Subgroups — C₂×C₃×#65053 #14437909

Order 1920.

976 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4086	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#4036	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#102	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#3964	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#3953	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#3947	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#3941	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65053	C₂	1	8	yes	maximal, direct product factor
9	C₂×#65053	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₂²⋊D₅	—	2	1	no	—
12	C₂²×C₃×C₂²⋊D₅	—	2	1	no	—
13	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₃×#4086	—	2	2	no	—
17	C₃×#4086	C₂²	1	4	yes	—
18	C₂×C₃×C₄⋊Dic₅	—	2	1	no	—
19	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
20	C₂×C₃×#683	—	2	1	no	—
21	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
22	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
23	C₃×#4036	—	2	2	no	—
24	C₃×#4036	C₂²	1	4	yes	complemented
25	C₃×C₅×#102	C₂²	1	4	yes	complemented
26	C₃×#3964	C₂²	1	4	yes	complemented
27	C₃×#3953	C₂²	1	4	yes	complemented
28	C₃×#3947	C₂²	1	4	yes	complemented
29	C₃×#3941	C₂²	1	4	yes	complemented
30	C₂×C₃×#490	—	5	1	no	maximal, Hall
31	C₂×#4086	C₂×C₃	1	1	yes	characteristic
32	C₂×#4036	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂×C₅×#102	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂×#3964	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂×#3953	C₂×C₃	1	1	yes	characteristic, complemented
36	C₂×#3947	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂×#3941	C₂×C₃	1	1	yes	characteristic, complemented
38	#65053	C₂×C₃	1	8	yes	direct product factor
39	C₂⁴×C₃×C₅	—	2	1	no	—
40	C₂³×C₃×D₅	—	2	1	no	—
41	C₂×C₃×C₅×D₄	—	2	1	no	—
42	C₂×C₃×C₅×D₄	—	2	2	no	—
43	C₂×C₃×C₅×D₄	—	2	2	no	—
44	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
45	C₂²×C₃×C₄×C₅	—	2	1	no	—
46	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
48	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
49	C₂×C₃×C₂²⋊D₅	—	4	4	no	—
50	C₂×C₃×C₂²⋊D₅	—	4	4	no	—
51	C₂²×C₃×Dic₅	—	2	1	no	—
52	C₂²×C₃×Dic₅	D₄	1	1	yes	characteristic
53	C₂²×C₃×Dic₅	D₄	1	1	yes	characteristic
54	C₂×C₃×D₂₀	—	2	2	no	—
55	C₂×C₃×D₂₀	—	2	2	no	—
56	C₂×C₃×D₂₀	—	2	1	no	—
57	C₂×C₃×D₂₀	C₂³	1	2	yes	—
58	C₂×C₃×C₅×C₈	—	2	2	no	—
59	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
60	C₃×C₅×C₄⋊C₄	—	2	1	no	—
61	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
62	C₃×C₄⋊Dic₅	—	2	1	no	—
63	C₃×C₄⋊Dic₅	—	2	4	no	—
64	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
65	C₃×#683	—	2	4	no	—
66	C₃×C₄×Dic₅	D₄	1	2	yes	—
67	C₃×C₄×Dic₅	C₂³	1	2	yes	—
68	C₂×C₃×#168	—	2	2	no	—
69	C₂×C₃×#168	C₂³	1	2	yes	—
70	C₂×C₃×#127	—	5	1	no	—
71	C₂×C₃×#125	—	5	1	no	—
72	C₃×#490	—	5	8	no	—
73	C₂×C₃×#102	—	5	1	no	—
74	C₂×C₃×#102	—	5	1	no	—
75	C₂×C₃×#102	—	5	1	no	—
76	C₂×C₃×#102	D₅	1	1	yes	characteristic, complemented
77	C₂×C₃×#97	—	5	1	no	—
78	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
79	C₂²×C₂²⋊D₅	—	2	1	no	—
80	C₂²×C₂²⋊D₅	—	2	1	no	—
81	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
82	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
84	#4086	—	2	2	no	—
85	#4086	C₂²×C₃	1	4	yes	—
86	C₂×C₄⋊Dic₅	—	2	1	no	—
87	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
88	C₂×#683	—	2	1	no	—
89	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
90	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
91	#4036	—	2	2	no	—
92	#4036	C₂²×C₃	1	4	yes	complemented
93	C₅×#102	C₂²×C₃	1	4	yes	complemented
94	#3964	C₂²×C₃	1	4	yes	complemented
95	#3953	C₂²×C₃	1	4	yes	complemented
96	#3947	C₂²×C₃	1	4	yes	complemented
97	#3941	C₂²×C₃	1	4	yes	complemented
98	C₂×#490	—	5	1	no	Sylow
99	C₂³×C₃×C₅	—	2	2	no	—
100	C₂³×C₃×C₅	—	4	2	no	—
101	C₂³×C₃×C₅	—	4	2	no	—
102	C₂³×C₃×C₅	—	4	2	no	—
103	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₃×D₅	—	2	2	no	—
105	C₂²×C₃×D₅	—	4	2	no	—
106	C₂²×C₃×D₅	—	4	2	no	—
107	C₂²×C₃×D₅	—	4	2	no	—
108	C₃×C₅×D₄	—	2	2	no	—
109	C₃×C₅×D₄	—	2	2	no	—
110	C₃×C₅×D₄	—	4	2	no	—
111	C₂×C₃×C₄×C₅	—	2	2	no	—
112	C₂×C₃×C₄×C₅	—	4	2	no	—
113	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
114	C₂×C₃×C₄×C₅	#41	1	2	yes	—
115	C₂×C₃×C₄×C₅	#41	1	2	yes	—
116	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
117	C₃×C₂²⋊D₅	—	4	8	no	—
118	C₃×C₂²⋊D₅	—	4	8	no	—
119	C₂×C₃×Dic₅	—	2	2	no	—
120	C₂×C₃×Dic₅	—	2	2	no	—
121	C₂×C₃×Dic₅	—	2	2	no	—
122	C₂×C₃×Dic₅	—	4	2	no	—
123	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
124	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
125	C₃×D₂₀	—	2	2	no	—
126	C₃×D₂₀	—	2	2	no	—
127	C₃×D₂₀	—	4	2	no	—
128	C₃×C₅×C₈	—	2	2	no	—
129	C₃×#168	—	2	2	no	—
130	C₂²×C₃×D₄	—	5	1	no	—
131	C₂²×C₃×D₄	—	10	1	no	—
132	C₂²×C₃×D₄	—	10	1	no	—
133	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
134	C₂²×C₃×C₈	—	5	1	no	—
135	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
136	C₃×#127	—	5	4	no	—
137	C₃×#127	—	10	2	no	—
138	C₃×#125	—	5	4	no	—
139	C₃×#125	—	10	2	no	—
140	C₂×C₃×C₄⋊C₄	—	5	1	no	—
141	C₂×C₃×C₄⋊C₄	—	10	1	no	—
142	C₂×C₃×C₄⋊C₄	—	10	1	no	—
143	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
144	C₂×C₃×C₄²	—	5	1	no	—
145	C₃×#102	—	5	4	no	—
146	C₃×#102	—	5	4	no	—
147	C₃×#102	—	5	4	no	—
148	C₃×#102	C₂×D₅	1	4	yes	complemented
149	C₃×#97	—	5	4	no	—
150	C₂⁴×C₅	—	2	1	no	—
151	C₂³×D₅	—	2	1	no	—
152	C₂×C₅×D₄	—	2	1	no	—
153	C₂×C₅×D₄	—	2	2	no	—
154	C₂×C₅×D₄	—	2	2	no	—
155	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
156	C₂²×C₄×C₅	—	2	1	no	—
157	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
158	C₂×C₂²⋊D₅	—	2	4	no	—
159	C₂×C₂²⋊D₅	—	2	4	no	—
160	C₂×C₂²⋊D₅	—	4	4	no	—
161	C₂×C₂²⋊D₅	—	4	4	no	—
162	C₂²×Dic₅	—	2	1	no	—
163	C₂²×Dic₅	C₃×D₄	1	1	yes	characteristic
164	C₂²×Dic₅	C₃×D₄	1	1	yes	characteristic
165	C₂×D₂₀	—	2	2	no	—
166	C₂×D₂₀	—	2	2	no	—
167	C₂×D₂₀	—	2	1	no	—
168	C₂×D₂₀	C₂³×C₃	1	2	yes	—
169	C₂×C₅×C₈	—	2	2	no	—
170	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
171	C₅×C₄⋊C₄	—	2	1	no	—
172	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
173	C₄⋊Dic₅	—	2	1	no	—
174	C₄⋊Dic₅	—	2	4	no	—
175	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
176	#683	—	2	4	no	—
177	C₄×Dic₅	C₃×D₄	1	2	yes	—
178	C₄×Dic₅	C₂³×C₃	1	2	yes	—
179	C₂×#168	—	2	2	no	—
180	C₂×#168	C₂³×C₃	1	2	yes	—
181	C₂×#127	—	5	1	no	—
182	C₂×#125	—	5	1	no	—
183	#490	—	5	8	no	—
184	C₂×#102	—	5	1	no	—
185	C₂×#102	—	5	1	no	—
186	C₂×#102	—	5	1	no	—
187	C₂×#102	C₃×D₅	1	1	yes	characteristic, complemented
188	C₂×#97	—	5	1	no	—
189	C₂²×C₃×C₅	—	4	2	no	—
190	C₂²×C₃×C₅	—	4	2	no	—
191	C₂²×C₃×C₅	—	4	2	no	—
192	C₂²×C₃×C₅	—	8	4	no	—
193	C₂²×C₃×C₅	#124	1	2	yes	—
194	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
195	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
196	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₃×D₅	—	4	2	no	—
198	C₂×C₃×D₅	—	4	2	no	—
199	C₂×C₃×D₅	—	4	2	no	—
200	C₂×C₃×D₅	—	8	4	no	—
201	C₃×C₄×C₅	—	4	2	no	—
202	C₃×C₄×C₅	#124	1	2	yes	—
203	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
204	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
205	C₃×Dic₅	—	2	2	no	—
206	C₃×Dic₅	—	2	2	no	—
207	C₃×Dic₅	—	4	2	no	—
208	C₂⁴×C₃	—	2	1	no	—
209	C₂⁴×C₃	—	10	1	no	—
210	C₂×C₃×D₄	—	2	2	no	—
211	C₂×C₃×D₄	—	2	1	no	—
212	C₂×C₃×D₄	—	2	2	no	—
213	C₂×C₃×D₄	—	5	2	no	—
214	C₂×C₃×D₄	—	10	4	no	—
215	C₂×C₃×D₄	—	10	4	no	—
216	C₂×C₃×D₄	—	10	2	no	—
217	C₂×C₃×D₄	—	10	1	no	—
218	C₂×C₃×D₄	—	10	2	no	—
219	C₂×C₃×D₄	—	20	4	no	—
220	C₂×C₃×D₄	—	20	4	no	—
221	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
222	C₂²×C₃×C₄	—	2	1	no	—
223	C₂²×C₃×C₄	—	5	1	no	—
224	C₂²×C₃×C₄	—	5	1	no	—
225	C₂²×C₃×C₄	—	10	1	no	—
226	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
227	C₂×C₃×C₈	—	2	2	no	—
228	C₂×C₃×C₈	—	5	2	no	—
229	C₂×C₃×C₈	—	10	2	no	—
230	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
231	C₃×C₄⋊C₄	—	2	1	no	—
232	C₃×C₄⋊C₄	—	5	2	no	—
233	C₃×C₄⋊C₄	—	10	4	no	—
234	C₃×C₄⋊C₄	—	10	4	no	—
235	C₃×C₄⋊C₄	—	10	1	no	—
236	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
237	C₃×C₄²	—	5	2	no	—
238	C₃×C₄²	—	5	2	no	—
239	C₂³×C₅	—	2	2	no	—
240	C₂³×C₅	—	4	2	no	—
241	C₂³×C₅	—	4	2	no	—
242	C₂³×C₅	—	4	2	no	—
243	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
244	C₂²×D₅	—	2	2	no	—
245	C₂²×D₅	—	4	2	no	—
246	C₂²×D₅	—	4	2	no	—
247	C₂²×D₅	—	4	2	no	—
248	C₅×D₄	—	2	2	no	—
249	C₅×D₄	—	2	2	no	—
250	C₅×D₄	—	4	2	no	—
251	C₂×C₄×C₅	—	2	2	no	—
252	C₂×C₄×C₅	—	4	2	no	—
253	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
254	C₂×C₄×C₅	C₃×#41	1	2	yes	—
255	C₂×C₄×C₅	C₃×#41	1	2	yes	—
256	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
257	C₂²⋊D₅	—	4	8	no	—
258	C₂²⋊D₅	—	4	8	no	—
259	C₂×Dic₅	—	2	2	no	—
260	C₂×Dic₅	—	2	2	no	—
261	C₂×Dic₅	—	2	2	no	—
262	C₂×Dic₅	—	4	2	no	—
263	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
264	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
265	D₂₀	—	2	2	no	—
266	D₂₀	—	2	2	no	—
267	D₂₀	—	4	2	no	—
268	C₅×C₈	—	2	2	no	—
269	#168	—	2	2	no	—
270	C₂²×D₄	—	5	1	no	—
271	C₂²×D₄	—	10	1	no	—
272	C₂²×D₄	—	10	1	no	—
273	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
274	C₂²×C₈	—	5	1	no	—
275	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
276	#127	—	5	4	no	—
277	#127	—	10	2	no	—
278	#125	—	5	4	no	—
279	#125	—	10	2	no	—
280	C₂×C₄⋊C₄	—	5	1	no	—
281	C₂×C₄⋊C₄	—	10	1	no	—
282	C₂×C₄⋊C₄	—	10	1	no	—
283	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
284	C₂×C₄²	—	5	1	no	—
285	#102	—	5	4	no	—
286	#102	—	5	4	no	—
287	#102	—	5	4	no	—
288	#102	C₂×C₃×D₅	1	4	yes	complemented
289	#97	—	5	4	no	—
290	C₂×C₃×C₅	—	8	2	no	—
291	C₂×C₃×C₅	#490	1	4	yes	complemented
292	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
293	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
294	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
295	C₃×D₅	—	8	2	no	—
296	C₂³×C₃	—	2	2	no	—
297	C₂³×C₃	—	4	2	no	—
298	C₂³×C₃	—	4	2	no	—
299	C₂³×C₃	—	4	2	no	—
300	C₂³×C₃	—	10	2	no	—
301	C₂³×C₃	—	20	2	no	—
302	C₂³×C₃	—	20	2	no	—
303	C₂³×C₃	—	20	2	no	—
304	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
305	C₃×D₄	—	2	2	no	—
306	C₃×D₄	—	2	2	no	—
307	C₃×D₄	—	4	2	no	—
308	C₃×D₄	—	10	2	no	—
309	C₃×D₄	—	10	2	no	—
310	C₃×D₄	—	20	8	no	—
311	C₃×D₄	—	20	8	no	—
312	C₃×D₄	—	20	2	no	—
313	C₂×C₃×C₄	—	2	2	no	—
314	C₂×C₃×C₄	—	4	2	no	—
315	C₂×C₃×C₄	—	5	2	no	—
316	C₂×C₃×C₄	—	5	2	no	—
317	C₂×C₃×C₄	—	10	2	no	—
318	C₂×C₃×C₄	—	10	2	no	—
319	C₂×C₃×C₄	—	10	2	no	—
320	C₂×C₃×C₄	—	20	2	no	—
321	C₂×C₃×C₄	#709	1	2	yes	—
322	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
323	C₂×C₃×C₄	#711	1	2	yes	—
324	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
325	C₃×C₈	—	2	2	no	—
326	C₃×C₈	—	10	2	no	—
327	C₂²×C₅	—	4	2	no	—
328	C₂²×C₅	—	4	2	no	—
329	C₂²×C₅	—	4	2	no	—
330	C₂²×C₅	—	8	4	no	—
331	C₂²×C₅	C₃×#124	1	2	yes	—
332	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
333	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
334	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
335	C₂×D₅	—	4	2	no	—
336	C₂×D₅	—	4	2	no	—
337	C₂×D₅	—	4	2	no	—
338	C₂×D₅	—	8	4	no	—
339	C₄×C₅	—	4	2	no	—
340	C₄×C₅	C₃×#124	1	2	yes	—
341	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
342	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
343	Dic₅	—	2	2	no	—
344	Dic₅	—	2	2	no	—
345	Dic₅	—	4	2	no	—
346	C₂⁴	—	2	1	no	—
347	C₂⁴	—	10	1	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	5	2	no	—
352	C₂×D₄	—	10	4	no	—
353	C₂×D₄	—	10	4	no	—
354	C₂×D₄	—	10	2	no	—
355	C₂×D₄	—	10	1	no	—
356	C₂×D₄	—	10	2	no	—
357	C₂×D₄	—	20	4	no	—
358	C₂×D₄	—	20	4	no	—
359	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	5	1	no	—
362	C₂²×C₄	—	5	1	no	—
363	C₂²×C₄	—	10	1	no	—
364	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	5	2	no	—
367	C₂×C₈	—	10	2	no	—
368	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	5	2	no	—
371	C₄⋊C₄	—	10	4	no	—
372	C₄⋊C₄	—	10	4	no	—
373	C₄⋊C₄	—	10	1	no	—
374	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
375	C₄²	—	5	2	no	—
376	C₄²	—	5	2	no	—
377	C₃×C₅	C₂×#490	1	1	yes	characteristic, complemented, Hall
378	C₂²×C₃	—	4	2	no	—
379	C₂²×C₃	—	4	2	no	—
380	C₂²×C₃	—	4	2	no	—
381	C₂²×C₃	—	8	4	no	—
382	C₂²×C₃	—	20	2	no	—
383	C₂²×C₃	—	20	2	no	—
384	C₂²×C₃	—	20	2	no	—
385	C₂²×C₃	—	40	4	no	—
386	C₂²×C₃	#4031	1	2	yes	—
387	C₂²×C₃	#4057	1	2	yes	—
388	C₂²×C₃	#4060	1	2	yes	—
389	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
390	C₃×C₄	—	4	2	no	—
391	C₃×C₄	—	10	2	no	—
392	C₃×C₄	—	10	2	no	—
393	C₃×C₄	—	20	2	no	—
394	C₃×C₄	#4031	1	2	yes	—
395	C₃×C₄	C₂×#709	1	1	yes	characteristic
396	C₃×C₄	C₂×#711	1	1	yes	characteristic
397	C₂×C₅	—	8	2	no	—
398	C₂×C₅	C₃×#490	1	4	yes	complemented
399	C₂×C₅	C₂×C₃×#124	1	1	yes	characteristic
400	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
401	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
402	D₅	—	8	2	no	—
403	C₂³	—	2	2	no	—
404	C₂³	—	4	2	no	—
405	C₂³	—	4	2	no	—
406	C₂³	—	4	2	no	—
407	C₂³	—	10	2	no	—
408	C₂³	—	20	2	no	—
409	C₂³	—	20	2	no	—
410	C₂³	—	20	2	no	—
411	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
412	D₄	—	2	2	no	—
413	D₄	—	2	2	no	—
414	D₄	—	4	2	no	—
415	D₄	—	10	2	no	—
416	D₄	—	10	2	no	—
417	D₄	—	20	8	no	—
418	D₄	—	20	8	no	—
419	D₄	—	20	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	5	2	no	—
423	C₂×C₄	—	5	2	no	—
424	C₂×C₄	—	10	2	no	—
425	C₂×C₄	—	10	2	no	—
426	C₂×C₄	—	10	2	no	—
427	C₂×C₄	—	20	2	no	—
428	C₂×C₄	C₃×#709	1	2	yes	—
429	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
430	C₂×C₄	C₃×#711	1	2	yes	—
431	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
432	C₈	—	2	2	no	—
433	C₈	—	10	2	no	—
434	C₂×C₃	—	8	2	no	—
435	C₂×C₃	—	40	2	no	—
436	C₂×C₃	#65053	1	4	yes	direct product factor
437	C₂×C₃	C₂×#4031	1	1	yes	characteristic
438	C₂×C₃	C₂×#4057	1	1	yes	characteristic
439	C₂×C₃	C₂×#4060	1	1	yes	characteristic
440	C₅	C₂×C₃×#490	1	1	yes	characteristic, complemented, Sylow
441	C₂²	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	8	4	no	—
445	C₂²	—	20	2	no	—
446	C₂²	—	20	2	no	—
447	C₂²	—	20	2	no	—
448	C₂²	—	40	4	no	—
449	C₂²	C₃×#4031	1	2	yes	—
450	C₂²	C₃×#4057	1	2	yes	—
451	C₂²	C₃×#4060	1	2	yes	—
452	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
453	C₄	—	4	2	no	—
454	C₄	—	10	2	no	—
455	C₄	—	10	2	no	—
456	C₄	—	20	2	no	—
457	C₄	C₃×#4031	1	2	yes	—
458	C₄	C₂×C₃×#709	1	1	yes	characteristic
459	C₄	C₂×C₃×#711	1	1	yes	characteristic
460	C₃	C₂×#65053	1	1	yes	characteristic, direct product factor, Sylow
461	C₂	—	8	2	no	—
462	C₂	—	40	2	no	—
463	C₂	C₃×#65053	1	4	yes	direct product factor
464	C₂	C₂×C₃×#4031	1	1	yes	characteristic
465	C₂	C₂×C₃×#4057	1	1	yes	characteristic
466	C₂	C₂×C₃×#4060	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×#102	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂×C₃×#4086	C₂
hypercenter	C₂×C₃×#102	D₅
hypocenter	C₅	C₂×C₃×#490
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#102

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#4036	C₂	semidirect
3. C₂×C₃×C₅×#102	C₂	semidirect
4. C₂×C₃×#3964	C₂	semidirect
5. C₂×C₃×#3953	C₂	semidirect
6. C₂×C₃×#3947	C₂	semidirect
7. C₂×C₃×#3941	C₂	semidirect
8. C₃×#65053	C₂	direct (N × H)
9. C₂×#65053	C₃	direct (N × H)
24. C₃×#4036	C₂²	semidirect
25. C₃×C₅×#102	C₂²	semidirect
26. C₃×#3964	C₂²	semidirect
27. C₃×#3953	C₂²	semidirect
28. C₃×#3947	C₂²	semidirect
29. C₃×#3941	C₂²	semidirect
32. C₂×#4036	C₂×C₃	semidirect
33. C₂×C₅×#102	C₂×C₃	semidirect
34. C₂×#3964	C₂×C₃	semidirect
35. C₂×#3953	C₂×C₃	semidirect
36. C₂×#3947	C₂×C₃	semidirect
37. C₂×#3941	C₂×C₃	semidirect
38. #65053	C₂×C₃	direct (N × H)
76. C₂×C₃×#102	D₅	semidirect
92. #4036	C₂²×C₃	semidirect
93. C₅×#102	C₂²×C₃	semidirect
94. #3964	C₂²×C₃	semidirect
95. #3953	C₂²×C₃	semidirect
96. #3947	C₂²×C₃	semidirect
97. #3941	C₂²×C₃	semidirect
148. C₃×#102	C₂×D₅	semidirect
187. C₂×#102	C₃×D₅	semidirect
288. #102	C₂×C₃×D₅	semidirect
291. C₂×C₃×C₅	#490	semidirect
377. C₃×C₅	C₂×#490	semidirect
398. C₂×C₅	C₃×#490	semidirect
436. C₂×C₃	#65053	direct (N × H)
440. C₅	C₂×C₃×#490	semidirect
460. C₃	C₂×#65053	direct (N × H)
463. C₂	C₃×#65053	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×C₃×#4086	2
C₂×C₃×#4036	2
C₂×C₃×C₅×#102	2
C₂×C₃×#3964	2
C₂×C₃×#3953	2
C₂×C₃×#3947	2
C₂×C₃×#3941	2
C₃×#65053	2
C₂×#65053	3
C₂×C₃×#490	5

Subgroups — C2×C3×#65053 #14437909

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65053 #14437909