Subgroups — C₃×C₅×#2733 #14275767

Order 1920.

1184 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×#124	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#394	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#392	C₂	1	4	yes	maximal, complemented
4	C₃×C₅×#391	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#390	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#388	C₂	1	4	yes	maximal, complemented
7	C₅×#2733	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
9	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
10	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
11	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
12	C₃×C₅×#124	—	2	8	no	—
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
16	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
17	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
18	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
19	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
20	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
21	C₃×C₅×#95	C₂²	1	2	yes	—
22	C₃×C₅×#95	C₂²	1	4	yes	—
23	C₃×#2733	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂×C₅×#124	C₂×C₃	1	2	yes	complemented
25	C₅×#394	C₂×C₃	1	2	yes	complemented
26	C₅×#392	C₂×C₃	1	4	yes	complemented
27	C₅×#391	C₂×C₃	1	1	yes	characteristic, complemented
28	C₅×#390	C₂×C₃	1	2	yes	complemented
29	C₅×#388	C₂×C₃	1	4	yes	complemented
30	C₂⁴×C₃×C₅	C₂³	1	4	yes	—
31	C₂×C₃×C₅×Q₈	—	4	1	no	—
32	C₂×C₃×C₅×Q₈	—	4	1	no	—
33	C₂×C₃×C₅×Q₈	D₄	1	4	yes	complemented
34	C₂×C₃×C₅×D₄	—	2	4	no	—
35	C₂×C₃×C₅×D₄	—	2	4	no	—
36	C₂×C₃×C₅×D₄	—	4	2	no	—
37	C₂×C₃×C₅×D₄	—	4	2	no	—
38	C₂×C₃×C₅×D₄	—	4	2	no	—
39	C₂×C₃×C₅×D₄	—	4	2	no	—
40	C₂×C₃×C₅×D₄	—	4	4	no	—
41	C₂×C₃×C₅×D₄	—	4	2	no	—
42	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
43	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
44	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
46	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
47	C₃×C₅×C₄⋊C₄	—	4	2	no	—
48	C₃×C₅×C₄⋊C₄	—	4	1	no	—
49	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
50	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
51	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
52	C₃×C₅×C₂²⋊C₄	—	4	4	no	—
53	C₃×C₄²×C₅	—	2	4	no	—
54	C₃×C₄²×C₅	—	4	1	no	—
55	C₂×C₃×#124	C₂×C₅	1	2	yes	complemented
56	C₃×#394	C₂×C₅	1	2	yes	complemented
57	C₃×#392	C₂×C₅	1	4	yes	complemented
58	C₃×#391	C₂×C₅	1	1	yes	characteristic, complemented
59	C₃×#390	C₂×C₅	1	2	yes	complemented
60	C₃×#388	C₂×C₅	1	4	yes	complemented
61	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
62	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
63	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
64	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
65	C₅×#124	—	2	8	no	—
66	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
67	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
68	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
69	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
70	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
71	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
72	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
73	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
74	C₅×#95	C₂²×C₃	1	2	yes	—
75	C₅×#95	C₂²×C₃	1	4	yes	—
76	#2733	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
77	C₂³×C₃×C₅	—	2	4	no	—
78	C₂³×C₃×C₅	—	2	4	no	—
79	C₂³×C₃×C₅	—	2	4	no	—
80	C₂³×C₃×C₅	—	2	4	no	—
81	C₂³×C₃×C₅	—	2	4	no	—
82	C₂³×C₃×C₅	—	2	4	no	—
83	C₂³×C₃×C₅	—	2	4	no	—
84	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
85	C₃×C₅×Q₈	—	4	4	no	—
86	C₃×C₅×D₄	—	4	8	no	—
87	C₃×C₅×D₄	—	4	8	no	—
88	C₃×C₅×D₄	—	4	8	no	—
89	C₂×C₃×C₄×C₅	—	2	2	no	—
90	C₂×C₃×C₄×C₅	—	2	1	no	—
91	C₂×C₃×C₄×C₅	—	2	2	no	—
92	C₂×C₃×C₄×C₅	—	2	1	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	4	no	—
97	C₂×C₃×C₄×C₅	—	2	4	no	—
98	C₂×C₃×C₄×C₅	—	2	4	no	—
99	C₂×C₃×C₄×C₅	—	2	2	no	—
100	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
101	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
102	C₂×C₃×C₄×C₅	#41	1	4	yes	—
103	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
104	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
105	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
106	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
107	C₃×#124	—	2	8	no	—
108	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
109	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
110	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
111	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
112	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
113	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
114	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
115	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
116	C₃×#95	C₂²×C₅	1	2	yes	—
117	C₃×#95	C₂²×C₅	1	4	yes	—
118	C₂⁴×C₅	C₂³×C₃	1	4	yes	—
119	C₂×C₅×Q₈	—	4	1	no	—
120	C₂×C₅×Q₈	—	4	1	no	—
121	C₂×C₅×Q₈	C₃×D₄	1	4	yes	complemented
122	C₂×C₅×D₄	—	2	4	no	—
123	C₂×C₅×D₄	—	2	4	no	—
124	C₂×C₅×D₄	—	4	2	no	—
125	C₂×C₅×D₄	—	4	2	no	—
126	C₂×C₅×D₄	—	4	2	no	—
127	C₂×C₅×D₄	—	4	2	no	—
128	C₂×C₅×D₄	—	4	4	no	—
129	C₂×C₅×D₄	—	4	2	no	—
130	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
131	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
132	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
133	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
134	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
135	C₅×C₄⋊C₄	—	4	2	no	—
136	C₅×C₄⋊C₄	—	4	1	no	—
137	C₅×C₂²⋊C₄	—	2	8	no	—
138	C₅×C₂²⋊C₄	—	2	8	no	—
139	C₅×C₂²⋊C₄	—	2	8	no	—
140	C₅×C₂²⋊C₄	—	4	4	no	—
141	C₄²×C₅	—	2	4	no	—
142	C₄²×C₅	—	4	1	no	—
143	C₂×#124	C₂×C₃×C₅	1	2	yes	complemented
144	#394	C₂×C₃×C₅	1	2	yes	complemented
145	#392	C₂×C₃×C₅	1	4	yes	complemented
146	#391	C₂×C₃×C₅	1	1	yes	characteristic, complemented
147	#390	C₂×C₃×C₅	1	2	yes	complemented
148	#388	C₂×C₃×C₅	1	4	yes	complemented
149	C₂²×C₃×C₅	—	4	4	no	—
150	C₂²×C₃×C₅	—	4	4	no	—
151	C₂²×C₃×C₅	—	4	4	no	—
152	C₂²×C₃×C₅	—	4	4	no	—
153	C₂²×C₃×C₅	—	4	4	no	—
154	C₂²×C₃×C₅	—	4	4	no	—
155	C₂²×C₃×C₅	—	4	4	no	—
156	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
157	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
158	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
159	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
160	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
161	C₃×C₄×C₅	—	2	4	no	—
162	C₃×C₄×C₅	—	2	2	no	—
163	C₃×C₄×C₅	—	2	4	no	—
164	C₃×C₄×C₅	—	4	4	no	—
165	C₃×C₄×C₅	—	4	2	no	—
166	C₂⁴×C₃	C₂³×C₅	1	4	yes	—
167	C₂×C₃×Q₈	—	4	1	no	—
168	C₂×C₃×Q₈	—	4	1	no	—
169	C₂×C₃×Q₈	C₅×D₄	1	4	yes	complemented
170	C₂×C₃×D₄	—	2	4	no	—
171	C₂×C₃×D₄	—	2	4	no	—
172	C₂×C₃×D₄	—	4	2	no	—
173	C₂×C₃×D₄	—	4	2	no	—
174	C₂×C₃×D₄	—	4	2	no	—
175	C₂×C₃×D₄	—	4	2	no	—
176	C₂×C₃×D₄	—	4	4	no	—
177	C₂×C₃×D₄	—	4	2	no	—
178	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
179	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
180	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
181	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
182	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
183	C₃×C₄⋊C₄	—	4	2	no	—
184	C₃×C₄⋊C₄	—	4	1	no	—
185	C₃×C₂²⋊C₄	—	2	8	no	—
186	C₃×C₂²⋊C₄	—	2	8	no	—
187	C₃×C₂²⋊C₄	—	2	8	no	—
188	C₃×C₂²⋊C₄	—	4	4	no	—
189	C₃×C₄²	—	2	4	no	—
190	C₃×C₄²	—	4	1	no	—
191	C₂³×C₅	—	2	4	no	—
192	C₂³×C₅	—	2	4	no	—
193	C₂³×C₅	—	2	4	no	—
194	C₂³×C₅	—	2	4	no	—
195	C₂³×C₅	—	2	4	no	—
196	C₂³×C₅	—	2	4	no	—
197	C₂³×C₅	—	2	4	no	—
198	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
199	C₅×Q₈	—	4	4	no	—
200	C₅×D₄	—	4	8	no	—
201	C₅×D₄	—	4	8	no	—
202	C₅×D₄	—	4	8	no	—
203	C₂×C₄×C₅	—	2	2	no	—
204	C₂×C₄×C₅	—	2	1	no	—
205	C₂×C₄×C₅	—	2	2	no	—
206	C₂×C₄×C₅	—	2	1	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	4	no	—
211	C₂×C₄×C₅	—	2	4	no	—
212	C₂×C₄×C₅	—	2	4	no	—
213	C₂×C₄×C₅	—	2	2	no	—
214	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
215	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
216	C₂×C₄×C₅	C₃×#41	1	4	yes	—
217	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
218	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
219	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
220	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
221	#124	—	2	8	no	—
222	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
223	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
224	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
225	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
226	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
227	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
228	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
229	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
230	#95	C₂²×C₃×C₅	1	2	yes	—
231	#95	C₂²×C₃×C₅	1	4	yes	—
232	C₂×C₃×C₅	—	8	4	no	—
233	C₂×C₃×C₅	#534	1	1	yes	characteristic
234	C₂×C₃×C₅	#538	1	2	yes	—
235	C₂×C₃×C₅	#550	1	2	yes	—
236	C₂×C₃×C₅	#555	1	1	yes	characteristic
237	C₂×C₃×C₅	H(3,𝔽₄)	1	1	yes	characteristic
238	C₂³×C₃	—	2	4	no	—
239	C₂³×C₃	—	2	4	no	—
240	C₂³×C₃	—	2	4	no	—
241	C₂³×C₃	—	2	4	no	—
242	C₂³×C₃	—	2	4	no	—
243	C₂³×C₃	—	2	4	no	—
244	C₂³×C₃	—	2	4	no	—
245	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
246	C₃×Q₈	—	4	4	no	—
247	C₃×D₄	—	4	8	no	—
248	C₃×D₄	—	4	8	no	—
249	C₃×D₄	—	4	8	no	—
250	C₂×C₃×C₄	—	2	2	no	—
251	C₂×C₃×C₄	—	2	1	no	—
252	C₂×C₃×C₄	—	2	2	no	—
253	C₂×C₃×C₄	—	2	1	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	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	C₂×C₅×D₄	1	4	yes	—
262	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
263	C₂×C₃×C₄	C₅×#41	1	4	yes	—
264	C₂²×C₅	—	4	4	no	—
265	C₂²×C₅	—	4	4	no	—
266	C₂²×C₅	—	4	4	no	—
267	C₂²×C₅	—	4	4	no	—
268	C₂²×C₅	—	4	4	no	—
269	C₂²×C₅	—	4	4	no	—
270	C₂²×C₅	—	4	4	no	—
271	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
272	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
273	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
274	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
275	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
276	C₄×C₅	—	2	4	no	—
277	C₄×C₅	—	2	2	no	—
278	C₄×C₅	—	2	4	no	—
279	C₄×C₅	—	4	2	no	—
280	C₄×C₅	—	4	4	no	—
281	C₂⁴	C₂³×C₃×C₅	1	4	yes	—
282	C₂×Q₈	—	4	1	no	—
283	C₂×Q₈	—	4	1	no	—
284	C₂×Q₈	C₃×C₅×D₄	1	4	yes	complemented
285	C₂×D₄	—	2	4	no	—
286	C₂×D₄	—	2	4	no	—
287	C₂×D₄	—	4	2	no	—
288	C₂×D₄	—	4	2	no	—
289	C₂×D₄	—	4	2	no	—
290	C₂×D₄	—	4	2	no	—
291	C₂×D₄	—	4	4	no	—
292	C₂×D₄	—	4	2	no	—
293	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
294	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
295	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
296	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
297	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
298	C₄⋊C₄	—	4	2	no	—
299	C₄⋊C₄	—	4	1	no	—
300	C₂²⋊C₄	—	2	8	no	—
301	C₂²⋊C₄	—	2	8	no	—
302	C₂²⋊C₄	—	2	8	no	—
303	C₂²⋊C₄	—	4	4	no	—
304	C₄²	—	2	4	no	—
305	C₄²	—	4	1	no	—
306	C₃×C₅	#2733	1	1	yes	characteristic, direct product factor, Hall
307	C₂²×C₃	—	4	4	no	—
308	C₂²×C₃	—	4	4	no	—
309	C₂²×C₃	—	4	4	no	—
310	C₂²×C₃	—	4	4	no	—
311	C₂²×C₃	—	4	4	no	—
312	C₂²×C₃	—	4	4	no	—
313	C₂²×C₃	—	4	4	no	—
314	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
315	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
316	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
317	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
318	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
319	C₃×C₄	—	2	4	no	—
320	C₃×C₄	—	2	2	no	—
321	C₃×C₄	—	2	4	no	—
322	C₃×C₄	—	4	4	no	—
323	C₃×C₄	—	4	2	no	—
324	C₂×C₅	—	8	4	no	—
325	C₂×C₅	C₃×#534	1	1	yes	characteristic
326	C₂×C₅	C₃×#538	1	2	yes	—
327	C₂×C₅	C₃×#550	1	2	yes	—
328	C₂×C₅	C₃×#555	1	1	yes	characteristic
329	C₂×C₅	C₃×H(3,𝔽₄)	1	1	yes	characteristic
330	C₂³	—	2	4	no	—
331	C₂³	—	2	4	no	—
332	C₂³	—	2	4	no	—
333	C₂³	—	2	4	no	—
334	C₂³	—	2	4	no	—
335	C₂³	—	2	4	no	—
336	C₂³	—	2	4	no	—
337	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
338	Q₈	—	4	4	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	1	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
354	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
355	C₂×C₄	C₃×C₅×#41	1	4	yes	—
356	C₂×C₃	—	8	4	no	—
357	C₂×C₃	C₅×#534	1	1	yes	characteristic
358	C₂×C₃	C₅×#538	1	2	yes	—
359	C₂×C₃	C₅×#550	1	2	yes	—
360	C₂×C₃	C₅×#555	1	1	yes	characteristic
361	C₂×C₃	C₅×H(3,𝔽₄)	1	1	yes	characteristic
362	C₅	C₃×#2733	1	1	yes	characteristic, direct product factor, Sylow
363	C₂²	—	4	4	no	—
364	C₂²	—	4	4	no	—
365	C₂²	—	4	4	no	—
366	C₂²	—	4	4	no	—
367	C₂²	—	4	4	no	—
368	C₂²	—	4	4	no	—
369	C₂²	—	4	4	no	—
370	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
371	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
372	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
373	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
374	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
375	C₄	—	2	4	no	—
376	C₄	—	2	2	no	—
377	C₄	—	2	4	no	—
378	C₄	—	4	4	no	—
379	C₄	—	4	2	no	—
380	C₃	C₅×#2733	1	1	yes	characteristic, direct product factor, Sylow
381	C₂	—	8	4	no	—
382	C₂	C₃×C₅×#534	1	1	yes	characteristic
383	C₂	C₃×C₅×#538	1	2	yes	—
384	C₂	C₃×C₅×#550	1	2	yes	—
385	C₂	C₃×C₅×#555	1	1	yes	characteristic
386	C₂	C₃×C₅×H(3,𝔽₄)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
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
1. C₂×C₃×C₅×#124	C₂	semidirect
2. C₃×C₅×#394	C₂	semidirect
3. C₃×C₅×#392	C₂	semidirect
4. C₃×C₅×#391	C₂	semidirect
5. C₃×C₅×#390	C₂	semidirect
6. C₃×C₅×#388	C₂	semidirect
7. C₅×#2733	C₃	direct (N × H)
23. C₃×#2733	C₅	direct (N × H)
24. C₂×C₅×#124	C₂×C₃	semidirect
25. C₅×#394	C₂×C₃	semidirect
26. C₅×#392	C₂×C₃	semidirect
27. C₅×#391	C₂×C₃	semidirect
28. C₅×#390	C₂×C₃	semidirect
29. C₅×#388	C₂×C₃	semidirect
33. C₂×C₃×C₅×Q₈	D₄	semidirect
55. C₂×C₃×#124	C₂×C₅	semidirect
56. C₃×#394	C₂×C₅	semidirect
57. C₃×#392	C₂×C₅	semidirect
58. C₃×#391	C₂×C₅	semidirect
59. C₃×#390	C₂×C₅	semidirect
60. C₃×#388	C₂×C₅	semidirect
76. #2733	C₃×C₅	direct (N × H)
121. C₂×C₅×Q₈	C₃×D₄	semidirect
143. C₂×#124	C₂×C₃×C₅	semidirect
144. #394	C₂×C₃×C₅	semidirect
145. #392	C₂×C₃×C₅	semidirect
146. #391	C₂×C₃×C₅	semidirect
147. #390	C₂×C₃×C₅	semidirect
148. #388	C₂×C₃×C₅	semidirect
169. C₂×C₃×Q₈	C₅×D₄	semidirect
284. C₂×Q₈	C₃×C₅×D₄	semidirect
306. C₃×C₅	#2733	direct (N × H)
362. C₅	C₃×#2733	direct (N × H)
380. C₃	C₅×#2733	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×#124	2
C₃×C₅×#394	2
C₃×C₅×#392	2
C₃×C₅×#391	2
C₃×C₅×#390	2
C₃×C₅×#388	2
C₅×#2733	3
C₃×#2733	5

Subgroups — C3×C5×#2733 #14275767

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2733 #14275767