Subgroups — C₃×#65970 #11755647

Order 960.

456 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	C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#4092	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#4090	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic
5	C₂×C₃×#683	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4042	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#4042	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×D₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#4035	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#4035	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#4033	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#4027	C₂	1	1	yes	maximal, characteristic
13	C₃×#4027	C₂	1	1	yes	maximal, characteristic
14	C₃×#4024	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#4024	C₂	1	1	yes	maximal, characteristic, complemented
16	#65970	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic
20	C₂²×C₃×Dic₅	C₂²	1	1	yes	characteristic
21	C₂²×C₃×Dic₅	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
25	C₂×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
26	C₂×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
27	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₃×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic
33	C₃×#685	C₂²	1	1	yes	characteristic
34	C₃×#685	C₂²	1	1	yes	characteristic
35	C₃×#685	C₂²	1	1	yes	characteristic
36	C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
37	C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
38	C₃×#683	C₂²	1	1	yes	characteristic
39	C₃×#683	C₂²	1	1	yes	characteristic
40	C₃×#683	C₂²	1	1	yes	characteristic
41	C₃×#683	C₂²	1	1	yes	characteristic
42	C₃×#683	C₂²	1	1	yes	characteristic
43	C₃×#683	C₂²	1	1	yes	characteristic
44	C₃×#683	C₂²	1	1	yes	characteristic
45	C₃×#683	C₂²	1	1	yes	characteristic
46	C₃×#683	C₂²	1	1	yes	characteristic
47	C₃×#683	C₂²	1	1	yes	characteristic
48	C₃×#683	C₂²	1	1	yes	characteristic
49	C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
50	C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
51	C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
52	C₃×#554	—	5	1	no	maximal, Hall
53	C₅×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
54	#4092	C₂×C₃	1	1	yes	characteristic, complemented
55	#4090	C₂×C₃	1	1	yes	characteristic, complemented
56	C₄×C₂²⋊D₅	C₂×C₃	1	1	yes	characteristic
57	C₂×#683	C₂×C₃	1	1	yes	characteristic, complemented
58	#4042	C₂×C₃	1	1	yes	characteristic, complemented
59	#4042	C₂×C₃	1	1	yes	characteristic, complemented
60	D₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
61	#4035	C₂×C₃	1	1	yes	characteristic, complemented
62	#4035	C₂×C₃	1	1	yes	characteristic, complemented
63	#4033	C₂×C₃	1	1	yes	characteristic, complemented
64	#4027	C₂×C₃	1	1	yes	characteristic
65	#4027	C₂×C₃	1	1	yes	characteristic
66	#4024	C₂×C₃	1	1	yes	characteristic, complemented
67	#4024	C₂×C₃	1	1	yes	characteristic, complemented
68	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
69	C₂²×C₃×D₅	C₂³	1	1	yes	characteristic
70	C₃×C₅×Q₈	—	4	1	no	—
71	C₂×C₃×C₄×C₅	—	4	1	no	—
72	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
73	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
74	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
75	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
76	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
77	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
78	C₃×C₂²⋊D₅	Q₈	1	4	yes	complemented
79	C₂×C₃×Dic₅	—	2	2	no	—
80	C₂×C₃×Dic₅	—	4	1	no	—
81	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
82	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
83	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
84	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
85	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
86	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
87	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
88	C₃×C₄×D₅	—	2	2	no	—
89	C₃×C₄×D₅	—	4	1	no	—
90	C₃×C₄×D₅	—	4	1	no	—
91	C₃×Dic₁₀	—	2	2	no	—
92	C₃×Dic₁₀	—	4	1	no	—
93	C₃×C₄⋊Q₈	—	5	1	no	—
94	C₃×#125	—	5	1	no	—
95	C₃×#125	—	5	1	no	—
96	C₃×C₂²⋊Q₈	—	5	1	no	—
97	C₃×C₂²⋊Q₈	—	5	1	no	—
98	C₃×C₂²⋊Q₈	—	5	1	no	—
99	C₃×C₂²⋊Q₈	—	5	1	no	—
100	C₃×C₂²⋊Q₈	—	5	1	no	—
101	C₃×C₂²⋊Q₈	D₅	1	1	yes	characteristic, complemented
102	C₃×C₄×Q₈	—	5	1	no	—
103	C₃×C₄×D₄	—	5	1	no	—
104	C₃×C₄×D₄	—	5	1	no	—
105	C₃×C₄×D₄	—	5	1	no	—
106	C₂×C₃×C₄⋊C₄	—	5	1	no	—
107	C₂×C₃×C₄⋊C₄	—	5	1	no	—
108	C₂×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
109	C₂²×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
110	C₂×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
111	C₂²×Dic₅	C₂²×C₃	1	1	yes	characteristic
112	C₂²×Dic₅	C₂²×C₃	1	1	yes	characteristic
113	C₂×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
114	C₂×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
115	C₂×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
116	C₂×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
117	C₂×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
118	C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
119	C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
120	C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
121	C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
122	C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
123	C₂²⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
124	#685	C₂²×C₃	1	1	yes	characteristic
125	#685	C₂²×C₃	1	1	yes	characteristic
126	#685	C₂²×C₃	1	1	yes	characteristic
127	C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
128	C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
129	#683	C₂²×C₃	1	1	yes	characteristic
130	#683	C₂²×C₃	1	1	yes	characteristic
131	#683	C₂²×C₃	1	1	yes	characteristic
132	#683	C₂²×C₃	1	1	yes	characteristic
133	#683	C₂²×C₃	1	1	yes	characteristic
134	#683	C₂²×C₃	1	1	yes	characteristic
135	#683	C₂²×C₃	1	1	yes	characteristic
136	#683	C₂²×C₃	1	1	yes	characteristic
137	#683	C₂²×C₃	1	1	yes	characteristic
138	#683	C₂²×C₃	1	1	yes	characteristic
139	#683	C₂²×C₃	1	1	yes	characteristic
140	C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
141	C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
142	C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
143	#554	—	5	1	no	Sylow
144	C₂²×C₃×C₅	—	2	1	no	—
145	C₂²×C₃×C₅	—	2	1	no	—
146	C₂²×C₃×C₅	C₂×Q₈	1	2	yes	—
147	C₂²×C₃×C₅	C₂⁴	1	1	yes	characteristic
148	C₂×C₃×D₅	—	2	1	no	—
149	C₂×C₃×D₅	—	2	1	no	—
150	C₂×C₃×D₅	C₂×Q₈	1	2	yes	—
151	C₃×C₄×C₅	—	2	1	no	—
152	C₃×C₄×C₅	—	2	1	no	—
153	C₃×C₄×C₅	—	2	1	no	—
154	C₃×C₄×C₅	—	2	1	no	—
155	C₃×C₄×C₅	—	2	1	no	—
156	C₃×C₄×C₅	—	2	1	no	—
157	C₃×Dic₅	—	2	1	no	—
158	C₃×Dic₅	—	2	1	no	—
159	C₃×Dic₅	—	2	1	no	—
160	C₃×Dic₅	—	2	1	no	—
161	C₃×Dic₅	—	2	1	no	—
162	C₃×Dic₅	C₂×Q₈	1	2	yes	—
163	C₃×Dic₅	#41	1	2	yes	—
164	C₂×C₃×Q₈	—	5	1	no	—
165	C₂×C₃×Q₈	—	5	1	no	—
166	C₂×C₃×Q₈	C₂×D₅	1	1	yes	characteristic
167	C₂×C₃×D₄	—	5	1	no	—
168	C₂²×C₃×C₄	—	5	1	no	—
169	C₂²×C₃×C₄	—	5	1	no	—
170	C₂²×C₃×C₄	—	5	1	no	—
171	C₂²×C₃×C₄	—	5	1	no	—
172	C₂²×C₃×C₄	—	5	1	no	—
173	C₂²×C₃×C₄	C₂×D₅	1	1	yes	characteristic
174	C₃×C₄⋊C₄	—	5	1	no	—
175	C₃×C₄⋊C₄	—	5	1	no	—
176	C₃×C₄⋊C₄	—	5	1	no	—
177	C₃×C₄⋊C₄	—	5	1	no	—
178	C₃×C₄⋊C₄	—	5	1	no	—
179	C₃×C₄⋊C₄	—	5	1	no	—
180	C₃×C₄⋊C₄	—	5	1	no	—
181	C₃×C₄⋊C₄	—	5	1	no	—
182	C₃×C₄⋊C₄	—	5	1	no	—
183	C₃×C₄⋊C₄	—	5	1	no	—
184	C₃×C₄⋊C₄	—	5	1	no	—
185	C₃×C₄⋊C₄	—	5	1	no	—
186	C₃×C₄⋊C₄	—	5	1	no	—
187	C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
188	C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
189	C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
190	C₃×C₂²⋊C₄	—	5	1	no	—
191	C₃×C₂²⋊C₄	—	5	1	no	—
192	C₃×C₂²⋊C₄	—	5	1	no	—
193	C₃×C₂²⋊C₄	—	5	1	no	—
194	C₃×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
195	C₃×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
196	C₃×C₄²	—	5	1	no	—
197	C₃×C₄²	—	5	1	no	—
198	C₃×C₄²	—	5	1	no	—
199	C₂³×C₅	C₂³×C₃	1	1	yes	characteristic
200	C₂²×D₅	C₂³×C₃	1	1	yes	characteristic
201	C₅×Q₈	—	4	1	no	—
202	C₂×C₄×C₅	—	4	1	no	—
203	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
204	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
205	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
206	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
207	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
208	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
209	C₂²⋊D₅	C₃×Q₈	1	4	yes	complemented
210	C₂×Dic₅	—	2	2	no	—
211	C₂×Dic₅	—	4	1	no	—
212	C₂×Dic₅	C₂³×C₃	1	1	yes	characteristic
213	C₂×Dic₅	C₂³×C₃	1	1	yes	characteristic
214	C₂×Dic₅	C₂³×C₃	1	1	yes	characteristic
215	C₂×Dic₅	C₂³×C₃	1	1	yes	characteristic
216	C₂×Dic₅	C₂³×C₃	1	1	yes	characteristic
217	C₂×Dic₅	C₂³×C₃	1	1	yes	characteristic
218	C₂×Dic₅	C₂³×C₃	1	1	yes	characteristic
219	C₄×D₅	—	2	2	no	—
220	C₄×D₅	—	4	1	no	—
221	C₄×D₅	—	4	1	no	—
222	Dic₁₀	—	2	2	no	—
223	Dic₁₀	—	4	1	no	—
224	C₄⋊Q₈	—	5	1	no	—
225	#125	—	5	1	no	—
226	#125	—	5	1	no	—
227	C₂²⋊Q₈	—	5	1	no	—
228	C₂²⋊Q₈	—	5	1	no	—
229	C₂²⋊Q₈	—	5	1	no	—
230	C₂²⋊Q₈	—	5	1	no	—
231	C₂²⋊Q₈	—	5	1	no	—
232	C₂²⋊Q₈	C₃×D₅	1	1	yes	characteristic, complemented
233	C₄×Q₈	—	5	1	no	—
234	C₄×D₄	—	5	1	no	—
235	C₄×D₄	—	5	1	no	—
236	C₄×D₄	—	5	1	no	—
237	C₂×C₄⋊C₄	—	5	1	no	—
238	C₂×C₄⋊C₄	—	5	1	no	—
239	C₂×C₃×C₅	—	2	2	no	—
240	C₂×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
241	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
242	C₂×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
243	C₃×D₅	—	2	2	no	—
244	C₂³×C₃	—	5	1	no	—
245	C₂³×C₃	C₂²×D₅	1	1	yes	characteristic
246	C₃×Q₈	—	4	1	no	—
247	C₃×Q₈	—	10	2	no	—
248	C₃×Q₈	—	20	1	no	—
249	C₃×D₄	—	5	4	no	—
250	C₂×C₃×C₄	—	4	1	no	—
251	C₂×C₃×C₄	—	5	1	no	—
252	C₂×C₃×C₄	—	5	1	no	—
253	C₂×C₃×C₄	—	5	1	no	—
254	C₂×C₃×C₄	—	5	1	no	—
255	C₂×C₃×C₄	—	5	1	no	—
256	C₂×C₃×C₄	—	5	1	no	—
257	C₂×C₃×C₄	—	5	1	no	—
258	C₂×C₃×C₄	—	10	2	no	—
259	C₂×C₃×C₄	—	10	2	no	—
260	C₂×C₃×C₄	—	20	1	no	—
261	C₂×C₃×C₄	—	20	1	no	—
262	C₂×C₃×C₄	—	20	1	no	—
263	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
264	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
265	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
266	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
267	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
268	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
269	C₂²×C₅	—	2	1	no	—
270	C₂²×C₅	—	2	1	no	—
271	C₂²×C₅	C₂×C₃×Q₈	1	2	yes	—
272	C₂²×C₅	C₂⁴×C₃	1	1	yes	characteristic
273	C₂×D₅	—	2	1	no	—
274	C₂×D₅	—	2	1	no	—
275	C₂×D₅	C₂×C₃×Q₈	1	2	yes	—
276	C₄×C₅	—	2	1	no	—
277	C₄×C₅	—	2	1	no	—
278	C₄×C₅	—	2	1	no	—
279	C₄×C₅	—	2	1	no	—
280	C₄×C₅	—	2	1	no	—
281	C₄×C₅	—	2	1	no	—
282	Dic₅	—	2	1	no	—
283	Dic₅	—	2	1	no	—
284	Dic₅	—	2	1	no	—
285	Dic₅	—	2	1	no	—
286	Dic₅	—	2	1	no	—
287	Dic₅	C₂×C₃×Q₈	1	2	yes	—
288	Dic₅	C₃×#41	1	2	yes	—
289	C₂×Q₈	—	5	1	no	—
290	C₂×Q₈	—	5	1	no	—
291	C₂×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
292	C₂×D₄	—	5	1	no	—
293	C₂²×C₄	—	5	1	no	—
294	C₂²×C₄	—	5	1	no	—
295	C₂²×C₄	—	5	1	no	—
296	C₂²×C₄	—	5	1	no	—
297	C₂²×C₄	—	5	1	no	—
298	C₂²×C₄	C₂×C₃×D₅	1	1	yes	characteristic
299	C₄⋊C₄	—	5	1	no	—
300	C₄⋊C₄	—	5	1	no	—
301	C₄⋊C₄	—	5	1	no	—
302	C₄⋊C₄	—	5	1	no	—
303	C₄⋊C₄	—	5	1	no	—
304	C₄⋊C₄	—	5	1	no	—
305	C₄⋊C₄	—	5	1	no	—
306	C₄⋊C₄	—	5	1	no	—
307	C₄⋊C₄	—	5	1	no	—
308	C₄⋊C₄	—	5	1	no	—
309	C₄⋊C₄	—	5	1	no	—
310	C₄⋊C₄	—	5	1	no	—
311	C₄⋊C₄	—	5	1	no	—
312	C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
313	C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
314	C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
315	C₂²⋊C₄	—	5	1	no	—
316	C₂²⋊C₄	—	5	1	no	—
317	C₂²⋊C₄	—	5	1	no	—
318	C₂²⋊C₄	—	5	1	no	—
319	C₂²⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
320	C₂²⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
321	C₄²	—	5	1	no	—
322	C₄²	—	5	1	no	—
323	C₄²	—	5	1	no	—
324	C₃×C₅	#554	1	1	yes	characteristic, complemented, Hall
325	C₂²×C₃	—	2	1	no	—
326	C₂²×C₃	—	2	1	no	—
327	C₂²×C₃	—	5	2	no	—
328	C₂²×C₃	—	10	1	no	—
329	C₂²×C₃	—	10	1	no	—
330	C₂²×C₃	Q₈×D₅	1	2	yes	—
331	C₂²×C₃	C₂³×D₅	1	1	yes	characteristic
332	C₃×C₄	—	2	1	no	—
333	C₃×C₄	—	2	1	no	—
334	C₃×C₄	—	2	1	no	—
335	C₃×C₄	—	2	1	no	—
336	C₃×C₄	—	2	1	no	—
337	C₃×C₄	—	2	1	no	—
338	C₃×C₄	—	5	2	no	—
339	C₃×C₄	—	5	2	no	—
340	C₃×C₄	—	10	1	no	—
341	C₃×C₄	—	10	1	no	—
342	C₃×C₄	—	10	1	no	—
343	C₃×C₄	—	10	1	no	—
344	C₃×C₄	—	10	1	no	—
345	C₂×C₅	—	2	2	no	—
346	C₂×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
347	C₂×C₅	C₂×C₃×#41	1	1	yes	characteristic
348	C₂×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
349	D₅	—	2	2	no	—
350	C₂³	—	5	1	no	—
351	C₂³	C₂²×C₃×D₅	1	1	yes	characteristic
352	Q₈	—	4	1	no	—
353	Q₈	—	10	2	no	—
354	Q₈	—	20	1	no	—
355	D₄	—	5	4	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	5	1	no	—
358	C₂×C₄	—	5	1	no	—
359	C₂×C₄	—	5	1	no	—
360	C₂×C₄	—	5	1	no	—
361	C₂×C₄	—	5	1	no	—
362	C₂×C₄	—	5	1	no	—
363	C₂×C₄	—	5	1	no	—
364	C₂×C₄	—	10	2	no	—
365	C₂×C₄	—	10	2	no	—
366	C₂×C₄	—	20	1	no	—
367	C₂×C₄	—	20	1	no	—
368	C₂×C₄	—	20	1	no	—
369	C₂×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
370	C₂×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
371	C₂×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
372	C₂×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
373	C₂×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
374	C₂×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
375	C₂×C₃	—	2	2	no	—
376	C₂×C₃	—	10	2	no	—
377	C₂×C₃	#4144	1	1	yes	characteristic
378	C₂×C₃	C₂×Q₈×D₅	1	1	yes	characteristic
379	C₂×C₃	D₅×#41	1	1	yes	characteristic
380	C₅	C₃×#554	1	1	yes	characteristic, complemented, Sylow
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	5	2	no	—
384	C₂²	—	10	1	no	—
385	C₂²	—	10	1	no	—
386	C₂²	C₃×Q₈×D₅	1	2	yes	—
387	C₂²	C₂³×C₃×D₅	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	5	2	no	—
395	C₄	—	5	2	no	—
396	C₄	—	10	1	no	—
397	C₄	—	10	1	no	—
398	C₄	—	10	1	no	—
399	C₄	—	10	1	no	—
400	C₄	—	10	1	no	—
401	C₃	#65970	1	1	yes	characteristic, direct product factor, Sylow
402	C₂	—	2	2	no	—
403	C₂	—	10	2	no	—
404	C₂	C₃×#4144	1	1	yes	characteristic
405	C₂	C₂×C₃×Q₈×D₅	1	1	yes	characteristic
406	C₂	C₃×D₅×#41	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×D₅
Fitting	C₃×C₅×C₂²⋊Q₈	C₂
socle	C₂²×C₃×C₅	C₂⁴
prime radical	C₂×C₃×C₂²⋊D₅	C₂²
hypercenter	C₃×C₂²⋊Q₈	D₅
hypocenter	C₅	C₃×#554
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₂²⋊Q₈	C₂	semidirect
2. C₃×#4092	C₂	semidirect
3. C₃×#4090	C₂	semidirect
5. C₂×C₃×#683	C₂	semidirect
6. C₃×#4042	C₂	semidirect
7. C₃×#4042	C₂	semidirect
8. C₃×D₅×C₄⋊C₄	C₂	semidirect
9. C₃×#4035	C₂	semidirect
10. C₃×#4035	C₂	semidirect
11. C₃×#4033	C₂	semidirect
14. C₃×#4024	C₂	semidirect
15. C₃×#4024	C₂	semidirect
16. #65970	C₃	direct (N × H)
53. C₅×C₂²⋊Q₈	C₂×C₃	semidirect
54. #4092	C₂×C₃	semidirect
55. #4090	C₂×C₃	semidirect
57. C₂×#683	C₂×C₃	semidirect
58. #4042	C₂×C₃	semidirect
59. #4042	C₂×C₃	semidirect
60. D₅×C₄⋊C₄	C₂×C₃	semidirect
61. #4035	C₂×C₃	semidirect
62. #4035	C₂×C₃	semidirect
63. #4033	C₂×C₃	semidirect
66. #4024	C₂×C₃	semidirect
67. #4024	C₂×C₃	semidirect
78. C₃×C₂²⋊D₅	Q₈	semidirect
101. C₃×C₂²⋊Q₈	D₅	semidirect
209. C₂²⋊D₅	C₃×Q₈	semidirect
232. C₂²⋊Q₈	C₃×D₅	semidirect
324. C₃×C₅	#554	semidirect
380. C₅	C₃×#554	semidirect
401. C₃	#65970	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×C₂²⋊Q₈	2
C₃×#4092	2
C₃×#4090	2
C₃×C₄×C₂²⋊D₅	2
C₂×C₃×#683	2
C₃×#4042	2
C₃×D₅×C₄⋊C₄	2
C₃×#4035	2
C₃×#4033	2
C₃×#4027	2
C₃×#4024	2
#65970	3
C₃×#554	5

Subgroups — C3×#65970 #11755647

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#65970 #11755647