Subgroups — C₂₃×#10047 #19157673

Order 5888.

802 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#493	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2548	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#1982	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₃×#331	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₃×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×SD₁₆×C₂₃	—	2	1	no	—
9	C₂²×D₈×C₂₃	—	2	2	no	—
10	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
11	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
12	C₂×C₂₃×#124	—	2	1	no	—
13	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
14	C₂₃×#493	—	2	2	no	—
15	C₂₃×#493	—	2	2	no	—
16	C₂₃×#460	—	2	2	no	—
17	C₂₃×#460	—	2	2	no	—
18	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₂₃×#102	—	2	1	no	—
21	C₂×C₂₃×#102	—	2	2	no	—
22	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
23	C₂₃×#394	—	2	2	no	—
24	C₂₃×#390	—	2	1	no	—
25	C₂₃×#390	—	2	2	no	—
26	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
27	C₂₃×#331	—	2	2	no	—
28	C₂₃×Q₈⋊C₈	—	2	2	no	—
29	C₂²×Q₈×C₂₃	D₄	1	1	yes	characteristic
30	C₂²×D₄×C₂₃	—	2	1	no	—
31	C₂²×D₄×C₂₃	—	2	1	no	—
32	C₂²×D₄×C₂₃	—	2	1	no	—
33	C₂²×D₄×C₂₃	—	2	1	no	—
34	C₂²×D₄×C₂₃	—	2	1	no	—
35	C₂²×D₄×C₂₃	D₄	1	2	yes	—
36	C₂×SD₁₆×C₂₃	—	2	4	no	—
37	C₂×SD₁₆×C₂₃	—	4	2	no	—
38	C₂×SD₁₆×C₂₃	—	4	2	no	—
39	C₂×D₈×C₂₃	—	2	8	no	—
40	C₂×D₈×C₂₃	—	4	8	no	—
41	C₂²×C₈×C₂₃	—	2	1	no	—
42	C₂²×C₈×C₂₃	—	2	1	no	—
43	C₂²×C₈×C₂₃	—	2	1	no	—
44	C₂₃×#127	—	2	1	no	—
45	C₂₃×#127	—	2	1	no	—
46	C₂₃×#127	—	2	1	no	—
47	C₂₃×#127	—	2	1	no	—
48	C₂₃×#127	—	2	1	no	—
49	C₂₃×#127	—	2	1	no	—
50	C₂₃×#127	—	2	1	no	—
51	C₂₃×#127	D₄	1	2	yes	—
52	C₂₃×#124	—	4	2	no	—
53	C₂₃×#124	—	4	2	no	—
54	C₄×Q₈×C₂₃	—	2	1	no	—
55	C₄×Q₈×C₂₃	—	2	1	no	—
56	C₄×Q₈×C₂₃	—	2	1	no	—
57	C₄×Q₈×C₂₃	—	2	1	no	—
58	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
59	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
60	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
61	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
62	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
63	C₂×C₄²×C₂₃	—	2	1	no	—
64	C₂×C₄²×C₂₃	—	2	1	no	—
65	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
66	C₂₃×C₄⋊C₈	—	2	1	no	—
67	C₂₃×C₄⋊C₈	—	2	1	no	—
68	C₂₃×C₄⋊C₈	—	2	1	no	—
69	C₂₃×C₄⋊C₈	D₄	1	2	yes	—
70	C₂₃×#102	—	2	4	no	—
71	C₂₃×#102	—	4	4	no	—
72	C₄×C₈×C₂₃	—	2	1	no	—
73	C₄×C₈×C₂₃	D₄	1	2	yes	—
74	C₂₃×#95	—	2	1	no	—
75	C₂⁴×C₂₃	—	2	2	no	—
76	C₂⁴×C₂₃	—	4	1	no	—
77	C₂×Q₈×C₂₃	—	2	1	no	—
78	C₂×Q₈×C₂₃	—	2	1	no	—
79	C₂×Q₈×C₂₃	—	2	1	no	—
80	C₂×Q₈×C₂₃	—	2	1	no	—
81	C₂×Q₈×C₂₃	—	2	1	no	—
82	C₂×Q₈×C₂₃	D₈	1	2	yes	complemented
83	C₂×D₄×C₂₃	—	2	2	no	—
84	C₂×D₄×C₂₃	—	2	2	no	—
85	C₂×D₄×C₂₃	—	2	2	no	—
86	C₂×D₄×C₂₃	—	2	2	no	—
87	C₂×D₄×C₂₃	—	2	2	no	—
88	C₂×D₄×C₂₃	—	4	4	no	—
89	C₂×D₄×C₂₃	—	4	4	no	—
90	C₂×D₄×C₂₃	—	4	1	no	—
91	C₂×D₄×C₂₃	—	4	1	no	—
92	C₂×D₄×C₂₃	—	4	1	no	—
93	C₂×D₄×C₂₃	—	4	1	no	—
94	C₂×D₄×C₂₃	—	4	1	no	—
95	C₂×D₄×C₂₃	—	4	1	no	—
96	C₂×D₄×C₂₃	—	4	1	no	—
97	C₂×D₄×C₂₃	—	4	1	no	—
98	C₂×D₄×C₂₃	—	4	1	no	—
99	C₂×D₄×C₂₃	—	4	1	no	—
100	C₂×D₄×C₂₃	—	4	2	no	—
101	C₂×D₄×C₂₃	—	4	1	no	—
102	C₂×D₄×C₂₃	—	4	2	no	—
103	C₂×D₄×C₂₃	—	4	2	no	—
104	C₂×D₄×C₂₃	—	4	1	no	—
105	C₂×D₄×C₂₃	—	4	1	no	—
106	C₂×D₄×C₂₃	—	4	1	no	—
107	C₂×D₄×C₂₃	—	4	1	no	—
108	C₂×D₄×C₂₃	—	4	2	no	—
109	C₂²×C₄×C₂₃	—	2	1	no	—
110	C₂²×C₄×C₂₃	—	2	1	no	—
111	C₂²×C₄×C₂₃	—	2	2	no	—
112	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
115	SD₁₆×C₂₃	—	4	8	no	—
116	D₈×C₂₃	—	4	16	no	—
117	C₂×C₈×C₂₃	—	2	4	no	—
118	C₂×C₈×C₂₃	—	2	2	no	—
119	C₂×C₈×C₂₃	—	2	2	no	—
120	C₂×C₈×C₂₃	—	4	1	no	—
121	C₂×C₈×C₂₃	—	4	1	no	—
122	C₂×C₈×C₂₃	—	4	1	no	—
123	C₂×C₈×C₂₃	—	4	2	no	—
124	C₄⋊C₄×C₂₃	—	2	1	no	—
125	C₄⋊C₄×C₂₃	—	2	1	no	—
126	C₄⋊C₄×C₂₃	—	2	2	no	—
127	C₄⋊C₄×C₂₃	—	2	2	no	—
128	C₄⋊C₄×C₂₃	—	4	1	no	—
129	C₄⋊C₄×C₂₃	—	4	1	no	—
130	C₂²⋊C₄×C₂₃	—	4	8	no	—
131	C₂²⋊C₄×C₂₃	—	8	4	no	—
132	C₄²×C₂₃	—	4	1	no	—
133	C₄²×C₂₃	—	4	1	no	—
134	C₄²×C₂₃	—	4	1	no	—
135	C₄²×C₂₃	—	4	1	no	—
136	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₂₃	#41	1	1	yes	characteristic
140	#10047	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₂³×C₂₃	—	4	2	no	—
142	C₂³×C₂₃	—	4	2	no	—
143	C₂³×C₂₃	—	4	2	no	—
144	C₂³×C₂₃	—	4	2	no	—
145	C₂³×C₂₃	—	4	4	no	—
146	C₂³×C₂₃	—	4	4	no	—
147	C₂³×C₂₃	—	8	1	no	—
148	C₂³×C₂₃	—	8	1	no	—
149	C₂³×C₂₃	—	8	2	no	—
150	C₂³×C₂₃	—	8	2	no	—
151	C₂³×C₂₃	#120	1	1	yes	characteristic
152	Q₈×C₂₃	—	2	2	no	—
153	Q₈×C₂₃	—	2	2	no	—
154	Q₈×C₂₃	—	4	1	no	—
155	Q₈×C₂₃	—	4	1	no	—
156	D₄×C₂₃	—	4	4	no	—
157	D₄×C₂₃	—	4	4	no	—
158	D₄×C₂₃	—	4	2	no	—
159	D₄×C₂₃	—	4	2	no	—
160	D₄×C₂₃	—	4	4	no	—
161	D₄×C₂₃	—	8	2	no	—
162	D₄×C₂₃	—	8	2	no	—
163	D₄×C₂₃	—	8	1	no	—
164	D₄×C₂₃	—	8	1	no	—
165	D₄×C₂₃	—	8	2	no	—
166	D₄×C₂₃	—	8	1	no	—
167	D₄×C₂₃	—	8	1	no	—
168	D₄×C₂₃	—	8	1	no	—
169	D₄×C₂₃	—	8	1	no	—
170	D₄×C₂₃	—	8	1	no	—
171	D₄×C₂₃	—	8	1	no	—
172	D₄×C₂₃	—	8	1	no	—
173	D₄×C₂₃	—	8	1	no	—
174	C₂×C₄×C₂₃	—	2	2	no	—
175	C₂×C₄×C₂₃	—	2	2	no	—
176	C₂×C₄×C₂₃	—	4	1	no	—
177	C₂×C₄×C₂₃	—	4	1	no	—
178	C₂×C₄×C₂₃	—	4	1	no	—
179	C₂×C₄×C₂₃	—	4	2	no	—
180	C₂×C₄×C₂₃	—	4	2	no	—
181	C₂×C₄×C₂₃	—	4	2	no	—
182	C₂×C₄×C₂₃	—	4	2	no	—
183	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
184	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
185	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
186	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
187	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
188	C₂×C₄×C₂₃	#127	1	1	yes	characteristic
189	C₂×C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
190	C₂×C₄×C₂₃	#135	1	1	yes	characteristic
191	C₂×C₄×C₂₃	#135	1	2	yes	—
192	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	1	yes	characteristic
193	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	1	yes	characteristic
194	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
195	C₈×C₂₃	—	2	4	no	—
196	C₈×C₂₃	—	4	2	no	—
197	C₈×C₂₃	—	8	1	no	—
198	C₂×#493	C₂×C₂₃	1	1	yes	characteristic
199	C₂×#460	C₂×C₂₃	1	1	yes	characteristic, complemented
200	#2548	C₂×C₂₃	1	1	yes	characteristic, complemented
201	#1982	C₂×C₂₃	1	1	yes	characteristic, complemented
202	C₂×#331	C₂×C₂₃	1	1	yes	characteristic, complemented
203	C₂×Q₈⋊C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
204	#1279	C₂×C₂₃	1	1	yes	characteristic, complemented
205	C₂²×C₂₃	—	8	4	no	—
206	C₂²×C₂₃	—	8	4	no	—
207	C₂²×C₂₃	—	8	2	no	—
208	C₂²×C₂₃	—	8	2	no	—
209	C₂²×C₂₃	—	8	2	no	—
210	C₂²×C₂₃	—	8	2	no	—
211	C₂²×C₂₃	—	8	2	no	—
212	C₂²×C₂₃	—	8	2	no	—
213	C₂²×C₂₃	—	16	2	no	—
214	C₂²×C₂₃	—	16	2	no	—
215	C₂²×C₂₃	#392	1	1	yes	characteristic
216	C₂²×C₂₃	#447	1	1	yes	characteristic
217	C₂²×C₂₃	#449	1	1	yes	characteristic
218	C₂²×C₂₃	#449	1	2	yes	—
219	C₂²×C₂₃	#453	1	2	yes	—
220	C₄×C₂₃	—	2	1	no	—
221	C₄×C₂₃	—	2	1	no	—
222	C₄×C₂₃	—	4	2	no	—
223	C₄×C₂₃	—	8	2	no	—
224	C₄×C₂₃	—	8	1	no	—
225	C₄×C₂₃	#447	1	1	yes	characteristic
226	C₄×C₂₃	#449	1	1	yes	characteristic
227	C₄×C₂₃	#463	1	2	yes	—
228	C₄×C₂₃	#466	1	1	yes	characteristic
229	C₄×C₂₃	#469	1	1	yes	characteristic
230	C₄×C₂₃	#495	1	1	yes	characteristic
231	C₄×C₂₃	#496	1	1	yes	characteristic
232	C₂²×SD₁₆	—	2	1	no	—
233	C₂²×D₈	—	2	2	no	—
234	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
235	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
236	C₂×#124	—	2	1	no	—
237	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
238	#493	—	2	2	no	—
239	#493	—	2	2	no	—
240	#460	—	2	2	no	—
241	#460	—	2	2	no	—
242	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
243	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
244	C₂×#102	—	2	1	no	—
245	C₂×#102	—	2	2	no	—
246	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
247	#394	—	2	2	no	—
248	#390	—	2	2	no	—
249	#390	—	2	1	no	—
250	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
251	#331	—	2	2	no	—
252	Q₈⋊C₈	—	2	2	no	—
253	C₂×C₂₃	—	16	2	no	—
254	C₂×C₂₃	—	16	2	no	—
255	C₂×C₂₃	#1620	1	2	yes	—
256	C₂×C₂₃	#1621	1	2	yes	—
257	C₂×C₂₃	#1999	1	1	yes	characteristic
258	C₂×C₂₃	#2002	1	1	yes	characteristic
259	C₂×C₂₃	#2012	1	1	yes	characteristic
260	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
261	C₂²×D₄	—	2	1	no	—
262	C₂²×D₄	—	2	1	no	—
263	C₂²×D₄	—	2	1	no	—
264	C₂²×D₄	—	2	1	no	—
265	C₂²×D₄	—	2	1	no	—
266	C₂²×D₄	D₄×C₂₃	1	2	yes	—
267	C₂×SD₁₆	—	2	4	no	—
268	C₂×SD₁₆	—	4	2	no	—
269	C₂×SD₁₆	—	4	2	no	—
270	C₂×D₈	—	2	8	no	—
271	C₂×D₈	—	4	8	no	—
272	C₂²×C₈	—	2	1	no	—
273	C₂²×C₈	—	2	1	no	—
274	C₂²×C₈	—	2	1	no	—
275	#127	—	2	1	no	—
276	#127	—	2	1	no	—
277	#127	—	2	1	no	—
278	#127	—	2	1	no	—
279	#127	—	2	1	no	—
280	#127	—	2	1	no	—
281	#127	—	2	1	no	—
282	#127	D₄×C₂₃	1	2	yes	—
283	#124	—	4	2	no	—
284	#124	—	4	2	no	—
285	C₄×Q₈	—	2	1	no	—
286	C₄×Q₈	—	2	1	no	—
287	C₄×Q₈	—	2	1	no	—
288	C₄×Q₈	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
291	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
292	C₂×C₂²⋊C₄	—	2	4	no	—
293	C₂×C₂²⋊C₄	—	2	4	no	—
294	C₂×C₄²	—	2	1	no	—
295	C₂×C₄²	—	2	1	no	—
296	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
297	C₄⋊C₈	—	2	1	no	—
298	C₄⋊C₈	—	2	1	no	—
299	C₄⋊C₈	—	2	1	no	—
300	C₄⋊C₈	D₄×C₂₃	1	2	yes	—
301	#102	—	2	4	no	—
302	#102	—	4	4	no	—
303	C₄×C₈	—	2	1	no	—
304	C₄×C₈	D₄×C₂₃	1	2	yes	—
305	#95	—	2	1	no	—
306	C₂₃	#10047	1	1	yes	characteristic, direct product factor, Sylow
307	C₂⁴	—	2	2	no	—
308	C₂⁴	—	4	1	no	—
309	C₂×Q₈	—	2	1	no	—
310	C₂×Q₈	—	2	1	no	—
311	C₂×Q₈	—	2	1	no	—
312	C₂×Q₈	—	2	1	no	—
313	C₂×Q₈	—	2	1	no	—
314	C₂×Q₈	D₈×C₂₃	1	2	yes	complemented
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	4	4	no	—
321	C₂×D₄	—	4	4	no	—
322	C₂×D₄	—	4	1	no	—
323	C₂×D₄	—	4	1	no	—
324	C₂×D₄	—	4	1	no	—
325	C₂×D₄	—	4	1	no	—
326	C₂×D₄	—	4	1	no	—
327	C₂×D₄	—	4	1	no	—
328	C₂×D₄	—	4	1	no	—
329	C₂×D₄	—	4	1	no	—
330	C₂×D₄	—	4	1	no	—
331	C₂×D₄	—	4	1	no	—
332	C₂×D₄	—	4	2	no	—
333	C₂×D₄	—	4	1	no	—
334	C₂×D₄	—	4	2	no	—
335	C₂×D₄	—	4	2	no	—
336	C₂×D₄	—	4	1	no	—
337	C₂×D₄	—	4	1	no	—
338	C₂×D₄	—	4	1	no	—
339	C₂×D₄	—	4	1	no	—
340	C₂×D₄	—	4	2	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
345	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
346	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
347	SD₁₆	—	4	8	no	—
348	D₈	—	4	16	no	—
349	C₂×C₈	—	2	4	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	4	1	no	—
353	C₂×C₈	—	4	1	no	—
354	C₂×C₈	—	4	1	no	—
355	C₂×C₈	—	4	2	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	4	1	no	—
361	C₄⋊C₄	—	4	1	no	—
362	C₂²⋊C₄	—	4	8	no	—
363	C₂²⋊C₄	—	8	4	no	—
364	C₄²	—	4	1	no	—
365	C₄²	—	4	1	no	—
366	C₄²	—	4	1	no	—
367	C₄²	—	4	1	no	—
368	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
369	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
370	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
371	C₄²	#41×C₂₃	1	1	yes	characteristic
372	C₂³	—	4	2	no	—
373	C₂³	—	4	2	no	—
374	C₂³	—	4	2	no	—
375	C₂³	—	4	2	no	—
376	C₂³	—	4	4	no	—
377	C₂³	—	4	4	no	—
378	C₂³	—	8	1	no	—
379	C₂³	—	8	1	no	—
380	C₂³	—	8	2	no	—
381	C₂³	—	8	2	no	—
382	C₂³	C₂₃×#120	1	1	yes	characteristic
383	Q₈	—	2	2	no	—
384	Q₈	—	2	2	no	—
385	Q₈	—	4	1	no	—
386	Q₈	—	4	1	no	—
387	D₄	—	4	4	no	—
388	D₄	—	4	4	no	—
389	D₄	—	4	2	no	—
390	D₄	—	4	2	no	—
391	D₄	—	4	4	no	—
392	D₄	—	8	2	no	—
393	D₄	—	8	2	no	—
394	D₄	—	8	1	no	—
395	D₄	—	8	1	no	—
396	D₄	—	8	2	no	—
397	D₄	—	8	1	no	—
398	D₄	—	8	1	no	—
399	D₄	—	8	1	no	—
400	D₄	—	8	1	no	—
401	D₄	—	8	1	no	—
402	D₄	—	8	1	no	—
403	D₄	—	8	1	no	—
404	D₄	—	8	1	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
415	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
416	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
417	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
418	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
419	C₂×C₄	C₂₃×#127	1	1	yes	characteristic
420	C₂×C₄	C₂×D₈×C₂₃	1	1	yes	characteristic
421	C₂×C₄	C₂₃×#135	1	1	yes	characteristic
422	C₂×C₄	C₂₃×#135	1	2	yes	—
423	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
424	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
425	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
426	C₈	—	2	4	no	—
427	C₈	—	4	2	no	—
428	C₈	—	8	1	no	—
429	C₂²	—	8	2	no	—
430	C₂²	—	8	2	no	—
431	C₂²	—	8	2	no	—
432	C₂²	—	8	2	no	—
433	C₂²	—	8	2	no	—
434	C₂²	—	8	2	no	—
435	C₂²	—	8	4	no	—
436	C₂²	—	8	4	no	—
437	C₂²	—	16	2	no	—
438	C₂²	—	16	2	no	—
439	C₂²	C₂₃×#392	1	1	yes	characteristic
440	C₂²	C₂₃×#447	1	1	yes	characteristic
441	C₂²	C₂₃×#449	1	1	yes	characteristic
442	C₂²	C₂₃×#449	1	2	yes	—
443	C₂²	C₂₃×#453	1	2	yes	—
444	C₄	—	2	1	no	—
445	C₄	—	2	1	no	—
446	C₄	—	4	2	no	—
447	C₄	—	8	1	no	—
448	C₄	—	8	2	no	—
449	C₄	C₂₃×#447	1	1	yes	characteristic
450	C₄	C₂₃×#449	1	1	yes	characteristic
451	C₄	C₂₃×#463	1	2	yes	—
452	C₄	C₂₃×#466	1	1	yes	characteristic
453	C₄	C₂₃×#469	1	1	yes	characteristic
454	C₄	C₂₃×#495	1	1	yes	characteristic
455	C₄	C₂₃×#496	1	1	yes	characteristic
456	C₂	—	16	2	no	—
457	C₂	—	16	2	no	—
458	C₂	C₂₃×#1620	1	2	yes	—
459	C₂	C₂₃×#1621	1	2	yes	—
460	C₂	C₂₃×#1999	1	1	yes	characteristic
461	C₂	C₂₃×#2002	1	1	yes	characteristic
462	C₂	C₂₃×#2012	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₂₃
prime radical	C₂×C₂₃×#493	C₂
LCS	G ▷ C₂×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×#460	C₂	semidirect
3. C₂₃×#2548	C₂	semidirect
4. C₂₃×#1982	C₂	semidirect
5. C₂×C₂₃×#331	C₂	semidirect
6. C₂×C₂₃×Q₈⋊C₈	C₂	semidirect
7. C₂₃×#1279	C₂	semidirect
82. C₂×Q₈×C₂₃	D₈	semidirect
140. #10047	C₂₃	direct (N × H)
199. C₂×#460	C₂×C₂₃	semidirect
200. #2548	C₂×C₂₃	semidirect
201. #1982	C₂×C₂₃	semidirect
202. C₂×#331	C₂×C₂₃	semidirect
203. C₂×Q₈⋊C₈	C₂×C₂₃	semidirect
204. #1279	C₂×C₂₃	semidirect
306. C₂₃	#10047	direct (N × H)
314. C₂×Q₈	D₈×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#493	2
C₂×C₂₃×#460	2
C₂₃×#2548	2
C₂₃×#1982	2
C₂×C₂₃×#331	2
C₂×C₂₃×Q₈⋊C₈	2
C₂₃×#1279	2
#10047	23

Subgroups — C23×#10047 #19157673

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#10047 #19157673