Subgroups — C₅×D₃×#324 #14280765

Order 1920.

656 conjugacy classes of subgroups.

The subgroup lattice has 396 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	1	yes	maximal, characteristic
2	C₅×D₃×C₂²⋊C₈	C₂	1	2	yes	maximal
3	C₃×C₅×#324	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4528	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4469	C₂	1	2	yes	maximal, complemented
6	C₂×C₅×#324	—	3	1	no	maximal, Hall
7	C₂²×C₄×C₅×D₃	C₄	1	1	yes	characteristic
8	C₂²×C₄×C₅×D₃	C₄	1	1	yes	characteristic
9	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
11	C₂×C₅×C₄⋊Dic₃	C₄	1	1	yes	characteristic
12	C₂×C₅×Dic₃⋊C₄	C₄	1	1	yes	characteristic
13	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
14	C₂×C₅×D₃×C₈	—	2	2	no	—
15	C₅×D₃×C₄⋊C₄	—	2	2	no	—
16	C₅×D₃×C₄⋊C₄	—	2	2	no	—
17	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
18	C₅×#830	C₂²	1	2	yes	—
19	C₅×(C₂×D₃)⋊C₈	—	2	2	no	—
20	D₃×#324	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂²×C₅×C₄⋊C₄	—	3	1	no	—
22	C₂×C₅×C₂²⋊C₈	—	3	2	no	—
23	C₅×#324	—	3	2	no	—
24	C₅×#324	—	3	1	no	—
25	C₅×#324	D₃	1	1	yes	characteristic, direct product factor
26	C₂³×C₅×D₃	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
30	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄×C₅×D₃	—	2	1	no	—
34	C₂×C₄×C₅×D₃	—	2	1	no	—
35	C₂×C₄×C₅×D₃	—	2	2	no	—
36	C₂×C₄×C₅×D₃	—	2	1	no	—
37	C₂×C₄×C₅×D₃	—	2	1	no	—
38	C₂×C₄×C₅×D₃	—	4	2	no	—
39	C₂×C₄×C₅×D₃	—	4	2	no	—
40	C₂×C₄×C₅×D₃	C₈	1	4	yes	complemented
41	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
42	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
43	C₂×C₃×C₅×C₈	—	2	2	no	—
44	C₃×C₅×C₄⋊C₄	—	2	2	no	—
45	C₅×C₄⋊Dic₃	—	2	2	no	—
46	C₅×Dic₃⋊C₄	—	2	2	no	—
47	C₅×Dic₃⋊C₄	—	2	2	no	—
48	C₂×C₅×C₃⋊C₈	—	2	2	no	—
49	C₅×D₃×C₈	—	4	4	no	—
50	C₂×D₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
51	D₃×C₂²⋊C₈	C₂×C₅	1	2	yes	—
52	C₃×#324	C₂×C₅	1	1	yes	characteristic, complemented
53	#4528	C₂×C₅	1	1	yes	characteristic, complemented
54	#4469	C₂×C₅	1	2	yes	complemented
55	C₂³×C₄×C₅	—	3	1	no	—
56	C₂³×C₄×C₅	—	3	1	no	—
57	C₂³×C₄×C₅	—	3	1	no	—
58	C₂²×C₅×C₈	—	6	2	no	—
59	C₂×C₅×C₄⋊C₄	—	3	1	no	—
60	C₂×C₅×C₄⋊C₄	—	3	1	no	—
61	C₂×C₅×C₄⋊C₄	—	3	1	no	—
62	C₂×C₅×C₄⋊C₄	—	6	2	no	—
63	C₂×C₅×C₄⋊C₄	—	6	2	no	—
64	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
65	C₅×C₂²⋊C₈	—	3	2	no	—
66	C₅×C₂²⋊C₈	—	6	2	no	—
67	C₅×C₂²⋊C₈	C₂×D₃	1	2	yes	—
68	C₂×#324	—	3	1	no	Sylow
69	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₅×D₃	—	2	2	no	—
71	C₂²×C₅×D₃	—	2	2	no	—
72	C₂²×C₅×D₃	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₅×D₃	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₅×D₃	C₂×C₈	1	2	yes	—
75	C₂²×C₅×D₃	M₁₆	1	2	yes	—
76	C₂×C₃×C₄×C₅	—	2	1	no	—
77	C₂×C₃×C₄×C₅	—	2	1	no	—
78	C₂×C₃×C₄×C₅	—	2	1	no	—
79	C₂×C₃×C₄×C₅	—	4	1	no	—
80	C₂×C₃×C₄×C₅	—	4	1	no	—
81	C₂×C₃×C₄×C₅	C₂×C₈	1	2	yes	complemented
82	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
83	C₂×C₅×Dic₃	—	2	1	no	—
84	C₂×C₅×Dic₃	—	2	1	no	—
85	C₂×C₅×Dic₃	—	2	1	no	—
86	C₂×C₅×Dic₃	—	4	1	no	—
87	C₂×C₅×Dic₃	—	4	1	no	—
88	C₂×C₅×Dic₃	C₂²⋊C₄	1	2	yes	—
89	C₂×C₅×Dic₃	C₂×C₈	1	2	yes	complemented
90	C₄×C₅×D₃	—	2	4	no	—
91	C₄×C₅×D₃	—	2	4	no	—
92	C₄×C₅×D₃	—	2	4	no	—
93	C₄×C₅×D₃	—	4	2	no	—
94	C₄×C₅×D₃	—	4	2	no	—
95	C₄×C₅×D₃	—	4	2	no	—
96	C₃×C₅×C₈	—	4	2	no	—
97	C₅×C₃⋊C₈	—	4	2	no	—
98	C₂²×C₄×D₃	C₄×C₅	1	1	yes	characteristic
99	C₂²×C₄×D₃	C₄×C₅	1	1	yes	characteristic
100	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
101	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
102	C₂×C₄⋊Dic₃	C₄×C₅	1	1	yes	characteristic
103	C₂×Dic₃⋊C₄	C₄×C₅	1	1	yes	characteristic
104	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
105	C₂×D₃×C₈	—	2	2	no	—
106	D₃×C₄⋊C₄	—	2	2	no	—
107	D₃×C₄⋊C₄	—	2	2	no	—
108	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
109	#830	C₂²×C₅	1	2	yes	—
110	(C₂×D₃)⋊C₈	—	2	2	no	—
111	C₂⁴×C₅	—	3	1	no	—
112	C₂²×C₄×C₅	—	3	1	no	—
113	C₂²×C₄×C₅	—	3	1	no	—
114	C₂²×C₄×C₅	—	3	4	no	—
115	C₂²×C₄×C₅	—	3	2	no	—
116	C₂²×C₄×C₅	—	3	2	no	—
117	C₂²×C₄×C₅	—	3	1	no	—
118	C₂²×C₄×C₅	—	6	1	no	—
119	C₂²×C₄×C₅	—	6	1	no	—
120	C₂²×C₄×C₅	—	6	2	no	—
121	C₂²×C₄×C₅	—	6	1	no	—
122	C₂²×C₄×C₅	—	6	1	no	—
123	C₂²×C₄×C₅	—	12	2	no	—
124	C₂²×C₄×C₅	—	12	2	no	—
125	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
126	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
127	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
128	C₂×C₅×C₈	—	2	2	no	—
129	C₂×C₅×C₈	—	6	2	no	—
130	C₂×C₅×C₈	—	12	4	no	—
131	C₅×C₄⋊C₄	—	2	2	no	—
132	C₅×C₄⋊C₄	—	6	2	no	—
133	C₅×C₄⋊C₄	—	6	2	no	—
134	C₅×C₄⋊C₄	—	6	2	no	—
135	C₂²×C₄⋊C₄	—	3	1	no	—
136	C₂×C₂²⋊C₈	—	3	2	no	—
137	#324	—	3	1	no	—
138	#324	—	3	2	no	—
139	#324	C₅×D₃	1	1	yes	characteristic, direct product factor
140	C₂²×C₃×C₅	—	2	1	no	—
141	C₂²×C₃×C₅	—	2	1	no	—
142	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
143	C₂²×C₃×C₅	C₂²×C₈	1	1	yes	characteristic
144	C₂²×C₃×C₅	C₂×M₁₆	1	1	yes	characteristic
145	C₂×C₅×D₃	—	2	1	no	—
146	C₂×C₅×D₃	—	2	1	no	—
147	C₂×C₅×D₃	—	2	4	no	—
148	C₂×C₅×D₃	—	2	4	no	—
149	C₂×C₅×D₃	C₂²⋊C₈	1	2	yes	—
150	C₂×C₅×D₃	C₂²⋊C₈	1	2	yes	—
151	C₂×C₅×D₃	#99	1	2	yes	—
152	C₂×C₅×D₃	#101	1	2	yes	—
153	C₃×C₄×C₅	—	2	2	no	—
154	C₃×C₄×C₅	—	2	2	no	—
155	C₃×C₄×C₅	—	4	1	no	—
156	C₅×Dic₃	—	2	2	no	—
157	C₅×Dic₃	—	2	2	no	—
158	C₅×Dic₃	—	4	1	no	—
159	C₂³×D₃	C₂×C₄×C₅	1	1	yes	characteristic
160	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
161	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
162	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
163	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
164	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
165	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
166	C₂×C₄×D₃	—	2	1	no	—
167	C₂×C₄×D₃	—	2	1	no	—
168	C₂×C₄×D₃	—	2	2	no	—
169	C₂×C₄×D₃	—	2	1	no	—
170	C₂×C₄×D₃	—	2	1	no	—
171	C₂×C₄×D₃	—	4	2	no	—
172	C₂×C₄×D₃	—	4	2	no	—
173	C₂×C₄×D₃	C₅×C₈	1	4	yes	complemented
174	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
175	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
176	C₂×C₃×C₈	—	2	2	no	—
177	C₃×C₄⋊C₄	—	2	2	no	—
178	C₄⋊Dic₃	—	2	2	no	—
179	Dic₃⋊C₄	—	2	2	no	—
180	Dic₃⋊C₄	—	2	2	no	—
181	C₂×C₃⋊C₈	—	2	2	no	—
182	D₃×C₈	—	4	4	no	—
183	C₂³×C₅	—	3	1	no	—
184	C₂³×C₅	—	3	1	no	—
185	C₂³×C₅	—	3	2	no	—
186	C₂³×C₅	—	3	2	no	—
187	C₂³×C₅	—	6	2	no	—
188	C₂³×C₅	—	6	2	no	—
189	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
190	C₂×C₄×C₅	—	2	1	no	—
191	C₂×C₄×C₅	—	2	1	no	—
192	C₂×C₄×C₅	—	2	1	no	—
193	C₂×C₄×C₅	—	3	2	no	—
194	C₂×C₄×C₅	—	3	2	no	—
195	C₂×C₄×C₅	—	4	1	no	—
196	C₂×C₄×C₅	—	4	1	no	—
197	C₂×C₄×C₅	—	6	4	no	—
198	C₂×C₄×C₅	—	6	4	no	—
199	C₂×C₄×C₅	—	6	4	no	—
200	C₂×C₄×C₅	—	6	1	no	—
201	C₂×C₄×C₅	—	6	1	no	—
202	C₂×C₄×C₅	—	6	1	no	—
203	C₂×C₄×C₅	—	12	2	no	—
204	C₂×C₄×C₅	—	12	2	no	—
205	C₂×C₄×C₅	—	12	2	no	—
206	C₂×C₄×C₅	—	12	1	no	—
207	C₂×C₄×C₅	—	12	1	no	—
208	C₂×C₄×C₅	D₃×C₈	1	2	yes	complemented
209	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
210	C₅×C₈	—	4	2	no	—
211	C₅×C₈	—	12	2	no	—
212	C₂³×C₄	—	3	1	no	—
213	C₂³×C₄	—	3	1	no	—
214	C₂³×C₄	—	3	1	no	—
215	C₂²×C₈	—	6	2	no	—
216	C₂×C₄⋊C₄	—	3	1	no	—
217	C₂×C₄⋊C₄	—	3	1	no	—
218	C₂×C₄⋊C₄	—	3	1	no	—
219	C₂×C₄⋊C₄	—	6	2	no	—
220	C₂×C₄⋊C₄	—	6	2	no	—
221	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
222	C₂²⋊C₈	—	3	2	no	—
223	C₂²⋊C₈	—	6	2	no	—
224	C₂²⋊C₈	C₂×C₅×D₃	1	2	yes	—
225	C₂×C₃×C₅	—	2	1	no	—
226	C₂×C₃×C₅	—	2	1	no	—
227	C₂×C₃×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
228	C₂×C₃×C₅	C₂×#99	1	1	yes	characteristic
229	C₂×C₃×C₅	C₂×#101	1	1	yes	characteristic
230	C₅×D₃	—	2	2	no	—
231	C₅×D₃	#324	1	4	yes	direct product factor
232	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
233	C₂²×D₃	—	2	2	no	—
234	C₂²×D₃	—	2	2	no	—
235	C₂²×D₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
236	C₂²×D₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
237	C₂²×D₃	C₂×C₅×C₈	1	2	yes	—
238	C₂²×D₃	C₅×M₁₆	1	2	yes	—
239	C₂×C₃×C₄	—	2	1	no	—
240	C₂×C₃×C₄	—	2	1	no	—
241	C₂×C₃×C₄	—	2	1	no	—
242	C₂×C₃×C₄	—	4	1	no	—
243	C₂×C₃×C₄	—	4	1	no	—
244	C₂×C₃×C₄	C₂×C₅×C₈	1	2	yes	complemented
245	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
246	C₂×Dic₃	—	2	1	no	—
247	C₂×Dic₃	—	2	1	no	—
248	C₂×Dic₃	—	2	1	no	—
249	C₂×Dic₃	—	4	1	no	—
250	C₂×Dic₃	—	4	1	no	—
251	C₂×Dic₃	C₅×C₂²⋊C₄	1	2	yes	—
252	C₂×Dic₃	C₂×C₅×C₈	1	2	yes	complemented
253	C₄×D₃	—	2	4	no	—
254	C₄×D₃	—	2	4	no	—
255	C₄×D₃	—	2	4	no	—
256	C₄×D₃	—	4	2	no	—
257	C₄×D₃	—	4	2	no	—
258	C₄×D₃	—	4	2	no	—
259	C₃×C₈	—	4	2	no	—
260	C₃⋊C₈	—	4	2	no	—
261	C₂²×C₅	—	2	1	no	—
262	C₂²×C₅	—	2	1	no	—
263	C₂²×C₅	—	3	2	no	—
264	C₂²×C₅	—	3	2	no	—
265	C₂²×C₅	—	3	2	no	—
266	C₂²×C₅	—	3	2	no	—
267	C₂²×C₅	—	6	4	no	—
268	C₂²×C₅	—	6	4	no	—
269	C₂²×C₅	—	6	1	no	—
270	C₂²×C₅	—	6	1	no	—
271	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
272	C₂²×C₅	C₂×D₃×C₈	1	1	yes	characteristic
273	C₂²×C₅	D₃×M₁₆	1	1	yes	characteristic
274	C₄×C₅	—	2	2	no	—
275	C₄×C₅	—	2	2	no	—
276	C₄×C₅	—	4	1	no	—
277	C₄×C₅	—	6	2	no	—
278	C₄×C₅	—	6	2	no	—
279	C₄×C₅	—	12	1	no	—
280	C₂⁴	—	3	1	no	—
281	C₂²×C₄	—	3	1	no	—
282	C₂²×C₄	—	3	1	no	—
283	C₂²×C₄	—	3	4	no	—
284	C₂²×C₄	—	3	2	no	—
285	C₂²×C₄	—	3	2	no	—
286	C₂²×C₄	—	3	1	no	—
287	C₂²×C₄	—	6	1	no	—
288	C₂²×C₄	—	6	1	no	—
289	C₂²×C₄	—	6	2	no	—
290	C₂²×C₄	—	6	1	no	—
291	C₂²×C₄	—	6	1	no	—
292	C₂²×C₄	—	12	2	no	—
293	C₂²×C₄	—	12	2	no	—
294	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
295	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
296	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	6	2	no	—
299	C₂×C₈	—	12	4	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	6	2	no	—
302	C₄⋊C₄	—	6	2	no	—
303	C₄⋊C₄	—	6	2	no	—
304	C₃×C₅	C₂×#324	1	1	yes	characteristic, complemented, Hall
305	C₂²×C₃	—	2	1	no	—
306	C₂²×C₃	—	2	1	no	—
307	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
308	C₂²×C₃	C₂²×C₅×C₈	1	1	yes	characteristic
309	C₂²×C₃	C₂×C₅×M₁₆	1	1	yes	characteristic
310	C₂×D₃	—	2	1	no	—
311	C₂×D₃	—	2	1	no	—
312	C₂×D₃	—	2	4	no	—
313	C₂×D₃	—	2	4	no	—
314	C₂×D₃	C₅×C₂²⋊C₈	1	2	yes	—
315	C₂×D₃	C₅×C₂²⋊C₈	1	2	yes	—
316	C₂×D₃	C₅×#99	1	2	yes	—
317	C₂×D₃	C₅×#101	1	2	yes	—
318	C₃×C₄	—	2	2	no	—
319	C₃×C₄	—	2	2	no	—
320	C₃×C₄	—	4	1	no	—
321	Dic₃	—	2	2	no	—
322	Dic₃	—	2	2	no	—
323	Dic₃	—	4	1	no	—
324	C₂×C₅	—	2	1	no	—
325	C₂×C₅	—	2	1	no	—
326	C₂×C₅	—	3	4	no	—
327	C₂×C₅	—	6	2	no	—
328	C₂×C₅	D₃×C₂²⋊C₈	1	1	yes	characteristic
329	C₂×C₅	D₃×#99	1	1	yes	characteristic
330	C₂×C₅	D₃×#101	1	1	yes	characteristic
331	C₂³	—	3	1	no	—
332	C₂³	—	3	1	no	—
333	C₂³	—	3	2	no	—
334	C₂³	—	3	2	no	—
335	C₂³	—	6	2	no	—
336	C₂³	—	6	2	no	—
337	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	3	2	no	—
342	C₂×C₄	—	3	2	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	6	4	no	—
346	C₂×C₄	—	6	4	no	—
347	C₂×C₄	—	6	4	no	—
348	C₂×C₄	—	6	1	no	—
349	C₂×C₄	—	6	1	no	—
350	C₂×C₄	—	6	1	no	—
351	C₂×C₄	—	12	2	no	—
352	C₂×C₄	—	12	2	no	—
353	C₂×C₄	—	12	2	no	—
354	C₂×C₄	—	12	1	no	—
355	C₂×C₄	—	12	1	no	—
356	C₂×C₄	C₅×D₃×C₈	1	2	yes	complemented
357	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
358	C₈	—	4	2	no	—
359	C₈	—	12	2	no	—
360	C₂×C₃	—	2	1	no	—
361	C₂×C₃	—	2	1	no	—
362	C₂×C₃	C₂×C₅×C₂²⋊C₈	1	1	yes	characteristic
363	C₂×C₃	C₂×C₅×#99	1	1	yes	characteristic
364	C₂×C₃	C₂×C₅×#101	1	1	yes	characteristic
365	D₃	—	2	2	no	—
366	D₃	C₅×#324	1	4	yes	direct product factor
367	C₅	D₃×#324	1	1	yes	characteristic, direct product factor, Sylow
368	C₂²	—	2	1	no	—
369	C₂²	—	2	1	no	—
370	C₂²	—	3	2	no	—
371	C₂²	—	3	2	no	—
372	C₂²	—	3	2	no	—
373	C₂²	—	3	2	no	—
374	C₂²	—	6	4	no	—
375	C₂²	—	6	4	no	—
376	C₂²	—	6	1	no	—
377	C₂²	—	6	1	no	—
378	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
379	C₂²	C₂×C₅×D₃×C₈	1	1	yes	characteristic
380	C₂²	C₅×D₃×M₁₆	1	1	yes	characteristic
381	C₄	—	2	2	no	—
382	C₄	—	2	2	no	—
383	C₄	—	4	1	no	—
384	C₄	—	6	2	no	—
385	C₄	—	6	2	no	—
386	C₄	—	12	1	no	—
387	C₃	C₂×C₅×#324	1	1	yes	characteristic, complemented, Sylow
388	C₂	—	2	1	no	—
389	C₂	—	2	1	no	—
390	C₂	—	3	4	no	—
391	C₂	—	6	2	no	—
392	C₂	C₅×D₃×C₂²⋊C₈	1	1	yes	characteristic
393	C₂	C₅×D₃×#99	1	1	yes	characteristic
394	C₂	C₅×D₃×#101	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	D₃×C₂²⋊C₄
commutator	C₂²×C₃	C₂²×C₅×C₈
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#324	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂³×C₅×D₃	C₂×C₄
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#324	D₃
hypocenter	C₃	C₂×C₅×#324
LCS	G ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#324

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×#324	C₂	semidirect
4. C₅×#4528	C₂	semidirect
5. C₅×#4469	C₂	semidirect
20. D₃×#324	C₅	direct (N × H)
25. C₅×#324	D₃	direct (N × H)
40. C₂×C₄×C₅×D₃	C₈	semidirect
52. C₃×#324	C₂×C₅	semidirect
53. #4528	C₂×C₅	semidirect
54. #4469	C₂×C₅	semidirect
81. C₂×C₃×C₄×C₅	C₂×C₈	semidirect
89. C₂×C₅×Dic₃	C₂×C₈	semidirect
139. #324	C₅×D₃	direct (N × H)
173. C₂×C₄×D₃	C₅×C₈	semidirect
208. C₂×C₄×C₅	D₃×C₈	semidirect
231. C₅×D₃	#324	direct (N × H)
244. C₂×C₃×C₄	C₂×C₅×C₈	semidirect
252. C₂×Dic₃	C₂×C₅×C₈	semidirect
304. C₃×C₅	C₂×#324	semidirect
356. C₂×C₄	C₅×D₃×C₈	semidirect
366. D₃	C₅×#324	direct (N × H)
367. C₅	D₃×#324	direct (N × H)
387. C₃	C₂×C₅×#324	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
C₅×D₃×C₂²⋊C₈	2
C₃×C₅×#324	2
C₅×#4528	2
C₅×#4469	2
C₂×C₅×#324	3
D₃×#324	5

Subgroups — C5×D3×#324 #14280765

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#324 #14280765