Subgroups — C₃×C₅×#3093 #14276127

Order 1920.

828 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#525	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#485	C₂	1	4	yes	maximal, complemented
4	C₃×C₅×#482	C₂	1	4	yes	maximal, complemented
5	C₃×C₅×#428	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#417	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#407	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#3093	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
12	C₃×C₅×#123	—	2	1	no	—
13	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
14	C₃×C₅×#121	C₂²	1	2	yes	—
15	C₃×C₅×#120	—	2	1	no	—
16	C₃×C₄×C₅×D₄	—	2	2	no	—
17	C₃×C₅×#117	—	2	2	no	—
18	C₃×C₅×#117	C₂²	1	4	yes	—
19	C₃×C₅×#117	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
21	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
22	C₂×C₃×C₄²×C₅	—	2	1	no	—
23	C₃×C₅×#107	C₂²	1	4	yes	complemented
24	C₃×C₅×#106	C₂²	1	4	yes	complemented
25	C₃×C₅×#103	C₂²	1	4	yes	complemented
26	C₃×C₅×#102	C₂²	1	4	yes	complemented
27	C₃×C₅×C₂²⋊C₈	C₂²	1	4	yes	—
28	C₃×#3093	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₅×#525	C₂×C₃	1	1	yes	characteristic
30	C₂×C₅×#117	C₂×C₃	1	1	yes	characteristic, complemented
31	C₅×#485	C₂×C₃	1	4	yes	complemented
32	C₅×#482	C₂×C₃	1	4	yes	complemented
33	C₅×#428	C₂×C₃	1	2	yes	complemented
34	C₅×#417	C₂×C₃	1	2	yes	complemented
35	C₅×#407	C₂×C₃	1	1	yes	characteristic, complemented
36	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
37	C₃×C₅×#41	—	2	4	no	—
38	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
39	C₂×C₃×C₅×D₄	—	2	2	no	—
40	C₂×C₃×C₅×D₄	—	2	1	no	—
41	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	—	2	4	no	—
43	C₂²×C₃×C₄×C₅	—	2	2	no	—
44	C₂²×C₃×C₄×C₅	—	2	1	no	—
45	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
46	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
47	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
48	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
49	C₃×C₅×M₁₆	—	2	4	no	—
50	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
51	C₃×C₅×C₄⋊C₄	—	2	2	no	—
52	C₃×C₅×C₄⋊C₄	—	2	2	no	—
53	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
54	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
55	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
56	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
57	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
58	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
59	C₃×C₄²×C₅	—	2	4	no	—
60	C₃×C₄²×C₅	—	2	1	no	—
61	C₃×#525	C₂×C₅	1	1	yes	characteristic
62	C₂×C₃×#117	C₂×C₅	1	1	yes	characteristic, complemented
63	C₃×#485	C₂×C₅	1	4	yes	complemented
64	C₃×#482	C₂×C₅	1	4	yes	complemented
65	C₃×#428	C₂×C₅	1	2	yes	complemented
66	C₃×#417	C₂×C₅	1	2	yes	complemented
67	C₃×#407	C₂×C₅	1	1	yes	characteristic, complemented
68	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
69	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
70	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
71	C₅×#123	—	2	1	no	—
72	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
73	C₅×#121	C₂²×C₃	1	2	yes	—
74	C₅×#120	—	2	1	no	—
75	C₄×C₅×D₄	—	2	2	no	—
76	C₅×#117	—	2	2	no	—
77	C₅×#117	C₂²×C₃	1	1	yes	characteristic
78	C₅×#117	C₂²×C₃	1	4	yes	—
79	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
80	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
81	C₂×C₄²×C₅	—	2	1	no	—
82	C₅×#107	C₂²×C₃	1	4	yes	complemented
83	C₅×#106	C₂²×C₃	1	4	yes	complemented
84	C₅×#103	C₂²×C₃	1	4	yes	complemented
85	C₅×#102	C₂²×C₃	1	4	yes	complemented
86	C₅×C₂²⋊C₈	C₂²×C₃	1	4	yes	—
87	#3093	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
88	C₂³×C₃×C₅	—	2	2	no	—
89	C₂³×C₃×C₅	—	2	1	no	—
90	C₂³×C₃×C₅	—	4	2	no	—
91	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
92	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
93	C₃×C₅×Q₈	—	2	2	no	—
94	C₃×C₅×D₄	—	2	2	no	—
95	C₃×C₅×D₄	—	4	4	no	—
96	C₃×C₅×D₄	—	4	2	no	—
97	C₂×C₃×C₄×C₅	—	2	2	no	—
98	C₂×C₃×C₄×C₅	—	2	4	no	—
99	C₂×C₃×C₄×C₅	—	2	4	no	—
100	C₂×C₃×C₄×C₅	—	2	4	no	—
101	C₂×C₃×C₄×C₅	—	2	2	no	—
102	C₂×C₃×C₄×C₅	—	2	1	no	—
103	C₂×C₃×C₄×C₅	—	4	4	no	—
104	C₂×C₃×C₄×C₅	—	4	2	no	—
105	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
106	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	#41	1	4	yes	—
108	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
109	C₃×C₅×C₈	—	2	4	no	—
110	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
111	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
112	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
113	C₃×#123	—	2	1	no	—
114	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
115	C₃×#121	C₂²×C₅	1	2	yes	—
116	C₃×#120	—	2	1	no	—
117	C₃×C₄×D₄	—	2	2	no	—
118	C₃×#117	—	2	2	no	—
119	C₃×#117	C₂²×C₅	1	1	yes	characteristic
120	C₃×#117	C₂²×C₅	1	4	yes	—
121	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
122	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
123	C₂×C₃×C₄²	—	2	1	no	—
124	C₃×#107	C₂²×C₅	1	4	yes	complemented
125	C₃×#106	C₂²×C₅	1	4	yes	complemented
126	C₃×#103	C₂²×C₅	1	4	yes	complemented
127	C₃×#102	C₂²×C₅	1	4	yes	complemented
128	C₃×C₂²⋊C₈	C₂²×C₅	1	4	yes	—
129	C₂⁴×C₅	C₃×D₄	1	1	yes	characteristic
130	C₅×#41	—	2	4	no	—
131	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
132	C₂×C₅×D₄	—	2	2	no	—
133	C₂×C₅×D₄	—	2	1	no	—
134	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
135	C₂²×C₄×C₅	—	2	4	no	—
136	C₂²×C₄×C₅	—	2	2	no	—
137	C₂²×C₄×C₅	—	2	1	no	—
138	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
140	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
141	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
142	C₅×M₁₆	—	2	4	no	—
143	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
144	C₅×C₄⋊C₄	—	2	2	no	—
145	C₅×C₄⋊C₄	—	2	2	no	—
146	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
147	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
148	C₅×C₂²⋊C₄	—	2	4	no	—
149	C₅×C₂²⋊C₄	—	2	1	no	—
150	C₅×C₂²⋊C₄	—	2	2	no	—
151	C₅×C₂²⋊C₄	—	2	2	no	—
152	C₄²×C₅	—	2	4	no	—
153	C₄²×C₅	—	2	1	no	—
154	#525	C₂×C₃×C₅	1	1	yes	characteristic
155	C₂×#117	C₂×C₃×C₅	1	1	yes	characteristic, complemented
156	#485	C₂×C₃×C₅	1	4	yes	complemented
157	#482	C₂×C₃×C₅	1	4	yes	complemented
158	#428	C₂×C₃×C₅	1	2	yes	complemented
159	#417	C₂×C₃×C₅	1	2	yes	complemented
160	#407	C₂×C₃×C₅	1	1	yes	characteristic, complemented
161	C₂²×C₃×C₅	—	2	2	no	—
162	C₂²×C₃×C₅	—	2	2	no	—
163	C₂²×C₃×C₅	—	2	2	no	—
164	C₂²×C₃×C₅	—	2	2	no	—
165	C₂²×C₃×C₅	—	4	4	no	—
166	C₂²×C₃×C₅	—	4	1	no	—
167	C₂²×C₃×C₅	—	4	2	no	—
168	C₂²×C₃×C₅	#123	1	2	yes	—
169	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
170	C₃×C₄×C₅	—	2	2	no	—
171	C₃×C₄×C₅	—	4	1	no	—
172	C₃×C₄×C₅	—	4	4	no	—
173	C₃×C₄×C₅	—	4	2	no	—
174	C₃×C₄×C₅	#123	1	2	yes	—
175	C₃×C₄×C₅	C₂×#41	1	2	yes	—
176	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
177	C₃×#41	—	2	4	no	—
178	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
179	C₂×C₃×D₄	—	2	2	no	—
180	C₂×C₃×D₄	—	2	1	no	—
181	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
182	C₂²×C₃×C₄	—	2	4	no	—
183	C₂²×C₃×C₄	—	2	2	no	—
184	C₂²×C₃×C₄	—	2	1	no	—
185	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
186	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
187	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
188	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
189	C₃×M₁₆	—	2	4	no	—
190	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
191	C₃×C₄⋊C₄	—	2	2	no	—
192	C₃×C₄⋊C₄	—	2	2	no	—
193	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
194	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
195	C₃×C₂²⋊C₄	—	2	4	no	—
196	C₃×C₂²⋊C₄	—	2	1	no	—
197	C₃×C₂²⋊C₄	—	2	2	no	—
198	C₃×C₂²⋊C₄	—	2	2	no	—
199	C₃×C₄²	—	2	4	no	—
200	C₃×C₄²	—	2	1	no	—
201	C₂³×C₅	—	2	2	no	—
202	C₂³×C₅	—	2	1	no	—
203	C₂³×C₅	—	4	2	no	—
204	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
205	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
206	C₅×Q₈	—	2	2	no	—
207	C₅×D₄	—	2	2	no	—
208	C₅×D₄	—	4	4	no	—
209	C₅×D₄	—	4	2	no	—
210	C₂×C₄×C₅	—	2	2	no	—
211	C₂×C₄×C₅	—	2	4	no	—
212	C₂×C₄×C₅	—	2	4	no	—
213	C₂×C₄×C₅	—	2	4	no	—
214	C₂×C₄×C₅	—	2	2	no	—
215	C₂×C₄×C₅	—	2	1	no	—
216	C₂×C₄×C₅	—	4	4	no	—
217	C₂×C₄×C₅	—	4	2	no	—
218	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
219	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
220	C₂×C₄×C₅	C₃×#41	1	4	yes	—
221	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
222	C₅×C₈	—	2	4	no	—
223	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
224	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
225	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
226	#123	—	2	1	no	—
227	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
228	#121	C₂²×C₃×C₅	1	2	yes	—
229	#120	—	2	1	no	—
230	C₄×D₄	—	2	2	no	—
231	#117	—	2	2	no	—
232	#117	C₂²×C₃×C₅	1	4	yes	—
233	#117	C₂²×C₃×C₅	1	1	yes	characteristic
234	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
235	C₂×C₂²⋊C₄	—	2	1	no	—
236	C₂×C₄²	—	2	1	no	—
237	#107	C₂²×C₃×C₅	1	4	yes	complemented
238	#106	C₂²×C₃×C₅	1	4	yes	complemented
239	#103	C₂²×C₃×C₅	1	4	yes	complemented
240	#102	C₂²×C₃×C₅	1	4	yes	complemented
241	C₂²⋊C₈	C₂²×C₃×C₅	1	4	yes	—
242	C₂×C₃×C₅	—	2	2	no	—
243	C₂×C₃×C₅	—	4	2	no	—
244	C₂×C₃×C₅	—	8	1	no	—
245	C₂×C₃×C₅	C₂×#123	1	1	yes	characteristic
246	C₂×C₃×C₅	#575	1	2	yes	—
247	C₂³×C₃	—	2	2	no	—
248	C₂³×C₃	—	2	1	no	—
249	C₂³×C₃	—	4	2	no	—
250	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
251	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
252	C₃×Q₈	—	2	2	no	—
253	C₃×D₄	—	2	2	no	—
254	C₃×D₄	—	4	4	no	—
255	C₃×D₄	—	4	2	no	—
256	C₂×C₃×C₄	—	2	2	no	—
257	C₂×C₃×C₄	—	2	4	no	—
258	C₂×C₃×C₄	—	2	4	no	—
259	C₂×C₃×C₄	—	2	4	no	—
260	C₂×C₃×C₄	—	2	2	no	—
261	C₂×C₃×C₄	—	2	1	no	—
262	C₂×C₃×C₄	—	4	4	no	—
263	C₂×C₃×C₄	—	4	2	no	—
264	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
265	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
266	C₂×C₃×C₄	C₅×#41	1	4	yes	—
267	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
268	C₃×C₈	—	2	4	no	—
269	C₂²×C₅	—	2	2	no	—
270	C₂²×C₅	—	2	2	no	—
271	C₂²×C₅	—	2	2	no	—
272	C₂²×C₅	—	2	2	no	—
273	C₂²×C₅	—	4	4	no	—
274	C₂²×C₅	—	4	2	no	—
275	C₂²×C₅	—	4	1	no	—
276	C₂²×C₅	C₃×#123	1	2	yes	—
277	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
278	C₄×C₅	—	2	2	no	—
279	C₄×C₅	—	4	4	no	—
280	C₄×C₅	—	4	2	no	—
281	C₄×C₅	—	4	1	no	—
282	C₄×C₅	C₃×#123	1	2	yes	—
283	C₄×C₅	C₂×C₃×#41	1	2	yes	—
284	C₂⁴	C₃×C₅×D₄	1	1	yes	characteristic
285	#41	—	2	4	no	—
286	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	1	no	—
289	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
290	C₂²×C₄	—	2	4	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
294	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
295	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
296	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
297	M₁₆	—	2	4	no	—
298	C₂×C₈	C₂³×C₃×C₅	1	4	yes	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
302	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
303	C₂²⋊C₄	—	2	4	no	—
304	C₂²⋊C₄	—	2	1	no	—
305	C₂²⋊C₄	—	2	2	no	—
306	C₂²⋊C₄	—	2	2	no	—
307	C₄²	—	2	4	no	—
308	C₄²	—	2	1	no	—
309	C₃×C₅	#3093	1	1	yes	characteristic, direct product factor, Hall
310	C₂²×C₃	—	2	2	no	—
311	C₂²×C₃	—	2	2	no	—
312	C₂²×C₃	—	2	2	no	—
313	C₂²×C₃	—	2	2	no	—
314	C₂²×C₃	—	4	4	no	—
315	C₂²×C₃	—	4	1	no	—
316	C₂²×C₃	—	4	2	no	—
317	C₂²×C₃	C₅×#123	1	2	yes	—
318	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
319	C₃×C₄	—	2	2	no	—
320	C₃×C₄	—	4	1	no	—
321	C₃×C₄	—	4	4	no	—
322	C₃×C₄	—	4	2	no	—
323	C₃×C₄	C₅×#123	1	2	yes	—
324	C₃×C₄	C₂×C₅×#41	1	2	yes	—
325	C₂×C₅	—	2	2	no	—
326	C₂×C₅	—	4	2	no	—
327	C₂×C₅	—	8	1	no	—
328	C₂×C₅	C₂×C₃×#123	1	1	yes	characteristic
329	C₂×C₅	C₃×#575	1	2	yes	—
330	C₂³	—	2	2	no	—
331	C₂³	—	2	1	no	—
332	C₂³	—	4	2	no	—
333	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
334	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
335	Q₈	—	2	2	no	—
336	D₄	—	2	2	no	—
337	D₄	—	4	4	no	—
338	D₄	—	4	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	4	4	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
348	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
349	C₂×C₄	C₃×C₅×#41	1	4	yes	—
350	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
351	C₈	—	2	4	no	—
352	C₂×C₃	—	2	2	no	—
353	C₂×C₃	—	4	2	no	—
354	C₂×C₃	—	8	1	no	—
355	C₂×C₃	C₂×C₅×#123	1	1	yes	characteristic
356	C₂×C₃	C₅×#575	1	2	yes	—
357	C₅	C₃×#3093	1	1	yes	characteristic, direct product factor, Sylow
358	C₂²	—	2	2	no	—
359	C₂²	—	2	2	no	—
360	C₂²	—	2	2	no	—
361	C₂²	—	2	2	no	—
362	C₂²	—	4	4	no	—
363	C₂²	—	4	1	no	—
364	C₂²	—	4	2	no	—
365	C₂²	C₃×C₅×#123	1	2	yes	—
366	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
367	C₄	—	2	2	no	—
368	C₄	—	4	1	no	—
369	C₄	—	4	4	no	—
370	C₄	—	4	2	no	—
371	C₄	C₃×C₅×#123	1	2	yes	—
372	C₄	C₂×C₃×C₅×#41	1	2	yes	—
373	C₃	C₅×#3093	1	1	yes	characteristic, direct product factor, Sylow
374	C₂	—	2	2	no	—
375	C₂	—	4	2	no	—
376	C₂	—	8	1	no	—
377	C₂	C₂×C₃×C₅×#123	1	1	yes	characteristic
378	C₂	C₃×C₅×#575	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×#525	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂³×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×#117	C₂	semidirect
3. C₃×C₅×#485	C₂	semidirect
4. C₃×C₅×#482	C₂	semidirect
5. C₃×C₅×#428	C₂	semidirect
6. C₃×C₅×#417	C₂	semidirect
7. C₃×C₅×#407	C₂	semidirect
8. C₅×#3093	C₃	direct (N × H)
23. C₃×C₅×#107	C₂²	semidirect
24. C₃×C₅×#106	C₂²	semidirect
25. C₃×C₅×#103	C₂²	semidirect
26. C₃×C₅×#102	C₂²	semidirect
28. C₃×#3093	C₅	direct (N × H)
30. C₂×C₅×#117	C₂×C₃	semidirect
31. C₅×#485	C₂×C₃	semidirect
32. C₅×#482	C₂×C₃	semidirect
33. C₅×#428	C₂×C₃	semidirect
34. C₅×#417	C₂×C₃	semidirect
35. C₅×#407	C₂×C₃	semidirect
62. C₂×C₃×#117	C₂×C₅	semidirect
63. C₃×#485	C₂×C₅	semidirect
64. C₃×#482	C₂×C₅	semidirect
65. C₃×#428	C₂×C₅	semidirect
66. C₃×#417	C₂×C₅	semidirect
67. C₃×#407	C₂×C₅	semidirect
82. C₅×#107	C₂²×C₃	semidirect
83. C₅×#106	C₂²×C₃	semidirect
84. C₅×#103	C₂²×C₃	semidirect
85. C₅×#102	C₂²×C₃	semidirect
87. #3093	C₃×C₅	direct (N × H)
124. C₃×#107	C₂²×C₅	semidirect
125. C₃×#106	C₂²×C₅	semidirect
126. C₃×#103	C₂²×C₅	semidirect
127. C₃×#102	C₂²×C₅	semidirect
155. C₂×#117	C₂×C₃×C₅	semidirect
156. #485	C₂×C₃×C₅	semidirect
157. #482	C₂×C₃×C₅	semidirect
158. #428	C₂×C₃×C₅	semidirect
159. #417	C₂×C₃×C₅	semidirect
160. #407	C₂×C₃×C₅	semidirect
237. #107	C₂²×C₃×C₅	semidirect
238. #106	C₂²×C₃×C₅	semidirect
239. #103	C₂²×C₃×C₅	semidirect
240. #102	C₂²×C₃×C₅	semidirect
309. C₃×C₅	#3093	direct (N × H)
357. C₅	C₃×#3093	direct (N × H)
373. C₃	C₅×#3093	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×#525	2
C₂×C₃×C₅×#117	2
C₃×C₅×#485	2
C₃×C₅×#482	2
C₃×C₅×#428	2
C₃×C₅×#417	2
C₃×C₅×#407	2
C₅×#3093	3
C₃×#3093	5

Subgroups — C3×C5×#3093 #14276127

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3093 #14276127