Subgroups — C₃×C₅×#3058 #14276092

Order 1920.

1048 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#131	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#535	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#469	C₂	1	4	yes	maximal, complemented
5	C₃×C₅×#466	C₂	1	4	yes	maximal, complemented
6	C₃×C₅×#427	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#418	C₂	1	2	yes	maximal, complemented
8	C₅×#3058	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
11	C₂×C₃×C₅×D₈	—	2	4	no	—
12	C₂×C₃×C₅×D₈	C₂²	1	2	yes	—
13	C₂×C₃×C₅×D₈	C₂²	1	2	yes	—
14	C₃×C₅×#131	—	2	4	no	—
15	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	complemented
17	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	complemented
19	C₃×C₅×#127	—	2	2	no	—
20	C₃×C₅×#124	—	2	2	no	—
21	C₃×C₅×#121	C₂²	1	8	yes	complemented
22	C₃×C₅×#120	—	2	4	no	—
23	C₃×C₅×#117	C₂²	1	2	yes	—
24	C₃×C₅×#107	C₂²	1	2	yes	complemented
25	C₃×C₅×#106	C₂²	1	2	yes	complemented
26	C₃×C₅×#102	C₂²	1	8	yes	complemented
27	C₃×#3058	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₂²×C₅×D₈	C₂×C₃	1	1	yes	characteristic, complemented
29	C₂×C₅×#131	C₂×C₃	1	1	yes	characteristic, complemented
30	C₅×#535	C₂×C₃	1	2	yes	complemented
31	C₅×#469	C₂×C₃	1	4	yes	complemented
32	C₅×#466	C₂×C₃	1	4	yes	complemented
33	C₅×#427	C₂×C₃	1	1	yes	characteristic, complemented
34	C₅×#418	C₂×C₃	1	2	yes	complemented
35	C₂⁴×C₃×C₅	—	2	2	no	—
36	C₃×C₅×#41	—	2	2	no	—
37	C₃×C₅×#41	—	2	2	no	—
38	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
39	C₂×C₃×C₅×D₄	—	2	8	no	—
40	C₂×C₃×C₅×D₄	—	2	4	no	—
41	C₂×C₃×C₅×D₄	—	2	2	no	—
42	C₂×C₃×C₅×D₄	—	2	4	no	—
43	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
44	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
45	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
46	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
47	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
48	C₃×C₅×D₈	—	2	4	no	—
49	C₃×C₅×D₈	—	2	4	no	—
50	C₃×C₅×M₁₆	—	2	2	no	—
51	C₃×C₅×M₁₆	—	2	4	no	—
52	C₂×C₃×C₅×C₈	—	2	4	no	—
53	C₂×C₃×C₅×C₈	D₄	1	4	yes	complemented
54	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
55	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
56	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
57	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
58	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
59	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
60	C₃×C₄²×C₅	—	2	2	no	—
61	C₂²×C₃×D₈	C₂×C₅	1	1	yes	characteristic, complemented
62	C₂×C₃×#131	C₂×C₅	1	1	yes	characteristic, complemented
63	C₃×#535	C₂×C₅	1	2	yes	complemented
64	C₃×#469	C₂×C₅	1	4	yes	complemented
65	C₃×#466	C₂×C₅	1	4	yes	complemented
66	C₃×#427	C₂×C₅	1	1	yes	characteristic, complemented
67	C₃×#418	C₂×C₅	1	2	yes	complemented
68	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
69	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
70	C₂×C₅×D₈	—	2	4	no	—
71	C₂×C₅×D₈	C₂²×C₃	1	2	yes	—
72	C₂×C₅×D₈	C₂²×C₃	1	2	yes	—
73	C₅×#131	—	2	4	no	—
74	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
75	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	complemented
76	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
77	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	complemented
78	C₅×#127	—	2	2	no	—
79	C₅×#124	—	2	2	no	—
80	C₅×#121	C₂²×C₃	1	8	yes	complemented
81	C₅×#120	—	2	4	no	—
82	C₅×#117	C₂²×C₃	1	2	yes	—
83	C₅×#107	C₂²×C₃	1	2	yes	complemented
84	C₅×#106	C₂²×C₃	1	2	yes	complemented
85	C₅×#102	C₂²×C₃	1	8	yes	complemented
86	#3058	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
87	C₂³×C₃×C₅	—	2	4	no	—
88	C₂³×C₃×C₅	—	4	4	no	—
89	C₂³×C₃×C₅	—	8	4	no	—
90	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
91	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
92	C₃×C₅×Q₈	—	2	2	no	—
93	C₃×C₅×D₄	—	2	4	no	—
94	C₃×C₅×D₄	—	2	2	no	—
95	C₃×C₅×D₄	—	2	4	no	—
96	C₃×C₅×D₄	—	2	4	no	—
97	C₃×C₅×D₄	—	4	4	no	—
98	C₃×C₅×D₄	—	8	8	no	—
99	C₂×C₃×C₄×C₅	—	2	2	no	—
100	C₂×C₃×C₄×C₅	—	2	2	no	—
101	C₂×C₃×C₄×C₅	—	2	4	no	—
102	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
103	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
105	C₂×C₃×C₄×C₅	#41	1	2	yes	—
106	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
107	C₃×C₅×C₈	—	2	2	no	—
108	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
109	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
110	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
111	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
112	C₂×C₃×D₈	—	2	4	no	—
113	C₂×C₃×D₈	C₂²×C₅	1	2	yes	—
114	C₂×C₃×D₈	C₂²×C₅	1	2	yes	—
115	C₃×#131	—	2	4	no	—
116	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
117	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	complemented
118	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
119	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	complemented
120	C₃×#127	—	2	2	no	—
121	C₃×#124	—	2	2	no	—
122	C₃×#121	C₂²×C₅	1	8	yes	complemented
123	C₃×#120	—	2	4	no	—
124	C₃×#117	C₂²×C₅	1	2	yes	—
125	C₃×#107	C₂²×C₅	1	2	yes	complemented
126	C₃×#106	C₂²×C₅	1	2	yes	complemented
127	C₃×#102	C₂²×C₅	1	8	yes	complemented
128	C₂⁴×C₅	—	2	2	no	—
129	C₅×#41	—	2	2	no	—
130	C₅×#41	—	2	2	no	—
131	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
132	C₂×C₅×D₄	—	2	8	no	—
133	C₂×C₅×D₄	—	2	4	no	—
134	C₂×C₅×D₄	—	2	2	no	—
135	C₂×C₅×D₄	—	2	4	no	—
136	C₂×C₅×D₄	C₃×D₄	1	2	yes	—
137	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
138	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
139	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
140	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
141	C₅×D₈	—	2	4	no	—
142	C₅×D₈	—	2	4	no	—
143	C₅×M₁₆	—	2	2	no	—
144	C₅×M₁₆	—	2	4	no	—
145	C₂×C₅×C₈	—	2	4	no	—
146	C₂×C₅×C₈	C₃×D₄	1	4	yes	complemented
147	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
148	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
149	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
150	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
151	C₅×C₂²⋊C₄	—	2	2	no	—
152	C₅×C₂²⋊C₄	—	2	8	no	—
153	C₄²×C₅	—	2	2	no	—
154	C₂²×D₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
155	C₂×#131	C₂×C₃×C₅	1	1	yes	characteristic, complemented
156	#535	C₂×C₃×C₅	1	2	yes	complemented
157	#469	C₂×C₃×C₅	1	4	yes	complemented
158	#466	C₂×C₃×C₅	1	4	yes	complemented
159	#427	C₂×C₃×C₅	1	1	yes	characteristic, complemented
160	#418	C₂×C₃×C₅	1	2	yes	complemented
161	C₂²×C₃×C₅	—	2	2	no	—
162	C₂²×C₃×C₅	—	2	2	no	—
163	C₂²×C₃×C₅	—	2	4	no	—
164	C₂²×C₃×C₅	—	4	4	no	—
165	C₂²×C₃×C₅	—	4	8	no	—
166	C₂²×C₃×C₅	—	8	8	no	—
167	C₂²×C₃×C₅	#121	1	2	yes	—
168	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
169	C₃×C₄×C₅	—	2	2	no	—
170	C₃×C₄×C₅	—	4	4	no	—
171	C₃×C₄×C₅	#121	1	2	yes	—
172	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
173	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
174	C₂⁴×C₃	—	2	2	no	—
175	C₃×#41	—	2	2	no	—
176	C₃×#41	—	2	2	no	—
177	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
178	C₂×C₃×D₄	—	2	8	no	—
179	C₂×C₃×D₄	—	2	4	no	—
180	C₂×C₃×D₄	—	2	2	no	—
181	C₂×C₃×D₄	—	2	4	no	—
182	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
183	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
184	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
185	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
186	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
187	C₃×D₈	—	2	4	no	—
188	C₃×D₈	—	2	4	no	—
189	C₃×M₁₆	—	2	2	no	—
190	C₃×M₁₆	—	2	4	no	—
191	C₂×C₃×C₈	—	2	4	no	—
192	C₂×C₃×C₈	C₅×D₄	1	4	yes	complemented
193	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
194	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
195	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
196	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
197	C₃×C₂²⋊C₄	—	2	2	no	—
198	C₃×C₂²⋊C₄	—	2	8	no	—
199	C₃×C₄²	—	2	2	no	—
200	C₂³×C₅	—	2	4	no	—
201	C₂³×C₅	—	4	4	no	—
202	C₂³×C₅	—	8	4	no	—
203	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
204	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
205	C₅×Q₈	—	2	2	no	—
206	C₅×D₄	—	2	4	no	—
207	C₅×D₄	—	2	2	no	—
208	C₅×D₄	—	2	4	no	—
209	C₅×D₄	—	2	4	no	—
210	C₅×D₄	—	4	4	no	—
211	C₅×D₄	—	8	8	no	—
212	C₂×C₄×C₅	—	2	2	no	—
213	C₂×C₄×C₅	—	2	2	no	—
214	C₂×C₄×C₅	—	2	4	no	—
215	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
216	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
217	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
218	C₂×C₄×C₅	C₃×#41	1	2	yes	—
219	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
220	C₅×C₈	—	2	2	no	—
221	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
222	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
223	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
224	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
225	C₂×D₈	—	2	4	no	—
226	C₂×D₈	C₂²×C₃×C₅	1	2	yes	—
227	C₂×D₈	C₂²×C₃×C₅	1	2	yes	—
228	#131	—	2	4	no	—
229	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
230	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	complemented
231	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
232	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	complemented
233	#127	—	2	2	no	—
234	#124	—	2	2	no	—
235	#121	C₂²×C₃×C₅	1	8	yes	complemented
236	#120	—	2	4	no	—
237	#117	C₂²×C₃×C₅	1	2	yes	—
238	#107	C₂²×C₃×C₅	1	2	yes	complemented
239	#106	C₂²×C₃×C₅	1	2	yes	complemented
240	#102	C₂²×C₃×C₅	1	8	yes	complemented
241	C₂×C₃×C₅	—	2	2	no	—
242	C₂×C₃×C₅	—	4	2	no	—
243	C₂×C₃×C₅	—	8	4	no	—
244	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
245	C₂×C₃×C₅	#576	1	2	yes	—
246	C₂³×C₃	—	2	4	no	—
247	C₂³×C₃	—	4	4	no	—
248	C₂³×C₃	—	8	4	no	—
249	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
250	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
251	C₃×Q₈	—	2	2	no	—
252	C₃×D₄	—	2	4	no	—
253	C₃×D₄	—	2	2	no	—
254	C₃×D₄	—	2	4	no	—
255	C₃×D₄	—	2	4	no	—
256	C₃×D₄	—	4	4	no	—
257	C₃×D₄	—	8	8	no	—
258	C₂×C₃×C₄	—	2	2	no	—
259	C₂×C₃×C₄	—	2	2	no	—
260	C₂×C₃×C₄	—	2	4	no	—
261	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
262	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
263	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
264	C₂×C₃×C₄	C₅×#41	1	2	yes	—
265	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
266	C₃×C₈	—	2	2	no	—
267	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
268	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
269	C₂²×C₅	—	2	2	no	—
270	C₂²×C₅	—	2	4	no	—
271	C₂²×C₅	—	2	2	no	—
272	C₂²×C₅	—	4	8	no	—
273	C₂²×C₅	—	4	4	no	—
274	C₂²×C₅	—	8	8	no	—
275	C₂²×C₅	C₃×#121	1	2	yes	—
276	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
277	C₄×C₅	—	2	2	no	—
278	C₄×C₅	—	4	4	no	—
279	C₄×C₅	C₃×#121	1	2	yes	—
280	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
281	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
282	C₂⁴	—	2	2	no	—
283	#41	—	2	2	no	—
284	#41	—	2	2	no	—
285	C₂×Q₈	C₃×C₅×D₄	1	1	yes	characteristic
286	C₂×D₄	—	2	8	no	—
287	C₂×D₄	—	2	4	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	4	no	—
290	C₂×D₄	C₃×C₅×D₄	1	2	yes	—
291	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
292	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
293	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
294	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
295	D₈	—	2	4	no	—
296	D₈	—	2	4	no	—
297	M₁₆	—	2	2	no	—
298	M₁₆	—	2	4	no	—
299	C₂×C₈	—	2	4	no	—
300	C₂×C₈	C₃×C₅×D₄	1	4	yes	complemented
301	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
302	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
303	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
304	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
305	C₂²⋊C₄	—	2	2	no	—
306	C₂²⋊C₄	—	2	8	no	—
307	C₄²	—	2	2	no	—
308	C₃×C₅	#3058	1	1	yes	characteristic, direct product factor, Hall
309	C₂²×C₃	—	2	2	no	—
310	C₂²×C₃	—	2	2	no	—
311	C₂²×C₃	—	2	4	no	—
312	C₂²×C₃	—	4	4	no	—
313	C₂²×C₃	—	4	8	no	—
314	C₂²×C₃	—	8	8	no	—
315	C₂²×C₃	C₅×#121	1	2	yes	—
316	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
317	C₃×C₄	—	2	2	no	—
318	C₃×C₄	—	4	4	no	—
319	C₃×C₄	C₅×#121	1	2	yes	—
320	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
321	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
322	C₂×C₅	—	2	2	no	—
323	C₂×C₅	—	4	2	no	—
324	C₂×C₅	—	8	4	no	—
325	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
326	C₂×C₅	C₃×#576	1	2	yes	—
327	C₂³	—	2	4	no	—
328	C₂³	—	4	4	no	—
329	C₂³	—	8	4	no	—
330	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
331	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
332	Q₈	—	2	2	no	—
333	D₄	—	2	4	no	—
334	D₄	—	2	4	no	—
335	D₄	—	2	2	no	—
336	D₄	—	2	4	no	—
337	D₄	—	4	4	no	—
338	D₄	—	8	8	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
343	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
344	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
345	C₂×C₄	C₃×C₅×#41	1	2	yes	—
346	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
347	C₈	—	2	2	no	—
348	C₈	C₂×C₃×C₅×D₄	1	2	yes	—
349	C₈	C₂×C₃×C₅×D₄	1	2	yes	—
350	C₂×C₃	—	2	2	no	—
351	C₂×C₃	—	4	2	no	—
352	C₂×C₃	—	8	4	no	—
353	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
354	C₂×C₃	C₅×#576	1	2	yes	—
355	C₅	C₃×#3058	1	1	yes	characteristic, direct product factor, Sylow
356	C₂²	—	2	2	no	—
357	C₂²	—	2	2	no	—
358	C₂²	—	2	4	no	—
359	C₂²	—	4	4	no	—
360	C₂²	—	4	8	no	—
361	C₂²	—	8	8	no	—
362	C₂²	C₃×C₅×#121	1	2	yes	—
363	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
364	C₄	—	2	2	no	—
365	C₄	—	4	4	no	—
366	C₄	C₃×C₅×#121	1	2	yes	—
367	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
368	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
369	C₃	C₅×#3058	1	1	yes	characteristic, direct product factor, Sylow
370	C₂	—	2	2	no	—
371	C₂	—	4	2	no	—
372	C₂	—	8	4	no	—
373	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
374	C₂	C₃×C₅×#576	1	2	yes	—

	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 ◁ C₂×C₃×C₅×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×D₈	C₂	semidirect
2. C₂×C₃×C₅×#131	C₂	semidirect
3. C₃×C₅×#535	C₂	semidirect
4. C₃×C₅×#469	C₂	semidirect
5. C₃×C₅×#466	C₂	semidirect
6. C₃×C₅×#427	C₂	semidirect
7. C₃×C₅×#418	C₂	semidirect
8. C₅×#3058	C₃	direct (N × H)
16. C₂×C₃×C₅×M₁₆	C₂²	semidirect
18. C₂²×C₃×C₅×C₈	C₂²	semidirect
21. C₃×C₅×#121	C₂²	semidirect
24. C₃×C₅×#107	C₂²	semidirect
25. C₃×C₅×#106	C₂²	semidirect
26. C₃×C₅×#102	C₂²	semidirect
27. C₃×#3058	C₅	direct (N × H)
28. C₂²×C₅×D₈	C₂×C₃	semidirect
29. C₂×C₅×#131	C₂×C₃	semidirect
30. C₅×#535	C₂×C₃	semidirect
31. C₅×#469	C₂×C₃	semidirect
32. C₅×#466	C₂×C₃	semidirect
33. C₅×#427	C₂×C₃	semidirect
34. C₅×#418	C₂×C₃	semidirect
53. C₂×C₃×C₅×C₈	D₄	semidirect
61. C₂²×C₃×D₈	C₂×C₅	semidirect
62. C₂×C₃×#131	C₂×C₅	semidirect
63. C₃×#535	C₂×C₅	semidirect
64. C₃×#469	C₂×C₅	semidirect
65. C₃×#466	C₂×C₅	semidirect
66. C₃×#427	C₂×C₅	semidirect
67. C₃×#418	C₂×C₅	semidirect
75. C₂×C₅×M₁₆	C₂²×C₃	semidirect
77. C₂²×C₅×C₈	C₂²×C₃	semidirect
80. C₅×#121	C₂²×C₃	semidirect
83. C₅×#107	C₂²×C₃	semidirect
84. C₅×#106	C₂²×C₃	semidirect
85. C₅×#102	C₂²×C₃	semidirect
86. #3058	C₃×C₅	direct (N × H)
117. C₂×C₃×M₁₆	C₂²×C₅	semidirect
119. C₂²×C₃×C₈	C₂²×C₅	semidirect
122. C₃×#121	C₂²×C₅	semidirect
125. C₃×#107	C₂²×C₅	semidirect
126. C₃×#106	C₂²×C₅	semidirect
127. C₃×#102	C₂²×C₅	semidirect
146. C₂×C₅×C₈	C₃×D₄	semidirect
154. C₂²×D₈	C₂×C₃×C₅	semidirect
155. C₂×#131	C₂×C₃×C₅	semidirect
156. #535	C₂×C₃×C₅	semidirect
157. #469	C₂×C₃×C₅	semidirect
158. #466	C₂×C₃×C₅	semidirect
159. #427	C₂×C₃×C₅	semidirect
160. #418	C₂×C₃×C₅	semidirect
192. C₂×C₃×C₈	C₅×D₄	semidirect
230. C₂×M₁₆	C₂²×C₃×C₅	semidirect
232. C₂²×C₈	C₂²×C₃×C₅	semidirect
235. #121	C₂²×C₃×C₅	semidirect
238. #107	C₂²×C₃×C₅	semidirect
239. #106	C₂²×C₃×C₅	semidirect
240. #102	C₂²×C₃×C₅	semidirect
300. C₂×C₈	C₃×C₅×D₄	semidirect
308. C₃×C₅	#3058	direct (N × H)
355. C₅	C₃×#3058	direct (N × H)
369. C₃	C₅×#3058	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₅×D₈	2
C₂×C₃×C₅×#131	2
C₃×C₅×#535	2
C₃×C₅×#469	2
C₃×C₅×#466	2
C₃×C₅×#427	2
C₃×C₅×#418	2
C₅×#3058	3
C₃×#3058	5

Subgroups — C3×C5×#3058 #14276092

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3058 #14276092