Subgroups — C₃×C₅×#2365 #14275399

Order 1920.

1104 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×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄×C₅×Q₈	C₂	1	2	yes	maximal
3	C₃×C₅×#391	C₂	1	2	yes	maximal
4	C₃×C₅×#389	C₂	1	2	yes	maximal
5	C₃×C₅×#387	C₂	1	4	yes	maximal
6	C₃×C₄×C₅×C₄⋊C₄	C₂	1	2	yes	maximal
7	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
8	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
9	C₅×#2365	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
11	C₃×C₅×C₄⋊Q₈	C₄	1	8	yes	complemented
12	C₃×C₄×C₅×Q₈	—	2	8	no	—
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	2	yes	—
23	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
24	C₃×C₅×#95	C₂²	1	2	yes	—
25	C₃×C₅×#95	C₂²	1	2	yes	—
26	C₃×C₅×#95	C₂²	1	4	yes	—
27	C₃×C₅×#95	C₂²	1	4	yes	—
28	C₃×#2365	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₂×C₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
30	C₂×C₄×C₅×Q₈	C₂×C₃	1	2	yes	—
31	C₅×#391	C₂×C₃	1	2	yes	—
32	C₅×#389	C₂×C₃	1	2	yes	—
33	C₅×#387	C₂×C₃	1	4	yes	—
34	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
35	C₄×C₅×C₄⋊C₄	C₂×C₃	1	2	yes	—
36	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
37	C₂×C₃×C₅×Q₈	—	2	4	no	—
38	C₂×C₃×C₅×Q₈	—	2	4	no	—
39	C₂×C₃×C₅×Q₈	C₂×C₄	1	8	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	4	yes	—
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
46	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
48	C₃×C₅×C₄⋊C₄	—	2	8	no	—
49	C₃×C₅×C₄⋊C₄	—	2	2	no	—
50	C₃×C₅×C₄⋊C₄	—	2	2	no	—
51	C₃×C₅×C₄⋊C₄	C₂×C₄	1	8	yes	—
52	C₃×C₅×C₄⋊C₄	C₂×C₄	1	8	yes	—
53	C₃×C₅×C₄⋊C₄	D₄	1	4	yes	—
54	C₃×C₅×C₄⋊C₄	Q₈	1	4	yes	complemented
55	C₃×C₄²×C₅	—	2	8	no	—
56	C₃×C₄²×C₅	—	2	4	no	—
57	C₃×C₄²×C₅	—	2	4	no	—
58	C₃×C₄²×C₅	C₂×C₄	1	4	yes	—
59	C₂×C₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic
60	C₂×C₃×C₄×Q₈	C₂×C₅	1	2	yes	—
61	C₃×#391	C₂×C₅	1	2	yes	—
62	C₃×#389	C₂×C₅	1	2	yes	—
63	C₃×#387	C₂×C₅	1	4	yes	—
64	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
65	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
66	C₃×C₄×C₄⋊C₄	C₂×C₅	1	2	yes	—
67	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
68	C₅×C₄⋊Q₈	C₃×C₄	1	8	yes	complemented
69	C₄×C₅×Q₈	—	2	8	no	—
70	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
71	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
72	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
73	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
74	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
75	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
76	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
77	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
78	C₂×C₄²×C₅	C₂²×C₃	1	4	yes	—
79	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
80	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
81	C₅×#95	C₂²×C₃	1	2	yes	—
82	C₅×#95	C₂²×C₃	1	2	yes	—
83	C₅×#95	C₂²×C₃	1	4	yes	—
84	C₅×#95	C₂²×C₃	1	4	yes	—
85	#2365	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
86	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
87	C₃×C₅×Q₈	—	2	16	no	—
88	C₂×C₃×C₄×C₅	—	2	2	no	—
89	C₂×C₃×C₄×C₅	—	2	4	no	—
90	C₂×C₃×C₄×C₅	—	2	2	no	—
91	C₂×C₃×C₄×C₅	—	2	4	no	—
92	C₂×C₃×C₄×C₅	—	2	1	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	2	no	—
97	C₂×C₃×C₄×C₅	—	2	2	no	—
98	C₂×C₃×C₄×C₅	—	2	2	no	—
99	C₂×C₃×C₄×C₅	—	2	2	no	—
100	C₂×C₃×C₄×C₅	—	2	2	no	—
101	C₂×C₃×C₄×C₅	—	2	2	no	—
102	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
103	C₂×C₃×C₄×C₅	C₂²×C₄	1	8	yes	—
104	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
105	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
106	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
107	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
108	C₂×C₃×C₄×C₅	C₂×Q₈	1	4	yes	—
109	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
110	C₂×C₃×C₄×C₅	#41	1	2	yes	—
111	C₂×C₃×C₄×C₅	#41	1	2	yes	—
112	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
113	C₃×C₄⋊Q₈	C₄×C₅	1	8	yes	complemented
114	C₃×C₄×Q₈	—	2	8	no	—
115	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
116	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
117	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
118	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
119	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
120	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
121	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
122	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
123	C₂×C₃×C₄²	C₂²×C₅	1	4	yes	—
124	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
125	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
126	C₃×#95	C₂²×C₅	1	2	yes	—
127	C₃×#95	C₂²×C₅	1	2	yes	—
128	C₃×#95	C₂²×C₅	1	4	yes	—
129	C₃×#95	C₂²×C₅	1	4	yes	—
130	C₂×C₅×Q₈	—	2	4	no	—
131	C₂×C₅×Q₈	—	2	4	no	—
132	C₂×C₅×Q₈	C₂×C₃×C₄	1	8	yes	—
133	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
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	1	yes	characteristic
137	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
138	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
139	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
140	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
141	C₅×C₄⋊C₄	—	2	8	no	—
142	C₅×C₄⋊C₄	—	2	2	no	—
143	C₅×C₄⋊C₄	—	2	2	no	—
144	C₅×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	—
145	C₅×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	—
146	C₅×C₄⋊C₄	C₃×D₄	1	4	yes	—
147	C₅×C₄⋊C₄	C₃×Q₈	1	4	yes	complemented
148	C₄²×C₅	—	2	8	no	—
149	C₄²×C₅	—	2	4	no	—
150	C₄²×C₅	—	2	4	no	—
151	C₄²×C₅	C₂×C₃×C₄	1	4	yes	—
152	C₂×C₄⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic
153	C₂×C₄×Q₈	C₂×C₃×C₅	1	2	yes	—
154	#391	C₂×C₃×C₅	1	2	yes	—
155	#389	C₂×C₃×C₅	1	2	yes	—
156	#387	C₂×C₃×C₅	1	4	yes	—
157	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
158	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
159	C₄×C₄⋊C₄	C₂×C₃×C₅	1	2	yes	—
160	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
161	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
162	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
163	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
164	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
165	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
166	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
167	C₃×C₄×C₅	—	2	8	no	—
168	C₃×C₄×C₅	—	2	2	no	—
169	C₃×C₄×C₅	—	2	4	no	—
170	C₃×C₄×C₅	—	2	4	no	—
171	C₃×C₄×C₅	—	4	2	no	—
172	C₃×C₄×C₅	—	4	2	no	—
173	C₃×C₄×C₅	C₄×D₄	1	4	yes	—
174	C₃×C₄×C₅	C₄×Q₈	1	4	yes	complemented
175	C₂×C₃×Q₈	—	2	4	no	—
176	C₂×C₃×Q₈	—	2	4	no	—
177	C₂×C₃×Q₈	C₂×C₄×C₅	1	8	yes	—
178	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
179	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
180	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
181	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
182	C₂²×C₃×C₄	C₂³×C₅	1	2	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	1	yes	characteristic
186	C₃×C₄⋊C₄	—	2	8	no	—
187	C₃×C₄⋊C₄	—	2	2	no	—
188	C₃×C₄⋊C₄	—	2	2	no	—
189	C₃×C₄⋊C₄	C₂×C₄×C₅	1	8	yes	—
190	C₃×C₄⋊C₄	C₂×C₄×C₅	1	8	yes	—
191	C₃×C₄⋊C₄	C₅×D₄	1	4	yes	—
192	C₃×C₄⋊C₄	C₅×Q₈	1	4	yes	complemented
193	C₃×C₄²	—	2	8	no	—
194	C₃×C₄²	—	2	4	no	—
195	C₃×C₄²	—	2	4	no	—
196	C₃×C₄²	C₂×C₄×C₅	1	4	yes	—
197	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
198	C₅×Q₈	—	2	16	no	—
199	C₂×C₄×C₅	—	2	2	no	—
200	C₂×C₄×C₅	—	2	4	no	—
201	C₂×C₄×C₅	—	2	2	no	—
202	C₂×C₄×C₅	—	2	4	no	—
203	C₂×C₄×C₅	—	2	1	no	—
204	C₂×C₄×C₅	—	2	1	no	—
205	C₂×C₄×C₅	—	2	2	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	2	no	—
210	C₂×C₄×C₅	—	2	2	no	—
211	C₂×C₄×C₅	—	2	2	no	—
212	C₂×C₄×C₅	—	2	2	no	—
213	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
214	C₂×C₄×C₅	C₂²×C₃×C₄	1	8	yes	—
215	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
216	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
217	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
218	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
219	C₂×C₄×C₅	C₂×C₃×Q₈	1	4	yes	—
220	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
221	C₂×C₄×C₅	C₃×#41	1	2	yes	—
222	C₂×C₄×C₅	C₃×#41	1	2	yes	—
223	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
224	C₄⋊Q₈	C₃×C₄×C₅	1	8	yes	complemented
225	C₄×Q₈	—	2	8	no	—
226	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
227	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
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×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
232	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
233	C₂×C₄²	C₂²×C₃×C₅	1	4	yes	—
234	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
235	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
236	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
237	#95	C₂²×C₃×C₅	1	2	yes	—
238	#95	C₂²×C₃×C₅	1	2	yes	—
239	#95	C₂²×C₃×C₅	1	4	yes	—
240	#95	C₂²×C₃×C₅	1	4	yes	—
241	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
242	C₂×C₃×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
243	C₂×C₃×C₅	#519	1	1	yes	characteristic
244	C₂×C₃×C₅	#547	1	1	yes	characteristic
245	C₂×C₃×C₅	D₄×Q₈	1	1	yes	characteristic
246	C₂×C₃×C₅	#556	1	1	yes	characteristic
247	C₂×C₃×C₅	#557	1	1	yes	characteristic
248	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
249	C₃×Q₈	—	2	16	no	—
250	C₂×C₃×C₄	—	2	2	no	—
251	C₂×C₃×C₄	—	2	4	no	—
252	C₂×C₃×C₄	—	2	2	no	—
253	C₂×C₃×C₄	—	2	4	no	—
254	C₂×C₃×C₄	—	2	1	no	—
255	C₂×C₃×C₄	—	2	1	no	—
256	C₂×C₃×C₄	—	2	2	no	—
257	C₂×C₃×C₄	—	2	2	no	—
258	C₂×C₃×C₄	—	2	2	no	—
259	C₂×C₃×C₄	—	2	2	no	—
260	C₂×C₃×C₄	—	2	2	no	—
261	C₂×C₃×C₄	—	2	2	no	—
262	C₂×C₃×C₄	—	2	2	no	—
263	C₂×C₃×C₄	—	2	2	no	—
264	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
265	C₂×C₃×C₄	C₂²×C₄×C₅	1	8	yes	—
266	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
267	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
268	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
269	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
270	C₂×C₃×C₄	C₂×C₅×Q₈	1	4	yes	—
271	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
272	C₂×C₃×C₄	C₅×#41	1	2	yes	—
273	C₂×C₃×C₄	C₅×#41	1	2	yes	—
274	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
275	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
276	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
277	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
278	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
279	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
280	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
281	C₄×C₅	—	2	8	no	—
282	C₄×C₅	—	2	2	no	—
283	C₄×C₅	—	2	4	no	—
284	C₄×C₅	—	2	4	no	—
285	C₄×C₅	—	4	2	no	—
286	C₄×C₅	—	4	2	no	—
287	C₄×C₅	C₃×C₄×D₄	1	4	yes	—
288	C₄×C₅	C₃×C₄×Q₈	1	4	yes	complemented
289	C₂×Q₈	—	2	4	no	—
290	C₂×Q₈	—	2	4	no	—
291	C₂×Q₈	C₂×C₃×C₄×C₅	1	8	yes	—
292	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
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	4	yes	—
296	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
297	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
298	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
299	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
300	C₄⋊C₄	—	2	8	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	C₂×C₃×C₄×C₅	1	8	yes	—
304	C₄⋊C₄	C₂×C₃×C₄×C₅	1	8	yes	—
305	C₄⋊C₄	C₃×C₅×D₄	1	4	yes	—
306	C₄⋊C₄	C₃×C₅×Q₈	1	4	yes	complemented
307	C₄²	—	2	8	no	—
308	C₄²	—	2	4	no	—
309	C₄²	—	2	4	no	—
310	C₄²	C₂×C₃×C₄×C₅	1	4	yes	—
311	C₃×C₅	#2365	1	1	yes	characteristic, direct product factor, Hall
312	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
313	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
314	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
315	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
316	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
317	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
318	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
319	C₃×C₄	—	2	8	no	—
320	C₃×C₄	—	2	2	no	—
321	C₃×C₄	—	2	4	no	—
322	C₃×C₄	—	2	4	no	—
323	C₃×C₄	—	4	2	no	—
324	C₃×C₄	—	4	2	no	—
325	C₃×C₄	C₄×C₅×D₄	1	4	yes	—
326	C₃×C₄	C₄×C₅×Q₈	1	4	yes	complemented
327	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
328	C₂×C₅	C₂×C₃×C₄×Q₈	1	1	yes	characteristic
329	C₂×C₅	C₃×#519	1	1	yes	characteristic
330	C₂×C₅	C₃×#547	1	1	yes	characteristic
331	C₂×C₅	C₃×D₄×Q₈	1	1	yes	characteristic
332	C₂×C₅	C₃×#556	1	1	yes	characteristic
333	C₂×C₅	C₃×#557	1	1	yes	characteristic
334	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
335	Q₈	—	2	16	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
351	C₂×C₄	C₂²×C₃×C₄×C₅	1	8	yes	—
352	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
353	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
354	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
355	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
356	C₂×C₄	C₂×C₃×C₅×Q₈	1	4	yes	—
357	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
358	C₂×C₄	C₃×C₅×#41	1	2	yes	—
359	C₂×C₄	C₃×C₅×#41	1	2	yes	—
360	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
361	C₂×C₃	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
362	C₂×C₃	C₅×#519	1	1	yes	characteristic
363	C₂×C₃	C₅×#547	1	1	yes	characteristic
364	C₂×C₃	C₅×D₄×Q₈	1	1	yes	characteristic
365	C₂×C₃	C₅×#556	1	1	yes	characteristic
366	C₂×C₃	C₅×#557	1	1	yes	characteristic
367	C₅	C₃×#2365	1	1	yes	characteristic, direct product factor, Sylow
368	C₂²	C₂³×C₃×C₄×C₅	1	1	yes	characteristic
369	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
370	C₂²	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
371	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
372	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
373	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
374	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
375	C₄	—	2	8	no	—
376	C₄	—	2	2	no	—
377	C₄	—	2	4	no	—
378	C₄	—	2	4	no	—
379	C₄	—	4	2	no	—
380	C₄	—	4	2	no	—
381	C₄	C₃×C₄×C₅×D₄	1	4	yes	—
382	C₄	C₃×C₄×C₅×Q₈	1	4	yes	complemented
383	C₃	C₅×#2365	1	1	yes	characteristic, direct product factor, Sylow
384	C₂	C₂×C₃×C₄×C₅×D₄	1	1	yes	characteristic
385	C₂	C₂×C₃×C₄×C₅×Q₈	1	1	yes	characteristic
386	C₂	C₃×C₅×#519	1	1	yes	characteristic
387	C₂	C₃×C₅×#547	1	1	yes	characteristic
388	C₂	C₃×C₅×D₄×Q₈	1	1	yes	characteristic
389	C₂	C₃×C₅×#556	1	1	yes	characteristic
390	C₂	C₃×C₅×#557	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×#2365	C₃	direct (N × H)
11. C₃×C₅×C₄⋊Q₈	C₄	semidirect
28. C₃×#2365	C₅	direct (N × H)
54. C₃×C₅×C₄⋊C₄	Q₈	semidirect
68. C₅×C₄⋊Q₈	C₃×C₄	semidirect
85. #2365	C₃×C₅	direct (N × H)
113. C₃×C₄⋊Q₈	C₄×C₅	semidirect
147. C₅×C₄⋊C₄	C₃×Q₈	semidirect
174. C₃×C₄×C₅	C₄×Q₈	semidirect
192. C₃×C₄⋊C₄	C₅×Q₈	semidirect
224. C₄⋊Q₈	C₃×C₄×C₅	semidirect
288. C₄×C₅	C₃×C₄×Q₈	semidirect
306. C₄⋊C₄	C₃×C₅×Q₈	semidirect
311. C₃×C₅	#2365	direct (N × H)
326. C₃×C₄	C₄×C₅×Q₈	semidirect
367. C₅	C₃×#2365	direct (N × H)
382. C₄	C₃×C₄×C₅×Q₈	semidirect
383. C₃	C₅×#2365	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×C₄⋊Q₈	2
C₂×C₃×C₄×C₅×Q₈	2
C₃×C₅×#391	2
C₃×C₅×#389	2
C₃×C₅×#387	2
C₃×C₄×C₅×C₄⋊C₄	2
C₅×#2365	3
C₃×#2365	5

Subgroups — C3×C5×#2365 #14275399

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2365 #14275399