Subgroups — C₃×C₅×#2548 #14275582

Order 1920.

1352 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#127	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#124	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#394	C₂	1	4	yes	maximal, complemented
5	C₃×C₅×#390	C₂	1	4	yes	maximal, complemented
6	C₃×C₅×#390	C₂	1	2	yes	maximal, complemented
7	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2548	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
11	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
12	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
13	C₃×C₅×#127	—	2	4	no	—
14	C₃×C₅×#124	—	2	8	no	—
15	C₃×C₄×C₅×Q₈	—	2	4	no	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	8	yes	—
20	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	8	yes	—
21	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
22	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
23	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
24	C₃×C₅×#95	C₂²	1	2	yes	—
25	C₃×#2548	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₂×C₅×#127	C₂×C₃	1	1	yes	characteristic
27	C₂×C₅×#124	C₂×C₃	1	2	yes	complemented
28	C₂×C₄×C₅×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
29	C₅×#394	C₂×C₃	1	4	yes	complemented
30	C₅×#390	C₂×C₃	1	2	yes	complemented
31	C₅×#390	C₂×C₃	1	4	yes	complemented
32	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂⁴×C₃×C₅	C₂³	1	4	yes	—
34	C₂×C₃×C₅×Q₈	—	2	2	no	—
35	C₂×C₃×C₅×Q₈	—	2	2	no	—
36	C₂×C₃×C₅×Q₈	D₄	1	4	yes	complemented
37	C₂×C₃×C₅×D₄	—	2	4	no	—
38	C₂×C₃×C₅×D₄	—	2	4	no	—
39	C₂×C₃×C₅×D₄	—	2	4	no	—
40	C₂×C₃×C₅×D₄	—	2	4	no	—
41	C₂×C₃×C₅×D₄	—	2	4	no	—
42	C₂×C₃×C₅×D₄	—	2	8	no	—
43	C₂×C₃×C₅×D₄	—	4	4	no	—
44	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
46	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
47	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
48	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
49	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₃×C₅×C₄⋊C₄	—	2	4	no	—
51	C₃×C₅×C₄⋊C₄	—	2	2	no	—
52	C₃×C₅×C₄⋊C₄	—	2	4	no	—
53	C₃×C₅×C₂²⋊C₄	—	2	16	no	—
54	C₃×C₅×C₂²⋊C₄	—	4	8	no	—
55	C₃×C₄²×C₅	—	2	4	no	—
56	C₃×C₄²×C₅	—	2	4	no	—
57	C₃×C₄²×C₅	D₄	1	4	yes	—
58	C₂×C₃×#127	C₂×C₅	1	1	yes	characteristic
59	C₂×C₃×#124	C₂×C₅	1	2	yes	complemented
60	C₂×C₃×C₄×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
61	C₃×#394	C₂×C₅	1	4	yes	complemented
62	C₃×#390	C₂×C₅	1	2	yes	complemented
63	C₃×#390	C₂×C₅	1	4	yes	complemented
64	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
65	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
66	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
67	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
68	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
69	C₅×#127	—	2	4	no	—
70	C₅×#124	—	2	8	no	—
71	C₄×C₅×Q₈	—	2	4	no	—
72	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
73	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
74	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
75	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	8	yes	—
76	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	8	yes	—
77	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
78	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
79	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
80	C₅×#95	C₂²×C₃	1	2	yes	—
81	#2548	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
82	C₂³×C₃×C₅	—	2	4	no	—
83	C₂³×C₃×C₅	—	2	4	no	—
84	C₂³×C₃×C₅	—	2	4	no	—
85	C₂³×C₃×C₅	—	2	8	no	—
86	C₂³×C₃×C₅	—	2	8	no	—
87	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
88	C₃×C₅×Q₈	—	2	8	no	—
89	C₃×C₅×D₄	—	4	8	no	—
90	C₃×C₅×D₄	—	4	8	no	—
91	C₃×C₅×D₄	—	4	8	no	—
92	C₂×C₃×C₄×C₅	—	2	2	no	—
93	C₂×C₃×C₄×C₅	—	2	2	no	—
94	C₂×C₃×C₄×C₅	—	2	2	no	—
95	C₂×C₃×C₄×C₅	—	2	4	no	—
96	C₂×C₃×C₄×C₅	—	2	2	no	—
97	C₂×C₃×C₄×C₅	—	2	4	no	—
98	C₂×C₃×C₄×C₅	—	2	4	no	—
99	C₂×C₃×C₄×C₅	—	2	4	no	—
100	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
101	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
102	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
103	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
104	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
105	C₂×C₃×C₄×C₅	#41	1	2	yes	—
106	C₂×C₃×C₄×C₅	#41	1	4	yes	—
107	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
108	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
109	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
110	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
111	C₃×#127	—	2	4	no	—
112	C₃×#124	—	2	8	no	—
113	C₃×C₄×Q₈	—	2	4	no	—
114	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
115	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
116	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
117	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	8	yes	—
118	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	8	yes	—
119	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
120	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
121	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
122	C₃×#95	C₂²×C₅	1	2	yes	—
123	C₂⁴×C₅	C₂³×C₃	1	4	yes	—
124	C₂×C₅×Q₈	—	2	2	no	—
125	C₂×C₅×Q₈	—	2	2	no	—
126	C₂×C₅×Q₈	C₃×D₄	1	4	yes	complemented
127	C₂×C₅×D₄	—	2	4	no	—
128	C₂×C₅×D₄	—	2	4	no	—
129	C₂×C₅×D₄	—	2	4	no	—
130	C₂×C₅×D₄	—	2	4	no	—
131	C₂×C₅×D₄	—	2	4	no	—
132	C₂×C₅×D₄	—	2	8	no	—
133	C₂×C₅×D₄	—	4	4	no	—
134	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
135	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
136	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
137	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
138	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
139	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
140	C₅×C₄⋊C₄	—	2	4	no	—
141	C₅×C₄⋊C₄	—	2	2	no	—
142	C₅×C₄⋊C₄	—	2	4	no	—
143	C₅×C₂²⋊C₄	—	2	16	no	—
144	C₅×C₂²⋊C₄	—	4	8	no	—
145	C₄²×C₅	—	2	4	no	—
146	C₄²×C₅	—	2	4	no	—
147	C₄²×C₅	C₃×D₄	1	4	yes	—
148	C₂×#127	C₂×C₃×C₅	1	1	yes	characteristic
149	C₂×#124	C₂×C₃×C₅	1	2	yes	complemented
150	C₂×C₄×Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
151	#394	C₂×C₃×C₅	1	4	yes	complemented
152	#390	C₂×C₃×C₅	1	4	yes	complemented
153	#390	C₂×C₃×C₅	1	2	yes	complemented
154	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
155	C₂²×C₃×C₅	—	4	4	no	—
156	C₂²×C₃×C₅	—	4	4	no	—
157	C₂²×C₃×C₅	—	4	4	no	—
158	C₂²×C₃×C₅	—	4	8	no	—
159	C₂²×C₃×C₅	—	4	8	no	—
160	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
161	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
162	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
163	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
164	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
165	C₃×C₄×C₅	—	2	4	no	—
166	C₃×C₄×C₅	—	2	2	no	—
167	C₃×C₄×C₅	—	4	2	no	—
168	C₃×C₄×C₅	—	4	4	no	—
169	C₃×C₄×C₅	#121	1	4	yes	—
170	C₃×C₄×C₅	#124	1	4	yes	complemented
171	C₂⁴×C₃	C₂³×C₅	1	4	yes	—
172	C₂×C₃×Q₈	—	2	2	no	—
173	C₂×C₃×Q₈	—	2	2	no	—
174	C₂×C₃×Q₈	C₅×D₄	1	4	yes	complemented
175	C₂×C₃×D₄	—	2	4	no	—
176	C₂×C₃×D₄	—	2	4	no	—
177	C₂×C₃×D₄	—	2	4	no	—
178	C₂×C₃×D₄	—	2	4	no	—
179	C₂×C₃×D₄	—	2	4	no	—
180	C₂×C₃×D₄	—	2	8	no	—
181	C₂×C₃×D₄	—	4	4	no	—
182	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
183	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
184	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
185	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
186	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
187	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
188	C₃×C₄⋊C₄	—	2	4	no	—
189	C₃×C₄⋊C₄	—	2	2	no	—
190	C₃×C₄⋊C₄	—	2	4	no	—
191	C₃×C₂²⋊C₄	—	2	16	no	—
192	C₃×C₂²⋊C₄	—	4	8	no	—
193	C₃×C₄²	—	2	4	no	—
194	C₃×C₄²	—	2	4	no	—
195	C₃×C₄²	C₅×D₄	1	4	yes	—
196	C₂³×C₅	—	2	4	no	—
197	C₂³×C₅	—	2	4	no	—
198	C₂³×C₅	—	2	4	no	—
199	C₂³×C₅	—	2	8	no	—
200	C₂³×C₅	—	2	8	no	—
201	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
202	C₅×Q₈	—	2	8	no	—
203	C₅×D₄	—	4	8	no	—
204	C₅×D₄	—	4	8	no	—
205	C₅×D₄	—	4	8	no	—
206	C₂×C₄×C₅	—	2	2	no	—
207	C₂×C₄×C₅	—	2	2	no	—
208	C₂×C₄×C₅	—	2	2	no	—
209	C₂×C₄×C₅	—	2	4	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	C₂×C₃×D₄	1	2	yes	—
215	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
216	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
217	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
218	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
219	C₂×C₄×C₅	C₃×#41	1	2	yes	—
220	C₂×C₄×C₅	C₃×#41	1	4	yes	—
221	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
222	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
223	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
224	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
225	#127	—	2	4	no	—
226	#124	—	2	8	no	—
227	C₄×Q₈	—	2	4	no	—
228	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
229	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
230	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
231	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	8	yes	—
232	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	8	yes	—
233	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
234	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
235	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
236	#95	C₂²×C₃×C₅	1	2	yes	—
237	C₂×C₃×C₅	—	8	4	no	—
238	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
239	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
240	C₂×C₃×C₅	#535	1	1	yes	characteristic
241	C₂×C₃×C₅	#550	1	2	yes	—
242	C₂×C₃×C₅	#559	1	2	yes	—
243	C₂³×C₃	—	2	4	no	—
244	C₂³×C₃	—	2	4	no	—
245	C₂³×C₃	—	2	4	no	—
246	C₂³×C₃	—	2	8	no	—
247	C₂³×C₃	—	2	8	no	—
248	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
249	C₃×Q₈	—	2	8	no	—
250	C₃×D₄	—	4	8	no	—
251	C₃×D₄	—	4	8	no	—
252	C₃×D₄	—	4	8	no	—
253	C₂×C₃×C₄	—	2	2	no	—
254	C₂×C₃×C₄	—	2	2	no	—
255	C₂×C₃×C₄	—	2	2	no	—
256	C₂×C₃×C₄	—	2	4	no	—
257	C₂×C₃×C₄	—	2	2	no	—
258	C₂×C₃×C₄	—	2	4	no	—
259	C₂×C₃×C₄	—	2	4	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	4	yes	—
263	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
264	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
265	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
266	C₂×C₃×C₄	C₅×#41	1	2	yes	—
267	C₂×C₃×C₄	C₅×#41	1	4	yes	—
268	C₂²×C₅	—	4	8	no	—
269	C₂²×C₅	—	4	4	no	—
270	C₂²×C₅	—	4	4	no	—
271	C₂²×C₅	—	4	4	no	—
272	C₂²×C₅	—	4	8	no	—
273	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
274	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
275	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
276	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
277	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
278	C₄×C₅	—	2	4	no	—
279	C₄×C₅	—	2	2	no	—
280	C₄×C₅	—	4	2	no	—
281	C₄×C₅	—	4	4	no	—
282	C₄×C₅	C₃×#121	1	4	yes	—
283	C₄×C₅	C₃×#124	1	4	yes	complemented
284	C₂⁴	C₂³×C₃×C₅	1	4	yes	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	C₃×C₅×D₄	1	4	yes	complemented
288	C₂×D₄	—	2	4	no	—
289	C₂×D₄	—	2	4	no	—
290	C₂×D₄	—	2	4	no	—
291	C₂×D₄	—	2	4	no	—
292	C₂×D₄	—	2	4	no	—
293	C₂×D₄	—	2	8	no	—
294	C₂×D₄	—	4	4	no	—
295	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
296	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
297	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
298	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
299	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
300	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
301	C₄⋊C₄	—	2	4	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	4	no	—
304	C₂²⋊C₄	—	2	16	no	—
305	C₂²⋊C₄	—	4	8	no	—
306	C₄²	—	2	4	no	—
307	C₄²	—	2	4	no	—
308	C₄²	C₃×C₅×D₄	1	4	yes	—
309	C₃×C₅	#2548	1	1	yes	characteristic, direct product factor, Hall
310	C₂²×C₃	—	4	4	no	—
311	C₂²×C₃	—	4	4	no	—
312	C₂²×C₃	—	4	4	no	—
313	C₂²×C₃	—	4	8	no	—
314	C₂²×C₃	—	4	8	no	—
315	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
316	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
317	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
318	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
319	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
320	C₃×C₄	—	2	4	no	—
321	C₃×C₄	—	2	2	no	—
322	C₃×C₄	—	4	2	no	—
323	C₃×C₄	—	4	4	no	—
324	C₃×C₄	C₅×#121	1	4	yes	—
325	C₃×C₄	C₅×#124	1	4	yes	complemented
326	C₂×C₅	—	8	4	no	—
327	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
328	C₂×C₅	C₂×C₃×#124	1	1	yes	characteristic
329	C₂×C₅	C₃×#535	1	1	yes	characteristic
330	C₂×C₅	C₃×#550	1	2	yes	—
331	C₂×C₅	C₃×#559	1	2	yes	—
332	C₂³	—	2	4	no	—
333	C₂³	—	2	4	no	—
334	C₂³	—	2	4	no	—
335	C₂³	—	2	8	no	—
336	C₂³	—	2	8	no	—
337	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
338	Q₈	—	2	8	no	—
339	D₄	—	4	8	no	—
340	D₄	—	4	8	no	—
341	D₄	—	4	8	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
351	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
352	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
353	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
354	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
355	C₂×C₄	C₃×C₅×#41	1	2	yes	—
356	C₂×C₄	C₃×C₅×#41	1	4	yes	—
357	C₂×C₃	—	8	4	no	—
358	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
359	C₂×C₃	C₂×C₅×#124	1	1	yes	characteristic
360	C₂×C₃	C₅×#535	1	1	yes	characteristic
361	C₂×C₃	C₅×#550	1	2	yes	—
362	C₂×C₃	C₅×#559	1	2	yes	—
363	C₅	C₃×#2548	1	1	yes	characteristic, direct product factor, Sylow
364	C₂²	—	4	4	no	—
365	C₂²	—	4	4	no	—
366	C₂²	—	4	4	no	—
367	C₂²	—	4	8	no	—
368	C₂²	—	4	8	no	—
369	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
370	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
371	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
372	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
373	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
374	C₄	—	2	4	no	—
375	C₄	—	2	2	no	—
376	C₄	—	4	2	no	—
377	C₄	—	4	4	no	—
378	C₄	C₃×C₅×#121	1	4	yes	—
379	C₄	C₃×C₅×#124	1	4	yes	complemented
380	C₃	C₅×#2548	1	1	yes	characteristic, direct product factor, Sylow
381	C₂	—	8	4	no	—
382	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
383	C₂	C₂×C₃×C₅×#124	1	1	yes	characteristic
384	C₂	C₃×C₅×#535	1	1	yes	characteristic
385	C₂	C₃×C₅×#550	1	2	yes	—
386	C₂	C₃×C₅×#559	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂×C₃×C₅×#127	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×#124	C₂	semidirect
3. C₂×C₃×C₄×C₅×Q₈	C₂	semidirect
4. C₃×C₅×#394	C₂	semidirect
5. C₃×C₅×#390	C₂	semidirect
6. C₃×C₅×#390	C₂	semidirect
7. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
8. C₅×#2548	C₃	direct (N × H)
25. C₃×#2548	C₅	direct (N × H)
27. C₂×C₅×#124	C₂×C₃	semidirect
28. C₂×C₄×C₅×Q₈	C₂×C₃	semidirect
29. C₅×#394	C₂×C₃	semidirect
30. C₅×#390	C₂×C₃	semidirect
31. C₅×#390	C₂×C₃	semidirect
32. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
36. C₂×C₃×C₅×Q₈	D₄	semidirect
59. C₂×C₃×#124	C₂×C₅	semidirect
60. C₂×C₃×C₄×Q₈	C₂×C₅	semidirect
61. C₃×#394	C₂×C₅	semidirect
62. C₃×#390	C₂×C₅	semidirect
63. C₃×#390	C₂×C₅	semidirect
64. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
81. #2548	C₃×C₅	direct (N × H)
126. C₂×C₅×Q₈	C₃×D₄	semidirect
149. C₂×#124	C₂×C₃×C₅	semidirect
150. C₂×C₄×Q₈	C₂×C₃×C₅	semidirect
151. #394	C₂×C₃×C₅	semidirect
152. #390	C₂×C₃×C₅	semidirect
153. #390	C₂×C₃×C₅	semidirect
154. C₄×C₄⋊C₄	C₂×C₃×C₅	semidirect
170. C₃×C₄×C₅	#124	semidirect
174. C₂×C₃×Q₈	C₅×D₄	semidirect
283. C₄×C₅	C₃×#124	semidirect
287. C₂×Q₈	C₃×C₅×D₄	semidirect
309. C₃×C₅	#2548	direct (N × H)
325. C₃×C₄	C₅×#124	semidirect
363. C₅	C₃×#2548	direct (N × H)
379. C₄	C₃×C₅×#124	semidirect
380. C₃	C₅×#2548	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×#127	2
C₂×C₃×C₅×#124	2
C₂×C₃×C₄×C₅×Q₈	2
C₃×C₅×#394	2
C₃×C₅×#390	2
C₃×C₄×C₅×C₄⋊C₄	2
C₅×#2548	3
C₃×#2548	5

Subgroups — C3×C5×#2548 #14275582

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2548 #14275582