Subgroups — C₃×C₅×#3260 #14276294

Order 1920.

692 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#541	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#540	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#479	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#478	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#468	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#465	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#461	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#460	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#424	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#3260	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
12	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
13	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₃×C₅×#127	C₂²	1	1	yes	characteristic
17	C₃×C₅×#126	—	2	2	no	—
18	C₃×C₅×#125	—	2	2	no	—
19	C₃×C₅×#125	C₂²	1	1	yes	characteristic
20	C₃×C₅×#125	C₂²	1	1	yes	characteristic
21	C₃×C₅×#123	—	2	2	no	—
22	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₃×C₅×#121	—	2	2	no	—
24	C₃×C₅×#121	C₂²	1	2	yes	—
25	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
26	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
27	C₃×C₅×#117	C₂²	1	1	yes	characteristic
28	C₃×C₅×#107	C₂²	1	2	yes	—
29	C₃×C₅×#106	C₂²	1	2	yes	—
30	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
31	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
32	C₃×C₅×#103	C₂²	1	2	yes	—
33	C₃×C₅×#103	C₂²	1	2	yes	—
34	C₃×C₅×#102	C₂²	1	2	yes	—
35	C₃×C₅×#102	C₂²	1	2	yes	—
36	C₃×#3260	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
37	C₅×#541	C₂×C₃	1	1	yes	characteristic, complemented
38	C₅×#540	C₂×C₃	1	1	yes	characteristic
39	C₅×#479	C₂×C₃	1	2	yes	complemented
40	C₅×#478	C₂×C₃	1	2	yes	complemented
41	C₅×#468	C₂×C₃	1	2	yes	complemented
42	C₅×#465	C₂×C₃	1	2	yes	complemented
43	C₅×#461	C₂×C₃	1	2	yes	complemented
44	C₅×#460	C₂×C₃	1	2	yes	complemented
45	C₅×#424	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
47	C₂×C₃×C₅×D₄	—	2	2	no	—
48	C₂×C₃×C₅×D₄	—	2	2	no	—
49	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
50	C₂²×C₃×C₄×C₅	—	2	2	no	—
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₃×C₅×SD₁₆	—	4	2	no	—
53	C₃×C₅×SD₁₆	—	4	2	no	—
54	C₃×C₅×M₁₆	—	4	1	no	—
55	C₂×C₃×C₅×C₈	—	4	1	no	—
56	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
57	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
58	C₃×C₅×C₄⋊C₄	—	2	2	no	—
59	C₃×C₅×C₄⋊C₄	—	2	2	no	—
60	C₃×C₅×C₄⋊C₄	—	2	2	no	—
61	C₃×C₅×C₄⋊C₄	—	2	2	no	—
62	C₃×C₅×C₄⋊C₄	—	2	2	no	—
63	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
64	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
65	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
66	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
67	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
68	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
69	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
70	C₃×C₄²×C₅	—	2	2	no	—
71	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
72	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
73	C₃×#541	C₂×C₅	1	1	yes	characteristic, complemented
74	C₃×#540	C₂×C₅	1	1	yes	characteristic
75	C₃×#479	C₂×C₅	1	2	yes	complemented
76	C₃×#478	C₂×C₅	1	2	yes	complemented
77	C₃×#468	C₂×C₅	1	2	yes	complemented
78	C₃×#465	C₂×C₅	1	2	yes	complemented
79	C₃×#461	C₂×C₅	1	2	yes	complemented
80	C₃×#460	C₂×C₅	1	2	yes	complemented
81	C₃×#424	C₂×C₅	1	1	yes	characteristic, complemented
82	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
83	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
84	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
85	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
86	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
87	C₅×#127	C₂²×C₃	1	1	yes	characteristic
88	C₅×#126	—	2	2	no	—
89	C₅×#125	—	2	2	no	—
90	C₅×#125	C₂²×C₃	1	1	yes	characteristic
91	C₅×#125	C₂²×C₃	1	1	yes	characteristic
92	C₅×#123	—	2	2	no	—
93	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
94	C₅×#121	—	2	2	no	—
95	C₅×#121	C₂²×C₃	1	2	yes	—
96	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
97	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
98	C₅×#117	C₂²×C₃	1	1	yes	characteristic
99	C₅×#107	C₂²×C₃	1	2	yes	—
100	C₅×#106	C₂²×C₃	1	2	yes	—
101	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
102	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
103	C₅×#103	C₂²×C₃	1	2	yes	—
104	C₅×#103	C₂²×C₃	1	2	yes	—
105	C₅×#102	C₂²×C₃	1	2	yes	—
106	C₅×#102	C₂²×C₃	1	2	yes	—
107	#3260	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
108	C₂³×C₃×C₅	—	2	2	no	—
109	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
110	C₃×C₅×Q₈	—	2	2	no	—
111	C₃×C₅×Q₈	—	2	2	no	—
112	C₃×C₅×D₄	—	2	2	no	—
113	C₃×C₅×D₄	—	2	2	no	—
114	C₃×C₅×D₄	—	8	2	no	—
115	C₃×C₅×D₄	—	8	2	no	—
116	C₂×C₃×C₄×C₅	—	2	1	no	—
117	C₂×C₃×C₄×C₅	—	2	1	no	—
118	C₂×C₃×C₄×C₅	—	2	2	no	—
119	C₂×C₃×C₄×C₅	—	2	2	no	—
120	C₂×C₃×C₄×C₅	—	2	2	no	—
121	C₂×C₃×C₄×C₅	—	8	2	no	—
122	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
123	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
124	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
125	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
126	C₃×C₅×C₈	—	2	2	no	—
127	C₃×C₅×C₈	—	2	2	no	—
128	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
129	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
130	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
131	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
132	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
133	C₃×#127	C₂²×C₅	1	1	yes	characteristic
134	C₃×#126	—	2	2	no	—
135	C₃×#125	—	2	2	no	—
136	C₃×#125	C₂²×C₅	1	1	yes	characteristic
137	C₃×#125	C₂²×C₅	1	1	yes	characteristic
138	C₃×#123	—	2	2	no	—
139	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
140	C₃×#121	—	2	2	no	—
141	C₃×#121	C₂²×C₅	1	2	yes	—
142	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
143	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
144	C₃×#117	C₂²×C₅	1	1	yes	characteristic
145	C₃×#107	C₂²×C₅	1	2	yes	—
146	C₃×#106	C₂²×C₅	1	2	yes	—
147	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
148	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
149	C₃×#103	C₂²×C₅	1	2	yes	—
150	C₃×#103	C₂²×C₅	1	2	yes	—
151	C₃×#102	C₂²×C₅	1	2	yes	—
152	C₃×#102	C₂²×C₅	1	2	yes	—
153	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
154	C₂×C₅×D₄	—	2	2	no	—
155	C₂×C₅×D₄	—	2	2	no	—
156	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
157	C₂²×C₄×C₅	—	2	2	no	—
158	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
159	C₅×SD₁₆	—	4	2	no	—
160	C₅×SD₁₆	—	4	2	no	—
161	C₅×M₁₆	—	4	1	no	—
162	C₂×C₅×C₈	—	4	1	no	—
163	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
164	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
165	C₅×C₄⋊C₄	—	2	2	no	—
166	C₅×C₄⋊C₄	—	2	2	no	—
167	C₅×C₄⋊C₄	—	2	2	no	—
168	C₅×C₄⋊C₄	—	2	2	no	—
169	C₅×C₄⋊C₄	—	2	2	no	—
170	C₅×C₄⋊C₄	C₃×D₄	1	2	yes	—
171	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
172	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
173	C₅×C₂²⋊C₄	—	2	2	no	—
174	C₅×C₂²⋊C₄	—	2	2	no	—
175	C₅×C₂²⋊C₄	—	2	2	no	—
176	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
177	C₄²×C₅	—	2	2	no	—
178	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
179	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
180	#541	C₂×C₃×C₅	1	1	yes	characteristic, complemented
181	#540	C₂×C₃×C₅	1	1	yes	characteristic
182	#479	C₂×C₃×C₅	1	2	yes	complemented
183	#478	C₂×C₃×C₅	1	2	yes	complemented
184	#468	C₂×C₃×C₅	1	2	yes	complemented
185	#465	C₂×C₃×C₅	1	2	yes	complemented
186	#461	C₂×C₃×C₅	1	2	yes	complemented
187	#460	C₂×C₃×C₅	1	2	yes	complemented
188	#424	C₂×C₃×C₅	1	1	yes	characteristic, complemented
189	C₂²×C₃×C₅	—	2	1	no	—
190	C₂²×C₃×C₅	—	2	2	no	—
191	C₂²×C₃×C₅	—	4	2	no	—
192	C₂²×C₃×C₅	—	4	2	no	—
193	C₂²×C₃×C₅	—	4	2	no	—
194	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
195	C₃×C₄×C₅	—	2	1	no	—
196	C₃×C₄×C₅	—	2	2	no	—
197	C₃×C₄×C₅	—	2	2	no	—
198	C₃×C₄×C₅	—	4	2	no	—
199	C₃×C₄×C₅	—	4	2	no	—
200	C₃×C₄×C₅	—	4	2	no	—
201	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
202	C₃×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
203	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
204	C₂×C₃×D₄	—	2	2	no	—
205	C₂×C₃×D₄	—	2	2	no	—
206	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
207	C₂²×C₃×C₄	—	2	2	no	—
208	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
209	C₃×SD₁₆	—	4	2	no	—
210	C₃×SD₁₆	—	4	2	no	—
211	C₃×M₁₆	—	4	1	no	—
212	C₂×C₃×C₈	—	4	1	no	—
213	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
214	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
215	C₃×C₄⋊C₄	—	2	2	no	—
216	C₃×C₄⋊C₄	—	2	2	no	—
217	C₃×C₄⋊C₄	—	2	2	no	—
218	C₃×C₄⋊C₄	—	2	2	no	—
219	C₃×C₄⋊C₄	—	2	2	no	—
220	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	—
221	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
222	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
223	C₃×C₂²⋊C₄	—	2	2	no	—
224	C₃×C₂²⋊C₄	—	2	2	no	—
225	C₃×C₂²⋊C₄	—	2	2	no	—
226	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
227	C₃×C₄²	—	2	2	no	—
228	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
229	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
230	C₂³×C₅	—	2	2	no	—
231	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
232	C₅×Q₈	—	2	2	no	—
233	C₅×Q₈	—	2	2	no	—
234	C₅×D₄	—	2	2	no	—
235	C₅×D₄	—	2	2	no	—
236	C₅×D₄	—	8	2	no	—
237	C₅×D₄	—	8	2	no	—
238	C₂×C₄×C₅	—	2	1	no	—
239	C₂×C₄×C₅	—	2	1	no	—
240	C₂×C₄×C₅	—	2	2	no	—
241	C₂×C₄×C₅	—	2	2	no	—
242	C₂×C₄×C₅	—	2	2	no	—
243	C₂×C₄×C₅	—	8	2	no	—
244	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
245	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
246	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
247	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
248	C₅×C₈	—	2	2	no	—
249	C₅×C₈	—	2	2	no	—
250	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
251	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
252	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
253	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
254	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
255	#127	C₂²×C₃×C₅	1	1	yes	characteristic
256	#126	—	2	2	no	—
257	#125	—	2	2	no	—
258	#125	C₂²×C₃×C₅	1	1	yes	characteristic
259	#125	C₂²×C₃×C₅	1	1	yes	characteristic
260	#123	—	2	2	no	—
261	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
262	#121	—	2	2	no	—
263	#121	C₂²×C₃×C₅	1	2	yes	—
264	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
265	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
266	#117	C₂²×C₃×C₅	1	1	yes	characteristic
267	#107	C₂²×C₃×C₅	1	2	yes	—
268	#106	C₂²×C₃×C₅	1	2	yes	—
269	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	—
270	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	—
271	#103	C₂²×C₃×C₅	1	2	yes	—
272	#103	C₂²×C₃×C₅	1	2	yes	—
273	#102	C₂²×C₃×C₅	1	2	yes	—
274	#102	C₂²×C₃×C₅	1	2	yes	—
275	C₂×C₃×C₅	—	4	1	no	—
276	C₂×C₃×C₅	—	8	2	no	—
277	C₂×C₃×C₅	#537	1	1	yes	characteristic
278	C₂×C₃×C₅	#577	1	2	yes	—
279	C₂³×C₃	—	2	2	no	—
280	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
281	C₃×Q₈	—	2	2	no	—
282	C₃×Q₈	—	2	2	no	—
283	C₃×D₄	—	2	2	no	—
284	C₃×D₄	—	2	2	no	—
285	C₃×D₄	—	8	2	no	—
286	C₃×D₄	—	8	2	no	—
287	C₂×C₃×C₄	—	2	1	no	—
288	C₂×C₃×C₄	—	2	1	no	—
289	C₂×C₃×C₄	—	2	2	no	—
290	C₂×C₃×C₄	—	2	2	no	—
291	C₂×C₃×C₄	—	2	2	no	—
292	C₂×C₃×C₄	—	8	2	no	—
293	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
294	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
295	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
296	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
297	C₃×C₈	—	2	2	no	—
298	C₃×C₈	—	2	2	no	—
299	C₂²×C₅	—	2	2	no	—
300	C₂²×C₅	—	2	1	no	—
301	C₂²×C₅	—	4	2	no	—
302	C₂²×C₅	—	4	2	no	—
303	C₂²×C₅	—	4	2	no	—
304	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
305	C₄×C₅	—	2	2	no	—
306	C₄×C₅	—	2	2	no	—
307	C₄×C₅	—	2	1	no	—
308	C₄×C₅	—	4	2	no	—
309	C₄×C₅	—	4	2	no	—
310	C₄×C₅	—	4	2	no	—
311	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
312	C₄×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
313	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
319	SD₁₆	—	4	2	no	—
320	SD₁₆	—	4	2	no	—
321	M₁₆	—	4	1	no	—
322	C₂×C₈	—	4	1	no	—
323	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
324	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	C₃×C₅×D₄	1	2	yes	—
331	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
332	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
333	C₂²⋊C₄	—	2	2	no	—
334	C₂²⋊C₄	—	2	2	no	—
335	C₂²⋊C₄	—	2	2	no	—
336	C₂²⋊C₄	C₃×C₅×D₄	1	2	yes	—
337	C₄²	—	2	2	no	—
338	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
339	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
340	C₃×C₅	#3260	1	1	yes	characteristic, direct product factor, Hall
341	C₂²×C₃	—	2	1	no	—
342	C₂²×C₃	—	2	2	no	—
343	C₂²×C₃	—	4	2	no	—
344	C₂²×C₃	—	4	2	no	—
345	C₂²×C₃	—	4	2	no	—
346	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
347	C₃×C₄	—	2	1	no	—
348	C₃×C₄	—	2	2	no	—
349	C₃×C₄	—	2	2	no	—
350	C₃×C₄	—	4	2	no	—
351	C₃×C₄	—	4	2	no	—
352	C₃×C₄	—	4	2	no	—
353	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
354	C₃×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
355	C₂×C₅	—	4	1	no	—
356	C₂×C₅	—	8	2	no	—
357	C₂×C₅	C₃×#537	1	1	yes	characteristic
358	C₂×C₅	C₃×#577	1	2	yes	—
359	C₂³	—	2	2	no	—
360	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
361	Q₈	—	2	2	no	—
362	Q₈	—	2	2	no	—
363	D₄	—	2	2	no	—
364	D₄	—	2	2	no	—
365	D₄	—	8	2	no	—
366	D₄	—	8	2	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	8	2	no	—
373	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
374	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
375	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
376	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
377	C₈	—	2	2	no	—
378	C₈	—	2	2	no	—
379	C₂×C₃	—	4	1	no	—
380	C₂×C₃	—	8	2	no	—
381	C₂×C₃	C₅×#537	1	1	yes	characteristic
382	C₂×C₃	C₅×#577	1	2	yes	—
383	C₅	C₃×#3260	1	1	yes	characteristic, direct product factor, Sylow
384	C₂²	—	2	1	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	4	2	no	—
389	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
390	C₄	—	2	1	no	—
391	C₄	—	2	2	no	—
392	C₄	—	2	2	no	—
393	C₄	—	4	2	no	—
394	C₄	—	4	2	no	—
395	C₄	—	4	2	no	—
396	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
397	C₄	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
398	C₃	C₅×#3260	1	1	yes	characteristic, direct product factor, Sylow
399	C₂	—	4	1	no	—
400	C₂	—	8	2	no	—
401	C₂	C₃×C₅×#537	1	1	yes	characteristic
402	C₂	C₃×C₅×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₃×C₅×#540	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₅×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#541	C₂	semidirect
3. C₃×C₅×#479	C₂	semidirect
4. C₃×C₅×#478	C₂	semidirect
5. C₃×C₅×#468	C₂	semidirect
6. C₃×C₅×#465	C₂	semidirect
7. C₃×C₅×#461	C₂	semidirect
8. C₃×C₅×#460	C₂	semidirect
9. C₃×C₅×#424	C₂	semidirect
10. C₅×#3260	C₃	direct (N × H)
36. C₃×#3260	C₅	direct (N × H)
37. C₅×#541	C₂×C₃	semidirect
39. C₅×#479	C₂×C₃	semidirect
40. C₅×#478	C₂×C₃	semidirect
41. C₅×#468	C₂×C₃	semidirect
42. C₅×#465	C₂×C₃	semidirect
43. C₅×#461	C₂×C₃	semidirect
44. C₅×#460	C₂×C₃	semidirect
45. C₅×#424	C₂×C₃	semidirect
73. C₃×#541	C₂×C₅	semidirect
75. C₃×#479	C₂×C₅	semidirect
76. C₃×#478	C₂×C₅	semidirect
77. C₃×#468	C₂×C₅	semidirect
78. C₃×#465	C₂×C₅	semidirect
79. C₃×#461	C₂×C₅	semidirect
80. C₃×#460	C₂×C₅	semidirect
81. C₃×#424	C₂×C₅	semidirect
107. #3260	C₃×C₅	direct (N × H)
180. #541	C₂×C₃×C₅	semidirect
182. #479	C₂×C₃×C₅	semidirect
183. #478	C₂×C₃×C₅	semidirect
184. #468	C₂×C₃×C₅	semidirect
185. #465	C₂×C₃×C₅	semidirect
186. #461	C₂×C₃×C₅	semidirect
187. #460	C₂×C₃×C₅	semidirect
188. #424	C₂×C₃×C₅	semidirect
340. C₃×C₅	#3260	direct (N × H)
383. C₅	C₃×#3260	direct (N × H)
398. C₃	C₅×#3260	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×#541	2
C₃×C₅×#540	2
C₃×C₅×#479	2
C₃×C₅×#478	2
C₃×C₅×#468	2
C₃×C₅×#465	2
C₃×C₅×#461	2
C₃×C₅×#460	2
C₃×C₅×#424	2
C₅×#3260	3
C₃×#3260	5

Subgroups — C3×C5×#3260 #14276294

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3260 #14276294