Subgroups — C₂×C₃×#65292 #14431522

Order 1920.

936 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4076	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₂²⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65292	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×#3941	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#3941	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#3940	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#3939	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#65292	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₂²⋊D₅	—	2	1	no	—
12	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
13	C₃×C₅×#117	—	2	2	no	—
14	C₃×C₅×#117	C₂²	1	4	yes	complemented
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
18	C₂×C₃×C₄²×C₅	—	2	1	no	—
19	C₃×#4076	—	2	2	no	—
20	C₃×#4076	C₂²	1	4	yes	—
21	C₂×C₃×#685	—	2	1	no	—
22	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
23	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
24	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
25	C₃×C₂²⋊#168	C₂²	1	4	yes	complemented
26	C₃×#3941	C₂²	1	4	yes	complemented
27	C₃×#3941	C₂²	1	4	yes	complemented
28	C₃×#3940	C₂²	1	4	yes	complemented
29	C₃×#3939	C₂²	1	4	yes	complemented
30	C₂×C₃×#482	—	5	1	no	maximal, Hall
31	C₂×C₅×#117	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂×#4076	C₂×C₃	1	1	yes	characteristic
33	C₂×C₂²⋊#168	C₂×C₃	1	1	yes	characteristic, complemented
34	#65292	C₂×C₃	1	8	yes	direct product factor
35	C₂×#3941	C₂×C₃	1	1	yes	characteristic, complemented
36	C₂×#3941	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂×#3940	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂×#3939	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
40	C₂³×C₃×D₅	—	2	1	no	—
41	C₂²×C₃×C₄×C₅	—	2	2	no	—
42	C₂²×C₃×C₄×C₅	—	2	2	no	—
43	C₂²×C₃×C₄×C₅	—	2	1	no	—
44	C₂²×C₃×C₄×C₅	—	2	1	no	—
45	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
46	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
47	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
48	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
49	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
50	C₂×C₃×C₂²⋊D₅	—	4	4	no	—
51	C₂²×C₃×Dic₅	—	2	1	no	—
52	C₂×C₃×D₂₀	—	2	2	no	—
53	C₂×C₃×D₂₀	—	2	2	no	—
54	C₂×C₃×D₂₀	—	2	1	no	—
55	C₂×C₃×D₂₀	C₂³	1	2	yes	—
56	C₃×C₅×C₄⋊C₄	—	2	1	no	—
57	C₃×C₅×C₄⋊C₄	—	2	1	no	—
58	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
59	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
60	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
61	C₃×C₄²×C₅	—	2	4	no	—
62	C₃×#685	—	2	4	no	—
63	C₃×C₄⋊Dic₅	—	2	1	no	—
64	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
65	C₂×C₃×#168	—	2	2	no	—
66	C₂×C₃×#168	—	2	2	no	—
67	C₂×C₃×#168	C₂³	1	2	yes	—
68	C₂×C₃×#168	C₂³	1	2	yes	—
69	C₂×C₃×#121	—	5	1	no	—
70	C₂×C₃×#117	D₅	1	1	yes	characteristic, complemented
71	C₃×#482	—	5	8	no	—
72	C₂×C₃×#107	—	5	1	no	—
73	C₂×C₃×#106	—	5	1	no	—
74	C₂×C₃×#102	—	5	1	no	—
75	C₂×C₃×#102	—	5	1	no	—
76	C₂×C₃×C₂²⋊C₈	—	5	1	no	—
77	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
78	C₂²×C₂²⋊D₅	—	2	1	no	—
79	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
80	C₅×#117	—	2	2	no	—
81	C₅×#117	C₂²×C₃	1	4	yes	complemented
82	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
85	C₂×C₄²×C₅	—	2	1	no	—
86	#4076	—	2	2	no	—
87	#4076	C₂²×C₃	1	4	yes	—
88	C₂×#685	—	2	1	no	—
89	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
90	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
91	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
92	C₂²⋊#168	C₂²×C₃	1	4	yes	complemented
93	#3941	C₂²×C₃	1	4	yes	complemented
94	#3941	C₂²×C₃	1	4	yes	complemented
95	#3940	C₂²×C₃	1	4	yes	complemented
96	#3939	C₂²×C₃	1	4	yes	complemented
97	C₂×#482	—	5	1	no	Sylow
98	C₂³×C₃×C₅	—	2	2	no	—
99	C₂³×C₃×C₅	—	2	2	no	—
100	C₂³×C₃×C₅	—	2	2	no	—
101	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
102	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₃×D₅	—	2	2	no	—
104	C₂²×C₃×D₅	—	4	2	no	—
105	C₂²×C₃×D₅	—	4	2	no	—
106	C₂²×C₃×D₅	—	4	2	no	—
107	C₂×C₃×C₄×C₅	—	2	2	no	—
108	C₂×C₃×C₄×C₅	—	2	4	no	—
109	C₂×C₃×C₄×C₅	—	2	2	no	—
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	—	2	2	no	—
112	C₂×C₃×C₄×C₅	—	2	2	no	—
113	C₂×C₃×C₄×C₅	—	4	2	no	—
114	C₂×C₃×C₄×C₅	—	4	2	no	—
115	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
116	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
117	C₂×C₃×C₄×C₅	#41	1	2	yes	—
118	C₂×C₃×C₄×C₅	#41	1	2	yes	—
119	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
120	C₃×C₂²⋊D₅	—	4	8	no	—
121	C₂×C₃×Dic₅	—	2	2	no	—
122	C₂×C₃×Dic₅	—	4	2	no	—
123	C₃×D₂₀	—	2	2	no	—
124	C₃×D₂₀	—	2	2	no	—
125	C₃×D₂₀	—	4	2	no	—
126	C₃×#168	—	2	2	no	—
127	C₃×#168	—	2	2	no	—
128	C₂²×C₃×D₄	—	5	1	no	—
129	C₂²×C₃×D₄	—	10	1	no	—
130	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
131	C₂²×C₃×C₈	—	5	1	no	—
132	C₂²×C₃×C₈	—	5	1	no	—
133	C₃×#121	—	5	4	no	—
134	C₃×#121	—	10	2	no	—
135	C₃×#117	—	2	2	no	—
136	C₃×#117	C₂×D₅	1	4	yes	complemented
137	C₂×C₃×C₄⋊C₄	—	5	1	no	—
138	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
139	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
140	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
141	C₂×C₃×C₂²⋊C₄	—	10	1	no	—
142	C₂×C₃×C₄²	—	2	1	no	—
143	C₃×#107	—	5	4	no	—
144	C₃×#106	—	5	4	no	—
145	C₃×#102	—	5	4	no	—
146	C₃×#102	—	5	4	no	—
147	C₃×C₂²⋊C₈	—	5	4	no	—
148	C₂⁴×C₅	C₃×D₄	1	1	yes	characteristic
149	C₂³×D₅	—	2	1	no	—
150	C₂²×C₄×C₅	—	2	2	no	—
151	C₂²×C₄×C₅	—	2	2	no	—
152	C₂²×C₄×C₅	—	2	1	no	—
153	C₂²×C₄×C₅	—	2	1	no	—
154	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
156	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
157	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
158	C₂×C₂²⋊D₅	—	2	4	no	—
159	C₂×C₂²⋊D₅	—	4	4	no	—
160	C₂²×Dic₅	—	2	1	no	—
161	C₂×D₂₀	—	2	2	no	—
162	C₂×D₂₀	—	2	2	no	—
163	C₂×D₂₀	—	2	1	no	—
164	C₂×D₂₀	C₂³×C₃	1	2	yes	—
165	C₅×C₄⋊C₄	—	2	1	no	—
166	C₅×C₄⋊C₄	—	2	1	no	—
167	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
168	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
169	C₅×C₂²⋊C₄	—	2	4	no	—
170	C₄²×C₅	—	2	4	no	—
171	#685	—	2	4	no	—
172	C₄⋊Dic₅	—	2	1	no	—
173	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
174	C₂×#168	—	2	2	no	—
175	C₂×#168	—	2	2	no	—
176	C₂×#168	C₂³×C₃	1	2	yes	—
177	C₂×#168	C₂³×C₃	1	2	yes	—
178	C₂×#121	—	5	1	no	—
179	C₂×#117	C₃×D₅	1	1	yes	characteristic, complemented
180	#482	—	5	8	no	—
181	C₂×#107	—	5	1	no	—
182	C₂×#106	—	5	1	no	—
183	C₂×#102	—	5	1	no	—
184	C₂×#102	—	5	1	no	—
185	C₂×C₂²⋊C₈	—	5	1	no	—
186	C₂²×C₃×C₅	—	2	2	no	—
187	C₂²×C₃×C₅	—	2	2	no	—
188	C₂²×C₃×C₅	—	2	2	no	—
189	C₂²×C₃×C₅	—	4	4	no	—
190	C₂²×C₃×C₅	#123	1	2	yes	—
191	C₂²×C₃×C₅	#135	1	2	yes	—
192	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
193	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₃×D₅	—	4	2	no	—
195	C₂×C₃×D₅	—	4	2	no	—
196	C₂×C₃×D₅	—	4	2	no	—
197	C₂×C₃×D₅	—	8	4	no	—
198	C₃×C₄×C₅	—	2	2	no	—
199	C₃×C₄×C₅	—	4	2	no	—
200	C₃×C₄×C₅	—	4	2	no	—
201	C₃×C₄×C₅	#123	1	2	yes	—
202	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
203	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
204	C₃×Dic₅	—	4	2	no	—
205	C₂⁴×C₃	—	10	1	no	—
206	C₂⁴×C₃	C₂²⋊D₅	1	1	yes	characteristic
207	C₂×C₃×D₄	—	5	2	no	—
208	C₂×C₃×D₄	—	10	4	no	—
209	C₂×C₃×D₄	—	10	2	no	—
210	C₂×C₃×D₄	—	10	2	no	—
211	C₂×C₃×D₄	—	10	1	no	—
212	C₂×C₃×D₄	—	20	4	no	—
213	C₂²×C₃×C₄	—	2	2	no	—
214	C₂²×C₃×C₄	—	2	2	no	—
215	C₂²×C₃×C₄	—	2	1	no	—
216	C₂²×C₃×C₄	—	2	1	no	—
217	C₂²×C₃×C₄	—	10	1	no	—
218	C₂²×C₃×C₄	C₂²⋊D₅	1	2	yes	—
219	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
220	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
221	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
222	C₂×C₃×C₈	—	5	2	no	—
223	C₂×C₃×C₈	—	5	2	no	—
224	C₂×C₃×C₈	—	10	2	no	—
225	C₂×C₃×C₈	—	10	2	no	—
226	C₃×C₄⋊C₄	—	2	1	no	—
227	C₃×C₄⋊C₄	—	2	1	no	—
228	C₃×C₄⋊C₄	—	5	2	no	—
229	C₃×C₄⋊C₄	—	10	1	no	—
230	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
231	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
232	C₃×C₂²⋊C₄	—	2	4	no	—
233	C₃×C₂²⋊C₄	—	10	4	no	—
234	C₃×C₄²	—	2	4	no	—
235	C₂³×C₅	—	2	2	no	—
236	C₂³×C₅	—	2	2	no	—
237	C₂³×C₅	—	2	2	no	—
238	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
239	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
240	C₂²×D₅	—	2	2	no	—
241	C₂²×D₅	—	4	2	no	—
242	C₂²×D₅	—	4	2	no	—
243	C₂²×D₅	—	4	2	no	—
244	C₂×C₄×C₅	—	2	2	no	—
245	C₂×C₄×C₅	—	2	4	no	—
246	C₂×C₄×C₅	—	2	2	no	—
247	C₂×C₄×C₅	—	2	2	no	—
248	C₂×C₄×C₅	—	2	2	no	—
249	C₂×C₄×C₅	—	2	2	no	—
250	C₂×C₄×C₅	—	4	2	no	—
251	C₂×C₄×C₅	—	4	2	no	—
252	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
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	C₂×Dic₅	—	2	2	no	—
259	C₂×Dic₅	—	4	2	no	—
260	D₂₀	—	2	2	no	—
261	D₂₀	—	2	2	no	—
262	D₂₀	—	4	2	no	—
263	#168	—	2	2	no	—
264	#168	—	2	2	no	—
265	C₂²×D₄	—	5	1	no	—
266	C₂²×D₄	—	10	1	no	—
267	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
268	C₂²×C₈	—	5	1	no	—
269	C₂²×C₈	—	5	1	no	—
270	#121	—	5	4	no	—
271	#121	—	10	2	no	—
272	#117	—	2	2	no	—
273	#117	C₂×C₃×D₅	1	4	yes	complemented
274	C₂×C₄⋊C₄	—	5	1	no	—
275	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
276	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
277	C₂×C₂²⋊C₄	—	2	1	no	—
278	C₂×C₂²⋊C₄	—	10	1	no	—
279	C₂×C₄²	—	2	1	no	—
280	#107	—	5	4	no	—
281	#106	—	5	4	no	—
282	#102	—	5	4	no	—
283	#102	—	5	4	no	—
284	C₂²⋊C₈	—	5	4	no	—
285	C₂×C₃×C₅	—	4	2	no	—
286	C₂×C₃×C₅	#482	1	4	yes	complemented
287	C₂×C₃×C₅	C₂×#123	1	1	yes	characteristic
288	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
289	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
290	C₃×D₅	—	8	2	no	—
291	C₂³×C₃	—	2	2	no	—
292	C₂³×C₃	—	2	2	no	—
293	C₂³×C₃	—	2	2	no	—
294	C₂³×C₃	—	10	2	no	—
295	C₂³×C₃	—	20	2	no	—
296	C₂³×C₃	—	20	2	no	—
297	C₂³×C₃	—	20	2	no	—
298	C₂³×C₃	C₂×C₂²⋊D₅	1	2	yes	—
299	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
300	C₃×D₄	—	10	2	no	—
301	C₃×D₄	—	10	2	no	—
302	C₃×D₄	—	20	8	no	—
303	C₃×D₄	—	20	2	no	—
304	C₂×C₃×C₄	—	2	2	no	—
305	C₂×C₃×C₄	—	2	2	no	—
306	C₂×C₃×C₄	—	2	2	no	—
307	C₂×C₃×C₄	—	2	4	no	—
308	C₂×C₃×C₄	—	2	2	no	—
309	C₂×C₃×C₄	—	2	2	no	—
310	C₂×C₃×C₄	—	4	2	no	—
311	C₂×C₃×C₄	—	4	2	no	—
312	C₂×C₃×C₄	—	10	2	no	—
313	C₂×C₃×C₄	—	20	2	no	—
314	C₂×C₃×C₄	#709	1	2	yes	—
315	C₂×C₃×C₄	#709	1	2	yes	—
316	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
317	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
318	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
319	C₃×C₈	—	10	2	no	—
320	C₃×C₈	—	10	2	no	—
321	C₂²×C₅	—	2	2	no	—
322	C₂²×C₅	—	2	2	no	—
323	C₂²×C₅	—	2	2	no	—
324	C₂²×C₅	—	4	4	no	—
325	C₂²×C₅	C₃×#123	1	2	yes	—
326	C₂²×C₅	C₃×#135	1	2	yes	—
327	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
328	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
329	C₂×D₅	—	4	2	no	—
330	C₂×D₅	—	4	2	no	—
331	C₂×D₅	—	4	2	no	—
332	C₂×D₅	—	8	4	no	—
333	C₄×C₅	—	2	2	no	—
334	C₄×C₅	—	4	2	no	—
335	C₄×C₅	—	4	2	no	—
336	C₄×C₅	C₃×#123	1	2	yes	—
337	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
338	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
339	Dic₅	—	4	2	no	—
340	C₂⁴	—	10	1	no	—
341	C₂⁴	C₃×C₂²⋊D₅	1	1	yes	characteristic
342	C₂×D₄	—	5	2	no	—
343	C₂×D₄	—	10	4	no	—
344	C₂×D₄	—	10	2	no	—
345	C₂×D₄	—	10	2	no	—
346	C₂×D₄	—	10	1	no	—
347	C₂×D₄	—	20	4	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	10	1	no	—
353	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
354	C₂²×C₄	C₃×C₂²⋊D₅	1	2	yes	—
355	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
356	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
357	C₂×C₈	—	5	2	no	—
358	C₂×C₈	—	5	2	no	—
359	C₂×C₈	—	10	2	no	—
360	C₂×C₈	—	10	2	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	5	2	no	—
364	C₄⋊C₄	—	10	1	no	—
365	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
366	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
367	C₂²⋊C₄	—	2	4	no	—
368	C₂²⋊C₄	—	10	4	no	—
369	C₄²	—	2	4	no	—
370	C₃×C₅	C₂×#482	1	1	yes	characteristic, complemented, Hall
371	C₂²×C₃	—	2	2	no	—
372	C₂²×C₃	—	2	2	no	—
373	C₂²×C₃	—	2	2	no	—
374	C₂²×C₃	—	4	4	no	—
375	C₂²×C₃	—	20	2	no	—
376	C₂²×C₃	—	20	2	no	—
377	C₂²×C₃	—	20	2	no	—
378	C₂²×C₃	—	40	4	no	—
379	C₂²×C₃	#4075	1	2	yes	—
380	C₂²×C₃	#4095	1	2	yes	—
381	C₂²×C₃	#4096	1	2	yes	—
382	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
383	C₃×C₄	—	2	2	no	—
384	C₃×C₄	—	4	2	no	—
385	C₃×C₄	—	4	2	no	—
386	C₃×C₄	—	20	2	no	—
387	C₃×C₄	#4075	1	2	yes	—
388	C₃×C₄	C₂×#709	1	1	yes	characteristic
389	C₃×C₄	C₂×#709	1	1	yes	characteristic
390	C₂×C₅	—	4	2	no	—
391	C₂×C₅	C₃×#482	1	4	yes	complemented
392	C₂×C₅	C₂×C₃×#123	1	1	yes	characteristic
393	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
394	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
395	D₅	—	8	2	no	—
396	C₂³	—	2	2	no	—
397	C₂³	—	2	2	no	—
398	C₂³	—	2	2	no	—
399	C₂³	—	10	2	no	—
400	C₂³	—	20	2	no	—
401	C₂³	—	20	2	no	—
402	C₂³	—	20	2	no	—
403	C₂³	C₂×C₃×C₂²⋊D₅	1	2	yes	—
404	C₂³	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
405	D₄	—	10	2	no	—
406	D₄	—	10	2	no	—
407	D₄	—	20	8	no	—
408	D₄	—	20	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	10	2	no	—
418	C₂×C₄	—	20	2	no	—
419	C₂×C₄	C₃×#709	1	2	yes	—
420	C₂×C₄	C₃×#709	1	2	yes	—
421	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
422	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
423	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
424	C₈	—	10	2	no	—
425	C₈	—	10	2	no	—
426	C₂×C₃	—	4	2	no	—
427	C₂×C₃	—	40	2	no	—
428	C₂×C₃	#65292	1	4	yes	direct product factor
429	C₂×C₃	C₂×#4075	1	1	yes	characteristic
430	C₂×C₃	C₂×#4095	1	1	yes	characteristic
431	C₂×C₃	C₂×#4096	1	1	yes	characteristic
432	C₅	C₂×C₃×#482	1	1	yes	characteristic, complemented, Sylow
433	C₂²	—	2	2	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	4	4	no	—
437	C₂²	—	20	2	no	—
438	C₂²	—	20	2	no	—
439	C₂²	—	20	2	no	—
440	C₂²	—	40	4	no	—
441	C₂²	C₃×#4075	1	2	yes	—
442	C₂²	C₃×#4095	1	2	yes	—
443	C₂²	C₃×#4096	1	2	yes	—
444	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
445	C₄	—	2	2	no	—
446	C₄	—	4	2	no	—
447	C₄	—	4	2	no	—
448	C₄	—	20	2	no	—
449	C₄	C₃×#4075	1	2	yes	—
450	C₄	C₂×C₃×#709	1	1	yes	characteristic
451	C₄	C₂×C₃×#709	1	1	yes	characteristic
452	C₃	C₂×#65292	1	1	yes	characteristic, direct product factor, Sylow
453	C₂	—	4	2	no	—
454	C₂	—	40	2	no	—
455	C₂	C₃×#65292	1	4	yes	direct product factor
456	C₂	C₂×C₃×#4075	1	1	yes	characteristic
457	C₂	C₂×C₃×#4095	1	1	yes	characteristic
458	C₂	C₂×C₃×#4096	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂×C₂²⋊D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×#117	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂×C₃×#4076	C₂
hypercenter	C₂×C₃×#117	D₅
hypocenter	C₅	C₂×C₃×#482
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂³×C₃×C₄ ◁ C₂×C₃×#117

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#117	C₂	semidirect
3. C₂×C₃×C₂²⋊#168	C₂	semidirect
4. C₃×#65292	C₂	direct (N × H)
5. C₂×C₃×#3941	C₂	semidirect
6. C₂×C₃×#3941	C₂	semidirect
7. C₂×C₃×#3940	C₂	semidirect
8. C₂×C₃×#3939	C₂	semidirect
9. C₂×#65292	C₃	direct (N × H)
14. C₃×C₅×#117	C₂²	semidirect
25. C₃×C₂²⋊#168	C₂²	semidirect
26. C₃×#3941	C₂²	semidirect
27. C₃×#3941	C₂²	semidirect
28. C₃×#3940	C₂²	semidirect
29. C₃×#3939	C₂²	semidirect
31. C₂×C₅×#117	C₂×C₃	semidirect
33. C₂×C₂²⋊#168	C₂×C₃	semidirect
34. #65292	C₂×C₃	direct (N × H)
35. C₂×#3941	C₂×C₃	semidirect
36. C₂×#3941	C₂×C₃	semidirect
37. C₂×#3940	C₂×C₃	semidirect
38. C₂×#3939	C₂×C₃	semidirect
70. C₂×C₃×#117	D₅	semidirect
81. C₅×#117	C₂²×C₃	semidirect
92. C₂²⋊#168	C₂²×C₃	semidirect
93. #3941	C₂²×C₃	semidirect
94. #3941	C₂²×C₃	semidirect
95. #3940	C₂²×C₃	semidirect
96. #3939	C₂²×C₃	semidirect
136. C₃×#117	C₂×D₅	semidirect
179. C₂×#117	C₃×D₅	semidirect
273. #117	C₂×C₃×D₅	semidirect
286. C₂×C₃×C₅	#482	semidirect
370. C₃×C₅	C₂×#482	semidirect
391. C₂×C₅	C₃×#482	semidirect
428. C₂×C₃	#65292	direct (N × H)
432. C₅	C₂×C₃×#482	semidirect
452. C₃	C₂×#65292	direct (N × H)
455. C₂	C₃×#65292	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×C₅×#117	2
C₂×C₃×#4076	2
C₂×C₃×C₂²⋊#168	2
C₃×#65292	2
C₂×C₃×#3941	2
C₂×C₃×#3940	2
C₂×C₃×#3939	2
C₂×#65292	3
C₂×C₃×#482	5

Subgroups — C2×C3×#65292 #14431522

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65292 #14431522