Subgroups — C₂×C₂₃×#1635 #19166113

Order 5888.

1206 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#547	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#487	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#1635	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₂₃×#332	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₂₃	—	2	1	no	—
10	C₂₃×#547	—	2	2	no	—
11	C₂₃×#547	—	2	2	no	—
12	C₂₃×#547	—	2	2	no	—
13	C₂₃×#547	C₂²	1	4	yes	—
14	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₂₃×#123	—	2	2	no	—
17	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
18	C₂×C₂₃×#121	—	2	1	no	—
19	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₂₃	—	2	1	no	—
22	C₂₃×#487	—	2	2	no	—
23	C₂₃×#487	C₂²	1	4	yes	complemented
24	C₂₃×#476	—	2	2	no	—
25	C₂₃×#476	—	2	2	no	—
26	C₂₃×#476	C₂²	1	4	yes	complemented
27	C₂₃×#476	C₂²	1	4	yes	complemented
28	C₂×C₂₃×#106	—	2	1	no	—
29	C₂×C₂₃×#106	—	2	1	no	—
30	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₂₃×#103	—	2	2	no	—
33	C₂×C₂₃×#102	—	2	1	no	—
34	C₂×C₂₃×#102	—	2	1	no	—
35	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
36	C₂₃×#332	C₂²	1	4	yes	complemented
37	C₂₃×D₄⋊C₈	C₂²	1	4	yes	complemented
38	C₂₃×D₄⋊C₈	C₂²	1	4	yes	complemented
39	C₂×#41×C₂₃	—	2	4	no	—
40	C₂×#41×C₂₃	—	2	4	no	—
41	C₂×#41×C₂₃	—	4	4	no	—
42	C₂×#41×C₂₃	—	4	4	no	—
43	C₂²×Q₈×C₂₃	—	2	1	no	—
44	C₂²×Q₈×C₂₃	—	2	1	no	—
45	C₂²×D₄×C₂₃	—	2	2	no	—
46	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
47	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₂₃	—	2	2	no	—
49	C₂³×C₄×C₂₃	—	2	1	no	—
50	C₂³×C₄×C₂₃	—	2	1	no	—
51	C₂²×C₈×C₂₃	—	2	1	no	—
52	C₂²×C₈×C₂₃	—	2	1	no	—
53	C₂²×C₈×C₂₃	—	2	1	no	—
54	C₂₃×C₄⋊Q₈	—	2	1	no	—
55	C₂₃×C₄⋊Q₈	—	2	1	no	—
56	C₂₃×C₄⋊Q₈	—	2	1	no	—
57	C₂₃×C₄⋊Q₈	—	2	1	no	—
58	C₂₃×C₄⋊Q₈	—	2	1	no	—
59	C₂₃×C₄⋊Q₈	D₄	1	2	yes	—
60	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
61	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
62	C₂₃×#123	—	2	8	no	—
63	C₂₃×#123	—	2	8	no	—
64	C₂₃×C₂²⋊Q₈	—	2	4	no	—
65	C₂₃×C₂²⋊Q₈	—	2	4	no	—
66	C₂₃×#121	—	2	4	no	—
67	C₂₃×#121	—	2	4	no	—
68	C₄×D₄×C₂₃	—	2	1	no	—
69	C₄×D₄×C₂₃	—	2	1	no	—
70	C₄×D₄×C₂₃	—	2	1	no	—
71	C₄×D₄×C₂₃	—	2	1	no	—
72	C₄×D₄×C₂₃	D₄	1	2	yes	—
73	C₄×D₄×C₂₃	D₄	1	2	yes	—
74	C₄×D₄×C₂₃	C₂³	1	2	yes	—
75	C₄×D₄×C₂₃	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
77	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
78	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
79	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
80	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
81	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
82	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
83	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
85	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
88	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
89	C₂₃×#106	—	2	4	no	—
90	C₂₃×#106	—	2	4	no	—
91	C₂₃×C₄⋊C₈	—	2	1	no	—
92	C₂₃×C₄⋊C₈	—	2	1	no	—
93	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
94	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
95	C₂₃×#103	—	2	8	no	—
96	C₂₃×#102	—	2	4	no	—
97	C₂₃×#102	—	2	4	no	—
98	C₄×C₈×C₂₃	—	2	1	no	—
99	C₄×C₈×C₂₃	C₂³	1	2	yes	—
100	C₂⁴×C₂₃	—	2	1	no	—
101	C₂⁴×C₂₃	—	2	1	no	—
102	#41×C₂₃	—	4	8	no	—
103	#41×C₂₃	—	4	16	no	—
104	#41×C₂₃	—	4	8	no	—
105	C₂×Q₈×C₂₃	—	2	2	no	—
106	C₂×Q₈×C₂₃	—	2	2	no	—
107	C₂×Q₈×C₂₃	—	2	2	no	—
108	C₂×Q₈×C₂₃	—	4	4	no	—
109	C₂×Q₈×C₂₃	—	4	1	no	—
110	C₂×Q₈×C₂₃	—	4	2	no	—
111	C₂×Q₈×C₂₃	—	4	2	no	—
112	C₂×D₄×C₂₃	—	2	8	no	—
113	C₂×D₄×C₂₃	—	2	1	no	—
114	C₂×D₄×C₂₃	—	2	1	no	—
115	C₂×D₄×C₂₃	—	2	2	no	—
116	C₂×D₄×C₂₃	—	2	2	no	—
117	C₂×D₄×C₂₃	—	2	2	no	—
118	C₂×D₄×C₂₃	—	4	8	no	—
119	C₂×D₄×C₂₃	SD₁₆	1	4	yes	—
120	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
121	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₂₃	—	2	8	no	—
123	C₂²×C₄×C₂₃	—	2	1	no	—
124	C₂²×C₄×C₂₃	—	2	1	no	—
125	C₂²×C₄×C₂₃	—	2	2	no	—
126	C₂²×C₄×C₂₃	—	2	2	no	—
127	C₂²×C₄×C₂₃	—	2	2	no	—
128	C₂²×C₄×C₂₃	—	2	2	no	—
129	C₂²×C₄×C₂₃	—	2	2	no	—
130	C₂²×C₄×C₂₃	—	4	8	no	—
131	C₂²×C₄×C₂₃	—	4	2	no	—
132	C₂²×C₄×C₂₃	—	4	2	no	—
133	C₂²×C₄×C₂₃	—	4	2	no	—
134	C₂²×C₄×C₂₃	—	4	2	no	—
135	C₂²×C₄×C₂₃	—	4	1	no	—
136	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₂₃	—	2	2	no	—
140	C₂×C₈×C₂₃	—	2	2	no	—
141	C₂×C₈×C₂₃	—	2	2	no	—
142	C₂×C₈×C₂₃	—	4	2	no	—
143	C₂×C₈×C₂₃	—	4	2	no	—
144	C₂×C₈×C₂₃	—	4	2	no	—
145	C₄⋊C₄×C₂₃	—	2	8	no	—
146	C₄⋊C₄×C₂₃	—	2	1	no	—
147	C₄⋊C₄×C₂₃	—	2	2	no	—
148	C₄⋊C₄×C₂₃	—	2	1	no	—
149	C₄⋊C₄×C₂₃	—	2	2	no	—
150	C₄⋊C₄×C₂₃	—	2	2	no	—
151	C₄⋊C₄×C₂₃	—	2	2	no	—
152	C₄⋊C₄×C₂₃	—	2	2	no	—
153	C₄⋊C₄×C₂₃	—	4	1	no	—
154	C₄⋊C₄×C₂₃	—	4	1	no	—
155	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
156	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
157	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
158	C₂²⋊C₄×C₂₃	—	2	8	no	—
159	C₂²⋊C₄×C₂₃	—	2	2	no	—
160	C₂²⋊C₄×C₂₃	—	2	2	no	—
161	C₂²⋊C₄×C₂₃	—	2	2	no	—
162	C₂²⋊C₄×C₂₃	—	2	2	no	—
163	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
166	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
167	C₂×#1635	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
168	C₂³×C₂₃	—	2	2	no	—
169	C₂³×C₂₃	—	2	4	no	—
170	C₂³×C₂₃	—	2	2	no	—
171	C₂³×C₂₃	—	4	2	no	—
172	C₂³×C₂₃	—	4	2	no	—
173	C₂³×C₂₃	—	4	2	no	—
174	C₂³×C₂₃	—	4	2	no	—
175	C₂³×C₂₃	—	4	2	no	—
176	C₂³×C₂₃	#120	1	1	yes	characteristic
177	Q₈×C₂₃	—	4	4	no	—
178	Q₈×C₂₃	—	4	2	no	—
179	Q₈×C₂₃	—	4	2	no	—
180	Q₈×C₂₃	—	4	4	no	—
181	Q₈×C₂₃	—	8	2	no	—
182	D₄×C₂₃	—	2	2	no	—
183	D₄×C₂₃	—	2	2	no	—
184	D₄×C₂₃	—	2	2	no	—
185	D₄×C₂₃	—	2	4	no	—
186	D₄×C₂₃	—	4	16	no	—
187	D₄×C₂₃	—	4	2	no	—
188	D₄×C₂₃	C₂×SD₁₆	1	4	yes	—
189	C₂×C₄×C₂₃	—	2	2	no	—
190	C₂×C₄×C₂₃	—	2	2	no	—
191	C₂×C₄×C₂₃	—	2	2	no	—
192	C₂×C₄×C₂₃	—	2	4	no	—
193	C₂×C₄×C₂₃	—	4	16	no	—
194	C₂×C₄×C₂₃	—	4	2	no	—
195	C₂×C₄×C₂₃	—	4	4	no	—
196	C₂×C₄×C₂₃	—	4	2	no	—
197	C₂×C₄×C₂₃	—	4	2	no	—
198	C₂×C₄×C₂₃	—	4	2	no	—
199	C₂×C₄×C₂₃	—	4	2	no	—
200	C₂×C₄×C₂₃	—	4	2	no	—
201	C₂×C₄×C₂₃	—	4	4	no	—
202	C₂×C₄×C₂₃	—	4	4	no	—
203	C₂×C₄×C₂₃	—	4	2	no	—
204	C₂×C₄×C₂₃	—	8	2	no	—
205	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
206	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
207	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
208	C₂×C₄×C₂₃	C₂×SD₁₆	1	2	yes	—
209	C₂×C₄×C₂₃	#135	1	2	yes	—
210	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
211	C₂×C₄×C₂₃	#137	1	2	yes	—
212	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
215	C₈×C₂₃	—	4	2	no	—
216	C₈×C₂₃	—	4	2	no	—
217	C₈×C₂₃	—	4	2	no	—
218	C₂×#547	C₂×C₂₃	1	1	yes	characteristic
219	C₂×#487	C₂×C₂₃	1	1	yes	characteristic, complemented
220	C₂×#476	C₂×C₂₃	1	1	yes	characteristic, complemented
221	C₂×#476	C₂×C₂₃	1	1	yes	characteristic, complemented
222	#1635	C₂×C₂₃	1	8	yes	direct product factor
223	C₂×#332	C₂×C₂₃	1	1	yes	characteristic, complemented
224	C₂×D₄⋊C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
225	C₂×D₄⋊C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
226	C₂²×C₂₃	—	2	4	no	—
227	C₂²×C₂₃	—	4	8	no	—
228	C₂²×C₂₃	—	4	2	no	—
229	C₂²×C₂₃	—	4	2	no	—
230	C₂²×C₂₃	—	4	2	no	—
231	C₂²×C₂₃	—	4	2	no	—
232	C₂²×C₂₃	—	4	2	no	—
233	C₂²×C₂₃	—	8	4	no	—
234	C₂²×C₂₃	#450	1	2	yes	—
235	C₂²×C₂₃	#452	1	2	yes	—
236	C₂²×C₂₃	#454	1	2	yes	—
237	C₂²×C₂₃	C₂×#120	1	1	yes	characteristic
238	C₄×C₂₃	—	2	1	no	—
239	C₄×C₂₃	—	2	1	no	—
240	C₄×C₂₃	—	4	2	no	—
241	C₄×C₂₃	—	4	4	no	—
242	C₄×C₂₃	—	4	2	no	—
243	C₄×C₂₃	—	8	2	no	—
244	C₄×C₂₃	#450	1	2	yes	—
245	C₄×C₂₃	#452	1	2	yes	—
246	C₄×C₂₃	C₂²×SD₁₆	1	1	yes	characteristic
247	C₄×C₂₃	C₂×#135	1	1	yes	characteristic
248	C₄×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
249	C₄×C₂₃	C₂×#137	1	1	yes	characteristic
250	C₂²×#41	—	2	1	no	—
251	#547	—	2	2	no	—
252	#547	—	2	2	no	—
253	#547	—	2	2	no	—
254	#547	C₂²×C₂₃	1	4	yes	—
255	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
256	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
257	C₂×#123	—	2	2	no	—
258	C₂×C₂²⋊Q₈	—	2	1	no	—
259	C₂×#121	—	2	1	no	—
260	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
261	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
262	C₂²×C₄⋊C₄	—	2	1	no	—
263	#487	—	2	2	no	—
264	#487	C₂²×C₂₃	1	4	yes	complemented
265	#476	—	2	2	no	—
266	#476	—	2	2	no	—
267	#476	C₂²×C₂₃	1	4	yes	complemented
268	#476	C₂²×C₂₃	1	4	yes	complemented
269	C₂×#106	—	2	1	no	—
270	C₂×#106	—	2	1	no	—
271	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
272	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
273	C₂×#103	—	2	2	no	—
274	C₂×#102	—	2	1	no	—
275	C₂×#102	—	2	1	no	—
276	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
277	#332	C₂²×C₂₃	1	4	yes	complemented
278	D₄⋊C₈	C₂²×C₂₃	1	4	yes	complemented
279	D₄⋊C₈	C₂²×C₂₃	1	4	yes	complemented
280	C₂×C₂₃	—	4	4	no	—
281	C₂×C₂₃	—	8	2	no	—
282	C₂×C₂₃	#1635	1	4	yes	direct product factor
283	C₂×C₂₃	C₂×#450	1	1	yes	characteristic
284	C₂×C₂₃	C₂×#452	1	1	yes	characteristic
285	C₂×C₂₃	C₂×#454	1	1	yes	characteristic
286	C₂×#41	—	2	4	no	—
287	C₂×#41	—	2	4	no	—
288	C₂×#41	—	4	4	no	—
289	C₂×#41	—	4	4	no	—
290	C₂²×Q₈	—	2	1	no	—
291	C₂²×Q₈	—	2	1	no	—
292	C₂²×D₄	—	2	2	no	—
293	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
294	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
295	C₂³×C₄	—	2	2	no	—
296	C₂³×C₄	—	2	1	no	—
297	C₂³×C₄	—	2	1	no	—
298	C₂²×C₈	—	2	1	no	—
299	C₂²×C₈	—	2	1	no	—
300	C₂²×C₈	—	2	1	no	—
301	C₄⋊Q₈	—	2	1	no	—
302	C₄⋊Q₈	—	2	1	no	—
303	C₄⋊Q₈	—	2	1	no	—
304	C₄⋊Q₈	—	2	1	no	—
305	C₄⋊Q₈	—	2	1	no	—
306	C₄⋊Q₈	D₄×C₂₃	1	2	yes	—
307	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
308	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
309	#123	—	2	8	no	—
310	#123	—	2	8	no	—
311	C₂²⋊Q₈	—	2	4	no	—
312	C₂²⋊Q₈	—	2	4	no	—
313	#121	—	2	4	no	—
314	#121	—	2	4	no	—
315	C₄×D₄	—	2	1	no	—
316	C₄×D₄	—	2	1	no	—
317	C₄×D₄	—	2	1	no	—
318	C₄×D₄	—	2	1	no	—
319	C₄×D₄	D₄×C₂₃	1	2	yes	—
320	C₄×D₄	D₄×C₂₃	1	2	yes	—
321	C₄×D₄	C₂³×C₂₃	1	2	yes	—
322	C₄×D₄	C₂³×C₂₃	1	2	yes	—
323	C₂×C₄⋊C₄	—	2	2	no	—
324	C₂×C₄⋊C₄	—	2	4	no	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	—	2	4	no	—
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
330	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
331	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
332	C₂×C₂²⋊C₄	—	2	2	no	—
333	C₂×C₂²⋊C₄	—	2	1	no	—
334	C₂×C₂²⋊C₄	—	2	1	no	—
335	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
336	#106	—	2	4	no	—
337	#106	—	2	4	no	—
338	C₄⋊C₈	—	2	1	no	—
339	C₄⋊C₈	—	2	1	no	—
340	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
341	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
342	#103	—	2	8	no	—
343	#102	—	2	4	no	—
344	#102	—	2	4	no	—
345	C₄×C₈	—	2	1	no	—
346	C₄×C₈	C₂³×C₂₃	1	2	yes	—
347	C₂₃	C₂×#1635	1	1	yes	characteristic, direct product factor, Sylow
348	C₂⁴	—	2	1	no	—
349	C₂⁴	—	2	1	no	—
350	#41	—	4	8	no	—
351	#41	—	4	16	no	—
352	#41	—	4	8	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	2	2	no	—
355	C₂×Q₈	—	2	2	no	—
356	C₂×Q₈	—	4	4	no	—
357	C₂×Q₈	—	4	1	no	—
358	C₂×Q₈	—	4	2	no	—
359	C₂×Q₈	—	4	2	no	—
360	C₂×D₄	—	2	8	no	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	4	8	no	—
367	C₂×D₄	SD₁₆×C₂₃	1	4	yes	—
368	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
369	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
370	C₂²×C₄	—	2	8	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	4	8	no	—
379	C₂²×C₄	—	4	2	no	—
380	C₂²×C₄	—	4	2	no	—
381	C₂²×C₄	—	4	2	no	—
382	C₂²×C₄	—	4	2	no	—
383	C₂²×C₄	—	4	1	no	—
384	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
385	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
386	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	4	2	no	—
391	C₂×C₈	—	4	2	no	—
392	C₂×C₈	—	4	2	no	—
393	C₄⋊C₄	—	2	8	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	4	1	no	—
402	C₄⋊C₄	—	4	1	no	—
403	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
404	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
405	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
406	C₂²⋊C₄	—	2	8	no	—
407	C₂²⋊C₄	—	2	2	no	—
408	C₂²⋊C₄	—	2	2	no	—
409	C₂²⋊C₄	—	2	2	no	—
410	C₂²⋊C₄	—	2	2	no	—
411	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
412	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
413	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
414	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
415	C₂³	—	2	4	no	—
416	C₂³	—	2	2	no	—
417	C₂³	—	2	2	no	—
418	C₂³	—	4	2	no	—
419	C₂³	—	4	2	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	4	2	no	—
422	C₂³	—	4	2	no	—
423	C₂³	C₂₃×#120	1	1	yes	characteristic
424	Q₈	—	4	4	no	—
425	Q₈	—	4	2	no	—
426	Q₈	—	4	2	no	—
427	Q₈	—	4	4	no	—
428	Q₈	—	8	2	no	—
429	D₄	—	2	2	no	—
430	D₄	—	2	2	no	—
431	D₄	—	2	2	no	—
432	D₄	—	2	4	no	—
433	D₄	—	4	16	no	—
434	D₄	—	4	2	no	—
435	D₄	C₂×SD₁₆×C₂₃	1	4	yes	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	4	16	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	4	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	4	no	—
449	C₂×C₄	—	4	4	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	8	2	no	—
452	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
453	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
454	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
455	C₂×C₄	C₂×SD₁₆×C₂₃	1	2	yes	—
456	C₂×C₄	C₂₃×#135	1	2	yes	—
457	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
458	C₂×C₄	C₂₃×#137	1	2	yes	—
459	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
460	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
461	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
462	C₈	—	4	2	no	—
463	C₈	—	4	2	no	—
464	C₈	—	4	2	no	—
465	C₂²	—	2	4	no	—
466	C₂²	—	4	8	no	—
467	C₂²	—	4	2	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	8	4	no	—
473	C₂²	C₂₃×#450	1	2	yes	—
474	C₂²	C₂₃×#452	1	2	yes	—
475	C₂²	C₂₃×#454	1	2	yes	—
476	C₂²	C₂×C₂₃×#120	1	1	yes	characteristic
477	C₄	—	2	1	no	—
478	C₄	—	2	1	no	—
479	C₄	—	4	2	no	—
480	C₄	—	4	4	no	—
481	C₄	—	4	2	no	—
482	C₄	—	8	2	no	—
483	C₄	C₂₃×#450	1	2	yes	—
484	C₄	C₂₃×#452	1	2	yes	—
485	C₄	C₂²×SD₁₆×C₂₃	1	1	yes	characteristic
486	C₄	C₂×C₂₃×#135	1	1	yes	characteristic
487	C₄	C₂×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
488	C₄	C₂×C₂₃×#137	1	1	yes	characteristic
489	C₂	—	4	4	no	—
490	C₂	—	8	2	no	—
491	C₂	C₂₃×#1635	1	4	yes	direct product factor
492	C₂	C₂×C₂₃×#450	1	1	yes	characteristic
493	C₂	C₂×C₂₃×#452	1	1	yes	characteristic
494	C₂	C₂×C₂₃×#454	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₃
prime radical	C₂×C₂₃×#547	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₃×#487	C₂	semidirect
3. C₂×C₂₃×#476	C₂	semidirect
4. C₂×C₂₃×#476	C₂	semidirect
5. C₂₃×#1635	C₂	direct (N × H)
6. C₂×C₂₃×#332	C₂	semidirect
7. C₂×C₂₃×D₄⋊C₈	C₂	semidirect
8. C₂×C₂₃×D₄⋊C₈	C₂	semidirect
23. C₂₃×#487	C₂²	semidirect
26. C₂₃×#476	C₂²	semidirect
27. C₂₃×#476	C₂²	semidirect
36. C₂₃×#332	C₂²	semidirect
37. C₂₃×D₄⋊C₈	C₂²	semidirect
38. C₂₃×D₄⋊C₈	C₂²	semidirect
167. C₂×#1635	C₂₃	direct (N × H)
219. C₂×#487	C₂×C₂₃	semidirect
220. C₂×#476	C₂×C₂₃	semidirect
221. C₂×#476	C₂×C₂₃	semidirect
222. #1635	C₂×C₂₃	direct (N × H)
223. C₂×#332	C₂×C₂₃	semidirect
224. C₂×D₄⋊C₈	C₂×C₂₃	semidirect
225. C₂×D₄⋊C₈	C₂×C₂₃	semidirect
264. #487	C₂²×C₂₃	semidirect
267. #476	C₂²×C₂₃	semidirect
268. #476	C₂²×C₂₃	semidirect
277. #332	C₂²×C₂₃	semidirect
278. D₄⋊C₈	C₂²×C₂₃	semidirect
279. D₄⋊C₈	C₂²×C₂₃	semidirect
282. C₂×C₂₃	#1635	direct (N × H)
347. C₂₃	C₂×#1635	direct (N × H)
491. C₂	C₂₃×#1635	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×#547	2
C₂×C₂₃×#487	2
C₂×C₂₃×#476	2
C₂₃×#1635	2
C₂×C₂₃×#332	2
C₂×C₂₃×D₄⋊C₈	2
C₂×#1635	23

Subgroups — C2×C23×#1635 #19166113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#1635 #19166113