Subgroups — C₂×C₃×C₅×#563 #14276562

Order 1920.

2048 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#563	C₂	1	16	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₄⋊Q₈	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₅×#126	C₂	1	4	yes	maximal, complemented
4	C₂×C₃×C₅×#125	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×C₅×#124	C₂	1	1	yes	maximal, characteristic
6	C₂×C₃×C₅×#123	C₂	1	2	yes	maximal
7	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	4	yes	maximal, complemented
8	C₂×C₅×#563	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
10	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
12	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
13	C₃×C₅×C₄⋊Q₈	C₂²	1	16	yes	complemented
14	C₃×C₅×#126	C₂²	1	32	yes	complemented
15	C₃×C₅×#125	C₂²	1	16	yes	complemented
16	C₃×C₅×#124	C₂²	1	8	yes	—
17	C₃×C₅×#123	C₂²	1	16	yes	—
18	C₃×C₅×C₂²⋊Q₈	C₂²	1	32	yes	complemented
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
22	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
23	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
24	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
25	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
26	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
29	C₂×C₃×#563	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
30	C₅×#563	C₂×C₃	1	16	yes	direct product factor
31	C₂×C₅×C₄⋊Q₈	C₂×C₃	1	2	yes	complemented
32	C₂×C₅×#126	C₂×C₃	1	4	yes	complemented
33	C₂×C₅×#125	C₂×C₃	1	2	yes	complemented
34	C₂×C₅×#124	C₂×C₃	1	1	yes	characteristic
35	C₂×C₅×#123	C₂×C₃	1	2	yes	—
36	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	4	yes	complemented
37	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
38	C₂×C₃×C₅×Q₈	—	4	4	no	—
39	C₂×C₃×C₅×Q₈	—	4	2	no	—
40	C₂×C₃×C₅×Q₈	C₂³	1	8	yes	—
41	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
42	C₂×C₃×C₅×D₄	—	4	2	no	—
43	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
44	C₂²×C₃×C₄×C₅	—	4	4	no	—
45	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
46	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
47	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
48	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
49	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	8	yes	—
51	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
52	C₃×C₅×C₄⋊C₄	C₂³	1	16	yes	—
53	C₃×C₅×C₄⋊C₄	C₂³	1	16	yes	—
54	C₃×C₅×C₄⋊C₄	C₂³	1	16	yes	—
55	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
56	C₃×C₅×C₂²⋊C₄	C₂³	1	16	yes	—
57	C₃×C₅×C₂²⋊C₄	C₂³	1	16	yes	—
58	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
59	C₃×C₄²×C₅	C₂³	1	4	yes	—
60	C₃×C₄²×C₅	C₂³	1	8	yes	—
61	C₃×#563	C₂×C₅	1	16	yes	direct product factor
62	C₂×C₃×C₄⋊Q₈	C₂×C₅	1	2	yes	complemented
63	C₂×C₃×#126	C₂×C₅	1	4	yes	complemented
64	C₂×C₃×#125	C₂×C₅	1	2	yes	complemented
65	C₂×C₃×#124	C₂×C₅	1	1	yes	characteristic
66	C₂×C₃×#123	C₂×C₅	1	2	yes	—
67	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	4	yes	complemented
68	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
69	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
70	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
71	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
72	C₅×C₄⋊Q₈	C₂²×C₃	1	16	yes	complemented
73	C₅×#126	C₂²×C₃	1	32	yes	complemented
74	C₅×#125	C₂²×C₃	1	16	yes	complemented
75	C₅×#124	C₂²×C₃	1	8	yes	—
76	C₅×#123	C₂²×C₃	1	16	yes	—
77	C₅×C₂²⋊Q₈	C₂²×C₃	1	32	yes	complemented
78	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
79	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
80	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
81	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
82	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
83	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
84	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
85	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
86	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
88	C₂×#563	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
89	C₂³×C₃×C₅	—	2	4	no	—
90	C₂³×C₃×C₅	—	2	8	no	—
91	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
92	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
93	C₃×C₅×Q₈	—	4	8	no	—
94	C₃×C₅×Q₈	—	4	4	no	—
95	C₃×C₅×D₄	—	4	4	no	—
96	C₂×C₃×C₄×C₅	—	2	8	no	—
97	C₂×C₃×C₄×C₅	—	2	2	no	—
98	C₂×C₃×C₄×C₅	—	2	4	no	—
99	C₂×C₃×C₄×C₅	—	2	4	no	—
100	C₂×C₃×C₄×C₅	—	2	8	no	—
101	C₂×C₃×C₄×C₅	—	4	8	no	—
102	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
103	C₂×C₃×C₄×C₅	C₂⁴	1	8	yes	—
104	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
105	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
106	C₂×C₃×C₄×C₅	C₂⁴	1	8	yes	—
107	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
108	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
109	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
110	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
111	C₃×C₄⋊Q₈	C₂²×C₅	1	16	yes	complemented
112	C₃×#126	C₂²×C₅	1	32	yes	complemented
113	C₃×#125	C₂²×C₅	1	16	yes	complemented
114	C₃×#124	C₂²×C₅	1	8	yes	—
115	C₃×#123	C₂²×C₅	1	16	yes	—
116	C₃×C₂²⋊Q₈	C₂²×C₅	1	32	yes	complemented
117	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
118	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
119	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
120	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
121	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
122	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
123	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
124	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
125	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
126	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
127	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
128	C₂×C₅×Q₈	—	4	4	no	—
129	C₂×C₅×Q₈	—	4	2	no	—
130	C₂×C₅×Q₈	C₂³×C₃	1	8	yes	—
131	C₂×C₅×Q₈	C₂³×C₃	1	4	yes	—
132	C₂×C₅×D₄	—	4	2	no	—
133	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
134	C₂²×C₄×C₅	—	4	4	no	—
135	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
136	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
137	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
138	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
139	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
140	C₂²×C₄×C₅	C₂³×C₃	1	8	yes	—
141	C₅×C₄⋊C₄	C₂³×C₃	1	8	yes	—
142	C₅×C₄⋊C₄	C₂³×C₃	1	16	yes	—
143	C₅×C₄⋊C₄	C₂³×C₃	1	16	yes	—
144	C₅×C₄⋊C₄	C₂³×C₃	1	16	yes	—
145	C₅×C₄⋊C₄	C₂³×C₃	1	8	yes	—
146	C₅×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
147	C₅×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
148	C₅×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
149	C₄²×C₅	C₂³×C₃	1	4	yes	—
150	C₄²×C₅	C₂³×C₃	1	8	yes	—
151	#563	C₂×C₃×C₅	1	16	yes	direct product factor
152	C₂×C₄⋊Q₈	C₂×C₃×C₅	1	2	yes	complemented
153	C₂×#126	C₂×C₃×C₅	1	4	yes	complemented
154	C₂×#125	C₂×C₃×C₅	1	2	yes	complemented
155	C₂×#124	C₂×C₃×C₅	1	1	yes	characteristic
156	C₂×#123	C₂×C₃×C₅	1	2	yes	—
157	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	4	yes	complemented
158	C₂²×C₃×C₅	—	2	4	no	—
159	C₂²×C₃×C₅	—	2	8	no	—
160	C₂²×C₃×C₅	—	4	8	no	—
161	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
162	C₂²×C₃×C₅	2₋¹⁺⁴	1	4	yes	—
163	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
164	C₃×C₄×C₅	—	2	8	no	—
165	C₃×C₄×C₅	—	2	2	no	—
166	C₃×C₄×C₅	—	2	4	no	—
167	C₃×C₄×C₅	—	2	4	no	—
168	C₃×C₄×C₅	—	2	8	no	—
169	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
170	C₂×C₃×Q₈	—	4	4	no	—
171	C₂×C₃×Q₈	—	4	2	no	—
172	C₂×C₃×Q₈	C₂³×C₅	1	8	yes	—
173	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
174	C₂×C₃×D₄	—	4	2	no	—
175	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
176	C₂²×C₃×C₄	—	4	4	no	—
177	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
178	C₂²×C₃×C₄	C₂³×C₅	1	4	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	8	yes	—
183	C₃×C₄⋊C₄	C₂³×C₅	1	8	yes	—
184	C₃×C₄⋊C₄	C₂³×C₅	1	16	yes	—
185	C₃×C₄⋊C₄	C₂³×C₅	1	16	yes	—
186	C₃×C₄⋊C₄	C₂³×C₅	1	16	yes	—
187	C₃×C₄⋊C₄	C₂³×C₅	1	8	yes	—
188	C₃×C₂²⋊C₄	C₂³×C₅	1	16	yes	—
189	C₃×C₂²⋊C₄	C₂³×C₅	1	16	yes	—
190	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
191	C₃×C₄²	C₂³×C₅	1	4	yes	—
192	C₃×C₄²	C₂³×C₅	1	8	yes	—
193	C₂³×C₅	—	2	4	no	—
194	C₂³×C₅	—	2	8	no	—
195	C₂³×C₅	C₂⁴×C₃	1	4	yes	—
196	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
197	C₅×Q₈	—	4	8	no	—
198	C₅×Q₈	—	4	4	no	—
199	C₅×D₄	—	4	4	no	—
200	C₂×C₄×C₅	—	2	8	no	—
201	C₂×C₄×C₅	—	2	2	no	—
202	C₂×C₄×C₅	—	2	4	no	—
203	C₂×C₄×C₅	—	2	4	no	—
204	C₂×C₄×C₅	—	2	8	no	—
205	C₂×C₄×C₅	—	4	8	no	—
206	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
207	C₂×C₄×C₅	C₂⁴×C₃	1	8	yes	—
208	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
209	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
210	C₂×C₄×C₅	C₂⁴×C₃	1	8	yes	—
211	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
212	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
213	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
214	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
215	C₄⋊Q₈	C₂²×C₃×C₅	1	16	yes	complemented
216	#126	C₂²×C₃×C₅	1	32	yes	complemented
217	#125	C₂²×C₃×C₅	1	16	yes	complemented
218	#124	C₂²×C₃×C₅	1	8	yes	—
219	#123	C₂²×C₃×C₅	1	16	yes	—
220	C₂²⋊Q₈	C₂²×C₃×C₅	1	32	yes	complemented
221	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
222	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
223	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
224	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
225	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
226	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
227	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
228	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
229	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
230	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
231	C₂×C₃×C₅	—	4	4	no	—
232	C₂×C₃×C₅	#563	1	4	yes	direct product factor
233	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
234	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	2	yes	—
235	C₂³×C₃	—	2	4	no	—
236	C₂³×C₃	—	2	8	no	—
237	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
238	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
239	C₃×Q₈	—	4	8	no	—
240	C₃×Q₈	—	4	4	no	—
241	C₃×D₄	—	4	4	no	—
242	C₂×C₃×C₄	—	2	8	no	—
243	C₂×C₃×C₄	—	2	2	no	—
244	C₂×C₃×C₄	—	2	4	no	—
245	C₂×C₃×C₄	—	2	4	no	—
246	C₂×C₃×C₄	—	2	8	no	—
247	C₂×C₃×C₄	—	4	8	no	—
248	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
249	C₂×C₃×C₄	C₂⁴×C₅	1	8	yes	—
250	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
251	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
252	C₂×C₃×C₄	C₂⁴×C₅	1	8	yes	—
253	C₂²×C₅	—	2	4	no	—
254	C₂²×C₅	—	2	8	no	—
255	C₂²×C₅	—	4	8	no	—
256	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
257	C₂²×C₅	C₃×2₋¹⁺⁴	1	4	yes	—
258	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
259	C₄×C₅	—	2	8	no	—
260	C₄×C₅	—	2	2	no	—
261	C₄×C₅	—	2	4	no	—
262	C₄×C₅	—	2	4	no	—
263	C₄×C₅	—	2	8	no	—
264	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
265	C₂×Q₈	—	4	4	no	—
266	C₂×Q₈	—	4	2	no	—
267	C₂×Q₈	C₂³×C₃×C₅	1	8	yes	—
268	C₂×Q₈	C₂³×C₃×C₅	1	4	yes	—
269	C₂×D₄	—	4	2	no	—
270	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
271	C₂²×C₄	—	4	4	no	—
272	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
273	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
274	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
275	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
276	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
277	C₂²×C₄	C₂³×C₃×C₅	1	8	yes	—
278	C₄⋊C₄	C₂³×C₃×C₅	1	8	yes	—
279	C₄⋊C₄	C₂³×C₃×C₅	1	16	yes	—
280	C₄⋊C₄	C₂³×C₃×C₅	1	16	yes	—
281	C₄⋊C₄	C₂³×C₃×C₅	1	16	yes	—
282	C₄⋊C₄	C₂³×C₃×C₅	1	8	yes	—
283	C₂²⋊C₄	C₂³×C₃×C₅	1	16	yes	—
284	C₂²⋊C₄	C₂³×C₃×C₅	1	16	yes	—
285	C₂²⋊C₄	C₂³×C₃×C₅	1	8	yes	—
286	C₄²	C₂³×C₃×C₅	1	4	yes	—
287	C₄²	C₂³×C₃×C₅	1	8	yes	—
288	C₃×C₅	C₂×#563	1	1	yes	characteristic, direct product factor, Hall
289	C₂²×C₃	—	2	4	no	—
290	C₂²×C₃	—	2	8	no	—
291	C₂²×C₃	—	4	8	no	—
292	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
293	C₂²×C₃	C₅×2₋¹⁺⁴	1	4	yes	—
294	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
295	C₃×C₄	—	2	8	no	—
296	C₃×C₄	—	2	2	no	—
297	C₃×C₄	—	2	4	no	—
298	C₃×C₄	—	2	4	no	—
299	C₃×C₄	—	2	8	no	—
300	C₂×C₅	—	4	4	no	—
301	C₂×C₅	C₃×#563	1	4	yes	direct product factor
302	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
303	C₂×C₅	C₂×C₃×2₋¹⁺⁴	1	2	yes	—
304	C₂³	—	2	4	no	—
305	C₂³	—	2	8	no	—
306	C₂³	C₂⁴×C₃×C₅	1	4	yes	—
307	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
308	Q₈	—	4	8	no	—
309	Q₈	—	4	4	no	—
310	D₄	—	4	4	no	—
311	C₂×C₄	—	2	8	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	2	8	no	—
316	C₂×C₄	—	4	8	no	—
317	C₂×C₄	C₂⁴×C₃×C₅	1	4	yes	—
318	C₂×C₄	C₂⁴×C₃×C₅	1	8	yes	—
319	C₂×C₄	C₂⁴×C₃×C₅	1	4	yes	—
320	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
321	C₂×C₄	C₂⁴×C₃×C₅	1	8	yes	—
322	C₂×C₃	—	4	4	no	—
323	C₂×C₃	C₅×#563	1	4	yes	direct product factor
324	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
325	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	2	yes	—
326	C₅	C₂×C₃×#563	1	1	yes	characteristic, direct product factor, Sylow
327	C₂²	—	2	4	no	—
328	C₂²	—	2	8	no	—
329	C₂²	—	4	8	no	—
330	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
331	C₂²	C₃×C₅×2₋¹⁺⁴	1	4	yes	—
332	C₂²	C₂⁵×C₃×C₅	1	1	yes	characteristic
333	C₄	—	2	8	no	—
334	C₄	—	2	2	no	—
335	C₄	—	2	4	no	—
336	C₄	—	2	4	no	—
337	C₄	—	2	8	no	—
338	C₃	C₂×C₅×#563	1	1	yes	characteristic, direct product factor, Sylow
339	C₂	—	4	4	no	—
340	C₂	C₃×C₅×#563	1	4	yes	direct product factor
341	C₂	C₂×C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
342	C₂	C₂×C₃×C₅×2₋¹⁺⁴	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃×C₅
prime radical	C₂²×C₃×C₅×D₄	C₂²
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
1. C₃×C₅×#563	C₂	direct (N × H)
2. C₂×C₃×C₅×C₄⋊Q₈	C₂	semidirect
3. C₂×C₃×C₅×#126	C₂	semidirect
4. C₂×C₃×C₅×#125	C₂	semidirect
7. C₂×C₃×C₅×C₂²⋊Q₈	C₂	semidirect
8. C₂×C₅×#563	C₃	direct (N × H)
13. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
14. C₃×C₅×#126	C₂²	semidirect
15. C₃×C₅×#125	C₂²	semidirect
18. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
29. C₂×C₃×#563	C₅	direct (N × H)
30. C₅×#563	C₂×C₃	direct (N × H)
31. C₂×C₅×C₄⋊Q₈	C₂×C₃	semidirect
32. C₂×C₅×#126	C₂×C₃	semidirect
33. C₂×C₅×#125	C₂×C₃	semidirect
36. C₂×C₅×C₂²⋊Q₈	C₂×C₃	semidirect
61. C₃×#563	C₂×C₅	direct (N × H)
62. C₂×C₃×C₄⋊Q₈	C₂×C₅	semidirect
63. C₂×C₃×#126	C₂×C₅	semidirect
64. C₂×C₃×#125	C₂×C₅	semidirect
67. C₂×C₃×C₂²⋊Q₈	C₂×C₅	semidirect
72. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
73. C₅×#126	C₂²×C₃	semidirect
74. C₅×#125	C₂²×C₃	semidirect
77. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
88. C₂×#563	C₃×C₅	direct (N × H)
111. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
112. C₃×#126	C₂²×C₅	semidirect
113. C₃×#125	C₂²×C₅	semidirect
116. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
151. #563	C₂×C₃×C₅	direct (N × H)
152. C₂×C₄⋊Q₈	C₂×C₃×C₅	semidirect
153. C₂×#126	C₂×C₃×C₅	semidirect
154. C₂×#125	C₂×C₃×C₅	semidirect
157. C₂×C₂²⋊Q₈	C₂×C₃×C₅	semidirect
215. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
216. #126	C₂²×C₃×C₅	semidirect
217. #125	C₂²×C₃×C₅	semidirect
220. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
232. C₂×C₃×C₅	#563	direct (N × H)
288. C₃×C₅	C₂×#563	direct (N × H)
301. C₂×C₅	C₃×#563	direct (N × H)
323. C₂×C₃	C₅×#563	direct (N × H)
326. C₅	C₂×C₃×#563	direct (N × H)
338. C₃	C₂×C₅×#563	direct (N × H)
340. C₂	C₃×C₅×#563	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×#563	2
C₂×C₃×C₅×C₄⋊Q₈	2
C₂×C₃×C₅×#126	2
C₂×C₃×C₅×#125	2
C₂×C₃×C₅×#124	2
C₂×C₃×C₅×#123	2
C₂×C₃×C₅×C₂²⋊Q₈	2
C₂×C₅×#563	3
C₂×C₃×#563	5

Subgroups — C2×C3×C5×#563 #14276562

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×#563 #14276562