Subgroups — C₄×C₂₃×#473 #19169180

Order 5888.

882 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#473	C₂	1	1	yes	maximal, characteristic
2	C₄×C₂₃×#137	C₂	1	2	yes	maximal
3	C₂×C₄×Q₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₂₃×#131	C₂	1	1	yes	maximal, characteristic
5	C₂₃×#1979	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1952	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1930	C₂	1	2	yes	maximal, complemented
8	C₂₃×#1908	C₂	1	2	yes	maximal
9	C₂₃×#1816	C₂	1	1	yes	maximal, characteristic
10	C₄×C₂₃×#108	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₂₃×#101	C₂	1	2	yes	maximal, complemented
12	C₂×C₂₃×#137	C₂²	1	2	yes	—
13	C₂²×Q₁₆×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×Q₈×C₂₃	C₂²	1	2	yes	—
18	C₂₃×#473	C₄	1	8	yes	direct product factor
19	C₂₃×#441	—	2	2	no	—
20	C₂₃×#440	—	2	2	no	—
21	C₄×Q₁₆×C₂₃	—	2	1	no	—
22	C₄×Q₁₆×C₂₃	—	2	1	no	—
23	C₄×Q₁₆×C₂₃	—	2	1	no	—
24	C₄×Q₁₆×C₂₃	—	2	1	no	—
25	C₄×Q₁₆×C₂₃	—	2	2	no	—
26	C₄×SD₁₆×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×#419	C₂²	1	2	yes	—
32	C₂₃×#417	C₂²	1	2	yes	—
33	C₂×C₂₃×#103	C₂²	1	2	yes	—
34	C₂×C₂₃×#101	C₂²	1	2	yes	—
35	C₂×C₂₃×#101	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×Q₈×C₂₃	C₂³	1	2	yes	—
50	C₂₃×#137	—	2	4	no	—
51	C₂₃×#137	C₂×C₄	1	8	yes	—
52	C₂×Q₁₆×C₂₃	—	2	2	no	—
53	C₂×Q₁₆×C₂₃	—	2	1	no	—
54	C₂×Q₁₆×C₂₃	—	2	1	no	—
55	C₂×Q₁₆×C₂₃	—	2	2	no	—
56	C₂×Q₁₆×C₂₃	C₂×C₄	1	4	yes	complemented
57	C₂×SD₁₆×C₂₃	—	2	2	no	—
58	C₂₃×#131	—	2	2	no	—
59	C₂₃×#131	—	2	2	no	—
60	C₂₃×#131	—	2	2	no	—
61	C₂₃×#131	C₂×C₄	1	4	yes	—
62	C₂×M₁₆×C₂₃	—	2	1	no	—
63	C₂×M₁₆×C₂₃	—	2	1	no	—
64	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
65	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
66	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
67	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₂₃	—	2	1	no	—
69	C₂²×C₈×C₂₃	—	2	1	no	—
70	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
72	C₄×Q₈×C₂₃	—	2	2	no	—
73	C₄×Q₈×C₂₃	—	2	2	no	—
74	C₄×Q₈×C₂₃	—	2	2	no	—
75	C₄×Q₈×C₂₃	—	2	2	no	—
76	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
77	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
78	C₄×D₄×C₂₃	—	2	1	no	—
79	C₄×D₄×C₂₃	—	2	1	no	—
80	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
81	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
82	C₂₃×#117	—	2	1	no	—
83	C₂₃×#117	C₂³	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
85	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
86	C₂×C₄²×C₂₃	—	2	1	no	—
87	C₂×C₄²×C₂₃	—	2	2	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×#103	—	2	2	no	—
97	C₂₃×#103	—	2	2	no	—
98	C₂₃×#103	—	2	2	no	—
99	C₂₃×#103	—	2	2	no	—
100	C₂₃×#102	—	2	2	no	—
101	C₂₃×#101	—	2	4	no	—
102	C₂₃×#101	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	#41×C₂₃	—	2	1	no	—
116	#41×C₂₃	—	2	1	no	—
117	#41×C₂₃	C₂²×C₄	1	2	yes	—
118	#41×C₂₃	#41	1	2	yes	—
119	C₂×Q₈×C₂₃	—	2	2	no	—
120	C₂×Q₈×C₂₃	—	2	2	no	—
121	C₂×Q₈×C₂₃	—	2	2	no	—
122	C₂×Q₈×C₂₃	—	2	2	no	—
123	C₂×Q₈×C₂₃	—	2	2	no	—
124	C₂×Q₈×C₂₃	C₂²×C₄	1	4	yes	—
125	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
126	C₂×D₄×C₂₃	—	2	1	no	—
127	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₂₃	—	2	1	no	—
129	C₂²×C₄×C₂₃	—	2	2	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	#41	1	1	yes	characteristic
134	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
135	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
136	Q₁₆×C₂₃	—	2	8	no	—
137	Q₁₆×C₂₃	—	2	4	no	—
138	Q₁₆×C₂₃	—	2	4	no	—
139	SD₁₆×C₂₃	—	2	8	no	—
140	M₁₆×C₂₃	—	2	4	no	—
141	M₁₆×C₂₃	—	2	1	no	—
142	M₁₆×C₂₃	—	2	1	no	—
143	M₁₆×C₂₃	—	2	2	no	—
144	M₁₆×C₂₃	—	2	4	no	—
145	M₁₆×C₂₃	—	2	2	no	—
146	M₁₆×C₂₃	—	2	2	no	—
147	M₁₆×C₂₃	C₂²×C₄	1	2	yes	—
148	M₁₆×C₂₃	C₂²×C₄	1	4	yes	—
149	M₁₆×C₂₃	#41	1	2	yes	—
150	C₂×C₈×C₂₃	—	2	4	no	—
151	C₂×C₈×C₂₃	—	2	2	no	—
152	C₂×C₈×C₂₃	—	2	1	no	—
153	C₂×C₈×C₂₃	—	2	1	no	—
154	C₂×C₈×C₂₃	—	2	1	no	—
155	C₂×C₈×C₂₃	—	2	1	no	—
156	C₂×C₈×C₂₃	—	2	4	no	—
157	C₂×C₈×C₂₃	—	2	2	no	—
158	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
159	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
160	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
161	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
162	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
163	C₂×C₈×C₂₃	#41	1	2	yes	—
164	C₄⋊C₄×C₂₃	—	2	1	no	—
165	C₄⋊C₄×C₂₃	—	2	1	no	—
166	C₄⋊C₄×C₂₃	—	2	2	no	—
167	C₄⋊C₄×C₂₃	—	2	2	no	—
168	C₄⋊C₄×C₂₃	—	4	2	no	—
169	C₄⋊C₄×C₂₃	—	4	2	no	—
170	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
171	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
172	C₂²⋊C₄×C₂₃	—	2	1	no	—
173	C₂²⋊C₄×C₂₃	—	2	1	no	—
174	C₂²⋊C₄×C₂₃	—	2	1	no	—
175	C₄²×C₂₃	—	2	1	no	—
176	C₄²×C₂₃	—	2	1	no	—
177	C₄²×C₂₃	—	2	1	no	—
178	C₄²×C₂₃	—	4	2	no	—
179	C₄²×C₂₃	—	4	2	no	—
180	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
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	C₄×#473	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₂³×C₂₃	—	2	1	no	—
186	C₂³×C₂₃	C₂×#41	1	1	yes	characteristic
187	Q₈×C₂₃	—	2	1	no	—
188	Q₈×C₂₃	—	2	4	no	—
189	Q₈×C₂₃	—	2	4	no	—
190	Q₈×C₂₃	—	4	2	no	—
191	Q₈×C₂₃	—	4	2	no	—
192	Q₈×C₂₃	C₄×D₄	1	2	yes	—
193	D₄×C₂₃	—	2	2	no	—
194	D₄×C₂₃	—	2	2	no	—
195	D₄×C₂₃	—	2	1	no	—
196	D₄×C₂₃	C₄×D₄	1	2	yes	—
197	C₂×C₄×C₂₃	—	2	1	no	—
198	C₂×C₄×C₂₃	—	2	2	no	—
199	C₂×C₄×C₂₃	—	2	2	no	—
200	C₂×C₄×C₂₃	—	2	2	no	—
201	C₂×C₄×C₂₃	—	2	4	no	—
202	C₂×C₄×C₂₃	—	2	1	no	—
203	C₂×C₄×C₂₃	—	2	1	no	—
204	C₂×C₄×C₂₃	—	4	1	no	—
205	C₂×C₄×C₂₃	—	4	2	no	—
206	C₂×C₄×C₂₃	—	4	2	no	—
207	C₂×C₄×C₂₃	—	4	2	no	—
208	C₂×C₄×C₂₃	—	4	2	no	—
209	C₂×C₄×C₂₃	—	4	2	no	—
210	C₂×C₄×C₂₃	—	8	2	no	—
211	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
212	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
213	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
214	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
215	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
216	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
219	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
220	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
221	C₈×C₂₃	—	2	2	no	—
222	C₈×C₂₃	—	2	4	no	—
223	C₈×C₂₃	—	2	1	no	—
224	C₈×C₂₃	—	2	2	no	—
225	C₈×C₂₃	—	2	1	no	—
226	C₈×C₂₃	—	4	2	no	—
227	C₈×C₂₃	C₄×D₄	1	2	yes	—
228	C₈×C₂₃	C₄×D₄	1	2	yes	—
229	C₂×#473	C₂×C₂₃	1	1	yes	characteristic
230	C₄×#137	C₂×C₂₃	1	2	yes	—
231	C₂×C₄×Q₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
232	C₄×#131	C₂×C₂₃	1	1	yes	characteristic
233	#1979	C₂×C₂₃	1	1	yes	characteristic, complemented
234	#1952	C₂×C₂₃	1	1	yes	characteristic, complemented
235	#1930	C₂×C₂₃	1	2	yes	complemented
236	#1908	C₂×C₂₃	1	2	yes	—
237	#1816	C₂×C₂₃	1	1	yes	characteristic
238	C₄×#108	C₂×C₂₃	1	1	yes	characteristic, complemented
239	C₄×#101	C₂×C₂₃	1	2	yes	complemented
240	C₂²×C₂₃	—	2	1	no	—
241	C₂²×C₂₃	—	2	1	no	—
242	C₂²×C₂₃	—	2	2	no	—
243	C₂²×C₂₃	—	4	1	no	—
244	C₂²×C₂₃	—	4	1	no	—
245	C₂²×C₂₃	C₄×#41	1	1	yes	characteristic
246	C₂²×C₂₃	C₂×#121	1	1	yes	characteristic
247	C₂²×C₂₃	#529	1	1	yes	characteristic
248	C₄×C₂₃	—	2	1	no	—
249	C₄×C₂₃	—	2	1	no	—
250	C₄×C₂₃	—	2	1	no	—
251	C₄×C₂₃	—	2	2	no	—
252	C₄×C₂₃	—	4	1	no	—
253	C₄×C₂₃	—	4	1	no	—
254	C₄×C₂₃	—	4	4	no	—
255	C₄×C₂₃	—	8	2	no	—
256	C₄×C₂₃	#473	1	2	yes	direct product factor
257	C₄×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
258	C₄×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
259	C₄×C₂₃	#525	1	1	yes	characteristic
260	C₄×C₂₃	#532	1	1	yes	characteristic
261	C₂×#137	C₂²×C₂₃	1	2	yes	—
262	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
263	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
264	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
265	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
266	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
267	#473	C₄×C₂₃	1	8	yes	direct product factor
268	#441	—	2	2	no	—
269	#440	—	2	2	no	—
270	C₄×Q₁₆	—	2	2	no	—
271	C₄×Q₁₆	—	2	1	no	—
272	C₄×Q₁₆	—	2	1	no	—
273	C₄×Q₁₆	—	2	1	no	—
274	C₄×Q₁₆	—	2	1	no	—
275	C₄×SD₁₆	—	2	2	no	—
276	C₂×#108	C₂²×C₂₃	1	1	yes	characteristic
277	C₂×#108	C₂²×C₂₃	1	1	yes	characteristic
278	#428	C₂²×C₂₃	1	2	yes	—
279	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
280	#419	C₂²×C₂₃	1	2	yes	—
281	#417	C₂²×C₂₃	1	2	yes	—
282	C₂×#103	C₂²×C₂₃	1	2	yes	—
283	C₂×#101	C₂²×C₂₃	1	2	yes	—
284	C₂×#101	C₂²×C₂₃	1	2	yes	—
285	#405	—	2	1	no	—
286	#405	—	2	1	no	—
287	#405	C₂²×C₂₃	1	1	yes	characteristic
288	#405	C₂²×C₂₃	1	1	yes	characteristic
289	C₄×M₁₆	—	2	1	no	—
290	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
291	C₄×M₁₆	C₂²×C₂₃	1	2	yes	—
292	C₂×C₄×C₈	—	2	1	no	—
293	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
294	#343	C₂²×C₂₃	1	2	yes	—
295	#343	C₂²×C₂₃	1	2	yes	—
296	#341	C₂²×C₂₃	1	2	yes	—
297	C₂×C₂₃	—	2	1	no	—
298	C₂×C₂₃	—	2	1	no	—
299	C₂×C₂₃	—	4	2	no	—
300	C₂×C₂₃	C₄×#121	1	1	yes	characteristic
301	C₂×C₂₃	C₂×#473	1	1	yes	characteristic
302	C₂×C₂₃	#3067	1	1	yes	characteristic
303	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
304	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
305	#137	—	2	4	no	—
306	#137	C₂×C₄×C₂₃	1	8	yes	—
307	C₂×Q₁₆	—	2	2	no	—
308	C₂×Q₁₆	—	2	1	no	—
309	C₂×Q₁₆	—	2	1	no	—
310	C₂×Q₁₆	—	2	2	no	—
311	C₂×Q₁₆	C₂×C₄×C₂₃	1	4	yes	complemented
312	C₂×SD₁₆	—	2	2	no	—
313	#131	—	2	2	no	—
314	#131	—	2	2	no	—
315	#131	—	2	2	no	—
316	#131	C₂×C₄×C₂₃	1	4	yes	—
317	C₂×M₁₆	—	2	1	no	—
318	C₂×M₁₆	—	2	1	no	—
319	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
320	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
321	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
322	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
323	C₂²×C₈	—	2	1	no	—
324	C₂²×C₈	—	2	1	no	—
325	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
326	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
327	C₄×Q₈	—	2	2	no	—
328	C₄×Q₈	—	2	2	no	—
329	C₄×Q₈	—	2	2	no	—
330	C₄×Q₈	—	2	2	no	—
331	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
332	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
333	C₄×D₄	—	2	1	no	—
334	C₄×D₄	—	2	1	no	—
335	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
336	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
337	#117	—	2	1	no	—
338	#117	C₂³×C₂₃	1	1	yes	characteristic
339	C₂×C₄⋊C₄	—	2	2	no	—
340	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
341	C₂×C₄²	—	2	1	no	—
342	C₂×C₄²	—	2	2	no	—
343	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
344	#108	—	2	2	no	—
345	#108	C₂×C₄×C₂₃	1	4	yes	complemented
346	#107	—	2	1	no	—
347	#107	—	2	1	no	—
348	#107	—	2	2	no	—
349	#106	—	2	2	no	—
350	#103	—	2	2	no	—
351	#103	—	2	2	no	—
352	#103	—	2	2	no	—
353	#103	—	2	2	no	—
354	#103	—	2	2	no	—
355	#102	—	2	2	no	—
356	#101	—	2	4	no	—
357	#101	C₂×C₄×C₂₃	1	8	yes	complemented
358	#97	—	2	1	no	—
359	#97	—	2	1	no	—
360	#97	—	2	1	no	—
361	#97	—	2	2	no	—
362	C₄×C₈	—	2	1	no	—
363	C₄×C₈	—	2	1	no	—
364	C₄×C₈	—	2	1	no	—
365	C₄×C₈	—	2	2	no	—
366	C₄×C₈	D₄×C₂₃	1	1	yes	characteristic
367	C₄×C₈	D₄×C₂₃	1	1	yes	characteristic
368	C₄×C₈	D₄×C₂₃	1	1	yes	characteristic
369	C₄×C₈	D₄×C₂₃	1	1	yes	characteristic
370	C₂₃	C₄×#473	1	1	yes	characteristic, direct product factor, Sylow
371	#41	—	2	1	no	—
372	#41	—	2	1	no	—
373	#41	C₂²×C₄×C₂₃	1	2	yes	—
374	#41	#41×C₂₃	1	2	yes	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	2	2	no	—
377	C₂×Q₈	—	2	2	no	—
378	C₂×Q₈	—	2	2	no	—
379	C₂×Q₈	—	2	2	no	—
380	C₂×Q₈	C₂²×C₄×C₂₃	1	4	yes	—
381	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
382	C₂×D₄	—	2	1	no	—
383	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
390	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
391	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
392	Q₁₆	—	2	8	no	—
393	Q₁₆	—	2	4	no	—
394	Q₁₆	—	2	4	no	—
395	SD₁₆	—	2	8	no	—
396	M₁₆	—	2	4	no	—
397	M₁₆	—	2	1	no	—
398	M₁₆	—	2	1	no	—
399	M₁₆	—	2	2	no	—
400	M₁₆	—	2	4	no	—
401	M₁₆	—	2	2	no	—
402	M₁₆	—	2	2	no	—
403	M₁₆	C₂²×C₄×C₂₃	1	2	yes	—
404	M₁₆	C₂²×C₄×C₂₃	1	4	yes	—
405	M₁₆	#41×C₂₃	1	2	yes	—
406	C₂×C₈	—	2	4	no	—
407	C₂×C₈	—	2	1	no	—
408	C₂×C₈	—	2	1	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	2	1	no	—
411	C₂×C₈	—	2	1	no	—
412	C₂×C₈	—	2	4	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
415	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
416	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
417	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
418	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
419	C₂×C₈	#41×C₂₃	1	2	yes	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	4	2	no	—
425	C₄⋊C₄	—	4	2	no	—
426	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
427	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
428	C₂²⋊C₄	—	2	1	no	—
429	C₂²⋊C₄	—	2	1	no	—
430	C₂²⋊C₄	—	2	1	no	—
431	C₄²	—	2	1	no	—
432	C₄²	—	2	1	no	—
433	C₄²	—	2	1	no	—
434	C₄²	—	4	2	no	—
435	C₄²	—	4	2	no	—
436	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
437	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
438	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
439	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
440	C₂³	—	2	1	no	—
441	C₂³	C₂×#41×C₂₃	1	1	yes	characteristic
442	Q₈	—	2	1	no	—
443	Q₈	—	2	4	no	—
444	Q₈	—	2	4	no	—
445	Q₈	—	4	2	no	—
446	Q₈	—	4	2	no	—
447	Q₈	C₄×D₄×C₂₃	1	2	yes	—
448	D₄	—	2	2	no	—
449	D₄	—	2	2	no	—
450	D₄	—	2	1	no	—
451	D₄	C₄×D₄×C₂₃	1	2	yes	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	8	2	no	—
466	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
467	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
468	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
469	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
470	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
471	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
472	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
473	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
474	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
475	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
476	C₈	—	2	2	no	—
477	C₈	—	2	4	no	—
478	C₈	—	2	1	no	—
479	C₈	—	2	2	no	—
480	C₈	—	2	1	no	—
481	C₈	—	4	2	no	—
482	C₈	C₄×D₄×C₂₃	1	2	yes	—
483	C₈	C₄×D₄×C₂₃	1	2	yes	—
484	C₂²	—	2	1	no	—
485	C₂²	—	2	1	no	—
486	C₂²	—	2	2	no	—
487	C₂²	—	4	1	no	—
488	C₂²	—	4	1	no	—
489	C₂²	C₄×#41×C₂₃	1	1	yes	characteristic
490	C₂²	C₂×C₂₃×#121	1	1	yes	characteristic
491	C₂²	C₂₃×#529	1	1	yes	characteristic
492	C₄	—	2	1	no	—
493	C₄	—	2	1	no	—
494	C₄	—	2	1	no	—
495	C₄	—	2	2	no	—
496	C₄	—	4	1	no	—
497	C₄	—	4	1	no	—
498	C₄	—	4	4	no	—
499	C₄	—	8	2	no	—
500	C₄	C₂₃×#473	1	2	yes	direct product factor
501	C₄	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
502	C₄	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
503	C₄	C₂₃×#525	1	1	yes	characteristic
504	C₄	C₂₃×#532	1	1	yes	characteristic
505	C₂	—	2	1	no	—
506	C₂	—	2	1	no	—
507	C₂	—	4	2	no	—
508	C₂	C₄×C₂₃×#121	1	1	yes	characteristic
509	C₂	C₂×C₂₃×#473	1	1	yes	characteristic
510	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×#41×C₂₃	C₂³
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
3. C₂×C₄×Q₁₆×C₂₃	C₂	semidirect
5. C₂₃×#1979	C₂	semidirect
6. C₂₃×#1952	C₂	semidirect
7. C₂₃×#1930	C₂	semidirect
10. C₄×C₂₃×#108	C₂	semidirect
11. C₄×C₂₃×#101	C₂	semidirect
18. C₂₃×#473	C₄	direct (N × H)
56. C₂×Q₁₆×C₂₃	C₂×C₄	semidirect
90. C₂₃×#108	C₂×C₄	semidirect
102. C₂₃×#101	C₂×C₄	semidirect
184. C₄×#473	C₂₃	direct (N × H)
231. C₂×C₄×Q₁₆	C₂×C₂₃	semidirect
233. #1979	C₂×C₂₃	semidirect
234. #1952	C₂×C₂₃	semidirect
235. #1930	C₂×C₂₃	semidirect
238. C₄×#108	C₂×C₂₃	semidirect
239. C₄×#101	C₂×C₂₃	semidirect
256. C₄×C₂₃	#473	direct (N × H)
267. #473	C₄×C₂₃	direct (N × H)
311. C₂×Q₁₆	C₂×C₄×C₂₃	semidirect
345. #108	C₂×C₄×C₂₃	semidirect
357. #101	C₂×C₄×C₂₃	semidirect
370. C₂₃	C₄×#473	direct (N × H)
500. C₄	C₂₃×#473	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×#473	2
C₄×C₂₃×#137	2
C₂×C₄×Q₁₆×C₂₃	2
C₄×C₂₃×#131	2
C₂₃×#1979	2
C₂₃×#1952	2
C₂₃×#1930	2
C₂₃×#1908	2
C₂₃×#1816	2
C₄×C₂₃×#108	2
C₄×C₂₃×#101	2
C₄×#473	23

Subgroups — C4×C23×#473 #19169180

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₂₃×#473 #19169180