Subgroups — C₂×C₃×#65315 #14416315

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#688	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₄×D₂₀	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×#3967	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65315	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃×#3941	C₂	1	1	yes	maximal, characteristic
7	C₂×C₃×#3939	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#3935	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#65315	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₄×D₅	—	2	1	no	—
13	C₃×C₄×C₅×Q₈	—	2	2	no	—
14	C₃×C₄×C₅×Q₈	C₂²	1	4	yes	complemented
15	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₄²×C₅	—	2	1	no	—
18	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
19	C₂×C₃×#688	C₄	1	8	yes	complemented
20	C₂×C₃×#688	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×C₄×D₂₀	—	2	2	no	—
26	C₃×C₄×D₂₀	C₂²	1	4	yes	—
27	C₃×#3967	C₂²	1	4	yes	complemented
28	C₃×#3941	C₂²	1	4	yes	—
29	C₃×#3939	C₂²	1	4	yes	complemented
30	C₃×#3935	C₂²	1	4	yes	complemented
31	C₂×C₃×#440	—	5	1	no	maximal, Hall
32	C₂×C₄×C₅×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂²×#688	C₂×C₃	1	1	yes	characteristic
34	C₂×C₄×D₂₀	C₂×C₃	1	1	yes	characteristic
35	C₂×#3967	C₂×C₃	1	1	yes	characteristic, complemented
36	#65315	C₂×C₃	1	8	yes	direct product factor
37	C₂×#3941	C₂×C₃	1	1	yes	characteristic
38	C₂×#3939	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂×#3935	C₂×C₃	1	1	yes	characteristic, complemented
40	C₂³×C₃×D₅	—	2	1	no	—
41	C₂×C₃×C₅×Q₈	—	2	1	no	—
42	C₂×C₃×C₅×Q₈	—	2	2	no	—
43	C₂×C₃×C₅×Q₈	C₂×C₄	1	4	yes	complemented
44	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
45	C₂²×C₃×C₄×C₅	—	2	1	no	—
46	C₂²×C₃×C₄×C₅	—	2	1	no	—
47	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
48	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
49	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₂²×C₃×Dic₅	—	2	1	no	—
51	C₂×C₃×D₂₀	—	2	1	no	—
52	C₂×C₃×D₂₀	—	2	2	no	—
53	C₂×C₃×D₂₀	C₂×C₄	1	4	yes	—
54	C₂×C₃×D₂₀	C₂³	1	2	yes	—
55	C₂×C₃×C₄×D₅	—	2	4	no	—
56	C₂×C₃×C₄×D₅	—	4	4	no	—
57	C₃×C₅×C₄⋊C₄	—	2	4	no	—
58	C₃×C₅×C₄⋊C₄	—	2	1	no	—
59	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
60	C₃×C₄²×C₅	—	2	4	no	—
61	C₃×C₄²×C₅	D₄	1	2	yes	—
62	C₃×C₄²×C₅	C₂³	1	2	yes	—
63	C₃×#688	C₂×C₄	1	16	yes	complemented
64	C₃×#685	—	2	4	no	—
65	C₃×C₄⋊Dic₅	—	2	1	no	—
66	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
67	C₂×C₃×#168	—	2	2	no	—
68	C₂×C₃×#168	C₂×C₄	1	4	yes	complemented
69	C₂×C₃×#168	C₂³	1	2	yes	—
70	C₂×C₃×#168	C₂³	1	2	yes	—
71	C₂²×C₃×SD₁₆	—	5	1	no	—
72	C₂×C₃×C₄×Q₈	D₅	1	1	yes	characteristic, complemented
73	C₂×C₃×C₄×D₄	—	5	1	no	—
74	C₃×#440	—	5	8	no	—
75	C₂×C₃×#107	—	5	1	no	—
76	C₂×C₃×#103	—	5	1	no	—
77	C₂×C₃×#102	—	5	1	no	—
78	C₂×C₃×#97	—	5	1	no	—
79	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
80	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
81	C₂²×C₄×D₅	—	2	1	no	—
82	C₄×C₅×Q₈	—	2	2	no	—
83	C₄×C₅×Q₈	C₂²×C₃	1	4	yes	complemented
84	C₂×C₅×C₄⋊C₄	—	2	1	no	—
85	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
86	C₂×C₄²×C₅	—	2	1	no	—
87	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
88	C₂×#688	C₃×C₄	1	8	yes	complemented
89	C₂×#688	C₂²×C₃	1	4	yes	—
90	C₂×#685	—	2	1	no	—
91	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
92	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
93	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
94	C₄×D₂₀	—	2	2	no	—
95	C₄×D₂₀	C₂²×C₃	1	4	yes	—
96	#3967	C₂²×C₃	1	4	yes	complemented
97	#3941	C₂²×C₃	1	4	yes	—
98	#3939	C₂²×C₃	1	4	yes	complemented
99	#3935	C₂²×C₃	1	4	yes	complemented
100	C₂×#440	—	5	1	no	Sylow
101	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₃×D₅	—	2	4	no	—
103	C₂²×C₃×D₅	—	2	2	no	—
104	C₂²×C₃×D₅	—	4	2	no	—
105	C₂²×C₃×D₅	—	4	2	no	—
106	C₃×C₅×Q₈	—	2	4	no	—
107	C₃×C₅×Q₈	—	2	2	no	—
108	C₃×C₅×Q₈	C₂²×C₄	1	4	yes	complemented
109	C₂×C₃×C₄×C₅	—	2	4	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	—	2	2	no	—
114	C₂×C₃×C₄×C₅	—	4	2	no	—
115	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
116	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
117	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
118	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
119	C₂×C₃×C₄×C₅	#41	1	2	yes	—
120	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
121	C₂×C₃×Dic₅	—	2	2	no	—
122	C₂×C₃×Dic₅	—	4	2	no	—
123	C₃×D₂₀	—	2	4	no	—
124	C₃×D₂₀	—	2	2	no	—
125	C₃×D₂₀	C₂²×C₄	1	4	yes	—
126	C₃×C₄×D₅	—	4	8	no	—
127	C₃×#168	—	2	2	no	—
128	C₃×#168	C₂²×C₄	1	4	yes	complemented
129	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic
130	C₂²×C₃×D₄	—	5	1	no	—
131	C₂³×C₃×C₄	—	10	1	no	—
132	C₂×C₃×SD₁₆	—	5	8	no	—
133	C₂×C₃×SD₁₆	—	5	4	no	—
134	C₂²×C₃×C₈	—	5	1	no	—
135	C₂²×C₃×C₈	—	5	1	no	—
136	C₃×C₄×Q₈	—	2	2	no	—
137	C₃×C₄×Q₈	C₂×D₅	1	4	yes	complemented
138	C₃×C₄×D₄	—	5	4	no	—
139	C₃×C₄×D₄	—	10	2	no	—
140	C₂×C₃×C₄⋊C₄	—	2	1	no	—
141	C₂×C₃×C₄⋊C₄	—	5	1	no	—
142	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
143	C₂×C₃×C₂²⋊C₄	—	10	1	no	—
144	C₂×C₃×C₄²	—	2	1	no	—
145	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
146	C₃×#107	—	5	4	no	—
147	C₃×#103	—	5	4	no	—
148	C₃×#102	—	5	4	no	—
149	C₃×#97	—	5	4	no	—
150	C₂³×D₅	—	2	1	no	—
151	C₂×C₅×Q₈	—	2	1	no	—
152	C₂×C₅×Q₈	—	2	2	no	—
153	C₂×C₅×Q₈	C₂×C₃×C₄	1	4	yes	complemented
154	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
155	C₂²×C₄×C₅	—	2	1	no	—
156	C₂²×C₄×C₅	—	2	1	no	—
157	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
160	C₂²×Dic₅	—	2	1	no	—
161	C₂×D₂₀	—	2	1	no	—
162	C₂×D₂₀	—	2	2	no	—
163	C₂×D₂₀	C₂×C₃×C₄	1	4	yes	—
164	C₂×D₂₀	C₂³×C₃	1	2	yes	—
165	C₂×C₄×D₅	—	2	4	no	—
166	C₂×C₄×D₅	—	4	4	no	—
167	C₅×C₄⋊C₄	—	2	4	no	—
168	C₅×C₄⋊C₄	—	2	1	no	—
169	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
170	C₄²×C₅	—	2	4	no	—
171	C₄²×C₅	C₃×D₄	1	2	yes	—
172	C₄²×C₅	C₂³×C₃	1	2	yes	—
173	#688	C₂×C₃×C₄	1	16	yes	complemented
174	#685	—	2	4	no	—
175	C₄⋊Dic₅	—	2	1	no	—
176	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
177	C₂×#168	—	2	2	no	—
178	C₂×#168	C₂×C₃×C₄	1	4	yes	complemented
179	C₂×#168	C₂³×C₃	1	2	yes	—
180	C₂×#168	C₂³×C₃	1	2	yes	—
181	C₂²×SD₁₆	—	5	1	no	—
182	C₂×C₄×Q₈	C₃×D₅	1	1	yes	characteristic, complemented
183	C₂×C₄×D₄	—	5	1	no	—
184	#440	—	5	8	no	—
185	C₂×#107	—	5	1	no	—
186	C₂×#103	—	5	1	no	—
187	C₂×#102	—	5	1	no	—
188	C₂×#97	—	5	1	no	—
189	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
190	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
191	C₂²×C₃×C₅	#137	1	2	yes	—
192	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₃×D₅	—	2	4	no	—
194	C₂×C₃×D₅	—	4	2	no	—
195	C₂×C₃×D₅	—	4	2	no	—
196	C₂×C₃×D₅	—	4	8	no	—
197	C₃×C₄×C₅	—	2	4	no	—
198	C₃×C₄×C₅	—	2	2	no	—
199	C₃×C₄×C₅	—	2	2	no	—
200	C₃×C₄×C₅	—	4	2	no	—
201	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
202	C₃×C₄×C₅	C₂³×C₄	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	C₂×C₃×Q₈	—	2	2	no	—
207	C₂×C₃×Q₈	—	2	1	no	—
208	C₂×C₃×Q₈	C₄×D₅	1	4	yes	complemented
209	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
210	C₂×C₃×D₄	—	5	4	no	—
211	C₂×C₃×D₄	—	5	2	no	—
212	C₂×C₃×D₄	—	10	2	no	—
213	C₂×C₃×D₄	—	10	1	no	—
214	C₂²×C₃×C₄	—	2	1	no	—
215	C₂²×C₃×C₄	—	2	1	no	—
216	C₂²×C₃×C₄	—	10	1	no	—
217	C₂²×C₃×C₄	—	10	4	no	—
218	C₂²×C₃×C₄	—	20	4	no	—
219	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
220	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
221	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
222	C₃×SD₁₆	—	5	16	no	—
223	C₂×C₃×C₈	—	5	4	no	—
224	C₂×C₃×C₈	—	5	2	no	—
225	C₂×C₃×C₈	—	5	2	no	—
226	C₂×C₃×C₈	—	10	2	no	—
227	C₃×C₄⋊C₄	—	2	4	no	—
228	C₃×C₄⋊C₄	—	2	1	no	—
229	C₃×C₄⋊C₄	—	5	2	no	—
230	C₃×C₄⋊C₄	—	10	1	no	—
231	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
232	C₃×C₂²⋊C₄	—	10	4	no	—
233	C₃×C₄²	—	2	4	no	—
234	C₃×C₄²	C₂²⋊D₅	1	2	yes	—
235	C₃×C₄²	C₂²×D₅	1	2	yes	—
236	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
237	C₂²×D₅	—	2	4	no	—
238	C₂²×D₅	—	2	2	no	—
239	C₂²×D₅	—	4	2	no	—
240	C₂²×D₅	—	4	2	no	—
241	C₅×Q₈	—	2	4	no	—
242	C₅×Q₈	—	2	2	no	—
243	C₅×Q₈	C₂²×C₃×C₄	1	4	yes	complemented
244	C₂×C₄×C₅	—	2	4	no	—
245	C₂×C₄×C₅	—	2	2	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	—	4	2	no	—
250	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
251	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
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	C₂⁴×C₃	1	1	yes	characteristic
256	C₂×Dic₅	—	2	2	no	—
257	C₂×Dic₅	—	4	2	no	—
258	D₂₀	—	2	4	no	—
259	D₂₀	—	2	2	no	—
260	D₂₀	C₂²×C₃×C₄	1	4	yes	—
261	C₄×D₅	—	4	8	no	—
262	#168	—	2	2	no	—
263	#168	C₂²×C₃×C₄	1	4	yes	complemented
264	C₂²×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
265	C₂²×D₄	—	5	1	no	—
266	C₂³×C₄	—	10	1	no	—
267	C₂×SD₁₆	—	5	8	no	—
268	C₂×SD₁₆	—	5	4	no	—
269	C₂²×C₈	—	5	1	no	—
270	C₂²×C₈	—	5	1	no	—
271	C₄×Q₈	—	2	2	no	—
272	C₄×Q₈	C₂×C₃×D₅	1	4	yes	complemented
273	C₄×D₄	—	5	4	no	—
274	C₄×D₄	—	10	2	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	—	5	1	no	—
277	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
278	C₂×C₂²⋊C₄	—	10	1	no	—
279	C₂×C₄²	—	2	1	no	—
280	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
281	#107	—	5	4	no	—
282	#103	—	5	4	no	—
283	#102	—	5	4	no	—
284	#97	—	5	4	no	—
285	C₂×C₃×C₅	#440	1	4	yes	complemented
286	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
287	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
288	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
289	C₃×D₅	—	4	4	no	—
290	C₂³×C₃	—	10	2	no	—
291	C₂³×C₃	—	10	4	no	—
292	C₂³×C₃	—	20	2	no	—
293	C₂³×C₃	—	20	2	no	—
294	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
295	C₃×Q₈	—	2	2	no	—
296	C₃×Q₈	—	2	4	no	—
297	C₃×Q₈	C₂×C₄×D₅	1	4	yes	complemented
298	C₃×D₄	—	5	4	no	—
299	C₃×D₄	—	10	2	no	—
300	C₃×D₄	—	10	4	no	—
301	C₂×C₃×C₄	—	2	2	no	—
302	C₂×C₃×C₄	—	2	4	no	—
303	C₂×C₃×C₄	—	2	2	no	—
304	C₂×C₃×C₄	—	2	2	no	—
305	C₂×C₃×C₄	—	2	2	no	—
306	C₂×C₃×C₄	—	4	2	no	—
307	C₂×C₃×C₄	—	10	2	no	—
308	C₂×C₃×C₄	—	20	8	no	—
309	C₂×C₃×C₄	—	20	2	no	—
310	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
311	C₂×C₃×C₄	#709	1	2	yes	—
312	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
313	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
314	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
315	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
316	C₃×C₈	—	5	4	no	—
317	C₃×C₈	—	10	2	no	—
318	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
319	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
320	C₂²×C₅	C₃×#137	1	2	yes	—
321	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
322	C₂×D₅	—	2	4	no	—
323	C₂×D₅	—	4	2	no	—
324	C₂×D₅	—	4	2	no	—
325	C₂×D₅	—	4	8	no	—
326	C₄×C₅	—	2	2	no	—
327	C₄×C₅	—	2	2	no	—
328	C₄×C₅	—	2	4	no	—
329	C₄×C₅	—	4	2	no	—
330	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
331	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
332	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
333	Dic₅	—	4	2	no	—
334	C₂⁴	—	10	1	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	1	no	—
337	C₂×Q₈	C₃×C₄×D₅	1	4	yes	complemented
338	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
339	C₂×D₄	—	5	4	no	—
340	C₂×D₄	—	5	2	no	—
341	C₂×D₄	—	10	2	no	—
342	C₂×D₄	—	10	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	10	1	no	—
346	C₂²×C₄	—	10	4	no	—
347	C₂²×C₄	—	20	4	no	—
348	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
349	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
350	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
351	SD₁₆	—	5	16	no	—
352	C₂×C₈	—	5	4	no	—
353	C₂×C₈	—	5	2	no	—
354	C₂×C₈	—	5	2	no	—
355	C₂×C₈	—	10	2	no	—
356	C₄⋊C₄	—	2	4	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	5	2	no	—
359	C₄⋊C₄	—	10	1	no	—
360	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
361	C₂²⋊C₄	—	10	4	no	—
362	C₄²	—	2	4	no	—
363	C₄²	C₃×C₂²⋊D₅	1	2	yes	—
364	C₄²	C₂²×C₃×D₅	1	2	yes	—
365	C₃×C₅	C₂×#440	1	1	yes	characteristic, complemented, Hall
366	C₂²×C₃	—	10	4	no	—
367	C₂²×C₃	—	20	8	no	—
368	C₂²×C₃	—	20	2	no	—
369	C₂²×C₃	—	20	2	no	—
370	C₂²×C₃	C₄×C₂²⋊D₅	1	2	yes	—
371	C₂²×C₃	#4088	1	2	yes	—
372	C₂²×C₃	#4095	1	2	yes	—
373	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
374	C₃×C₄	—	2	4	no	—
375	C₃×C₄	—	2	2	no	—
376	C₃×C₄	—	2	2	no	—
377	C₃×C₄	—	4	2	no	—
378	C₃×C₄	—	20	2	no	—
379	C₃×C₄	C₄×C₂²⋊D₅	1	2	yes	—
380	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
381	C₃×C₄	C₂×#709	1	1	yes	characteristic
382	C₂×C₅	C₃×#440	1	4	yes	complemented
383	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
384	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
385	C₂×C₅	C₂×C₃×#137	1	1	yes	characteristic
386	D₅	—	4	4	no	—
387	C₂³	—	10	2	no	—
388	C₂³	—	10	4	no	—
389	C₂³	—	20	2	no	—
390	C₂³	—	20	2	no	—
391	C₂³	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
392	Q₈	—	2	2	no	—
393	Q₈	—	2	4	no	—
394	Q₈	C₂×C₃×C₄×D₅	1	4	yes	complemented
395	D₄	—	5	4	no	—
396	D₄	—	10	2	no	—
397	D₄	—	10	4	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	10	2	no	—
405	C₂×C₄	—	20	8	no	—
406	C₂×C₄	—	20	2	no	—
407	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
408	C₂×C₄	C₃×#709	1	2	yes	—
409	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
410	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
411	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
412	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
413	C₈	—	5	4	no	—
414	C₈	—	10	2	no	—
415	C₂×C₃	—	20	4	no	—
416	C₂×C₃	#65315	1	4	yes	direct product factor
417	C₂×C₃	C₂×C₄×C₂²⋊D₅	1	1	yes	characteristic
418	C₂×C₃	C₂×#4088	1	1	yes	characteristic
419	C₂×C₃	C₂×#4095	1	1	yes	characteristic
420	C₅	C₂×C₃×#440	1	1	yes	characteristic, complemented, Sylow
421	C₂²	—	10	4	no	—
422	C₂²	—	20	8	no	—
423	C₂²	—	20	2	no	—
424	C₂²	—	20	2	no	—
425	C₂²	C₃×C₄×C₂²⋊D₅	1	2	yes	—
426	C₂²	C₃×#4088	1	2	yes	—
427	C₂²	C₃×#4095	1	2	yes	—
428	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
429	C₄	—	2	4	no	—
430	C₄	—	2	2	no	—
431	C₄	—	2	2	no	—
432	C₄	—	4	2	no	—
433	C₄	—	20	2	no	—
434	C₄	C₃×C₄×C₂²⋊D₅	1	2	yes	—
435	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
436	C₄	C₂×C₃×#709	1	1	yes	characteristic
437	C₃	C₂×#65315	1	1	yes	characteristic, direct product factor, Sylow
438	C₂	—	20	4	no	—
439	C₂	C₃×#65315	1	4	yes	direct product factor
440	C₂	C₂×C₃×C₄×C₂²⋊D₅	1	1	yes	characteristic
441	C₂	C₂×C₃×#4088	1	1	yes	characteristic
442	C₂	C₂×C₃×#4095	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂×C₂²⋊D₅
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₄×C₅×Q₈	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₃×D₂₀	C₂²
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₂×C₃×C₄×Q₈	D₅
hypocenter	C₅	C₂×C₃×#440
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×C₄² ◁ C₂×C₃×C₄×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₄×C₅×Q₈	C₂	semidirect
4. C₂×C₃×#3967	C₂	semidirect
5. C₃×#65315	C₂	direct (N × H)
7. C₂×C₃×#3939	C₂	semidirect
8. C₂×C₃×#3935	C₂	semidirect
9. C₂×#65315	C₃	direct (N × H)
14. C₃×C₄×C₅×Q₈	C₂²	semidirect
19. C₂×C₃×#688	C₄	semidirect
27. C₃×#3967	C₂²	semidirect
29. C₃×#3939	C₂²	semidirect
30. C₃×#3935	C₂²	semidirect
32. C₂×C₄×C₅×Q₈	C₂×C₃	semidirect
35. C₂×#3967	C₂×C₃	semidirect
36. #65315	C₂×C₃	direct (N × H)
38. C₂×#3939	C₂×C₃	semidirect
39. C₂×#3935	C₂×C₃	semidirect
43. C₂×C₃×C₅×Q₈	C₂×C₄	semidirect
63. C₃×#688	C₂×C₄	semidirect
68. C₂×C₃×#168	C₂×C₄	semidirect
72. C₂×C₃×C₄×Q₈	D₅	semidirect
83. C₄×C₅×Q₈	C₂²×C₃	semidirect
88. C₂×#688	C₃×C₄	semidirect
96. #3967	C₂²×C₃	semidirect
98. #3939	C₂²×C₃	semidirect
99. #3935	C₂²×C₃	semidirect
108. C₃×C₅×Q₈	C₂²×C₄	semidirect
128. C₃×#168	C₂²×C₄	semidirect
137. C₃×C₄×Q₈	C₂×D₅	semidirect
153. C₂×C₅×Q₈	C₂×C₃×C₄	semidirect
173. #688	C₂×C₃×C₄	semidirect
178. C₂×#168	C₂×C₃×C₄	semidirect
182. C₂×C₄×Q₈	C₃×D₅	semidirect
208. C₂×C₃×Q₈	C₄×D₅	semidirect
243. C₅×Q₈	C₂²×C₃×C₄	semidirect
263. #168	C₂²×C₃×C₄	semidirect
272. C₄×Q₈	C₂×C₃×D₅	semidirect
285. C₂×C₃×C₅	#440	semidirect
297. C₃×Q₈	C₂×C₄×D₅	semidirect
337. C₂×Q₈	C₃×C₄×D₅	semidirect
365. C₃×C₅	C₂×#440	semidirect
382. C₂×C₅	C₃×#440	semidirect
394. Q₈	C₂×C₃×C₄×D₅	semidirect
416. C₂×C₃	#65315	direct (N × H)
420. C₅	C₂×C₃×#440	semidirect
437. C₃	C₂×#65315	direct (N × H)
439. C₂	C₃×#65315	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×C₅×Q₈	2
C₂²×C₃×#688	2
C₂×C₃×C₄×D₂₀	2
C₂×C₃×#3967	2
C₃×#65315	2
C₂×C₃×#3941	2
C₂×C₃×#3939	2
C₂×C₃×#3935	2
C₂×#65315	3
C₂×C₃×#440	5

Subgroups — C2×C3×#65315 #14416315

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65315 #14416315