Subgroups — C₂×C₃×#65136 #14429932

Order 1920.

896 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×D₂₀	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#4016	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#3953	C₂	1	1	yes	maximal, characteristic
5	C₂×C₃×#3953	C₂	1	1	yes	maximal, characteristic
6	C₂×C₃×#3950	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#3949	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65136	C₂	1	8	yes	maximal, direct product factor
9	C₂×#65136	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₄×D₅	—	2	1	no	—
12	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₂×C₃×#685	—	2	1	no	—
16	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
19	C₂×C₃×#683	—	2	1	no	—
20	C₂×C₃×#683	—	2	1	no	—
21	C₃×C₄×D₂₀	—	2	2	no	—
22	C₃×C₄×D₂₀	C₂²	1	4	yes	—
23	C₃×#4016	—	2	2	no	—
24	C₃×#4016	C₂²	1	4	yes	complemented
25	C₃×C₅×C₄⋊C₈	C₂²	1	4	yes	complemented
26	C₃×#3953	C₂²	1	4	yes	—
27	C₃×#3953	C₂²	1	4	yes	—
28	C₃×#3950	C₂²	1	4	yes	complemented
29	C₃×#3949	C₂²	1	4	yes	complemented
30	C₂×C₃×#478	—	5	1	no	maximal, Hall
31	C₂×C₄×D₂₀	C₂×C₃	1	1	yes	characteristic
32	C₂×#4016	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂×C₅×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂×#3953	C₂×C₃	1	1	yes	characteristic
35	C₂×#3953	C₂×C₃	1	1	yes	characteristic
36	C₂×#3950	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂×#3949	C₂×C₃	1	1	yes	characteristic, complemented
38	#65136	C₂×C₃	1	8	yes	direct product factor
39	C₂³×C₃×D₅	—	2	1	no	—
40	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
43	C₂²×C₃×Dic₅	—	2	1	no	—
44	C₂²×C₃×Dic₅	—	2	1	no	—
45	C₂²×C₃×Dic₅	—	2	1	no	—
46	C₂×C₃×D₂₀	—	2	1	no	—
47	C₂×C₃×D₂₀	—	2	2	no	—
48	C₂×C₃×D₂₀	Q₈	1	4	yes	—
49	C₂×C₃×D₂₀	C₂³	1	2	yes	—
50	C₂×C₃×C₄×D₅	—	2	4	no	—
51	C₂×C₃×C₄×D₅	—	4	4	no	—
52	C₂×C₃×C₅×C₈	—	2	2	no	—
53	C₂×C₃×C₅×C₈	—	2	2	no	—
54	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
55	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
56	C₃×C₄²×C₅	D₄	1	2	yes	—
57	C₃×C₄²×C₅	C₂³	1	2	yes	—
58	C₃×#685	—	2	4	no	—
59	C₃×C₄⋊Dic₅	—	2	1	no	—
60	C₃×C₄⋊Dic₅	—	2	1	no	—
61	C₃×C₄⋊Dic₅	—	2	1	no	—
62	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
63	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
64	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
65	C₃×#683	—	2	4	no	—
66	C₃×#683	—	2	4	no	—
67	C₂×C₃×#125	—	5	1	no	—
68	C₂×C₃×C₄×D₄	—	5	1	no	—
69	C₃×#478	—	5	8	no	—
70	C₂×C₃×#107	—	5	1	no	—
71	C₂×C₃×#106	—	5	1	no	—
72	C₂×C₃×C₄⋊C₈	D₅	1	1	yes	characteristic, complemented
73	C₂×C₃×#102	—	5	1	no	—
74	C₂×C₃×#102	—	5	1	no	—
75	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
76	C₂²×C₄×D₅	—	2	1	no	—
77	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
78	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
79	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
80	C₂×#685	—	2	1	no	—
81	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
84	C₂×#683	—	2	1	no	—
85	C₂×#683	—	2	1	no	—
86	C₄×D₂₀	—	2	2	no	—
87	C₄×D₂₀	C₂²×C₃	1	4	yes	—
88	#4016	—	2	2	no	—
89	#4016	C₂²×C₃	1	4	yes	complemented
90	C₅×C₄⋊C₈	C₂²×C₃	1	4	yes	complemented
91	#3953	C₂²×C₃	1	4	yes	—
92	#3953	C₂²×C₃	1	4	yes	—
93	#3950	C₂²×C₃	1	4	yes	complemented
94	#3949	C₂²×C₃	1	4	yes	complemented
95	C₂×#478	—	5	1	no	Sylow
96	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₃×D₅	—	2	4	no	—
98	C₂²×C₃×D₅	—	2	2	no	—
99	C₂²×C₃×D₅	—	4	2	no	—
100	C₂²×C₃×D₅	—	4	2	no	—
101	C₂×C₃×C₄×C₅	—	2	2	no	—
102	C₂×C₃×C₄×C₅	—	2	2	no	—
103	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
104	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
105	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
107	C₂×C₃×C₄×C₅	#41	1	2	yes	—
108	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
109	C₂×C₃×Dic₅	—	2	2	no	—
110	C₂×C₃×Dic₅	—	2	2	no	—
111	C₂×C₃×Dic₅	—	2	2	no	—
112	C₂×C₃×Dic₅	—	4	2	no	—
113	C₂×C₃×Dic₅	—	4	2	no	—
114	C₂×C₃×Dic₅	—	4	2	no	—
115	C₃×D₂₀	—	2	4	no	—
116	C₃×D₂₀	—	2	2	no	—
117	C₃×D₂₀	C₂×Q₈	1	4	yes	—
118	C₃×C₄×D₅	—	4	8	no	—
119	C₃×C₅×C₈	—	2	2	no	—
120	C₃×C₅×C₈	—	2	2	no	—
121	C₂²×C₃×D₄	—	5	1	no	—
122	C₂³×C₃×C₄	—	10	1	no	—
123	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
124	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
125	C₃×#125	—	5	4	no	—
126	C₃×#125	—	10	2	no	—
127	C₃×C₄×D₄	—	5	4	no	—
128	C₃×C₄×D₄	—	10	2	no	—
129	C₂×C₃×C₄⋊C₄	—	5	1	no	—
130	C₂×C₃×C₄⋊C₄	—	5	1	no	—
131	C₂×C₃×C₄⋊C₄	—	5	1	no	—
132	C₂×C₃×C₄⋊C₄	—	10	1	no	—
133	C₂×C₃×C₄⋊C₄	—	10	1	no	—
134	C₂×C₃×C₂²⋊C₄	—	10	1	no	—
135	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
136	C₃×#107	—	5	4	no	—
137	C₃×#106	—	5	4	no	—
138	C₃×C₄⋊C₈	C₂×D₅	1	4	yes	complemented
139	C₃×#102	—	5	4	no	—
140	C₃×#102	—	5	4	no	—
141	C₂³×D₅	—	2	1	no	—
142	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
145	C₂²×Dic₅	—	2	1	no	—
146	C₂²×Dic₅	—	2	1	no	—
147	C₂²×Dic₅	—	2	1	no	—
148	C₂×D₂₀	—	2	1	no	—
149	C₂×D₂₀	—	2	2	no	—
150	C₂×D₂₀	C₃×Q₈	1	4	yes	—
151	C₂×D₂₀	C₂³×C₃	1	2	yes	—
152	C₂×C₄×D₅	—	2	4	no	—
153	C₂×C₄×D₅	—	4	4	no	—
154	C₂×C₅×C₈	—	2	2	no	—
155	C₂×C₅×C₈	—	2	2	no	—
156	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
157	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
158	C₄²×C₅	C₃×D₄	1	2	yes	—
159	C₄²×C₅	C₂³×C₃	1	2	yes	—
160	#685	—	2	4	no	—
161	C₄⋊Dic₅	—	2	1	no	—
162	C₄⋊Dic₅	—	2	1	no	—
163	C₄⋊Dic₅	—	2	1	no	—
164	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
165	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
166	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
167	#683	—	2	4	no	—
168	#683	—	2	4	no	—
169	C₂×#125	—	5	1	no	—
170	C₂×C₄×D₄	—	5	1	no	—
171	#478	—	5	8	no	—
172	C₂×#107	—	5	1	no	—
173	C₂×#106	—	5	1	no	—
174	C₂×C₄⋊C₈	C₃×D₅	1	1	yes	characteristic, complemented
175	C₂×#102	—	5	1	no	—
176	C₂×#102	—	5	1	no	—
177	C₂²×C₃×C₅	C₂²⋊Q₈	1	2	yes	—
178	C₂²×C₃×C₅	#135	1	2	yes	—
179	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
180	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₃×D₅	—	2	4	no	—
182	C₂×C₃×D₅	—	4	2	no	—
183	C₂×C₃×D₅	—	4	2	no	—
184	C₂×C₃×D₅	—	4	8	no	—
185	C₃×C₄×C₅	—	2	2	no	—
186	C₃×C₄×C₅	—	2	2	no	—
187	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
188	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
189	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
190	C₃×Dic₅	—	4	2	no	—
191	C₃×Dic₅	—	4	2	no	—
192	C₃×Dic₅	—	4	2	no	—
193	C₂⁴×C₃	—	10	1	no	—
194	C₂×C₃×D₄	—	5	4	no	—
195	C₂×C₃×D₄	—	5	2	no	—
196	C₂×C₃×D₄	—	10	1	no	—
197	C₂×C₃×D₄	—	10	2	no	—
198	C₂²×C₃×C₄	—	10	1	no	—
199	C₂²×C₃×C₄	—	10	1	no	—
200	C₂²×C₃×C₄	—	10	1	no	—
201	C₂²×C₃×C₄	—	10	4	no	—
202	C₂²×C₃×C₄	—	20	4	no	—
203	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
204	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
205	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
206	C₂×C₃×C₈	—	2	2	no	—
207	C₂×C₃×C₈	—	2	2	no	—
208	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
209	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
210	C₃×C₄⋊C₄	—	5	2	no	—
211	C₃×C₄⋊C₄	—	5	2	no	—
212	C₃×C₄⋊C₄	—	5	2	no	—
213	C₃×C₄⋊C₄	—	10	4	no	—
214	C₃×C₄⋊C₄	—	10	4	no	—
215	C₃×C₄⋊C₄	—	10	1	no	—
216	C₃×C₄⋊C₄	—	10	1	no	—
217	C₃×C₄⋊C₄	—	10	1	no	—
218	C₃×C₂²⋊C₄	—	10	4	no	—
219	C₃×C₄²	D₂₀	1	2	yes	—
220	C₃×C₄²	C₂²×D₅	1	2	yes	—
221	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
222	C₂²×D₅	—	2	4	no	—
223	C₂²×D₅	—	2	2	no	—
224	C₂²×D₅	—	4	2	no	—
225	C₂²×D₅	—	4	2	no	—
226	C₂×C₄×C₅	—	2	2	no	—
227	C₂×C₄×C₅	—	2	2	no	—
228	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
229	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
230	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
231	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
232	C₂×C₄×C₅	C₃×#41	1	2	yes	—
233	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
234	C₂×Dic₅	—	2	2	no	—
235	C₂×Dic₅	—	2	2	no	—
236	C₂×Dic₅	—	2	2	no	—
237	C₂×Dic₅	—	4	2	no	—
238	C₂×Dic₅	—	4	2	no	—
239	C₂×Dic₅	—	4	2	no	—
240	D₂₀	—	2	4	no	—
241	D₂₀	—	2	2	no	—
242	D₂₀	C₂×C₃×Q₈	1	4	yes	—
243	C₄×D₅	—	4	8	no	—
244	C₅×C₈	—	2	2	no	—
245	C₅×C₈	—	2	2	no	—
246	C₂²×D₄	—	5	1	no	—
247	C₂³×C₄	—	10	1	no	—
248	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
249	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
250	#125	—	5	4	no	—
251	#125	—	10	2	no	—
252	C₄×D₄	—	5	4	no	—
253	C₄×D₄	—	10	2	no	—
254	C₂×C₄⋊C₄	—	5	1	no	—
255	C₂×C₄⋊C₄	—	5	1	no	—
256	C₂×C₄⋊C₄	—	5	1	no	—
257	C₂×C₄⋊C₄	—	10	1	no	—
258	C₂×C₄⋊C₄	—	10	1	no	—
259	C₂×C₂²⋊C₄	—	10	1	no	—
260	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
261	#107	—	5	4	no	—
262	#106	—	5	4	no	—
263	C₄⋊C₈	C₂×C₃×D₅	1	4	yes	complemented
264	#102	—	5	4	no	—
265	#102	—	5	4	no	—
266	C₂×C₃×C₅	#478	1	4	yes	complemented
267	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
268	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
269	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
270	C₃×D₅	—	4	4	no	—
271	C₂³×C₃	—	10	2	no	—
272	C₂³×C₃	—	10	4	no	—
273	C₂³×C₃	—	20	2	no	—
274	C₂³×C₃	—	20	2	no	—
275	C₂³×C₃	C₂×D₂₀	1	1	yes	characteristic
276	C₃×D₄	—	5	4	no	—
277	C₃×D₄	—	10	2	no	—
278	C₃×D₄	—	10	4	no	—
279	C₂×C₃×C₄	—	2	2	no	—
280	C₂×C₃×C₄	—	2	2	no	—
281	C₂×C₃×C₄	—	10	2	no	—
282	C₂×C₃×C₄	—	10	2	no	—
283	C₂×C₃×C₄	—	10	2	no	—
284	C₂×C₃×C₄	—	20	8	no	—
285	C₂×C₃×C₄	—	20	2	no	—
286	C₂×C₃×C₄	—	20	2	no	—
287	C₂×C₃×C₄	—	20	2	no	—
288	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
289	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
290	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
291	C₂×C₃×C₄	#711	1	2	yes	—
292	C₂×C₃×C₄	Q₈×D₅	1	2	yes	—
293	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
294	C₃×C₈	—	2	2	no	—
295	C₃×C₈	—	2	2	no	—
296	C₂²×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
297	C₂²×C₅	C₃×#135	1	2	yes	—
298	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
299	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
300	C₂×D₅	—	2	4	no	—
301	C₂×D₅	—	4	2	no	—
302	C₂×D₅	—	4	2	no	—
303	C₂×D₅	—	4	8	no	—
304	C₄×C₅	—	2	2	no	—
305	C₄×C₅	—	2	2	no	—
306	C₄×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
307	C₄×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
308	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
309	Dic₅	—	4	2	no	—
310	Dic₅	—	4	2	no	—
311	Dic₅	—	4	2	no	—
312	C₂⁴	—	10	1	no	—
313	C₂×D₄	—	5	4	no	—
314	C₂×D₄	—	5	2	no	—
315	C₂×D₄	—	10	1	no	—
316	C₂×D₄	—	10	2	no	—
317	C₂²×C₄	—	10	1	no	—
318	C₂²×C₄	—	10	1	no	—
319	C₂²×C₄	—	10	1	no	—
320	C₂²×C₄	—	10	4	no	—
321	C₂²×C₄	—	20	4	no	—
322	C₂²×C₄	C₃×D₂₀	1	1	yes	characteristic
323	C₂²×C₄	C₃×D₂₀	1	1	yes	characteristic
324	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
328	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
329	C₄⋊C₄	—	5	2	no	—
330	C₄⋊C₄	—	5	2	no	—
331	C₄⋊C₄	—	5	2	no	—
332	C₄⋊C₄	—	10	1	no	—
333	C₄⋊C₄	—	10	1	no	—
334	C₄⋊C₄	—	10	1	no	—
335	C₄⋊C₄	—	10	4	no	—
336	C₄⋊C₄	—	10	4	no	—
337	C₂²⋊C₄	—	10	4	no	—
338	C₄²	C₃×D₂₀	1	2	yes	—
339	C₄²	C₂²×C₃×D₅	1	2	yes	—
340	C₃×C₅	C₂×#478	1	1	yes	characteristic, complemented, Hall
341	C₂²×C₃	—	10	4	no	—
342	C₂²×C₃	—	20	2	no	—
343	C₂²×C₃	—	20	2	no	—
344	C₂²×C₃	—	20	8	no	—
345	C₂²×C₃	#4043	1	2	yes	—
346	C₂²×C₃	#4050	1	2	yes	—
347	C₂²×C₃	#4054	1	2	yes	—
348	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
349	C₃×C₄	—	2	2	no	—
350	C₃×C₄	—	2	2	no	—
351	C₃×C₄	—	20	2	no	—
352	C₃×C₄	—	20	2	no	—
353	C₃×C₄	—	20	2	no	—
354	C₃×C₄	#4043	1	2	yes	—
355	C₃×C₄	C₂×#711	1	1	yes	characteristic
356	C₃×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
357	C₂×C₅	C₃×#478	1	4	yes	complemented
358	C₂×C₅	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
359	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
360	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
361	D₅	—	4	4	no	—
362	C₂³	—	10	2	no	—
363	C₂³	—	10	4	no	—
364	C₂³	—	20	2	no	—
365	C₂³	—	20	2	no	—
366	C₂³	C₂×C₃×D₂₀	1	1	yes	characteristic
367	D₄	—	5	4	no	—
368	D₄	—	10	2	no	—
369	D₄	—	10	4	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	10	2	no	—
373	C₂×C₄	—	10	2	no	—
374	C₂×C₄	—	10	2	no	—
375	C₂×C₄	—	20	8	no	—
376	C₂×C₄	—	20	2	no	—
377	C₂×C₄	—	20	2	no	—
378	C₂×C₄	—	20	2	no	—
379	C₂×C₄	C₂×C₃×D₂₀	1	2	yes	—
380	C₂×C₄	C₂×C₃×D₂₀	1	2	yes	—
381	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
382	C₂×C₄	C₃×#711	1	2	yes	—
383	C₂×C₄	C₃×Q₈×D₅	1	2	yes	—
384	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
385	C₈	—	2	2	no	—
386	C₈	—	2	2	no	—
387	C₂×C₃	—	20	4	no	—
388	C₂×C₃	#65136	1	4	yes	direct product factor
389	C₂×C₃	C₂×#4043	1	1	yes	characteristic
390	C₂×C₃	C₂×#4050	1	1	yes	characteristic
391	C₂×C₃	C₂×#4054	1	1	yes	characteristic
392	C₅	C₂×C₃×#478	1	1	yes	characteristic, complemented, Sylow
393	C₂²	—	10	4	no	—
394	C₂²	—	20	8	no	—
395	C₂²	—	20	2	no	—
396	C₂²	—	20	2	no	—
397	C₂²	C₃×#4043	1	2	yes	—
398	C₂²	C₃×#4050	1	2	yes	—
399	C₂²	C₃×#4054	1	2	yes	—
400	C₂²	C₂²×C₃×D₂₀	1	1	yes	characteristic
401	C₄	—	2	2	no	—
402	C₄	—	2	2	no	—
403	C₄	—	20	2	no	—
404	C₄	—	20	2	no	—
405	C₄	—	20	2	no	—
406	C₄	C₃×#4043	1	2	yes	—
407	C₄	C₂×C₃×#711	1	1	yes	characteristic
408	C₄	C₂×C₃×Q₈×D₅	1	1	yes	characteristic
409	C₃	C₂×#65136	1	1	yes	characteristic, direct product factor, Sylow
410	C₂	—	20	4	no	—
411	C₂	C₃×#65136	1	4	yes	direct product factor
412	C₂	C₂×C₃×#4043	1	1	yes	characteristic
413	C₂	C₂×C₃×#4050	1	1	yes	characteristic
414	C₂	C₂×C₃×#4054	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂×D₂₀
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×C₄⋊C₈	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₃×D₂₀	C₂²
hypercenter	C₂×C₃×C₄⋊C₈	D₅
hypocenter	C₅	C₂×C₃×#478
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×C₄² ◁ C₂×C₃×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#4016	C₂	semidirect
3. C₂×C₃×C₅×C₄⋊C₈	C₂	semidirect
6. C₂×C₃×#3950	C₂	semidirect
7. C₂×C₃×#3949	C₂	semidirect
8. C₃×#65136	C₂	direct (N × H)
9. C₂×#65136	C₃	direct (N × H)
24. C₃×#4016	C₂²	semidirect
25. C₃×C₅×C₄⋊C₈	C₂²	semidirect
28. C₃×#3950	C₂²	semidirect
29. C₃×#3949	C₂²	semidirect
32. C₂×#4016	C₂×C₃	semidirect
33. C₂×C₅×C₄⋊C₈	C₂×C₃	semidirect
36. C₂×#3950	C₂×C₃	semidirect
37. C₂×#3949	C₂×C₃	semidirect
38. #65136	C₂×C₃	direct (N × H)
72. C₂×C₃×C₄⋊C₈	D₅	semidirect
89. #4016	C₂²×C₃	semidirect
90. C₅×C₄⋊C₈	C₂²×C₃	semidirect
93. #3950	C₂²×C₃	semidirect
94. #3949	C₂²×C₃	semidirect
138. C₃×C₄⋊C₈	C₂×D₅	semidirect
174. C₂×C₄⋊C₈	C₃×D₅	semidirect
263. C₄⋊C₈	C₂×C₃×D₅	semidirect
266. C₂×C₃×C₅	#478	semidirect
340. C₃×C₅	C₂×#478	semidirect
357. C₂×C₅	C₃×#478	semidirect
388. C₂×C₃	#65136	direct (N × H)
392. C₅	C₂×C₃×#478	semidirect
409. C₃	C₂×#65136	direct (N × H)
411. C₂	C₃×#65136	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×C₄×D₂₀	2
C₂×C₃×#4016	2
C₂×C₃×C₅×C₄⋊C₈	2
C₂×C₃×#3953	2
C₂×C₃×#3950	2
C₂×C₃×#3949	2
C₃×#65136	2
C₂×#65136	3
C₂×C₃×#478	5

Subgroups — C2×C3×#65136 #14429932

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65136 #14429932