Subgroups — C₄×C₂₃×#472 #19169179

Order 5888.

946 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#472	C₂	1	1	yes	maximal, characteristic
2	C₄×C₂₃×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
3	C₂×C₄×D₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₂₃×#131	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#1978	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1952	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1931	C₂	1	2	yes	maximal, complemented
8	C₂₃×#1907	C₂	1	2	yes	maximal, complemented
9	C₂₃×#1816	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₂₃×#108	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₂₃×#100	C₂	1	2	yes	maximal, complemented
12	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
13	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
14	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
15	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
16	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
18	C₂₃×#472	C₄	1	8	yes	direct product factor
19	C₂₃×#442	—	2	2	no	—
20	C₂₃×#440	—	2	2	no	—
21	C₄×SD₁₆×C₂₃	—	2	2	no	—
22	C₄×D₈×C₂₃	—	2	1	no	—
23	C₄×D₈×C₂₃	—	2	1	no	—
24	C₄×D₈×C₂₃	—	2	1	no	—
25	C₄×D₈×C₂₃	—	2	1	no	—
26	C₄×D₈×C₂₃	—	2	2	no	—
27	C₂×C₂₃×#108	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×#108	C₂²	1	1	yes	characteristic
29	C₂₃×#428	C₂²	1	2	yes	—
30	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
31	C₂₃×#418	C₂²	1	2	yes	—
32	C₂₃×#417	C₂²	1	2	yes	—
33	C₂×C₂₃×#102	C₂²	1	2	yes	—
34	C₂×C₂₃×#100	C₂²	1	2	yes	—
35	C₂×C₂₃×#100	C₂²	1	2	yes	—
36	C₂₃×#405	—	2	1	no	—
37	C₂₃×#405	—	2	1	no	—
38	C₂₃×#405	C₂²	1	1	yes	characteristic
39	C₂₃×#405	C₂²	1	1	yes	characteristic
40	C₄×M₁₆×C₂₃	—	2	1	no	—
41	C₄×M₁₆×C₂₃	C₂²	1	2	yes	—
42	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₈×C₂₃	—	2	1	no	—
44	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
45	C₂₃×#343	C₂²	1	2	yes	—
46	C₂₃×#343	C₂²	1	2	yes	—
47	C₂₃×#341	C₂²	1	2	yes	—
48	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
50	C₂³×C₄×C₂₃	—	2	2	no	—
51	C₂₃×AGL(1,ℤ/8)	—	2	4	no	—
52	C₂₃×AGL(1,ℤ/8)	C₂×C₄	1	8	yes	complemented
53	C₂×SD₁₆×C₂₃	—	2	2	no	—
54	C₂×D₈×C₂₃	—	2	2	no	—
55	C₂×D₈×C₂₃	—	2	1	no	—
56	C₂×D₈×C₂₃	—	2	1	no	—
57	C₂×D₈×C₂₃	—	2	2	no	—
58	C₂×D₈×C₂₃	C₂×C₄	1	4	yes	complemented
59	C₂₃×#131	—	2	2	no	—
60	C₂₃×#131	—	2	2	no	—
61	C₂₃×#131	—	2	2	no	—
62	C₂₃×#131	C₂×C₄	1	4	yes	complemented
63	C₂×M₁₆×C₂₃	—	2	1	no	—
64	C₂×M₁₆×C₂₃	—	2	1	no	—
65	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
66	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
67	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
68	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₂₃	—	2	1	no	—
70	C₂²×C₈×C₂₃	—	2	1	no	—
71	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
73	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
74	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
75	C₄×D₄×C₂₃	—	2	1	no	—
76	C₄×D₄×C₂₃	—	2	1	no	—
77	C₄×D₄×C₂₃	—	2	2	no	—
78	C₄×D₄×C₂₃	—	2	2	no	—
79	C₄×D₄×C₂₃	—	2	2	no	—
80	C₄×D₄×C₂₃	—	2	2	no	—
81	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
82	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
83	C₂₃×#117	—	2	1	no	—
84	C₂₃×#117	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
86	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
87	C₂×C₄²×C₂₃	—	2	1	no	—
88	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
89	C₂₃×#108	—	2	2	no	—
90	C₂₃×#108	C₂×C₄	1	4	yes	complemented
91	C₂₃×#107	—	2	1	no	—
92	C₂₃×#107	—	2	1	no	—
93	C₂₃×#107	—	2	2	no	—
94	C₂₃×#106	—	2	2	no	—
95	C₂₃×#103	—	2	2	no	—
96	C₂₃×#102	—	2	2	no	—
97	C₂₃×#102	—	2	2	no	—
98	C₂₃×#102	—	2	2	no	—
99	C₂₃×#102	—	2	2	no	—
100	C₂₃×#102	—	2	2	no	—
101	C₂₃×#100	—	2	4	no	—
102	C₂₃×#100	C₂×C₄	1	8	yes	complemented
103	C₂₃×#97	—	2	1	no	—
104	C₂₃×#97	—	2	1	no	—
105	C₂₃×#97	—	2	1	no	—
106	C₂₃×#97	—	2	2	no	—
107	C₄×C₈×C₂₃	—	2	1	no	—
108	C₄×C₈×C₂₃	—	2	1	no	—
109	C₄×C₈×C₂₃	—	2	1	no	—
110	C₄×C₈×C₂₃	—	2	2	no	—
111	C₄×C₈×C₂₃	D₄	1	1	yes	characteristic
112	C₄×C₈×C₂₃	D₄	1	1	yes	characteristic
113	C₄×C₈×C₂₃	D₄	1	1	yes	characteristic
114	C₄×C₈×C₂₃	D₄	1	1	yes	characteristic
115	C₂⁴×C₂₃	—	2	2	no	—
116	#41×C₂₃	—	2	1	no	—
117	#41×C₂₃	—	2	1	no	—
118	#41×C₂₃	C₂²×C₄	1	2	yes	—
119	#41×C₂₃	#41	1	2	yes	—
120	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
121	C₂×D₄×C₂₃	—	2	1	no	—
122	C₂×D₄×C₂₃	—	2	2	no	—
123	C₂×D₄×C₂₃	—	2	2	no	—
124	C₂×D₄×C₂₃	—	2	2	no	—
125	C₂×D₄×C₂₃	—	2	2	no	—
126	C₂×D₄×C₂₃	—	2	2	no	—
127	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
128	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₂₃	—	2	1	no	—
130	C₂²×C₄×C₂₃	—	2	1	no	—
131	C₂²×C₄×C₂₃	—	2	1	no	—
132	C₂²×C₄×C₂₃	—	2	2	no	—
133	C₂²×C₄×C₂₃	—	4	2	no	—
134	C₂²×C₄×C₂₃	—	4	2	no	—
135	C₂²×C₄×C₂₃	—	8	4	no	—
136	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
137	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
138	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
139	SD₁₆×C₂₃	—	2	8	no	—
140	D₈×C₂₃	—	2	8	no	—
141	D₈×C₂₃	—	2	4	no	—
142	D₈×C₂₃	—	2	4	no	—
143	M₁₆×C₂₃	—	2	4	no	—
144	M₁₆×C₂₃	—	2	1	no	—
145	M₁₆×C₂₃	—	2	1	no	—
146	M₁₆×C₂₃	—	2	2	no	—
147	M₁₆×C₂₃	—	2	4	no	—
148	M₁₆×C₂₃	—	2	2	no	—
149	M₁₆×C₂₃	—	2	2	no	—
150	M₁₆×C₂₃	C₂²×C₄	1	2	yes	—
151	M₁₆×C₂₃	C₂²×C₄	1	4	yes	—
152	M₁₆×C₂₃	#41	1	2	yes	—
153	C₂×C₈×C₂₃	—	2	4	no	—
154	C₂×C₈×C₂₃	—	2	2	no	—
155	C₂×C₈×C₂₃	—	2	1	no	—
156	C₂×C₈×C₂₃	—	2	1	no	—
157	C₂×C₈×C₂₃	—	2	1	no	—
158	C₂×C₈×C₂₃	—	2	1	no	—
159	C₂×C₈×C₂₃	—	2	4	no	—
160	C₂×C₈×C₂₃	—	2	2	no	—
161	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
162	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
163	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
164	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
165	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
166	C₂×C₈×C₂₃	#41	1	2	yes	—
167	C₄⋊C₄×C₂₃	—	2	1	no	—
168	C₄⋊C₄×C₂₃	—	2	1	no	—
169	C₄⋊C₄×C₂₃	—	2	2	no	—
170	C₄⋊C₄×C₂₃	—	2	2	no	—
171	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
172	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
173	C₂²⋊C₄×C₂₃	—	2	1	no	—
174	C₂²⋊C₄×C₂₃	—	2	1	no	—
175	C₂²⋊C₄×C₂₃	—	2	1	no	—
176	C₂²⋊C₄×C₂₃	—	4	2	no	—
177	C₂²⋊C₄×C₂₃	—	4	2	no	—
178	C₄²×C₂₃	—	2	1	no	—
179	C₄²×C₂₃	—	2	1	no	—
180	C₄²×C₂₃	—	2	1	no	—
181	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
182	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
183	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
184	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
185	C₄×#472	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₂³×C₂₃	—	2	1	no	—
187	C₂³×C₂₃	—	2	4	no	—
188	C₂³×C₂₃	—	4	2	no	—
189	C₂³×C₂₃	—	4	2	no	—
190	C₂³×C₂₃	—	8	2	no	—
191	C₂³×C₂₃	—	8	2	no	—
192	C₂³×C₂₃	C₂×#41	1	1	yes	characteristic
193	Q₈×C₂₃	—	2	1	no	—
194	Q₈×C₂₃	C₄×D₄	1	2	yes	—
195	D₄×C₂₃	—	2	2	no	—
196	D₄×C₂₃	—	2	2	no	—
197	D₄×C₂₃	—	2	4	no	—
198	D₄×C₂₃	—	2	4	no	—
199	D₄×C₂₃	—	2	1	no	—
200	D₄×C₂₃	—	4	2	no	—
201	D₄×C₂₃	—	4	2	no	—
202	D₄×C₂₃	C₄×D₄	1	2	yes	—
203	C₂×C₄×C₂₃	—	2	1	no	—
204	C₂×C₄×C₂₃	—	2	2	no	—
205	C₂×C₄×C₂₃	—	2	2	no	—
206	C₂×C₄×C₂₃	—	2	2	no	—
207	C₂×C₄×C₂₃	—	2	1	no	—
208	C₂×C₄×C₂₃	—	2	1	no	—
209	C₂×C₄×C₂₃	—	4	1	no	—
210	C₂×C₄×C₂₃	—	4	2	no	—
211	C₂×C₄×C₂₃	—	4	2	no	—
212	C₂×C₄×C₂₃	—	4	2	no	—
213	C₂×C₄×C₂₃	—	8	4	no	—
214	C₂×C₄×C₂₃	—	8	4	no	—
215	C₂×C₄×C₂₃	—	8	2	no	—
216	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
217	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
218	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
219	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
220	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
221	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
224	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
225	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
226	C₈×C₂₃	—	2	2	no	—
227	C₈×C₂₃	—	2	4	no	—
228	C₈×C₂₃	—	2	1	no	—
229	C₈×C₂₃	—	2	2	no	—
230	C₈×C₂₃	—	2	1	no	—
231	C₈×C₂₃	—	4	2	no	—
232	C₈×C₂₃	C₄×D₄	1	2	yes	—
233	C₈×C₂₃	C₄×D₄	1	2	yes	—
234	C₂×#472	C₂×C₂₃	1	1	yes	characteristic
235	C₄×AGL(1,ℤ/8)	C₂×C₂₃	1	2	yes	complemented
236	C₂×C₄×D₈	C₂×C₂₃	1	1	yes	characteristic, complemented
237	C₄×#131	C₂×C₂₃	1	1	yes	characteristic, complemented
238	#1978	C₂×C₂₃	1	1	yes	characteristic, complemented
239	#1952	C₂×C₂₃	1	1	yes	characteristic, complemented
240	#1931	C₂×C₂₃	1	2	yes	complemented
241	#1907	C₂×C₂₃	1	2	yes	complemented
242	#1816	C₂×C₂₃	1	1	yes	characteristic, complemented
243	C₄×#108	C₂×C₂₃	1	1	yes	characteristic, complemented
244	C₄×#100	C₂×C₂₃	1	2	yes	complemented
245	C₂²×C₂₃	—	2	1	no	—
246	C₂²×C₂₃	—	2	1	no	—
247	C₂²×C₂₃	—	2	2	no	—
248	C₂²×C₂₃	—	4	1	no	—
249	C₂²×C₂₃	—	4	1	no	—
250	C₂²×C₂₃	—	4	4	no	—
251	C₂²×C₂₃	—	8	4	no	—
252	C₂²×C₂₃	—	8	4	no	—
253	C₂²×C₂₃	—	8	2	no	—
254	C₂²×C₂₃	—	8	2	no	—
255	C₂²×C₂₃	C₄×#41	1	1	yes	characteristic
256	C₂²×C₂₃	C₂×#121	1	1	yes	characteristic
257	C₂²×C₂₃	#529	1	1	yes	characteristic
258	C₄×C₂₃	—	2	1	no	—
259	C₄×C₂₃	—	2	1	no	—
260	C₄×C₂₃	—	2	1	no	—
261	C₄×C₂₃	—	2	2	no	—
262	C₄×C₂₃	—	4	1	no	—
263	C₄×C₂₃	—	4	1	no	—
264	C₄×C₂₃	—	8	2	no	—
265	C₄×C₂₃	#472	1	2	yes	direct product factor
266	C₄×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
267	C₄×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
268	C₄×C₂₃	#525	1	1	yes	characteristic
269	C₄×C₂₃	#532	1	1	yes	characteristic
270	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	—
271	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
272	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
273	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
274	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
275	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
276	#472	C₄×C₂₃	1	8	yes	direct product factor
277	#442	—	2	2	no	—
278	#440	—	2	2	no	—
279	C₄×SD₁₆	—	2	2	no	—
280	C₄×D₈	—	2	2	no	—
281	C₄×D₈	—	2	1	no	—
282	C₄×D₈	—	2	1	no	—
283	C₄×D₈	—	2	1	no	—
284	C₄×D₈	—	2	1	no	—
285	C₂×#108	C₂²×C₂₃	1	1	yes	characteristic
286	C₂×#108	C₂²×C₂₃	1	1	yes	characteristic
287	#428	C₂²×C₂₃	1	2	yes	—
288	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
289	#418	C₂²×C₂₃	1	2	yes	—
290	#417	C₂²×C₂₃	1	2	yes	—
291	C₂×#102	C₂²×C₂₃	1	2	yes	—
292	C₂×#100	C₂²×C₂₃	1	2	yes	—
293	C₂×#100	C₂²×C₂₃	1	2	yes	—
294	#405	—	2	1	no	—
295	#405	—	2	1	no	—
296	#405	C₂²×C₂₃	1	1	yes	characteristic
297	#405	C₂²×C₂₃	1	1	yes	characteristic
298	C₄×M₁₆	—	2	1	no	—
299	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
300	C₄×M₁₆	C₂²×C₂₃	1	2	yes	—
301	C₂×C₄×C₈	—	2	1	no	—
302	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
303	#343	C₂²×C₂₃	1	2	yes	—
304	#343	C₂²×C₂₃	1	2	yes	—
305	#341	C₂²×C₂₃	1	2	yes	—
306	C₂×C₂₃	—	2	1	no	—
307	C₂×C₂₃	—	2	1	no	—
308	C₂×C₂₃	—	4	2	no	—
309	C₂×C₂₃	—	8	4	no	—
310	C₂×C₂₃	C₄×#121	1	1	yes	characteristic
311	C₂×C₂₃	C₂×#472	1	1	yes	characteristic
312	C₂×C₂₃	#3067	1	1	yes	characteristic
313	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
314	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
315	C₂³×C₄	—	2	2	no	—
316	AGL(1,ℤ/8)	—	2	4	no	—
317	AGL(1,ℤ/8)	C₂×C₄×C₂₃	1	8	yes	complemented
318	C₂×SD₁₆	—	2	2	no	—
319	C₂×D₈	—	2	2	no	—
320	C₂×D₈	—	2	1	no	—
321	C₂×D₈	—	2	1	no	—
322	C₂×D₈	—	2	2	no	—
323	C₂×D₈	C₂×C₄×C₂₃	1	4	yes	complemented
324	#131	—	2	2	no	—
325	#131	—	2	2	no	—
326	#131	—	2	2	no	—
327	#131	C₂×C₄×C₂₃	1	4	yes	complemented
328	C₂×M₁₆	—	2	1	no	—
329	C₂×M₁₆	—	2	1	no	—
330	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
331	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
332	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
333	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
334	C₂²×C₈	—	2	1	no	—
335	C₂²×C₈	—	2	1	no	—
336	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
337	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
338	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
339	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
340	C₄×D₄	—	2	1	no	—
341	C₄×D₄	—	2	1	no	—
342	C₄×D₄	—	2	2	no	—
343	C₄×D₄	—	2	2	no	—
344	C₄×D₄	—	2	2	no	—
345	C₄×D₄	—	2	2	no	—
346	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
347	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
348	#117	—	2	1	no	—
349	#117	C₂³×C₂₃	1	1	yes	characteristic
350	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
351	C₂×C₂²⋊C₄	—	2	2	no	—
352	C₂×C₄²	—	2	1	no	—
353	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
354	#108	—	2	2	no	—
355	#108	C₂×C₄×C₂₃	1	4	yes	complemented
356	#107	—	2	1	no	—
357	#107	—	2	1	no	—
358	#107	—	2	2	no	—
359	#106	—	2	2	no	—
360	#103	—	2	2	no	—
361	#102	—	2	2	no	—
362	#102	—	2	2	no	—
363	#102	—	2	2	no	—
364	#102	—	2	2	no	—
365	#102	—	2	2	no	—
366	#100	—	2	4	no	—
367	#100	C₂×C₄×C₂₃	1	8	yes	complemented
368	#97	—	2	1	no	—
369	#97	—	2	1	no	—
370	#97	—	2	1	no	—
371	#97	—	2	2	no	—
372	C₄×C₈	—	2	1	no	—
373	C₄×C₈	—	2	1	no	—
374	C₄×C₈	—	2	1	no	—
375	C₄×C₈	—	2	2	no	—
376	C₄×C₈	D₄×C₂₃	1	1	yes	characteristic
377	C₄×C₈	D₄×C₂₃	1	1	yes	characteristic
378	C₄×C₈	D₄×C₂₃	1	1	yes	characteristic
379	C₄×C₈	D₄×C₂₃	1	1	yes	characteristic
380	C₂₃	C₄×#472	1	1	yes	characteristic, direct product factor, Sylow
381	C₂⁴	—	2	2	no	—
382	#41	—	2	1	no	—
383	#41	—	2	1	no	—
384	#41	C₂²×C₄×C₂₃	1	2	yes	—
385	#41	#41×C₂₃	1	2	yes	—
386	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	—	2	2	no	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
394	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	4	2	no	—
400	C₂²×C₄	—	4	2	no	—
401	C₂²×C₄	—	8	4	no	—
402	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
403	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
404	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
405	SD₁₆	—	2	8	no	—
406	D₈	—	2	8	no	—
407	D₈	—	2	4	no	—
408	D₈	—	2	4	no	—
409	M₁₆	—	2	4	no	—
410	M₁₆	—	2	1	no	—
411	M₁₆	—	2	1	no	—
412	M₁₆	—	2	2	no	—
413	M₁₆	—	2	4	no	—
414	M₁₆	—	2	2	no	—
415	M₁₆	—	2	2	no	—
416	M₁₆	C₂²×C₄×C₂₃	1	2	yes	—
417	M₁₆	C₂²×C₄×C₂₃	1	4	yes	—
418	M₁₆	#41×C₂₃	1	2	yes	—
419	C₂×C₈	—	2	4	no	—
420	C₂×C₈	—	2	1	no	—
421	C₂×C₈	—	2	1	no	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	4	no	—
426	C₂×C₈	—	2	2	no	—
427	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
428	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
429	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
430	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
431	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
432	C₂×C₈	#41×C₂₃	1	2	yes	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	—	2	2	no	—
437	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
438	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
439	C₂²⋊C₄	—	2	1	no	—
440	C₂²⋊C₄	—	2	1	no	—
441	C₂²⋊C₄	—	2	1	no	—
442	C₂²⋊C₄	—	4	2	no	—
443	C₂²⋊C₄	—	4	2	no	—
444	C₄²	—	2	1	no	—
445	C₄²	—	2	1	no	—
446	C₄²	—	2	1	no	—
447	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
448	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
449	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
450	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
451	C₂³	—	2	1	no	—
452	C₂³	—	2	4	no	—
453	C₂³	—	4	2	no	—
454	C₂³	—	4	2	no	—
455	C₂³	—	8	2	no	—
456	C₂³	—	8	2	no	—
457	C₂³	C₂×#41×C₂₃	1	1	yes	characteristic
458	Q₈	—	2	1	no	—
459	Q₈	C₄×D₄×C₂₃	1	2	yes	—
460	D₄	—	2	2	no	—
461	D₄	—	2	2	no	—
462	D₄	—	2	4	no	—
463	D₄	—	2	4	no	—
464	D₄	—	2	1	no	—
465	D₄	—	4	2	no	—
466	D₄	—	4	2	no	—
467	D₄	C₄×D₄×C₂₃	1	2	yes	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	8	4	no	—
479	C₂×C₄	—	8	4	no	—
480	C₂×C₄	—	8	2	no	—
481	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
482	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
483	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
484	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
485	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
486	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
487	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
488	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
489	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
490	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
491	C₈	—	2	2	no	—
492	C₈	—	2	4	no	—
493	C₈	—	2	1	no	—
494	C₈	—	2	2	no	—
495	C₈	—	2	1	no	—
496	C₈	—	4	2	no	—
497	C₈	C₄×D₄×C₂₃	1	2	yes	—
498	C₈	C₄×D₄×C₂₃	1	2	yes	—
499	C₂²	—	2	1	no	—
500	C₂²	—	2	1	no	—
501	C₂²	—	2	2	no	—
502	C₂²	—	4	1	no	—
503	C₂²	—	4	1	no	—
504	C₂²	—	4	4	no	—
505	C₂²	—	8	4	no	—
506	C₂²	—	8	4	no	—
507	C₂²	—	8	2	no	—
508	C₂²	—	8	2	no	—
509	C₂²	C₄×#41×C₂₃	1	1	yes	characteristic
510	C₂²	C₂×C₂₃×#121	1	1	yes	characteristic
511	C₂²	C₂₃×#529	1	1	yes	characteristic
512	C₄	—	2	1	no	—
513	C₄	—	2	1	no	—
514	C₄	—	2	1	no	—
515	C₄	—	2	2	no	—
516	C₄	—	4	1	no	—
517	C₄	—	4	1	no	—
518	C₄	—	8	2	no	—
519	C₄	C₂₃×#472	1	2	yes	direct product factor
520	C₄	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
521	C₄	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
522	C₄	C₂₃×#525	1	1	yes	characteristic
523	C₄	C₂₃×#532	1	1	yes	characteristic
524	C₂	—	2	1	no	—
525	C₂	—	2	1	no	—
526	C₂	—	4	2	no	—
527	C₂	—	8	4	no	—
528	C₂	C₄×C₂₃×#121	1	1	yes	characteristic
529	C₂	C₂×C₂₃×#472	1	1	yes	characteristic
530	C₂	C₂₃×#3067	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	#121
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
socle	C₂²×C₂₃	C₂×#121
prime radical	C₂×C₂₃×#472	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₂₃×AGL(1,ℤ/8)	C₂	semidirect
3. C₂×C₄×D₈×C₂₃	C₂	semidirect
4. C₄×C₂₃×#131	C₂	semidirect
5. C₂₃×#1978	C₂	semidirect
6. C₂₃×#1952	C₂	semidirect
7. C₂₃×#1931	C₂	semidirect
8. C₂₃×#1907	C₂	semidirect
9. C₂₃×#1816	C₂	semidirect
10. C₄×C₂₃×#108	C₂	semidirect
11. C₄×C₂₃×#100	C₂	semidirect
18. C₂₃×#472	C₄	direct (N × H)
52. C₂₃×AGL(1,ℤ/8)	C₂×C₄	semidirect
58. C₂×D₈×C₂₃	C₂×C₄	semidirect
62. C₂₃×#131	C₂×C₄	semidirect
90. C₂₃×#108	C₂×C₄	semidirect
102. C₂₃×#100	C₂×C₄	semidirect
185. C₄×#472	C₂₃	direct (N × H)
235. C₄×AGL(1,ℤ/8)	C₂×C₂₃	semidirect
236. C₂×C₄×D₈	C₂×C₂₃	semidirect
237. C₄×#131	C₂×C₂₃	semidirect
238. #1978	C₂×C₂₃	semidirect
239. #1952	C₂×C₂₃	semidirect
240. #1931	C₂×C₂₃	semidirect
241. #1907	C₂×C₂₃	semidirect
242. #1816	C₂×C₂₃	semidirect
243. C₄×#108	C₂×C₂₃	semidirect
244. C₄×#100	C₂×C₂₃	semidirect
265. C₄×C₂₃	#472	direct (N × H)
276. #472	C₄×C₂₃	direct (N × H)
317. AGL(1,ℤ/8)	C₂×C₄×C₂₃	semidirect
323. C₂×D₈	C₂×C₄×C₂₃	semidirect
327. #131	C₂×C₄×C₂₃	semidirect
355. #108	C₂×C₄×C₂₃	semidirect
367. #100	C₂×C₄×C₂₃	semidirect
380. C₂₃	C₄×#472	direct (N × H)
519. C₄	C₂₃×#472	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×#472	2
C₄×C₂₃×AGL(1,ℤ/8)	2
C₂×C₄×D₈×C₂₃	2
C₄×C₂₃×#131	2
C₂₃×#1978	2
C₂₃×#1952	2
C₂₃×#1931	2
C₂₃×#1907	2
C₂₃×#1816	2
C₄×C₂₃×#108	2
C₄×C₂₃×#100	2
C₄×#472	23

Subgroups — C4×C23×#472 #19169179

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₂₃×#472 #19169179