8	4	no	—
792	D₄	—	8	4	no	—
793	D₄	—	8	4	no	—
794	D₄	—	8	4	no	—
795	D₄	C₂²×D₄×C₂₃	1	4	yes	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	4	no	—
803	C₂×C₄	—	2	8	no	—
804	C₂×C₄	—	2	4	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	4	4	no	—
807	C₂×C₄	—	4	8	no	—
808	C₂×C₄	—	4	4	no	—
809	C₂×C₄	—	4	4	no	—
810	C₂×C₄	—	4	4	no	—
811	C₂×C₄	—	8	4	no	—
812	C₂×C₄	—	8	2	no	—
813	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
814	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
815	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
816	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
817	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
818	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
819	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
820	C₈	—	2	2	no	—
821	C₈	—	2	2	no	—
822	C₈	—	2	2	no	—
823	C₈	C₂²×D₄×C₂₃	1	2	yes	—
824	C₈	C₂²×D₄×C₂₃	1	2	yes	—
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	—	2	2	no	—
832	C₂²	—	4	2	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	4	4	no	—
836	C₂²	—	4	4	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	4	2	no	—
839	C₂²	—	4	4	no	—
840	C₂²	—	8	2	no	—
841	C₂²	—	8	8	no	—
842	C₂²	—	16	4	no	—
843	C₂²	—	16	8	no	—
844	C₂²	D₄²×C₂₃	1	2	yes	—
845	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
846	C₄	—	2	2	no	—
847	C₄	—	2	4	no	—
848	C₄	—	2	2	no	—
849	C₄	—	2	4	no	—
850	C₄	—	4	2	no	—
851	C₄	—	4	4	no	—
852	C₄	D₄²×C₂₃	1	2	yes	—
853	C₄	C₂³×D₄×C₂₃	1	1	yes	characteristic
854	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
855	C₂	—	2	2	no	—
856	C₂	—	4	2	no	—
857	C₂	—	4	2	no	—
858	C₂	—	4	4	no	—
859	C₂	—	8	2	no	—
860	C₂	—	8	4	no	—
861	C₂	C₂×D₄²×C₂₃	1	1	yes	characteristic
862	C₂	C₂₃×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂₃×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#576	C₂	semidirect
2. C₂×C₂₃×#575	C₂	semidirect
3. C₂₃×#3488	C₂	semidirect
4. C₂₃×#3275	C₂	semidirect
5. C₂₃×#3274	C₂	semidirect
6. C₂₃×#3271	C₂	semidirect
7. C₂₃×#3264	C₂	semidirect
8. C₂₃×#3155	C₂	semidirect
9. C₂₃×#3060	C₂	semidirect
10. C₂×C₂₃×#469	C₂	semidirect
11. C₂₃×#3045	C₂	semidirect
12. C₂₃×#3012	C₂	semidirect
13. C₂₃×#3006	C₂	semidirect
14. C₂₃×#2952	C₂	semidirect
15. C₂₃×#2930	C₂	semidirect
16. C₂×C₂₃×H(5,𝔽₂)	C₂²	semidirect
17. C₂²×#41×C₂₃	C₂²	semidirect
20. C₂×C₂₃×#137	C₂²	semidirect
21. C₂×C₂₃×#137	C₂²	semidirect
22. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
23. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
24. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
25. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
26. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
28. C₂×C₂₃×#135	C₂²	semidirect
29. C₂×C₂₃×#135	C₂²	semidirect
30. C₂×C₂₃×#135	C₂²	semidirect
31. C₂²×D₈×C₂₃	C₂²	semidirect
32. C₂²×D₈×C₂₃	C₂²	semidirect
33. C₂×C₂₃×#131	C₂²	semidirect
34. C₂²×M₁₆×C₂₃	C₂²	semidirect
35. C₂₃×#550	C₂²	semidirect
36. C₂₃×#548	C₂²	semidirect
38. C₂₃×#546	C₂²	semidirect
40. D₄²×C₂₃	C₂²	semidirect
42. C₂₃×#537	C₂²	semidirect
44. C₂₃×#535	C₂²	semidirect
48. C₂×C₂₃×#121	C₂²	semidirect
49. C₂₃×#520	C₂²	semidirect
50. C₂₃×#496	C₂²	semidirect
51. C₂₃×#495	C₂²	semidirect
52. C₂₃×#493	C₂²	semidirect
53. C₂₃×#470	C₂²	semidirect
54. C₂₃×#469	C₂²	semidirect
55. C₂₃×#469	C₂²	semidirect
56. C₂₃×#469	C₂²	semidirect
57. C₂₃×#465	C₂²	semidirect
58. C₂₃×#464	C₂²	semidirect
59. C₂₃×#463	C₂²	semidirect
60. C₂₃×#460	C₂²	semidirect
61. C₂₃×#459	C₂²	semidirect
62. C₂₃×#452	C₂²	semidirect
63. C₂₃×#450	C₂²	semidirect
64. C₂₃×#449	C₂²	semidirect
65. C₂₃×#449	C₂²	semidirect
66. C₂₃×#449	C₂²	semidirect
67. C₂₃×#448	C₂²	semidirect
68. C₂₃×#447	C₂²	semidirect
69. C₂₃×#447	C₂²	semidirect
70. C₂₃×#442	C₂²	semidirect
71. C₂₃×#441	C₂²	semidirect
72. C₄×SD₁₆×C₂₃	C₂²	semidirect
73. C₂₃×#436	C₂²	semidirect
74. C₂₃×#435	C₂²	semidirect
75. C₂×C₂₃×#106	C₂²	semidirect
76. C₂₃×#424	C₂²	semidirect
77. C₂₃×#417	C₂²	semidirect
78. C₂₃×#417	C₂²	semidirect
79. C₂×C₂₃×#102	C₂²	semidirect
80. C₂₃×#408	C₂²	semidirect
81. C₂₃×#407	C₂²	semidirect
82. C₂₃×#405	C₂²	semidirect
117. C₂₃×#135	D₄	semidirect
219. #41×C₂₃	C₂×D₄	semidirect
274. Q₁₆×C₂₃	C₂×D₄	semidirect
280. SD₁₆×C₂₃	C₂×D₄	semidirect
287. D₈×C₂₃	C₂×D₄	semidirect
295. C₂×C₈×C₂₃	C₂×D₄	semidirect
319. #61063	C₂₃	direct (N × H)
394. C₂×#576	C₂×C₂₃	semidirect
395. C₂×#575	C₂×C₂₃	semidirect
396. #3488	C₂×C₂₃	semidirect
397. #3275	C₂×C₂₃	semidirect
398. #3274	C₂×C₂₃	semidirect
399. #3271	C₂×C₂₃	semidirect
400. #3264	C₂×C₂₃	semidirect
401. #3155	C₂×C₂₃	semidirect
402. #3060	C₂×C₂₃	semidirect
403. C₂×#469	C₂×C₂₃	semidirect
404. #3045	C₂×C₂₃	semidirect
405. #3012	C₂×C₂₃	semidirect
406. #3006	C₂×C₂₃	semidirect
407. #2952	C₂×C₂₃	semidirect
408. #2930	C₂×C₂₃	semidirect
439. C₂×H(5,𝔽₂)	C₂²×C₂₃	semidirect
440. C₂²×#41	C₂²×C₂₃	semidirect
443. C₂×#137	C₂²×C₂₃	semidirect
444. C₂×#137	C₂²×C₂₃	semidirect
445. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
446. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
447. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
448. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
449. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
451. C₂×#135	C₂²×C₂₃	semidirect
452. C₂×#135	C₂²×C₂₃	semidirect
453. C₂×#135	C₂²×C₂₃	semidirect
454. C₂²×D₈	C₂²×C₂₃	semidirect
455. C₂²×D₈	C₂²×C₂₃	semidirect
456. C₂×#131	C₂²×C₂₃	semidirect
457. C₂²×M₁₆	C₂²×C₂₃	semidirect
458. #550	C₂²×C₂₃	semidirect
459. #548	C₂²×C₂₃	semidirect
461. #546	C₂²×C₂₃	semidirect
463. D₄²	C₂²×C₂₃	semidirect
465. #537	C₂²×C₂₃	semidirect
467. #535	C₂²×C₂₃	semidirect
471. C₂×#121	C₂²×C₂₃	semidirect
472. #520	C₂²×C₂₃	semidirect
473. #496	C₂²×C₂₃	semidirect
474. #495	C₂²×C₂₃	semidirect
475. #493	C₂²×C₂₃	semidirect
476. #470	C₂²×C₂₃	semidirect
477. #469	C₂²×C₂₃	semidirect
478. #469	C₂²×C₂₃	semidirect
479. #469	C₂²×C₂₃	semidirect
480. #465	C₂²×C₂₃	semidirect
481. #464	C₂²×C₂₃	semidirect
482. #463	C₂²×C₂₃	semidirect
483. #460	C₂²×C₂₃	semidirect
484. #459	C₂²×C₂₃	semidirect
485. #452	C₂²×C₂₃	semidirect
486. #450	C₂²×C₂₃	semidirect
487. #449	C₂²×C₂₃	semidirect
488. #449	C₂²×C₂₃	semidirect
489. #449	C₂²×C₂₃	semidirect
490. #448	C₂²×C₂₃	semidirect
491. #447	C₂²×C₂₃	semidirect
492. #447	C₂²×C₂₃	semidirect
493. #442	C₂²×C₂₃	semidirect
494. #441	C₂²×C₂₃	semidirect
495. C₄×SD₁₆	C₂²×C₂₃	semidirect
496. #436	C₂²×C₂₃	semidirect
497. #435	C₂²×C₂₃	semidirect
498. C₂×#106	C₂²×C₂₃	semidirect
499. #424	C₂²×C₂₃	semidirect
500. #417	C₂²×C₂₃	semidirect
501. #417	C₂²×C₂₃	semidirect
502. C₂×#102	C₂²×C₂₃	semidirect
503. #408	C₂²×C₂₃	semidirect
504. #407	C₂²×C₂₃	semidirect
505. #405	C₂²×C₂₃	semidirect
548. #135	D₄×C₂₃	semidirect
632. C₂₃	#61063	direct (N × H)
651. #41	C₂×D₄×C₂₃	semidirect
706. Q₁₆	C₂×D₄×C₂₃	semidirect
712. SD₁₆	C₂×D₄×C₂₃	semidirect
719. D₈	C₂×D₄×C₂₃	semidirect
727. C₂×C₈	C₂×D₄×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#576	2
C₂×C₂₃×#575	2
C₂₃×#3488	2
C₂₃×#3275	2
C₂₃×#3274	2
C₂₃×#3271	2
C₂₃×#3264	2
C₂₃×#3155	2
C₂₃×#3060	2
C₂×C₂₃×#469	2
C₂₃×#3045	2
C₂₃×#3012	2
C₂₃×#3006	2
C₂₃×#2952	2
C₂₃×#2930	2
#61063	23

Subgroups — C23×#61063 #19208689

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61063 #19208689