Subgroups — C₅×D₃×#396 #14331683

Order 1920.

1816 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃×C₄⋊C₄	C₂	1	3	yes	maximal, complemented
2	C₂×C₅×D₃×C₂²⋊C₄	C₂	1	3	yes	maximal
3	C₃×C₅×#396	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4994	C₂	1	3	yes	maximal, complemented
5	C₅×#4948	C₂	1	3	yes	maximal, complemented
6	C₅×#4676	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×D₃×#95	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#396	—	3	1	no	maximal, Hall
9	C₂⁴×C₅×D₃	C₂²	1	1	yes	characteristic
10	C₂²×C₄×C₅×D₃	C₂²	1	3	yes	—
11	C₂²×C₄×C₅×D₃	C₂²	1	3	yes	—
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	3	yes	complemented
13	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	3	yes	—
14	C₂×C₅×#217	C₂²	1	3	yes	—
15	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	3	yes	—
16	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	3	yes	—
17	C₂×C₅×C₄⋊Dic₃	C₂²	1	3	yes	complemented
18	C₂×C₅×Dic₃⋊C₄	C₂²	1	3	yes	complemented
19	C₂×C₅×Dic₃⋊C₄	C₂²	1	3	yes	complemented
20	C₅×D₃×C₄⋊C₄	—	2	12	no	—
21	C₅×D₃×C₂²⋊C₄	—	2	12	no	—
22	C₃×C₅×#95	C₂²	1	1	yes	characteristic, complemented
23	C₅×C₃⋊#95	C₂²	1	3	yes	complemented
24	D₃×#396	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂²×C₅×C₄⋊C₄	—	3	3	no	—
26	C₂²×C₅×C₂²⋊C₄	—	3	3	no	—
27	C₅×#396	—	3	1	no	—
28	C₅×#396	—	3	3	no	—
29	C₅×#396	—	3	3	no	—
30	C₅×#396	D₃	1	1	yes	characteristic, direct product factor
31	C₂×C₅×#95	—	3	1	no	—
32	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
33	C₂³×C₅×D₃	—	2	6	no	—
34	C₂³×C₅×D₃	—	2	6	no	—
35	C₂³×C₅×D₃	Q₈	1	4	yes	—
36	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
37	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
38	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	—
39	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	—
40	C₂²×C₅×Dic₃	C₂³	1	3	yes	—
41	C₂²×C₅×Dic₃	C₂³	1	3	yes	—
42	C₂×C₄×C₅×D₃	—	2	6	no	—
43	C₂×C₄×C₅×D₃	—	2	6	no	—
44	C₂×C₄×C₅×D₃	—	2	6	no	—
45	C₂×C₄×C₅×D₃	—	2	6	no	—
46	C₂×C₄×C₅×D₃	—	2	6	no	—
47	C₂×C₄×C₅×D₃	D₄	1	12	yes	—
48	C₃×C₅×C₄⋊C₄	—	2	6	no	—
49	C₃×C₅×C₂²⋊C₄	—	2	6	no	—
50	C₅×#217	—	2	6	no	—
51	C₅×(C₂×D₃)⋊C₄	—	2	6	no	—
52	C₅×(C₂×D₃)⋊C₄	—	2	6	no	—
53	C₅×C₄⋊Dic₃	—	2	6	no	—
54	C₅×Dic₃⋊C₄	—	2	6	no	—
55	C₅×Dic₃⋊C₄	—	2	6	no	—
56	C₂×D₃×C₄⋊C₄	C₂×C₅	1	3	yes	complemented
57	C₂×D₃×C₂²⋊C₄	C₂×C₅	1	3	yes	—
58	C₃×#396	C₂×C₅	1	1	yes	characteristic, complemented
59	#4994	C₂×C₅	1	3	yes	complemented
60	#4948	C₂×C₅	1	3	yes	complemented
61	#4676	C₂×C₅	1	1	yes	characteristic, complemented
62	D₃×#95	C₂×C₅	1	1	yes	characteristic, complemented
63	C₂⁵×C₅	—	3	1	no	—
64	C₂³×C₄×C₅	—	3	3	no	—
65	C₂³×C₄×C₅	—	3	3	no	—
66	C₂×C₅×C₄⋊C₄	—	3	3	no	—
67	C₂×C₅×C₄⋊C₄	—	3	3	no	—
68	C₂×C₅×C₄⋊C₄	—	3	3	no	—
69	C₂×C₅×C₄⋊C₄	—	6	12	no	—
70	C₂×C₅×C₄⋊C₄	C₂×D₃	1	3	yes	complemented
71	C₂×C₅×C₂²⋊C₄	—	3	3	no	—
72	C₂×C₅×C₂²⋊C₄	—	3	3	no	—
73	C₂×C₅×C₂²⋊C₄	—	3	3	no	—
74	C₂×C₅×C₂²⋊C₄	—	6	12	no	—
75	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	3	yes	—
76	C₅×#95	—	3	3	no	—
77	C₅×#95	C₂×D₃	1	1	yes	characteristic, complemented
78	C₂×#396	—	3	1	no	Sylow
79	C₂³×C₃×C₅	—	2	3	no	—
80	C₂³×C₃×C₅	—	2	3	no	—
81	C₂³×C₃×C₅	C₂×Q₈	1	2	yes	—
82	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
83	C₂²×C₅×D₃	—	2	3	no	—
84	C₂²×C₅×D₃	—	2	3	no	—
85	C₂²×C₅×D₃	—	2	24	no	—
86	C₂²×C₅×D₃	—	4	12	no	—
87	C₂²×C₅×D₃	—	4	4	no	—
88	C₂²×C₅×D₃	C₂×D₄	1	6	yes	—
89	C₂²×C₅×D₃	C₂×Q₈	1	2	yes	—
90	C₂²×C₅×D₃	C₂×Q₈	1	2	yes	—
91	C₂²×C₅×D₃	#41	1	6	yes	—
92	C₂×C₃×C₄×C₅	—	2	3	no	—
93	C₂×C₃×C₄×C₅	—	2	3	no	—
94	C₂×C₃×C₄×C₅	—	2	3	no	—
95	C₂×C₃×C₄×C₅	—	2	3	no	—
96	C₂×C₃×C₄×C₅	—	2	3	no	—
97	C₂×C₃×C₄×C₅	C₂×D₄	1	6	yes	—
98	C₂×C₅×Dic₃	—	2	3	no	—
99	C₂×C₅×Dic₃	—	2	3	no	—
100	C₂×C₅×Dic₃	—	2	3	no	—
101	C₂×C₅×Dic₃	—	2	3	no	—
102	C₂×C₅×Dic₃	—	2	3	no	—
103	C₂×C₅×Dic₃	C₂×D₄	1	6	yes	—
104	C₄×C₅×D₃	—	2	24	no	—
105	C₄×C₅×D₃	—	4	12	no	—
106	C₂⁴×D₃	C₂²×C₅	1	1	yes	characteristic
107	C₂²×C₄×D₃	C₂²×C₅	1	3	yes	—
108	C₂²×C₄×D₃	C₂²×C₅	1	3	yes	—
109	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	3	yes	complemented
110	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	3	yes	—
111	C₂×#217	C₂²×C₅	1	3	yes	—
112	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	3	yes	—
113	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	3	yes	—
114	C₂×C₄⋊Dic₃	C₂²×C₅	1	3	yes	complemented
115	C₂×Dic₃⋊C₄	C₂²×C₅	1	3	yes	complemented
116	C₂×Dic₃⋊C₄	C₂²×C₅	1	3	yes	complemented
117	D₃×C₄⋊C₄	—	2	12	no	—
118	D₃×C₂²⋊C₄	—	2	12	no	—
119	C₃×#95	C₂²×C₅	1	1	yes	characteristic, complemented
120	C₃⋊#95	C₂²×C₅	1	3	yes	complemented
121	C₂⁴×C₅	—	3	1	no	—
122	C₂⁴×C₅	—	3	4	no	—
123	C₂⁴×C₅	—	3	1	no	—
124	C₂⁴×C₅	—	6	6	no	—
125	C₂⁴×C₅	—	6	6	no	—
126	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
127	C₂²×C₄×C₅	—	3	3	no	—
128	C₂²×C₄×C₅	—	3	12	no	—
129	C₂²×C₄×C₅	—	3	3	no	—
130	C₂²×C₄×C₅	—	6	6	no	—
131	C₂²×C₄×C₅	—	6	6	no	—
132	C₂²×C₄×C₅	—	6	6	no	—
133	C₂²×C₄×C₅	—	6	6	no	—
134	C₂²×C₄×C₅	—	6	6	no	—
135	C₂²×C₄×C₅	C₂²×D₃	1	3	yes	—
136	C₂²×C₄×C₅	C₂²×D₃	1	3	yes	—
137	C₅×C₄⋊C₄	—	2	6	no	—
138	C₅×C₄⋊C₄	—	6	6	no	—
139	C₅×C₄⋊C₄	—	6	6	no	—
140	C₅×C₄⋊C₄	—	6	6	no	—
141	C₅×C₂²⋊C₄	—	2	6	no	—
142	C₅×C₂²⋊C₄	—	6	6	no	—
143	C₅×C₂²⋊C₄	—	6	6	no	—
144	C₅×C₂²⋊C₄	—	6	6	no	—
145	C₂²×C₄⋊C₄	—	3	3	no	—
146	C₂²×C₂²⋊C₄	—	3	3	no	—
147	#396	—	3	3	no	—
148	#396	—	3	3	no	—
149	#396	—	3	1	no	—
150	#396	C₅×D₃	1	1	yes	characteristic, direct product factor
151	C₂×#95	—	3	1	no	—
152	C₂²×C₃×C₅	—	2	6	no	—
153	C₂²×C₃×C₅	—	4	3	no	—
154	C₂²×C₃×C₅	—	4	1	no	—
155	C₂²×C₃×C₅	C₂²×D₄	1	3	yes	—
156	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
157	C₂²×C₃×C₅	C₂×#41	1	3	yes	—
158	C₂×C₅×D₃	—	2	6	no	—
159	C₂×C₅×D₃	—	4	3	no	—
160	C₂×C₅×D₃	—	4	1	no	—
161	C₂×C₅×D₃	—	4	16	no	—
162	C₂×C₅×D₃	#121	1	12	yes	—
163	C₂×C₅×D₃	C₂²⋊Q₈	1	12	yes	—
164	C₂×C₅×D₃	#126	1	4	yes	—
165	C₃×C₄×C₅	—	2	6	no	—
166	C₃×C₄×C₅	—	4	3	no	—
167	C₅×Dic₃	—	2	6	no	—
168	C₅×Dic₃	—	4	3	no	—
169	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
170	C₂³×D₃	—	2	6	no	—
171	C₂³×D₃	—	2	6	no	—
172	C₂³×D₃	C₅×Q₈	1	4	yes	—
173	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
174	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
175	C₂²×C₃×C₄	C₂³×C₅	1	3	yes	—
176	C₂²×C₃×C₄	C₂³×C₅	1	3	yes	—
177	C₂²×Dic₃	C₂³×C₅	1	3	yes	—
178	C₂²×Dic₃	C₂³×C₅	1	3	yes	—
179	C₂×C₄×D₃	—	2	6	no	—
180	C₂×C₄×D₃	—	2	6	no	—
181	C₂×C₄×D₃	—	2	6	no	—
182	C₂×C₄×D₃	—	2	6	no	—
183	C₂×C₄×D₃	—	2	6	no	—
184	C₂×C₄×D₃	C₅×D₄	1	12	yes	—
185	C₃×C₄⋊C₄	—	2	6	no	—
186	C₃×C₂²⋊C₄	—	2	6	no	—
187	#217	—	2	6	no	—
188	(C₂×D₃)⋊C₄	—	2	6	no	—
189	(C₂×D₃)⋊C₄	—	2	6	no	—
190	C₄⋊Dic₃	—	2	6	no	—
191	Dic₃⋊C₄	—	2	6	no	—
192	Dic₃⋊C₄	—	2	6	no	—
193	C₂³×C₅	—	2	3	no	—
194	C₂³×C₅	—	2	3	no	—
195	C₂³×C₅	—	3	6	no	—
196	C₂³×C₅	—	3	2	no	—
197	C₂³×C₅	—	3	6	no	—
198	C₂³×C₅	—	3	2	no	—
199	C₂³×C₅	—	6	24	no	—
200	C₂³×C₅	—	6	3	no	—
201	C₂³×C₅	—	6	3	no	—
202	C₂³×C₅	—	12	4	no	—
203	C₂³×C₅	—	12	12	no	—
204	C₂³×C₅	D₃×Q₈	1	2	yes	—
205	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
206	C₂×C₄×C₅	—	2	3	no	—
207	C₂×C₄×C₅	—	2	3	no	—
208	C₂×C₄×C₅	—	2	3	no	—
209	C₂×C₄×C₅	—	2	3	no	—
210	C₂×C₄×C₅	—	2	3	no	—
211	C₂×C₄×C₅	—	3	6	no	—
212	C₂×C₄×C₅	—	6	24	no	—
213	C₂×C₄×C₅	—	6	3	no	—
214	C₂×C₄×C₅	—	6	3	no	—
215	C₂×C₄×C₅	—	6	3	no	—
216	C₂×C₄×C₅	—	6	3	no	—
217	C₂×C₄×C₅	—	6	3	no	—
218	C₂×C₄×C₅	—	12	12	no	—
219	C₂×C₄×C₅	D₃×D₄	1	6	yes	—
220	C₂⁵	—	3	1	no	—
221	C₂³×C₄	—	3	3	no	—
222	C₂³×C₄	—	3	3	no	—
223	C₂×C₄⋊C₄	—	3	3	no	—
224	C₂×C₄⋊C₄	—	3	3	no	—
225	C₂×C₄⋊C₄	—	3	3	no	—
226	C₂×C₄⋊C₄	—	6	12	no	—
227	C₂×C₄⋊C₄	C₂×C₅×D₃	1	3	yes	complemented
228	C₂×C₂²⋊C₄	—	3	3	no	—
229	C₂×C₂²⋊C₄	—	3	3	no	—
230	C₂×C₂²⋊C₄	—	3	3	no	—
231	C₂×C₂²⋊C₄	—	6	12	no	—
232	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	3	yes	—
233	#95	—	3	3	no	—
234	#95	C₂×C₅×D₃	1	1	yes	characteristic, complemented
235	C₂×C₃×C₅	—	4	2	no	—
236	C₂×C₃×C₅	C₂×#121	1	3	yes	—
237	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	3	yes	—
238	C₂×C₃×C₅	C₂×#126	1	1	yes	characteristic
239	C₅×D₃	—	4	2	no	—
240	C₅×D₃	#396	1	8	yes	direct product factor
241	C₂³×C₃	—	2	3	no	—
242	C₂³×C₃	—	2	3	no	—
243	C₂³×C₃	C₂×C₅×Q₈	1	2	yes	—
244	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
245	C₂²×D₃	—	2	3	no	—
246	C₂²×D₃	—	2	3	no	—
247	C₂²×D₃	—	2	24	no	—
248	C₂²×D₃	—	4	12	no	—
249	C₂²×D₃	—	4	4	no	—
250	C₂²×D₃	C₂×C₅×D₄	1	6	yes	—
251	C₂²×D₃	C₂×C₅×Q₈	1	2	yes	—
252	C₂²×D₃	C₂×C₅×Q₈	1	2	yes	—
253	C₂²×D₃	C₅×#41	1	6	yes	—
254	C₂×C₃×C₄	—	2	3	no	—
255	C₂×C₃×C₄	—	2	3	no	—
256	C₂×C₃×C₄	—	2	3	no	—
257	C₂×C₃×C₄	—	2	3	no	—
258	C₂×C₃×C₄	—	2	3	no	—
259	C₂×C₃×C₄	C₂×C₅×D₄	1	6	yes	—
260	C₂×Dic₃	—	2	3	no	—
261	C₂×Dic₃	—	2	3	no	—
262	C₂×Dic₃	—	2	3	no	—
263	C₂×Dic₃	—	2	3	no	—
264	C₂×Dic₃	—	2	3	no	—
265	C₂×Dic₃	C₂×C₅×D₄	1	6	yes	—
266	C₄×D₃	—	2	24	no	—
267	C₄×D₃	—	4	12	no	—
268	C₂²×C₅	—	2	6	no	—
269	C₂²×C₅	—	3	4	no	—
270	C₂²×C₅	—	3	12	no	—
271	C₂²×C₅	—	3	12	no	—
272	C₂²×C₅	—	4	1	no	—
273	C₂²×C₅	—	4	3	no	—
274	C₂²×C₅	—	6	6	no	—
275	C₂²×C₅	—	12	16	no	—
276	C₂²×C₅	—	12	1	no	—
277	C₂²×C₅	—	12	3	no	—
278	C₂²×C₅	C₂×D₃×D₄	1	3	yes	—
279	C₂²×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
280	C₂²×C₅	D₃×#41	1	3	yes	—
281	C₄×C₅	—	2	6	no	—
282	C₄×C₅	—	4	3	no	—
283	C₄×C₅	—	6	6	no	—
284	C₄×C₅	—	12	3	no	—
285	C₂⁴	—	3	1	no	—
286	C₂⁴	—	3	4	no	—
287	C₂⁴	—	3	1	no	—
288	C₂⁴	—	6	6	no	—
289	C₂⁴	—	6	6	no	—
290	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
291	C₂²×C₄	—	3	3	no	—
292	C₂²×C₄	—	3	12	no	—
293	C₂²×C₄	—	3	3	no	—
294	C₂²×C₄	—	6	6	no	—
295	C₂²×C₄	—	6	6	no	—
296	C₂²×C₄	—	6	6	no	—
297	C₂²×C₄	—	6	6	no	—
298	C₂²×C₄	—	6	6	no	—
299	C₂²×C₄	C₂²×C₅×D₃	1	3	yes	—
300	C₂²×C₄	C₂²×C₅×D₃	1	3	yes	—
301	C₄⋊C₄	—	2	6	no	—
302	C₄⋊C₄	—	6	6	no	—
303	C₄⋊C₄	—	6	6	no	—
304	C₄⋊C₄	—	6	6	no	—
305	C₂²⋊C₄	—	2	6	no	—
306	C₂²⋊C₄	—	6	6	no	—
307	C₂²⋊C₄	—	6	6	no	—
308	C₂²⋊C₄	—	6	6	no	—
309	C₃×C₅	C₂×#396	1	1	yes	characteristic, complemented, Hall
310	C₂²×C₃	—	2	6	no	—
311	C₂²×C₃	—	4	3	no	—
312	C₂²×C₃	—	4	1	no	—
313	C₂²×C₃	C₂²×C₅×D₄	1	3	yes	—
314	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
315	C₂²×C₃	C₂×C₅×#41	1	3	yes	—
316	C₂×D₃	—	2	6	no	—
317	C₂×D₃	—	4	3	no	—
318	C₂×D₃	—	4	1	no	—
319	C₂×D₃	—	4	16	no	—
320	C₂×D₃	C₅×#121	1	12	yes	—
321	C₂×D₃	C₅×C₂²⋊Q₈	1	12	yes	—
322	C₂×D₃	C₅×#126	1	4	yes	—
323	C₃×C₄	—	2	6	no	—
324	C₃×C₄	—	4	3	no	—
325	Dic₃	—	2	6	no	—
326	Dic₃	—	4	3	no	—
327	C₂×C₅	—	3	8	no	—
328	C₂×C₅	—	4	2	no	—
329	C₂×C₅	—	12	2	no	—
330	C₂×C₅	D₃×#121	1	3	yes	—
331	C₂×C₅	D₃×C₂²⋊Q₈	1	3	yes	—
332	C₂×C₅	D₃×#126	1	1	yes	characteristic
333	C₂³	—	2	3	no	—
334	C₂³	—	2	3	no	—
335	C₂³	—	3	6	no	—
336	C₂³	—	3	2	no	—
337	C₂³	—	3	6	no	—
338	C₂³	—	3	2	no	—
339	C₂³	—	6	24	no	—
340	C₂³	—	6	3	no	—
341	C₂³	—	6	3	no	—
342	C₂³	—	12	4	no	—
343	C₂³	—	12	12	no	—
344	C₂³	C₅×D₃×Q₈	1	2	yes	—
345	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
346	C₂×C₄	—	2	3	no	—
347	C₂×C₄	—	2	3	no	—
348	C₂×C₄	—	2	3	no	—
349	C₂×C₄	—	2	3	no	—
350	C₂×C₄	—	2	3	no	—
351	C₂×C₄	—	3	6	no	—
352	C₂×C₄	—	6	24	no	—
353	C₂×C₄	—	6	3	no	—
354	C₂×C₄	—	6	3	no	—
355	C₂×C₄	—	6	3	no	—
356	C₂×C₄	—	6	3	no	—
357	C₂×C₄	—	6	3	no	—
358	C₂×C₄	—	12	12	no	—
359	C₂×C₄	C₅×D₃×D₄	1	6	yes	—
360	C₂×C₃	—	4	2	no	—
361	C₂×C₃	C₂×C₅×#121	1	3	yes	—
362	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	3	yes	—
363	C₂×C₃	C₂×C₅×#126	1	1	yes	characteristic
364	D₃	—	4	2	no	—
365	D₃	C₅×#396	1	8	yes	direct product factor
366	C₅	D₃×#396	1	1	yes	characteristic, direct product factor, Sylow
367	C₂²	—	2	6	no	—
368	C₂²	—	3	4	no	—
369	C₂²	—	3	12	no	—
370	C₂²	—	3	12	no	—
371	C₂²	—	4	1	no	—
372	C₂²	—	4	3	no	—
373	C₂²	—	6	6	no	—
374	C₂²	—	12	16	no	—
375	C₂²	—	12	1	no	—
376	C₂²	—	12	3	no	—
377	C₂²	C₂×C₅×D₃×D₄	1	3	yes	—
378	C₂²	C₂×C₅×D₃×Q₈	1	1	yes	characteristic
379	C₂²	C₅×D₃×#41	1	3	yes	—
380	C₄	—	2	6	no	—
381	C₄	—	4	3	no	—
382	C₄	—	6	6	no	—
383	C₄	—	12	3	no	—
384	C₃	C₂×C₅×#396	1	1	yes	characteristic, complemented, Sylow
385	C₂	—	3	8	no	—
386	C₂	—	4	2	no	—
387	C₂	—	12	2	no	—
388	C₂	C₅×D₃×#121	1	3	yes	—
389	C₂	C₅×D₃×C₂²⋊Q₈	1	3	yes	—
390	C₂	C₅×D₃×#126	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator, cosocle	C₂³×C₃	C₂⁴×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₃×C₅×#396	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂⁴×C₅×D₃	C₂²
hypercenter	C₅×#396	D₃
hypocenter	C₃	C₂×C₅×#396
LCS	G ▷ C₂³×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₅×#396

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×D₃×C₄⋊C₄	C₂	semidirect
3. C₃×C₅×#396	C₂	semidirect
4. C₅×#4994	C₂	semidirect
5. C₅×#4948	C₂	semidirect
6. C₅×#4676	C₂	semidirect
7. C₅×D₃×#95	C₂	semidirect
12. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
17. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
18. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
19. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
22. C₃×C₅×#95	C₂²	semidirect
23. C₅×C₃⋊#95	C₂²	semidirect
24. D₃×#396	C₅	direct (N × H)
30. C₅×#396	D₃	direct (N × H)
56. C₂×D₃×C₄⋊C₄	C₂×C₅	semidirect
58. C₃×#396	C₂×C₅	semidirect
59. #4994	C₂×C₅	semidirect
60. #4948	C₂×C₅	semidirect
61. #4676	C₂×C₅	semidirect
62. D₃×#95	C₂×C₅	semidirect
70. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
77. C₅×#95	C₂×D₃	semidirect
109. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
114. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
115. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
116. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
119. C₃×#95	C₂²×C₅	semidirect
120. C₃⋊#95	C₂²×C₅	semidirect
150. #396	C₅×D₃	direct (N × H)
227. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
234. #95	C₂×C₅×D₃	semidirect
240. C₅×D₃	#396	direct (N × H)
309. C₃×C₅	C₂×#396	semidirect
365. D₃	C₅×#396	direct (N × H)
366. C₅	D₃×#396	direct (N × H)
384. C₃	C₂×C₅×#396	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×C₄⋊C₄	2
C₂×C₅×D₃×C₂²⋊C₄	2
C₃×C₅×#396	2
C₅×#4994	2
C₅×#4948	2
C₅×#4676	2
C₅×D₃×#95	2
C₂×C₅×#396	3
D₃×#396	5

Subgroups — C5×D3×#396 #14331683

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#396 #14331683