Subgroups — C₂₃×#24460 #19172086

Order 5888.

1352 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#577	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#472	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3045	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₃×#454	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3008	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2898	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2052	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2046	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2012	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2004	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1907	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1883	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1876	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1866	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1792	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
17	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
18	C₂₃×#577	—	2	4	no	—
19	C₂₃×#577	—	2	4	no	—
20	C₂×C₂₃×#137	—	2	1	no	—
21	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×AGL(1,ℤ/8)	—	2	1	no	—
23	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
24	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₂₃×#135	—	2	1	no	—
27	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic
28	C₂²×SD₁₆×C₂₃	—	2	1	no	—
29	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
30	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
32	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic, complemented
33	C₂₃×#535	C₂²	1	1	yes	characteristic
34	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic, complemented
35	C₂₃×#520	C₂²	1	1	yes	characteristic, complemented
36	C₂₃×#472	—	2	4	no	—
37	C₂₃×#464	—	2	1	no	—
38	C₂₃×#463	—	2	1	no	—
39	C₂₃×#460	—	2	1	no	—
40	C₂₃×#459	—	2	1	no	—
41	C₂₃×#454	—	2	4	no	—
42	C₂₃×#449	—	2	1	no	—
43	C₂₃×#449	—	2	1	no	—
44	C₂₃×#447	—	2	1	no	—
45	C₂₃×#447	—	2	1	no	—
46	C₂×C₂₃×#108	C₂²	1	1	yes	characteristic, complemented
47	C₂₃×#424	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₂₃×#104	C₂²	1	1	yes	characteristic
49	C₂×C₂₃×#104	C₂²	1	1	yes	characteristic
50	C₂×C₂₃×#104	C₂²	1	1	yes	characteristic, complemented
51	C₂₃×#419	—	2	1	no	—
52	C₂₃×#419	C₂²	1	1	yes	characteristic, complemented
53	C₂₃×#418	C₂²	1	1	yes	characteristic
54	C₂₃×#417	—	2	1	no	—
55	C₂₃×#417	C₂²	1	1	yes	characteristic
56	C₂₃×#417	C₂²	1	1	yes	characteristic
57	C₂₃×#416	—	2	1	no	—
58	C₂₃×#416	C₂²	1	1	yes	characteristic
59	C₂×C₂₃×#103	—	2	1	no	—
60	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₂₃×#101	C₂²	1	1	yes	characteristic, complemented
63	C₂×C₂₃×#100	C₂²	1	1	yes	characteristic
64	C₂×C₂₃×#100	C₂²	1	1	yes	characteristic, complemented
65	C₂₃×#408	C₂²	1	1	yes	characteristic
66	C₂₃×#390	C₂²	1	1	yes	characteristic
67	C₂₃×#343	C₂²	1	1	yes	characteristic, complemented
68	C₂₃×#341	C₂²	1	1	yes	characteristic, complemented
69	C₂₃×#339	C₂²	1	1	yes	characteristic, complemented
70	C₂₃×#336	C₂²	1	1	yes	characteristic, complemented
71	C₂₃×2₋¹⁺⁴	—	2	2	no	—
72	C₂₃×2₋¹⁺⁴	—	2	2	no	—
73	C₂₃×2₋¹⁺⁴	—	4	1	no	—
74	C₂₃×2₋¹⁺⁴	D₄	1	4	yes	complemented
75	C₂₃×H(5,𝔽₂)	—	2	2	no	—
76	C₂₃×H(5,𝔽₂)	—	2	2	no	—
77	C₂₃×H(5,𝔽₂)	—	2	2	no	—
78	C₂₃×H(5,𝔽₂)	—	4	1	no	—
79	C₂×#41×C₂₃	—	2	1	no	—
80	C₂×#41×C₂₃	—	2	1	no	—
81	C₂×#41×C₂₃	—	2	1	no	—
82	C₂×#41×C₂₃	—	2	1	no	—
83	C₂×#41×C₂₃	—	4	1	no	—
84	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
85	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
86	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
87	C₂²×Q₈×C₂₃	—	2	1	no	—
88	C₂²×Q₈×C₂₃	—	2	1	no	—
89	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₂₃	—	2	1	no	—
91	C₂²×D₄×C₂₃	—	2	1	no	—
92	C₂²×D₄×C₂₃	—	4	1	no	—
93	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
95	C₂₃×#137	—	2	8	no	—
96	C₂₃×#137	—	2	2	no	—
97	C₂₃×#137	—	2	2	no	—
98	C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
99	C₂₃×AGL(1,ℤ/8)	—	2	2	no	—
100	C₂₃×AGL(1,ℤ/8)	—	2	2	no	—
101	C₂₃×AGL(1,ℤ/8)	—	2	2	no	—
102	C₂₃×AGL(1,ℤ/8)	—	2	2	no	—
103	C₂₃×AGL(1,ℤ/8)	—	2	2	no	—
104	C₂₃×AGL(1,ℤ/8)	D₄	1	4	yes	complemented
105	C₂₃×#135	—	2	8	no	—
106	C₂₃×#135	—	2	2	no	—
107	C₂₃×#135	—	2	2	no	—
108	C₂×Q₁₆×C₂₃	—	2	1	no	—
109	C₂×Q₁₆×C₂₃	D₄	1	1	yes	characteristic
110	C₂×SD₁₆×C₂₃	—	2	8	no	—
111	C₂×SD₁₆×C₂₃	—	2	1	no	—
112	C₂×SD₁₆×C₂₃	—	2	2	no	—
113	C₂×SD₁₆×C₂₃	—	2	1	no	—
114	C₂×SD₁₆×C₂₃	—	2	2	no	—
115	C₂×SD₁₆×C₂₃	—	2	1	no	—
116	C₂×SD₁₆×C₂₃	—	2	1	no	—
117	C₂×SD₁₆×C₂₃	—	2	1	no	—
118	C₂×SD₁₆×C₂₃	—	2	1	no	—
119	C₂×SD₁₆×C₂₃	D₄	1	1	yes	characteristic
120	C₂×SD₁₆×C₂₃	D₄	1	1	yes	characteristic
121	C₂×D₈×C₂₃	—	2	1	no	—
122	C₂×D₈×C₂₃	—	2	2	no	—
123	C₂×D₈×C₂₃	—	2	1	no	—
124	C₂×D₈×C₂₃	—	2	1	no	—
125	C₂×D₈×C₂₃	—	2	1	no	—
126	C₂×D₈×C₂₃	—	2	1	no	—
127	C₂×D₈×C₂₃	—	4	1	no	—
128	C₂×D₈×C₂₃	D₄	1	1	yes	characteristic
129	C₂₃×#131	—	2	2	no	—
130	C₂₃×#131	—	2	2	no	—
131	C₂₃×#131	—	2	2	no	—
132	C₂₃×#131	—	4	1	no	—
133	C₂×M₁₆×C₂₃	—	2	1	no	—
134	C₂×M₁₆×C₂₃	—	2	1	no	—
135	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
136	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
137	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
138	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
139	C₂²×C₈×C₂₃	—	2	1	no	—
140	C₂²×C₈×C₂₃	—	2	1	no	—
141	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
142	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
143	C₂₃×#127	—	2	1	no	—
144	C₂₃×#124	—	2	2	no	—
145	C₂₃×#124	—	2	1	no	—
146	C₂₃×#124	—	4	1	no	—
147	C₂₃×#121	—	2	1	no	—
148	C₂₃×#121	—	2	1	no	—
149	C₂₃×#120	—	4	1	no	—
150	C₄×Q₈×C₂₃	—	2	1	no	—
151	C₄×D₄×C₂₃	—	2	1	no	—
152	C₄×D₄×C₂₃	—	4	1	no	—
153	C₂₃×#117	—	2	1	no	—
154	C₂₃×#117	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
156	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
157	C₂×C₂²⋊C₄×C₂₃	—	4	1	no	—
158	C₂×C₂²⋊C₄×C₂₃	—	4	1	no	—
159	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
160	C₂₃×#108	—	2	2	no	—
161	C₂₃×C₄⋊C₈	—	2	1	no	—
162	C₂₃×C₄⋊C₈	—	2	1	no	—
163	C₂₃×#104	—	2	2	no	—
164	C₂₃×#104	—	2	2	no	—
165	C₂₃×#104	—	4	1	no	—
166	C₂₃×#103	—	2	1	no	—
167	C₂₃×#103	—	2	1	no	—
168	C₂₃×#103	—	2	1	no	—
169	C₂₃×#103	—	2	1	no	—
170	C₂₃×#103	—	2	1	no	—
171	C₂₃×#103	—	2	1	no	—
172	C₂₃×#103	D₄	1	1	yes	characteristic
173	C₂₃×#103	D₄	1	1	yes	characteristic
174	C₂₃×#102	—	2	1	no	—
175	C₂₃×#102	—	2	1	no	—
176	C₂₃×#102	—	2	1	no	—
177	C₂₃×#102	—	2	1	no	—
178	C₂₃×#102	—	2	1	no	—
179	C₂₃×#102	—	2	1	no	—
180	C₂₃×#102	D₄	1	1	yes	characteristic
181	C₂₃×#102	D₄	1	1	yes	characteristic
182	C₂₃×#101	—	2	2	no	—
183	C₂₃×#100	—	2	2	no	—
184	C₂₃×#100	—	2	2	no	—
185	C₂₃×C₂²⋊C₈	—	2	1	no	—
186	C₂₃×C₂²⋊C₈	—	2	1	no	—
187	C₂⁴×C₂₃	—	2	1	no	—
188	C₂⁴×C₂₃	—	2	1	no	—
189	C₂⁴×C₂₃	—	4	1	no	—
190	#41×C₂₃	—	2	1	no	—
191	#41×C₂₃	—	2	1	no	—
192	#41×C₂₃	—	2	1	no	—
193	#41×C₂₃	—	2	1	no	—
194	#41×C₂₃	—	2	4	no	—
195	#41×C₂₃	—	2	4	no	—
196	#41×C₂₃	—	2	4	no	—
197	#41×C₂₃	—	2	1	no	—
198	#41×C₂₃	—	2	1	no	—
199	#41×C₂₃	—	2	1	no	—
200	#41×C₂₃	—	2	1	no	—
201	#41×C₂₃	—	4	4	no	—
202	#41×C₂₃	—	4	2	no	—
203	#41×C₂₃	—	4	2	no	—
204	#41×C₂₃	—	4	2	no	—
205	#41×C₂₃	—	4	4	no	—
206	#41×C₂₃	—	4	2	no	—
207	#41×C₂₃	—	4	2	no	—
208	#41×C₂₃	C₂×D₄	1	2	yes	—
209	#41×C₂₃	C₂×D₄	1	2	yes	—
210	#41×C₂₃	C₂×D₄	1	2	yes	—
211	#41×C₂₃	#41	1	2	yes	—
212	C₂×Q₈×C₂₃	—	2	1	no	—
213	C₂×Q₈×C₂₃	—	2	4	no	—
214	C₂×Q₈×C₂₃	—	2	4	no	—
215	C₂×Q₈×C₂₃	—	2	1	no	—
216	C₂×Q₈×C₂₃	—	2	1	no	—
217	C₂×Q₈×C₂₃	—	2	1	no	—
218	C₂×Q₈×C₂₃	—	2	1	no	—
219	C₂×Q₈×C₂₃	—	4	1	no	—
220	C₂×Q₈×C₂₃	—	4	2	no	—
221	C₂×Q₈×C₂₃	—	4	2	no	—
222	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
223	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
224	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
225	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
226	C₂×D₄×C₂₃	—	2	1	no	—
227	C₂×D₄×C₂₃	—	2	1	no	—
228	C₂×D₄×C₂₃	—	2	4	no	—
229	C₂×D₄×C₂₃	—	2	1	no	—
230	C₂×D₄×C₂₃	—	2	1	no	—
231	C₂×D₄×C₂₃	—	2	1	no	—
232	C₂×D₄×C₂₃	—	2	1	no	—
233	C₂×D₄×C₂₃	—	2	1	no	—
234	C₂×D₄×C₂₃	—	2	1	no	—
235	C₂×D₄×C₂₃	—	2	1	no	—
236	C₂×D₄×C₂₃	—	2	1	no	—
237	C₂×D₄×C₂₃	—	2	1	no	—
238	C₂×D₄×C₂₃	—	2	1	no	—
239	C₂×D₄×C₂₃	—	2	1	no	—
240	C₂×D₄×C₂₃	—	2	1	no	—
241	C₂×D₄×C₂₃	—	4	2	no	—
242	C₂×D₄×C₂₃	—	4	1	no	—
243	C₂×D₄×C₂₃	—	4	1	no	—
244	C₂×D₄×C₂₃	—	4	1	no	—
245	C₂×D₄×C₂₃	—	4	1	no	—
246	C₂×D₄×C₂₃	—	4	2	no	—
247	C₂×D₄×C₂₃	—	4	4	no	—
248	C₂×D₄×C₂₃	—	4	4	no	—
249	C₂×D₄×C₂₃	—	4	1	no	—
250	C₂×D₄×C₂₃	—	4	2	no	—
251	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
252	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
253	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
254	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₂₃	—	2	1	no	—
256	C₂²×C₄×C₂₃	—	2	1	no	—
257	C₂²×C₄×C₂₃	—	2	1	no	—
258	C₂²×C₄×C₂₃	—	2	1	no	—
259	C₂²×C₄×C₂₃	—	2	1	no	—
260	C₂²×C₄×C₂₃	—	2	1	no	—
261	C₂²×C₄×C₂₃	—	4	1	no	—
262	C₂²×C₄×C₂₃	—	4	1	no	—
263	C₂²×C₄×C₂₃	—	4	1	no	—
264	C₂²×C₄×C₂₃	—	4	1	no	—
265	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
266	Q₁₆×C₂₃	—	2	4	no	—
267	Q₁₆×C₂₃	—	2	2	no	—
268	SD₁₆×C₂₃	—	2	4	no	—
269	SD₁₆×C₂₃	—	2	4	no	—
270	SD₁₆×C₂₃	—	2	4	no	—
271	SD₁₆×C₂₃	—	2	2	no	—
272	SD₁₆×C₂₃	—	2	4	no	—
273	SD₁₆×C₂₃	—	2	2	no	—
274	SD₁₆×C₂₃	—	4	2	no	—
275	SD₁₆×C₂₃	—	4	2	no	—
276	D₈×C₂₃	—	2	4	no	—
277	D₈×C₂₃	—	2	2	no	—
278	D₈×C₂₃	—	4	2	no	—
279	D₈×C₂₃	—	4	2	no	—
280	D₈×C₂₃	—	4	2	no	—
281	D₈×C₂₃	—	4	2	no	—
282	M₁₆×C₂₃	—	2	4	no	—
283	M₁₆×C₂₃	—	2	1	no	—
284	M₁₆×C₂₃	—	2	1	no	—
285	M₁₆×C₂₃	—	2	1	no	—
286	M₁₆×C₂₃	—	2	1	no	—
287	M₁₆×C₂₃	—	2	1	no	—
288	M₁₆×C₂₃	—	2	1	no	—
289	M₁₆×C₂₃	—	2	1	no	—
290	M₁₆×C₂₃	—	4	2	no	—
291	M₁₆×C₂₃	C₂×D₄	1	2	yes	—
292	C₂×C₈×C₂₃	—	2	4	no	—
293	C₂×C₈×C₂₃	—	2	1	no	—
294	C₂×C₈×C₂₃	—	2	1	no	—
295	C₂×C₈×C₂₃	—	2	1	no	—
296	C₂×C₈×C₂₃	—	2	1	no	—
297	C₂×C₈×C₂₃	—	2	1	no	—
298	C₂×C₈×C₂₃	—	2	1	no	—
299	C₂×C₈×C₂₃	—	2	1	no	—
300	C₂×C₈×C₂₃	—	2	1	no	—
301	C₂×C₈×C₂₃	—	4	2	no	—
302	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
303	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
304	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
305	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
306	C₄⋊C₄×C₂₃	—	2	1	no	—
307	C₄⋊C₄×C₂₃	—	2	1	no	—
308	C₄⋊C₄×C₂₃	—	4	1	no	—
309	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
310	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
311	C₂²⋊C₄×C₂₃	—	2	1	no	—
312	C₂²⋊C₄×C₂₃	—	4	1	no	—
313	C₂²⋊C₄×C₂₃	—	4	1	no	—
314	C₂²⋊C₄×C₂₃	—	4	1	no	—
315	C₂²⋊C₄×C₂₃	—	4	4	no	—
316	C₂²⋊C₄×C₂₃	—	8	2	no	—
317	C₄²×C₂₃	—	2	1	no	—
318	C₄²×C₂₃	—	2	1	no	—
319	C₄²×C₂₃	—	2	1	no	—
320	C₄²×C₂₃	—	4	1	no	—
321	#24460	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
322	C₂³×C₂₃	—	2	1	no	—
323	C₂³×C₂₃	—	2	1	no	—
324	C₂³×C₂₃	—	2	1	no	—
325	C₂³×C₂₃	—	2	2	no	—
326	C₂³×C₂₃	—	4	4	no	—
327	C₂³×C₂₃	—	4	1	no	—
328	C₂³×C₂₃	—	4	1	no	—
329	C₂³×C₂₃	—	4	1	no	—
330	C₂³×C₂₃	—	4	1	no	—
331	C₂³×C₂₃	—	4	1	no	—
332	C₂³×C₂₃	—	8	1	no	—
333	C₂³×C₂₃	—	8	1	no	—
334	C₂³×C₂₃	—	8	1	no	—
335	C₂³×C₂₃	—	8	1	no	—
336	C₂³×C₂₃	—	16	1	no	—
337	C₂³×C₂₃	—	16	1	no	—
338	C₂³×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
339	Q₈×C₂₃	—	2	1	no	—
340	Q₈×C₂₃	—	2	1	no	—
341	Q₈×C₂₃	—	2	2	no	—
342	Q₈×C₂₃	—	2	1	no	—
343	Q₈×C₂₃	—	2	2	no	—
344	Q₈×C₂₃	—	2	1	no	—
345	Q₈×C₂₃	—	4	4	no	—
346	Q₈×C₂₃	—	4	1	no	—
347	Q₈×C₂₃	—	4	1	no	—
348	Q₈×C₂₃	#120	1	2	yes	—
349	Q₈×C₂₃	#121	1	2	yes	—
350	D₄×C₂₃	—	2	2	no	—
351	D₄×C₂₃	—	2	2	no	—
352	D₄×C₂₃	—	2	2	no	—
353	D₄×C₂₃	—	2	2	no	—
354	D₄×C₂₃	—	2	2	no	—
355	D₄×C₂₃	—	2	1	no	—
356	D₄×C₂₃	—	2	1	no	—
357	D₄×C₂₃	—	2	2	no	—
358	D₄×C₂₃	—	2	1	no	—
359	D₄×C₂₃	—	2	1	no	—
360	D₄×C₂₃	—	4	4	no	—
361	D₄×C₂₃	—	4	4	no	—
362	D₄×C₂₃	—	4	4	no	—
363	D₄×C₂₃	—	4	1	no	—
364	D₄×C₂₃	—	4	1	no	—
365	D₄×C₂₃	—	4	1	no	—
366	D₄×C₂₃	—	4	1	no	—
367	D₄×C₂₃	—	4	1	no	—
368	D₄×C₂₃	—	4	1	no	—
369	D₄×C₂₃	—	4	1	no	—
370	D₄×C₂₃	—	4	1	no	—
371	D₄×C₂₃	—	16	1	no	—
372	D₄×C₂₃	—	16	1	no	—
373	D₄×C₂₃	#120	1	2	yes	—
374	D₄×C₂₃	#121	1	2	yes	—
375	C₂×C₄×C₂₃	—	2	1	no	—
376	C₂×C₄×C₂₃	—	2	1	no	—
377	C₂×C₄×C₂₃	—	2	2	no	—
378	C₂×C₄×C₂₃	—	2	2	no	—
379	C₂×C₄×C₂₃	—	2	2	no	—
380	C₂×C₄×C₂₃	—	2	2	no	—
381	C₂×C₄×C₂₃	—	2	2	no	—
382	C₂×C₄×C₂₃	—	2	1	no	—
383	C₂×C₄×C₂₃	—	2	1	no	—
384	C₂×C₄×C₂₃	—	2	1	no	—
385	C₂×C₄×C₂₃	—	4	4	no	—
386	C₂×C₄×C₂₃	—	4	4	no	—
387	C₂×C₄×C₂₃	—	4	4	no	—
388	C₂×C₄×C₂₃	—	4	1	no	—
389	C₂×C₄×C₂₃	—	4	1	no	—
390	C₂×C₄×C₂₃	—	4	1	no	—
391	C₂×C₄×C₂₃	—	4	1	no	—
392	C₂×C₄×C₂₃	—	4	1	no	—
393	C₂×C₄×C₂₃	—	4	1	no	—
394	C₂×C₄×C₂₃	—	4	1	no	—
395	C₂×C₄×C₂₃	—	4	1	no	—
396	C₂×C₄×C₂₃	—	8	1	no	—
397	C₂×C₄×C₂₃	—	16	1	no	—
398	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
403	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
404	C₈×C₂₃	—	2	1	no	—
405	C₈×C₂₃	—	2	2	no	—
406	C₈×C₂₃	—	2	1	no	—
407	C₈×C₂₃	—	2	1	no	—
408	C₈×C₂₃	—	2	1	no	—
409	C₈×C₂₃	—	4	1	no	—
410	C₈×C₂₃	—	4	1	no	—
411	C₈×C₂₃	—	4	1	no	—
412	C₂×#577	C₂×C₂₃	1	1	yes	characteristic, complemented
413	C₂×#472	C₂×C₂₃	1	1	yes	characteristic, complemented
414	#3045	C₂×C₂₃	1	1	yes	characteristic, complemented
415	C₂×#454	C₂×C₂₃	1	1	yes	characteristic, complemented
416	#3008	C₂×C₂₃	1	1	yes	characteristic, complemented
417	#2898	C₂×C₂₃	1	1	yes	characteristic, complemented
418	#2052	C₂×C₂₃	1	1	yes	characteristic, complemented
419	#2046	C₂×C₂₃	1	1	yes	characteristic, complemented
420	#2012	C₂×C₂₃	1	1	yes	characteristic, complemented
421	#2004	C₂×C₂₃	1	1	yes	characteristic, complemented
422	#1907	C₂×C₂₃	1	1	yes	characteristic, complemented
423	#1883	C₂×C₂₃	1	1	yes	characteristic, complemented
424	#1876	C₂×C₂₃	1	1	yes	characteristic, complemented
425	#1866	C₂×C₂₃	1	1	yes	characteristic, complemented
426	#1792	C₂×C₂₃	1	1	yes	characteristic, complemented
427	C₂²×C₂₃	—	2	1	no	—
428	C₂²×C₂₃	—	2	1	no	—
429	C₂²×C₂₃	—	2	2	no	—
430	C₂²×C₂₃	—	2	2	no	—
431	C₂²×C₂₃	—	4	1	no	—
432	C₂²×C₂₃	—	4	1	no	—
433	C₂²×C₂₃	—	4	1	no	—
434	C₂²×C₂₃	—	4	1	no	—
435	C₂²×C₂₃	—	4	1	no	—
436	C₂²×C₂₃	—	4	2	no	—
437	C₂²×C₂₃	—	4	1	no	—
438	C₂²×C₂₃	—	4	1	no	—
439	C₂²×C₂₃	—	8	2	no	—
440	C₂²×C₂₃	—	8	2	no	—
441	C₂²×C₂₃	—	8	1	no	—
442	C₂²×C₂₃	—	8	1	no	—
443	C₂²×C₂₃	—	8	1	no	—
444	C₂²×C₂₃	—	8	1	no	—
445	C₂²×C₂₃	—	8	1	no	—
446	C₂²×C₂₃	—	16	1	no	—
447	C₂²×C₂₃	—	16	1	no	—
448	C₂²×C₂₃	—	16	4	no	—
449	C₂²×C₂₃	#534	1	1	yes	characteristic
450	C₂²×C₂₃	D₄²	1	1	yes	characteristic
451	C₂²×C₂₃	#546	1	1	yes	characteristic
452	C₄×C₂₃	—	2	2	no	—
453	C₄×C₂₃	—	2	2	no	—
454	C₄×C₂₃	—	4	1	no	—
455	C₄×C₂₃	—	4	2	no	—
456	C₄×C₂₃	—	4	1	no	—
457	C₄×C₂₃	—	4	1	no	—
458	C₄×C₂₃	—	8	1	no	—
459	C₄×C₂₃	—	8	1	no	—
460	C₄×C₂₃	C₂×#120	1	1	yes	characteristic
461	C₄×C₂₃	C₂×#121	1	1	yes	characteristic
462	C₄×C₂₃	D₄²	1	1	yes	characteristic
463	C₄×C₂₃	#546	1	1	yes	characteristic
464	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	1	yes	characteristic
465	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	1	yes	characteristic
466	#577	—	2	4	no	—
467	#577	—	2	4	no	—
468	C₂×#137	—	2	1	no	—
469	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic
470	C₂×AGL(1,ℤ/8)	—	2	1	no	—
471	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic
472	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic
473	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic, complemented
474	C₂×#135	—	2	1	no	—
475	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic
476	C₂²×SD₁₆	—	2	1	no	—
477	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
478	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
479	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
480	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic, complemented
481	#535	C₂²×C₂₃	1	1	yes	characteristic
482	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic, complemented
483	#520	C₂²×C₂₃	1	1	yes	characteristic, complemented
484	#472	—	2	4	no	—
485	#464	—	2	1	no	—
486	#463	—	2	1	no	—
487	#460	—	2	1	no	—
488	#459	—	2	1	no	—
489	#454	—	2	4	no	—
490	#449	—	2	1	no	—
491	#449	—	2	1	no	—
492	#447	—	2	1	no	—
493	#447	—	2	1	no	—
494	C₂×#108	C₂²×C₂₃	1	1	yes	characteristic, complemented
495	#424	C₂²×C₂₃	1	1	yes	characteristic, complemented
496	C₂×#104	C₂²×C₂₃	1	1	yes	characteristic
497	C₂×#104	C₂²×C₂₃	1	1	yes	characteristic
498	C₂×#104	C₂²×C₂₃	1	1	yes	characteristic, complemented
499	#419	—	2	1	no	—
500	#419	C₂²×C₂₃	1	1	yes	characteristic, complemented
501	#418	C₂²×C₂₃	1	1	yes	characteristic
502	#417	—	2	1	no	—
503	#417	C₂²×C₂₃	1	1	yes	characteristic
504	#417	C₂²×C₂₃	1	1	yes	characteristic
505	#416	—	2	1	no	—
506	#416	C₂²×C₂₃	1	1	yes	characteristic
507	C₂×#103	—	2	1	no	—
508	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
509	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
510	C₂×#101	C₂²×C₂₃	1	1	yes	characteristic, complemented
511	C₂×#100	C₂²×C₂₃	1	1	yes	characteristic
512	C₂×#100	C₂²×C₂₃	1	1	yes	characteristic, complemented
513	#408	C₂²×C₂₃	1	1	yes	characteristic
514	#390	C₂²×C₂₃	1	1	yes	characteristic
515	#343	C₂²×C₂₃	1	1	yes	characteristic, complemented
516	#341	C₂²×C₂₃	1	1	yes	characteristic, complemented
517	#339	C₂²×C₂₃	1	1	yes	characteristic, complemented
518	#336	C₂²×C₂₃	1	1	yes	characteristic, complemented
519	C₂×C₂₃	—	2	1	no	—
520	C₂×C₂₃	—	2	1	no	—
521	C₂×C₂₃	—	4	2	no	—
522	C₂×C₂₃	—	4	2	no	—
523	C₂×C₂₃	—	8	1	no	—
524	C₂×C₂₃	—	8	2	no	—
525	C₂×C₂₃	—	16	1	no	—
526	C₂×C₂₃	#2410	1	1	yes	characteristic
527	C₂×C₂₃	#3288	1	1	yes	characteristic
528	C₂×C₂₃	#3290	1	1	yes	characteristic
529	2₋¹⁺⁴	—	2	2	no	—
530	2₋¹⁺⁴	—	2	2	no	—
531	2₋¹⁺⁴	—	4	1	no	—
532	2₋¹⁺⁴	D₄×C₂₃	1	4	yes	complemented
533	H(5,𝔽₂)	—	2	2	no	—
534	H(5,𝔽₂)	—	2	2	no	—
535	H(5,𝔽₂)	—	2	2	no	—
536	H(5,𝔽₂)	—	4	1	no	—
537	C₂×#41	—	2	1	no	—
538	C₂×#41	—	2	1	no	—
539	C₂×#41	—	2	1	no	—
540	C₂×#41	—	2	1	no	—
541	C₂×#41	—	4	1	no	—
542	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
543	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
544	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
545	C₂²×Q₈	—	2	1	no	—
546	C₂²×Q₈	—	2	1	no	—
547	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
548	C₂²×D₄	—	2	1	no	—
549	C₂²×D₄	—	2	1	no	—
550	C₂²×D₄	—	4	1	no	—
551	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
552	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
553	#137	—	2	8	no	—
554	#137	—	2	2	no	—
555	#137	—	2	2	no	—
556	AGL(1,ℤ/8)	—	2	8	no	—
557	AGL(1,ℤ/8)	—	2	2	no	—
558	AGL(1,ℤ/8)	—	2	2	no	—
559	AGL(1,ℤ/8)	—	2	2	no	—
560	AGL(1,ℤ/8)	—	2	2	no	—
561	AGL(1,ℤ/8)	—	2	2	no	—
562	AGL(1,ℤ/8)	D₄×C₂₃	1	4	yes	complemented
563	#135	—	2	8	no	—
564	#135	—	2	2	no	—
565	#135	—	2	2	no	—
566	C₂×Q₁₆	—	2	1	no	—
567	C₂×Q₁₆	D₄×C₂₃	1	1	yes	characteristic
568	C₂×SD₁₆	—	2	8	no	—
569	C₂×SD₁₆	—	2	1	no	—
570	C₂×SD₁₆	—	2	2	no	—
571	C₂×SD₁₆	—	2	1	no	—
572	C₂×SD₁₆	—	2	2	no	—
573	C₂×SD₁₆	—	2	1	no	—
574	C₂×SD₁₆	—	2	1	no	—
575	C₂×SD₁₆	—	2	1	no	—
576	C₂×SD₁₆	—	2	1	no	—
577	C₂×SD₁₆	D₄×C₂₃	1	1	yes	characteristic
578	C₂×SD₁₆	D₄×C₂₃	1	1	yes	characteristic
579	C₂×D₈	—	2	1	no	—
580	C₂×D₈	—	2	2	no	—
581	C₂×D₈	—	2	1	no	—
582	C₂×D₈	—	2	1	no	—
583	C₂×D₈	—	2	1	no	—
584	C₂×D₈	—	2	1	no	—
585	C₂×D₈	—	4	1	no	—
586	C₂×D₈	D₄×C₂₃	1	1	yes	characteristic
587	#131	—	2	2	no	—
588	#131	—	2	2	no	—
589	#131	—	2	2	no	—
590	#131	—	4	1	no	—
591	C₂×M₁₆	—	2	1	no	—
592	C₂×M₁₆	—	2	1	no	—
593	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
594	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
595	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
596	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
597	C₂²×C₈	—	2	1	no	—
598	C₂²×C₈	—	2	1	no	—
599	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
600	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
601	#127	—	2	1	no	—
602	#124	—	2	2	no	—
603	#124	—	2	1	no	—
604	#124	—	4	1	no	—
605	#121	—	2	1	no	—
606	#121	—	2	1	no	—
607	#120	—	4	1	no	—
608	C₄×Q₈	—	2	1	no	—
609	C₄×D₄	—	2	1	no	—
610	C₄×D₄	—	4	1	no	—
611	#117	—	2	1	no	—
612	#117	C₂³×C₂₃	1	1	yes	characteristic
613	C₂×C₄⋊C₄	—	2	1	no	—
614	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
615	C₂×C₂²⋊C₄	—	4	1	no	—
616	C₂×C₂²⋊C₄	—	4	1	no	—
617	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
618	#108	—	2	2	no	—
619	C₄⋊C₈	—	2	1	no	—
620	C₄⋊C₈	—	2	1	no	—
621	#104	—	2	2	no	—
622	#104	—	2	2	no	—
623	#104	—	4	1	no	—
624	#103	—	2	1	no	—
625	#103	—	2	1	no	—
626	#103	—	2	1	no	—
627	#103	—	2	1	no	—
628	#103	—	2	1	no	—
629	#103	—	2	1	no	—
630	#103	D₄×C₂₃	1	1	yes	characteristic
631	#103	D₄×C₂₃	1	1	yes	characteristic
632	#102	—	2	1	no	—
633	#102	—	2	1	no	—
634	#102	—	2	1	no	—
635	#102	—	2	1	no	—
636	#102	—	2	1	no	—
637	#102	—	2	1	no	—
638	#102	D₄×C₂₃	1	1	yes	characteristic
639	#102	D₄×C₂₃	1	1	yes	characteristic
640	#101	—	2	2	no	—
641	#100	—	2	2	no	—
642	#100	—	2	2	no	—
643	C₂²⋊C₈	—	2	1	no	—
644	C₂²⋊C₈	—	2	1	no	—
645	C₂₃	#24460	1	1	yes	characteristic, direct product factor, Sylow
646	C₂⁴	—	2	1	no	—
647	C₂⁴	—	2	1	no	—
648	C₂⁴	—	4	1	no	—
649	#41	—	2	1	no	—
650	#41	—	2	1	no	—
651	#41	—	2	1	no	—
652	#41	—	2	1	no	—
653	#41	—	2	4	no	—
654	#41	—	2	4	no	—
655	#41	—	2	4	no	—
656	#41	—	2	1	no	—
657	#41	—	2	1	no	—
658	#41	—	2	1	no	—
659	#41	—	2	1	no	—
660	#41	—	4	4	no	—
661	#41	—	4	2	no	—
662	#41	—	4	2	no	—
663	#41	—	4	2	no	—
664	#41	—	4	4	no	—
665	#41	—	4	2	no	—
666	#41	—	4	2	no	—
667	#41	C₂×D₄×C₂₃	1	2	yes	—
668	#41	C₂×D₄×C₂₃	1	2	yes	—
669	#41	C₂×D₄×C₂₃	1	2	yes	—
670	#41	#41×C₂₃	1	2	yes	—
671	C₂×Q₈	—	2	1	no	—
672	C₂×Q₈	—	2	4	no	—
673	C₂×Q₈	—	2	4	no	—
674	C₂×Q₈	—	2	1	no	—
675	C₂×Q₈	—	2	1	no	—
676	C₂×Q₈	—	2	1	no	—
677	C₂×Q₈	—	2	1	no	—
678	C₂×Q₈	—	4	1	no	—
679	C₂×Q₈	—	4	2	no	—
680	C₂×Q₈	—	4	2	no	—
681	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
682	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
683	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
684	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
685	C₂×D₄	—	2	1	no	—
686	C₂×D₄	—	2	1	no	—
687	C₂×D₄	—	2	4	no	—
688	C₂×D₄	—	2	1	no	—
689	C₂×D₄	—	2	1	no	—
690	C₂×D₄	—	2	1	no	—
691	C₂×D₄	—	2	1	no	—
692	C₂×D₄	—	2	1	no	—
693	C₂×D₄	—	2	1	no	—
694	C₂×D₄	—	2	1	no	—
695	C₂×D₄	—	2	1	no	—
696	C₂×D₄	—	2	1	no	—
697	C₂×D₄	—	2	1	no	—
698	C₂×D₄	—	2	1	no	—
699	C₂×D₄	—	2	1	no	—
700	C₂×D₄	—	4	2	no	—
701	C₂×D₄	—	4	1	no	—
702	C₂×D₄	—	4	1	no	—
703	C₂×D₄	—	4	1	no	—
704	C₂×D₄	—	4	1	no	—
705	C₂×D₄	—	4	2	no	—
706	C₂×D₄	—	4	4	no	—
707	C₂×D₄	—	4	4	no	—
708	C₂×D₄	—	4	1	no	—
709	C₂×D₄	—	4	2	no	—
710	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
711	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
712	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
713	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
714	C₂²×C₄	—	2	1	no	—
715	C₂²×C₄	—	2	1	no	—
716	C₂²×C₄	—	2	1	no	—
717	C₂²×C₄	—	2	1	no	—
718	C₂²×C₄	—	2	1	no	—
719	C₂²×C₄	—	2	1	no	—
720	C₂²×C₄	—	4	1	no	—
721	C₂²×C₄	—	4	1	no	—
722	C₂²×C₄	—	4	1	no	—
723	C₂²×C₄	—	4	1	no	—
724	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
725	Q₁₆	—	2	4	no	—
726	Q₁₆	—	2	2	no	—
727	SD₁₆	—	2	4	no	—
728	SD₁₆	—	2	4	no	—
729	SD₁₆	—	2	4	no	—
730	SD₁₆	—	2	2	no	—
731	SD₁₆	—	2	4	no	—
732	SD₁₆	—	2	2	no	—
733	SD₁₆	—	4	2	no	—
734	SD₁₆	—	4	2	no	—
735	D₈	—	2	4	no	—
736	D₈	—	2	2	no	—
737	D₈	—	4	2	no	—
738	D₈	—	4	2	no	—
739	D₈	—	4	2	no	—
740	D₈	—	4	2	no	—
741	M₁₆	—	2	4	no	—
742	M₁₆	—	2	1	no	—
743	M₁₆	—	2	1	no	—
744	M₁₆	—	2	1	no	—
745	M₁₆	—	2	1	no	—
746	M₁₆	—	2	1	no	—
747	M₁₆	—	2	1	no	—
748	M₁₆	—	2	1	no	—
749	M₁₆	—	4	2	no	—
750	M₁₆	C₂×D₄×C₂₃	1	2	yes	—
751	C₂×C₈	—	2	4	no	—
752	C₂×C₈	—	2	1	no	—
753	C₂×C₈	—	2	1	no	—
754	C₂×C₈	—	2	1	no	—
755	C₂×C₈	—	2	1	no	—
756	C₂×C₈	—	2	1	no	—
757	C₂×C₈	—	2	1	no	—
758	C₂×C₈	—	2	1	no	—
759	C₂×C₈	—	2	1	no	—
760	C₂×C₈	—	4	2	no	—
761	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
762	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
763	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
764	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
765	C₄⋊C₄	—	2	1	no	—
766	C₄⋊C₄	—	2	1	no	—
767	C₄⋊C₄	—	4	1	no	—
768	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
769	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
770	C₂²⋊C₄	—	2	1	no	—
771	C₂²⋊C₄	—	4	1	no	—
772	C₂²⋊C₄	—	4	1	no	—
773	C₂²⋊C₄	—	4	1	no	—
774	C₂²⋊C₄	—	4	4	no	—
775	C₂²⋊C₄	—	8	2	no	—
776	C₄²	—	2	1	no	—
777	C₄²	—	2	1	no	—
778	C₄²	—	2	1	no	—
779	C₄²	—	4	1	no	—
780	C₂³	—	2	1	no	—
781	C₂³	—	2	1	no	—
782	C₂³	—	2	1	no	—
783	C₂³	—	2	2	no	—
784	C₂³	—	4	4	no	—
785	C₂³	—	4	1	no	—
786	C₂³	—	4	1	no	—
787	C₂³	—	4	1	no	—
788	C₂³	—	4	1	no	—
789	C₂³	—	4	1	no	—
790	C₂³	—	8	1	no	—
791	C₂³	—	8	1	no	—
792	C₂³	—	8	1	no	—
793	C₂³	—	8	1	no	—
794	C₂³	—	16	1	no	—
795	C₂³	—	16	1	no	—
796	C₂³	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
797	Q₈	—	2	1	no	—
798	Q₈	—	2	1	no	—
799	Q₈	—	2	2	no	—
800	Q₈	—	2	1	no	—
801	Q₈	—	2	2	no	—
802	Q₈	—	2	1	no	—
803	Q₈	—	4	4	no	—
804	Q₈	—	4	1	no	—
805	Q₈	—	4	1	no	—
806	Q₈	C₂₃×#120	1	2	yes	—
807	Q₈	C₂₃×#121	1	2	yes	—
808	D₄	—	2	2	no	—
809	D₄	—	2	2	no	—
810	D₄	—	2	2	no	—
811	D₄	—	2	2	no	—
812	D₄	—	2	2	no	—
813	D₄	—	2	1	no	—
814	D₄	—	2	1	no	—
815	D₄	—	2	2	no	—
816	D₄	—	2	1	no	—
817	D₄	—	2	1	no	—
818	D₄	—	4	4	no	—
819	D₄	—	4	4	no	—
820	D₄	—	4	4	no	—
821	D₄	—	4	1	no	—
822	D₄	—	4	1	no	—
823	D₄	—	4	1	no	—
824	D₄	—	4	1	no	—
825	D₄	—	4	1	no	—
826	D₄	—	4	1	no	—
827	D₄	—	4	1	no	—
828	D₄	—	4	1	no	—
829	D₄	—	16	1	no	—
830	D₄	—	16	1	no	—
831	D₄	C₂₃×#120	1	2	yes	—
832	D₄	C₂₃×#121	1	2	yes	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	4	4	no	—
844	C₂×C₄	—	4	4	no	—
845	C₂×C₄	—	4	4	no	—
846	C₂×C₄	—	4	1	no	—
847	C₂×C₄	—	4	1	no	—
848	C₂×C₄	—	4	1	no	—
849	C₂×C₄	—	4	1	no	—
850	C₂×C₄	—	4	1	no	—
851	C₂×C₄	—	4	1	no	—
852	C₂×C₄	—	4	1	no	—
853	C₂×C₄	—	4	1	no	—
854	C₂×C₄	—	8	1	no	—
855	C₂×C₄	—	16	1	no	—
856	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
857	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
858	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
859	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
860	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
861	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
862	C₈	—	2	1	no	—
863	C₈	—	2	2	no	—
864	C₈	—	2	1	no	—
865	C₈	—	2	1	no	—
866	C₈	—	2	1	no	—
867	C₈	—	4	1	no	—
868	C₈	—	4	1	no	—
869	C₈	—	4	1	no	—
870	C₂²	—	2	1	no	—
871	C₂²	—	2	1	no	—
872	C₂²	—	2	2	no	—
873	C₂²	—	2	2	no	—
874	C₂²	—	4	1	no	—
875	C₂²	—	4	1	no	—
876	C₂²	—	4	1	no	—
877	C₂²	—	4	1	no	—
878	C₂²	—	4	1	no	—
879	C₂²	—	4	2	no	—
880	C₂²	—	4	1	no	—
881	C₂²	—	4	1	no	—
882	C₂²	—	8	2	no	—
883	C₂²	—	8	2	no	—
884	C₂²	—	8	1	no	—
885	C₂²	—	8	1	no	—
886	C₂²	—	8	1	no	—
887	C₂²	—	8	1	no	—
888	C₂²	—	8	1	no	—
889	C₂²	—	16	1	no	—
890	C₂²	—	16	1	no	—
891	C₂²	—	16	4	no	—
892	C₂²	C₂₃×#534	1	1	yes	characteristic
893	C₂²	D₄²×C₂₃	1	1	yes	characteristic
894	C₂²	C₂₃×#546	1	1	yes	characteristic
895	C₄	—	2	2	no	—
896	C₄	—	2	2	no	—
897	C₄	—	4	1	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	1	no	—
900	C₄	—	4	1	no	—
901	C₄	—	8	1	no	—
902	C₄	—	8	1	no	—
903	C₄	C₂×C₂₃×#120	1	1	yes	characteristic
904	C₄	C₂×C₂₃×#121	1	1	yes	characteristic
905	C₄	D₄²×C₂₃	1	1	yes	characteristic
906	C₄	C₂₃×#546	1	1	yes	characteristic
907	C₂	—	2	1	no	—
908	C₂	—	2	1	no	—
909	C₂	—	4	2	no	—
910	C₂	—	4	2	no	—
911	C₂	—	8	1	no	—
912	C₂	—	8	2	no	—
913	C₂	—	16	1	no	—
914	C₂	C₂₃×#2410	1	1	yes	characteristic
915	C₂	C₂₃×#3288	1	1	yes	characteristic
916	C₂	C₂₃×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂²×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#577	C₂	semidirect
2. C₂×C₂₃×#472	C₂	semidirect
3. C₂₃×#3045	C₂	semidirect
4. C₂×C₂₃×#454	C₂	semidirect
5. C₂₃×#3008	C₂	semidirect
6. C₂₃×#2898	C₂	semidirect
7. C₂₃×#2052	C₂	semidirect
8. C₂₃×#2046	C₂	semidirect
9. C₂₃×#2012	C₂	semidirect
10. C₂₃×#2004	C₂	semidirect
11. C₂₃×#1907	C₂	semidirect
12. C₂₃×#1883	C₂	semidirect
13. C₂₃×#1876	C₂	semidirect
14. C₂₃×#1866	C₂	semidirect
15. C₂₃×#1792	C₂	semidirect
25. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
32. C₂×C₂₃×#131	C₂²	semidirect
34. C₂×C₂₃×#124	C₂²	semidirect
35. C₂₃×#520	C₂²	semidirect
46. C₂×C₂₃×#108	C₂²	semidirect
47. C₂₃×#424	C₂²	semidirect
50. C₂×C₂₃×#104	C₂²	semidirect
52. C₂₃×#419	C₂²	semidirect
60. C₂×C₂₃×#103	C₂²	semidirect
61. C₂×C₂₃×#102	C₂²	semidirect
62. C₂×C₂₃×#101	C₂²	semidirect
64. C₂×C₂₃×#100	C₂²	semidirect
67. C₂₃×#343	C₂²	semidirect
68. C₂₃×#341	C₂²	semidirect
69. C₂₃×#339	C₂²	semidirect
70. C₂₃×#336	C₂²	semidirect
74. C₂₃×2₋¹⁺⁴	D₄	semidirect
104. C₂₃×AGL(1,ℤ/8)	D₄	semidirect
321. #24460	C₂₃	direct (N × H)
412. C₂×#577	C₂×C₂₃	semidirect
413. C₂×#472	C₂×C₂₃	semidirect
414. #3045	C₂×C₂₃	semidirect
415. C₂×#454	C₂×C₂₃	semidirect
416. #3008	C₂×C₂₃	semidirect
417. #2898	C₂×C₂₃	semidirect
418. #2052	C₂×C₂₃	semidirect
419. #2046	C₂×C₂₃	semidirect
420. #2012	C₂×C₂₃	semidirect
421. #2004	C₂×C₂₃	semidirect
422. #1907	C₂×C₂₃	semidirect
423. #1883	C₂×C₂₃	semidirect
424. #1876	C₂×C₂₃	semidirect
425. #1866	C₂×C₂₃	semidirect
426. #1792	C₂×C₂₃	semidirect
473. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
480. C₂×#131	C₂²×C₂₃	semidirect
482. C₂×#124	C₂²×C₂₃	semidirect
483. #520	C₂²×C₂₃	semidirect
494. C₂×#108	C₂²×C₂₃	semidirect
495. #424	C₂²×C₂₃	semidirect
498. C₂×#104	C₂²×C₂₃	semidirect
500. #419	C₂²×C₂₃	semidirect
508. C₂×#103	C₂²×C₂₃	semidirect
509. C₂×#102	C₂²×C₂₃	semidirect
510. C₂×#101	C₂²×C₂₃	semidirect
512. C₂×#100	C₂²×C₂₃	semidirect
515. #343	C₂²×C₂₃	semidirect
516. #341	C₂²×C₂₃	semidirect
517. #339	C₂²×C₂₃	semidirect
518. #336	C₂²×C₂₃	semidirect
532. 2₋¹⁺⁴	D₄×C₂₃	semidirect
562. AGL(1,ℤ/8)	D₄×C₂₃	semidirect
645. C₂₃	#24460	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#577	2
C₂×C₂₃×#472	2
C₂₃×#3045	2
C₂×C₂₃×#454	2
C₂₃×#3008	2
C₂₃×#2898	2
C₂₃×#2052	2
C₂₃×#2046	2
C₂₃×#2012	2
C₂₃×#2004	2
C₂₃×#1907	2
C₂₃×#1883	2
C₂₃×#1876	2
C₂₃×#1866	2
C₂₃×#1792	2
#24460	23

Subgroups — C23×#24460 #19172086

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#24460 #19172086