Subgroups — C₂×C₃×C₅×#398 #14275425

Order 1920.

1384 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₅×C₄⋊C₄	C₂	1	2	yes	maximal
3	C₂²×C₃×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#398	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×C₅×#95	C₂	1	2	yes	maximal
6	C₂×C₃×C₅×#95	C₂	1	1	yes	maximal, characteristic
7	C₂×C₅×#398	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
9	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
12	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
13	C₂×C₃×C₅×C₄⋊C₄	—	2	4	no	—
14	C₂×C₃×C₅×C₄⋊C₄	—	2	8	no	—
15	C₂×C₃×C₅×C₄⋊C₄	—	2	4	no	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	8	yes	—
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
19	C₃×C₅×#95	C₂²	1	8	yes	—
20	C₃×C₅×#95	C₂²	1	4	yes	—
21	C₂×C₃×#398	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂²×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
23	C₂²×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
24	C₂²×C₅×C₄⋊C₄	C₂×C₃	1	2	yes	—
25	C₅×#398	C₂×C₃	1	8	yes	direct product factor
26	C₂×C₅×#95	C₂×C₃	1	2	yes	—
27	C₂×C₅×#95	C₂×C₃	1	1	yes	characteristic
28	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
29	C₂²×C₃×C₄×C₅	—	2	2	no	—
30	C₂²×C₃×C₄×C₅	—	2	4	no	—
31	C₂²×C₃×C₄×C₅	—	2	2	no	—
32	C₂²×C₃×C₄×C₅	—	2	4	no	—
33	C₂²×C₃×C₄×C₅	—	2	4	no	—
34	C₂²×C₃×C₄×C₅	—	2	4	no	—
35	C₂²×C₃×C₄×C₅	—	2	4	no	—
36	C₂²×C₃×C₄×C₅	—	2	2	no	—
37	C₂²×C₃×C₄×C₅	—	2	4	no	—
38	C₂²×C₃×C₄×C₅	—	2	4	no	—
39	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
40	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
41	C₂²×C₃×C₄×C₅	Q₈	1	8	yes	—
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	2	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
46	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
47	C₃×C₅×C₄⋊C₄	—	2	8	no	—
48	C₃×C₅×C₄⋊C₄	—	2	16	no	—
49	C₃×C₅×C₄⋊C₄	—	2	8	no	—
50	C₂²×C₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
51	C₂²×C₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
52	C₂²×C₃×C₄⋊C₄	C₂×C₅	1	2	yes	—
53	C₃×#398	C₂×C₅	1	8	yes	direct product factor
54	C₂×C₃×#95	C₂×C₅	1	2	yes	—
55	C₂×C₃×#95	C₂×C₅	1	1	yes	characteristic
56	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
57	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
58	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
59	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
60	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
61	C₂×C₅×C₄⋊C₄	—	2	4	no	—
62	C₂×C₅×C₄⋊C₄	—	2	8	no	—
63	C₂×C₅×C₄⋊C₄	—	2	4	no	—
64	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
65	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	8	yes	—
66	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
67	C₅×#95	C₂²×C₃	1	8	yes	—
68	C₅×#95	C₂²×C₃	1	4	yes	—
69	C₂×#398	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
70	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
71	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
72	C₂³×C₃×C₅	C₂×Q₈	1	4	yes	—
73	C₂³×C₃×C₅	#41	1	2	yes	—
74	C₂³×C₃×C₅	#41	1	4	yes	—
75	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
76	C₂×C₃×C₄×C₅	—	2	8	no	—
77	C₂×C₃×C₄×C₅	—	2	16	no	—
78	C₂×C₃×C₄×C₅	—	2	8	no	—
79	C₂×C₃×C₄×C₅	—	2	2	no	—
80	C₂×C₃×C₄×C₅	—	2	4	no	—
81	C₂×C₃×C₄×C₅	—	2	2	no	—
82	C₂×C₃×C₄×C₅	—	2	4	no	—
83	C₂×C₃×C₄×C₅	—	2	4	no	—
84	C₂×C₃×C₄×C₅	—	2	4	no	—
85	C₂×C₃×C₄×C₅	—	2	4	no	—
86	C₂×C₃×C₄×C₅	—	2	2	no	—
87	C₂×C₃×C₄×C₅	—	2	4	no	—
88	C₂×C₃×C₄×C₅	—	2	4	no	—
89	C₂×C₃×C₄×C₅	—	4	8	no	—
90	C₂×C₃×C₄×C₅	—	4	4	no	—
91	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
92	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
93	C₂×C₃×C₄×C₅	C₂×Q₈	1	8	yes	—
94	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
95	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
96	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
97	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
98	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
99	C₂×C₃×C₄⋊C₄	—	2	4	no	—
100	C₂×C₃×C₄⋊C₄	—	2	8	no	—
101	C₂×C₃×C₄⋊C₄	—	2	4	no	—
102	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
103	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
104	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	8	yes	—
105	C₃×#95	C₂²×C₅	1	8	yes	—
106	C₃×#95	C₂²×C₅	1	4	yes	—
107	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
108	C₂²×C₄×C₅	—	2	2	no	—
109	C₂²×C₄×C₅	—	2	4	no	—
110	C₂²×C₄×C₅	—	2	2	no	—
111	C₂²×C₄×C₅	—	2	4	no	—
112	C₂²×C₄×C₅	—	2	4	no	—
113	C₂²×C₄×C₅	—	2	4	no	—
114	C₂²×C₄×C₅	—	2	4	no	—
115	C₂²×C₄×C₅	—	2	2	no	—
116	C₂²×C₄×C₅	—	2	4	no	—
117	C₂²×C₄×C₅	—	2	4	no	—
118	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
119	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
120	C₂²×C₄×C₅	C₃×Q₈	1	8	yes	—
121	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
122	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
123	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
124	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
125	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
126	C₅×C₄⋊C₄	—	2	8	no	—
127	C₅×C₄⋊C₄	—	2	16	no	—
128	C₅×C₄⋊C₄	—	2	8	no	—
129	C₂²×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
130	C₂²×C₄⋊C₄	C₂×C₃×C₅	1	2	yes	—
131	C₂²×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
132	#398	C₂×C₃×C₅	1	8	yes	direct product factor
133	C₂×#95	C₂×C₃×C₅	1	2	yes	—
134	C₂×#95	C₂×C₃×C₅	1	1	yes	characteristic
135	C₂²×C₃×C₅	#121	1	4	yes	—
136	C₂²×C₃×C₅	C₂²⋊Q₈	1	8	yes	—
137	C₂²×C₃×C₅	#123	1	4	yes	—
138	C₂²×C₃×C₅	#125	1	8	yes	—
139	C₂²×C₃×C₅	C₄⋊Q₈	1	4	yes	—
140	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
141	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
142	C₂²×C₃×C₅	C₂²×Q₈	1	2	yes	—
143	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
144	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
145	C₃×C₄×C₅	—	2	4	no	—
146	C₃×C₄×C₅	—	2	8	no	—
147	C₃×C₄×C₅	—	2	4	no	—
148	C₃×C₄×C₅	—	4	4	no	—
149	C₃×C₄×C₅	—	4	2	no	—
150	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
151	C₂²×C₃×C₄	—	2	2	no	—
152	C₂²×C₃×C₄	—	2	4	no	—
153	C₂²×C₃×C₄	—	2	2	no	—
154	C₂²×C₃×C₄	—	2	4	no	—
155	C₂²×C₃×C₄	—	2	4	no	—
156	C₂²×C₃×C₄	—	2	4	no	—
157	C₂²×C₃×C₄	—	2	4	no	—
158	C₂²×C₃×C₄	—	2	2	no	—
159	C₂²×C₃×C₄	—	2	4	no	—
160	C₂²×C₃×C₄	—	2	4	no	—
161	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
162	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
163	C₂²×C₃×C₄	C₅×Q₈	1	8	yes	—
164	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
165	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
166	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
167	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
168	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
169	C₃×C₄⋊C₄	—	2	8	no	—
170	C₃×C₄⋊C₄	—	2	16	no	—
171	C₃×C₄⋊C₄	—	2	8	no	—
172	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
173	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
174	C₂³×C₅	C₂×C₃×Q₈	1	4	yes	—
175	C₂³×C₅	C₃×#41	1	2	yes	—
176	C₂³×C₅	C₃×#41	1	4	yes	—
177	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
178	C₂×C₄×C₅	—	2	8	no	—
179	C₂×C₄×C₅	—	2	16	no	—
180	C₂×C₄×C₅	—	2	8	no	—
181	C₂×C₄×C₅	—	2	2	no	—
182	C₂×C₄×C₅	—	2	4	no	—
183	C₂×C₄×C₅	—	2	2	no	—
184	C₂×C₄×C₅	—	2	4	no	—
185	C₂×C₄×C₅	—	2	4	no	—
186	C₂×C₄×C₅	—	2	4	no	—
187	C₂×C₄×C₅	—	2	4	no	—
188	C₂×C₄×C₅	—	2	2	no	—
189	C₂×C₄×C₅	—	2	4	no	—
190	C₂×C₄×C₅	—	2	4	no	—
191	C₂×C₄×C₅	—	4	8	no	—
192	C₂×C₄×C₅	—	4	4	no	—
193	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
194	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
195	C₂×C₄×C₅	C₂×C₃×Q₈	1	8	yes	—
196	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
197	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
198	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
199	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
200	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
201	C₂×C₄⋊C₄	—	2	4	no	—
202	C₂×C₄⋊C₄	—	2	8	no	—
203	C₂×C₄⋊C₄	—	2	4	no	—
204	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
205	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
206	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	8	yes	—
207	#95	C₂²×C₃×C₅	1	8	yes	—
208	#95	C₂²×C₃×C₅	1	4	yes	—
209	C₂×C₃×C₅	#398	1	8	yes	direct product factor
210	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
211	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	2	yes	—
212	C₂×C₃×C₅	C₂×#123	1	1	yes	characteristic
213	C₂×C₃×C₅	C₂×#125	1	2	yes	—
214	C₂×C₃×C₅	C₂×C₄⋊Q₈	1	1	yes	characteristic
215	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
216	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
217	C₂³×C₃	C₂×C₅×Q₈	1	4	yes	—
218	C₂³×C₃	C₅×#41	1	2	yes	—
219	C₂³×C₃	C₅×#41	1	4	yes	—
220	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
221	C₂×C₃×C₄	—	2	8	no	—
222	C₂×C₃×C₄	—	2	16	no	—
223	C₂×C₃×C₄	—	2	8	no	—
224	C₂×C₃×C₄	—	2	2	no	—
225	C₂×C₃×C₄	—	2	4	no	—
226	C₂×C₃×C₄	—	2	2	no	—
227	C₂×C₃×C₄	—	2	4	no	—
228	C₂×C₃×C₄	—	2	4	no	—
229	C₂×C₃×C₄	—	2	4	no	—
230	C₂×C₃×C₄	—	2	4	no	—
231	C₂×C₃×C₄	—	2	2	no	—
232	C₂×C₃×C₄	—	2	4	no	—
233	C₂×C₃×C₄	—	2	4	no	—
234	C₂×C₃×C₄	—	4	8	no	—
235	C₂×C₃×C₄	—	4	4	no	—
236	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
237	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
238	C₂×C₃×C₄	C₂×C₅×Q₈	1	8	yes	—
239	C₂²×C₅	C₃×#121	1	4	yes	—
240	C₂²×C₅	C₃×C₂²⋊Q₈	1	8	yes	—
241	C₂²×C₅	C₃×#123	1	4	yes	—
242	C₂²×C₅	C₃×#125	1	8	yes	—
243	C₂²×C₅	C₃×C₄⋊Q₈	1	4	yes	—
244	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
245	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
246	C₂²×C₅	C₂²×C₃×Q₈	1	2	yes	—
247	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
248	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
249	C₄×C₅	—	2	4	no	—
250	C₄×C₅	—	2	8	no	—
251	C₄×C₅	—	2	4	no	—
252	C₄×C₅	—	4	4	no	—
253	C₄×C₅	—	4	2	no	—
254	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	2	4	no	—
259	C₂²×C₄	—	2	4	no	—
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	4	no	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	C₃×C₅×D₄	1	4	yes	—
266	C₂²×C₄	C₃×C₅×D₄	1	4	yes	—
267	C₂²×C₄	C₃×C₅×Q₈	1	8	yes	—
268	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
269	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
270	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
271	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
272	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
273	C₄⋊C₄	—	2	8	no	—
274	C₄⋊C₄	—	2	16	no	—
275	C₄⋊C₄	—	2	8	no	—
276	C₃×C₅	C₂×#398	1	1	yes	characteristic, direct product factor, Hall
277	C₂²×C₃	C₅×#121	1	4	yes	—
278	C₂²×C₃	C₅×C₂²⋊Q₈	1	8	yes	—
279	C₂²×C₃	C₅×#123	1	4	yes	—
280	C₂²×C₃	C₅×#125	1	8	yes	—
281	C₂²×C₃	C₅×C₄⋊Q₈	1	4	yes	—
282	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
283	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
284	C₂²×C₃	C₂²×C₅×Q₈	1	2	yes	—
285	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
286	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
287	C₃×C₄	—	2	4	no	—
288	C₃×C₄	—	2	8	no	—
289	C₃×C₄	—	2	4	no	—
290	C₃×C₄	—	4	4	no	—
291	C₃×C₄	—	4	2	no	—
292	C₂×C₅	C₃×#398	1	8	yes	direct product factor
293	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
294	C₂×C₅	C₂×C₃×C₂²⋊Q₈	1	2	yes	—
295	C₂×C₅	C₂×C₃×#123	1	1	yes	characteristic
296	C₂×C₅	C₂×C₃×#125	1	2	yes	—
297	C₂×C₅	C₂×C₃×C₄⋊Q₈	1	1	yes	characteristic
298	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
299	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
300	C₂³	C₂×C₃×C₅×Q₈	1	4	yes	—
301	C₂³	C₃×C₅×#41	1	2	yes	—
302	C₂³	C₃×C₅×#41	1	4	yes	—
303	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	2	8	no	—
307	C₂×C₄	—	2	16	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	2	8	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	4	8	no	—
318	C₂×C₄	—	4	4	no	—
319	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
320	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
321	C₂×C₄	C₂×C₃×C₅×Q₈	1	8	yes	—
322	C₂×C₃	C₅×#398	1	8	yes	direct product factor
323	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
324	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	2	yes	—
325	C₂×C₃	C₂×C₅×#123	1	1	yes	characteristic
326	C₂×C₃	C₂×C₅×#125	1	2	yes	—
327	C₂×C₃	C₂×C₅×C₄⋊Q₈	1	1	yes	characteristic
328	C₅	C₂×C₃×#398	1	1	yes	characteristic, direct product factor, Sylow
329	C₂²	C₃×C₅×#121	1	4	yes	—
330	C₂²	C₃×C₅×C₂²⋊Q₈	1	8	yes	—
331	C₂²	C₃×C₅×#123	1	4	yes	—
332	C₂²	C₃×C₅×#125	1	8	yes	—
333	C₂²	C₃×C₅×C₄⋊Q₈	1	4	yes	—
334	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
335	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
336	C₂²	C₂²×C₃×C₅×Q₈	1	2	yes	—
337	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
338	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
339	C₄	—	2	4	no	—
340	C₄	—	2	8	no	—
341	C₄	—	2	4	no	—
342	C₄	—	4	4	no	—
343	C₄	—	4	2	no	—
344	C₃	C₂×C₅×#398	1	1	yes	characteristic, direct product factor, Sylow
345	C₂	C₃×C₅×#398	1	8	yes	direct product factor
346	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
347	C₂	C₂×C₃×C₅×C₂²⋊Q₈	1	2	yes	—
348	C₂	C₂×C₃×C₅×#123	1	1	yes	characteristic
349	C₂	C₂×C₃×C₅×#125	1	2	yes	—
350	C₂	C₂×C₃×C₅×C₄⋊Q₈	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. C₃×C₅×#398	C₂	direct (N × H)
7. C₂×C₅×#398	C₃	direct (N × H)
21. C₂×C₃×#398	C₅	direct (N × H)
25. C₅×#398	C₂×C₃	direct (N × H)
53. C₃×#398	C₂×C₅	direct (N × H)
69. C₂×#398	C₃×C₅	direct (N × H)
132. #398	C₂×C₃×C₅	direct (N × H)
209. C₂×C₃×C₅	#398	direct (N × H)
276. C₃×C₅	C₂×#398	direct (N × H)
292. C₂×C₅	C₃×#398	direct (N × H)
322. C₂×C₃	C₅×#398	direct (N × H)
328. C₅	C₂×C₃×#398	direct (N × H)
344. C₃	C₂×C₅×#398	direct (N × H)
345. C₂	C₃×C₅×#398	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₃×C₅×C₄⋊C₄	2
C₃×C₅×#398	2
C₂×C₃×C₅×#95	2
C₂×C₅×#398	3
C₂×C₃×#398	5

Subgroups — C2×C3×C5×#398 #14275425

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×#398 #14275425