Subgroups — C₂×C₅×#5632 #14482899

Order 1920.

3136 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×D₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₅×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#944	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄×C₅×#67	C₂	1	1	yes	maximal, characteristic
6	C₅×#5632	C₂	1	16	yes	maximal, direct product factor
7	C₂×C₅×#897	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#896	C₂	1	2	yes	maximal, complemented
9	C₂×C₅×#888	C₂	1	2	yes	maximal, complemented
10	C₂×C₅×#887	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#67⋊C₄	C₂	1	2	yes	maximal
12	C₂×C₅×#878	C₂	1	2	yes	maximal, complemented
13	C₂×C₅×D₄×Q₈	—	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×#67	C₂²	1	1	yes	characteristic
17	C₂³×C₅×Dic₃	C₂²	1	2	yes	—
18	C₂×C₅×D₃×Q₈	—	2	8	no	—
19	C₂×C₅×D₃×Q₈	C₂²	1	8	yes	complemented
20	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
21	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
22	C₂²×C₅×Dic₆	—	2	8	no	—
23	C₂²×C₅×Dic₆	C₂²	1	2	yes	—
24	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
25	C₂²×C₅×Dic₆	C₂²	1	2	yes	—
26	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
27	C₂²×C₅×Dic₆	C₂²	1	8	yes	complemented
28	C₃×C₅×C₂²⋊Q₈	C₂²	1	8	yes	complemented
29	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
31	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₂×C₅×#217	C₂²	1	1	yes	characteristic
33	C₅×#944	C₂²	1	8	yes	complemented
34	C₄×C₅×#67	C₂²	1	8	yes	—
35	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
36	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
38	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
39	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
40	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
41	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
43	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
44	C₅×#897	C₂²	1	8	yes	complemented
45	C₅×#896	C₂²	1	16	yes	complemented
46	C₅×#888	C₂²	1	16	yes	complemented
47	C₅×#887	C₂²	1	8	yes	complemented
48	C₅×#67⋊C₄	C₂²	1	16	yes	—
49	C₅×#878	C₂²	1	16	yes	complemented
50	C₂×#5632	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
51	C₂³×C₅×Q₈	—	3	1	no	—
52	C₂³×C₅×Q₈	—	3	1	no	—
53	C₅×D₄×Q₈	—	3	16	no	—
54	C₂×C₅×C₄⋊Q₈	—	3	1	no	—
55	C₂×C₅×C₄⋊Q₈	—	3	2	no	—
56	C₂×C₅×C₂²⋊Q₈	—	3	2	no	—
57	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
58	C₂×C₅×C₂²⋊Q₈	—	3	2	no	—
59	C₂×C₅×C₂²⋊Q₈	D₃	1	1	yes	characteristic, complemented
60	C₂×C₄×C₅×Q₈	—	3	1	no	—
61	C₂×C₄×C₅×D₄	—	3	1	no	—
62	C₂×C₄×C₅×D₄	—	3	2	no	—
63	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
64	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₅×Q₈	—	2	4	no	—
66	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
67	C₂²×C₃×C₄×C₅	—	2	4	no	—
68	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
69	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
70	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
71	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
72	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
73	C₂×C₅×#67	Q₈	1	8	yes	complemented
74	C₂×C₅×#67	C₂³	1	4	yes	—
75	C₂²×C₅×Dic₃	—	2	8	no	—
76	C₂²×C₅×Dic₃	C₂³	1	8	yes	—
77	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
78	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
79	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
80	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
81	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
82	C₅×D₃×Q₈	—	2	32	no	—
83	C₂×C₄×C₅×D₃	—	2	4	no	—
84	C₂×C₄×C₅×D₃	—	2	8	no	—
85	C₂×C₄×C₅×D₃	C₂³	1	8	yes	—
86	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
87	C₂×C₅×Dic₆	—	2	4	no	—
88	C₂×C₅×Dic₆	—	2	8	no	—
89	C₂×C₅×Dic₆	—	2	8	no	—
90	C₂×C₅×Dic₆	—	2	32	no	—
91	C₂×C₅×Dic₆	D₄	1	8	yes	complemented
92	C₂×C₅×Dic₆	C₂³	1	8	yes	—
93	C₂×C₅×Dic₆	C₂³	1	8	yes	—
94	C₂×C₅×Dic₆	C₂³	1	4	yes	—
95	C₂×C₅×Dic₆	C₂³	1	4	yes	—
96	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
97	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
98	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
99	C₅×#217	C₂³	1	4	yes	—
100	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
101	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
102	C₅×C₄⋊Dic₃	C₂³	1	8	yes	—
103	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
104	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
105	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
106	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
107	C₄×C₅×Dic₃	C₂³	1	8	yes	—
108	C₄×C₅×Dic₃	C₂³	1	4	yes	—
109	C₂²×D₃×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
110	C₂³×Dic₆	C₂×C₅	1	1	yes	characteristic, complemented
111	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
112	C₂×#944	C₂×C₅	1	1	yes	characteristic, complemented
113	C₂×C₄×#67	C₂×C₅	1	1	yes	characteristic
114	#5632	C₂×C₅	1	16	yes	direct product factor
115	C₂×#897	C₂×C₅	1	1	yes	characteristic, complemented
116	C₂×#896	C₂×C₅	1	2	yes	complemented
117	C₂×#888	C₂×C₅	1	2	yes	complemented
118	C₂×#887	C₂×C₅	1	1	yes	characteristic, complemented
119	C₂×#67⋊C₄	C₂×C₅	1	2	yes	—
120	C₂×#878	C₂×C₅	1	2	yes	complemented
121	C₂²×C₅×Q₈	—	3	8	no	—
122	C₂²×C₅×Q₈	—	3	1	no	—
123	C₂²×C₅×Q₈	—	3	2	no	—
124	C₂²×C₅×Q₈	—	3	2	no	—
125	C₂²×C₅×Q₈	—	3	1	no	—
126	C₂²×C₅×Q₈	—	3	8	no	—
127	C₂²×C₅×Q₈	—	6	8	no	—
128	C₂²×C₅×Q₈	—	6	8	no	—
129	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
130	C₂²×C₅×D₄	—	3	1	no	—
131	C₂³×C₄×C₅	—	3	2	no	—
132	C₂³×C₄×C₅	—	3	2	no	—
133	C₂³×C₄×C₅	—	3	1	no	—
134	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
135	C₅×C₄⋊Q₈	—	3	8	no	—
136	C₅×C₄⋊Q₈	—	3	16	no	—
137	C₅×C₂²⋊Q₈	—	3	16	no	—
138	C₅×C₂²⋊Q₈	—	3	8	no	—
139	C₅×C₂²⋊Q₈	—	3	16	no	—
140	C₅×C₂²⋊Q₈	C₂×D₃	1	8	yes	complemented
141	C₄×C₅×Q₈	—	3	8	no	—
142	C₄×C₅×D₄	—	3	8	no	—
143	C₄×C₅×D₄	—	3	16	no	—
144	C₂×C₅×C₄⋊C₄	—	3	1	no	—
145	C₂×C₅×C₄⋊C₄	—	3	2	no	—
146	C₂×C₅×C₄⋊C₄	—	3	2	no	—
147	C₂×C₅×C₄⋊C₄	—	3	2	no	—
148	C₂×C₅×C₄⋊C₄	—	3	2	no	—
149	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
150	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
151	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
152	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
153	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
154	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
155	C₂×C₄²×C₅	—	3	2	no	—
156	C₂×C₄²×C₅	—	3	1	no	—
157	C₂×D₄×Q₈	—	3	1	no	Sylow
158	C₂³×C₃×C₅	—	2	2	no	—
159	C₂³×C₃×C₅	—	2	2	no	—
160	C₂³×C₃×C₅	C₂×Q₈	1	4	yes	complemented
161	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
162	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
163	C₂²×C₅×D₃	—	2	2	no	—
164	C₂²×C₅×D₃	—	2	2	no	—
165	C₂²×C₅×D₃	C₂×Q₈	1	4	yes	complemented
166	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
167	C₃×C₅×Q₈	—	2	8	no	—
168	C₂×C₃×C₄×C₅	—	2	2	no	—
169	C₂×C₃×C₄×C₅	—	2	4	no	—
170	C₂×C₃×C₄×C₅	—	2	4	no	—
171	C₂×C₃×C₄×C₅	—	2	8	no	—
172	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
173	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
174	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
175	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
176	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
177	C₅×#67	C₂×Q₈	1	16	yes	complemented
178	C₂×C₅×Dic₃	—	2	2	no	—
179	C₂×C₅×Dic₃	—	2	4	no	—
180	C₂×C₅×Dic₃	—	2	2	no	—
181	C₂×C₅×Dic₃	—	2	16	no	—
182	C₂×C₅×Dic₃	C₂×D₄	1	8	yes	—
183	C₂×C₅×Dic₃	C₂×Q₈	1	4	yes	complemented
184	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
185	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
186	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
187	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
188	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
189	C₄×C₅×D₃	—	2	8	no	—
190	C₄×C₅×D₃	—	2	16	no	—
191	C₅×Dic₆	—	2	8	no	—
192	C₅×Dic₆	—	2	16	no	—
193	C₅×Dic₆	—	2	16	no	—
194	C₅×Dic₆	C₂×D₄	1	16	yes	complemented
195	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
196	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
197	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
198	C₂³×Dic₃	C₂²×C₅	1	2	yes	—
199	C₂×D₃×Q₈	—	2	8	no	—
200	C₂×D₃×Q₈	C₂²×C₅	1	8	yes	complemented
201	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
202	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
203	C₂²×Dic₆	—	2	8	no	—
204	C₂²×Dic₆	C₂²×C₅	1	2	yes	—
205	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
206	C₂²×Dic₆	C₂²×C₅	1	2	yes	—
207	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
208	C₂²×Dic₆	C₂²×C₅	1	8	yes	complemented
209	C₃×C₂²⋊Q₈	C₂²×C₅	1	8	yes	complemented
210	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
211	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
212	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
213	C₂×#217	C₂²×C₅	1	1	yes	characteristic
214	#944	C₂²×C₅	1	8	yes	complemented
215	C₄×#67	C₂²×C₅	1	8	yes	—
216	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
217	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
218	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
219	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
220	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
221	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
222	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
223	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
224	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
225	#897	C₂²×C₅	1	8	yes	complemented
226	#896	C₂²×C₅	1	16	yes	complemented
227	#888	C₂²×C₅	1	16	yes	complemented
228	#887	C₂²×C₅	1	8	yes	complemented
229	#67⋊C₄	C₂²×C₅	1	16	yes	—
230	#878	C₂²×C₅	1	16	yes	complemented
231	C₂⁴×C₅	—	3	1	no	—
232	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
233	C₂×C₅×Q₈	—	2	4	no	—
234	C₂×C₅×Q₈	—	3	8	no	—
235	C₂×C₅×Q₈	—	3	4	no	—
236	C₂×C₅×Q₈	—	3	8	no	—
237	C₂×C₅×Q₈	—	3	8	no	—
238	C₂×C₅×Q₈	—	3	4	no	—
239	C₂×C₅×Q₈	—	6	8	no	—
240	C₂×C₅×Q₈	—	6	8	no	—
241	C₂×C₅×Q₈	—	6	32	no	—
242	C₂×C₅×Q₈	—	6	32	no	—
243	C₂×C₅×Q₈	—	6	4	no	—
244	C₂×C₅×Q₈	C₂²×D₃	1	4	yes	—
245	C₂×C₅×D₄	—	3	8	no	—
246	C₂×C₅×D₄	—	3	4	no	—
247	C₂²×C₄×C₅	—	2	4	no	—
248	C₂²×C₄×C₅	—	3	1	no	—
249	C₂²×C₄×C₅	—	3	2	no	—
250	C₂²×C₄×C₅	—	3	8	no	—
251	C₂²×C₄×C₅	—	3	1	no	—
252	C₂²×C₄×C₅	—	3	1	no	—
253	C₂²×C₄×C₅	—	3	2	no	—
254	C₂²×C₄×C₅	—	3	8	no	—
255	C₂²×C₄×C₅	—	3	4	no	—
256	C₂²×C₄×C₅	—	6	8	no	—
257	C₂²×C₄×C₅	—	6	8	no	—
258	C₂²×C₄×C₅	—	6	4	no	—
259	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
260	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
261	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
262	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
263	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
264	C₅×C₄⋊C₄	—	3	4	no	—
265	C₅×C₄⋊C₄	—	3	8	no	—
266	C₅×C₄⋊C₄	—	3	8	no	—
267	C₅×C₄⋊C₄	—	3	8	no	—
268	C₅×C₄⋊C₄	—	3	8	no	—
269	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
270	C₅×C₄⋊C₄	C₂²×D₃	1	8	yes	—
271	C₅×C₂²⋊C₄	—	3	4	no	—
272	C₅×C₂²⋊C₄	—	3	4	no	—
273	C₅×C₂²⋊C₄	—	3	8	no	—
274	C₅×C₂²⋊C₄	C₂²×D₃	1	8	yes	—
275	C₄²×C₅	—	3	8	no	—
276	C₄²×C₅	—	3	4	no	—
277	C₂³×Q₈	—	3	1	no	—
278	C₂³×Q₈	—	3	1	no	—
279	D₄×Q₈	—	3	16	no	—
280	C₂×C₄⋊Q₈	—	3	1	no	—
281	C₂×C₄⋊Q₈	—	3	2	no	—
282	C₂×C₂²⋊Q₈	—	3	2	no	—
283	C₂×C₂²⋊Q₈	—	3	1	no	—
284	C₂×C₂²⋊Q₈	—	3	2	no	—
285	C₂×C₂²⋊Q₈	C₅×D₃	1	1	yes	characteristic, complemented
286	C₂×C₄×Q₈	—	3	1	no	—
287	C₂×C₄×D₄	—	3	1	no	—
288	C₂×C₄×D₄	—	3	2	no	—
289	C₂²×C₃×C₅	—	2	8	no	—
290	C₂²×C₃×C₅	—	2	2	no	—
291	C₂²×C₃×C₅	—	2	2	no	—
292	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
293	C₂²×C₃×C₅	C₂²×Q₈	1	2	yes	—
294	C₂²×C₃×C₅	C₂²×Q₈	1	4	yes	complemented
295	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
296	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
297	C₂×C₅×D₃	—	2	8	no	—
298	C₂×C₅×D₃	—	2	2	no	—
299	C₂×C₅×D₃	—	2	2	no	—
300	C₂×C₅×D₃	C₂²×Q₈	1	4	yes	complemented
301	C₃×C₄×C₅	—	2	2	no	—
302	C₃×C₄×C₅	—	2	4	no	—
303	C₃×C₄×C₅	—	2	4	no	—
304	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
305	C₅×Dic₃	—	2	2	no	—
306	C₅×Dic₃	—	2	4	no	—
307	C₅×Dic₃	—	2	2	no	—
308	C₅×Dic₃	C₂²×D₄	1	8	yes	—
309	C₅×Dic₃	C₂²×Q₈	1	4	yes	complemented
310	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
311	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
312	C₂×C₃×Q₈	—	2	4	no	—
313	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
314	C₂²×C₃×C₄	—	2	4	no	—
315	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
316	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
317	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
318	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
319	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
320	C₂×#67	C₅×Q₈	1	8	yes	complemented
321	C₂×#67	C₂³×C₅	1	4	yes	—
322	C₂²×Dic₃	—	2	8	no	—
323	C₂²×Dic₃	C₂³×C₅	1	8	yes	—
324	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
325	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
326	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
327	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
328	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
329	D₃×Q₈	—	2	32	no	—
330	C₂×C₄×D₃	—	2	4	no	—
331	C₂×C₄×D₃	—	2	8	no	—
332	C₂×C₄×D₃	C₂³×C₅	1	8	yes	—
333	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
334	C₂×Dic₆	—	2	4	no	—
335	C₂×Dic₆	—	2	8	no	—
336	C₂×Dic₆	—	2	8	no	—
337	C₂×Dic₆	—	2	32	no	—
338	C₂×Dic₆	C₅×D₄	1	8	yes	complemented
339	C₂×Dic₆	C₂³×C₅	1	8	yes	—
340	C₂×Dic₆	C₂³×C₅	1	8	yes	—
341	C₂×Dic₆	C₂³×C₅	1	4	yes	—
342	C₂×Dic₆	C₂³×C₅	1	4	yes	—
343	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
344	C₃×C₄⋊C₄	C₂³×C₅	1	8	yes	—
345	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
346	#217	C₂³×C₅	1	4	yes	—
347	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
348	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
349	C₄⋊Dic₃	C₂³×C₅	1	8	yes	—
350	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
351	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
352	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
353	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
354	C₄×Dic₃	C₂³×C₅	1	8	yes	—
355	C₄×Dic₃	C₂³×C₅	1	4	yes	—
356	C₂³×C₅	—	2	2	no	—
357	C₂³×C₅	—	2	2	no	—
358	C₂³×C₅	—	3	4	no	—
359	C₂³×C₅	—	3	2	no	—
360	C₂³×C₅	—	6	2	no	—
361	C₂³×C₅	—	6	2	no	—
362	C₂³×C₅	D₃×Q₈	1	4	yes	complemented
363	C₂³×C₅	C₂³×D₃	1	2	yes	—
364	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
365	C₅×Q₈	—	2	8	no	—
366	C₅×Q₈	—	3	16	no	—
367	C₅×Q₈	—	6	16	no	—
368	C₅×Q₈	—	6	16	no	—
369	C₅×Q₈	—	6	8	no	—
370	C₅×D₄	—	3	16	no	—
371	C₂×C₄×C₅	—	2	2	no	—
372	C₂×C₄×C₅	—	2	4	no	—
373	C₂×C₄×C₅	—	2	4	no	—
374	C₂×C₄×C₅	—	2	8	no	—
375	C₂×C₄×C₅	—	3	8	no	—
376	C₂×C₄×C₅	—	3	4	no	—
377	C₂×C₄×C₅	—	3	2	no	—
378	C₂×C₄×C₅	—	3	4	no	—
379	C₂×C₄×C₅	—	3	2	no	—
380	C₂×C₄×C₅	—	3	2	no	—
381	C₂×C₄×C₅	—	3	4	no	—
382	C₂×C₄×C₅	—	6	16	no	—
383	C₂×C₄×C₅	—	6	16	no	—
384	C₂×C₄×C₅	—	6	2	no	—
385	C₂×C₄×C₅	—	6	4	no	—
386	C₂×C₄×C₅	—	6	2	no	—
387	C₂×C₄×C₅	—	6	8	no	—
388	C₂×C₄×C₅	D₃×D₄	1	4	yes	—
389	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
390	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
391	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
392	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
393	C₂²×Q₈	—	3	8	no	—
394	C₂²×Q₈	—	3	1	no	—
395	C₂²×Q₈	—	3	2	no	—
396	C₂²×Q₈	—	3	2	no	—
397	C₂²×Q₈	—	3	1	no	—
398	C₂²×Q₈	—	3	8	no	—
399	C₂²×Q₈	—	6	8	no	—
400	C₂²×Q₈	—	6	8	no	—
401	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
402	C₂²×D₄	—	3	1	no	—
403	C₂³×C₄	—	3	2	no	—
404	C₂³×C₄	—	3	2	no	—
405	C₂³×C₄	—	3	1	no	—
406	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
407	C₄⋊Q₈	—	3	8	no	—
408	C₄⋊Q₈	—	3	16	no	—
409	C₂²⋊Q₈	—	3	16	no	—
410	C₂²⋊Q₈	—	3	8	no	—
411	C₂²⋊Q₈	—	3	16	no	—
412	C₂²⋊Q₈	C₂×C₅×D₃	1	8	yes	complemented
413	C₄×Q₈	—	3	8	no	—
414	C₄×D₄	—	3	8	no	—
415	C₄×D₄	—	3	16	no	—
416	C₂×C₄⋊C₄	—	3	1	no	—
417	C₂×C₄⋊C₄	—	3	2	no	—
418	C₂×C₄⋊C₄	—	3	2	no	—
419	C₂×C₄⋊C₄	—	3	2	no	—
420	C₂×C₄⋊C₄	—	3	2	no	—
421	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
422	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
423	C₂×C₂²⋊C₄	—	3	1	no	—
424	C₂×C₂²⋊C₄	—	3	1	no	—
425	C₂×C₂²⋊C₄	—	3	2	no	—
426	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
427	C₂×C₄²	—	3	2	no	—
428	C₂×C₄²	—	3	1	no	—
429	C₂×C₃×C₅	—	2	4	no	—
430	C₂×C₃×C₅	D₄×Q₈	1	4	yes	complemented
431	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
432	C₂×C₃×C₅	C₂³×Q₈	1	1	yes	characteristic
433	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
434	C₅×D₃	—	2	4	no	—
435	C₂³×C₃	—	2	2	no	—
436	C₂³×C₃	—	2	2	no	—
437	C₂³×C₃	C₂×C₅×Q₈	1	4	yes	complemented
438	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
439	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
440	C₂²×D₃	—	2	2	no	—
441	C₂²×D₃	—	2	2	no	—
442	C₂²×D₃	C₂×C₅×Q₈	1	4	yes	complemented
443	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
444	C₃×Q₈	—	2	8	no	—
445	C₂×C₃×C₄	—	2	2	no	—
446	C₂×C₃×C₄	—	2	4	no	—
447	C₂×C₃×C₄	—	2	4	no	—
448	C₂×C₃×C₄	—	2	8	no	—
449	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
450	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
451	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
452	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
453	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
454	#67	C₂×C₅×Q₈	1	16	yes	complemented
455	C₂×Dic₃	—	2	2	no	—
456	C₂×Dic₃	—	2	4	no	—
457	C₂×Dic₃	—	2	2	no	—
458	C₂×Dic₃	—	2	16	no	—
459	C₂×Dic₃	C₂×C₅×D₄	1	8	yes	—
460	C₂×Dic₃	C₂×C₅×Q₈	1	4	yes	complemented
461	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
462	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
463	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
464	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
465	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
466	C₄×D₃	—	2	8	no	—
467	C₄×D₃	—	2	16	no	—
468	Dic₆	—	2	8	no	—
469	Dic₆	—	2	16	no	—
470	Dic₆	—	2	16	no	—
471	Dic₆	C₂×C₅×D₄	1	16	yes	complemented
472	C₂²×C₅	—	2	8	no	—
473	C₂²×C₅	—	2	2	no	—
474	C₂²×C₅	—	2	2	no	—
475	C₂²×C₅	—	3	4	no	—
476	C₂²×C₅	—	6	8	no	—
477	C₂²×C₅	—	6	2	no	—
478	C₂²×C₅	—	6	2	no	—
479	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
480	C₂²×C₅	C₂×D₃×Q₈	1	2	yes	—
481	C₂²×C₅	C₂×D₃×Q₈	1	4	yes	complemented
482	C₂²×C₅	#1010	1	2	yes	—
483	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
484	C₄×C₅	—	2	2	no	—
485	C₄×C₅	—	2	4	no	—
486	C₄×C₅	—	2	4	no	—
487	C₄×C₅	—	3	8	no	—
488	C₄×C₅	—	3	4	no	—
489	C₄×C₅	—	6	2	no	—
490	C₄×C₅	—	6	4	no	—
491	C₄×C₅	—	6	2	no	—
492	C₄×C₅	C₂×D₃×D₄	1	4	yes	—
493	C₂⁴	—	3	1	no	—
494	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
495	C₂×Q₈	—	2	4	no	—
496	C₂×Q₈	—	3	8	no	—
497	C₂×Q₈	—	3	4	no	—
498	C₂×Q₈	—	3	8	no	—
499	C₂×Q₈	—	3	8	no	—
500	C₂×Q₈	—	3	4	no	—
501	C₂×Q₈	—	6	8	no	—
502	C₂×Q₈	—	6	8	no	—
503	C₂×Q₈	—	6	32	no	—
504	C₂×Q₈	—	6	32	no	—
505	C₂×Q₈	—	6	4	no	—
506	C₂×Q₈	C₂²×C₅×D₃	1	4	yes	—
507	C₂×D₄	—	3	8	no	—
508	C₂×D₄	—	3	4	no	—
509	C₂²×C₄	—	2	4	no	—
510	C₂²×C₄	—	3	1	no	—
511	C₂²×C₄	—	3	2	no	—
512	C₂²×C₄	—	3	1	no	—
513	C₂²×C₄	—	3	1	no	—
514	C₂²×C₄	—	3	2	no	—
515	C₂²×C₄	—	3	8	no	—
516	C₂²×C₄	—	3	8	no	—
517	C₂²×C₄	—	3	4	no	—
518	C₂²×C₄	—	6	8	no	—
519	C₂²×C₄	—	6	8	no	—
520	C₂²×C₄	—	6	4	no	—
521	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
522	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
523	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
524	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
525	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
526	C₄⋊C₄	—	3	4	no	—
527	C₄⋊C₄	—	3	8	no	—
528	C₄⋊C₄	—	3	8	no	—
529	C₄⋊C₄	—	3	8	no	—
530	C₄⋊C₄	—	3	8	no	—
531	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
532	C₄⋊C₄	C₂²×C₅×D₃	1	8	yes	—
533	C₂²⋊C₄	—	3	4	no	—
534	C₂²⋊C₄	—	3	4	no	—
535	C₂²⋊C₄	—	3	8	no	—
536	C₂²⋊C₄	C₂²×C₅×D₃	1	8	yes	—
537	C₄²	—	3	8	no	—
538	C₄²	—	3	4	no	—
539	C₃×C₅	C₂×D₄×Q₈	1	1	yes	characteristic, complemented, Hall
540	C₂²×C₃	—	2	8	no	—
541	C₂²×C₃	—	2	2	no	—
542	C₂²×C₃	—	2	2	no	—
543	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
544	C₂²×C₃	C₂²×C₅×Q₈	1	2	yes	—
545	C₂²×C₃	C₂²×C₅×Q₈	1	4	yes	complemented
546	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
547	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
548	C₂×D₃	—	2	8	no	—
549	C₂×D₃	—	2	2	no	—
550	C₂×D₃	—	2	2	no	—
551	C₂×D₃	C₂²×C₅×Q₈	1	4	yes	complemented
552	C₃×C₄	—	2	2	no	—
553	C₃×C₄	—	2	4	no	—
554	C₃×C₄	—	2	4	no	—
555	C₃×C₄	C₂²×C₅×D₄	1	4	yes	—
556	Dic₃	—	2	2	no	—
557	Dic₃	—	2	4	no	—
558	Dic₃	—	2	2	no	—
559	Dic₃	C₂²×C₅×D₄	1	8	yes	—
560	Dic₃	C₂²×C₅×Q₈	1	4	yes	complemented
561	C₂×C₅	—	2	4	no	—
562	C₂×C₅	—	6	4	no	—
563	C₂×C₅	#5632	1	4	yes	direct product factor
564	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
565	C₂×C₅	C₂²×D₃×Q₈	1	1	yes	characteristic
566	C₂×C₅	C₂×#1010	1	1	yes	characteristic
567	C₂³	—	2	2	no	—
568	C₂³	—	2	2	no	—
569	C₂³	—	3	4	no	—
570	C₂³	—	3	2	no	—
571	C₂³	—	6	2	no	—
572	C₂³	—	6	2	no	—
573	C₂³	C₅×D₃×Q₈	1	4	yes	complemented
574	C₂³	C₂³×C₅×D₃	1	2	yes	—
575	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
576	Q₈	—	2	8	no	—
577	Q₈	—	3	16	no	—
578	Q₈	—	6	16	no	—
579	Q₈	—	6	16	no	—
580	Q₈	—	6	8	no	—
581	D₄	—	3	16	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	4	no	—
584	C₂×C₄	—	2	4	no	—
585	C₂×C₄	—	2	8	no	—
586	C₂×C₄	—	3	8	no	—
587	C₂×C₄	—	3	4	no	—
588	C₂×C₄	—	3	2	no	—
589	C₂×C₄	—	3	4	no	—
590	C₂×C₄	—	3	2	no	—
591	C₂×C₄	—	3	2	no	—
592	C₂×C₄	—	3	4	no	—
593	C₂×C₄	—	6	16	no	—
594	C₂×C₄	—	6	16	no	—
595	C₂×C₄	—	6	4	no	—
596	C₂×C₄	—	6	2	no	—
597	C₂×C₄	—	6	2	no	—
598	C₂×C₄	—	6	8	no	—
599	C₂×C₄	C₅×D₃×D₄	1	4	yes	—
600	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
601	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
602	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
603	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
604	C₂×C₃	—	2	4	no	—
605	C₂×C₃	C₅×D₄×Q₈	1	4	yes	complemented
606	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
607	C₂×C₃	C₂³×C₅×Q₈	1	1	yes	characteristic
608	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
609	D₃	—	2	4	no	—
610	C₅	C₂×#5632	1	1	yes	characteristic, direct product factor, Sylow
611	C₂²	—	2	2	no	—
612	C₂²	—	2	2	no	—
613	C₂²	—	2	8	no	—
614	C₂²	—	3	4	no	—
615	C₂²	—	6	2	no	—
616	C₂²	—	6	2	no	—
617	C₂²	—	6	8	no	—
618	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
619	C₂²	C₂×C₅×D₃×Q₈	1	2	yes	—
620	C₂²	C₂×C₅×D₃×Q₈	1	4	yes	complemented
621	C₂²	C₅×#1010	1	2	yes	—
622	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
623	C₄	—	2	2	no	—
624	C₄	—	2	4	no	—
625	C₄	—	2	4	no	—
626	C₄	—	3	8	no	—
627	C₄	—	3	4	no	—
628	C₄	—	6	4	no	—
629	C₄	—	6	2	no	—
630	C₄	—	6	2	no	—
631	C₄	C₂×C₅×D₃×D₄	1	4	yes	—
632	C₃	C₂×C₅×D₄×Q₈	1	1	yes	characteristic, complemented, Sylow
633	C₂	—	2	4	no	—
634	C₂	—	6	4	no	—
635	C₂	C₅×#5632	1	4	yes	direct product factor
636	C₂	C₂²×C₅×D₃×D₄	1	1	yes	characteristic
637	C₂	C₂²×C₅×D₃×Q₈	1	1	yes	characteristic
638	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	C₂²×C₅×#67	C₂²
hypercenter	C₂×C₅×C₂²⋊Q₈	D₃
hypocenter	C₃	C₂×C₅×D₄×Q₈
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
1. C₂²×C₅×D₃×Q₈	C₂	semidirect
2. C₂³×C₅×Dic₆	C₂	semidirect
3. C₂×C₃×C₅×C₂²⋊Q₈	C₂	semidirect
4. C₂×C₅×#944	C₂	semidirect
6. C₅×#5632	C₂	direct (N × H)
7. C₂×C₅×#897	C₂	semidirect
8. C₂×C₅×#896	C₂	semidirect
9. C₂×C₅×#888	C₂	semidirect
10. C₂×C₅×#887	C₂	semidirect
12. C₂×C₅×#878	C₂	semidirect
19. C₂×C₅×D₃×Q₈	C₂²	semidirect
27. C₂²×C₅×Dic₆	C₂²	semidirect
28. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
33. C₅×#944	C₂²	semidirect
44. C₅×#897	C₂²	semidirect
45. C₅×#896	C₂²	semidirect
46. C₅×#888	C₂²	semidirect
47. C₅×#887	C₂²	semidirect
49. C₅×#878	C₂²	semidirect
50. C₂×#5632	C₅	direct (N × H)
59. C₂×C₅×C₂²⋊Q₈	D₃	semidirect
73. C₂×C₅×#67	Q₈	semidirect
91. C₂×C₅×Dic₆	D₄	semidirect
109. C₂²×D₃×Q₈	C₂×C₅	semidirect
110. C₂³×Dic₆	C₂×C₅	semidirect
111. C₂×C₃×C₂²⋊Q₈	C₂×C₅	semidirect
112. C₂×#944	C₂×C₅	semidirect
114. #5632	C₂×C₅	direct (N × H)
115. C₂×#897	C₂×C₅	semidirect
116. C₂×#896	C₂×C₅	semidirect
117. C₂×#888	C₂×C₅	semidirect
118. C₂×#887	C₂×C₅	semidirect
120. C₂×#878	C₂×C₅	semidirect
140. C₅×C₂²⋊Q₈	C₂×D₃	semidirect
160. C₂³×C₃×C₅	C₂×Q₈	semidirect
165. C₂²×C₅×D₃	C₂×Q₈	semidirect
177. C₅×#67	C₂×Q₈	semidirect
183. C₂×C₅×Dic₃	C₂×Q₈	semidirect
194. C₅×Dic₆	C₂×D₄	semidirect
200. C₂×D₃×Q₈	C₂²×C₅	semidirect
208. C₂²×Dic₆	C₂²×C₅	semidirect
209. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
214. #944	C₂²×C₅	semidirect
225. #897	C₂²×C₅	semidirect
226. #896	C₂²×C₅	semidirect
227. #888	C₂²×C₅	semidirect
228. #887	C₂²×C₅	semidirect
230. #878	C₂²×C₅	semidirect
285. C₂×C₂²⋊Q₈	C₅×D₃	semidirect
294. C₂²×C₃×C₅	C₂²×Q₈	semidirect
300. C₂×C₅×D₃	C₂²×Q₈	semidirect
309. C₅×Dic₃	C₂²×Q₈	semidirect
320. C₂×#67	C₅×Q₈	semidirect
338. C₂×Dic₆	C₅×D₄	semidirect
362. C₂³×C₅	D₃×Q₈	semidirect
412. C₂²⋊Q₈	C₂×C₅×D₃	semidirect
430. C₂×C₃×C₅	D₄×Q₈	semidirect
437. C₂³×C₃	C₂×C₅×Q₈	semidirect
442. C₂²×D₃	C₂×C₅×Q₈	semidirect
454. #67	C₂×C₅×Q₈	semidirect
460. C₂×Dic₃	C₂×C₅×Q₈	semidirect
471. Dic₆	C₂×C₅×D₄	semidirect
481. C₂²×C₅	C₂×D₃×Q₈	semidirect
539. C₃×C₅	C₂×D₄×Q₈	semidirect
545. C₂²×C₃	C₂²×C₅×Q₈	semidirect
551. C₂×D₃	C₂²×C₅×Q₈	semidirect
560. Dic₃	C₂²×C₅×Q₈	semidirect
563. C₂×C₅	#5632	direct (N × H)
573. C₂³	C₅×D₃×Q₈	semidirect
605. C₂×C₃	C₅×D₄×Q₈	semidirect
610. C₅	C₂×#5632	direct (N × H)
620. C₂²	C₂×C₅×D₃×Q₈	semidirect
632. C₃	C₂×C₅×D₄×Q₈	semidirect
635. C₂	C₅×#5632	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×C₅×D₃×Q₈	2
C₂³×C₅×Dic₆	2
C₂×C₃×C₅×C₂²⋊Q₈	2
C₂×C₅×#944	2
C₂×C₄×C₅×#67	2
C₅×#5632	2
C₂×C₅×#897	2
C₂×C₅×#896	2
C₂×C₅×#888	2
C₂×C₅×#887	2
C₂×C₅×#67⋊C₄	2
C₂×C₅×#878	2
C₂×C₅×D₄×Q₈	3
C₂×#5632	5

Subgroups — C2×C5×#5632 #14482899

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5632 #14482899