Subgroups — C₂×C₅×#5671 #14483991

Order 1920.

2224 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#124	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×#936	C₂	1	1	yes	maximal, characteristic
5	C₂×C₅×D₄×Dic₃	C₂	1	1	yes	maximal, characteristic
6	C₅×#5671	C₂	1	16	yes	maximal, direct product factor
7	C₂×C₅×#879	C₂	1	2	yes	maximal, complemented
8	C₂×C₅×#879	C₂	1	2	yes	maximal, complemented
9	C₂×C₅×#878	C₂	1	2	yes	maximal, complemented
10	C₂×C₅×#877	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×C₅×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×C₅×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅×#556	—	3	1	no	maximal, Hall
14	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₂³×C₅×Dic₃	C₂²	1	2	yes	—
17	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
18	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
19	C₃×C₅×#124	C₂²	1	8	yes	—
20	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
23	C₂×C₅×#217	C₂²	1	2	yes	—
24	C₂×C₅×#217	C₂²	1	2	yes	—
25	C₂×C₅×#217	C₂²	1	2	yes	—
26	C₅×Q₈×Dic₃	C₂²	1	8	yes	complemented
27	C₅×#944	C₂²	1	8	yes	complemented
28	C₅×#936	C₂²	1	8	yes	—
29	C₅×D₄×Dic₃	C₂²	1	8	yes	—
30	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
31	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
32	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
33	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
35	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
40	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
42	C₅×#879	C₂²	1	16	yes	complemented
43	C₅×#879	C₂²	1	16	yes	complemented
44	C₅×#878	C₂²	1	16	yes	complemented
45	C₅×#877	C₂²	1	16	yes	complemented
46	C₄×C₅×Dic₆	C₂²	1	8	yes	complemented
47	C₄×C₅×Dic₆	C₂²	1	8	yes	complemented
48	C₂×#5671	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
49	C₅×#556	—	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×#124	—	3	1	no	—
54	C₂×C₅×#124	D₃	1	1	yes	characteristic
55	C₂×C₅×C₂²⋊Q₈	—	3	2	no	—
56	C₂×C₄×C₅×Q₈	—	3	1	no	—
57	C₂×C₄×C₅×Q₈	—	3	1	no	—
58	C₂×C₄×C₅×Q₈	—	3	1	no	—
59	C₂×C₄×C₅×D₄	—	3	1	no	—
60	C₂×C₅×#117	—	3	2	no	—
61	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
62	C₂×C₃×C₅×Q₈	—	2	4	no	—
63	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
64	C₂×C₃×C₅×D₄	—	2	4	no	—
65	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
66	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
67	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
68	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
69	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
70	C₂²×C₅×Dic₃	—	2	8	no	—
71	C₂²×C₅×Dic₃	C₂³	1	8	yes	—
72	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
73	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
74	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
75	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
76	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
77	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
78	C₂×C₅×Dic₆	—	2	4	no	—
79	C₂×C₅×Dic₆	—	2	4	no	—
80	C₂×C₅×Dic₆	C₂³	1	4	yes	—
81	C₂×C₅×Dic₆	C₂³	1	4	yes	—
82	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
83	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
84	C₃×C₄²×C₅	C₂³	1	4	yes	—
85	C₅×#217	C₂³	1	8	yes	—
86	C₅×#217	C₂³	1	8	yes	—
87	C₅×#217	C₂³	1	8	yes	—
88	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
89	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
90	C₅×C₄⋊Dic₃	C₂³	1	8	yes	—
91	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
92	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
93	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
94	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
95	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
96	C₄×C₅×Dic₃	C₂³	1	8	yes	—
97	C₄×C₅×Dic₃	C₂³	1	4	yes	—
98	C₄×C₅×Dic₃	C₂³	1	4	yes	—
99	C₄×C₅×Dic₃	C₂³	1	8	yes	—
100	C₂×C₃×#124	C₂×C₅	1	1	yes	characteristic
101	C₂×Q₈×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
102	C₂×#944	C₂×C₅	1	1	yes	characteristic, complemented
103	C₂×#936	C₂×C₅	1	1	yes	characteristic
104	C₂×D₄×Dic₃	C₂×C₅	1	1	yes	characteristic
105	#5671	C₂×C₅	1	16	yes	direct product factor
106	C₂×#879	C₂×C₅	1	2	yes	complemented
107	C₂×#879	C₂×C₅	1	2	yes	complemented
108	C₂×#878	C₂×C₅	1	2	yes	complemented
109	C₂×#877	C₂×C₅	1	2	yes	complemented
110	C₂×C₄×Dic₆	C₂×C₅	1	1	yes	characteristic, complemented
111	C₂×C₄×Dic₆	C₂×C₅	1	1	yes	characteristic, complemented
112	C₂²×C₅×Q₈	—	3	1	no	—
113	C₂²×C₅×Q₈	—	3	1	no	—
114	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
115	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
116	C₂³×C₄×C₅	—	3	2	no	—
117	C₅×C₄⋊Q₈	—	3	8	no	—
118	C₅×#126	—	3	16	no	—
119	C₅×#126	—	3	16	no	—
120	C₅×#124	—	3	8	no	—
121	C₅×#124	C₂×D₃	1	8	yes	—
122	C₅×C₂²⋊Q₈	—	3	16	no	—
123	C₄×C₅×Q₈	—	3	8	no	—
124	C₄×C₅×Q₈	—	3	8	no	—
125	C₄×C₅×Q₈	—	3	8	no	—
126	C₄×C₅×D₄	—	3	8	no	—
127	C₅×#117	—	3	16	no	—
128	C₂×C₅×C₄⋊C₄	—	3	1	no	—
129	C₂×C₅×C₄⋊C₄	—	3	2	no	—
130	C₂×C₅×C₄⋊C₄	—	3	2	no	—
131	C₂×C₅×C₄⋊C₄	—	3	1	no	—
132	C₂×C₅×C₄⋊C₄	—	3	2	no	—
133	C₂×C₅×C₄⋊C₄	—	3	1	no	—
134	C₂×C₅×C₄⋊C₄	—	3	2	no	—
135	C₂×C₅×C₄⋊C₄	—	3	1	no	—
136	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
137	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
138	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
139	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
140	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
141	C₂×C₄²×C₅	—	3	2	no	—
142	C₂×C₄²×C₅	—	3	2	no	—
143	C₂×C₄²×C₅	—	3	1	no	—
144	C₂×C₄²×C₅	—	3	1	no	—
145	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
146	C₂×#556	—	3	1	no	Sylow
147	C₂³×C₃×C₅	—	2	4	no	—
148	C₂³×C₃×C₅	—	2	4	no	—
149	C₂³×C₃×C₅	—	2	4	no	—
150	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
151	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
152	C₃×C₅×Q₈	—	2	8	no	—
153	C₃×C₅×D₄	—	2	8	no	—
154	C₂×C₃×C₄×C₅	—	2	2	no	—
155	C₂×C₃×C₄×C₅	—	2	4	no	—
156	C₂×C₃×C₄×C₅	—	2	2	no	—
157	C₂×C₃×C₄×C₅	#41	1	4	yes	—
158	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
159	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
160	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
161	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
162	C₂×C₅×Dic₃	—	2	4	no	—
163	C₂×C₅×Dic₃	—	2	2	no	—
164	C₂×C₅×Dic₃	—	2	4	no	—
165	C₂×C₅×Dic₃	—	2	2	no	—
166	C₂×C₅×Dic₃	—	2	2	no	—
167	C₂×C₅×Dic₃	—	2	16	no	—
168	C₂×C₅×Dic₃	#41	1	4	yes	—
169	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
170	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
171	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
172	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
173	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
174	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
175	C₅×Dic₆	—	2	8	no	—
176	C₅×Dic₆	—	2	8	no	—
177	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
178	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
179	C₂³×Dic₃	C₂²×C₅	1	2	yes	—
180	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
181	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
182	C₃×#124	C₂²×C₅	1	8	yes	—
183	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
184	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
185	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
186	C₂×#217	C₂²×C₅	1	2	yes	—
187	C₂×#217	C₂²×C₅	1	2	yes	—
188	C₂×#217	C₂²×C₅	1	2	yes	—
189	Q₈×Dic₃	C₂²×C₅	1	8	yes	complemented
190	#944	C₂²×C₅	1	8	yes	complemented
191	#936	C₂²×C₅	1	8	yes	—
192	D₄×Dic₃	C₂²×C₅	1	8	yes	—
193	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
194	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
195	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
196	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
197	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
198	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
199	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
200	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
201	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
202	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
203	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
204	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
205	#879	C₂²×C₅	1	16	yes	complemented
206	#879	C₂²×C₅	1	16	yes	complemented
207	#878	C₂²×C₅	1	16	yes	complemented
208	#877	C₂²×C₅	1	16	yes	complemented
209	C₄×Dic₆	C₂²×C₅	1	8	yes	complemented
210	C₄×Dic₆	C₂²×C₅	1	8	yes	complemented
211	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
212	C₂×C₅×Q₈	—	2	4	no	—
213	C₂×C₅×Q₈	—	3	4	no	—
214	C₂×C₅×Q₈	—	3	4	no	—
215	C₂×C₅×Q₈	—	6	4	no	—
216	C₂×C₅×Q₈	—	6	4	no	—
217	C₂×C₅×Q₈	C₂²×D₃	1	4	yes	—
218	C₂×C₅×D₄	—	2	4	no	—
219	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
220	C₂²×C₄×C₅	—	3	1	no	—
221	C₂²×C₄×C₅	—	3	8	no	—
222	C₂²×C₄×C₅	—	3	1	no	—
223	C₂²×C₄×C₅	—	3	2	no	—
224	C₂²×C₄×C₅	—	3	1	no	—
225	C₂²×C₄×C₅	—	3	2	no	—
226	C₂²×C₄×C₅	—	3	1	no	—
227	C₂²×C₄×C₅	—	6	8	no	—
228	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
229	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
230	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
231	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
232	C₅×C₄⋊C₄	—	3	4	no	—
233	C₅×C₄⋊C₄	—	3	8	no	—
234	C₅×C₄⋊C₄	—	3	4	no	—
235	C₅×C₄⋊C₄	—	3	8	no	—
236	C₅×C₄⋊C₄	—	3	8	no	—
237	C₅×C₄⋊C₄	—	3	4	no	—
238	C₅×C₄⋊C₄	—	3	4	no	—
239	C₅×C₄⋊C₄	—	3	8	no	—
240	C₅×C₂²⋊C₄	—	3	8	no	—
241	C₅×C₂²⋊C₄	—	3	8	no	—
242	C₅×C₂²⋊C₄	—	3	8	no	—
243	C₅×C₂²⋊C₄	C₂²×D₃	1	8	yes	—
244	C₅×C₂²⋊C₄	C₂²×D₃	1	8	yes	—
245	C₄²×C₅	—	3	8	no	—
246	C₄²×C₅	—	3	8	no	—
247	C₄²×C₅	—	3	4	no	—
248	C₄²×C₅	—	3	4	no	—
249	C₄²×C₅	C₂²×D₃	1	4	yes	—
250	#556	—	3	16	no	—
251	C₂×C₄⋊Q₈	—	3	1	no	—
252	C₂×#126	—	3	2	no	—
253	C₂×#126	—	3	2	no	—
254	C₂×#124	—	3	1	no	—
255	C₂×#124	C₅×D₃	1	1	yes	characteristic
256	C₂×C₂²⋊Q₈	—	3	2	no	—
257	C₂×C₄×Q₈	—	3	1	no	—
258	C₂×C₄×Q₈	—	3	1	no	—
259	C₂×C₄×Q₈	—	3	1	no	—
260	C₂×C₄×D₄	—	3	1	no	—
261	C₂×#117	—	3	2	no	—
262	C₂²×C₃×C₅	—	2	4	no	—
263	C₂²×C₃×C₅	—	2	4	no	—
264	C₂²×C₃×C₅	—	2	4	no	—
265	C₂²×C₃×C₅	—	4	8	no	—
266	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
267	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
268	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
269	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
270	C₃×C₄×C₅	—	2	2	no	—
271	C₃×C₄×C₅	—	2	4	no	—
272	C₃×C₄×C₅	—	2	2	no	—
273	C₃×C₄×C₅	C₂×#41	1	4	yes	—
274	C₅×Dic₃	—	2	4	no	—
275	C₅×Dic₃	—	2	2	no	—
276	C₅×Dic₃	—	2	4	no	—
277	C₅×Dic₃	—	2	2	no	—
278	C₅×Dic₃	—	2	2	no	—
279	C₅×Dic₃	C₂×#41	1	4	yes	—
280	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
281	C₂×C₃×Q₈	—	2	4	no	—
282	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
283	C₂×C₃×D₄	—	2	4	no	—
284	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
285	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
286	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
287	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
288	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
289	C₂²×Dic₃	—	2	8	no	—
290	C₂²×Dic₃	C₂³×C₅	1	8	yes	—
291	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
292	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
293	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
294	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
295	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
296	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
297	C₂×Dic₆	—	2	4	no	—
298	C₂×Dic₆	—	2	4	no	—
299	C₂×Dic₆	C₂³×C₅	1	4	yes	—
300	C₂×Dic₆	C₂³×C₅	1	4	yes	—
301	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
302	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
303	C₃×C₄²	C₂³×C₅	1	4	yes	—
304	#217	C₂³×C₅	1	8	yes	—
305	#217	C₂³×C₅	1	8	yes	—
306	#217	C₂³×C₅	1	8	yes	—
307	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
308	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
309	C₄⋊Dic₃	C₂³×C₅	1	8	yes	—
310	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
311	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
312	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
313	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
314	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
315	C₄×Dic₃	C₂³×C₅	1	8	yes	—
316	C₄×Dic₃	C₂³×C₅	1	4	yes	—
317	C₄×Dic₃	C₂³×C₅	1	4	yes	—
318	C₄×Dic₃	C₂³×C₅	1	8	yes	—
319	C₂³×C₅	—	2	4	no	—
320	C₂³×C₅	—	2	4	no	—
321	C₂³×C₅	—	2	4	no	—
322	C₂³×C₅	C₂³×D₃	1	4	yes	—
323	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
324	C₅×Q₈	—	2	8	no	—
325	C₅×Q₈	—	6	8	no	—
326	C₅×Q₈	—	6	8	no	—
327	C₅×D₄	—	2	8	no	—
328	C₂×C₄×C₅	—	2	4	no	—
329	C₂×C₄×C₅	—	2	2	no	—
330	C₂×C₄×C₅	—	2	2	no	—
331	C₂×C₄×C₅	—	3	4	no	—
332	C₂×C₄×C₅	—	3	2	no	—
333	C₂×C₄×C₅	—	3	2	no	—
334	C₂×C₄×C₅	—	3	4	no	—
335	C₂×C₄×C₅	—	3	2	no	—
336	C₂×C₄×C₅	—	3	4	no	—
337	C₂×C₄×C₅	—	3	2	no	—
338	C₂×C₄×C₅	—	6	16	no	—
339	C₂×C₄×C₅	—	6	4	no	—
340	C₂×C₄×C₅	—	6	4	no	—
341	C₂×C₄×C₅	—	6	2	no	—
342	C₂×C₄×C₅	—	6	2	no	—
343	C₂×C₄×C₅	—	6	2	no	—
344	C₂×C₄×C₅	#237	1	4	yes	—
345	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
346	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
347	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
348	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
349	C₂²×Q₈	—	3	1	no	—
350	C₂²×Q₈	—	3	1	no	—
351	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
352	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
353	C₂³×C₄	—	3	2	no	—
354	C₄⋊Q₈	—	3	8	no	—
355	#126	—	3	16	no	—
356	#126	—	3	16	no	—
357	#124	—	3	8	no	—
358	#124	C₂×C₅×D₃	1	8	yes	—
359	C₂²⋊Q₈	—	3	16	no	—
360	C₄×Q₈	—	3	8	no	—
361	C₄×Q₈	—	3	8	no	—
362	C₄×Q₈	—	3	8	no	—
363	C₄×D₄	—	3	8	no	—
364	#117	—	3	16	no	—
365	C₂×C₄⋊C₄	—	3	1	no	—
366	C₂×C₄⋊C₄	—	3	2	no	—
367	C₂×C₄⋊C₄	—	3	1	no	—
368	C₂×C₄⋊C₄	—	3	2	no	—
369	C₂×C₄⋊C₄	—	3	2	no	—
370	C₂×C₄⋊C₄	—	3	1	no	—
371	C₂×C₄⋊C₄	—	3	1	no	—
372	C₂×C₄⋊C₄	—	3	2	no	—
373	C₂×C₂²⋊C₄	—	3	2	no	—
374	C₂×C₂²⋊C₄	—	3	2	no	—
375	C₂×C₂²⋊C₄	—	3	2	no	—
376	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
377	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
378	C₂×C₄²	—	3	2	no	—
379	C₂×C₄²	—	3	2	no	—
380	C₂×C₄²	—	3	1	no	—
381	C₂×C₄²	—	3	1	no	—
382	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
383	C₂×C₃×C₅	—	4	4	no	—
384	C₂×C₃×C₅	#556	1	4	yes	complemented
385	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
386	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
387	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
388	C₂³×C₃	—	2	4	no	—
389	C₂³×C₃	—	2	4	no	—
390	C₂³×C₃	—	2	4	no	—
391	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
392	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
393	C₃×Q₈	—	2	8	no	—
394	C₃×D₄	—	2	8	no	—
395	C₂×C₃×C₄	—	2	2	no	—
396	C₂×C₃×C₄	—	2	4	no	—
397	C₂×C₃×C₄	—	2	2	no	—
398	C₂×C₃×C₄	C₅×#41	1	4	yes	—
399	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
400	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
401	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
402	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
403	C₂×Dic₃	—	2	4	no	—
404	C₂×Dic₃	—	2	2	no	—
405	C₂×Dic₃	—	2	4	no	—
406	C₂×Dic₃	—	2	2	no	—
407	C₂×Dic₃	—	2	2	no	—
408	C₂×Dic₃	—	2	16	no	—
409	C₂×Dic₃	C₅×#41	1	4	yes	—
410	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
411	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
412	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
413	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
414	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
415	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
416	Dic₆	—	2	8	no	—
417	Dic₆	—	2	8	no	—
418	C₂²×C₅	—	2	4	no	—
419	C₂²×C₅	—	2	4	no	—
420	C₂²×C₅	—	2	4	no	—
421	C₂²×C₅	—	4	8	no	—
422	C₂²×C₅	C₂×#237	1	2	yes	—
423	C₂²×C₅	D₃×#41	1	2	yes	—
424	C₂²×C₅	#1010	1	2	yes	—
425	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
426	C₄×C₅	—	2	4	no	—
427	C₄×C₅	—	2	2	no	—
428	C₄×C₅	—	2	2	no	—
429	C₄×C₅	—	3	4	no	—
430	C₄×C₅	—	6	4	no	—
431	C₄×C₅	—	6	4	no	—
432	C₄×C₅	—	6	2	no	—
433	C₄×C₅	—	6	2	no	—
434	C₄×C₅	—	6	2	no	—
435	C₄×C₅	C₂×#237	1	4	yes	—
436	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
437	C₂×Q₈	—	2	4	no	—
438	C₂×Q₈	—	3	4	no	—
439	C₂×Q₈	—	3	4	no	—
440	C₂×Q₈	—	6	4	no	—
441	C₂×Q₈	—	6	4	no	—
442	C₂×Q₈	C₂²×C₅×D₃	1	4	yes	—
443	C₂×D₄	—	2	4	no	—
444	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
445	C₂²×C₄	—	3	1	no	—
446	C₂²×C₄	—	3	1	no	—
447	C₂²×C₄	—	3	2	no	—
448	C₂²×C₄	—	3	1	no	—
449	C₂²×C₄	—	3	2	no	—
450	C₂²×C₄	—	3	1	no	—
451	C₂²×C₄	—	3	8	no	—
452	C₂²×C₄	—	6	8	no	—
453	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
454	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
455	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
456	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
457	C₄⋊C₄	—	3	4	no	—
458	C₄⋊C₄	—	3	8	no	—
459	C₄⋊C₄	—	3	4	no	—
460	C₄⋊C₄	—	3	8	no	—
461	C₄⋊C₄	—	3	8	no	—
462	C₄⋊C₄	—	3	4	no	—
463	C₄⋊C₄	—	3	4	no	—
464	C₄⋊C₄	—	3	8	no	—
465	C₂²⋊C₄	—	3	8	no	—
466	C₂²⋊C₄	—	3	8	no	—
467	C₂²⋊C₄	—	3	8	no	—
468	C₂²⋊C₄	C₂²×C₅×D₃	1	8	yes	—
469	C₂²⋊C₄	C₂²×C₅×D₃	1	8	yes	—
470	C₄²	—	3	8	no	—
471	C₄²	—	3	8	no	—
472	C₄²	—	3	4	no	—
473	C₄²	—	3	4	no	—
474	C₄²	C₂²×C₅×D₃	1	4	yes	—
475	C₃×C₅	C₂×#556	1	1	yes	characteristic, complemented, Hall
476	C₂²×C₃	—	2	4	no	—
477	C₂²×C₃	—	2	4	no	—
478	C₂²×C₃	—	2	4	no	—
479	C₂²×C₃	—	4	8	no	—
480	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
481	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
482	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
483	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
484	C₃×C₄	—	2	2	no	—
485	C₃×C₄	—	2	4	no	—
486	C₃×C₄	—	2	2	no	—
487	C₃×C₄	C₂×C₅×#41	1	4	yes	—
488	Dic₃	—	2	4	no	—
489	Dic₃	—	2	2	no	—
490	Dic₃	—	2	4	no	—
491	Dic₃	—	2	2	no	—
492	Dic₃	—	2	2	no	—
493	Dic₃	C₂×C₅×#41	1	4	yes	—
494	C₂×C₅	—	4	4	no	—
495	C₂×C₅	#5671	1	4	yes	direct product factor
496	C₂×C₅	C₂²×#237	1	1	yes	characteristic
497	C₂×C₅	C₂×D₃×#41	1	1	yes	characteristic
498	C₂×C₅	C₂×#1010	1	1	yes	characteristic
499	C₂³	—	2	4	no	—
500	C₂³	—	2	4	no	—
501	C₂³	—	2	4	no	—
502	C₂³	C₂³×C₅×D₃	1	4	yes	—
503	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
504	Q₈	—	2	8	no	—
505	Q₈	—	6	8	no	—
506	Q₈	—	6	8	no	—
507	D₄	—	2	8	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	3	4	no	—
512	C₂×C₄	—	3	2	no	—
513	C₂×C₄	—	3	2	no	—
514	C₂×C₄	—	3	4	no	—
515	C₂×C₄	—	3	2	no	—
516	C₂×C₄	—	3	4	no	—
517	C₂×C₄	—	3	2	no	—
518	C₂×C₄	—	6	16	no	—
519	C₂×C₄	—	6	4	no	—
520	C₂×C₄	—	6	4	no	—
521	C₂×C₄	—	6	2	no	—
522	C₂×C₄	—	6	2	no	—
523	C₂×C₄	—	6	2	no	—
524	C₂×C₄	C₅×#237	1	4	yes	—
525	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
526	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
527	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
528	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
529	C₂×C₃	—	4	4	no	—
530	C₂×C₃	C₅×#556	1	4	yes	complemented
531	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
532	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
533	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
534	C₅	C₂×#5671	1	1	yes	characteristic, direct product factor, Sylow
535	C₂²	—	2	4	no	—
536	C₂²	—	2	4	no	—
537	C₂²	—	2	4	no	—
538	C₂²	—	4	8	no	—
539	C₂²	C₂×C₅×#237	1	2	yes	—
540	C₂²	C₅×D₃×#41	1	2	yes	—
541	C₂²	C₅×#1010	1	2	yes	—
542	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
543	C₄	—	2	4	no	—
544	C₄	—	2	2	no	—
545	C₄	—	2	2	no	—
546	C₄	—	3	4	no	—
547	C₄	—	6	4	no	—
548	C₄	—	6	4	no	—
549	C₄	—	6	2	no	—
550	C₄	—	6	2	no	—
551	C₄	—	6	2	no	—
552	C₄	C₂×C₅×#237	1	4	yes	—
553	C₃	C₂×C₅×#556	1	1	yes	characteristic, complemented, Sylow
554	C₂	—	4	4	no	—
555	C₂	C₅×#5671	1	4	yes	direct product factor
556	C₂	C₂²×C₅×#237	1	1	yes	characteristic
557	C₂	C₂×C₅×D₃×#41	1	1	yes	characteristic
558	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×#124	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₃×C₅×D₄	C₂²
hypercenter	C₂×C₅×#124	D₃
hypocenter	C₃	C₂×C₅×#556
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#124

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×#5671	C₂	direct (N × H)
7. C₂×C₅×#879	C₂	semidirect
8. C₂×C₅×#879	C₂	semidirect
9. C₂×C₅×#878	C₂	semidirect
10. C₂×C₅×#877	C₂	semidirect
11. C₂×C₄×C₅×Dic₆	C₂	semidirect
12. C₂×C₄×C₅×Dic₆	C₂	semidirect
26. C₅×Q₈×Dic₃	C₂²	semidirect
27. C₅×#944	C₂²	semidirect
42. C₅×#879	C₂²	semidirect
43. C₅×#879	C₂²	semidirect
44. C₅×#878	C₂²	semidirect
45. C₅×#877	C₂²	semidirect
46. C₄×C₅×Dic₆	C₂²	semidirect
47. C₄×C₅×Dic₆	C₂²	semidirect
48. C₂×#5671	C₅	direct (N × H)
101. C₂×Q₈×Dic₃	C₂×C₅	semidirect
102. C₂×#944	C₂×C₅	semidirect
105. #5671	C₂×C₅	direct (N × H)
106. C₂×#879	C₂×C₅	semidirect
107. C₂×#879	C₂×C₅	semidirect
108. C₂×#878	C₂×C₅	semidirect
109. C₂×#877	C₂×C₅	semidirect
110. C₂×C₄×Dic₆	C₂×C₅	semidirect
111. C₂×C₄×Dic₆	C₂×C₅	semidirect
189. Q₈×Dic₃	C₂²×C₅	semidirect
190. #944	C₂²×C₅	semidirect
205. #879	C₂²×C₅	semidirect
206. #879	C₂²×C₅	semidirect
207. #878	C₂²×C₅	semidirect
208. #877	C₂²×C₅	semidirect
209. C₄×Dic₆	C₂²×C₅	semidirect
210. C₄×Dic₆	C₂²×C₅	semidirect
384. C₂×C₃×C₅	#556	semidirect
475. C₃×C₅	C₂×#556	semidirect
495. C₂×C₅	#5671	direct (N × H)
530. C₂×C₃	C₅×#556	semidirect
534. C₅	C₂×#5671	direct (N × H)
553. C₃	C₂×C₅×#556	semidirect
555. C₂	C₅×#5671	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×#124	2
C₂×C₅×Q₈×Dic₃	2
C₂×C₅×#944	2
C₂×C₅×#936	2
C₂×C₅×D₄×Dic₃	2
C₅×#5671	2
C₂×C₅×#879	2
C₂×C₅×#878	2
C₂×C₅×#877	2
C₂×C₄×C₅×Dic₆	2
C₂×C₅×#556	3
C₂×#5671	5

Subgroups — C2×C5×#5671 #14483991

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5671 #14483991