Subgroups — C₃×C₅×#2628 #14275662

Order 1920.

976 conjugacy classes of subgroups.

The subgroup lattice has 428 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, complemented
2	C₂×C₃×C₅×#117	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#400	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#399	C₂	1	2	yes	maximal
5	C₃×C₅×#395	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#393	C₂	1	2	yes	maximal
7	C₃×C₅×#389	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#382	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#380	C₂	1	2	yes	maximal
10	C₅×#2628	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
12	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
13	C₃×C₅×C₄⋊Q₈	—	2	4	no	—
14	C₃×C₅×#117	—	2	4	no	—
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
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×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
24	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
26	C₃×C₅×#95	C₂²	1	4	yes	—
27	C₃×C₅×#95	C₂²	1	2	yes	—
28	C₃×C₅×#95	C₂²	1	2	yes	—
29	C₃×C₅×#95	C₂²	1	4	yes	—
30	C₃×#2628	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₂×C₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂×C₅×#117	C₂×C₃	1	1	yes	characteristic
33	C₅×#400	C₂×C₃	1	2	yes	complemented
34	C₅×#399	C₂×C₃	1	2	yes	—
35	C₅×#395	C₂×C₃	1	2	yes	complemented
36	C₅×#393	C₂×C₃	1	2	yes	—
37	C₅×#389	C₂×C₃	1	2	yes	complemented
38	C₅×#382	C₂×C₃	1	1	yes	characteristic, complemented
39	C₅×#380	C₂×C₃	1	2	yes	—
40	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
41	C₂×C₃×C₅×Q₈	—	2	4	no	—
42	C₂×C₃×C₅×Q₈	—	4	4	no	—
43	C₂²×C₃×C₄×C₅	—	2	2	no	—
44	C₂²×C₃×C₄×C₅	—	2	2	no	—
45	C₂²×C₃×C₄×C₅	Q₈	1	4	yes	complemented
46	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
48	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
49	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₃×C₅×C₄⋊C₄	—	2	2	no	—
55	C₃×C₅×C₄⋊C₄	—	2	2	no	—
56	C₃×C₅×C₄⋊C₄	—	2	4	no	—
57	C₃×C₅×C₄⋊C₄	—	2	4	no	—
58	C₃×C₅×C₄⋊C₄	—	2	4	no	—
59	C₃×C₅×C₄⋊C₄	—	4	4	no	—
60	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
61	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
62	C₃×C₅×C₂²⋊C₄	—	4	4	no	—
63	C₃×C₄²×C₅	—	2	2	no	—
64	C₃×C₄²×C₅	D₄	1	4	yes	—
65	C₂×C₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
66	C₂×C₃×#117	C₂×C₅	1	1	yes	characteristic
67	C₃×#400	C₂×C₅	1	2	yes	complemented
68	C₃×#399	C₂×C₅	1	2	yes	—
69	C₃×#395	C₂×C₅	1	2	yes	complemented
70	C₃×#393	C₂×C₅	1	2	yes	—
71	C₃×#389	C₂×C₅	1	2	yes	complemented
72	C₃×#382	C₂×C₅	1	1	yes	characteristic, complemented
73	C₃×#380	C₂×C₅	1	2	yes	—
74	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
75	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
76	C₅×C₄⋊Q₈	—	2	4	no	—
77	C₅×#117	—	2	4	no	—
78	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
79	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
80	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
81	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
82	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
84	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
85	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
86	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
87	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
89	C₅×#95	C₂²×C₃	1	4	yes	—
90	C₅×#95	C₂²×C₃	1	2	yes	—
91	C₅×#95	C₂²×C₃	1	2	yes	—
92	C₅×#95	C₂²×C₃	1	4	yes	—
93	#2628	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
94	C₂³×C₃×C₅	—	2	1	no	—
95	C₂³×C₃×C₅	—	2	1	no	—
96	C₂³×C₃×C₅	—	2	2	no	—
97	C₂³×C₃×C₅	—	2	2	no	—
98	C₂³×C₃×C₅	C₂×Q₈	1	2	yes	—
99	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
100	C₃×C₅×Q₈	—	4	8	no	—
101	C₂×C₃×C₄×C₅	—	2	1	no	—
102	C₂×C₃×C₄×C₅	—	2	1	no	—
103	C₂×C₃×C₄×C₅	—	2	2	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	—	2	8	no	—
106	C₂×C₃×C₄×C₅	—	2	1	no	—
107	C₂×C₃×C₄×C₅	—	2	1	no	—
108	C₂×C₃×C₄×C₅	—	2	4	no	—
109	C₂×C₃×C₄×C₅	—	2	4	no	—
110	C₂×C₃×C₄×C₅	—	2	4	no	—
111	C₂×C₃×C₄×C₅	—	2	4	no	—
112	C₂×C₃×C₄×C₅	—	2	2	no	—
113	C₂×C₃×C₄×C₅	—	2	4	no	—
114	C₂×C₃×C₄×C₅	—	2	2	no	—
115	C₂×C₃×C₄×C₅	—	2	4	no	—
116	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
117	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
118	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
119	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
120	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
121	C₂×C₃×C₄×C₅	#41	1	2	yes	—
122	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
123	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
124	C₃×C₄⋊Q₈	—	2	4	no	—
125	C₃×#117	—	2	4	no	—
126	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
127	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
128	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
129	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
130	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
131	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
132	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
133	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
134	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
135	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
136	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
137	C₃×#95	C₂²×C₅	1	4	yes	—
138	C₃×#95	C₂²×C₅	1	2	yes	—
139	C₃×#95	C₂²×C₅	1	2	yes	—
140	C₃×#95	C₂²×C₅	1	4	yes	—
141	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
142	C₂×C₅×Q₈	—	2	4	no	—
143	C₂×C₅×Q₈	—	4	4	no	—
144	C₂²×C₄×C₅	—	2	2	no	—
145	C₂²×C₄×C₅	—	2	2	no	—
146	C₂²×C₄×C₅	C₃×Q₈	1	4	yes	complemented
147	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
148	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
149	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
150	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
151	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
152	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
153	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
154	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
155	C₅×C₄⋊C₄	—	2	2	no	—
156	C₅×C₄⋊C₄	—	2	2	no	—
157	C₅×C₄⋊C₄	—	2	4	no	—
158	C₅×C₄⋊C₄	—	2	4	no	—
159	C₅×C₄⋊C₄	—	2	4	no	—
160	C₅×C₄⋊C₄	—	4	4	no	—
161	C₅×C₂²⋊C₄	—	2	2	no	—
162	C₅×C₂²⋊C₄	—	2	2	no	—
163	C₅×C₂²⋊C₄	—	4	4	no	—
164	C₄²×C₅	—	2	2	no	—
165	C₄²×C₅	C₃×D₄	1	4	yes	—
166	C₂×C₄⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
167	C₂×#117	C₂×C₃×C₅	1	1	yes	characteristic
168	#400	C₂×C₃×C₅	1	2	yes	complemented
169	#399	C₂×C₃×C₅	1	2	yes	—
170	#395	C₂×C₃×C₅	1	2	yes	complemented
171	#393	C₂×C₃×C₅	1	2	yes	—
172	#389	C₂×C₃×C₅	1	2	yes	complemented
173	#382	C₂×C₃×C₅	1	1	yes	characteristic, complemented
174	#380	C₂×C₃×C₅	1	2	yes	—
175	C₂²×C₃×C₅	—	2	2	no	—
176	C₂²×C₃×C₅	—	2	4	no	—
177	C₂²×C₃×C₅	—	4	1	no	—
178	C₂²×C₃×C₅	—	4	1	no	—
179	C₂²×C₃×C₅	—	4	2	no	—
180	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
181	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
182	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
183	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
184	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
185	C₃×C₄×C₅	—	2	2	no	—
186	C₃×C₄×C₅	—	2	2	no	—
187	C₃×C₄×C₅	—	2	2	no	—
188	C₃×C₄×C₅	—	4	1	no	—
189	C₃×C₄×C₅	—	4	4	no	—
190	C₃×C₄×C₅	—	4	1	no	—
191	C₃×C₄×C₅	—	4	4	no	—
192	C₃×C₄×C₅	C₂²⋊Q₈	1	4	yes	—
193	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
194	C₂×C₃×Q₈	—	2	4	no	—
195	C₂×C₃×Q₈	—	4	4	no	—
196	C₂²×C₃×C₄	—	2	2	no	—
197	C₂²×C₃×C₄	—	2	2	no	—
198	C₂²×C₃×C₄	C₅×Q₈	1	4	yes	complemented
199	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
200	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
201	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
202	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
203	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
204	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
205	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
206	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
207	C₃×C₄⋊C₄	—	2	2	no	—
208	C₃×C₄⋊C₄	—	2	2	no	—
209	C₃×C₄⋊C₄	—	2	4	no	—
210	C₃×C₄⋊C₄	—	2	4	no	—
211	C₃×C₄⋊C₄	—	2	4	no	—
212	C₃×C₄⋊C₄	—	4	4	no	—
213	C₃×C₂²⋊C₄	—	2	2	no	—
214	C₃×C₂²⋊C₄	—	2	2	no	—
215	C₃×C₂²⋊C₄	—	4	4	no	—
216	C₃×C₄²	—	2	2	no	—
217	C₃×C₄²	C₅×D₄	1	4	yes	—
218	C₂³×C₅	—	2	1	no	—
219	C₂³×C₅	—	2	1	no	—
220	C₂³×C₅	—	2	2	no	—
221	C₂³×C₅	—	2	2	no	—
222	C₂³×C₅	C₂×C₃×Q₈	1	2	yes	—
223	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
224	C₅×Q₈	—	4	8	no	—
225	C₂×C₄×C₅	—	2	1	no	—
226	C₂×C₄×C₅	—	2	1	no	—
227	C₂×C₄×C₅	—	2	2	no	—
228	C₂×C₄×C₅	—	2	2	no	—
229	C₂×C₄×C₅	—	2	8	no	—
230	C₂×C₄×C₅	—	2	1	no	—
231	C₂×C₄×C₅	—	2	1	no	—
232	C₂×C₄×C₅	—	2	4	no	—
233	C₂×C₄×C₅	—	2	4	no	—
234	C₂×C₄×C₅	—	2	4	no	—
235	C₂×C₄×C₅	—	2	4	no	—
236	C₂×C₄×C₅	—	2	2	no	—
237	C₂×C₄×C₅	—	2	4	no	—
238	C₂×C₄×C₅	—	2	2	no	—
239	C₂×C₄×C₅	—	2	4	no	—
240	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
241	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
242	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
243	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
244	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
245	C₂×C₄×C₅	C₃×#41	1	2	yes	—
246	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
247	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
248	C₄⋊Q₈	—	2	4	no	—
249	#117	—	2	4	no	—
250	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
251	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
252	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
253	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
254	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
255	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
256	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
257	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
258	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
259	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
260	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
261	#95	C₂²×C₃×C₅	1	4	yes	—
262	#95	C₂²×C₃×C₅	1	2	yes	—
263	#95	C₂²×C₃×C₅	1	2	yes	—
264	#95	C₂²×C₃×C₅	1	4	yes	—
265	C₂×C₃×C₅	—	4	2	no	—
266	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
267	C₂×C₃×C₅	#535	1	1	yes	characteristic
268	C₂×C₃×C₅	#536	1	1	yes	characteristic
269	C₂×C₃×C₅	#542	1	2	yes	—
270	C₂×C₃×C₅	#544	1	2	yes	—
271	C₂³×C₃	—	2	1	no	—
272	C₂³×C₃	—	2	1	no	—
273	C₂³×C₃	—	2	2	no	—
274	C₂³×C₃	—	2	2	no	—
275	C₂³×C₃	C₂×C₅×Q₈	1	2	yes	—
276	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
277	C₃×Q₈	—	4	8	no	—
278	C₂×C₃×C₄	—	2	1	no	—
279	C₂×C₃×C₄	—	2	1	no	—
280	C₂×C₃×C₄	—	2	2	no	—
281	C₂×C₃×C₄	—	2	2	no	—
282	C₂×C₃×C₄	—	2	8	no	—
283	C₂×C₃×C₄	—	2	1	no	—
284	C₂×C₃×C₄	—	2	1	no	—
285	C₂×C₃×C₄	—	2	4	no	—
286	C₂×C₃×C₄	—	2	4	no	—
287	C₂×C₃×C₄	—	2	4	no	—
288	C₂×C₃×C₄	—	2	4	no	—
289	C₂×C₃×C₄	—	2	2	no	—
290	C₂×C₃×C₄	—	2	4	no	—
291	C₂×C₃×C₄	—	2	2	no	—
292	C₂×C₃×C₄	—	2	4	no	—
293	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
294	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
295	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
296	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
297	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
298	C₂×C₃×C₄	C₅×#41	1	2	yes	—
299	C₂²×C₅	—	2	2	no	—
300	C₂²×C₅	—	2	4	no	—
301	C₂²×C₅	—	4	1	no	—
302	C₂²×C₅	—	4	1	no	—
303	C₂²×C₅	—	4	2	no	—
304	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
305	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
306	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
307	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
308	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
309	C₄×C₅	—	2	2	no	—
310	C₄×C₅	—	2	2	no	—
311	C₄×C₅	—	2	2	no	—
312	C₄×C₅	—	4	1	no	—
313	C₄×C₅	—	4	4	no	—
314	C₄×C₅	—	4	1	no	—
315	C₄×C₅	—	4	4	no	—
316	C₄×C₅	C₃×C₂²⋊Q₈	1	4	yes	—
317	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
318	C₂×Q₈	—	2	4	no	—
319	C₂×Q₈	—	4	4	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	C₃×C₅×Q₈	1	4	yes	complemented
323	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
324	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
325	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
326	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
327	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
328	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
329	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
330	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	—	2	4	no	—
335	C₄⋊C₄	—	2	4	no	—
336	C₄⋊C₄	—	4	4	no	—
337	C₂²⋊C₄	—	2	2	no	—
338	C₂²⋊C₄	—	2	2	no	—
339	C₂²⋊C₄	—	4	4	no	—
340	C₄²	—	2	2	no	—
341	C₄²	C₃×C₅×D₄	1	4	yes	—
342	C₃×C₅	#2628	1	1	yes	characteristic, direct product factor, Hall
343	C₂²×C₃	—	2	2	no	—
344	C₂²×C₃	—	2	4	no	—
345	C₂²×C₃	—	4	1	no	—
346	C₂²×C₃	—	4	1	no	—
347	C₂²×C₃	—	4	2	no	—
348	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
349	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
350	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
351	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
352	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
353	C₃×C₄	—	2	2	no	—
354	C₃×C₄	—	2	2	no	—
355	C₃×C₄	—	2	2	no	—
356	C₃×C₄	—	4	1	no	—
357	C₃×C₄	—	4	4	no	—
358	C₃×C₄	—	4	1	no	—
359	C₃×C₄	—	4	4	no	—
360	C₃×C₄	C₅×C₂²⋊Q₈	1	4	yes	—
361	C₂×C₅	—	4	2	no	—
362	C₂×C₅	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
363	C₂×C₅	C₃×#535	1	1	yes	characteristic
364	C₂×C₅	C₃×#536	1	1	yes	characteristic
365	C₂×C₅	C₃×#542	1	2	yes	—
366	C₂×C₅	C₃×#544	1	2	yes	—
367	C₂³	—	2	1	no	—
368	C₂³	—	2	1	no	—
369	C₂³	—	2	2	no	—
370	C₂³	—	2	2	no	—
371	C₂³	C₂×C₃×C₅×Q₈	1	2	yes	—
372	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
373	Q₈	—	4	8	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	8	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
390	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
391	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
392	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
393	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
394	C₂×C₄	C₃×C₅×#41	1	2	yes	—
395	C₂×C₃	—	4	2	no	—
396	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
397	C₂×C₃	C₅×#535	1	1	yes	characteristic
398	C₂×C₃	C₅×#536	1	1	yes	characteristic
399	C₂×C₃	C₅×#542	1	2	yes	—
400	C₂×C₃	C₅×#544	1	2	yes	—
401	C₅	C₃×#2628	1	1	yes	characteristic, direct product factor, Sylow
402	C₂²	—	2	2	no	—
403	C₂²	—	2	4	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	1	no	—
406	C₂²	—	4	2	no	—
407	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
408	C₂²	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
409	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
410	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
411	C₂²	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
412	C₄	—	2	2	no	—
413	C₄	—	2	2	no	—
414	C₄	—	2	2	no	—
415	C₄	—	4	4	no	—
416	C₄	—	4	1	no	—
417	C₄	—	4	1	no	—
418	C₄	—	4	4	no	—
419	C₄	C₃×C₅×C₂²⋊Q₈	1	4	yes	—
420	C₃	C₅×#2628	1	1	yes	characteristic, direct product factor, Sylow
421	C₂	—	4	2	no	—
422	C₂	C₂×C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
423	C₂	C₃×C₅×#535	1	1	yes	characteristic
424	C₂	C₃×C₅×#536	1	1	yes	characteristic
425	C₂	C₃×C₅×#542	1	2	yes	—
426	C₂	C₃×C₅×#544	1	2	yes	—

	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
3. C₃×C₅×#400	C₂	semidirect
5. C₃×C₅×#395	C₂	semidirect
7. C₃×C₅×#389	C₂	semidirect
8. C₃×C₅×#382	C₂	semidirect
10. C₅×#2628	C₃	direct (N × H)
30. C₃×#2628	C₅	direct (N × H)
31. C₂×C₅×C₄⋊Q₈	C₂×C₃	semidirect
33. C₅×#400	C₂×C₃	semidirect
35. C₅×#395	C₂×C₃	semidirect
37. C₅×#389	C₂×C₃	semidirect
38. C₅×#382	C₂×C₃	semidirect
45. C₂²×C₃×C₄×C₅	Q₈	semidirect
65. C₂×C₃×C₄⋊Q₈	C₂×C₅	semidirect
67. C₃×#400	C₂×C₅	semidirect
69. C₃×#395	C₂×C₅	semidirect
71. C₃×#389	C₂×C₅	semidirect
72. C₃×#382	C₂×C₅	semidirect
93. #2628	C₃×C₅	direct (N × H)
146. C₂²×C₄×C₅	C₃×Q₈	semidirect
166. C₂×C₄⋊Q₈	C₂×C₃×C₅	semidirect
168. #400	C₂×C₃×C₅	semidirect
170. #395	C₂×C₃×C₅	semidirect
172. #389	C₂×C₃×C₅	semidirect
173. #382	C₂×C₃×C₅	semidirect
198. C₂²×C₃×C₄	C₅×Q₈	semidirect
322. C₂²×C₄	C₃×C₅×Q₈	semidirect
342. C₃×C₅	#2628	direct (N × H)
401. C₅	C₃×#2628	direct (N × H)
420. C₃	C₅×#2628	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×#117	2
C₃×C₅×#400	2
C₃×C₅×#399	2
C₃×C₅×#395	2
C₃×C₅×#393	2
C₃×C₅×#389	2
C₃×C₅×#382	2
C₃×C₅×#380	2
C₅×#2628	3
C₃×#2628	5

Subgroups — C3×C5×#2628 #14275662

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2628 #14275662