Subgroups — C₂×C₂₃×#1932 #19168705

Order 5888.

1046 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#430	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#421	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₂₃×#104	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂₃×#413	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×M₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1932	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₂₃×#344	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₃×#339	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
14	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
16	C₂₃×#430	—	2	2	no	—
17	C₂₃×#430	C₂²	1	4	yes	complemented
18	C₂×C₂₃×#108	—	2	2	no	—
19	C₂₃×#421	—	2	2	no	—
20	C₂₃×#421	C₂²	1	4	yes	—
21	C₂×C₂₃×#104	—	2	2	no	—
22	C₂×C₂₃×#104	—	2	1	no	—
23	C₂×C₂₃×#104	—	2	1	no	—
24	C₂×C₂₃×#104	—	2	2	no	—
25	C₂×C₂₃×#104	C₂²	1	4	yes	—
26	C₂₃×#413	C₄	1	4	yes	complemented
27	C₂₃×#413	C₂²	1	4	yes	—
28	C₂×C₂₃×#101	C₄	1	2	yes	complemented
29	C₂×C₂₃×#100	C₄	1	2	yes	complemented
30	C₄×M₁₆×C₂₃	—	2	2	no	—
31	C₄×M₁₆×C₂₃	C₂²	1	4	yes	complemented
32	C₂×C₂₃×#97	—	2	1	no	—
33	C₂×C₄×C₈×C₂₃	—	2	1	no	—
34	C₂₃×#344	C₂²	1	4	yes	complemented
35	C₂₃×#339	C₂²	1	4	yes	complemented
36	C₂×#41×C₂₃	—	2	1	no	—
37	C₂×#41×C₂₃	—	2	1	no	—
38	C₂×#41×C₂₃	—	2	1	no	—
39	C₂×#41×C₂₃	—	2	1	no	—
40	C₂×#41×C₂₃	—	2	1	no	—
41	C₂×#41×C₂₃	—	2	1	no	—
42	C₂×#41×C₂₃	—	2	1	no	—
43	C₂×#41×C₂₃	—	2	1	no	—
44	C₂×#41×C₂₃	—	2	1	no	—
45	C₂×#41×C₂₃	—	2	1	no	—
46	C₂×#41×C₂₃	C₂×C₄	1	2	yes	—
47	C₂×#41×C₂₃	C₂³	1	2	yes	—
48	C₂²×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
49	C₂²×D₄×C₂₃	—	2	1	no	—
50	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₂₃	—	2	1	no	—
52	C₂³×C₄×C₂₃	—	2	1	no	—
53	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
54	C₂×M₁₆×C₂₃	—	2	1	no	—
55	C₂×M₁₆×C₂₃	—	2	1	no	—
56	C₂×M₁₆×C₂₃	—	2	1	no	—
57	C₂×M₁₆×C₂₃	—	2	1	no	—
58	C₂×M₁₆×C₂₃	—	2	1	no	—
59	C₂×M₁₆×C₂₃	—	2	1	no	—
60	C₂×M₁₆×C₂₃	—	2	1	no	—
61	C₂×M₁₆×C₂₃	—	2	1	no	—
62	C₂×M₁₆×C₂₃	—	2	1	no	—
63	C₂×M₁₆×C₂₃	—	2	1	no	—
64	C₂×M₁₆×C₂₃	—	2	1	no	—
65	C₂×M₁₆×C₂₃	—	2	1	no	—
66	C₂×M₁₆×C₂₃	—	2	1	no	—
67	C₂×M₁₆×C₂₃	—	2	1	no	—
68	C₂×M₁₆×C₂₃	C₂×C₄	1	2	yes	—
69	C₂×M₁₆×C₂₃	C₂×C₄	1	2	yes	—
70	C₂×M₁₆×C₂₃	C₂×C₄	1	2	yes	—
71	C₂×M₁₆×C₂₃	C₂×C₄	1	2	yes	—
72	C₂×M₁₆×C₂₃	D₄	1	2	yes	—
73	C₂×M₁₆×C₂₃	D₄	1	2	yes	—
74	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
75	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
76	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
77	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
78	C₂²×C₈×C₂₃	—	2	1	no	—
79	C₂²×C₈×C₂₃	—	2	1	no	—
80	C₂²×C₈×C₂₃	—	2	1	no	—
81	C₂²×C₈×C₂₃	—	2	1	no	—
82	C₂₃×#117	—	2	1	no	—
83	C₂₃×#117	—	2	1	no	—
84	C₂₃×#117	—	2	1	no	—
85	C₂₃×#117	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
88	C₂×C₄²×C₂₃	—	2	1	no	—
89	C₂×C₄²×C₂₃	—	2	1	no	—
90	C₂×C₄²×C₂₃	—	2	1	no	—
91	C₂×C₄²×C₂₃	—	2	1	no	—
92	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
93	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₂₃	D₄	1	2	yes	—
95	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
96	C₂₃×#108	—	2	8	no	—
97	C₂₃×#104	—	2	8	no	—
98	C₂₃×#104	—	2	4	no	—
99	C₂₃×#104	—	2	4	no	—
100	C₂₃×#101	C₂×C₄	1	8	yes	complemented
101	C₂₃×#100	C₂×C₄	1	8	yes	complemented
102	C₂₃×#97	—	2	4	no	—
103	C₄×C₈×C₂₃	—	2	4	no	—
104	C₂⁴×C₂₃	—	2	1	no	—
105	C₂⁴×C₂₃	#41	1	1	yes	characteristic
106	#41×C₂₃	—	2	2	no	—
107	#41×C₂₃	—	2	2	no	—
108	#41×C₂₃	—	2	2	no	—
109	#41×C₂₃	—	2	2	no	—
110	#41×C₂₃	—	2	2	no	—
111	#41×C₂₃	—	2	2	no	—
112	#41×C₂₃	—	2	2	no	—
113	#41×C₂₃	—	2	2	no	—
114	#41×C₂₃	—	4	1	no	—
115	#41×C₂₃	—	4	1	no	—
116	#41×C₂₃	—	4	1	no	—
117	#41×C₂₃	—	4	1	no	—
118	#41×C₂₃	—	4	1	no	—
119	#41×C₂₃	—	4	1	no	—
120	#41×C₂₃	—	4	1	no	—
121	#41×C₂₃	—	4	1	no	—
122	C₂×Q₈×C₂₃	—	2	1	no	—
123	C₂×Q₈×C₂₃	—	2	1	no	—
124	C₂×Q₈×C₂₃	—	2	1	no	—
125	C₂×Q₈×C₂₃	—	2	1	no	—
126	C₂×Q₈×C₂₃	—	2	1	no	—
127	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
128	C₂×D₄×C₂₃	—	2	2	no	—
129	C₂×D₄×C₂₃	—	2	2	no	—
130	C₂×D₄×C₂₃	—	2	1	no	—
131	C₂×D₄×C₂₃	—	2	1	no	—
132	C₂×D₄×C₂₃	—	2	1	no	—
133	C₂×D₄×C₂₃	—	2	1	no	—
134	C₂×D₄×C₂₃	—	2	1	no	—
135	C₂×D₄×C₂₃	—	4	1	no	—
136	C₂×D₄×C₂₃	—	4	1	no	—
137	C₂×D₄×C₂₃	—	4	1	no	—
138	C₂×D₄×C₂₃	—	4	1	no	—
139	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
140	C₂²×C₄×C₂₃	—	2	1	no	—
141	C₂²×C₄×C₂₃	—	2	1	no	—
142	C₂²×C₄×C₂₃	—	2	2	no	—
143	C₂²×C₄×C₂₃	—	2	1	no	—
144	C₂²×C₄×C₂₃	—	2	2	no	—
145	C₂²×C₄×C₂₃	—	2	2	no	—
146	C₂²×C₄×C₂₃	—	2	2	no	—
147	C₂²×C₄×C₂₃	—	4	4	no	—
148	C₂²×C₄×C₂₃	—	4	1	no	—
149	C₂²×C₄×C₂₃	—	4	1	no	—
150	C₂²×C₄×C₂₃	—	4	1	no	—
151	C₂²×C₄×C₂₃	—	4	1	no	—
152	C₂²×C₄×C₂₃	—	4	1	no	—
153	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
160	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
161	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
162	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
163	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
164	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
165	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
166	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
167	M₁₆×C₂₃	—	2	2	no	—
168	M₁₆×C₂₃	—	2	2	no	—
169	M₁₆×C₂₃	—	2	2	no	—
170	M₁₆×C₂₃	—	2	2	no	—
171	M₁₆×C₂₃	—	2	2	no	—
172	M₁₆×C₂₃	—	2	2	no	—
173	M₁₆×C₂₃	—	2	2	no	—
174	M₁₆×C₂₃	—	2	2	no	—
175	M₁₆×C₂₃	—	2	2	no	—
176	M₁₆×C₂₃	—	2	2	no	—
177	M₁₆×C₂₃	—	2	2	no	—
178	M₁₆×C₂₃	—	4	1	no	—
179	M₁₆×C₂₃	—	4	1	no	—
180	M₁₆×C₂₃	C₂²×C₄	1	4	yes	—
181	M₁₆×C₂₃	C₂²×C₄	1	4	yes	—
182	M₁₆×C₂₃	C₂×D₄	1	4	yes	—
183	C₂×C₈×C₂₃	—	2	2	no	—
184	C₂×C₈×C₂₃	—	2	2	no	—
185	C₂×C₈×C₂₃	—	2	2	no	—
186	C₂×C₈×C₂₃	—	2	2	no	—
187	C₂×C₈×C₂₃	—	2	2	no	—
188	C₂×C₈×C₂₃	—	2	2	no	—
189	C₂×C₈×C₂₃	—	2	2	no	—
190	C₂×C₈×C₂₃	—	2	2	no	—
191	C₂×C₈×C₂₃	—	2	2	no	—
192	C₂×C₈×C₂₃	—	2	2	no	—
193	C₂×C₈×C₂₃	—	4	1	no	—
194	C₂×C₈×C₂₃	—	4	1	no	—
195	C₄⋊C₄×C₂₃	—	2	2	no	—
196	C₄⋊C₄×C₂₃	—	4	1	no	—
197	C₂²⋊C₄×C₂₃	—	2	2	no	—
198	C₂²⋊C₄×C₂₃	—	4	1	no	—
199	C₄²×C₂₃	—	2	1	no	—
200	C₄²×C₂₃	—	2	2	no	—
201	C₄²×C₂₃	—	2	1	no	—
202	C₄²×C₂₃	—	2	2	no	—
203	C₄²×C₂₃	—	2	2	no	—
204	C₄²×C₂₃	—	4	1	no	—
205	C₄²×C₂₃	C₂×D₄	1	2	yes	—
206	C₄²×C₂₃	C₂×D₄	1	2	yes	—
207	C₂×#1932	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₂³×C₂₃	—	2	2	no	—
209	C₂³×C₂₃	—	4	2	no	—
210	C₂³×C₂₃	—	4	1	no	—
211	C₂³×C₂₃	—	4	1	no	—
212	C₂³×C₂₃	—	8	2	no	—
213	C₂³×C₂₃	#117	1	1	yes	characteristic
214	C₂³×C₂₃	#117	1	1	yes	characteristic
215	C₂³×C₂₃	#123	1	1	yes	characteristic
216	C₂³×C₂₃	#123	1	1	yes	characteristic
217	C₂³×C₂₃	#124	1	1	yes	characteristic
218	C₂³×C₂₃	#124	1	1	yes	characteristic
219	C₂³×C₂₃	C₂×#41	1	1	yes	characteristic
220	Q₈×C₂₃	—	2	2	no	—
221	Q₈×C₂₃	—	2	2	no	—
222	Q₈×C₂₃	—	4	1	no	—
223	Q₈×C₂₃	—	4	1	no	—
224	D₄×C₂₃	—	2	2	no	—
225	D₄×C₂₃	—	2	2	no	—
226	D₄×C₂₃	—	4	2	no	—
227	D₄×C₂₃	—	4	2	no	—
228	D₄×C₂₃	—	4	2	no	—
229	D₄×C₂₃	—	4	2	no	—
230	D₄×C₂₃	—	4	1	no	—
231	D₄×C₂₃	—	4	1	no	—
232	C₂×C₄×C₂₃	—	2	4	no	—
233	C₂×C₄×C₂₃	—	2	2	no	—
234	C₂×C₄×C₂₃	—	2	2	no	—
235	C₂×C₄×C₂₃	—	2	2	no	—
236	C₂×C₄×C₂₃	—	4	4	no	—
237	C₂×C₄×C₂₃	—	4	4	no	—
238	C₂×C₄×C₂₃	—	4	2	no	—
239	C₂×C₄×C₂₃	—	4	1	no	—
240	C₂×C₄×C₂₃	—	4	1	no	—
241	C₂×C₄×C₂₃	—	4	2	no	—
242	C₂×C₄×C₂₃	—	4	2	no	—
243	C₂×C₄×C₂₃	—	4	2	no	—
244	C₂×C₄×C₂₃	—	4	2	no	—
245	C₂×C₄×C₂₃	—	4	2	no	—
246	C₂×C₄×C₂₃	—	8	2	no	—
247	C₂×C₄×C₂₃	#117	1	1	yes	characteristic
248	C₂×C₄×C₂₃	#117	1	1	yes	characteristic
249	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
250	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
251	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
252	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
253	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
254	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
255	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
256	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
257	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
258	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
259	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
260	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
261	C₂×C₄×C₂₃	#123	1	1	yes	characteristic
262	C₂×C₄×C₂₃	#123	1	1	yes	characteristic
263	C₂×C₄×C₂₃	#124	1	1	yes	characteristic
264	C₂×C₄×C₂₃	#124	1	1	yes	characteristic
265	C₂×C₄×C₂₃	#126	1	1	yes	characteristic
266	C₂×C₄×C₂₃	#126	1	1	yes	characteristic
267	C₂×C₄×C₂₃	#126	1	1	yes	characteristic
268	C₂×C₄×C₂₃	#126	1	1	yes	characteristic
269	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
270	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
271	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
272	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
273	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
274	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
275	C₈×C₂₃	—	2	4	no	—
276	C₈×C₂₃	—	2	4	no	—
277	C₈×C₂₃	—	2	4	no	—
278	C₈×C₂₃	—	4	2	no	—
279	C₂×#430	C₂×C₂₃	1	1	yes	characteristic, complemented
280	C₂×#421	C₂×C₂₃	1	1	yes	characteristic
281	C₂²×#104	C₂×C₂₃	1	1	yes	characteristic
282	C₂×#413	C₂×C₂₃	1	1	yes	characteristic
283	C₂×C₄×M₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
284	#1932	C₂×C₂₃	1	8	yes	direct product factor
285	C₂×#344	C₂×C₂₃	1	1	yes	characteristic, complemented
286	C₂×#339	C₂×C₂₃	1	1	yes	characteristic, complemented
287	C₂²×C₂₃	—	2	2	no	—
288	C₂²×C₂₃	—	2	2	no	—
289	C₂²×C₂₃	—	2	2	no	—
290	C₂²×C₂₃	—	4	1	no	—
291	C₂²×C₂₃	—	4	1	no	—
292	C₂²×C₂₃	—	4	1	no	—
293	C₂²×C₂₃	—	4	1	no	—
294	C₂²×C₂₃	—	4	2	no	—
295	C₂²×C₂₃	—	8	2	no	—
296	C₂²×C₂₃	—	8	2	no	—
297	C₂²×C₂₃	—	8	2	no	—
298	C₂²×C₂₃	#388	1	1	yes	characteristic
299	C₂²×C₂₃	#388	1	1	yes	characteristic
300	C₂²×C₂₃	#388	1	1	yes	characteristic
301	C₂²×C₂₃	#388	1	1	yes	characteristic
302	C₂²×C₂₃	C₂×#117	1	1	yes	characteristic
303	C₂²×C₂₃	C₂×#123	1	1	yes	characteristic
304	C₂²×C₂₃	C₂×#124	1	1	yes	characteristic
305	C₄×C₂₃	—	2	4	no	—
306	C₄×C₂₃	—	4	2	no	—
307	C₄×C₂₃	—	4	2	no	—
308	C₄×C₂₃	—	8	2	no	—
309	C₄×C₂₃	#388	1	1	yes	characteristic
310	C₄×C₂₃	#388	1	1	yes	characteristic
311	C₄×C₂₃	#388	1	1	yes	characteristic
312	C₄×C₂₃	#388	1	1	yes	characteristic
313	C₄×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
314	C₄×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
315	C₄×C₂₃	C₂×#121	1	1	yes	characteristic
316	C₄×C₂₃	C₂×#126	1	1	yes	characteristic
317	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
318	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
319	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
320	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
321	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
322	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
323	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
324	#430	—	2	2	no	—
325	#430	C₂²×C₂₃	1	4	yes	complemented
326	C₂×#108	—	2	2	no	—
327	#421	—	2	2	no	—
328	#421	C₂²×C₂₃	1	4	yes	—
329	C₂×#104	—	2	2	no	—
330	C₂×#104	—	2	1	no	—
331	C₂×#104	—	2	1	no	—
332	C₂×#104	—	2	2	no	—
333	C₂×#104	C₂²×C₂₃	1	4	yes	—
334	#413	C₄×C₂₃	1	4	yes	complemented
335	#413	C₂²×C₂₃	1	4	yes	—
336	C₂×#101	C₄×C₂₃	1	2	yes	complemented
337	C₂×#100	C₄×C₂₃	1	2	yes	complemented
338	C₄×M₁₆	—	2	2	no	—
339	C₄×M₁₆	C₂²×C₂₃	1	4	yes	complemented
340	C₂×#97	—	2	1	no	—
341	C₂×C₄×C₈	—	2	1	no	—
342	#344	C₂²×C₂₃	1	4	yes	complemented
343	#339	C₂²×C₂₃	1	4	yes	complemented
344	C₂×C₂₃	—	2	1	no	—
345	C₂×C₂₃	—	2	1	no	—
346	C₂×C₂₃	—	2	1	no	—
347	C₂×C₂₃	—	2	1	no	—
348	C₂×C₂₃	—	2	1	no	—
349	C₂×C₂₃	—	2	1	no	—
350	C₂×C₂₃	—	8	2	no	—
351	C₂×C₂₃	#1932	1	2	yes	direct product factor
352	C₂×C₂₃	C₂×#388	1	1	yes	characteristic
353	C₂×#41	—	2	1	no	—
354	C₂×#41	—	2	1	no	—
355	C₂×#41	—	2	1	no	—
356	C₂×#41	—	2	1	no	—
357	C₂×#41	—	2	1	no	—
358	C₂×#41	—	2	1	no	—
359	C₂×#41	—	2	1	no	—
360	C₂×#41	—	2	1	no	—
361	C₂×#41	—	2	1	no	—
362	C₂×#41	—	2	1	no	—
363	C₂×#41	C₂×C₄×C₂₃	1	2	yes	—
364	C₂×#41	C₂³×C₂₃	1	2	yes	—
365	C₂²×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
366	C₂²×D₄	—	2	1	no	—
367	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
368	C₂³×C₄	—	2	1	no	—
369	C₂³×C₄	—	2	1	no	—
370	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
371	C₂×M₁₆	—	2	1	no	—
372	C₂×M₁₆	—	2	1	no	—
373	C₂×M₁₆	—	2	1	no	—
374	C₂×M₁₆	—	2	1	no	—
375	C₂×M₁₆	—	2	1	no	—
376	C₂×M₁₆	—	2	1	no	—
377	C₂×M₁₆	—	2	1	no	—
378	C₂×M₁₆	—	2	1	no	—
379	C₂×M₁₆	—	2	1	no	—
380	C₂×M₁₆	—	2	1	no	—
381	C₂×M₁₆	—	2	1	no	—
382	C₂×M₁₆	—	2	1	no	—
383	C₂×M₁₆	—	2	1	no	—
384	C₂×M₁₆	—	2	1	no	—
385	C₂×M₁₆	C₂×C₄×C₂₃	1	2	yes	—
386	C₂×M₁₆	C₂×C₄×C₂₃	1	2	yes	—
387	C₂×M₁₆	C₂×C₄×C₂₃	1	2	yes	—
388	C₂×M₁₆	C₂×C₄×C₂₃	1	2	yes	—
389	C₂×M₁₆	D₄×C₂₃	1	2	yes	—
390	C₂×M₁₆	D₄×C₂₃	1	2	yes	—
391	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
392	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
393	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
394	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
395	C₂²×C₈	—	2	1	no	—
396	C₂²×C₈	—	2	1	no	—
397	C₂²×C₈	—	2	1	no	—
398	C₂²×C₈	—	2	1	no	—
399	#117	—	2	1	no	—
400	#117	—	2	1	no	—
401	#117	—	2	1	no	—
402	#117	C₂³×C₂₃	1	2	yes	—
403	C₂×C₄⋊C₄	—	2	1	no	—
404	C₂×C₂²⋊C₄	—	2	1	no	—
405	C₂×C₄²	—	2	1	no	—
406	C₂×C₄²	—	2	1	no	—
407	C₂×C₄²	—	2	1	no	—
408	C₂×C₄²	—	2	1	no	—
409	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
410	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
411	C₂×C₄²	D₄×C₂₃	1	2	yes	—
412	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
413	#108	—	2	8	no	—
414	#104	—	2	8	no	—
415	#104	—	2	4	no	—
416	#104	—	2	4	no	—
417	#101	C₂×C₄×C₂₃	1	8	yes	complemented
418	#100	C₂×C₄×C₂₃	1	8	yes	complemented
419	#97	—	2	4	no	—
420	C₄×C₈	—	2	4	no	—
421	C₂₃	C₂×#1932	1	1	yes	characteristic, direct product factor, Sylow
422	C₂⁴	—	2	1	no	—
423	C₂⁴	#41×C₂₃	1	1	yes	characteristic
424	#41	—	2	2	no	—
425	#41	—	2	2	no	—
426	#41	—	2	2	no	—
427	#41	—	2	2	no	—
428	#41	—	2	2	no	—
429	#41	—	2	2	no	—
430	#41	—	2	2	no	—
431	#41	—	2	2	no	—
432	#41	—	4	1	no	—
433	#41	—	4	1	no	—
434	#41	—	4	1	no	—
435	#41	—	4	1	no	—
436	#41	—	4	1	no	—
437	#41	—	4	1	no	—
438	#41	—	4	1	no	—
439	#41	—	4	1	no	—
440	C₂×Q₈	—	2	1	no	—
441	C₂×Q₈	—	2	1	no	—
442	C₂×Q₈	—	2	1	no	—
443	C₂×Q₈	—	2	1	no	—
444	C₂×Q₈	—	2	1	no	—
445	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
446	C₂×D₄	—	2	2	no	—
447	C₂×D₄	—	2	2	no	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	4	1	no	—
454	C₂×D₄	—	4	1	no	—
455	C₂×D₄	—	4	1	no	—
456	C₂×D₄	—	4	1	no	—
457	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	4	4	no	—
466	C₂²×C₄	—	4	1	no	—
467	C₂²×C₄	—	4	1	no	—
468	C₂²×C₄	—	4	1	no	—
469	C₂²×C₄	—	4	1	no	—
470	C₂²×C₄	—	4	1	no	—
471	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
472	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
473	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
474	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
475	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
476	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
477	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
478	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
479	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
480	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
481	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
482	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
483	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
484	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
485	M₁₆	—	2	2	no	—
486	M₁₆	—	2	2	no	—
487	M₁₆	—	2	2	no	—
488	M₁₆	—	2	2	no	—
489	M₁₆	—	2	2	no	—
490	M₁₆	—	2	2	no	—
491	M₁₆	—	2	2	no	—
492	M₁₆	—	2	2	no	—
493	M₁₆	—	2	2	no	—
494	M₁₆	—	2	2	no	—
495	M₁₆	—	2	2	no	—
496	M₁₆	—	4	1	no	—
497	M₁₆	—	4	1	no	—
498	M₁₆	C₂²×C₄×C₂₃	1	4	yes	—
499	M₁₆	C₂²×C₄×C₂₃	1	4	yes	—
500	M₁₆	C₂×D₄×C₂₃	1	4	yes	—
501	C₂×C₈	—	2	2	no	—
502	C₂×C₈	—	2	2	no	—
503	C₂×C₈	—	2	2	no	—
504	C₂×C₈	—	2	2	no	—
505	C₂×C₈	—	2	2	no	—
506	C₂×C₈	—	2	2	no	—
507	C₂×C₈	—	2	2	no	—
508	C₂×C₈	—	2	2	no	—
509	C₂×C₈	—	2	2	no	—
510	C₂×C₈	—	2	2	no	—
511	C₂×C₈	—	4	1	no	—
512	C₂×C₈	—	4	1	no	—
513	C₄⋊C₄	—	2	2	no	—
514	C₄⋊C₄	—	4	1	no	—
515	C₂²⋊C₄	—	2	2	no	—
516	C₂²⋊C₄	—	4	1	no	—
517	C₄²	—	2	1	no	—
518	C₄²	—	2	2	no	—
519	C₄²	—	2	1	no	—
520	C₄²	—	2	2	no	—
521	C₄²	—	2	2	no	—
522	C₄²	—	4	1	no	—
523	C₄²	C₂×D₄×C₂₃	1	2	yes	—
524	C₄²	C₂×D₄×C₂₃	1	2	yes	—
525	C₂³	—	2	2	no	—
526	C₂³	—	4	2	no	—
527	C₂³	—	4	1	no	—
528	C₂³	—	4	1	no	—
529	C₂³	—	8	2	no	—
530	C₂³	C₂₃×#117	1	1	yes	characteristic
531	C₂³	C₂₃×#117	1	1	yes	characteristic
532	C₂³	C₂₃×#123	1	1	yes	characteristic
533	C₂³	C₂₃×#123	1	1	yes	characteristic
534	C₂³	C₂₃×#124	1	1	yes	characteristic
535	C₂³	C₂₃×#124	1	1	yes	characteristic
536	C₂³	C₂×#41×C₂₃	1	1	yes	characteristic
537	Q₈	—	2	2	no	—
538	Q₈	—	2	2	no	—
539	Q₈	—	4	1	no	—
540	Q₈	—	4	1	no	—
541	D₄	—	2	2	no	—
542	D₄	—	2	2	no	—
543	D₄	—	4	2	no	—
544	D₄	—	4	2	no	—
545	D₄	—	4	2	no	—
546	D₄	—	4	2	no	—
547	D₄	—	4	1	no	—
548	D₄	—	4	1	no	—
549	C₂×C₄	—	2	4	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	4	4	no	—
554	C₂×C₄	—	4	4	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	2	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	4	2	no	—
562	C₂×C₄	—	4	2	no	—
563	C₂×C₄	—	8	2	no	—
564	C₂×C₄	C₂₃×#117	1	1	yes	characteristic
565	C₂×C₄	C₂₃×#117	1	1	yes	characteristic
566	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
567	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
568	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
569	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
570	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
571	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
572	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
573	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
574	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
575	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
576	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
577	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
578	C₂×C₄	C₂₃×#123	1	1	yes	characteristic
579	C₂×C₄	C₂₃×#123	1	1	yes	characteristic
580	C₂×C₄	C₂₃×#124	1	1	yes	characteristic
581	C₂×C₄	C₂₃×#124	1	1	yes	characteristic
582	C₂×C₄	C₂₃×#126	1	1	yes	characteristic
583	C₂×C₄	C₂₃×#126	1	1	yes	characteristic
584	C₂×C₄	C₂₃×#126	1	1	yes	characteristic
585	C₂×C₄	C₂₃×#126	1	1	yes	characteristic
586	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
587	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
588	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
589	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
590	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
591	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
592	C₈	—	2	4	no	—
593	C₈	—	2	4	no	—
594	C₈	—	2	4	no	—
595	C₈	—	4	2	no	—
596	C₂²	—	2	2	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	2	2	no	—
599	C₂²	—	4	1	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	2	no	—
604	C₂²	—	8	2	no	—
605	C₂²	—	8	2	no	—
606	C₂²	—	8	2	no	—
607	C₂²	C₂₃×#388	1	1	yes	characteristic
608	C₂²	C₂₃×#388	1	1	yes	characteristic
609	C₂²	C₂₃×#388	1	1	yes	characteristic
610	C₂²	C₂₃×#388	1	1	yes	characteristic
611	C₂²	C₂×C₂₃×#117	1	1	yes	characteristic
612	C₂²	C₂×C₂₃×#123	1	1	yes	characteristic
613	C₂²	C₂×C₂₃×#124	1	1	yes	characteristic
614	C₄	—	2	4	no	—
615	C₄	—	4	2	no	—
616	C₄	—	4	2	no	—
617	C₄	—	8	2	no	—
618	C₄	C₂₃×#388	1	1	yes	characteristic
619	C₄	C₂₃×#388	1	1	yes	characteristic
620	C₄	C₂₃×#388	1	1	yes	characteristic
621	C₄	C₂₃×#388	1	1	yes	characteristic
622	C₄	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
623	C₄	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
624	C₄	C₂×C₂₃×#121	1	1	yes	characteristic
625	C₄	C₂×C₂₃×#126	1	1	yes	characteristic
626	C₂	—	2	1	no	—
627	C₂	—	2	1	no	—
628	C₂	—	2	1	no	—
629	C₂	—	2	1	no	—
630	C₂	—	2	1	no	—
631	C₂	—	2	1	no	—
632	C₂	—	8	2	no	—
633	C₂	C₂₃×#1932	1	2	yes	direct product factor
634	C₂	C₂×C₂₃×#388	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	#388
prime radical	C₂²×#41×C₂₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₂³×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#430	C₂	semidirect
5. C₂×C₄×M₁₆×C₂₃	C₂	semidirect
6. C₂₃×#1932	C₂	direct (N × H)
7. C₂×C₂₃×#344	C₂	semidirect
8. C₂×C₂₃×#339	C₂	semidirect
17. C₂₃×#430	C₂²	semidirect
26. C₂₃×#413	C₄	semidirect
28. C₂×C₂₃×#101	C₄	semidirect
29. C₂×C₂₃×#100	C₄	semidirect
31. C₄×M₁₆×C₂₃	C₂²	semidirect
34. C₂₃×#344	C₂²	semidirect
35. C₂₃×#339	C₂²	semidirect
100. C₂₃×#101	C₂×C₄	semidirect
101. C₂₃×#100	C₂×C₄	semidirect
207. C₂×#1932	C₂₃	direct (N × H)
279. C₂×#430	C₂×C₂₃	semidirect
283. C₂×C₄×M₁₆	C₂×C₂₃	semidirect
284. #1932	C₂×C₂₃	direct (N × H)
285. C₂×#344	C₂×C₂₃	semidirect
286. C₂×#339	C₂×C₂₃	semidirect
325. #430	C₂²×C₂₃	semidirect
334. #413	C₄×C₂₃	semidirect
336. C₂×#101	C₄×C₂₃	semidirect
337. C₂×#100	C₄×C₂₃	semidirect
339. C₄×M₁₆	C₂²×C₂₃	semidirect
342. #344	C₂²×C₂₃	semidirect
343. #339	C₂²×C₂₃	semidirect
351. C₂×C₂₃	#1932	direct (N × H)
417. #101	C₂×C₄×C₂₃	semidirect
418. #100	C₂×C₄×C₂₃	semidirect
421. C₂₃	C₂×#1932	direct (N × H)
633. C₂	C₂₃×#1932	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×#430	2
C₂×C₂₃×#421	2
C₂²×C₂₃×#104	2
C₂×C₂₃×#413	2
C₂×C₄×M₁₆×C₂₃	2
C₂₃×#1932	2
C₂×C₂₃×#344	2
C₂×C₂₃×#339	2
C₂×#1932	23

Subgroups — C2×C23×#1932 #19168705

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#1932 #19168705