Subgroups — C₂×C₃×C₅×#389 #14275325

Order 1920.

1600 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₃×C₅	C₂³
commutator	C₂²	C₂³×C₃×C₄×C₅
Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₃×C₅×#389	C₂	direct (N × H)
7. C₂×C₅×#389	C₃	direct (N × H)
15. C₂×C₃×C₅×C₄⋊C₄	C₄	semidirect
22. C₂×C₃×#389	C₅	direct (N × H)
27. C₅×#389	C₂×C₃	direct (N × H)
52. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
58. C₃×#389	C₂×C₅	direct (N × H)
67. C₂×C₅×C₄⋊C₄	C₃×C₄	semidirect
74. C₂×#389	C₃×C₅	direct (N × H)
96. C₂×C₃×C₄×C₅	C₄⋊C₄	semidirect
110. C₂×C₃×C₄⋊C₄	C₄×C₅	semidirect
140. C₅×C₄⋊C₄	C₂×C₃×C₄	semidirect
146. #389	C₂×C₃×C₅	direct (N × H)
166. C₃×C₄×C₅	C₂×C₄⋊C₄	semidirect
190. C₃×C₄⋊C₄	C₂×C₄×C₅	semidirect
213. C₂×C₄×C₅	C₃×C₄⋊C₄	semidirect
227. C₂×C₄⋊C₄	C₃×C₄×C₅	semidirect
234. C₂×C₃×C₅	#389	direct (N × H)
263. C₂×C₃×C₄	C₅×C₄⋊C₄	semidirect
288. C₄×C₅	C₂×C₃×C₄⋊C₄	semidirect
312. C₄⋊C₄	C₂×C₃×C₄×C₅	semidirect
314. C₃×C₅	C₂×#389	direct (N × H)
333. C₃×C₄	C₂×C₅×C₄⋊C₄	semidirect
334. C₂×C₅	C₃×#389	direct (N × H)
363. C₂×C₄	C₃×C₅×C₄⋊C₄	semidirect
370. C₂×C₃	C₅×#389	direct (N × H)
378. C₅	C₂×C₃×#389	direct (N × H)
397. C₄	C₂×C₃×C₅×C₄⋊C₄	semidirect
398. C₃	C₂×C₅×#389	direct (N × H)
399. C₂	C₃×C₅×#389	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₃×C₅×C₄⋊C₄	2
C₂²×C₃×C₄²×C₅	2
C₃×C₅×#389	2
C₂×C₃×C₅×#95	2
C₂×C₅×#389	3
C₂×C₃×#389	5

Subgroups — C2×C3×C5×#389 #14275325

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×#389 #14275325