Subgroups — C₂×C₅×#5625 #14481199

Order 1920.

2008 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×Q₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#944	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#926	C₂	1	1	yes	maximal, characteristic
5	C₂×C₅×#924	C₂	1	1	yes	maximal, characteristic
6	C₅×#5625	C₂	1	16	yes	maximal, direct product factor
7	C₂×C₅×#890	C₂	1	2	yes	maximal, complemented
8	C₂×C₅×#890	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#889	C₂	1	2	yes	maximal, complemented
10	C₂×C₅×#887	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#879	C₂	1	2	yes	maximal
12	C₂×C₅×#879	C₂	1	2	yes	maximal
13	C₂×C₅×#541	—	3	1	no	maximal, Hall
14	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
15	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
16	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
17	C₃×C₅×C₂²⋊Q₈	C₂²	1	8	yes	—
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₂×C₅×#217	C₂²	1	2	yes	—
22	C₂×C₅×#217	C₂²	1	1	yes	characteristic
23	C₂×C₅×#217	C₂²	1	1	yes	characteristic
24	C₅×Q₈×Dic₃	C₂²	1	8	yes	complemented
25	C₅×#944	C₂²	1	8	yes	complemented
26	C₅×#926	C₂²	1	8	yes	—
27	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
28	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
29	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
30	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
31	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
32	C₅×#924	C₂²	1	8	yes	—
33	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
34	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
35	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
36	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
37	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
38	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
39	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
40	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
42	C₅×#890	C₂²	1	16	yes	complemented
43	C₅×#890	C₂²	1	8	yes	complemented
44	C₅×#889	C₂²	1	16	yes	complemented
45	C₅×#887	C₂²	1	8	yes	complemented
46	C₅×#879	C₂²	1	16	yes	—
47	C₅×#879	C₂²	1	16	yes	—
48	C₂×#5625	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
49	C₅×#541	—	3	16	no	—
50	C₂×C₅×C₄⋊Q₈	—	3	1	no	—
51	C₂×C₅×#126	—	3	2	no	—
52	C₂×C₅×#126	—	3	2	no	—
53	C₂×C₅×#125	—	3	2	no	—
54	C₂×C₅×#125	—	3	1	no	—
55	C₂×C₅×#125	—	3	2	no	—
56	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
57	C₂×C₅×C₂²⋊Q₈	D₃	1	1	yes	characteristic
58	C₂×C₄×C₅×Q₈	—	3	1	no	—
59	C₂×C₄×C₅×Q₈	—	3	1	no	—
60	C₂×C₅×#117	—	3	1	no	—
61	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
62	C₂×C₃×C₅×Q₈	—	2	4	no	—
63	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
64	C₂²×C₃×C₄×C₅	—	2	4	no	—
65	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
66	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
67	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
68	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
69	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
70	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
71	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
72	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
73	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
74	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
75	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
76	C₂×C₅×Dic₆	—	2	4	no	—
77	C₂×C₅×Dic₆	C₂³	1	4	yes	—
78	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
79	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
80	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
81	C₅×#217	C₂³	1	8	yes	—
82	C₅×#217	C₂³	1	4	yes	—
83	C₅×#217	C₂³	1	4	yes	—
84	C₅×C₄⋊Dic₃	C₂³	1	8	yes	—
85	C₅×C₄⋊Dic₃	C₂³	1	8	yes	—
86	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
87	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
88	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
89	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
90	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
91	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
92	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
93	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
94	C₄×C₅×Dic₃	C₂³	1	8	yes	—
95	C₄×C₅×Dic₃	C₂³	1	8	yes	—
96	C₄×C₅×Dic₃	C₂³	1	4	yes	—
97	C₄×C₅×Dic₃	C₂³	1	4	yes	—
98	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic
99	C₂×Q₈×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
100	C₂×#944	C₂×C₅	1	1	yes	characteristic, complemented
101	C₂×#926	C₂×C₅	1	1	yes	characteristic
102	C₂×#924	C₂×C₅	1	1	yes	characteristic
103	#5625	C₂×C₅	1	16	yes	direct product factor
104	C₂×#890	C₂×C₅	1	2	yes	complemented
105	C₂×#890	C₂×C₅	1	1	yes	characteristic, complemented
106	C₂×#889	C₂×C₅	1	2	yes	complemented
107	C₂×#887	C₂×C₅	1	1	yes	characteristic, complemented
108	C₂×#879	C₂×C₅	1	2	yes	—
109	C₂×#879	C₂×C₅	1	2	yes	—
110	C₂²×C₅×Q₈	—	3	1	no	—
111	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
112	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
113	C₅×C₄⋊Q₈	—	3	8	no	—
114	C₅×#126	—	3	16	no	—
115	C₅×#126	—	3	16	no	—
116	C₅×#125	—	3	16	no	—
117	C₅×#125	—	3	8	no	—
118	C₅×#125	—	3	16	no	—
119	C₅×C₂²⋊Q₈	—	3	8	no	—
120	C₅×C₂²⋊Q₈	C₂×D₃	1	8	yes	—
121	C₄×C₅×Q₈	—	3	8	no	—
122	C₄×C₅×Q₈	—	3	8	no	—
123	C₅×#117	—	3	8	no	—
124	C₂×C₅×C₄⋊C₄	—	3	2	no	—
125	C₂×C₅×C₄⋊C₄	—	3	2	no	—
126	C₂×C₅×C₄⋊C₄	—	3	2	no	—
127	C₂×C₅×C₄⋊C₄	—	3	2	no	—
128	C₂×C₅×C₄⋊C₄	—	3	2	no	—
129	C₂×C₅×C₄⋊C₄	—	3	1	no	—
130	C₂×C₅×C₄⋊C₄	—	3	1	no	—
131	C₂×C₅×C₄⋊C₄	—	3	1	no	—
132	C₂×C₅×C₄⋊C₄	—	3	2	no	—
133	C₂×C₅×C₄⋊C₄	—	3	2	no	—
134	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
135	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
136	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
137	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
138	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
139	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
140	C₂×C₄²×C₅	—	3	1	no	—
141	C₂×C₄²×C₅	—	3	1	no	—
142	C₂×C₄²×C₅	—	3	2	no	—
143	C₂×C₄²×C₅	—	3	2	no	—
144	C₂×#541	—	3	1	no	Sylow
145	C₂³×C₃×C₅	—	2	2	no	—
146	C₂³×C₃×C₅	—	2	2	no	—
147	C₂³×C₃×C₅	—	2	2	no	—
148	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
149	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
150	C₃×C₅×Q₈	—	2	8	no	—
151	C₂×C₃×C₄×C₅	—	2	2	no	—
152	C₂×C₃×C₄×C₅	—	2	4	no	—
153	C₂×C₃×C₄×C₅	—	2	4	no	—
154	C₂×C₃×C₄×C₅	—	2	8	no	—
155	C₂×C₃×C₄×C₅	#41	1	4	yes	—
156	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
157	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
158	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
159	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
160	C₂×C₅×Dic₃	—	2	4	no	—
161	C₂×C₅×Dic₃	—	2	2	no	—
162	C₂×C₅×Dic₃	—	2	4	no	—
163	C₂×C₅×Dic₃	—	2	2	no	—
164	C₂×C₅×Dic₃	—	2	2	no	—
165	C₂×C₅×Dic₃	—	2	2	no	—
166	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
167	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
168	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
169	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
170	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
171	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
172	C₅×Dic₆	—	2	8	no	—
173	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
174	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
175	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
176	C₃×C₂²⋊Q₈	C₂²×C₅	1	8	yes	—
177	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
178	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
179	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
180	C₂×#217	C₂²×C₅	1	2	yes	—
181	C₂×#217	C₂²×C₅	1	1	yes	characteristic
182	C₂×#217	C₂²×C₅	1	1	yes	characteristic
183	Q₈×Dic₃	C₂²×C₅	1	8	yes	complemented
184	#944	C₂²×C₅	1	8	yes	complemented
185	#926	C₂²×C₅	1	8	yes	—
186	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
187	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
188	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
189	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
190	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
191	#924	C₂²×C₅	1	8	yes	—
192	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
193	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
194	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
195	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
196	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
197	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
198	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
199	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
200	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
201	#890	C₂²×C₅	1	16	yes	complemented
202	#890	C₂²×C₅	1	8	yes	complemented
203	#889	C₂²×C₅	1	16	yes	complemented
204	#887	C₂²×C₅	1	8	yes	complemented
205	#879	C₂²×C₅	1	16	yes	—
206	#879	C₂²×C₅	1	16	yes	—
207	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
208	C₂×C₅×Q₈	—	2	4	no	—
209	C₂×C₅×Q₈	—	3	4	no	—
210	C₂×C₅×Q₈	—	6	4	no	—
211	C₂×C₅×Q₈	C₂²×D₃	1	4	yes	—
212	C₂²×C₄×C₅	—	2	4	no	—
213	C₂²×C₄×C₅	—	3	1	no	—
214	C₂²×C₄×C₅	—	3	1	no	—
215	C₂²×C₄×C₅	—	3	1	no	—
216	C₂²×C₄×C₅	—	3	2	no	—
217	C₂²×C₄×C₅	—	3	1	no	—
218	C₂²×C₄×C₅	—	3	2	no	—
219	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
220	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
221	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
222	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
223	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
224	C₅×C₄⋊C₄	—	3	4	no	—
225	C₅×C₄⋊C₄	—	3	4	no	—
226	C₅×C₄⋊C₄	—	3	4	no	—
227	C₅×C₄⋊C₄	—	3	8	no	—
228	C₅×C₄⋊C₄	—	3	8	no	—
229	C₅×C₄⋊C₄	—	3	8	no	—
230	C₅×C₄⋊C₄	—	3	8	no	—
231	C₅×C₄⋊C₄	—	3	8	no	—
232	C₅×C₄⋊C₄	—	3	8	no	—
233	C₅×C₄⋊C₄	—	3	8	no	—
234	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
235	C₅×C₄⋊C₄	C₂²×D₃	1	8	yes	—
236	C₅×C₂²⋊C₄	—	3	4	no	—
237	C₅×C₂²⋊C₄	—	3	4	no	—
238	C₅×C₂²⋊C₄	—	3	8	no	—
239	C₅×C₂²⋊C₄	C₂²×D₃	1	8	yes	—
240	C₄²×C₅	—	3	4	no	—
241	C₄²×C₅	—	3	4	no	—
242	C₄²×C₅	—	3	8	no	—
243	C₄²×C₅	—	3	8	no	—
244	#541	—	3	16	no	—
245	C₂×C₄⋊Q₈	—	3	1	no	—
246	C₂×#126	—	3	2	no	—
247	C₂×#126	—	3	2	no	—
248	C₂×#125	—	3	2	no	—
249	C₂×#125	—	3	1	no	—
250	C₂×#125	—	3	2	no	—
251	C₂×C₂²⋊Q₈	—	3	1	no	—
252	C₂×C₂²⋊Q₈	C₅×D₃	1	1	yes	characteristic
253	C₂×C₄×Q₈	—	3	1	no	—
254	C₂×C₄×Q₈	—	3	1	no	—
255	C₂×#117	—	3	1	no	—
256	C₂²×C₃×C₅	—	2	2	no	—
257	C₂²×C₃×C₅	—	2	2	no	—
258	C₂²×C₃×C₅	—	2	2	no	—
259	C₂²×C₃×C₅	—	4	4	no	—
260	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
261	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
262	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
263	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
264	C₃×C₄×C₅	—	2	2	no	—
265	C₃×C₄×C₅	—	2	4	no	—
266	C₃×C₄×C₅	—	2	4	no	—
267	C₃×C₄×C₅	C₂×#41	1	4	yes	—
268	C₅×Dic₃	—	2	4	no	—
269	C₅×Dic₃	—	2	2	no	—
270	C₅×Dic₃	—	2	4	no	—
271	C₅×Dic₃	—	2	2	no	—
272	C₅×Dic₃	—	2	2	no	—
273	C₅×Dic₃	—	2	2	no	—
274	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
275	C₂×C₃×Q₈	—	2	4	no	—
276	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
277	C₂²×C₃×C₄	—	2	4	no	—
278	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
279	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
280	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
281	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
282	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
283	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
284	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
285	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
286	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
287	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
288	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
289	C₂×Dic₆	—	2	4	no	—
290	C₂×Dic₆	C₂³×C₅	1	4	yes	—
291	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
292	C₃×C₄⋊C₄	C₂³×C₅	1	8	yes	—
293	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
294	#217	C₂³×C₅	1	8	yes	—
295	#217	C₂³×C₅	1	4	yes	—
296	#217	C₂³×C₅	1	4	yes	—
297	C₄⋊Dic₃	C₂³×C₅	1	8	yes	—
298	C₄⋊Dic₃	C₂³×C₅	1	8	yes	—
299	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
300	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
301	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
302	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
303	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
304	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
305	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
306	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
307	C₄×Dic₃	C₂³×C₅	1	8	yes	—
308	C₄×Dic₃	C₂³×C₅	1	8	yes	—
309	C₄×Dic₃	C₂³×C₅	1	4	yes	—
310	C₄×Dic₃	C₂³×C₅	1	4	yes	—
311	C₂³×C₅	—	2	2	no	—
312	C₂³×C₅	—	2	2	no	—
313	C₂³×C₅	—	2	2	no	—
314	C₂³×C₅	C₂³×D₃	1	2	yes	—
315	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
316	C₅×Q₈	—	2	8	no	—
317	C₅×Q₈	—	6	8	no	—
318	C₂×C₄×C₅	—	2	2	no	—
319	C₂×C₄×C₅	—	2	4	no	—
320	C₂×C₄×C₅	—	2	4	no	—
321	C₂×C₄×C₅	—	2	8	no	—
322	C₂×C₄×C₅	—	3	2	no	—
323	C₂×C₄×C₅	—	3	2	no	—
324	C₂×C₄×C₅	—	3	2	no	—
325	C₂×C₄×C₅	—	3	4	no	—
326	C₂×C₄×C₅	—	3	2	no	—
327	C₂×C₄×C₅	—	3	4	no	—
328	C₂×C₄×C₅	—	6	4	no	—
329	C₂×C₄×C₅	—	6	2	no	—
330	C₂×C₄×C₅	—	6	2	no	—
331	C₂×C₄×C₅	—	6	4	no	—
332	C₂×C₄×C₅	—	6	2	no	—
333	C₂×C₄×C₅	—	6	2	no	—
334	C₂×C₄×C₅	#237	1	4	yes	—
335	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
336	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
337	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
338	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
339	C₂²×Q₈	—	3	1	no	—
340	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
341	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
342	C₄⋊Q₈	—	3	8	no	—
343	#126	—	3	16	no	—
344	#126	—	3	16	no	—
345	#125	—	3	16	no	—
346	#125	—	3	8	no	—
347	#125	—	3	16	no	—
348	C₂²⋊Q₈	—	3	8	no	—
349	C₂²⋊Q₈	C₂×C₅×D₃	1	8	yes	—
350	C₄×Q₈	—	3	8	no	—
351	C₄×Q₈	—	3	8	no	—
352	#117	—	3	8	no	—
353	C₂×C₄⋊C₄	—	3	1	no	—
354	C₂×C₄⋊C₄	—	3	1	no	—
355	C₂×C₄⋊C₄	—	3	1	no	—
356	C₂×C₄⋊C₄	—	3	2	no	—
357	C₂×C₄⋊C₄	—	3	2	no	—
358	C₂×C₄⋊C₄	—	3	2	no	—
359	C₂×C₄⋊C₄	—	3	2	no	—
360	C₂×C₄⋊C₄	—	3	2	no	—
361	C₂×C₄⋊C₄	—	3	2	no	—
362	C₂×C₄⋊C₄	—	3	2	no	—
363	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
365	C₂×C₂²⋊C₄	—	3	1	no	—
366	C₂×C₂²⋊C₄	—	3	1	no	—
367	C₂×C₂²⋊C₄	—	3	2	no	—
368	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
369	C₂×C₄²	—	3	1	no	—
370	C₂×C₄²	—	3	1	no	—
371	C₂×C₄²	—	3	2	no	—
372	C₂×C₄²	—	3	2	no	—
373	C₂×C₃×C₅	—	4	2	no	—
374	C₂×C₃×C₅	#541	1	4	yes	complemented
375	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
376	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
377	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
378	C₂³×C₃	—	2	2	no	—
379	C₂³×C₃	—	2	2	no	—
380	C₂³×C₃	—	2	2	no	—
381	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
382	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
383	C₃×Q₈	—	2	8	no	—
384	C₂×C₃×C₄	—	2	2	no	—
385	C₂×C₃×C₄	—	2	4	no	—
386	C₂×C₃×C₄	—	2	4	no	—
387	C₂×C₃×C₄	—	2	8	no	—
388	C₂×C₃×C₄	C₅×#41	1	4	yes	—
389	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
390	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
391	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
392	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
393	C₂×Dic₃	—	2	4	no	—
394	C₂×Dic₃	—	2	2	no	—
395	C₂×Dic₃	—	2	4	no	—
396	C₂×Dic₃	—	2	2	no	—
397	C₂×Dic₃	—	2	2	no	—
398	C₂×Dic₃	—	2	2	no	—
399	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
400	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
401	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
402	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
403	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
404	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
405	Dic₆	—	2	8	no	—
406	C₂²×C₅	—	2	2	no	—
407	C₂²×C₅	—	2	2	no	—
408	C₂²×C₅	—	2	2	no	—
409	C₂²×C₅	—	4	4	no	—
410	C₂²×C₅	C₂×#237	1	2	yes	—
411	C₂²×C₅	#1007	1	2	yes	—
412	C₂²×C₅	#1010	1	2	yes	—
413	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
414	C₄×C₅	—	2	2	no	—
415	C₄×C₅	—	2	4	no	—
416	C₄×C₅	—	2	4	no	—
417	C₄×C₅	—	6	4	no	—
418	C₄×C₅	—	6	2	no	—
419	C₄×C₅	—	6	2	no	—
420	C₄×C₅	—	6	4	no	—
421	C₄×C₅	—	6	2	no	—
422	C₄×C₅	—	6	2	no	—
423	C₄×C₅	C₂×#237	1	4	yes	—
424	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
425	C₂×Q₈	—	2	4	no	—
426	C₂×Q₈	—	3	4	no	—
427	C₂×Q₈	—	6	4	no	—
428	C₂×Q₈	C₂²×C₅×D₃	1	4	yes	—
429	C₂²×C₄	—	2	4	no	—
430	C₂²×C₄	—	3	1	no	—
431	C₂²×C₄	—	3	1	no	—
432	C₂²×C₄	—	3	1	no	—
433	C₂²×C₄	—	3	2	no	—
434	C₂²×C₄	—	3	1	no	—
435	C₂²×C₄	—	3	2	no	—
436	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
437	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
438	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
439	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
440	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
441	C₄⋊C₄	—	3	4	no	—
442	C₄⋊C₄	—	3	4	no	—
443	C₄⋊C₄	—	3	4	no	—
444	C₄⋊C₄	—	3	8	no	—
445	C₄⋊C₄	—	3	8	no	—
446	C₄⋊C₄	—	3	8	no	—
447	C₄⋊C₄	—	3	8	no	—
448	C₄⋊C₄	—	3	8	no	—
449	C₄⋊C₄	—	3	8	no	—
450	C₄⋊C₄	—	3	8	no	—
451	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
452	C₄⋊C₄	C₂²×C₅×D₃	1	8	yes	—
453	C₂²⋊C₄	—	3	4	no	—
454	C₂²⋊C₄	—	3	4	no	—
455	C₂²⋊C₄	—	3	8	no	—
456	C₂²⋊C₄	C₂²×C₅×D₃	1	8	yes	—
457	C₄²	—	3	4	no	—
458	C₄²	—	3	4	no	—
459	C₄²	—	3	8	no	—
460	C₄²	—	3	8	no	—
461	C₃×C₅	C₂×#541	1	1	yes	characteristic, complemented, Hall
462	C₂²×C₃	—	2	2	no	—
463	C₂²×C₃	—	2	2	no	—
464	C₂²×C₃	—	2	2	no	—
465	C₂²×C₃	—	4	4	no	—
466	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
467	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
468	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
469	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
470	C₃×C₄	—	2	2	no	—
471	C₃×C₄	—	2	4	no	—
472	C₃×C₄	—	2	4	no	—
473	C₃×C₄	C₂×C₅×#41	1	4	yes	—
474	Dic₃	—	2	4	no	—
475	Dic₃	—	2	2	no	—
476	Dic₃	—	2	4	no	—
477	Dic₃	—	2	2	no	—
478	Dic₃	—	2	2	no	—
479	Dic₃	—	2	2	no	—
480	C₂×C₅	—	4	2	no	—
481	C₂×C₅	#5625	1	4	yes	direct product factor
482	C₂×C₅	C₂²×#237	1	1	yes	characteristic
483	C₂×C₅	C₂×#1007	1	1	yes	characteristic
484	C₂×C₅	C₂×#1010	1	1	yes	characteristic
485	C₂³	—	2	2	no	—
486	C₂³	—	2	2	no	—
487	C₂³	—	2	2	no	—
488	C₂³	C₂³×C₅×D₃	1	2	yes	—
489	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
490	Q₈	—	2	8	no	—
491	Q₈	—	6	8	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	8	no	—
496	C₂×C₄	—	3	2	no	—
497	C₂×C₄	—	3	2	no	—
498	C₂×C₄	—	3	2	no	—
499	C₂×C₄	—	3	4	no	—
500	C₂×C₄	—	3	2	no	—
501	C₂×C₄	—	3	4	no	—
502	C₂×C₄	—	6	4	no	—
503	C₂×C₄	—	6	2	no	—
504	C₂×C₄	—	6	2	no	—
505	C₂×C₄	—	6	4	no	—
506	C₂×C₄	—	6	2	no	—
507	C₂×C₄	—	6	2	no	—
508	C₂×C₄	C₅×#237	1	4	yes	—
509	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
510	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
511	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
512	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
513	C₂×C₃	—	4	2	no	—
514	C₂×C₃	C₅×#541	1	4	yes	complemented
515	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
516	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
517	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
518	C₅	C₂×#5625	1	1	yes	characteristic, direct product factor, Sylow
519	C₂²	—	2	2	no	—
520	C₂²	—	2	2	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	4	4	no	—
523	C₂²	C₂×C₅×#237	1	2	yes	—
524	C₂²	C₅×#1007	1	2	yes	—
525	C₂²	C₅×#1010	1	2	yes	—
526	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
527	C₄	—	2	2	no	—
528	C₄	—	2	4	no	—
529	C₄	—	2	4	no	—
530	C₄	—	6	4	no	—
531	C₄	—	6	2	no	—
532	C₄	—	6	2	no	—
533	C₄	—	6	4	no	—
534	C₄	—	6	2	no	—
535	C₄	—	6	2	no	—
536	C₄	C₂×C₅×#237	1	4	yes	—
537	C₃	C₂×C₅×#541	1	1	yes	characteristic, complemented, Sylow
538	C₂	—	4	2	no	—
539	C₂	C₅×#5625	1	4	yes	direct product factor
540	C₂	C₂²×C₅×#237	1	1	yes	characteristic
541	C₂	C₂×C₅×#1007	1	1	yes	characteristic
542	C₂	C₂×C₅×#1010	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂×C₃×C₅×C₂²⋊Q₈	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂⁴×C₃×C₅	C₂³
hypercenter	C₂×C₅×C₂²⋊Q₈	D₃
hypocenter	C₃	C₂×C₅×#541
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×Q₈×Dic₃	C₂	semidirect
3. C₂×C₅×#944	C₂	semidirect
6. C₅×#5625	C₂	direct (N × H)
7. C₂×C₅×#890	C₂	semidirect
8. C₂×C₅×#890	C₂	semidirect
9. C₂×C₅×#889	C₂	semidirect
10. C₂×C₅×#887	C₂	semidirect
24. C₅×Q₈×Dic₃	C₂²	semidirect
25. C₅×#944	C₂²	semidirect
42. C₅×#890	C₂²	semidirect
43. C₅×#890	C₂²	semidirect
44. C₅×#889	C₂²	semidirect
45. C₅×#887	C₂²	semidirect
48. C₂×#5625	C₅	direct (N × H)
99. C₂×Q₈×Dic₃	C₂×C₅	semidirect
100. C₂×#944	C₂×C₅	semidirect
103. #5625	C₂×C₅	direct (N × H)
104. C₂×#890	C₂×C₅	semidirect
105. C₂×#890	C₂×C₅	semidirect
106. C₂×#889	C₂×C₅	semidirect
107. C₂×#887	C₂×C₅	semidirect
183. Q₈×Dic₃	C₂²×C₅	semidirect
184. #944	C₂²×C₅	semidirect
201. #890	C₂²×C₅	semidirect
202. #890	C₂²×C₅	semidirect
203. #889	C₂²×C₅	semidirect
204. #887	C₂²×C₅	semidirect
374. C₂×C₃×C₅	#541	semidirect
461. C₃×C₅	C₂×#541	semidirect
481. C₂×C₅	#5625	direct (N × H)
514. C₂×C₃	C₅×#541	semidirect
518. C₅	C₂×#5625	direct (N × H)
537. C₃	C₂×C₅×#541	semidirect
539. C₂	C₅×#5625	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×C₂²⋊Q₈	2
C₂×C₅×Q₈×Dic₃	2
C₂×C₅×#944	2
C₂×C₅×#926	2
C₂×C₅×#924	2
C₅×#5625	2
C₂×C₅×#890	2
C₂×C₅×#889	2
C₂×C₅×#887	2
C₂×C₅×#879	2
C₂×C₅×#541	3
C₂×#5625	5

Subgroups — C2×C5×#5625 #14481199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5625 #14481199