Subgroups — C₂×C₂₃×#2193 #19181162

Order 5888.

1098 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#578	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#509	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₂₃×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₃×#472	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2193	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₂₃×#362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₃×#359	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₃×#350	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂₃×2₋¹⁺⁴	—	2	1	no	—
10	C₂₃×#578	—	2	2	no	—
11	C₂₃×#578	—	2	2	no	—
12	C₂₃×#578	—	2	2	no	—
13	C₂₃×#578	C₂²	1	4	yes	complemented
14	C₂×C₂₃×#137	—	2	2	no	—
15	C₂×C₂₃×#137	—	2	1	no	—
16	C₂×C₂₃×AGL(1,ℤ/8)	—	2	1	no	—
17	C₂×C₂₃×#135	—	2	1	no	—
18	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic
19	C₂²×Q₁₆×C₂₃	—	2	1	no	—
20	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
21	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
23	C₂₃×#509	—	2	2	no	—
24	C₂₃×#509	C₂²	1	4	yes	complemented
25	C₂×C₂₃×SD₃₂	—	2	2	no	—
26	C₂×C₂₃×SD₃₂	—	2	2	no	—
27	C₂×C₂₃×SD₃₂	—	2	1	no	—
28	C₂×C₂₃×SD₃₂	C₂²	1	4	yes	complemented
29	C₂×C₂₃×D₁₆	—	2	1	no	—
30	C₂×C₂₃×M₃₂	C₂²	1	1	yes	characteristic
31	C₂²×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
32	C₂₃×#472	—	2	2	no	—
33	C₂₃×#472	C₂²	1	4	yes	complemented
34	C₂×C₂₃×#108	C₂²	1	1	yes	characteristic
35	C₂×C₂₃×#100	—	2	1	no	—
36	C₂₃×#362	C₂²	1	4	yes	complemented
37	C₂₃×#359	C₂²	1	4	yes	complemented
38	C₂₃×#350	C₂²	1	4	yes	complemented
39	C₂₃×2₋¹⁺⁴	—	2	4	no	—
40	C₂₃×2₋¹⁺⁴	—	2	4	no	—
41	C₂₃×2₋¹⁺⁴	—	4	2	no	—
42	C₂₃×2₋¹⁺⁴	—	4	2	no	—
43	C₂×#41×C₂₃	—	2	2	no	—
44	C₂×#41×C₂₃	—	2	1	no	—
45	C₂×#41×C₂₃	—	4	2	no	—
46	C₂×#41×C₂₃	—	4	1	no	—
47	C₂×#41×C₂₃	D₄	1	1	yes	characteristic
48	C₂²×Q₈×C₂₃	—	2	2	no	—
49	C₂²×Q₈×C₂₃	—	2	1	no	—
50	C₂²×Q₈×C₂₃	—	4	1	no	—
51	C₂²×D₄×C₂₃	—	2	1	no	—
52	C₂₃×#137	—	2	4	no	—
53	C₂₃×#137	—	2	8	no	—
54	C₂₃×#137	—	2	8	no	—
55	C₂₃×#137	—	2	4	no	—
56	C₂₃×AGL(1,ℤ/8)	—	2	4	no	—
57	C₂₃×AGL(1,ℤ/8)	—	4	2	no	—
58	C₂₃×#135	—	2	4	no	—
59	C₂₃×#135	—	2	4	no	—
60	C₂₃×#135	—	2	1	no	—
61	C₂₃×#135	—	2	1	no	—
62	C₂₃×#135	D₄	1	2	yes	—
63	C₂₃×#135	C₂³	1	2	yes	—
64	C₂×Q₁₆×C₂₃	—	2	2	no	—
65	C₂×Q₁₆×C₂₃	—	2	4	no	—
66	C₂×Q₁₆×C₂₃	—	2	4	no	—
67	C₂×Q₁₆×C₂₃	—	2	1	no	—
68	C₂×Q₁₆×C₂₃	—	2	1	no	—
69	C₂×Q₁₆×C₂₃	—	2	1	no	—
70	C₂×Q₁₆×C₂₃	D₄	1	1	yes	characteristic
71	C₂×Q₁₆×C₂₃	D₄	1	2	yes	—
72	C₂×Q₁₆×C₂₃	D₄	1	2	yes	—
73	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
74	C₂×SD₁₆×C₂₃	—	2	2	no	—
75	C₂×SD₁₆×C₂₃	—	2	1	no	—
76	C₂×SD₁₆×C₂₃	—	4	1	no	—
77	C₂×D₈×C₂₃	—	2	1	no	—
78	C₂×D₈×C₂₃	—	2	1	no	—
79	C₂×D₈×C₂₃	—	2	1	no	—
80	C₂×D₈×C₂₃	—	2	1	no	—
81	C₂×D₈×C₂₃	—	2	1	no	—
82	C₂×D₈×C₂₃	—	4	1	no	—
83	C₂×D₈×C₂₃	D₄	1	1	yes	characteristic
84	C₂×D₈×C₂₃	C₂³	1	2	yes	—
85	C₂₃×#131	—	2	1	no	—
86	C₂₃×#131	—	2	1	no	—
87	C₂₃×#131	D₄	1	2	yes	—
88	C₂₃×#131	C₂³	1	2	yes	—
89	C₂×M₁₆×C₂₃	—	2	1	no	—
90	C₂×M₁₆×C₂₃	—	2	1	no	—
91	C₂×M₁₆×C₂₃	D₄	1	1	yes	characteristic
92	C₂²×C₈×C₂₃	—	2	1	no	—
93	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
94	C₂₃×SD₃₂	—	2	8	no	—
95	C₂₃×SD₃₂	—	2	4	no	—
96	C₂₃×D₁₆	—	2	4	no	—
97	C₂₃×M₃₂	—	2	1	no	—
98	C₂₃×M₃₂	C₂³	1	2	yes	—
99	C₂×C₁₆×C₂₃	—	2	1	no	—
100	C₂×C₁₆×C₂₃	—	2	1	no	—
101	C₂×C₁₆×C₂₃	—	2	1	no	—
102	C₂×C₁₆×C₂₃	C₂³	1	2	yes	—
103	C₂₃×#108	—	2	1	no	—
104	C₂₃×#108	C₂³	1	2	yes	—
105	C₂₃×#100	—	2	4	no	—
106	C₂⁴×C₂₃	—	4	1	no	—
107	#41×C₂₃	—	2	1	no	—
108	#41×C₂₃	—	2	1	no	—
109	#41×C₂₃	—	2	8	no	—
110	#41×C₂₃	—	2	2	no	—
111	#41×C₂₃	—	2	2	no	—
112	#41×C₂₃	—	4	4	no	—
113	#41×C₂₃	—	4	8	no	—
114	#41×C₂₃	—	4	8	no	—
115	#41×C₂₃	—	4	4	no	—
116	#41×C₂₃	—	4	4	no	—
117	#41×C₂₃	—	4	1	no	—
118	#41×C₂₃	—	4	1	no	—
119	#41×C₂₃	D₈	1	2	yes	—
120	#41×C₂₃	C₂×D₄	1	2	yes	—
121	C₂×Q₈×C₂₃	—	2	8	no	—
122	C₂×Q₈×C₂₃	—	2	2	no	—
123	C₂×Q₈×C₂₃	—	2	1	no	—
124	C₂×Q₈×C₂₃	—	2	2	no	—
125	C₂×Q₈×C₂₃	—	2	2	no	—
126	C₂×Q₈×C₂₃	—	4	2	no	—
127	C₂×Q₈×C₂₃	—	4	4	no	—
128	C₂×Q₈×C₂₃	—	4	4	no	—
129	C₂×Q₈×C₂₃	—	4	4	no	—
130	C₂×Q₈×C₂₃	—	4	1	no	—
131	C₂×Q₈×C₂₃	—	4	1	no	—
132	C₂×Q₈×C₂₃	—	4	1	no	—
133	C₂×Q₈×C₂₃	D₈	1	1	yes	characteristic
134	C₂×D₄×C₂₃	—	2	1	no	—
135	C₂×D₄×C₂₃	—	2	1	no	—
136	C₂×D₄×C₂₃	—	2	2	no	—
137	C₂×D₄×C₂₃	—	4	2	no	—
138	C₂×D₄×C₂₃	—	4	1	no	—
139	C₂×D₄×C₂₃	—	4	1	no	—
140	C₂×D₄×C₂₃	—	4	1	no	—
141	C₂×D₄×C₂₃	—	4	1	no	—
142	C₂×D₄×C₂₃	—	4	1	no	—
143	C₂×D₄×C₂₃	—	4	1	no	—
144	C₂×D₄×C₂₃	D₈	1	1	yes	characteristic
145	C₂²×C₄×C₂₃	—	2	1	no	—
146	C₂²×C₄×C₂₃	—	4	2	no	—
147	C₂²×C₄×C₂₃	—	4	2	no	—
148	C₂²×C₄×C₂₃	—	4	1	no	—
149	C₂²×C₄×C₂₃	—	4	1	no	—
150	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
151	Q₁₆×C₂₃	—	2	8	no	—
152	Q₁₆×C₂₃	—	2	1	no	—
153	Q₁₆×C₂₃	—	2	2	no	—
154	Q₁₆×C₂₃	—	2	2	no	—
155	Q₁₆×C₂₃	—	2	2	no	—
156	Q₁₆×C₂₃	C₂×D₄	1	2	yes	—
157	Q₁₆×C₂₃	C₂×D₄	1	4	yes	—
158	SD₁₆×C₂₃	—	2	8	no	—
159	SD₁₆×C₂₃	—	2	2	no	—
160	SD₁₆×C₂₃	—	2	2	no	—
161	SD₁₆×C₂₃	—	4	4	no	—
162	D₈×C₂₃	—	2	1	no	—
163	D₈×C₂₃	—	2	2	no	—
164	D₈×C₂₃	—	2	2	no	—
165	D₈×C₂₃	—	4	4	no	—
166	D₈×C₂₃	—	4	1	no	—
167	D₈×C₂₃	—	4	1	no	—
168	D₈×C₂₃	C₂×D₄	1	2	yes	—
169	M₁₆×C₂₃	—	2	1	no	—
170	M₁₆×C₂₃	—	2	2	no	—
171	M₁₆×C₂₃	—	2	2	no	—
172	M₁₆×C₂₃	—	2	2	no	—
173	M₁₆×C₂₃	—	4	1	no	—
174	M₁₆×C₂₃	C₂×D₄	1	2	yes	—
175	C₂×C₈×C₂₃	—	2	1	no	—
176	C₂×C₈×C₂₃	—	2	2	no	—
177	C₂×C₈×C₂₃	—	2	2	no	—
178	C₂×C₈×C₂₃	—	4	1	no	—
179	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
180	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
181	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
182	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
183	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
184	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
185	C₁₆×C₂₃	—	2	2	no	—
186	C₁₆×C₂₃	—	2	2	no	—
187	C₂×#2193	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₂³×C₂₃	—	2	1	no	—
189	C₂³×C₂₃	—	4	1	no	—
190	C₂³×C₂₃	—	4	2	no	—
191	C₂³×C₂₃	—	8	1	no	—
192	C₂³×C₂₃	—	8	1	no	—
193	C₂³×C₂₃	—	16	2	no	—
194	C₂³×C₂₃	AGL(1,ℤ/8)	1	1	yes	characteristic
195	Q₈×C₂₃	—	2	1	no	—
196	Q₈×C₂₃	—	2	4	no	—
197	Q₈×C₂₃	—	2	2	no	—
198	Q₈×C₂₃	—	4	8	no	—
199	Q₈×C₂₃	—	4	2	no	—
200	Q₈×C₂₃	—	4	1	no	—
201	Q₈×C₂₃	—	4	2	no	—
202	Q₈×C₂₃	—	4	2	no	—
203	Q₈×C₂₃	C₂×D₈	1	2	yes	—
204	D₄×C₂₃	—	2	2	no	—
205	D₄×C₂₃	—	2	2	no	—
206	D₄×C₂₃	—	2	2	no	—
207	D₄×C₂₃	—	2	1	no	—
208	D₄×C₂₃	—	4	8	no	—
209	D₄×C₂₃	—	4	2	no	—
210	D₄×C₂₃	—	4	2	no	—
211	D₄×C₂₃	—	4	2	no	—
212	D₄×C₂₃	—	4	2	no	—
213	D₄×C₂₃	—	4	1	no	—
214	D₄×C₂₃	—	8	1	no	—
215	D₄×C₂₃	—	8	1	no	—
216	D₄×C₂₃	C₂×D₈	1	2	yes	—
217	C₂×C₄×C₂₃	—	2	1	no	—
218	C₂×C₄×C₂₃	—	2	2	no	—
219	C₂×C₄×C₂₃	—	2	2	no	—
220	C₂×C₄×C₂₃	—	4	8	no	—
221	C₂×C₄×C₂₃	—	4	8	no	—
222	C₂×C₄×C₂₃	—	4	2	no	—
223	C₂×C₄×C₂₃	—	4	2	no	—
224	C₂×C₄×C₂₃	—	4	2	no	—
225	C₂×C₄×C₂₃	—	4	1	no	—
226	C₂×C₄×C₂₃	—	4	2	no	—
227	C₂×C₄×C₂₃	—	4	2	no	—
228	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
229	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
230	C₂×C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
231	C₂×C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
232	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	1	yes	characteristic
233	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
234	C₈×C₂₃	—	2	2	no	—
235	C₈×C₂₃	—	4	2	no	—
236	C₈×C₂₃	#120	1	1	yes	characteristic
237	C₈×C₂₃	#120	1	1	yes	characteristic
238	C₈×C₂₃	C₂²×D₄	1	1	yes	characteristic
239	C₈×C₂₃	C₂²×D₄	1	1	yes	characteristic
240	C₂×#578	C₂×C₂₃	1	1	yes	characteristic, complemented
241	C₂×#509	C₂×C₂₃	1	1	yes	characteristic, complemented
242	C₂²×SD₃₂	C₂×C₂₃	1	1	yes	characteristic, complemented
243	C₂×#472	C₂×C₂₃	1	1	yes	characteristic, complemented
244	#2193	C₂×C₂₃	1	8	yes	direct product factor
245	C₂×#362	C₂×C₂₃	1	1	yes	characteristic, complemented
246	C₂×#359	C₂×C₂₃	1	1	yes	characteristic, complemented
247	C₂×#350	C₂×C₂₃	1	1	yes	characteristic, complemented
248	C₂²×C₂₃	—	2	2	no	—
249	C₂²×C₂₃	—	2	2	no	—
250	C₂²×C₂₃	—	4	2	no	—
251	C₂²×C₂₃	—	4	2	no	—
252	C₂²×C₂₃	—	8	2	no	—
253	C₂²×C₂₃	—	8	2	no	—
254	C₂²×C₂₃	—	16	2	no	—
255	C₂²×C₂₃	—	16	2	no	—
256	C₂²×C₂₃	—	16	2	no	—
257	C₂²×C₂₃	#447	1	1	yes	characteristic
258	C₂²×C₂₃	#447	1	1	yes	characteristic
259	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
260	C₄×C₂₃	—	2	2	no	—
261	C₄×C₂₃	—	4	4	no	—
262	C₄×C₂₃	—	4	2	no	—
263	C₄×C₂₃	#447	1	1	yes	characteristic
264	C₄×C₂₃	#447	1	1	yes	characteristic
265	C₄×C₂₃	C₂×#120	1	1	yes	characteristic
266	C₄×C₂₃	C₂²×D₈	1	1	yes	characteristic
267	C₂×2₋¹⁺⁴	—	2	1	no	—
268	#578	—	2	2	no	—
269	#578	—	2	2	no	—
270	#578	—	2	2	no	—
271	#578	C₂²×C₂₃	1	4	yes	complemented
272	C₂×#137	—	2	2	no	—
273	C₂×#137	—	2	1	no	—
274	C₂×AGL(1,ℤ/8)	—	2	1	no	—
275	C₂×#135	—	2	1	no	—
276	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic
277	C₂²×Q₁₆	—	2	1	no	—
278	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
279	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
280	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
281	#509	—	2	2	no	—
282	#509	C₂²×C₂₃	1	4	yes	complemented
283	C₂×SD₃₂	—	2	2	no	—
284	C₂×SD₃₂	—	2	2	no	—
285	C₂×SD₃₂	—	2	1	no	—
286	C₂×SD₃₂	C₂²×C₂₃	1	4	yes	complemented
287	C₂×D₁₆	—	2	1	no	—
288	C₂×M₃₂	C₂²×C₂₃	1	1	yes	characteristic
289	C₂²×C₁₆	C₂²×C₂₃	1	1	yes	characteristic
290	#472	—	2	2	no	—
291	#472	C₂²×C₂₃	1	4	yes	complemented
292	C₂×#108	C₂²×C₂₃	1	1	yes	characteristic
293	C₂×#100	—	2	1	no	—
294	#362	C₂²×C₂₃	1	4	yes	complemented
295	#359	C₂²×C₂₃	1	4	yes	complemented
296	#350	C₂²×C₂₃	1	4	yes	complemented
297	C₂×C₂₃	—	2	1	no	—
298	C₂×C₂₃	—	2	1	no	—
299	C₂×C₂₃	—	4	2	no	—
300	C₂×C₂₃	—	8	2	no	—
301	C₂×C₂₃	—	16	2	no	—
302	C₂×C₂₃	#2193	1	2	yes	direct product factor
303	C₂×C₂₃	C₂×#447	1	1	yes	characteristic
304	2₋¹⁺⁴	—	2	4	no	—
305	2₋¹⁺⁴	—	2	4	no	—
306	2₋¹⁺⁴	—	4	2	no	—
307	2₋¹⁺⁴	—	4	2	no	—
308	C₂×#41	—	2	2	no	—
309	C₂×#41	—	2	1	no	—
310	C₂×#41	—	4	2	no	—
311	C₂×#41	—	4	1	no	—
312	C₂×#41	D₄×C₂₃	1	1	yes	characteristic
313	C₂²×Q₈	—	2	2	no	—
314	C₂²×Q₈	—	2	1	no	—
315	C₂²×Q₈	—	4	1	no	—
316	C₂²×D₄	—	2	1	no	—
317	#137	—	2	4	no	—
318	#137	—	2	8	no	—
319	#137	—	2	8	no	—
320	#137	—	2	4	no	—
321	AGL(1,ℤ/8)	—	2	4	no	—
322	AGL(1,ℤ/8)	—	4	2	no	—
323	#135	—	2	4	no	—
324	#135	—	2	4	no	—
325	#135	—	2	1	no	—
326	#135	—	2	1	no	—
327	#135	D₄×C₂₃	1	2	yes	—
328	#135	C₂³×C₂₃	1	2	yes	—
329	C₂×Q₁₆	—	2	2	no	—
330	C₂×Q₁₆	—	2	4	no	—
331	C₂×Q₁₆	—	2	4	no	—
332	C₂×Q₁₆	—	2	1	no	—
333	C₂×Q₁₆	—	2	1	no	—
334	C₂×Q₁₆	—	2	1	no	—
335	C₂×Q₁₆	D₄×C₂₃	1	1	yes	characteristic
336	C₂×Q₁₆	D₄×C₂₃	1	2	yes	—
337	C₂×Q₁₆	D₄×C₂₃	1	2	yes	—
338	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
339	C₂×SD₁₆	—	2	2	no	—
340	C₂×SD₁₆	—	2	1	no	—
341	C₂×SD₁₆	—	4	1	no	—
342	C₂×D₈	—	2	1	no	—
343	C₂×D₈	—	2	1	no	—
344	C₂×D₈	—	2	1	no	—
345	C₂×D₈	—	2	1	no	—
346	C₂×D₈	—	2	1	no	—
347	C₂×D₈	—	4	1	no	—
348	C₂×D₈	D₄×C₂₃	1	1	yes	characteristic
349	C₂×D₈	C₂³×C₂₃	1	2	yes	—
350	#131	—	2	1	no	—
351	#131	—	2	1	no	—
352	#131	D₄×C₂₃	1	2	yes	—
353	#131	C₂³×C₂₃	1	2	yes	—
354	C₂×M₁₆	—	2	1	no	—
355	C₂×M₁₆	—	2	1	no	—
356	C₂×M₁₆	D₄×C₂₃	1	1	yes	characteristic
357	C₂²×C₈	—	2	1	no	—
358	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
359	SD₃₂	—	2	8	no	—
360	SD₃₂	—	2	4	no	—
361	D₁₆	—	2	4	no	—
362	M₃₂	—	2	1	no	—
363	M₃₂	C₂³×C₂₃	1	2	yes	—
364	C₂×C₁₆	—	2	1	no	—
365	C₂×C₁₆	—	2	1	no	—
366	C₂×C₁₆	—	2	1	no	—
367	C₂×C₁₆	C₂³×C₂₃	1	2	yes	—
368	#108	—	2	1	no	—
369	#108	C₂³×C₂₃	1	2	yes	—
370	#100	—	2	4	no	—
371	C₂₃	C₂×#2193	1	1	yes	characteristic, direct product factor, Sylow
372	C₂⁴	—	4	1	no	—
373	#41	—	2	1	no	—
374	#41	—	2	1	no	—
375	#41	—	2	8	no	—
376	#41	—	2	2	no	—
377	#41	—	2	2	no	—
378	#41	—	4	4	no	—
379	#41	—	4	8	no	—
380	#41	—	4	8	no	—
381	#41	—	4	4	no	—
382	#41	—	4	4	no	—
383	#41	—	4	1	no	—
384	#41	—	4	1	no	—
385	#41	D₈×C₂₃	1	2	yes	—
386	#41	C₂×D₄×C₂₃	1	2	yes	—
387	C₂×Q₈	—	2	8	no	—
388	C₂×Q₈	—	2	2	no	—
389	C₂×Q₈	—	2	1	no	—
390	C₂×Q₈	—	2	2	no	—
391	C₂×Q₈	—	2	2	no	—
392	C₂×Q₈	—	4	2	no	—
393	C₂×Q₈	—	4	4	no	—
394	C₂×Q₈	—	4	4	no	—
395	C₂×Q₈	—	4	4	no	—
396	C₂×Q₈	—	4	1	no	—
397	C₂×Q₈	—	4	1	no	—
398	C₂×Q₈	—	4	1	no	—
399	C₂×Q₈	D₈×C₂₃	1	1	yes	characteristic
400	C₂×D₄	—	2	1	no	—
401	C₂×D₄	—	2	1	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	4	2	no	—
404	C₂×D₄	—	4	1	no	—
405	C₂×D₄	—	4	1	no	—
406	C₂×D₄	—	4	1	no	—
407	C₂×D₄	—	4	1	no	—
408	C₂×D₄	—	4	1	no	—
409	C₂×D₄	—	4	1	no	—
410	C₂×D₄	D₈×C₂₃	1	1	yes	characteristic
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	4	2	no	—
413	C₂²×C₄	—	4	2	no	—
414	C₂²×C₄	—	4	1	no	—
415	C₂²×C₄	—	4	1	no	—
416	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
417	Q₁₆	—	2	8	no	—
418	Q₁₆	—	2	1	no	—
419	Q₁₆	—	2	2	no	—
420	Q₁₆	—	2	2	no	—
421	Q₁₆	—	2	2	no	—
422	Q₁₆	C₂×D₄×C₂₃	1	2	yes	—
423	Q₁₆	C₂×D₄×C₂₃	1	4	yes	—
424	SD₁₆	—	2	8	no	—
425	SD₁₆	—	2	2	no	—
426	SD₁₆	—	2	2	no	—
427	SD₁₆	—	4	4	no	—
428	D₈	—	2	1	no	—
429	D₈	—	2	2	no	—
430	D₈	—	2	2	no	—
431	D₈	—	4	4	no	—
432	D₈	—	4	1	no	—
433	D₈	—	4	1	no	—
434	D₈	C₂×D₄×C₂₃	1	2	yes	—
435	M₁₆	—	2	1	no	—
436	M₁₆	—	2	2	no	—
437	M₁₆	—	2	2	no	—
438	M₁₆	—	2	2	no	—
439	M₁₆	—	4	1	no	—
440	M₁₆	C₂×D₄×C₂₃	1	2	yes	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	2	no	—
443	C₂×C₈	—	2	2	no	—
444	C₂×C₈	—	4	1	no	—
445	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
446	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
447	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
448	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
449	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
450	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
451	C₁₆	—	2	2	no	—
452	C₁₆	—	2	2	no	—
453	C₂³	—	2	1	no	—
454	C₂³	—	4	1	no	—
455	C₂³	—	4	2	no	—
456	C₂³	—	8	1	no	—
457	C₂³	—	8	1	no	—
458	C₂³	—	16	2	no	—
459	C₂³	C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
460	Q₈	—	2	1	no	—
461	Q₈	—	2	4	no	—
462	Q₈	—	2	2	no	—
463	Q₈	—	4	8	no	—
464	Q₈	—	4	2	no	—
465	Q₈	—	4	1	no	—
466	Q₈	—	4	2	no	—
467	Q₈	—	4	2	no	—
468	Q₈	C₂×D₈×C₂₃	1	2	yes	—
469	D₄	—	2	2	no	—
470	D₄	—	2	2	no	—
471	D₄	—	2	1	no	—
472	D₄	—	2	2	no	—
473	D₄	—	4	8	no	—
474	D₄	—	4	2	no	—
475	D₄	—	4	2	no	—
476	D₄	—	4	2	no	—
477	D₄	—	4	1	no	—
478	D₄	—	4	2	no	—
479	D₄	—	8	1	no	—
480	D₄	—	8	1	no	—
481	D₄	C₂×D₈×C₂₃	1	2	yes	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	4	8	no	—
486	C₂×C₄	—	4	8	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
494	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
495	C₂×C₄	C₂×D₈×C₂₃	1	1	yes	characteristic
496	C₂×C₄	C₂×D₈×C₂₃	1	1	yes	characteristic
497	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
498	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
499	C₈	—	2	2	no	—
500	C₈	—	4	2	no	—
501	C₈	C₂₃×#120	1	1	yes	characteristic
502	C₈	C₂₃×#120	1	1	yes	characteristic
503	C₈	C₂²×D₄×C₂₃	1	1	yes	characteristic
504	C₈	C₂²×D₄×C₂₃	1	1	yes	characteristic
505	C₂²	—	2	2	no	—
506	C₂²	—	2	2	no	—
507	C₂²	—	4	2	no	—
508	C₂²	—	4	2	no	—
509	C₂²	—	8	2	no	—
510	C₂²	—	8	2	no	—
511	C₂²	—	16	2	no	—
512	C₂²	—	16	2	no	—
513	C₂²	—	16	2	no	—
514	C₂²	C₂₃×#447	1	1	yes	characteristic
515	C₂²	C₂₃×#447	1	1	yes	characteristic
516	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
517	C₄	—	2	2	no	—
518	C₄	—	4	4	no	—
519	C₄	—	4	2	no	—
520	C₄	C₂₃×#447	1	1	yes	characteristic
521	C₄	C₂₃×#447	1	1	yes	characteristic
522	C₄	C₂×C₂₃×#120	1	1	yes	characteristic
523	C₄	C₂²×D₈×C₂₃	1	1	yes	characteristic
524	C₂	—	2	1	no	—
525	C₂	—	2	1	no	—
526	C₂	—	4	2	no	—
527	C₂	—	8	2	no	—
528	C₂	—	16	2	no	—
529	C₂	C₂₃×#2193	1	2	yes	direct product factor
530	C₂	C₂×C₂₃×#447	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	#447
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₂₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂²×C₄×C₂₃ ◁ C₂×C₂₃×#131 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#578	C₂	semidirect
2. C₂×C₂₃×#509	C₂	semidirect
3. C₂²×C₂₃×SD₃₂	C₂	semidirect
4. C₂×C₂₃×#472	C₂	semidirect
5. C₂₃×#2193	C₂	direct (N × H)
6. C₂×C₂₃×#362	C₂	semidirect
7. C₂×C₂₃×#359	C₂	semidirect
8. C₂×C₂₃×#350	C₂	semidirect
13. C₂₃×#578	C₂²	semidirect
24. C₂₃×#509	C₂²	semidirect
28. C₂×C₂₃×SD₃₂	C₂²	semidirect
33. C₂₃×#472	C₂²	semidirect
36. C₂₃×#362	C₂²	semidirect
37. C₂₃×#359	C₂²	semidirect
38. C₂₃×#350	C₂²	semidirect
187. C₂×#2193	C₂₃	direct (N × H)
240. C₂×#578	C₂×C₂₃	semidirect
241. C₂×#509	C₂×C₂₃	semidirect
242. C₂²×SD₃₂	C₂×C₂₃	semidirect
243. C₂×#472	C₂×C₂₃	semidirect
244. #2193	C₂×C₂₃	direct (N × H)
245. C₂×#362	C₂×C₂₃	semidirect
246. C₂×#359	C₂×C₂₃	semidirect
247. C₂×#350	C₂×C₂₃	semidirect
271. #578	C₂²×C₂₃	semidirect
282. #509	C₂²×C₂₃	semidirect
286. C₂×SD₃₂	C₂²×C₂₃	semidirect
291. #472	C₂²×C₂₃	semidirect
294. #362	C₂²×C₂₃	semidirect
295. #359	C₂²×C₂₃	semidirect
296. #350	C₂²×C₂₃	semidirect
302. C₂×C₂₃	#2193	direct (N × H)
371. C₂₃	C₂×#2193	direct (N × H)
529. C₂	C₂₃×#2193	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×#578	2
C₂×C₂₃×#509	2
C₂²×C₂₃×SD₃₂	2
C₂×C₂₃×#472	2
C₂₃×#2193	2
C₂×C₂₃×#362	2
C₂×C₂₃×#359	2
C₂×C₂₃×#350	2
C₂×#2193	23

Subgroups — C2×C23×#2193 #19181162

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#2193 #19181162