Subgroups — C₂×C₂₃×#1929 #19168695

Order 5888.

1082 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₃×#108	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂₃×#104	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₃×#416	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂₃×#408	C₂	1	1	yes	maximal, characteristic
5	C₂×C₂₃×#405	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1929	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₂₃×#339	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₃×#336	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	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
13	C₂³×C₈×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	C₂×C₂₃×#108	—	2	4	no	—
17	C₂×C₂₃×#108	C₂²	1	4	yes	complemented
18	C₂×C₂₃×#104	—	2	4	no	—
19	C₂×C₂₃×#104	C₂²	1	4	yes	—
20	C₂₃×#416	C₄	1	4	yes	complemented
21	C₂₃×#416	C₂²	1	4	yes	—
22	C₂×C₂₃×#103	C₄	1	1	yes	characteristic, complemented
23	C₂×C₂₃×#103	C₄	1	1	yes	characteristic, complemented
24	C₂×C₂₃×#102	C₄	1	1	yes	characteristic, complemented
25	C₂×C₂₃×#102	C₄	1	1	yes	characteristic, complemented
26	C₂₃×#408	—	2	2	no	—
27	C₂₃×#408	C₂²	1	4	yes	—
28	C₂×C₂₃×C₂²⋊C₈	—	2	1	no	—
29	C₂×C₂₃×C₂²⋊C₈	—	2	1	no	—
30	C₂₃×#405	—	2	2	no	—
31	C₂₃×#405	C₂²	1	4	yes	complemented
32	C₂×C₂₃×#97	—	2	1	no	—
33	C₂×C₄×C₈×C₂₃	—	2	1	no	—
34	C₂₃×#339	C₂²	1	4	yes	complemented
35	C₂₃×#336	C₂²	1	4	yes	complemented
36	C₂×#41×C₂₃	—	2	1	no	—
37	C₂×#41×C₂₃	—	2	1	no	—
38	C₂×#41×C₂₃	—	2	2	no	—
39	C₂×#41×C₂₃	—	2	2	no	—
40	C₂×#41×C₂₃	—	2	2	no	—
41	C₂×#41×C₂₃	—	2	2	no	—
42	C₂×#41×C₂₃	C₂×C₄	1	2	yes	—
43	C₂×#41×C₂₃	C₂³	1	2	yes	—
44	C₂²×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
45	C₂²×D₄×C₂₃	—	2	1	no	—
46	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₂₃	—	2	1	no	—
48	C₂³×C₄×C₂₃	—	2	1	no	—
49	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
50	C₂×M₁₆×C₂₃	—	2	1	no	—
51	C₂×M₁₆×C₂₃	—	2	2	no	—
52	C₂×M₁₆×C₂₃	—	2	1	no	—
53	C₂×M₁₆×C₂₃	—	2	2	no	—
54	C₂×M₁₆×C₂₃	—	2	2	no	—
55	C₂×M₁₆×C₂₃	D₄	1	4	yes	—
56	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
57	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
58	C₂²×C₈×C₂₃	—	2	2	no	—
59	C₂²×C₈×C₂₃	—	2	1	no	—
60	C₂²×C₈×C₂₃	—	2	2	no	—
61	C₂²×C₈×C₂₃	—	2	2	no	—
62	C₂²×C₈×C₂₃	—	2	2	no	—
63	C₂²×C₈×C₂₃	—	2	1	no	—
64	C₂²×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
66	C₂²×C₈×C₂₃	C₂×C₄	1	2	yes	—
67	C₂²×C₈×C₂₃	D₄	1	2	yes	—
68	C₂²×C₈×C₂₃	D₄	1	1	yes	characteristic
69	C₂²×C₈×C₂₃	D₄	1	1	yes	characteristic
70	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
71	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
72	C₂₃×#117	—	2	1	no	—
73	C₂₃×#117	—	2	1	no	—
74	C₂₃×#117	C₂×C₄	1	2	yes	—
75	C₂₃×#117	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
78	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
79	C₂×C₄²×C₂₃	—	2	1	no	—
80	C₂×C₄²×C₂₃	—	2	2	no	—
81	C₂×C₄²×C₂₃	—	2	2	no	—
82	C₂×C₄²×C₂₃	—	2	1	no	—
83	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
84	C₂₃×#108	—	2	8	no	—
85	C₂₃×#104	—	2	8	no	—
86	C₂₃×#103	C₂×C₄	1	4	yes	complemented
87	C₂₃×#103	C₂×C₄	1	4	yes	complemented
88	C₂₃×#102	C₂×C₄	1	4	yes	complemented
89	C₂₃×#102	C₂×C₄	1	4	yes	complemented
90	C₂₃×C₂²⋊C₈	—	2	4	no	—
91	C₂₃×C₂²⋊C₈	—	2	4	no	—
92	C₂₃×#97	—	2	4	no	—
93	C₄×C₈×C₂₃	—	2	4	no	—
94	C₂⁴×C₂₃	—	2	1	no	—
95	C₂⁴×C₂₃	#41	1	1	yes	characteristic
96	#41×C₂₃	—	2	4	no	—
97	#41×C₂₃	—	2	4	no	—
98	#41×C₂₃	—	2	2	no	—
99	#41×C₂₃	—	2	2	no	—
100	#41×C₂₃	—	2	2	no	—
101	#41×C₂₃	—	2	2	no	—
102	#41×C₂₃	—	4	2	no	—
103	#41×C₂₃	—	4	2	no	—
104	#41×C₂₃	—	4	2	no	—
105	#41×C₂₃	—	4	2	no	—
106	C₂×Q₈×C₂₃	—	2	1	no	—
107	C₂×Q₈×C₂₃	—	2	2	no	—
108	C₂×Q₈×C₂₃	—	2	2	no	—
109	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
110	C₂×D₄×C₂₃	—	2	2	no	—
111	C₂×D₄×C₂₃	—	2	2	no	—
112	C₂×D₄×C₂₃	—	2	2	no	—
113	C₂×D₄×C₂₃	—	2	2	no	—
114	C₂×D₄×C₂₃	—	2	1	no	—
115	C₂×D₄×C₂₃	—	4	2	no	—
116	C₂×D₄×C₂₃	—	4	2	no	—
117	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
118	C₂²×C₄×C₂₃	—	2	4	no	—
119	C₂²×C₄×C₂₃	—	2	1	no	—
120	C₂²×C₄×C₂₃	—	2	1	no	—
121	C₂²×C₄×C₂₃	—	2	1	no	—
122	C₂²×C₄×C₂₃	—	2	2	no	—
123	C₂²×C₄×C₂₃	—	2	2	no	—
124	C₂²×C₄×C₂₃	—	2	2	no	—
125	C₂²×C₄×C₂₃	—	4	2	no	—
126	C₂²×C₄×C₂₃	—	4	2	no	—
127	C₂²×C₄×C₂₃	—	4	2	no	—
128	C₂²×C₄×C₂₃	—	4	2	no	—
129	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₂₃	#41	1	2	yes	—
135	C₂²×C₄×C₂₃	#41	1	2	yes	—
136	C₂²×C₄×C₂₃	#41	1	2	yes	—
137	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
138	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
139	M₁₆×C₂₃	—	2	4	no	—
140	M₁₆×C₂₃	—	2	2	no	—
141	M₁₆×C₂₃	—	2	2	no	—
142	M₁₆×C₂₃	—	2	2	no	—
143	M₁₆×C₂₃	—	4	2	no	—
144	M₁₆×C₂₃	C₂×D₄	1	4	yes	—
145	C₂×C₈×C₂₃	—	2	2	no	—
146	C₂×C₈×C₂₃	—	2	2	no	—
147	C₂×C₈×C₂₃	—	2	4	no	—
148	C₂×C₈×C₂₃	—	2	4	no	—
149	C₂×C₈×C₂₃	—	2	2	no	—
150	C₂×C₈×C₂₃	—	2	2	no	—
151	C₂×C₈×C₂₃	—	2	4	no	—
152	C₂×C₈×C₂₃	—	2	2	no	—
153	C₂×C₈×C₂₃	—	2	2	no	—
154	C₂×C₈×C₂₃	—	2	2	no	—
155	C₂×C₈×C₂₃	—	2	2	no	—
156	C₂×C₈×C₂₃	—	2	2	no	—
157	C₂×C₈×C₂₃	—	2	2	no	—
158	C₂×C₈×C₂₃	—	4	2	no	—
159	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
160	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
161	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
162	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
163	C₄⋊C₄×C₂₃	—	2	1	no	—
164	C₄⋊C₄×C₂₃	—	2	1	no	—
165	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
166	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
167	C₂²⋊C₄×C₂₃	—	2	2	no	—
168	C₂²⋊C₄×C₂₃	—	2	2	no	—
169	C₄²×C₂₃	—	2	2	no	—
170	C₄²×C₂₃	—	2	2	no	—
171	C₄²×C₂₃	—	2	2	no	—
172	C₄²×C₂₃	—	2	2	no	—
173	C₄²×C₂₃	—	4	2	no	—
174	C₂×#1929	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂³×C₂₃	—	2	2	no	—
176	C₂³×C₂₃	—	2	2	no	—
177	C₂³×C₂₃	—	2	2	no	—
178	C₂³×C₂₃	—	4	2	no	—
179	C₂³×C₂₃	—	4	2	no	—
180	C₂³×C₂₃	—	4	2	no	—
181	C₂³×C₂₃	C₄×D₄	1	1	yes	characteristic
182	C₂³×C₂₃	C₄×D₄	1	1	yes	characteristic
183	C₂³×C₂₃	#124	1	2	yes	—
184	C₂³×C₂₃	#126	1	2	yes	—
185	C₂³×C₂₃	C₂×#41	1	1	yes	characteristic
186	Q₈×C₂₃	—	2	2	no	—
187	Q₈×C₂₃	—	2	2	no	—
188	Q₈×C₂₃	—	4	2	no	—
189	D₄×C₂₃	—	2	2	no	—
190	D₄×C₂₃	—	2	2	no	—
191	D₄×C₂₃	—	4	2	no	—
192	D₄×C₂₃	—	4	2	no	—
193	D₄×C₂₃	—	4	4	no	—
194	D₄×C₂₃	—	4	2	no	—
195	C₂×C₄×C₂₃	—	2	4	no	—
196	C₂×C₄×C₂₃	—	2	2	no	—
197	C₂×C₄×C₂₃	—	2	2	no	—
198	C₂×C₄×C₂₃	—	2	2	no	—
199	C₂×C₄×C₂₃	—	4	8	no	—
200	C₂×C₄×C₂₃	—	4	2	no	—
201	C₂×C₄×C₂₃	—	4	2	no	—
202	C₂×C₄×C₂₃	—	4	2	no	—
203	C₂×C₄×C₂₃	—	4	2	no	—
204	C₂×C₄×C₂₃	—	4	2	no	—
205	C₂×C₄×C₂₃	—	4	2	no	—
206	C₂×C₄×C₂₃	—	4	2	no	—
207	C₂×C₄×C₂₃	—	4	4	no	—
208	C₂×C₄×C₂₃	#117	1	2	yes	—
209	C₂×C₄×C₂₃	#117	1	2	yes	—
210	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
211	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
212	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
213	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
214	C₂×C₄×C₂₃	#121	1	2	yes	—
215	C₂×C₄×C₂₃	#121	1	2	yes	—
216	C₂×C₄×C₂₃	#123	1	2	yes	—
217	C₂×C₄×C₂₃	#123	1	2	yes	—
218	C₂×C₄×C₂₃	#124	1	2	yes	—
219	C₂×C₄×C₂₃	#126	1	2	yes	—
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	2	no	—
228	C₈×C₂₃	—	2	4	no	—
229	C₈×C₂₃	—	2	2	no	—
230	C₈×C₂₃	—	2	2	no	—
231	C₈×C₂₃	—	4	2	no	—
232	C₂²×#108	C₂×C₂₃	1	1	yes	characteristic, complemented
233	C₂²×#104	C₂×C₂₃	1	1	yes	characteristic
234	C₂×#416	C₂×C₂₃	1	1	yes	characteristic
235	C₂×#408	C₂×C₂₃	1	1	yes	characteristic
236	C₂×#405	C₂×C₂₃	1	1	yes	characteristic, complemented
237	#1929	C₂×C₂₃	1	8	yes	direct product factor
238	C₂×#339	C₂×C₂₃	1	1	yes	characteristic, complemented
239	C₂×#336	C₂×C₂₃	1	1	yes	characteristic, complemented
240	C₂²×C₂₃	—	2	4	no	—
241	C₂²×C₂₃	—	2	4	no	—
242	C₂²×C₂₃	—	2	1	no	—
243	C₂²×C₂₃	—	2	1	no	—
244	C₂²×C₂₃	—	2	1	no	—
245	C₂²×C₂₃	—	2	1	no	—
246	C₂²×C₂₃	—	4	2	no	—
247	C₂²×C₂₃	—	4	2	no	—
248	C₂²×C₂₃	—	4	2	no	—
249	C₂²×C₂₃	—	8	4	no	—
250	C₂²×C₂₃	#388	1	2	yes	—
251	C₂²×C₂₃	#388	1	2	yes	—
252	C₂²×C₂₃	#443	1	2	yes	—
253	C₂²×C₂₃	#444	1	2	yes	—
254	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
255	C₂²×C₂₃	C₂×#124	1	1	yes	characteristic
256	C₂²×C₂₃	C₂×#126	1	1	yes	characteristic
257	C₄×C₂₃	—	4	4	no	—
258	C₄×C₂₃	—	4	2	no	—
259	C₄×C₂₃	—	4	2	no	—
260	C₄×C₂₃	—	4	2	no	—
261	C₄×C₂₃	#388	1	2	yes	—
262	C₄×C₂₃	#388	1	2	yes	—
263	C₄×C₂₃	C₂×#117	1	1	yes	characteristic
264	C₄×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
265	C₄×C₂₃	C₂×#121	1	1	yes	characteristic
266	C₄×C₂₃	C₂×#123	1	1	yes	characteristic
267	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
268	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
269	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
270	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
271	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
272	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
273	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
274	C₂×#108	—	2	4	no	—
275	C₂×#108	C₂²×C₂₃	1	4	yes	complemented
276	C₂×#104	—	2	4	no	—
277	C₂×#104	C₂²×C₂₃	1	4	yes	—
278	#416	C₄×C₂₃	1	4	yes	complemented
279	#416	C₂²×C₂₃	1	4	yes	—
280	C₂×#103	C₄×C₂₃	1	1	yes	characteristic, complemented
281	C₂×#103	C₄×C₂₃	1	1	yes	characteristic, complemented
282	C₂×#102	C₄×C₂₃	1	1	yes	characteristic, complemented
283	C₂×#102	C₄×C₂₃	1	1	yes	characteristic, complemented
284	#408	—	2	2	no	—
285	#408	C₂²×C₂₃	1	4	yes	—
286	C₂×C₂²⋊C₈	—	2	1	no	—
287	C₂×C₂²⋊C₈	—	2	1	no	—
288	#405	—	2	2	no	—
289	#405	C₂²×C₂₃	1	4	yes	complemented
290	C₂×#97	—	2	1	no	—
291	C₂×C₄×C₈	—	2	1	no	—
292	#339	C₂²×C₂₃	1	4	yes	complemented
293	#336	C₂²×C₂₃	1	4	yes	complemented
294	C₂×C₂₃	—	2	1	no	—
295	C₂×C₂₃	—	2	1	no	—
296	C₂×C₂₃	—	2	2	no	—
297	C₂×C₂₃	—	8	2	no	—
298	C₂×C₂₃	#1929	1	4	yes	direct product factor
299	C₂×C₂₃	C₂×#388	1	1	yes	characteristic
300	C₂×C₂₃	C₂×#443	1	1	yes	characteristic
301	C₂×C₂₃	C₂×#444	1	1	yes	characteristic
302	C₂×#41	—	2	1	no	—
303	C₂×#41	—	2	1	no	—
304	C₂×#41	—	2	2	no	—
305	C₂×#41	—	2	2	no	—
306	C₂×#41	—	2	2	no	—
307	C₂×#41	—	2	2	no	—
308	C₂×#41	C₂×C₄×C₂₃	1	2	yes	—
309	C₂×#41	C₂³×C₂₃	1	2	yes	—
310	C₂²×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
311	C₂²×D₄	—	2	1	no	—
312	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
313	C₂³×C₄	—	2	1	no	—
314	C₂³×C₄	—	2	1	no	—
315	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
316	C₂×M₁₆	—	2	1	no	—
317	C₂×M₁₆	—	2	2	no	—
318	C₂×M₁₆	—	2	1	no	—
319	C₂×M₁₆	—	2	2	no	—
320	C₂×M₁₆	—	2	2	no	—
321	C₂×M₁₆	D₄×C₂₃	1	4	yes	—
322	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
323	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
324	C₂²×C₈	—	2	2	no	—
325	C₂²×C₈	—	2	1	no	—
326	C₂²×C₈	—	2	2	no	—
327	C₂²×C₈	—	2	2	no	—
328	C₂²×C₈	—	2	2	no	—
329	C₂²×C₈	—	2	1	no	—
330	C₂²×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
331	C₂²×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
332	C₂²×C₈	C₂×C₄×C₂₃	1	2	yes	—
333	C₂²×C₈	D₄×C₂₃	1	1	yes	characteristic
334	C₂²×C₈	D₄×C₂₃	1	1	yes	characteristic
335	C₂²×C₈	D₄×C₂₃	1	2	yes	—
336	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
337	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
338	#117	—	2	1	no	—
339	#117	—	2	1	no	—
340	#117	C₂×C₄×C₂₃	1	2	yes	—
341	#117	C₂³×C₂₃	1	2	yes	—
342	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
343	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
344	C₂×C₂²⋊C₄	—	2	1	no	—
345	C₂×C₄²	—	2	1	no	—
346	C₂×C₄²	—	2	2	no	—
347	C₂×C₄²	—	2	2	no	—
348	C₂×C₄²	—	2	1	no	—
349	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
350	#108	—	2	8	no	—
351	#104	—	2	8	no	—
352	#103	C₂×C₄×C₂₃	1	4	yes	complemented
353	#103	C₂×C₄×C₂₃	1	4	yes	complemented
354	#102	C₂×C₄×C₂₃	1	4	yes	complemented
355	#102	C₂×C₄×C₂₃	1	4	yes	complemented
356	C₂²⋊C₈	—	2	4	no	—
357	C₂²⋊C₈	—	2	4	no	—
358	#97	—	2	4	no	—
359	C₄×C₈	—	2	4	no	—
360	C₂₃	C₂×#1929	1	1	yes	characteristic, direct product factor, Sylow
361	C₂⁴	—	2	1	no	—
362	C₂⁴	#41×C₂₃	1	1	yes	characteristic
363	#41	—	2	4	no	—
364	#41	—	2	4	no	—
365	#41	—	2	2	no	—
366	#41	—	2	2	no	—
367	#41	—	2	2	no	—
368	#41	—	2	2	no	—
369	#41	—	4	2	no	—
370	#41	—	4	2	no	—
371	#41	—	4	2	no	—
372	#41	—	4	2	no	—
373	C₂×Q₈	—	2	1	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	—	2	1	no	—
382	C₂×D₄	—	4	2	no	—
383	C₂×D₄	—	4	2	no	—
384	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	4	2	no	—
393	C₂²×C₄	—	4	2	no	—
394	C₂²×C₄	—	4	2	no	—
395	C₂²×C₄	—	4	2	no	—
396	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
397	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
398	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
399	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
400	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
401	C₂²×C₄	#41×C₂₃	1	2	yes	—
402	C₂²×C₄	#41×C₂₃	1	2	yes	—
403	C₂²×C₄	#41×C₂₃	1	2	yes	—
404	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
405	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
406	M₁₆	—	2	4	no	—
407	M₁₆	—	2	2	no	—
408	M₁₆	—	2	2	no	—
409	M₁₆	—	2	2	no	—
410	M₁₆	—	4	2	no	—
411	M₁₆	C₂×D₄×C₂₃	1	4	yes	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	4	no	—
415	C₂×C₈	—	2	4	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	2	4	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	—	4	2	no	—
426	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
427	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
428	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
429	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
433	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
434	C₂²⋊C₄	—	2	2	no	—
435	C₂²⋊C₄	—	2	2	no	—
436	C₄²	—	2	2	no	—
437	C₄²	—	2	2	no	—
438	C₄²	—	2	2	no	—
439	C₄²	—	2	2	no	—
440	C₄²	—	4	2	no	—
441	C₂³	—	2	2	no	—
442	C₂³	—	2	2	no	—
443	C₂³	—	2	2	no	—
444	C₂³	—	4	2	no	—
445	C₂³	—	4	2	no	—
446	C₂³	—	4	2	no	—
447	C₂³	C₄×D₄×C₂₃	1	1	yes	characteristic
448	C₂³	C₄×D₄×C₂₃	1	1	yes	characteristic
449	C₂³	C₂₃×#124	1	2	yes	—
450	C₂³	C₂₃×#126	1	2	yes	—
451	C₂³	C₂×#41×C₂₃	1	1	yes	characteristic
452	Q₈	—	2	2	no	—
453	Q₈	—	2	2	no	—
454	Q₈	—	4	2	no	—
455	D₄	—	2	2	no	—
456	D₄	—	2	2	no	—
457	D₄	—	4	4	no	—
458	D₄	—	4	2	no	—
459	D₄	—	4	2	no	—
460	D₄	—	4	2	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	4	8	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	4	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	C₂₃×#117	1	2	yes	—
475	C₂×C₄	C₂₃×#117	1	2	yes	—
476	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
477	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
478	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
479	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
480	C₂×C₄	C₂₃×#121	1	2	yes	—
481	C₂×C₄	C₂₃×#121	1	2	yes	—
482	C₂×C₄	C₂₃×#123	1	2	yes	—
483	C₂×C₄	C₂₃×#123	1	2	yes	—
484	C₂×C₄	C₂₃×#124	1	2	yes	—
485	C₂×C₄	C₂₃×#126	1	2	yes	—
486	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
487	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
488	C₂×C₄	C₂²×D₄×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	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
492	C₈	—	2	2	no	—
493	C₈	—	2	2	no	—
494	C₈	—	2	4	no	—
495	C₈	—	2	2	no	—
496	C₈	—	2	2	no	—
497	C₈	—	4	2	no	—
498	C₂²	—	2	4	no	—
499	C₂²	—	2	4	no	—
500	C₂²	—	2	1	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	2	1	no	—
504	C₂²	—	4	2	no	—
505	C₂²	—	4	2	no	—
506	C₂²	—	4	2	no	—
507	C₂²	—	8	4	no	—
508	C₂²	C₂₃×#388	1	2	yes	—
509	C₂²	C₂₃×#388	1	2	yes	—
510	C₂²	C₂₃×#443	1	2	yes	—
511	C₂²	C₂₃×#444	1	2	yes	—
512	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
513	C₂²	C₂×C₂₃×#124	1	1	yes	characteristic
514	C₂²	C₂×C₂₃×#126	1	1	yes	characteristic
515	C₄	—	4	4	no	—
516	C₄	—	4	2	no	—
517	C₄	—	4	2	no	—
518	C₄	—	4	2	no	—
519	C₄	C₂₃×#388	1	2	yes	—
520	C₄	C₂₃×#388	1	2	yes	—
521	C₄	C₂×C₂₃×#117	1	1	yes	characteristic
522	C₄	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
523	C₄	C₂×C₂₃×#121	1	1	yes	characteristic
524	C₄	C₂×C₂₃×#123	1	1	yes	characteristic
525	C₂	—	2	1	no	—
526	C₂	—	2	2	no	—
527	C₂	—	2	1	no	—
528	C₂	—	8	2	no	—
529	C₂	C₂₃×#1929	1	4	yes	direct product factor
530	C₂	C₂×C₂₃×#388	1	1	yes	characteristic
531	C₂	C₂×C₂₃×#443	1	1	yes	characteristic
532	C₂	C₂×C₂₃×#444	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₂₃	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
socle	C₂³×C₂₃	C₄×D₄
prime radical	C₂²×#41×C₂₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₃ ◁ C₂³×C₈×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₂₃×#108	C₂	semidirect
5. C₂×C₂₃×#405	C₂	semidirect
6. C₂₃×#1929	C₂	direct (N × H)
7. C₂×C₂₃×#339	C₂	semidirect
8. C₂×C₂₃×#336	C₂	semidirect
17. C₂×C₂₃×#108	C₂²	semidirect
20. C₂₃×#416	C₄	semidirect
22. C₂×C₂₃×#103	C₄	semidirect
23. C₂×C₂₃×#103	C₄	semidirect
24. C₂×C₂₃×#102	C₄	semidirect
25. C₂×C₂₃×#102	C₄	semidirect
31. C₂₃×#405	C₂²	semidirect
34. C₂₃×#339	C₂²	semidirect
35. C₂₃×#336	C₂²	semidirect
86. C₂₃×#103	C₂×C₄	semidirect
87. C₂₃×#103	C₂×C₄	semidirect
88. C₂₃×#102	C₂×C₄	semidirect
89. C₂₃×#102	C₂×C₄	semidirect
174. C₂×#1929	C₂₃	direct (N × H)
232. C₂²×#108	C₂×C₂₃	semidirect
236. C₂×#405	C₂×C₂₃	semidirect
237. #1929	C₂×C₂₃	direct (N × H)
238. C₂×#339	C₂×C₂₃	semidirect
239. C₂×#336	C₂×C₂₃	semidirect
275. C₂×#108	C₂²×C₂₃	semidirect
278. #416	C₄×C₂₃	semidirect
280. C₂×#103	C₄×C₂₃	semidirect
281. C₂×#103	C₄×C₂₃	semidirect
282. C₂×#102	C₄×C₂₃	semidirect
283. C₂×#102	C₄×C₂₃	semidirect
289. #405	C₂²×C₂₃	semidirect
292. #339	C₂²×C₂₃	semidirect
293. #336	C₂²×C₂₃	semidirect
298. C₂×C₂₃	#1929	direct (N × H)
352. #103	C₂×C₄×C₂₃	semidirect
353. #103	C₂×C₄×C₂₃	semidirect
354. #102	C₂×C₄×C₂₃	semidirect
355. #102	C₂×C₄×C₂₃	semidirect
360. C₂₃	C₂×#1929	direct (N × H)
529. C₂	C₂₃×#1929	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₂₃×#108	2
C₂²×C₂₃×#104	2
C₂×C₂₃×#416	2
C₂×C₂₃×#408	2
C₂×C₂₃×#405	2
C₂₃×#1929	2
C₂×C₂₃×#339	2
C₂×C₂₃×#336	2
C₂×#1929	23

Subgroups — C2×C23×#1929 #19168695

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#1929 #19168695