Subgroups — C₃×C₅×#3287 #14276321

Order 1920.

1008 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×C₃×C₅×#135	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#550	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#493	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#466	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#460	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#449	C₂	1	4	yes	maximal, complemented
7	C₃×C₄×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#3287	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×C₅×#41	C₂²	1	4	yes	—
11	C₃×C₅×#135	—	2	8	no	—
12	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×SD₁₆	C₂²	1	4	yes	—
14	C₂×C₃×C₅×D₈	C₂²	1	2	yes	—
15	C₂×C₃×C₅×D₈	C₂²	1	2	yes	—
16	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
17	C₃×C₅×#127	—	2	2	no	—
18	C₃×C₅×#127	C₂²	1	2	yes	—
19	C₃×C₅×#121	—	2	4	no	—
20	C₃×C₅×#121	C₂²	1	4	yes	—
21	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
22	C₃×C₄×C₅×D₄	—	2	2	no	—
23	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
24	C₃×C₅×#107	C₂²	1	1	yes	characteristic
25	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₃×C₅×#103	C₂²	1	2	yes	—
27	C₃×C₅×#102	C₂²	1	4	yes	—
28	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
29	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
30	C₃×#3287	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₂×C₅×#135	C₂×C₃	1	2	yes	complemented
32	C₅×#550	C₂×C₃	1	2	yes	complemented
33	C₅×#493	C₂×C₃	1	1	yes	characteristic, complemented
34	C₅×#466	C₂×C₃	1	2	yes	complemented
35	C₅×#460	C₂×C₃	1	2	yes	complemented
36	C₅×#449	C₂×C₃	1	4	yes	complemented
37	C₄×C₅×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
38	C₅×C₈×D₄	C₂×C₃	1	1	yes	characteristic, complemented
39	C₃×C₅×#41	—	2	8	no	—
40	C₃×C₅×#41	—	4	4	no	—
41	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
42	C₂×C₃×C₅×D₄	—	2	4	no	—
43	C₂×C₃×C₅×D₄	—	2	4	no	—
44	C₂×C₃×C₅×D₄	—	2	2	no	—
45	C₂×C₃×C₅×D₄	—	2	2	no	—
46	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
47	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
48	C₂²×C₃×C₄×C₅	—	2	4	no	—
49	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
50	C₃×C₅×Q₁₆	D₄	1	4	yes	complemented
51	C₃×C₅×SD₁₆	—	2	8	no	—
52	C₃×C₅×D₈	—	2	4	no	—
53	C₃×C₅×D₈	—	4	2	no	—
54	C₂×C₃×C₅×C₈	—	2	4	no	—
55	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
56	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
57	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
58	C₃×C₅×C₄⋊C₄	—	2	2	no	—
59	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
60	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
61	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
62	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
63	C₃×C₄²×C₅	—	2	2	no	—
64	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
65	C₂×C₃×#135	C₂×C₅	1	2	yes	complemented
66	C₃×#550	C₂×C₅	1	2	yes	complemented
67	C₃×#493	C₂×C₅	1	1	yes	characteristic, complemented
68	C₃×#466	C₂×C₅	1	2	yes	complemented
69	C₃×#460	C₂×C₅	1	2	yes	complemented
70	C₃×#449	C₂×C₅	1	4	yes	complemented
71	C₃×C₄×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
72	C₃×C₈×D₄	C₂×C₅	1	1	yes	characteristic, complemented
73	C₂×C₅×#41	C₂²×C₃	1	4	yes	—
74	C₅×#135	—	2	8	no	—
75	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
76	C₂×C₅×SD₁₆	C₂²×C₃	1	4	yes	—
77	C₂×C₅×D₈	C₂²×C₃	1	2	yes	—
78	C₂×C₅×D₈	C₂²×C₃	1	2	yes	—
79	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
80	C₅×#127	—	2	2	no	—
81	C₅×#127	C₂²×C₃	1	2	yes	—
82	C₅×#121	—	2	4	no	—
83	C₅×#121	C₂²×C₃	1	4	yes	—
84	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
85	C₄×C₅×D₄	—	2	2	no	—
86	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
87	C₅×#107	C₂²×C₃	1	1	yes	characteristic
88	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
89	C₅×#103	C₂²×C₃	1	2	yes	—
90	C₅×#102	C₂²×C₃	1	4	yes	—
91	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
92	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
93	#3287	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
94	C₂³×C₃×C₅	—	2	4	no	—
95	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
96	C₃×C₅×Q₈	—	2	2	no	—
97	C₃×C₅×Q₈	C₂×D₄	1	4	yes	—
98	C₃×C₅×D₄	—	2	2	no	—
99	C₃×C₅×D₄	—	2	4	no	—
100	C₃×C₅×D₄	—	2	4	no	—
101	C₃×C₅×D₄	—	4	8	no	—
102	C₃×C₅×D₄	—	4	4	no	—
103	C₃×C₅×D₄	—	8	2	no	—
104	C₃×C₅×D₄	—	8	4	no	—
105	C₂×C₃×C₄×C₅	—	2	2	no	—
106	C₂×C₃×C₄×C₅	—	2	2	no	—
107	C₂×C₃×C₄×C₅	—	2	2	no	—
108	C₂×C₃×C₄×C₅	—	2	2	no	—
109	C₂×C₃×C₄×C₅	—	4	8	no	—
110	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
111	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
112	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
114	C₃×C₅×C₈	—	2	2	no	—
115	C₃×C₅×C₈	—	2	1	no	—
116	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
117	C₂×C₃×#41	C₂²×C₅	1	4	yes	—
118	C₃×#135	—	2	8	no	—
119	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
120	C₂×C₃×SD₁₆	C₂²×C₅	1	4	yes	—
121	C₂×C₃×D₈	C₂²×C₅	1	2	yes	—
122	C₂×C₃×D₈	C₂²×C₅	1	2	yes	—
123	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
124	C₃×#127	—	2	2	no	—
125	C₃×#127	C₂²×C₅	1	2	yes	—
126	C₃×#121	—	2	4	no	—
127	C₃×#121	C₂²×C₅	1	4	yes	—
128	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
129	C₃×C₄×D₄	—	2	2	no	—
130	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
131	C₃×#107	C₂²×C₅	1	1	yes	characteristic
132	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
133	C₃×#103	C₂²×C₅	1	2	yes	—
134	C₃×#102	C₂²×C₅	1	4	yes	—
135	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
136	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
137	C₅×#41	—	2	8	no	—
138	C₅×#41	—	4	4	no	—
139	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
140	C₂×C₅×D₄	—	2	4	no	—
141	C₂×C₅×D₄	—	2	4	no	—
142	C₂×C₅×D₄	—	2	2	no	—
143	C₂×C₅×D₄	—	2	2	no	—
144	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
145	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
146	C₂²×C₄×C₅	—	2	4	no	—
147	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
148	C₅×Q₁₆	C₃×D₄	1	4	yes	complemented
149	C₅×SD₁₆	—	2	8	no	—
150	C₅×D₈	—	2	4	no	—
151	C₅×D₈	—	4	2	no	—
152	C₂×C₅×C₈	—	2	4	no	—
153	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
154	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
155	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
156	C₅×C₄⋊C₄	—	2	2	no	—
157	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
158	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
159	C₅×C₂²⋊C₄	—	2	4	no	—
160	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
161	C₄²×C₅	—	2	2	no	—
162	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
163	C₂×#135	C₂×C₃×C₅	1	2	yes	complemented
164	#550	C₂×C₃×C₅	1	2	yes	complemented
165	#493	C₂×C₃×C₅	1	1	yes	characteristic, complemented
166	#466	C₂×C₃×C₅	1	2	yes	complemented
167	#460	C₂×C₃×C₅	1	2	yes	complemented
168	#449	C₂×C₃×C₅	1	4	yes	complemented
169	C₄×Q₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
170	C₈×D₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
171	C₂²×C₃×C₅	—	2	2	no	—
172	C₂²×C₃×C₅	—	2	2	no	—
173	C₂²×C₃×C₅	—	2	2	no	—
174	C₂²×C₃×C₅	—	4	4	no	—
175	C₂²×C₃×C₅	—	4	4	no	—
176	C₂²×C₃×C₅	—	4	4	no	—
177	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
178	C₃×C₄×C₅	—	2	2	no	—
179	C₃×C₄×C₅	—	2	4	no	—
180	C₃×C₄×C₅	—	2	1	no	—
181	C₃×C₄×C₅	—	4	2	no	—
182	C₃×C₄×C₅	#135	1	2	yes	complemented
183	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
184	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
185	C₃×#41	—	2	8	no	—
186	C₃×#41	—	4	4	no	—
187	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
188	C₂×C₃×D₄	—	2	4	no	—
189	C₂×C₃×D₄	—	2	4	no	—
190	C₂×C₃×D₄	—	2	2	no	—
191	C₂×C₃×D₄	—	2	2	no	—
192	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
193	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
194	C₂²×C₃×C₄	—	2	4	no	—
195	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
196	C₃×Q₁₆	C₅×D₄	1	4	yes	complemented
197	C₃×SD₁₆	—	2	8	no	—
198	C₃×D₈	—	2	4	no	—
199	C₃×D₈	—	4	2	no	—
200	C₂×C₃×C₈	—	2	4	no	—
201	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
202	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
203	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
204	C₃×C₄⋊C₄	—	2	2	no	—
205	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
206	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
207	C₃×C₂²⋊C₄	—	2	4	no	—
208	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
209	C₃×C₄²	—	2	2	no	—
210	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
211	C₂³×C₅	—	2	4	no	—
212	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
213	C₅×Q₈	—	2	2	no	—
214	C₅×Q₈	C₂×C₃×D₄	1	4	yes	—
215	C₅×D₄	—	2	2	no	—
216	C₅×D₄	—	2	4	no	—
217	C₅×D₄	—	2	4	no	—
218	C₅×D₄	—	4	8	no	—
219	C₅×D₄	—	4	4	no	—
220	C₅×D₄	—	8	2	no	—
221	C₅×D₄	—	8	4	no	—
222	C₂×C₄×C₅	—	2	2	no	—
223	C₂×C₄×C₅	—	2	2	no	—
224	C₂×C₄×C₅	—	2	2	no	—
225	C₂×C₄×C₅	—	2	2	no	—
226	C₂×C₄×C₅	—	4	8	no	—
227	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
228	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
229	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
230	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
231	C₅×C₈	—	2	2	no	—
232	C₅×C₈	—	2	1	no	—
233	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
234	C₂×#41	C₂²×C₃×C₅	1	4	yes	—
235	#135	—	2	8	no	—
236	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
237	C₂×SD₁₆	C₂²×C₃×C₅	1	4	yes	—
238	C₂×D₈	C₂²×C₃×C₅	1	2	yes	—
239	C₂×D₈	C₂²×C₃×C₅	1	2	yes	—
240	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
241	#127	—	2	2	no	—
242	#127	C₂²×C₃×C₅	1	2	yes	—
243	#121	—	2	4	no	—
244	#121	C₂²×C₃×C₅	1	4	yes	—
245	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
246	C₄×D₄	—	2	2	no	—
247	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
248	#107	C₂²×C₃×C₅	1	1	yes	characteristic
249	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
250	#103	C₂²×C₃×C₅	1	2	yes	—
251	#102	C₂²×C₃×C₅	1	4	yes	—
252	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
253	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
254	C₂×C₃×C₅	—	4	2	no	—
255	C₂×C₃×C₅	—	8	4	no	—
256	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
257	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
258	C₂×C₃×C₅	#576	1	1	yes	characteristic
259	C₂³×C₃	—	2	4	no	—
260	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
261	C₃×Q₈	—	2	2	no	—
262	C₃×Q₈	C₂×C₅×D₄	1	4	yes	—
263	C₃×D₄	—	2	2	no	—
264	C₃×D₄	—	2	4	no	—
265	C₃×D₄	—	2	4	no	—
266	C₃×D₄	—	4	8	no	—
267	C₃×D₄	—	4	4	no	—
268	C₃×D₄	—	8	2	no	—
269	C₃×D₄	—	8	4	no	—
270	C₂×C₃×C₄	—	2	2	no	—
271	C₂×C₃×C₄	—	2	2	no	—
272	C₂×C₃×C₄	—	2	2	no	—
273	C₂×C₃×C₄	—	2	2	no	—
274	C₂×C₃×C₄	—	4	8	no	—
275	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
276	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
277	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
278	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
279	C₃×C₈	—	2	2	no	—
280	C₃×C₈	—	2	1	no	—
281	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
282	C₂²×C₅	—	2	2	no	—
283	C₂²×C₅	—	2	2	no	—
284	C₂²×C₅	—	2	2	no	—
285	C₂²×C₅	—	4	4	no	—
286	C₂²×C₅	—	4	4	no	—
287	C₂²×C₅	—	4	4	no	—
288	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
289	C₄×C₅	—	2	1	no	—
290	C₄×C₅	—	2	2	no	—
291	C₄×C₅	—	2	4	no	—
292	C₄×C₅	—	4	2	no	—
293	C₄×C₅	C₃×#135	1	2	yes	complemented
294	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
295	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
296	#41	—	2	8	no	—
297	#41	—	4	4	no	—
298	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
299	C₂×D₄	—	2	4	no	—
300	C₂×D₄	—	2	4	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
304	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
307	Q₁₆	C₃×C₅×D₄	1	4	yes	complemented
308	SD₁₆	—	2	8	no	—
309	D₈	—	2	4	no	—
310	D₈	—	4	2	no	—
311	C₂×C₈	—	2	4	no	—
312	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
313	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
314	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
317	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
318	C₂²⋊C₄	—	2	4	no	—
319	C₂²⋊C₄	C₃×C₅×D₄	1	2	yes	—
320	C₄²	—	2	2	no	—
321	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
322	C₃×C₅	#3287	1	1	yes	characteristic, direct product factor, Hall
323	C₂²×C₃	—	2	2	no	—
324	C₂²×C₃	—	2	2	no	—
325	C₂²×C₃	—	2	2	no	—
326	C₂²×C₃	—	4	4	no	—
327	C₂²×C₃	—	4	4	no	—
328	C₂²×C₃	—	4	4	no	—
329	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
330	C₃×C₄	—	2	2	no	—
331	C₃×C₄	—	2	4	no	—
332	C₃×C₄	—	2	1	no	—
333	C₃×C₄	—	4	2	no	—
334	C₃×C₄	C₅×#135	1	2	yes	complemented
335	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
336	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
337	C₂×C₅	—	4	2	no	—
338	C₂×C₅	—	8	4	no	—
339	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
340	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
341	C₂×C₅	C₃×#576	1	1	yes	characteristic
342	C₂³	—	2	4	no	—
343	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
344	Q₈	—	2	2	no	—
345	Q₈	C₂×C₃×C₅×D₄	1	4	yes	—
346	D₄	—	2	4	no	—
347	D₄	—	2	4	no	—
348	D₄	—	2	2	no	—
349	D₄	—	4	8	no	—
350	D₄	—	4	4	no	—
351	D₄	—	8	2	no	—
352	D₄	—	8	4	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	4	8	no	—
358	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
359	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
360	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
361	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
362	C₈	—	2	2	no	—
363	C₈	—	2	1	no	—
364	C₈	C₂×C₃×C₅×D₄	1	2	yes	—
365	C₂×C₃	—	4	2	no	—
366	C₂×C₃	—	8	4	no	—
367	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
368	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
369	C₂×C₃	C₅×#576	1	1	yes	characteristic
370	C₅	C₃×#3287	1	1	yes	characteristic, direct product factor, Sylow
371	C₂²	—	2	2	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	2	2	no	—
374	C₂²	—	4	4	no	—
375	C₂²	—	4	4	no	—
376	C₂²	—	4	4	no	—
377	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
378	C₄	—	2	2	no	—
379	C₄	—	2	4	no	—
380	C₄	—	2	1	no	—
381	C₄	—	4	2	no	—
382	C₄	C₃×C₅×#135	1	2	yes	complemented
383	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
384	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
385	C₃	C₅×#3287	1	1	yes	characteristic, direct product factor, Sylow
386	C₂	—	4	2	no	—
387	C₂	—	8	4	no	—
388	C₂	C₃×C₅×D₄²	1	1	yes	characteristic
389	C₂	C₂×C₃×C₅×#135	1	1	yes	characteristic
390	C₂	C₃×C₅×#576	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#135	C₂	semidirect
2. C₃×C₅×#550	C₂	semidirect
3. C₃×C₅×#493	C₂	semidirect
4. C₃×C₅×#466	C₂	semidirect
5. C₃×C₅×#460	C₂	semidirect
6. C₃×C₅×#449	C₂	semidirect
7. C₃×C₄×C₅×Q₁₆	C₂	semidirect
8. C₃×C₅×C₈×D₄	C₂	semidirect
9. C₅×#3287	C₃	direct (N × H)
30. C₃×#3287	C₅	direct (N × H)
31. C₂×C₅×#135	C₂×C₃	semidirect
32. C₅×#550	C₂×C₃	semidirect
33. C₅×#493	C₂×C₃	semidirect
34. C₅×#466	C₂×C₃	semidirect
35. C₅×#460	C₂×C₃	semidirect
36. C₅×#449	C₂×C₃	semidirect
37. C₄×C₅×Q₁₆	C₂×C₃	semidirect
38. C₅×C₈×D₄	C₂×C₃	semidirect
50. C₃×C₅×Q₁₆	D₄	semidirect
65. C₂×C₃×#135	C₂×C₅	semidirect
66. C₃×#550	C₂×C₅	semidirect
67. C₃×#493	C₂×C₅	semidirect
68. C₃×#466	C₂×C₅	semidirect
69. C₃×#460	C₂×C₅	semidirect
70. C₃×#449	C₂×C₅	semidirect
71. C₃×C₄×Q₁₆	C₂×C₅	semidirect
72. C₃×C₈×D₄	C₂×C₅	semidirect
93. #3287	C₃×C₅	direct (N × H)
148. C₅×Q₁₆	C₃×D₄	semidirect
163. C₂×#135	C₂×C₃×C₅	semidirect
164. #550	C₂×C₃×C₅	semidirect
165. #493	C₂×C₃×C₅	semidirect
166. #466	C₂×C₃×C₅	semidirect
167. #460	C₂×C₃×C₅	semidirect
168. #449	C₂×C₃×C₅	semidirect
169. C₄×Q₁₆	C₂×C₃×C₅	semidirect
170. C₈×D₄	C₂×C₃×C₅	semidirect
182. C₃×C₄×C₅	#135	semidirect
196. C₃×Q₁₆	C₅×D₄	semidirect
293. C₄×C₅	C₃×#135	semidirect
307. Q₁₆	C₃×C₅×D₄	semidirect
322. C₃×C₅	#3287	direct (N × H)
334. C₃×C₄	C₅×#135	semidirect
370. C₅	C₃×#3287	direct (N × H)
382. C₄	C₃×C₅×#135	semidirect
385. C₃	C₅×#3287	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×#135	2
C₃×C₅×#550	2
C₃×C₅×#493	2
C₃×C₅×#466	2
C₃×C₅×#460	2
C₃×C₅×#449	2
C₃×C₄×C₅×Q₁₆	2
C₃×C₅×C₈×D₄	2
C₅×#3287	3
C₃×#3287	5

Subgroups — C3×C5×#3287 #14276321

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3287 #14276321