Subgroups — C₃×C₅×#3283 #14276317

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 384 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×#547	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#494	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#467	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#461	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#452	C₂	1	4	yes	maximal, complemented
7	C₃×C₄×C₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#3283	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	2	yes	—
13	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
14	C₂×C₃×C₅×SD₁₆	C₂²	1	4	yes	—
15	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
17	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
18	C₃×C₅×#123	—	2	4	no	—
19	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
20	C₃×C₅×#121	—	2	2	no	—
21	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
22	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₅×C₄⋊C₄	—	2	2	no	—
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	4	yes	—
27	C₃×C₅×#102	C₂²	1	2	yes	—
28	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
29	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
30	C₃×#3283	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₂×C₅×#135	C₂×C₃	1	2	yes	complemented
32	C₅×#547	C₂×C₃	1	2	yes	complemented
33	C₅×#494	C₂×C₃	1	1	yes	characteristic, complemented
34	C₅×#467	C₂×C₃	1	2	yes	complemented
35	C₅×#461	C₂×C₃	1	2	yes	complemented
36	C₅×#452	C₂×C₃	1	4	yes	complemented
37	C₄×C₅×D₈	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	4	yes	—
42	C₂×C₃×C₅×D₄	—	2	4	no	—
43	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
44	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
45	C₂²×C₃×C₄×C₅	—	2	2	no	—
46	C₂²×C₃×C₄×C₅	—	2	4	no	—
47	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
48	C₃×C₅×Q₁₆	—	2	4	no	—
49	C₃×C₅×Q₁₆	—	4	2	no	—
50	C₃×C₅×SD₁₆	—	2	8	no	—
51	C₃×C₅×D₈	D₄	1	4	yes	complemented
52	C₂×C₃×C₅×C₈	—	2	4	no	—
53	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
54	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
55	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
56	C₃×C₅×C₄⋊C₄	—	2	2	no	—
57	C₃×C₅×C₄⋊C₄	—	2	4	no	—
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	—	2	2	no	—
63	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
64	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
65	C₂×C₃×#135	C₂×C₅	1	2	yes	complemented
66	C₃×#547	C₂×C₅	1	2	yes	complemented
67	C₃×#494	C₂×C₅	1	1	yes	characteristic, complemented
68	C₃×#467	C₂×C₅	1	2	yes	complemented
69	C₃×#461	C₂×C₅	1	2	yes	complemented
70	C₃×#452	C₂×C₅	1	4	yes	complemented
71	C₃×C₄×D₈	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	2	yes	—
76	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	—
77	C₂×C₅×SD₁₆	C₂²×C₃	1	4	yes	—
78	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
79	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
80	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
81	C₅×#123	—	2	4	no	—
82	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
83	C₅×#121	—	2	2	no	—
84	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
85	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
86	C₂×C₅×C₄⋊C₄	—	2	2	no	—
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	4	yes	—
90	C₅×#102	C₂²×C₃	1	2	yes	—
91	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
92	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
93	#3283	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
94	C₂³×C₃×C₅	—	2	2	no	—
95	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
96	C₃×C₅×Q₈	—	2	4	no	—
97	C₃×C₅×Q₈	—	2	4	no	—
98	C₃×C₅×D₄	—	2	2	no	—
99	C₃×C₅×D₄	—	2	2	no	—
100	C₃×C₅×D₄	—	4	8	no	—
101	C₃×C₅×D₄	C₂×D₄	1	4	yes	—
102	C₂×C₃×C₄×C₅	—	2	2	no	—
103	C₂×C₃×C₄×C₅	—	2	2	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	—	2	4	no	—
106	C₂×C₃×C₄×C₅	—	4	8	no	—
107	C₂×C₃×C₄×C₅	—	4	4	no	—
108	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
110	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
111	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
112	C₃×C₅×C₈	—	2	2	no	—
113	C₃×C₅×C₈	—	2	1	no	—
114	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
115	C₂×C₃×#41	C₂²×C₅	1	4	yes	—
116	C₃×#135	—	2	8	no	—
117	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	—
118	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	—
119	C₂×C₃×SD₁₆	C₂²×C₅	1	4	yes	—
120	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
121	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
122	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
123	C₃×#123	—	2	4	no	—
124	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
125	C₃×#121	—	2	2	no	—
126	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
127	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
128	C₂×C₃×C₄⋊C₄	—	2	2	no	—
129	C₃×#107	C₂²×C₅	1	1	yes	characteristic
130	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
131	C₃×#103	C₂²×C₅	1	4	yes	—
132	C₃×#102	C₂²×C₅	1	2	yes	—
133	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
134	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
135	C₅×#41	—	2	8	no	—
136	C₅×#41	—	4	4	no	—
137	C₂×C₅×Q₈	C₂³×C₃	1	4	yes	—
138	C₂×C₅×D₄	—	2	4	no	—
139	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
140	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
141	C₂²×C₄×C₅	—	2	2	no	—
142	C₂²×C₄×C₅	—	2	4	no	—
143	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
144	C₅×Q₁₆	—	2	4	no	—
145	C₅×Q₁₆	—	4	2	no	—
146	C₅×SD₁₆	—	2	8	no	—
147	C₅×D₈	C₃×D₄	1	4	yes	complemented
148	C₂×C₅×C₈	—	2	4	no	—
149	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
150	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
151	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
152	C₅×C₄⋊C₄	—	2	2	no	—
153	C₅×C₄⋊C₄	—	2	4	no	—
154	C₅×C₄⋊C₄	—	2	2	no	—
155	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
156	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
157	C₅×C₂²⋊C₄	—	2	4	no	—
158	C₅×C₂²⋊C₄	—	2	2	no	—
159	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
160	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
161	C₂×#135	C₂×C₃×C₅	1	2	yes	complemented
162	#547	C₂×C₃×C₅	1	2	yes	complemented
163	#494	C₂×C₃×C₅	1	1	yes	characteristic, complemented
164	#467	C₂×C₃×C₅	1	2	yes	complemented
165	#461	C₂×C₃×C₅	1	2	yes	complemented
166	#452	C₂×C₃×C₅	1	4	yes	complemented
167	C₄×D₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
168	C₈×D₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
169	C₂²×C₃×C₅	—	2	2	no	—
170	C₂²×C₃×C₅	—	2	4	no	—
171	C₂²×C₃×C₅	—	2	2	no	—
172	C₂²×C₃×C₅	—	2	2	no	—
173	C₂²×C₃×C₅	—	4	2	no	—
174	C₂²×C₃×C₅	—	4	2	no	—
175	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
176	C₃×C₄×C₅	—	2	2	no	—
177	C₃×C₄×C₅	—	2	1	no	—
178	C₃×C₄×C₅	—	4	4	no	—
179	C₃×C₄×C₅	—	4	2	no	—
180	C₃×C₄×C₅	#135	1	2	yes	complemented
181	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
182	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
183	C₃×#41	—	2	8	no	—
184	C₃×#41	—	4	4	no	—
185	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
186	C₂×C₃×D₄	—	2	4	no	—
187	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
188	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
189	C₂²×C₃×C₄	—	2	2	no	—
190	C₂²×C₃×C₄	—	2	4	no	—
191	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
192	C₃×Q₁₆	—	2	4	no	—
193	C₃×Q₁₆	—	4	2	no	—
194	C₃×SD₁₆	—	2	8	no	—
195	C₃×D₈	C₅×D₄	1	4	yes	complemented
196	C₂×C₃×C₈	—	2	4	no	—
197	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
198	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
199	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
200	C₃×C₄⋊C₄	—	2	2	no	—
201	C₃×C₄⋊C₄	—	2	4	no	—
202	C₃×C₄⋊C₄	—	2	2	no	—
203	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
204	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
205	C₃×C₂²⋊C₄	—	2	4	no	—
206	C₃×C₂²⋊C₄	—	2	2	no	—
207	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
208	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
209	C₂³×C₅	—	2	2	no	—
210	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
211	C₅×Q₈	—	2	4	no	—
212	C₅×Q₈	—	2	4	no	—
213	C₅×D₄	—	2	2	no	—
214	C₅×D₄	—	2	2	no	—
215	C₅×D₄	—	4	8	no	—
216	C₅×D₄	C₂×C₃×D₄	1	4	yes	—
217	C₂×C₄×C₅	—	2	2	no	—
218	C₂×C₄×C₅	—	2	2	no	—
219	C₂×C₄×C₅	—	2	2	no	—
220	C₂×C₄×C₅	—	2	4	no	—
221	C₂×C₄×C₅	—	4	8	no	—
222	C₂×C₄×C₅	—	4	4	no	—
223	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
224	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
225	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
226	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
227	C₅×C₈	—	2	2	no	—
228	C₅×C₈	—	2	1	no	—
229	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
230	C₂×#41	C₂²×C₃×C₅	1	4	yes	—
231	#135	—	2	8	no	—
232	C₂×Q₁₆	C₂²×C₃×C₅	1	2	yes	—
233	C₂×Q₁₆	C₂²×C₃×C₅	1	2	yes	—
234	C₂×SD₁₆	C₂²×C₃×C₅	1	4	yes	—
235	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
236	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
237	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
238	#123	—	2	4	no	—
239	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
240	#121	—	2	2	no	—
241	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
242	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
243	C₂×C₄⋊C₄	—	2	2	no	—
244	#107	C₂²×C₃×C₅	1	1	yes	characteristic
245	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
246	#103	C₂²×C₃×C₅	1	4	yes	—
247	#102	C₂²×C₃×C₅	1	2	yes	—
248	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
249	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
250	C₂×C₃×C₅	—	4	2	no	—
251	C₂×C₃×C₅	—	4	4	no	—
252	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
253	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
254	C₂×C₃×C₅	#578	1	1	yes	characteristic
255	C₂³×C₃	—	2	2	no	—
256	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
257	C₃×Q₈	—	2	4	no	—
258	C₃×Q₈	—	2	4	no	—
259	C₃×D₄	—	2	2	no	—
260	C₃×D₄	—	2	2	no	—
261	C₃×D₄	—	4	8	no	—
262	C₃×D₄	C₂×C₅×D₄	1	4	yes	—
263	C₂×C₃×C₄	—	2	2	no	—
264	C₂×C₃×C₄	—	2	2	no	—
265	C₂×C₃×C₄	—	2	2	no	—
266	C₂×C₃×C₄	—	2	4	no	—
267	C₂×C₃×C₄	—	4	8	no	—
268	C₂×C₃×C₄	—	4	4	no	—
269	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
270	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
271	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
272	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
273	C₃×C₈	—	2	2	no	—
274	C₃×C₈	—	2	1	no	—
275	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
276	C₂²×C₅	—	2	2	no	—
277	C₂²×C₅	—	2	2	no	—
278	C₂²×C₅	—	2	2	no	—
279	C₂²×C₅	—	2	4	no	—
280	C₂²×C₅	—	4	2	no	—
281	C₂²×C₅	—	4	2	no	—
282	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
283	C₄×C₅	—	2	1	no	—
284	C₄×C₅	—	2	2	no	—
285	C₄×C₅	—	4	2	no	—
286	C₄×C₅	—	4	4	no	—
287	C₄×C₅	C₃×#135	1	2	yes	complemented
288	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
289	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
290	#41	—	2	8	no	—
291	#41	—	4	4	no	—
292	C₂×Q₈	C₂³×C₃×C₅	1	4	yes	—
293	C₂×D₄	—	2	4	no	—
294	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
295	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
299	Q₁₆	—	2	4	no	—
300	Q₁₆	—	4	2	no	—
301	SD₁₆	—	2	8	no	—
302	D₈	C₃×C₅×D₄	1	4	yes	complemented
303	C₂×C₈	—	2	4	no	—
304	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
305	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
306	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	4	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
311	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
312	C₂²⋊C₄	—	2	4	no	—
313	C₂²⋊C₄	—	2	2	no	—
314	C₂²⋊C₄	C₃×C₅×D₄	1	2	yes	—
315	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
316	C₃×C₅	#3283	1	1	yes	characteristic, direct product factor, Hall
317	C₂²×C₃	—	2	2	no	—
318	C₂²×C₃	—	2	4	no	—
319	C₂²×C₃	—	2	2	no	—
320	C₂²×C₃	—	2	2	no	—
321	C₂²×C₃	—	4	2	no	—
322	C₂²×C₃	—	4	2	no	—
323	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
324	C₃×C₄	—	2	2	no	—
325	C₃×C₄	—	2	1	no	—
326	C₃×C₄	—	4	4	no	—
327	C₃×C₄	—	4	2	no	—
328	C₃×C₄	C₅×#135	1	2	yes	complemented
329	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
330	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
331	C₂×C₅	—	4	2	no	—
332	C₂×C₅	—	4	4	no	—
333	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
334	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
335	C₂×C₅	C₃×#578	1	1	yes	characteristic
336	C₂³	—	2	2	no	—
337	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
338	Q₈	—	2	4	no	—
339	Q₈	—	2	4	no	—
340	D₄	—	2	2	no	—
341	D₄	—	2	2	no	—
342	D₄	—	4	8	no	—
343	D₄	C₂×C₃×C₅×D₄	1	4	yes	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	4	8	no	—
349	C₂×C₄	—	4	4	no	—
350	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
351	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
352	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
353	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
354	C₈	—	2	2	no	—
355	C₈	—	2	1	no	—
356	C₈	C₂×C₃×C₅×D₄	1	2	yes	—
357	C₂×C₃	—	4	2	no	—
358	C₂×C₃	—	4	4	no	—
359	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
360	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
361	C₂×C₃	C₅×#578	1	1	yes	characteristic
362	C₅	C₃×#3283	1	1	yes	characteristic, direct product factor, Sylow
363	C₂²	—	2	2	no	—
364	C₂²	—	2	4	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	2	2	no	—
367	C₂²	—	4	2	no	—
368	C₂²	—	4	2	no	—
369	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
370	C₄	—	2	2	no	—
371	C₄	—	2	1	no	—
372	C₄	—	4	4	no	—
373	C₄	—	4	2	no	—
374	C₄	C₃×C₅×#135	1	2	yes	complemented
375	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
376	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
377	C₃	C₅×#3283	1	1	yes	characteristic, direct product factor, Sylow
378	C₂	—	4	2	no	—
379	C₂	—	4	4	no	—
380	C₂	C₃×C₅×D₄²	1	1	yes	characteristic
381	C₂	C₂×C₃×C₅×#135	1	1	yes	characteristic
382	C₂	C₃×C₅×#578	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×#547	C₂	semidirect
3. C₃×C₅×#494	C₂	semidirect
4. C₃×C₅×#467	C₂	semidirect
5. C₃×C₅×#461	C₂	semidirect
6. C₃×C₅×#452	C₂	semidirect
7. C₃×C₄×C₅×D₈	C₂	semidirect
8. C₃×C₅×C₈×D₄	C₂	semidirect
9. C₅×#3283	C₃	direct (N × H)
30. C₃×#3283	C₅	direct (N × H)
31. C₂×C₅×#135	C₂×C₃	semidirect
32. C₅×#547	C₂×C₃	semidirect
33. C₅×#494	C₂×C₃	semidirect
34. C₅×#467	C₂×C₃	semidirect
35. C₅×#461	C₂×C₃	semidirect
36. C₅×#452	C₂×C₃	semidirect
37. C₄×C₅×D₈	C₂×C₃	semidirect
38. C₅×C₈×D₄	C₂×C₃	semidirect
51. C₃×C₅×D₈	D₄	semidirect
65. C₂×C₃×#135	C₂×C₅	semidirect
66. C₃×#547	C₂×C₅	semidirect
67. C₃×#494	C₂×C₅	semidirect
68. C₃×#467	C₂×C₅	semidirect
69. C₃×#461	C₂×C₅	semidirect
70. C₃×#452	C₂×C₅	semidirect
71. C₃×C₄×D₈	C₂×C₅	semidirect
72. C₃×C₈×D₄	C₂×C₅	semidirect
93. #3283	C₃×C₅	direct (N × H)
147. C₅×D₈	C₃×D₄	semidirect
161. C₂×#135	C₂×C₃×C₅	semidirect
162. #547	C₂×C₃×C₅	semidirect
163. #494	C₂×C₃×C₅	semidirect
164. #467	C₂×C₃×C₅	semidirect
165. #461	C₂×C₃×C₅	semidirect
166. #452	C₂×C₃×C₅	semidirect
167. C₄×D₈	C₂×C₃×C₅	semidirect
168. C₈×D₄	C₂×C₃×C₅	semidirect
180. C₃×C₄×C₅	#135	semidirect
195. C₃×D₈	C₅×D₄	semidirect
287. C₄×C₅	C₃×#135	semidirect
302. D₈	C₃×C₅×D₄	semidirect
316. C₃×C₅	#3283	direct (N × H)
328. C₃×C₄	C₅×#135	semidirect
362. C₅	C₃×#3283	direct (N × H)
374. C₄	C₃×C₅×#135	semidirect
377. C₃	C₅×#3283	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×#547	2
C₃×C₅×#494	2
C₃×C₅×#467	2
C₃×C₅×#461	2
C₃×C₅×#452	2
C₃×C₄×C₅×D₈	2
C₃×C₅×C₈×D₄	2
C₅×#3283	3
C₃×#3283	5

Subgroups — C3×C5×#3283 #14276317

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3283 #14276317