Subgroups — C₃×C₅×#2355 #14275389

Order 1920.

960 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×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#391	C₂	1	2	yes	maximal
3	C₃×C₅×#387	C₂	1	4	yes	maximal
4	C₃×C₅×#384	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#382	C₂	1	2	yes	maximal
6	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
7	C₃×C₄×C₅×C₄⋊C₄	C₂	1	2	yes	maximal
8	C₃×C₄×C₅×C₄⋊C₄	C₂	1	2	yes	maximal
9	C₅×#2355	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₃×C₄×C₅×Q₈	C₄	1	8	yes	complemented
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
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	1	yes	characteristic
19	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
20	C₂×C₃×C₄²×C₅	C₂²	1	4	yes	—
21	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
22	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
23	C₃×C₅×#95	C₂²	1	4	yes	—
24	C₃×C₅×#95	C₂²	1	2	yes	—
25	C₃×C₅×#95	C₂²	1	4	yes	—
26	C₃×C₅×#95	C₂²	1	4	yes	—
27	C₃×#2355	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₂×C₄×C₅×Q₈	C₂×C₃	1	1	yes	characteristic
29	C₅×#391	C₂×C₃	1	2	yes	—
30	C₅×#387	C₂×C₃	1	4	yes	—
31	C₅×#384	C₂×C₃	1	1	yes	characteristic
32	C₅×#382	C₂×C₃	1	2	yes	—
33	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
34	C₄×C₅×C₄⋊C₄	C₂×C₃	1	2	yes	—
35	C₄×C₅×C₄⋊C₄	C₂×C₃	1	2	yes	—
36	C₂×C₃×C₅×Q₈	—	2	2	no	—
37	C₂×C₃×C₅×Q₈	—	2	2	no	—
38	C₂×C₃×C₅×Q₈	C₂×C₄	1	4	yes	—
39	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
42	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
44	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₃×C₅×C₄⋊C₄	—	2	4	no	—
48	C₃×C₅×C₄⋊C₄	—	2	2	no	—
49	C₃×C₅×C₄⋊C₄	—	2	4	no	—
50	C₃×C₅×C₄⋊C₄	—	4	2	no	—
51	C₃×C₅×C₄⋊C₄	C₂×C₄	1	8	yes	—
52	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
53	C₃×C₅×C₄⋊C₄	Q₈	1	4	yes	complemented
54	C₃×C₄²×C₅	—	2	4	no	—
55	C₃×C₄²×C₅	—	4	4	no	—
56	C₃×C₄²×C₅	C₂×C₄	1	8	yes	—
57	C₃×C₄²×C₅	C₂×C₄	1	4	yes	—
58	C₂×C₃×C₄×Q₈	C₂×C₅	1	1	yes	characteristic
59	C₃×#391	C₂×C₅	1	2	yes	—
60	C₃×#387	C₂×C₅	1	4	yes	—
61	C₃×#384	C₂×C₅	1	1	yes	characteristic
62	C₃×#382	C₂×C₅	1	2	yes	—
63	C₃×C₄×C₄⋊C₄	C₂×C₅	1	2	yes	—
64	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
65	C₃×C₄×C₄⋊C₄	C₂×C₅	1	2	yes	—
66	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
67	C₄×C₅×Q₈	C₃×C₄	1	8	yes	complemented
68	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
69	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
70	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
71	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
72	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
73	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
74	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
75	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
76	C₂×C₄²×C₅	C₂²×C₃	1	4	yes	—
77	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
78	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
79	C₅×#95	C₂²×C₃	1	4	yes	—
80	C₅×#95	C₂²×C₃	1	2	yes	—
81	C₅×#95	C₂²×C₃	1	4	yes	—
82	C₅×#95	C₂²×C₃	1	4	yes	—
83	#2355	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
84	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
85	C₃×C₅×Q₈	—	2	8	no	—
86	C₂×C₃×C₄×C₅	—	2	2	no	—
87	C₂×C₃×C₄×C₅	—	2	2	no	—
88	C₂×C₃×C₄×C₅	—	2	2	no	—
89	C₂×C₃×C₄×C₅	—	2	2	no	—
90	C₂×C₃×C₄×C₅	—	2	2	no	—
91	C₂×C₃×C₄×C₅	—	2	1	no	—
92	C₂×C₃×C₄×C₅	—	2	2	no	—
93	C₂×C₃×C₄×C₅	—	2	1	no	—
94	C₂×C₃×C₄×C₅	—	2	2	no	—
95	C₂×C₃×C₄×C₅	—	2	2	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	C₂²×C₄	1	4	yes	—
101	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
102	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
103	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
104	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
105	C₂×C₃×C₄×C₅	C₂×Q₈	1	4	yes	—
106	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
107	C₂×C₃×C₄×C₅	#41	1	2	yes	—
108	C₂×C₃×C₄×C₅	#41	1	2	yes	—
109	C₂×C₃×C₄×C₅	#41	1	2	yes	—
110	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
111	C₃×C₄×Q₈	C₄×C₅	1	8	yes	complemented
112	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
113	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
114	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
115	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
116	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
117	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
118	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
119	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
120	C₂×C₃×C₄²	C₂²×C₅	1	4	yes	—
121	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
122	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
123	C₃×#95	C₂²×C₅	1	4	yes	—
124	C₃×#95	C₂²×C₅	1	2	yes	—
125	C₃×#95	C₂²×C₅	1	4	yes	—
126	C₃×#95	C₂²×C₅	1	4	yes	—
127	C₂×C₅×Q₈	—	2	2	no	—
128	C₂×C₅×Q₈	—	2	2	no	—
129	C₂×C₅×Q₈	C₂×C₃×C₄	1	4	yes	—
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	2	yes	—
133	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
134	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
135	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
136	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
137	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
138	C₅×C₄⋊C₄	—	2	4	no	—
139	C₅×C₄⋊C₄	—	2	2	no	—
140	C₅×C₄⋊C₄	—	2	4	no	—
141	C₅×C₄⋊C₄	—	4	2	no	—
142	C₅×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	—
143	C₅×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
144	C₅×C₄⋊C₄	C₃×Q₈	1	4	yes	complemented
145	C₄²×C₅	—	2	4	no	—
146	C₄²×C₅	—	4	4	no	—
147	C₄²×C₅	C₂×C₃×C₄	1	8	yes	—
148	C₄²×C₅	C₂×C₃×C₄	1	4	yes	—
149	C₂×C₄×Q₈	C₂×C₃×C₅	1	1	yes	characteristic
150	#391	C₂×C₃×C₅	1	2	yes	—
151	#387	C₂×C₃×C₅	1	4	yes	—
152	#384	C₂×C₃×C₅	1	1	yes	characteristic
153	#382	C₂×C₃×C₅	1	2	yes	—
154	C₄×C₄⋊C₄	C₂×C₃×C₅	1	2	yes	—
155	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
156	C₄×C₄⋊C₄	C₂×C₃×C₅	1	2	yes	—
157	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
158	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
159	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
160	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
161	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
162	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
163	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
164	C₃×C₄×C₅	—	2	4	no	—
165	C₃×C₄×C₅	—	2	4	no	—
166	C₃×C₄×C₅	—	2	2	no	—
167	C₃×C₄×C₅	—	2	4	no	—
168	C₃×C₄×C₅	—	4	2	no	—
169	C₃×C₄×C₅	—	4	4	no	—
170	C₃×C₄×C₅	#117	1	4	yes	—
171	C₃×C₄×C₅	C₄×Q₈	1	4	yes	—
172	C₂×C₃×Q₈	—	2	2	no	—
173	C₂×C₃×Q₈	—	2	2	no	—
174	C₂×C₃×Q₈	C₂×C₄×C₅	1	4	yes	—
175	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
176	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
177	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
178	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
179	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
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	1	yes	characteristic
183	C₃×C₄⋊C₄	—	2	4	no	—
184	C₃×C₄⋊C₄	—	2	2	no	—
185	C₃×C₄⋊C₄	—	2	4	no	—
186	C₃×C₄⋊C₄	—	4	2	no	—
187	C₃×C₄⋊C₄	C₂×C₄×C₅	1	8	yes	—
188	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
189	C₃×C₄⋊C₄	C₅×Q₈	1	4	yes	complemented
190	C₃×C₄²	—	2	4	no	—
191	C₃×C₄²	—	4	4	no	—
192	C₃×C₄²	C₂×C₄×C₅	1	8	yes	—
193	C₃×C₄²	C₂×C₄×C₅	1	4	yes	—
194	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
195	C₅×Q₈	—	2	8	no	—
196	C₂×C₄×C₅	—	2	2	no	—
197	C₂×C₄×C₅	—	2	2	no	—
198	C₂×C₄×C₅	—	2	2	no	—
199	C₂×C₄×C₅	—	2	2	no	—
200	C₂×C₄×C₅	—	2	2	no	—
201	C₂×C₄×C₅	—	2	1	no	—
202	C₂×C₄×C₅	—	2	2	no	—
203	C₂×C₄×C₅	—	2	1	no	—
204	C₂×C₄×C₅	—	2	2	no	—
205	C₂×C₄×C₅	—	2	4	no	—
206	C₂×C₄×C₅	—	2	4	no	—
207	C₂×C₄×C₅	—	2	2	no	—
208	C₂×C₄×C₅	—	2	4	no	—
209	C₂×C₄×C₅	—	2	2	no	—
210	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
211	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
212	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
213	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
214	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
215	C₂×C₄×C₅	C₂×C₃×Q₈	1	4	yes	—
216	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
217	C₂×C₄×C₅	C₃×#41	1	2	yes	—
218	C₂×C₄×C₅	C₃×#41	1	2	yes	—
219	C₂×C₄×C₅	C₃×#41	1	2	yes	—
220	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
221	C₄×Q₈	C₃×C₄×C₅	1	8	yes	complemented
222	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
223	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
224	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
225	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
226	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
227	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
228	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
229	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
230	C₂×C₄²	C₂²×C₃×C₅	1	4	yes	—
231	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
232	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
233	#95	C₂²×C₃×C₅	1	4	yes	—
234	#95	C₂²×C₃×C₅	1	2	yes	—
235	#95	C₂²×C₃×C₅	1	4	yes	—
236	#95	C₂²×C₃×C₅	1	4	yes	—
237	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
238	C₂×C₃×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
239	C₂×C₃×C₅	#520	1	1	yes	characteristic
240	C₂×C₃×C₅	#554	1	1	yes	characteristic
241	C₂×C₃×C₅	#556	1	1	yes	characteristic
242	C₂×C₃×C₅	#557	1	1	yes	characteristic
243	C₂×C₃×C₅	#559	1	1	yes	characteristic
244	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
245	C₃×Q₈	—	2	8	no	—
246	C₂×C₃×C₄	—	2	2	no	—
247	C₂×C₃×C₄	—	2	2	no	—
248	C₂×C₃×C₄	—	2	2	no	—
249	C₂×C₃×C₄	—	2	2	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	2	no	—
260	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
261	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
262	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
263	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
264	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
265	C₂×C₃×C₄	C₂×C₅×Q₈	1	4	yes	—
266	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
267	C₂×C₃×C₄	C₅×#41	1	2	yes	—
268	C₂×C₃×C₄	C₅×#41	1	2	yes	—
269	C₂×C₃×C₄	C₅×#41	1	2	yes	—
270	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
271	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
272	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
273	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
274	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
275	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
276	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
277	C₄×C₅	—	2	4	no	—
278	C₄×C₅	—	2	4	no	—
279	C₄×C₅	—	2	2	no	—
280	C₄×C₅	—	2	4	no	—
281	C₄×C₅	—	4	4	no	—
282	C₄×C₅	—	4	2	no	—
283	C₄×C₅	C₃×#117	1	4	yes	—
284	C₄×C₅	C₃×C₄×Q₈	1	4	yes	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	C₂×C₃×C₄×C₅	1	4	yes	—
288	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
289	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
290	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
291	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
292	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
293	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
294	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
295	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
296	C₄⋊C₄	—	2	4	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	4	no	—
299	C₄⋊C₄	—	4	2	no	—
300	C₄⋊C₄	C₂×C₃×C₄×C₅	1	8	yes	—
301	C₄⋊C₄	C₂×C₃×C₄×C₅	1	4	yes	—
302	C₄⋊C₄	C₃×C₅×Q₈	1	4	yes	complemented
303	C₄²	—	2	4	no	—
304	C₄²	—	4	4	no	—
305	C₄²	C₂×C₃×C₄×C₅	1	8	yes	—
306	C₄²	C₂×C₃×C₄×C₅	1	4	yes	—
307	C₃×C₅	#2355	1	1	yes	characteristic, direct product factor, Hall
308	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
309	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
310	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
311	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
312	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
313	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
314	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
315	C₃×C₄	—	2	4	no	—
316	C₃×C₄	—	2	4	no	—
317	C₃×C₄	—	2	2	no	—
318	C₃×C₄	—	2	4	no	—
319	C₃×C₄	—	4	2	no	—
320	C₃×C₄	—	4	4	no	—
321	C₃×C₄	C₅×#117	1	4	yes	—
322	C₃×C₄	C₄×C₅×Q₈	1	4	yes	—
323	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
324	C₂×C₅	C₂×C₃×C₄×Q₈	1	1	yes	characteristic
325	C₂×C₅	C₃×#520	1	1	yes	characteristic
326	C₂×C₅	C₃×#554	1	1	yes	characteristic
327	C₂×C₅	C₃×#556	1	1	yes	characteristic
328	C₂×C₅	C₃×#557	1	1	yes	characteristic
329	C₂×C₅	C₃×#559	1	1	yes	characteristic
330	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
331	Q₈	—	2	8	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
347	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
348	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
349	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
350	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
351	C₂×C₄	C₂×C₃×C₅×Q₈	1	4	yes	—
352	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
353	C₂×C₄	C₃×C₅×#41	1	2	yes	—
354	C₂×C₄	C₃×C₅×#41	1	2	yes	—
355	C₂×C₄	C₃×C₅×#41	1	2	yes	—
356	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
357	C₂×C₃	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
358	C₂×C₃	C₅×#520	1	1	yes	characteristic
359	C₂×C₃	C₅×#554	1	1	yes	characteristic
360	C₂×C₃	C₅×#556	1	1	yes	characteristic
361	C₂×C₃	C₅×#557	1	1	yes	characteristic
362	C₂×C₃	C₅×#559	1	1	yes	characteristic
363	C₅	C₃×#2355	1	1	yes	characteristic, direct product factor, Sylow
364	C₂²	C₂³×C₃×C₄×C₅	1	1	yes	characteristic
365	C₂²	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
366	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
367	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
368	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
369	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
370	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
371	C₄	—	2	4	no	—
372	C₄	—	2	4	no	—
373	C₄	—	2	2	no	—
374	C₄	—	2	4	no	—
375	C₄	—	4	2	no	—
376	C₄	—	4	4	no	—
377	C₄	C₃×C₅×#117	1	4	yes	—
378	C₄	C₃×C₄×C₅×Q₈	1	4	yes	—
379	C₃	C₅×#2355	1	1	yes	characteristic, direct product factor, Sylow
380	C₂	C₂×C₃×C₅×#117	1	1	yes	characteristic
381	C₂	C₂×C₃×C₄×C₅×Q₈	1	1	yes	characteristic
382	C₂	C₃×C₅×#520	1	1	yes	characteristic
383	C₂	C₃×C₅×#554	1	1	yes	characteristic
384	C₂	C₃×C₅×#556	1	1	yes	characteristic
385	C₂	C₃×C₅×#557	1	1	yes	characteristic
386	C₂	C₃×C₅×#559	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₃×C₅	C₂⁴
commutator	C₂²	C₂³×C₃×C₄×C₅
Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
9. C₅×#2355	C₃	direct (N × H)
11. C₃×C₄×C₅×Q₈	C₄	semidirect
27. C₃×#2355	C₅	direct (N × H)
53. C₃×C₅×C₄⋊C₄	Q₈	semidirect
67. C₄×C₅×Q₈	C₃×C₄	semidirect
83. #2355	C₃×C₅	direct (N × H)
111. C₃×C₄×Q₈	C₄×C₅	semidirect
144. C₅×C₄⋊C₄	C₃×Q₈	semidirect
189. C₃×C₄⋊C₄	C₅×Q₈	semidirect
221. C₄×Q₈	C₃×C₄×C₅	semidirect
302. C₄⋊C₄	C₃×C₅×Q₈	semidirect
307. C₃×C₅	#2355	direct (N × H)
363. C₅	C₃×#2355	direct (N × H)
379. C₃	C₅×#2355	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×C₄×C₅×Q₈	2
C₃×C₅×#391	2
C₃×C₅×#387	2
C₃×C₅×#384	2
C₃×C₅×#382	2
C₃×C₄×C₅×C₄⋊C₄	2
C₅×#2355	3
C₃×#2355	5

Subgroups — C3×C5×#2355 #14275389

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2355 #14275389