Subgroups — C₃×#65971 #11755648

Order 960.

496 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	C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#4093	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#4092	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#685	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4044	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#4044	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4040	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#4040	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#4039	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#4038	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#4032	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#4028	C₂	1	1	yes	maximal, characteristic
14	C₃×D₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#4023	C₂	1	1	yes	maximal, characteristic, complemented
16	#65971	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂³×C₃×D₅	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic
21	C₂²×C₃×Dic₅	C₂²	1	1	yes	characteristic
22	C₂×C₃×D₂₀	C₂²	1	1	yes	characteristic
23	C₂×C₃×D₂₀	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₄×D₅	C₂²	1	1	yes	characteristic, complemented
27	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
28	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
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×#685	C₂²	1	1	yes	characteristic
37	C₃×#685	C₂²	1	1	yes	characteristic
38	C₃×#685	C₂²	1	1	yes	characteristic
39	C₃×#685	C₂²	1	1	yes	characteristic
40	C₃×#685	C₂²	1	1	yes	characteristic
41	C₃×#685	C₂²	1	1	yes	characteristic, complemented
42	C₃×#685	C₂²	1	1	yes	characteristic, complemented
43	C₃×#685	C₂²	1	1	yes	characteristic, complemented
44	C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
45	C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
46	C₃×#683	C₂²	1	1	yes	characteristic, complemented
47	C₃×#683	C₂²	1	1	yes	characteristic, complemented
48	C₃×#683	C₂²	1	1	yes	characteristic, complemented
49	C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
50	C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
51	C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
52	C₃×#551	—	5	1	no	maximal, Hall
53	C₅×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
54	#4093	C₂×C₃	1	1	yes	characteristic, complemented
55	#4092	C₂×C₃	1	1	yes	characteristic, complemented
56	C₄×C₂²⋊D₅	C₂×C₃	1	1	yes	characteristic, complemented
57	C₂×#685	C₂×C₃	1	1	yes	characteristic, complemented
58	#4044	C₂×C₃	1	1	yes	characteristic, complemented
59	#4044	C₂×C₃	1	1	yes	characteristic, complemented
60	#4040	C₂×C₃	1	1	yes	characteristic, complemented
61	#4040	C₂×C₃	1	1	yes	characteristic, complemented
62	#4039	C₂×C₃	1	1	yes	characteristic, complemented
63	#4038	C₂×C₃	1	1	yes	characteristic, complemented
64	#4032	C₂×C₃	1	1	yes	characteristic, complemented
65	#4028	C₂×C₃	1	1	yes	characteristic
66	D₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
67	#4023	C₂×C₃	1	1	yes	characteristic, complemented
68	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
69	C₂²×C₃×D₅	—	2	2	no	—
70	C₂²×C₃×D₅	—	2	2	no	—
71	C₂²×C₃×D₅	—	4	1	no	—
72	C₂²×C₃×D₅	C₂³	1	1	yes	characteristic
73	C₂²×C₃×D₅	C₂³	1	1	yes	characteristic
74	C₂²×C₃×D₅	C₂³	1	1	yes	characteristic
75	C₃×C₅×Q₈	—	4	1	no	—
76	C₂×C₃×C₄×C₅	—	4	1	no	—
77	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
78	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
79	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
80	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
81	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
82	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
83	C₃×C₂²⋊D₅	—	2	2	no	—
84	C₂×C₃×Dic₅	—	2	2	no	—
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	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
89	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
90	C₃×D₂₀	—	2	2	no	—
91	C₃×D₂₀	—	4	1	no	—
92	C₃×C₄×D₅	—	2	2	no	—
93	C₃×C₄×D₅	—	4	1	no	—
94	C₃×C₄×D₅	—	4	1	no	—
95	C₃×#126	—	5	1	no	—
96	C₃×#126	—	5	1	no	—
97	C₃×#124	—	5	1	no	—
98	C₃×#123	—	5	1	no	—
99	C₃×#123	—	5	1	no	—
100	C₃×#123	—	5	1	no	—
101	C₃×C₂²⋊Q₈	—	5	1	no	—
102	C₃×C₂²⋊Q₈	D₅	1	1	yes	characteristic, complemented
103	C₃×#120	—	5	1	no	—
104	C₃×C₄×D₄	—	5	1	no	—
105	C₃×C₄×D₄	—	5	1	no	—
106	C₃×#117	—	5	1	no	—
107	C₃×#117	—	5	1	no	—
108	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
109	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
110	C₂³×D₅	C₂²×C₃	1	1	yes	characteristic
111	C₂×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
112	C₂²×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
113	C₂×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
114	C₂²×Dic₅	C₂²×C₃	1	1	yes	characteristic
115	C₂×D₂₀	C₂²×C₃	1	1	yes	characteristic
116	C₂×D₂₀	C₂²×C₃	1	1	yes	characteristic
117	C₂×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
118	C₂×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
119	C₂×C₄×D₅	C₂²×C₃	1	1	yes	characteristic, complemented
120	C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
121	C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
122	C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
123	C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
124	C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
125	C₂²⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
126	#685	C₂²×C₃	1	1	yes	characteristic
127	#685	C₂²×C₃	1	1	yes	characteristic
128	#685	C₂²×C₃	1	1	yes	characteristic
129	#685	C₂²×C₃	1	1	yes	characteristic
130	#685	C₂²×C₃	1	1	yes	characteristic
131	#685	C₂²×C₃	1	1	yes	characteristic
132	#685	C₂²×C₃	1	1	yes	characteristic
133	#685	C₂²×C₃	1	1	yes	characteristic
134	#685	C₂²×C₃	1	1	yes	characteristic, complemented
135	#685	C₂²×C₃	1	1	yes	characteristic, complemented
136	#685	C₂²×C₃	1	1	yes	characteristic, complemented
137	C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
138	C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
139	#683	C₂²×C₃	1	1	yes	characteristic, complemented
140	#683	C₂²×C₃	1	1	yes	characteristic, complemented
141	#683	C₂²×C₃	1	1	yes	characteristic, complemented
142	C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
143	C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
144	C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
145	#551	—	5	1	no	Sylow
146	C₂²×C₃×C₅	—	2	1	no	—
147	C₂²×C₃×C₅	—	2	1	no	—
148	C₂²×C₃×C₅	#41	1	2	yes	—
149	C₂²×C₃×C₅	C₂⁴	1	1	yes	characteristic
150	C₂×C₃×D₅	—	2	1	no	—
151	C₂×C₃×D₅	—	2	1	no	—
152	C₂×C₃×D₅	—	2	1	no	—
153	C₂×C₃×D₅	—	2	1	no	—
154	C₂×C₃×D₅	—	2	1	no	—
155	C₂×C₃×D₅	—	2	1	no	—
156	C₂×C₃×D₅	—	2	1	no	—
157	C₂×C₃×D₅	—	2	1	no	—
158	C₂×C₃×D₅	—	4	4	no	—
159	C₂×C₃×D₅	#41	1	2	yes	—
160	C₃×C₄×C₅	—	2	1	no	—
161	C₃×C₄×C₅	—	2	1	no	—
162	C₃×C₄×C₅	—	2	1	no	—
163	C₃×C₄×C₅	—	2	1	no	—
164	C₃×C₄×C₅	—	2	1	no	—
165	C₃×C₄×C₅	—	2	1	no	—
166	C₃×Dic₅	—	2	1	no	—
167	C₃×Dic₅	—	2	1	no	—
168	C₃×Dic₅	—	2	1	no	—
169	C₃×Dic₅	—	2	1	no	—
170	C₃×Dic₅	—	2	1	no	—
171	C₂⁴×C₃	—	5	1	no	—
172	C₂×C₃×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
173	C₂×C₃×D₄	—	5	1	no	—
174	C₂×C₃×D₄	—	5	1	no	—
175	C₂×C₃×D₄	—	5	1	no	—
176	C₂²×C₃×C₄	—	5	1	no	—
177	C₂²×C₃×C₄	—	5	1	no	—
178	C₂²×C₃×C₄	—	5	1	no	—
179	C₂²×C₃×C₄	—	5	1	no	—
180	C₂²×C₃×C₄	C₂×D₅	1	1	yes	characteristic
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	C₂×D₅	1	1	yes	characteristic, complemented
187	C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
188	C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
189	C₃×C₂²⋊C₄	—	5	1	no	—
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	—	5	1	no	—
195	C₃×C₂²⋊C₄	—	5	1	no	—
196	C₃×C₂²⋊C₄	—	5	1	no	—
197	C₃×C₂²⋊C₄	—	5	1	no	—
198	C₃×C₂²⋊C₄	—	5	1	no	—
199	C₃×C₂²⋊C₄	—	5	1	no	—
200	C₃×C₂²⋊C₄	—	5	1	no	—
201	C₃×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
202	C₃×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
203	C₃×C₄²	—	5	1	no	—
204	C₃×C₄²	—	5	1	no	—
205	C₃×C₄²	—	5	1	no	—
206	C₂³×C₅	C₂³×C₃	1	1	yes	characteristic
207	C₂²×D₅	—	2	2	no	—
208	C₂²×D₅	—	2	2	no	—
209	C₂²×D₅	—	4	1	no	—
210	C₂²×D₅	C₂³×C₃	1	1	yes	characteristic
211	C₂²×D₅	C₂³×C₃	1	1	yes	characteristic
212	C₂²×D₅	C₂³×C₃	1	1	yes	characteristic
213	C₅×Q₈	—	4	1	no	—
214	C₂×C₄×C₅	—	4	1	no	—
215	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
216	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
217	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
218	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
219	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
220	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
221	C₂²⋊D₅	—	2	2	no	—
222	C₂×Dic₅	—	2	2	no	—
223	C₂×Dic₅	C₂³×C₃	1	1	yes	characteristic
224	C₂×Dic₅	C₂³×C₃	1	1	yes	characteristic
225	C₂×Dic₅	C₂³×C₃	1	1	yes	characteristic
226	C₂×Dic₅	C₂³×C₃	1	1	yes	characteristic
227	C₂×Dic₅	C₂³×C₃	1	1	yes	characteristic
228	D₂₀	—	2	2	no	—
229	D₂₀	—	4	1	no	—
230	C₄×D₅	—	2	2	no	—
231	C₄×D₅	—	4	1	no	—
232	C₄×D₅	—	4	1	no	—
233	#126	—	5	1	no	—
234	#126	—	5	1	no	—
235	#124	—	5	1	no	—
236	#123	—	5	1	no	—
237	#123	—	5	1	no	—
238	#123	—	5	1	no	—
239	C₂²⋊Q₈	—	5	1	no	—
240	C₂²⋊Q₈	C₃×D₅	1	1	yes	characteristic, complemented
241	#120	—	5	1	no	—
242	C₄×D₄	—	5	1	no	—
243	C₄×D₄	—	5	1	no	—
244	#117	—	5	1	no	—
245	#117	—	5	1	no	—
246	C₂×C₂²⋊C₄	—	5	1	no	—
247	C₂×C₂²⋊C₄	—	5	1	no	—
248	C₂×C₃×C₅	—	2	2	no	—
249	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
250	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
251	C₂×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
252	C₃×D₅	—	2	2	no	—
253	C₃×D₅	—	4	1	no	—
254	C₃×D₅	—	4	1	no	—
255	C₂³×C₃	—	5	1	no	—
256	C₂³×C₃	—	5	1	no	—
257	C₂³×C₃	—	5	1	no	—
258	C₂³×C₃	—	10	2	no	—
259	C₂³×C₃	—	10	2	no	—
260	C₂³×C₃	—	20	1	no	—
261	C₂³×C₃	C₂²×D₅	1	1	yes	characteristic
262	C₃×Q₈	—	4	1	no	—
263	C₃×D₄	—	10	2	no	—
264	C₃×D₄	—	10	2	no	—
265	C₃×D₄	—	20	1	no	—
266	C₂×C₃×C₄	—	4	1	no	—
267	C₂×C₃×C₄	—	5	1	no	—
268	C₂×C₃×C₄	—	5	1	no	—
269	C₂×C₃×C₄	—	5	1	no	—
270	C₂×C₃×C₄	—	5	1	no	—
271	C₂×C₃×C₄	—	5	1	no	—
272	C₂×C₃×C₄	—	10	2	no	—
273	C₂×C₃×C₄	—	10	2	no	—
274	C₂×C₃×C₄	—	20	1	no	—
275	C₂×C₃×C₄	—	20	1	no	—
276	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
277	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
278	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
279	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
280	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
281	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
282	C₂²×C₅	—	2	1	no	—
283	C₂²×C₅	—	2	1	no	—
284	C₂²×C₅	C₃×#41	1	2	yes	—
285	C₂²×C₅	C₂⁴×C₃	1	1	yes	characteristic
286	C₂×D₅	—	2	1	no	—
287	C₂×D₅	—	2	1	no	—
288	C₂×D₅	—	2	1	no	—
289	C₂×D₅	—	2	1	no	—
290	C₂×D₅	—	2	1	no	—
291	C₂×D₅	—	2	1	no	—
292	C₂×D₅	—	2	1	no	—
293	C₂×D₅	—	2	1	no	—
294	C₂×D₅	—	4	4	no	—
295	C₂×D₅	C₃×#41	1	2	yes	—
296	C₄×C₅	—	2	1	no	—
297	C₄×C₅	—	2	1	no	—
298	C₄×C₅	—	2	1	no	—
299	C₄×C₅	—	2	1	no	—
300	C₄×C₅	—	2	1	no	—
301	C₄×C₅	—	2	1	no	—
302	Dic₅	—	2	1	no	—
303	Dic₅	—	2	1	no	—
304	Dic₅	—	2	1	no	—
305	Dic₅	—	2	1	no	—
306	Dic₅	—	2	1	no	—
307	C₂⁴	—	5	1	no	—
308	C₂×Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
309	C₂×D₄	—	5	1	no	—
310	C₂×D₄	—	5	1	no	—
311	C₂×D₄	—	5	1	no	—
312	C₂²×C₄	—	5	1	no	—
313	C₂²×C₄	—	5	1	no	—
314	C₂²×C₄	—	5	1	no	—
315	C₂²×C₄	—	5	1	no	—
316	C₂²×C₄	C₂×C₃×D₅	1	1	yes	characteristic
317	C₄⋊C₄	—	5	1	no	—
318	C₄⋊C₄	—	5	1	no	—
319	C₄⋊C₄	—	5	1	no	—
320	C₄⋊C₄	—	5	1	no	—
321	C₄⋊C₄	—	5	1	no	—
322	C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
323	C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
324	C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
325	C₂²⋊C₄	—	5	1	no	—
326	C₂²⋊C₄	—	5	1	no	—
327	C₂²⋊C₄	—	5	1	no	—
328	C₂²⋊C₄	—	5	1	no	—
329	C₂²⋊C₄	—	5	1	no	—
330	C₂²⋊C₄	—	5	1	no	—
331	C₂²⋊C₄	—	5	1	no	—
332	C₂²⋊C₄	—	5	1	no	—
333	C₂²⋊C₄	—	5	1	no	—
334	C₂²⋊C₄	—	5	1	no	—
335	C₂²⋊C₄	—	5	1	no	—
336	C₂²⋊C₄	—	5	1	no	—
337	C₂²⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
338	C₂²⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
339	C₄²	—	5	1	no	—
340	C₄²	—	5	1	no	—
341	C₄²	—	5	1	no	—
342	C₃×C₅	#551	1	1	yes	characteristic, complemented, Hall
343	C₂²×C₃	—	2	1	no	—
344	C₂²×C₃	—	2	1	no	—
345	C₂²×C₃	—	5	2	no	—
346	C₂²×C₃	—	10	1	no	—
347	C₂²×C₃	—	10	1	no	—
348	C₂²×C₃	—	10	1	no	—
349	C₂²×C₃	—	10	1	no	—
350	C₂²×C₃	—	10	1	no	—
351	C₂²×C₃	—	10	1	no	—
352	C₂²×C₃	—	10	1	no	—
353	C₂²×C₃	—	10	1	no	—
354	C₂²×C₃	—	20	4	no	—
355	C₂²×C₃	#713	1	2	yes	—
356	C₂²×C₃	C₂³×D₅	1	1	yes	characteristic
357	C₃×C₄	—	2	1	no	—
358	C₃×C₄	—	2	1	no	—
359	C₃×C₄	—	2	1	no	—
360	C₃×C₄	—	2	1	no	—
361	C₃×C₄	—	2	1	no	—
362	C₃×C₄	—	2	1	no	—
363	C₃×C₄	—	10	1	no	—
364	C₃×C₄	—	10	1	no	—
365	C₃×C₄	—	10	1	no	—
366	C₃×C₄	—	10	1	no	—
367	C₃×C₄	—	10	1	no	—
368	C₂×C₅	—	2	2	no	—
369	C₂×C₅	C₂×C₃×#41	1	1	yes	characteristic
370	C₂×C₅	C₂×C₃×#41	1	1	yes	characteristic
371	C₂×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
372	D₅	—	2	2	no	—
373	D₅	—	4	1	no	—
374	D₅	—	4	1	no	—
375	C₂³	—	5	1	no	—
376	C₂³	—	5	1	no	—
377	C₂³	—	5	1	no	—
378	C₂³	—	10	2	no	—
379	C₂³	—	10	2	no	—
380	C₂³	—	20	1	no	—
381	C₂³	C₂²×C₃×D₅	1	1	yes	characteristic
382	Q₈	—	4	1	no	—
383	D₄	—	10	2	no	—
384	D₄	—	10	2	no	—
385	D₄	—	20	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	5	1	no	—
388	C₂×C₄	—	5	1	no	—
389	C₂×C₄	—	5	1	no	—
390	C₂×C₄	—	5	1	no	—
391	C₂×C₄	—	5	1	no	—
392	C₂×C₄	—	10	2	no	—
393	C₂×C₄	—	10	2	no	—
394	C₂×C₄	—	20	1	no	—
395	C₂×C₄	—	20	1	no	—
396	C₂×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
397	C₂×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
398	C₂×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
399	C₂×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
400	C₂×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
401	C₂×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
402	C₂×C₃	—	2	2	no	—
403	C₂×C₃	—	10	2	no	—
404	C₂×C₃	—	20	1	no	—
405	C₂×C₃	—	20	1	no	—
406	C₂×C₃	#4144	1	1	yes	characteristic
407	C₂×C₃	C₂×#713	1	1	yes	characteristic
408	C₂×C₃	D₅×#41	1	1	yes	characteristic
409	C₅	C₃×#551	1	1	yes	characteristic, complemented, Sylow
410	C₂²	—	2	1	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	5	2	no	—
413	C₂²	—	10	1	no	—
414	C₂²	—	10	1	no	—
415	C₂²	—	10	1	no	—
416	C₂²	—	10	1	no	—
417	C₂²	—	10	1	no	—
418	C₂²	—	10	1	no	—
419	C₂²	—	10	1	no	—
420	C₂²	—	10	1	no	—
421	C₂²	—	20	4	no	—
422	C₂²	C₃×#713	1	2	yes	—
423	C₂²	C₂³×C₃×D₅	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	10	1	no	—
431	C₄	—	10	1	no	—
432	C₄	—	10	1	no	—
433	C₄	—	10	1	no	—
434	C₄	—	10	1	no	—
435	C₃	#65971	1	1	yes	characteristic, direct product factor, Sylow
436	C₂	—	2	2	no	—
437	C₂	—	10	2	no	—
438	C₂	—	20	1	no	—
439	C₂	—	20	1	no	—
440	C₂	C₃×#4144	1	1	yes	characteristic
441	C₂	C₂×C₃×#713	1	1	yes	characteristic
442	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	C₃×#4028	C₂
hypercenter	C₃×C₂²⋊Q₈	D₅
hypocenter	C₅	C₃×#551
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×#4093	C₂	semidirect
3. C₃×#4092	C₂	semidirect
4. C₃×C₄×C₂²⋊D₅	C₂	semidirect
5. C₂×C₃×#685	C₂	semidirect
6. C₃×#4044	C₂	semidirect
7. C₃×#4044	C₂	semidirect
8. C₃×#4040	C₂	semidirect
9. C₃×#4040	C₂	semidirect
10. C₃×#4039	C₂	semidirect
11. C₃×#4038	C₂	semidirect
12. C₃×#4032	C₂	semidirect
14. C₃×D₅×C₂²⋊C₄	C₂	semidirect
15. C₃×#4023	C₂	semidirect
16. #65971	C₃	direct (N × H)
18. C₂×C₃×C₅×Q₈	C₂²	semidirect
26. C₂×C₃×C₄×D₅	C₂²	semidirect
27. C₃×C₅×C₄⋊C₄	C₂²	semidirect
28. C₃×C₅×C₄⋊C₄	C₂²	semidirect
29. C₃×C₅×C₄⋊C₄	C₂²	semidirect
41. C₃×#685	C₂²	semidirect
42. C₃×#685	C₂²	semidirect
43. C₃×#685	C₂²	semidirect
44. C₃×C₄⋊Dic₅	C₂²	semidirect
45. C₃×C₄⋊Dic₅	C₂²	semidirect
46. C₃×#683	C₂²	semidirect
47. C₃×#683	C₂²	semidirect
48. C₃×#683	C₂²	semidirect
49. C₃×C₄×Dic₅	C₂²	semidirect
50. C₃×C₄×Dic₅	C₂²	semidirect
51. C₃×C₄×Dic₅	C₂²	semidirect
53. C₅×C₂²⋊Q₈	C₂×C₃	semidirect
54. #4093	C₂×C₃	semidirect
55. #4092	C₂×C₃	semidirect
56. C₄×C₂²⋊D₅	C₂×C₃	semidirect
57. C₂×#685	C₂×C₃	semidirect
58. #4044	C₂×C₃	semidirect
59. #4044	C₂×C₃	semidirect
60. #4040	C₂×C₃	semidirect
61. #4040	C₂×C₃	semidirect
62. #4039	C₂×C₃	semidirect
63. #4038	C₂×C₃	semidirect
64. #4032	C₂×C₃	semidirect
66. D₅×C₂²⋊C₄	C₂×C₃	semidirect
67. #4023	C₂×C₃	semidirect
102. C₃×C₂²⋊Q₈	D₅	semidirect
111. C₂×C₅×Q₈	C₂²×C₃	semidirect
119. C₂×C₄×D₅	C₂²×C₃	semidirect
120. C₅×C₄⋊C₄	C₂²×C₃	semidirect
121. C₅×C₄⋊C₄	C₂²×C₃	semidirect
122. C₅×C₄⋊C₄	C₂²×C₃	semidirect
134. #685	C₂²×C₃	semidirect
135. #685	C₂²×C₃	semidirect
136. #685	C₂²×C₃	semidirect
137. C₄⋊Dic₅	C₂²×C₃	semidirect
138. C₄⋊Dic₅	C₂²×C₃	semidirect
139. #683	C₂²×C₃	semidirect
140. #683	C₂²×C₃	semidirect
141. #683	C₂²×C₃	semidirect
142. C₄×Dic₅	C₂²×C₃	semidirect
143. C₄×Dic₅	C₂²×C₃	semidirect
144. C₄×Dic₅	C₂²×C₃	semidirect
172. C₂×C₃×Q₈	C₂×D₅	semidirect
186. C₃×C₄⋊C₄	C₂×D₅	semidirect
187. C₃×C₄⋊C₄	C₂×D₅	semidirect
188. C₃×C₄⋊C₄	C₂×D₅	semidirect
240. C₂²⋊Q₈	C₃×D₅	semidirect
308. C₂×Q₈	C₂×C₃×D₅	semidirect
322. C₄⋊C₄	C₂×C₃×D₅	semidirect
323. C₄⋊C₄	C₂×C₃×D₅	semidirect
324. C₄⋊C₄	C₂×C₃×D₅	semidirect
342. C₃×C₅	#551	semidirect
409. C₅	C₃×#551	semidirect
435. C₃	#65971	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×#4093	2
C₃×#4092	2
C₃×C₄×C₂²⋊D₅	2
C₂×C₃×#685	2
C₃×#4044	2
C₃×#4040	2
C₃×#4039	2
C₃×#4038	2
C₃×#4032	2
C₃×#4028	2
C₃×D₅×C₂²⋊C₄	2
C₃×#4023	2
#65971	3
C₃×#551	5

Subgroups — C3×#65971 #11755648

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#65971 #11755648