Subgroups — C₃×C₅×#3039 #14276073

Order 1920.

960 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×#137	C₂	1	2	yes	maximal
2	C₂×C₃×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄×C₅×#41	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#462	C₂	1	4	yes	maximal, complemented
5	C₃×C₅×#461	C₂	1	4	yes	maximal, complemented
6	C₃×C₅×#423	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#419	C₂	1	2	yes	maximal, complemented
8	C₅×#3039	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
11	C₃×C₅×#137	—	2	8	no	—
12	C₂×C₃×C₅×Q₁₆	C₂²	1	4	yes	—
13	C₂×C₃×C₅×SD₁₆	C₂²	1	4	yes	—
14	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
15	C₃×C₅×C₄⋊Q₈	—	2	1	no	—
16	C₃×C₅×C₄⋊Q₈	—	2	1	no	—
17	C₃×C₅×C₄⋊Q₈	C₂²	1	4	yes	—
18	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
19	C₃×C₄×C₅×D₄	—	2	2	no	—
20	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
21	C₃×C₅×#117	—	2	1	no	—
22	C₃×C₅×#117	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₅×C₄⋊C₄	—	2	2	no	—
24	C₂×C₃×C₄²×C₅	—	2	1	no	—
25	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
26	C₃×C₅×C₄⋊C₈	C₂²	1	4	yes	—
27	C₃×C₅×#103	C₂²	1	8	yes	—
28	C₃×#3039	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₂×C₅×#137	C₂×C₃	1	2	yes	—
30	C₂×C₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
31	C₄×C₅×#41	C₂×C₃	1	1	yes	characteristic
32	C₅×#462	C₂×C₃	1	4	yes	complemented
33	C₅×#461	C₂×C₃	1	4	yes	complemented
34	C₅×#423	C₂×C₃	1	1	yes	characteristic, complemented
35	C₅×#419	C₂×C₃	1	2	yes	complemented
36	C₃×C₅×#41	—	2	2	no	—
37	C₃×C₅×#41	D₄	1	4	yes	—
38	C₂×C₃×C₅×Q₈	—	2	2	no	—
39	C₂×C₃×C₅×Q₈	—	2	4	no	—
40	C₂×C₃×C₅×Q₈	—	2	4	no	—
41	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
42	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
43	C₂×C₃×C₅×D₄	—	2	1	no	—
44	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
45	C₂²×C₃×C₄×C₅	—	2	1	no	—
46	C₂²×C₃×C₄×C₅	—	2	2	no	—
47	C₂²×C₃×C₄×C₅	—	2	2	no	—
48	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
49	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₃×C₅×Q₁₆	—	2	8	no	—
51	C₃×C₅×SD₁₆	—	2	8	no	—
52	C₃×C₅×M₁₆	—	2	4	no	—
53	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
54	C₃×C₅×C₄⋊C₄	—	2	4	no	—
55	C₃×C₅×C₄⋊C₄	—	2	4	no	—
56	C₃×C₅×C₄⋊C₄	—	2	2	no	—
57	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
58	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
59	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
60	C₃×C₄²×C₅	—	2	1	no	—
61	C₃×C₄²×C₅	—	2	2	no	—
62	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
63	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
64	C₃×C₄²×C₅	C₂³	1	2	yes	—
65	C₂×C₃×#137	C₂×C₅	1	2	yes	—
66	C₂×C₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
67	C₃×C₄×#41	C₂×C₅	1	1	yes	characteristic
68	C₃×#462	C₂×C₅	1	4	yes	complemented
69	C₃×#461	C₂×C₅	1	4	yes	complemented
70	C₃×#423	C₂×C₅	1	1	yes	characteristic, complemented
71	C₃×#419	C₂×C₅	1	2	yes	complemented
72	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
73	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
74	C₅×#137	—	2	8	no	—
75	C₂×C₅×Q₁₆	C₂²×C₃	1	4	yes	—
76	C₂×C₅×SD₁₆	C₂²×C₃	1	4	yes	—
77	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
78	C₅×C₄⋊Q₈	—	2	1	no	—
79	C₅×C₄⋊Q₈	—	2	1	no	—
80	C₅×C₄⋊Q₈	C₂²×C₃	1	4	yes	—
81	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
82	C₄×C₅×D₄	—	2	2	no	—
83	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
84	C₅×#117	—	2	1	no	—
85	C₅×#117	C₂²×C₃	1	1	yes	characteristic
86	C₂×C₅×C₄⋊C₄	—	2	2	no	—
87	C₂×C₄²×C₅	—	2	1	no	—
88	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
89	C₅×C₄⋊C₈	C₂²×C₃	1	4	yes	—
90	C₅×#103	C₂²×C₃	1	8	yes	—
91	#3039	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
92	C₂³×C₃×C₅	—	2	1	no	—
93	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
94	C₃×C₅×Q₈	—	2	1	no	—
95	C₃×C₅×Q₈	—	2	4	no	—
96	C₃×C₅×Q₈	—	2	4	no	—
97	C₃×C₅×Q₈	—	4	4	no	—
98	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
99	C₃×C₅×D₄	—	2	4	no	—
100	C₃×C₅×D₄	—	2	1	no	—
101	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
102	C₂×C₃×C₄×C₅	—	2	1	no	—
103	C₂×C₃×C₄×C₅	—	2	4	no	—
104	C₂×C₃×C₄×C₅	—	2	4	no	—
105	C₂×C₃×C₄×C₅	—	2	2	no	—
106	C₂×C₃×C₄×C₅	—	2	4	no	—
107	C₂×C₃×C₄×C₅	—	4	4	no	—
108	C₂×C₃×C₄×C₅	—	4	4	no	—
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	C₂×D₄	1	2	yes	—
112	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
113	C₂×C₃×C₄×C₅	#41	1	2	yes	—
114	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
115	C₃×C₅×C₈	—	2	4	no	—
116	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
117	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
118	C₃×#137	—	2	8	no	—
119	C₂×C₃×Q₁₆	C₂²×C₅	1	4	yes	—
120	C₂×C₃×SD₁₆	C₂²×C₅	1	4	yes	—
121	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
122	C₃×C₄⋊Q₈	—	2	1	no	—
123	C₃×C₄⋊Q₈	—	2	1	no	—
124	C₃×C₄⋊Q₈	C₂²×C₅	1	4	yes	—
125	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
126	C₃×C₄×D₄	—	2	2	no	—
127	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
128	C₃×#117	—	2	1	no	—
129	C₃×#117	C₂²×C₅	1	1	yes	characteristic
130	C₂×C₃×C₄⋊C₄	—	2	2	no	—
131	C₂×C₃×C₄²	—	2	1	no	—
132	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
133	C₃×C₄⋊C₈	C₂²×C₅	1	4	yes	—
134	C₃×#103	C₂²×C₅	1	8	yes	—
135	C₅×#41	—	2	2	no	—
136	C₅×#41	C₃×D₄	1	4	yes	—
137	C₂×C₅×Q₈	—	2	2	no	—
138	C₂×C₅×Q₈	—	2	4	no	—
139	C₂×C₅×Q₈	—	2	4	no	—
140	C₂×C₅×Q₈	C₂³×C₃	1	4	yes	—
141	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
142	C₂×C₅×D₄	—	2	1	no	—
143	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
144	C₂²×C₄×C₅	—	2	1	no	—
145	C₂²×C₄×C₅	—	2	2	no	—
146	C₂²×C₄×C₅	—	2	2	no	—
147	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
148	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
149	C₅×Q₁₆	—	2	8	no	—
150	C₅×SD₁₆	—	2	8	no	—
151	C₅×M₁₆	—	2	4	no	—
152	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
153	C₅×C₄⋊C₄	—	2	4	no	—
154	C₅×C₄⋊C₄	—	2	4	no	—
155	C₅×C₄⋊C₄	—	2	2	no	—
156	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
157	C₅×C₂²⋊C₄	—	2	1	no	—
158	C₅×C₂²⋊C₄	—	2	2	no	—
159	C₄²×C₅	—	2	1	no	—
160	C₄²×C₅	—	2	2	no	—
161	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
162	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
163	C₄²×C₅	C₂³×C₃	1	2	yes	—
164	C₂×#137	C₂×C₃×C₅	1	2	yes	—
165	C₂×C₄⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
166	C₄×#41	C₂×C₃×C₅	1	1	yes	characteristic
167	#462	C₂×C₃×C₅	1	4	yes	complemented
168	#461	C₂×C₃×C₅	1	4	yes	complemented
169	#423	C₂×C₃×C₅	1	1	yes	characteristic, complemented
170	#419	C₂×C₃×C₅	1	2	yes	complemented
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	#121	1	2	yes	—
175	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
176	C₃×C₄×C₅	—	2	2	no	—
177	C₃×C₄×C₅	—	2	2	no	—
178	C₃×C₄×C₅	—	4	4	no	—
179	C₃×C₄×C₅	—	4	2	no	—
180	C₃×C₄×C₅	#121	1	2	yes	—
181	C₃×C₄×C₅	#137	1	4	yes	complemented
182	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
183	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
184	C₃×#41	—	2	2	no	—
185	C₃×#41	C₅×D₄	1	4	yes	—
186	C₂×C₃×Q₈	—	2	2	no	—
187	C₂×C₃×Q₈	—	2	4	no	—
188	C₂×C₃×Q₈	—	2	4	no	—
189	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
190	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
191	C₂×C₃×D₄	—	2	1	no	—
192	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
193	C₂²×C₃×C₄	—	2	1	no	—
194	C₂²×C₃×C₄	—	2	2	no	—
195	C₂²×C₃×C₄	—	2	2	no	—
196	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
197	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
198	C₃×Q₁₆	—	2	8	no	—
199	C₃×SD₁₆	—	2	8	no	—
200	C₃×M₁₆	—	2	4	no	—
201	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
202	C₃×C₄⋊C₄	—	2	4	no	—
203	C₃×C₄⋊C₄	—	2	4	no	—
204	C₃×C₄⋊C₄	—	2	2	no	—
205	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
206	C₃×C₂²⋊C₄	—	2	1	no	—
207	C₃×C₂²⋊C₄	—	2	2	no	—
208	C₃×C₄²	—	2	1	no	—
209	C₃×C₄²	—	2	2	no	—
210	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
211	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
212	C₃×C₄²	C₂³×C₅	1	2	yes	—
213	C₂³×C₅	—	2	1	no	—
214	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
215	C₅×Q₈	—	2	1	no	—
216	C₅×Q₈	—	2	4	no	—
217	C₅×Q₈	—	2	4	no	—
218	C₅×Q₈	—	4	4	no	—
219	C₅×Q₈	C₂×C₃×D₄	1	2	yes	—
220	C₅×D₄	—	2	4	no	—
221	C₅×D₄	—	2	1	no	—
222	C₅×D₄	C₂×C₃×D₄	1	2	yes	—
223	C₂×C₄×C₅	—	2	1	no	—
224	C₂×C₄×C₅	—	2	4	no	—
225	C₂×C₄×C₅	—	2	4	no	—
226	C₂×C₄×C₅	—	2	2	no	—
227	C₂×C₄×C₅	—	2	4	no	—
228	C₂×C₄×C₅	—	4	4	no	—
229	C₂×C₄×C₅	—	4	4	no	—
230	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
231	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
232	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
233	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
234	C₂×C₄×C₅	C₃×#41	1	2	yes	—
235	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
236	C₅×C₈	—	2	4	no	—
237	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
238	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
239	#137	—	2	8	no	—
240	C₂×Q₁₆	C₂²×C₃×C₅	1	4	yes	—
241	C₂×SD₁₆	C₂²×C₃×C₅	1	4	yes	—
242	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
243	C₄⋊Q₈	—	2	1	no	—
244	C₄⋊Q₈	—	2	1	no	—
245	C₄⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
246	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
247	C₄×D₄	—	2	2	no	—
248	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
249	#117	—	2	1	no	—
250	#117	C₂²×C₃×C₅	1	1	yes	characteristic
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄²	—	2	1	no	—
253	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
254	C₄⋊C₈	C₂²×C₃×C₅	1	4	yes	—
255	#103	C₂²×C₃×C₅	1	8	yes	—
256	C₂×C₃×C₅	—	2	2	no	—
257	C₂×C₃×C₅	—	4	2	no	—
258	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
259	C₂×C₃×C₅	C₂×#137	1	2	yes	—
260	C₂³×C₃	—	2	1	no	—
261	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
262	C₃×Q₈	—	2	1	no	—
263	C₃×Q₈	—	2	4	no	—
264	C₃×Q₈	—	2	4	no	—
265	C₃×Q₈	—	4	4	no	—
266	C₃×Q₈	C₂×C₅×D₄	1	2	yes	—
267	C₃×D₄	—	2	4	no	—
268	C₃×D₄	—	2	1	no	—
269	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
270	C₂×C₃×C₄	—	2	1	no	—
271	C₂×C₃×C₄	—	2	4	no	—
272	C₂×C₃×C₄	—	2	4	no	—
273	C₂×C₃×C₄	—	2	2	no	—
274	C₂×C₃×C₄	—	2	4	no	—
275	C₂×C₃×C₄	—	4	4	no	—
276	C₂×C₃×C₄	—	4	4	no	—
277	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
278	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
279	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
280	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
281	C₂×C₃×C₄	C₅×#41	1	2	yes	—
282	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
283	C₃×C₈	—	2	4	no	—
284	C₂²×C₅	—	2	2	no	—
285	C₂²×C₅	—	2	2	no	—
286	C₂²×C₅	—	4	2	no	—
287	C₂²×C₅	C₃×#121	1	2	yes	—
288	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
289	C₄×C₅	—	2	2	no	—
290	C₄×C₅	—	2	2	no	—
291	C₄×C₅	—	4	2	no	—
292	C₄×C₅	—	4	4	no	—
293	C₄×C₅	C₃×#121	1	2	yes	—
294	C₄×C₅	C₃×#137	1	4	yes	complemented
295	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
296	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
297	#41	—	2	2	no	—
298	#41	C₃×C₅×D₄	1	4	yes	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	2	4	no	—
301	C₂×Q₈	—	2	4	no	—
302	C₂×Q₈	C₂³×C₃×C₅	1	4	yes	—
303	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
310	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
311	Q₁₆	—	2	8	no	—
312	SD₁₆	—	2	8	no	—
313	M₁₆	—	2	4	no	—
314	C₂×C₈	C₂³×C₃×C₅	1	4	yes	—
315	C₄⋊C₄	—	2	4	no	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
319	C₂²⋊C₄	—	2	1	no	—
320	C₂²⋊C₄	—	2	2	no	—
321	C₄²	—	2	1	no	—
322	C₄²	—	2	2	no	—
323	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
324	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
325	C₄²	C₂³×C₃×C₅	1	2	yes	—
326	C₃×C₅	#3039	1	1	yes	characteristic, direct product factor, Hall
327	C₂²×C₃	—	2	2	no	—
328	C₂²×C₃	—	2	2	no	—
329	C₂²×C₃	—	4	2	no	—
330	C₂²×C₃	C₅×#121	1	2	yes	—
331	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
332	C₃×C₄	—	2	2	no	—
333	C₃×C₄	—	2	2	no	—
334	C₃×C₄	—	4	4	no	—
335	C₃×C₄	—	4	2	no	—
336	C₃×C₄	C₅×#121	1	2	yes	—
337	C₃×C₄	C₅×#137	1	4	yes	complemented
338	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
339	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
340	C₂×C₅	—	2	2	no	—
341	C₂×C₅	—	4	2	no	—
342	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
343	C₂×C₅	C₂×C₃×#137	1	2	yes	—
344	C₂³	—	2	1	no	—
345	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
346	Q₈	—	2	1	no	—
347	Q₈	—	2	4	no	—
348	Q₈	—	2	4	no	—
349	Q₈	—	4	4	no	—
350	Q₈	C₂×C₃×C₅×D₄	1	2	yes	—
351	D₄	—	2	4	no	—
352	D₄	—	2	1	no	—
353	D₄	C₂×C₃×C₅×D₄	1	2	yes	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	4	4	no	—
360	C₂×C₄	—	4	4	no	—
361	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
362	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
363	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
364	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
365	C₂×C₄	C₃×C₅×#41	1	2	yes	—
366	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
367	C₈	—	2	4	no	—
368	C₂×C₃	—	2	2	no	—
369	C₂×C₃	—	4	2	no	—
370	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
371	C₂×C₃	C₂×C₅×#137	1	2	yes	—
372	C₅	C₃×#3039	1	1	yes	characteristic, direct product factor, Sylow
373	C₂²	—	2	2	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	4	2	no	—
376	C₂²	C₃×C₅×#121	1	2	yes	—
377	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
378	C₄	—	2	2	no	—
379	C₄	—	2	2	no	—
380	C₄	—	4	4	no	—
381	C₄	—	4	2	no	—
382	C₄	C₃×C₅×#121	1	2	yes	—
383	C₄	C₃×C₅×#137	1	4	yes	complemented
384	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
385	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
386	C₃	C₅×#3039	1	1	yes	characteristic, direct product factor, Sylow
387	C₂	—	2	2	no	—
388	C₂	—	4	2	no	—
389	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
390	C₂	C₂×C₃×C₅×#137	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₂×C₃×C₅×#41	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂×C₃×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×C₄⋊Q₈	C₂	semidirect
4. C₃×C₅×#462	C₂	semidirect
5. C₃×C₅×#461	C₂	semidirect
6. C₃×C₅×#423	C₂	semidirect
7. C₃×C₅×#419	C₂	semidirect
8. C₅×#3039	C₃	direct (N × H)
28. C₃×#3039	C₅	direct (N × H)
30. C₂×C₅×C₄⋊Q₈	C₂×C₃	semidirect
32. C₅×#462	C₂×C₃	semidirect
33. C₅×#461	C₂×C₃	semidirect
34. C₅×#423	C₂×C₃	semidirect
35. C₅×#419	C₂×C₃	semidirect
66. C₂×C₃×C₄⋊Q₈	C₂×C₅	semidirect
68. C₃×#462	C₂×C₅	semidirect
69. C₃×#461	C₂×C₅	semidirect
70. C₃×#423	C₂×C₅	semidirect
71. C₃×#419	C₂×C₅	semidirect
91. #3039	C₃×C₅	direct (N × H)
165. C₂×C₄⋊Q₈	C₂×C₃×C₅	semidirect
167. #462	C₂×C₃×C₅	semidirect
168. #461	C₂×C₃×C₅	semidirect
169. #423	C₂×C₃×C₅	semidirect
170. #419	C₂×C₃×C₅	semidirect
181. C₃×C₄×C₅	#137	semidirect
294. C₄×C₅	C₃×#137	semidirect
326. C₃×C₅	#3039	direct (N × H)
337. C₃×C₄	C₅×#137	semidirect
372. C₅	C₃×#3039	direct (N × H)
383. C₄	C₃×C₅×#137	semidirect
386. C₃	C₅×#3039	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×#137	2
C₂×C₃×C₅×C₄⋊Q₈	2
C₃×C₄×C₅×#41	2
C₃×C₅×#462	2
C₃×C₅×#461	2
C₃×C₅×#423	2
C₃×C₅×#419	2
C₅×#3039	3
C₃×#3039	5

Subgroups — C3×C5×#3039 #14276073

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3039 #14276073