Subgroups — C₃×C₅×#2677 #14275711

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 468 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	2	yes	maximal, complemented
2	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	2	yes	maximal
3	C₃×C₅×#399	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#398	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#395	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#393	C₂	1	1	yes	maximal, characteristic
7	C₃×C₅×#388	C₂	1	2	yes	maximal
8	C₃×C₅×#387	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#385	C₂	1	1	yes	maximal, characteristic
10	C₅×#2677	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
12	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
13	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
14	C₃×C₅×C₄⋊Q₈	—	2	8	no	—
15	C₃×C₅×C₂²⋊Q₈	—	2	8	no	—
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	2	yes	—
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
23	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
24	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
28	C₃×C₅×#95	C₂²	1	2	yes	—
29	C₃×C₅×#95	C₂²	1	1	yes	characteristic
30	C₃×C₅×#95	C₂²	1	2	yes	—
31	C₃×C₅×#95	C₂²	1	2	yes	—
32	C₃×C₅×#95	C₂²	1	2	yes	—
33	C₃×C₅×#95	C₂²	1	1	yes	characteristic
34	C₃×#2677	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
35	C₂×C₅×C₄⋊Q₈	C₂×C₃	1	2	yes	complemented
36	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	2	yes	—
37	C₅×#399	C₂×C₃	1	1	yes	characteristic
38	C₅×#398	C₂×C₃	1	2	yes	complemented
39	C₅×#395	C₂×C₃	1	2	yes	complemented
40	C₅×#393	C₂×C₃	1	1	yes	characteristic
41	C₅×#388	C₂×C₃	1	2	yes	—
42	C₅×#387	C₂×C₃	1	2	yes	complemented
43	C₅×#385	C₂×C₃	1	1	yes	characteristic
44	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
45	C₂×C₃×C₅×Q₈	—	2	4	no	—
46	C₂×C₃×C₅×Q₈	—	2	4	no	—
47	C₂×C₃×C₅×Q₈	—	2	4	no	—
48	C₂×C₃×C₅×Q₈	—	4	2	no	—
49	C₂×C₃×C₅×Q₈	—	4	1	no	—
50	C₂²×C₃×C₄×C₅	—	2	4	no	—
51	C₂²×C₃×C₄×C₅	—	4	1	no	—
52	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
55	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
56	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
57	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
58	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
59	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
60	C₃×C₅×C₄⋊C₄	—	2	4	no	—
61	C₃×C₅×C₄⋊C₄	—	2	4	no	—
62	C₃×C₅×C₄⋊C₄	—	2	4	no	—
63	C₃×C₅×C₄⋊C₄	—	2	4	no	—
64	C₃×C₅×C₄⋊C₄	—	2	4	no	—
65	C₃×C₅×C₄⋊C₄	—	4	1	no	—
66	C₃×C₅×C₄⋊C₄	D₄	1	8	yes	—
67	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
68	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
69	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
70	C₃×C₅×C₂²⋊C₄	Q₈	1	4	yes	complemented
71	C₃×C₄²×C₅	—	2	4	no	—
72	C₂×C₃×C₄⋊Q₈	C₂×C₅	1	2	yes	complemented
73	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	2	yes	—
74	C₃×#399	C₂×C₅	1	1	yes	characteristic
75	C₃×#398	C₂×C₅	1	2	yes	complemented
76	C₃×#395	C₂×C₅	1	2	yes	complemented
77	C₃×#393	C₂×C₅	1	1	yes	characteristic
78	C₃×#388	C₂×C₅	1	2	yes	—
79	C₃×#387	C₂×C₅	1	2	yes	complemented
80	C₃×#385	C₂×C₅	1	1	yes	characteristic
81	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
82	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
83	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
84	C₅×C₄⋊Q₈	—	2	8	no	—
85	C₅×C₂²⋊Q₈	—	2	8	no	—
86	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
87	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
88	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
89	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
90	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
91	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
93	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
94	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
95	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
96	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
97	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
98	C₅×#95	C₂²×C₃	1	2	yes	—
99	C₅×#95	C₂²×C₃	1	1	yes	characteristic
100	C₅×#95	C₂²×C₃	1	2	yes	—
101	C₅×#95	C₂²×C₃	1	2	yes	—
102	C₅×#95	C₂²×C₃	1	2	yes	—
103	C₅×#95	C₂²×C₃	1	1	yes	characteristic
104	#2677	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
105	C₂³×C₃×C₅	—	2	2	no	—
106	C₂³×C₃×C₅	—	2	1	no	—
107	C₂³×C₃×C₅	—	2	1	no	—
108	C₂³×C₃×C₅	—	2	2	no	—
109	C₂³×C₃×C₅	C₂×Q₈	1	2	yes	—
110	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
111	C₃×C₅×Q₈	—	4	8	no	—
112	C₃×C₅×Q₈	—	4	4	no	—
113	C₂×C₃×C₄×C₅	—	2	2	no	—
114	C₂×C₃×C₄×C₅	—	2	2	no	—
115	C₂×C₃×C₄×C₅	—	2	2	no	—
116	C₂×C₃×C₄×C₅	—	2	2	no	—
117	C₂×C₃×C₄×C₅	—	2	2	no	—
118	C₂×C₃×C₄×C₅	—	2	2	no	—
119	C₂×C₃×C₄×C₅	—	2	2	no	—
120	C₂×C₃×C₄×C₅	—	2	2	no	—
121	C₂×C₃×C₄×C₅	—	2	2	no	—
122	C₂×C₃×C₄×C₅	—	2	2	no	—
123	C₂×C₃×C₄×C₅	—	2	2	no	—
124	C₂×C₃×C₄×C₅	—	2	2	no	—
125	C₂×C₃×C₄×C₅	—	2	1	no	—
126	C₂×C₃×C₄×C₅	—	2	1	no	—
127	C₂×C₃×C₄×C₅	—	2	2	no	—
128	C₂×C₃×C₄×C₅	—	2	2	no	—
129	C₂×C₃×C₄×C₅	—	2	2	no	—
130	C₂×C₃×C₄×C₅	—	2	2	no	—
131	C₂×C₃×C₄×C₅	—	4	4	no	—
132	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
133	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
134	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
135	C₂×C₃×C₄×C₅	C₂×Q₈	1	4	yes	—
136	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
137	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
138	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
139	C₃×C₄⋊Q₈	—	2	8	no	—
140	C₃×C₂²⋊Q₈	—	2	8	no	—
141	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
142	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
143	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
144	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
145	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
146	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
147	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
148	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
149	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
150	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
151	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
152	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
153	C₃×#95	C₂²×C₅	1	2	yes	—
154	C₃×#95	C₂²×C₅	1	1	yes	characteristic
155	C₃×#95	C₂²×C₅	1	2	yes	—
156	C₃×#95	C₂²×C₅	1	2	yes	—
157	C₃×#95	C₂²×C₅	1	2	yes	—
158	C₃×#95	C₂²×C₅	1	1	yes	characteristic
159	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
160	C₂×C₅×Q₈	—	2	4	no	—
161	C₂×C₅×Q₈	—	2	4	no	—
162	C₂×C₅×Q₈	—	2	4	no	—
163	C₂×C₅×Q₈	—	4	2	no	—
164	C₂×C₅×Q₈	—	4	1	no	—
165	C₂²×C₄×C₅	—	2	4	no	—
166	C₂²×C₄×C₅	—	4	1	no	—
167	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
168	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
169	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
170	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
171	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
172	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
173	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
174	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
175	C₅×C₄⋊C₄	—	2	4	no	—
176	C₅×C₄⋊C₄	—	2	4	no	—
177	C₅×C₄⋊C₄	—	2	4	no	—
178	C₅×C₄⋊C₄	—	2	4	no	—
179	C₅×C₄⋊C₄	—	2	4	no	—
180	C₅×C₄⋊C₄	—	4	1	no	—
181	C₅×C₄⋊C₄	C₃×D₄	1	8	yes	—
182	C₅×C₂²⋊C₄	—	2	4	no	—
183	C₅×C₂²⋊C₄	—	2	4	no	—
184	C₅×C₂²⋊C₄	—	4	1	no	—
185	C₅×C₂²⋊C₄	C₃×Q₈	1	4	yes	complemented
186	C₄²×C₅	—	2	4	no	—
187	C₂×C₄⋊Q₈	C₂×C₃×C₅	1	2	yes	complemented
188	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	2	yes	—
189	#399	C₂×C₃×C₅	1	1	yes	characteristic
190	#398	C₂×C₃×C₅	1	2	yes	complemented
191	#395	C₂×C₃×C₅	1	2	yes	complemented
192	#393	C₂×C₃×C₅	1	1	yes	characteristic
193	#388	C₂×C₃×C₅	1	2	yes	—
194	#387	C₂×C₃×C₅	1	2	yes	complemented
195	#385	C₂×C₃×C₅	1	1	yes	characteristic
196	C₂²×C₃×C₅	—	2	2	no	—
197	C₂²×C₃×C₅	—	2	4	no	—
198	C₂²×C₃×C₅	—	4	2	no	—
199	C₂²×C₃×C₅	—	4	1	no	—
200	C₂²×C₃×C₅	—	4	1	no	—
201	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
202	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
203	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
204	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
205	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
206	C₃×C₄×C₅	—	2	4	no	—
207	C₃×C₄×C₅	—	2	4	no	—
208	C₃×C₄×C₅	—	2	4	no	—
209	C₃×C₄×C₅	—	2	4	no	—
210	C₃×C₄×C₅	—	4	2	no	—
211	C₃×C₄×C₅	—	4	2	no	—
212	C₃×C₄×C₅	—	4	1	no	—
213	C₃×C₄×C₅	—	4	1	no	—
214	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
215	C₂×C₃×Q₈	—	2	4	no	—
216	C₂×C₃×Q₈	—	2	4	no	—
217	C₂×C₃×Q₈	—	2	4	no	—
218	C₂×C₃×Q₈	—	4	2	no	—
219	C₂×C₃×Q₈	—	4	1	no	—
220	C₂²×C₃×C₄	—	2	4	no	—
221	C₂²×C₃×C₄	—	4	1	no	—
222	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
223	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
224	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
225	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
226	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
227	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
228	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
229	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
230	C₃×C₄⋊C₄	—	2	4	no	—
231	C₃×C₄⋊C₄	—	2	4	no	—
232	C₃×C₄⋊C₄	—	2	4	no	—
233	C₃×C₄⋊C₄	—	2	4	no	—
234	C₃×C₄⋊C₄	—	2	4	no	—
235	C₃×C₄⋊C₄	—	4	1	no	—
236	C₃×C₄⋊C₄	C₅×D₄	1	8	yes	—
237	C₃×C₂²⋊C₄	—	2	4	no	—
238	C₃×C₂²⋊C₄	—	2	4	no	—
239	C₃×C₂²⋊C₄	—	4	1	no	—
240	C₃×C₂²⋊C₄	C₅×Q₈	1	4	yes	complemented
241	C₃×C₄²	—	2	4	no	—
242	C₂³×C₅	—	2	2	no	—
243	C₂³×C₅	—	2	1	no	—
244	C₂³×C₅	—	2	1	no	—
245	C₂³×C₅	—	2	2	no	—
246	C₂³×C₅	C₂×C₃×Q₈	1	2	yes	—
247	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
248	C₅×Q₈	—	4	8	no	—
249	C₅×Q₈	—	4	4	no	—
250	C₂×C₄×C₅	—	2	2	no	—
251	C₂×C₄×C₅	—	2	2	no	—
252	C₂×C₄×C₅	—	2	2	no	—
253	C₂×C₄×C₅	—	2	2	no	—
254	C₂×C₄×C₅	—	2	2	no	—
255	C₂×C₄×C₅	—	2	2	no	—
256	C₂×C₄×C₅	—	2	2	no	—
257	C₂×C₄×C₅	—	2	2	no	—
258	C₂×C₄×C₅	—	2	2	no	—
259	C₂×C₄×C₅	—	2	2	no	—
260	C₂×C₄×C₅	—	2	2	no	—
261	C₂×C₄×C₅	—	2	2	no	—
262	C₂×C₄×C₅	—	2	1	no	—
263	C₂×C₄×C₅	—	2	1	no	—
264	C₂×C₄×C₅	—	2	2	no	—
265	C₂×C₄×C₅	—	2	2	no	—
266	C₂×C₄×C₅	—	2	2	no	—
267	C₂×C₄×C₅	—	2	2	no	—
268	C₂×C₄×C₅	—	4	4	no	—
269	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
270	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
271	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
272	C₂×C₄×C₅	C₂×C₃×Q₈	1	4	yes	—
273	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
274	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
275	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
276	C₄⋊Q₈	—	2	8	no	—
277	C₂²⋊Q₈	—	2	8	no	—
278	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
279	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
280	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
281	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
282	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
283	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
284	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
285	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
286	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
287	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
288	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
289	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
290	#95	C₂²×C₃×C₅	1	2	yes	—
291	#95	C₂²×C₃×C₅	1	1	yes	characteristic
292	#95	C₂²×C₃×C₅	1	2	yes	—
293	#95	C₂²×C₃×C₅	1	2	yes	—
294	#95	C₂²×C₃×C₅	1	2	yes	—
295	#95	C₂²×C₃×C₅	1	1	yes	characteristic
296	C₂×C₃×C₅	—	4	2	no	—
297	C₂×C₃×C₅	#536	1	2	yes	—
298	C₂×C₃×C₅	#544	1	1	yes	characteristic
299	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
300	C₂×C₃×C₅	D₄×Q₈	1	2	yes	—
301	C₂×C₃×C₅	#563	1	1	yes	characteristic
302	C₂³×C₃	—	2	2	no	—
303	C₂³×C₃	—	2	1	no	—
304	C₂³×C₃	—	2	1	no	—
305	C₂³×C₃	—	2	2	no	—
306	C₂³×C₃	C₂×C₅×Q₈	1	2	yes	—
307	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
308	C₃×Q₈	—	4	8	no	—
309	C₃×Q₈	—	4	4	no	—
310	C₂×C₃×C₄	—	2	2	no	—
311	C₂×C₃×C₄	—	2	2	no	—
312	C₂×C₃×C₄	—	2	2	no	—
313	C₂×C₃×C₄	—	2	2	no	—
314	C₂×C₃×C₄	—	2	2	no	—
315	C₂×C₃×C₄	—	2	2	no	—
316	C₂×C₃×C₄	—	2	2	no	—
317	C₂×C₃×C₄	—	2	2	no	—
318	C₂×C₃×C₄	—	2	2	no	—
319	C₂×C₃×C₄	—	2	2	no	—
320	C₂×C₃×C₄	—	2	2	no	—
321	C₂×C₃×C₄	—	2	2	no	—
322	C₂×C₃×C₄	—	2	1	no	—
323	C₂×C₃×C₄	—	2	1	no	—
324	C₂×C₃×C₄	—	2	2	no	—
325	C₂×C₃×C₄	—	2	2	no	—
326	C₂×C₃×C₄	—	2	2	no	—
327	C₂×C₃×C₄	—	2	2	no	—
328	C₂×C₃×C₄	—	4	4	no	—
329	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
330	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
331	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
332	C₂×C₃×C₄	C₂×C₅×Q₈	1	4	yes	—
333	C₂²×C₅	—	2	2	no	—
334	C₂²×C₅	—	2	4	no	—
335	C₂²×C₅	—	4	1	no	—
336	C₂²×C₅	—	4	2	no	—
337	C₂²×C₅	—	4	1	no	—
338	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
339	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
340	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
341	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
342	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
343	C₄×C₅	—	2	4	no	—
344	C₄×C₅	—	2	4	no	—
345	C₄×C₅	—	2	4	no	—
346	C₄×C₅	—	2	4	no	—
347	C₄×C₅	—	4	1	no	—
348	C₄×C₅	—	4	2	no	—
349	C₄×C₅	—	4	2	no	—
350	C₄×C₅	—	4	1	no	—
351	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
352	C₂×Q₈	—	2	4	no	—
353	C₂×Q₈	—	2	4	no	—
354	C₂×Q₈	—	2	4	no	—
355	C₂×Q₈	—	4	2	no	—
356	C₂×Q₈	—	4	1	no	—
357	C₂²×C₄	—	2	4	no	—
358	C₂²×C₄	—	4	1	no	—
359	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
360	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
361	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
362	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
363	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
364	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
365	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
366	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
367	C₄⋊C₄	—	2	4	no	—
368	C₄⋊C₄	—	2	4	no	—
369	C₄⋊C₄	—	2	4	no	—
370	C₄⋊C₄	—	2	4	no	—
371	C₄⋊C₄	—	2	4	no	—
372	C₄⋊C₄	—	4	1	no	—
373	C₄⋊C₄	C₃×C₅×D₄	1	8	yes	—
374	C₂²⋊C₄	—	2	4	no	—
375	C₂²⋊C₄	—	2	4	no	—
376	C₂²⋊C₄	—	4	1	no	—
377	C₂²⋊C₄	C₃×C₅×Q₈	1	4	yes	complemented
378	C₄²	—	2	4	no	—
379	C₃×C₅	#2677	1	1	yes	characteristic, direct product factor, Hall
380	C₂²×C₃	—	2	2	no	—
381	C₂²×C₃	—	2	4	no	—
382	C₂²×C₃	—	4	2	no	—
383	C₂²×C₃	—	4	1	no	—
384	C₂²×C₃	—	4	1	no	—
385	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
386	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
387	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
388	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
389	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
390	C₃×C₄	—	2	4	no	—
391	C₃×C₄	—	2	4	no	—
392	C₃×C₄	—	2	4	no	—
393	C₃×C₄	—	2	4	no	—
394	C₃×C₄	—	4	2	no	—
395	C₃×C₄	—	4	2	no	—
396	C₃×C₄	—	4	1	no	—
397	C₃×C₄	—	4	1	no	—
398	C₂×C₅	—	4	2	no	—
399	C₂×C₅	C₃×#536	1	2	yes	—
400	C₂×C₅	C₃×#544	1	1	yes	characteristic
401	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
402	C₂×C₅	C₃×D₄×Q₈	1	2	yes	—
403	C₂×C₅	C₃×#563	1	1	yes	characteristic
404	C₂³	—	2	2	no	—
405	C₂³	—	2	1	no	—
406	C₂³	—	2	1	no	—
407	C₂³	—	2	2	no	—
408	C₂³	C₂×C₃×C₅×Q₈	1	2	yes	—
409	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
410	Q₈	—	4	8	no	—
411	Q₈	—	4	4	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	4	4	no	—
431	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
432	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
433	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
434	C₂×C₄	C₂×C₃×C₅×Q₈	1	4	yes	—
435	C₂×C₃	—	4	2	no	—
436	C₂×C₃	C₅×#536	1	2	yes	—
437	C₂×C₃	C₅×#544	1	1	yes	characteristic
438	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
439	C₂×C₃	C₅×D₄×Q₈	1	2	yes	—
440	C₂×C₃	C₅×#563	1	1	yes	characteristic
441	C₅	C₃×#2677	1	1	yes	characteristic, direct product factor, Sylow
442	C₂²	—	2	2	no	—
443	C₂²	—	2	4	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	4	1	no	—
446	C₂²	—	4	1	no	—
447	C₂²	C₂²×C₃×C₅×D₄	1	2	yes	—
448	C₂²	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
449	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
450	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
451	C₂²	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
452	C₄	—	2	4	no	—
453	C₄	—	2	4	no	—
454	C₄	—	2	4	no	—
455	C₄	—	2	4	no	—
456	C₄	—	4	2	no	—
457	C₄	—	4	2	no	—
458	C₄	—	4	1	no	—
459	C₄	—	4	1	no	—
460	C₃	C₅×#2677	1	1	yes	characteristic, direct product factor, Sylow
461	C₂	—	4	2	no	—
462	C₂	C₃×C₅×#536	1	2	yes	—
463	C₂	C₃×C₅×#544	1	1	yes	characteristic
464	C₂	C₃×C₅×D₄²	1	1	yes	characteristic
465	C₂	C₃×C₅×D₄×Q₈	1	2	yes	—
466	C₂	C₃×C₅×#563	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂⁴×C₃×C₅	C₂³
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×C₄⋊Q₈	C₂	semidirect
4. C₃×C₅×#398	C₂	semidirect
5. C₃×C₅×#395	C₂	semidirect
8. C₃×C₅×#387	C₂	semidirect
10. C₅×#2677	C₃	direct (N × H)
34. C₃×#2677	C₅	direct (N × H)
35. C₂×C₅×C₄⋊Q₈	C₂×C₃	semidirect
38. C₅×#398	C₂×C₃	semidirect
39. C₅×#395	C₂×C₃	semidirect
42. C₅×#387	C₂×C₃	semidirect
70. C₃×C₅×C₂²⋊C₄	Q₈	semidirect
72. C₂×C₃×C₄⋊Q₈	C₂×C₅	semidirect
75. C₃×#398	C₂×C₅	semidirect
76. C₃×#395	C₂×C₅	semidirect
79. C₃×#387	C₂×C₅	semidirect
104. #2677	C₃×C₅	direct (N × H)
185. C₅×C₂²⋊C₄	C₃×Q₈	semidirect
187. C₂×C₄⋊Q₈	C₂×C₃×C₅	semidirect
190. #398	C₂×C₃×C₅	semidirect
191. #395	C₂×C₃×C₅	semidirect
194. #387	C₂×C₃×C₅	semidirect
240. C₃×C₂²⋊C₄	C₅×Q₈	semidirect
377. C₂²⋊C₄	C₃×C₅×Q₈	semidirect
379. C₃×C₅	#2677	direct (N × H)
441. C₅	C₃×#2677	direct (N × H)
460. C₃	C₅×#2677	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×C₅×C₂²⋊Q₈	2
C₃×C₅×#399	2
C₃×C₅×#398	2
C₃×C₅×#395	2
C₃×C₅×#393	2
C₃×C₅×#388	2
C₃×C₅×#387	2
C₃×C₅×#385	2
C₅×#2677	3
C₃×#2677	5

Subgroups — C3×C5×#2677 #14275711

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2677 #14275711