Subgroups — C₂×C₅×#5568 #14484000

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×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#947	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#944	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5568	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₅×#898	C₂	1	2	yes	maximal, complemented
6	C₂×C₅×#896	C₂	1	2	yes	maximal, complemented
7	C₂×C₅×#893	C₂	1	1	yes	maximal, characteristic
8	C₂×C₅×#887	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#876	C₂	1	2	yes	maximal, complemented
10	C₂×C₅×#875	C₂	1	1	yes	maximal, characteristic
11	C₂×C₅×#872	C₂	1	2	yes	maximal, 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×C₅×D₁₂	C₂²	1	1	yes	characteristic
16	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
17	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
18	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
19	C₃×C₄×C₅×Q₈	C₂²	1	8	yes	complemented
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
22	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
24	C₅×#947	C₂²	1	8	yes	—
25	C₅×#944	C₂²	1	8	yes	complemented
26	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
27	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
28	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
29	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
30	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
31	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
32	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
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	2	yes	—
36	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
37	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
40	C₅×#898	C₂²	1	16	yes	complemented
41	C₅×#896	C₂²	1	16	yes	complemented
42	C₅×#893	C₂²	1	8	yes	—
43	C₅×#887	C₂²	1	8	yes	complemented
44	C₅×#876	C₂²	1	16	yes	complemented
45	C₅×#875	C₂²	1	8	yes	—
46	C₅×#872	C₂²	1	16	yes	complemented
47	C₄×C₅×Dic₆	C₂²	1	8	yes	complemented
48	C₂×#5568	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	—	3	1	no	—
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	D₃	1	1	yes	characteristic, complemented
59	C₂×C₄×C₅×D₄	—	3	1	no	—
60	C₂×C₅×#117	—	3	2	no	—
61	C₂³×C₅×D₃	C₂³	1	2	yes	—
62	C₂×C₃×C₅×Q₈	—	2	4	no	—
63	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
64	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
65	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
69	C₂²×C₅×Dic₃	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	2	yes	—
73	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
74	C₂×C₅×D₁₂	—	2	4	no	—
75	C₂×C₅×D₁₂	C₂³	1	4	yes	—
76	C₂×C₄×C₅×D₃	—	2	8	no	—
77	C₂×C₄×C₅×D₃	C₂³	1	8	yes	—
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×C₄⋊C₄	C₂³	1	4	yes	—
83	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
84	C₃×C₄²×C₅	C₂³	1	4	yes	—
85	C₃×C₄²×C₅	C₂³	1	8	yes	—
86	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
87	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
88	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
89	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
90	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
91	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
92	C₅×Dic₃⋊C₄	C₂³	1	4	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	C₅×Dic₃⋊C₄	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×C₄×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
101	C₂×#947	C₂×C₅	1	1	yes	characteristic
102	C₂×#944	C₂×C₅	1	1	yes	characteristic, complemented
103	#5568	C₂×C₅	1	16	yes	direct product factor
104	C₂×#898	C₂×C₅	1	2	yes	complemented
105	C₂×#896	C₂×C₅	1	2	yes	complemented
106	C₂×#893	C₂×C₅	1	1	yes	characteristic
107	C₂×#887	C₂×C₅	1	1	yes	characteristic, complemented
108	C₂×#876	C₂×C₅	1	2	yes	complemented
109	C₂×#875	C₂×C₅	1	1	yes	characteristic
110	C₂×#872	C₂×C₅	1	2	yes	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	—	3	1	no	—
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	—	3	8	no	—
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	C₂×D₃	1	8	yes	complemented
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	C₂×D₃	1	1	yes	characteristic
135	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
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	—	3	2	no	—
140	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
141	C₂×C₄²×C₅	—	3	2	no	—
142	C₂×C₄²×C₅	—	3	1	no	—
143	C₂×C₄²×C₅	—	3	1	no	—
144	C₂×C₄²×C₅	C₂×D₃	1	2	yes	—
145	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
146	C₂×#556	—	3	1	no	Sylow
147	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
148	C₂²×C₅×D₃	—	2	4	no	—
149	C₂²×C₅×D₃	—	2	4	no	—
150	C₂²×C₅×D₃	—	2	4	no	—
151	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
152	C₃×C₅×Q₈	—	2	8	no	—
153	C₂×C₃×C₄×C₅	—	2	2	no	—
154	C₂×C₃×C₄×C₅	—	2	4	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	4	yes	—
159	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
160	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
161	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
162	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
163	C₂×C₅×Dic₃	—	2	4	no	—
164	C₂×C₅×Dic₃	—	2	2	no	—
165	C₂×C₅×Dic₃	—	2	2	no	—
166	C₂×C₅×Dic₃	—	2	2	no	—
167	C₂×C₅×Dic₃	#41	1	4	yes	—
168	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
169	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
170	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
171	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
172	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
173	C₅×D₁₂	—	2	8	no	—
174	C₄×C₅×D₃	—	2	16	no	—
175	C₅×Dic₆	—	2	8	no	—
176	C₅×Dic₆	—	2	8	no	—
177	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
178	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
179	C₂²×C₄×D₃	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×C₄×Q₈	C₂²×C₅	1	8	yes	complemented
183	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
184	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
185	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
186	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
187	#947	C₂²×C₅	1	8	yes	—
188	#944	C₂²×C₅	1	8	yes	complemented
189	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
190	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
191	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
192	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
193	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
194	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
195	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
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	2	yes	—
199	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
200	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
201	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
202	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
203	#898	C₂²×C₅	1	16	yes	complemented
204	#896	C₂²×C₅	1	16	yes	complemented
205	#893	C₂²×C₅	1	8	yes	—
206	#887	C₂²×C₅	1	8	yes	complemented
207	#876	C₂²×C₅	1	16	yes	complemented
208	#875	C₂²×C₅	1	8	yes	—
209	#872	C₂²×C₅	1	16	yes	complemented
210	C₄×Dic₆	C₂²×C₅	1	8	yes	complemented
211	C₂⁴×C₅	—	3	2	no	—
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	—	3	4	no	—
219	C₂×C₅×D₄	—	6	4	no	—
220	C₂²×C₄×C₅	—	3	1	no	—
221	C₂²×C₄×C₅	—	3	1	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	8	no	—
226	C₂²×C₄×C₅	—	6	8	no	—
227	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
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	8	no	—
235	C₅×C₄⋊C₄	—	3	4	no	—
236	C₅×C₄⋊C₄	—	3	4	no	—
237	C₅×C₄⋊C₄	—	3	8	no	—
238	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
239	C₅×C₄⋊C₄	C₂²×D₃	1	8	yes	—
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	—	3	8	no	—
244	C₅×C₂²⋊C₄	—	3	8	no	—
245	C₄²×C₅	—	3	8	no	—
246	C₄²×C₅	—	3	4	no	—
247	C₄²×C₅	—	3	4	no	—
248	C₄²×C₅	C₂²×D₃	1	8	yes	—
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	—	3	1	no	—
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	C₅×D₃	1	1	yes	characteristic, complemented
260	C₂×C₄×D₄	—	3	1	no	—
261	C₂×#117	—	3	2	no	—
262	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
263	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
264	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
265	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
266	C₂×C₅×D₃	—	2	4	no	—
267	C₂×C₅×D₃	—	2	4	no	—
268	C₂×C₅×D₃	—	2	4	no	—
269	C₂×C₅×D₃	—	4	8	no	—
270	C₃×C₄×C₅	—	2	2	no	—
271	C₃×C₄×C₅	—	2	4	no	—
272	C₃×C₄×C₅	—	2	4	no	—
273	C₃×C₄×C₅	—	2	2	no	—
274	C₃×C₄×C₅	C₂×#41	1	4	yes	—
275	C₅×Dic₃	—	2	4	no	—
276	C₅×Dic₃	—	2	2	no	—
277	C₅×Dic₃	—	2	2	no	—
278	C₅×Dic₃	—	2	2	no	—
279	C₅×Dic₃	C₂×#41	1	4	yes	—
280	C₂³×D₃	C₂³×C₅	1	2	yes	—
281	C₂×C₃×Q₈	—	2	4	no	—
282	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
283	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
284	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
285	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
286	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
287	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
288	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
289	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
290	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
291	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
292	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
293	C₂×D₁₂	—	2	4	no	—
294	C₂×D₁₂	C₂³×C₅	1	4	yes	—
295	C₂×C₄×D₃	—	2	8	no	—
296	C₂×C₄×D₃	C₂³×C₅	1	8	yes	—
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×C₄⋊C₄	C₂³×C₅	1	4	yes	—
302	C₃×C₄⋊C₄	C₂³×C₅	1	8	yes	—
303	C₃×C₄²	C₂³×C₅	1	4	yes	—
304	C₃×C₄²	C₂³×C₅	1	8	yes	—
305	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
306	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
307	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
308	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
309	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
310	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
311	Dic₃⋊C₄	C₂³×C₅	1	4	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	Dic₃⋊C₄	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	—	3	4	no	—
320	C₂³×C₅	—	6	4	no	—
321	C₂³×C₅	—	6	4	no	—
322	C₂³×C₅	—	6	4	no	—
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	—	6	8	no	—
328	C₂×C₄×C₅	—	2	4	no	—
329	C₂×C₄×C₅	—	2	2	no	—
330	C₂×C₄×C₅	—	2	4	no	—
331	C₂×C₄×C₅	—	2	2	no	—
332	C₂×C₄×C₅	—	3	4	no	—
333	C₂×C₄×C₅	—	3	2	no	—
334	C₂×C₄×C₅	—	3	2	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	2	no	—
341	C₂×C₄×C₅	—	6	2	no	—
342	C₂×C₄×C₅	—	6	2	no	—
343	C₂×C₄×C₅	#235	1	4	yes	—
344	C₂×C₄×C₅	C₂³×D₃	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	—	3	1	no	—
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	—	3	8	no	—
359	C₂²⋊Q₈	—	3	16	no	—
360	C₄×Q₈	—	3	8	no	—
361	C₄×Q₈	—	3	8	no	—
362	C₄×Q₈	C₂×C₅×D₃	1	8	yes	complemented
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	2	no	—
368	C₂×C₄⋊C₄	—	3	1	no	—
369	C₂×C₄⋊C₄	—	3	1	no	—
370	C₂×C₄⋊C₄	—	3	2	no	—
371	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
372	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
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	—	3	2	no	—
377	C₂×C₂²⋊C₄	—	3	2	no	—
378	C₂×C₄²	—	3	2	no	—
379	C₂×C₄²	—	3	1	no	—
380	C₂×C₄²	—	3	1	no	—
381	C₂×C₄²	C₂×C₅×D₃	1	2	yes	—
382	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
383	C₂×C₃×C₅	#556	1	4	yes	complemented
384	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
385	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
386	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
387	C₅×D₃	—	4	4	no	—
388	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
389	C₂²×D₃	—	2	4	no	—
390	C₂²×D₃	—	2	4	no	—
391	C₂²×D₃	—	2	4	no	—
392	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
393	C₃×Q₈	—	2	8	no	—
394	C₂×C₃×C₄	—	2	2	no	—
395	C₂×C₃×C₄	—	2	4	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	4	yes	—
400	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
401	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
402	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
403	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
404	C₂×Dic₃	—	2	4	no	—
405	C₂×Dic₃	—	2	2	no	—
406	C₂×Dic₃	—	2	2	no	—
407	C₂×Dic₃	—	2	2	no	—
408	C₂×Dic₃	C₅×#41	1	4	yes	—
409	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
410	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
411	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
412	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
413	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
414	D₁₂	—	2	8	no	—
415	C₄×D₃	—	2	16	no	—
416	Dic₆	—	2	8	no	—
417	Dic₆	—	2	8	no	—
418	C₂²×C₅	—	6	4	no	—
419	C₂²×C₅	—	6	4	no	—
420	C₂²×C₅	—	6	4	no	—
421	C₂²×C₅	—	12	8	no	—
422	C₂²×C₅	C₂×#235	1	2	yes	—
423	C₂²×C₅	#1007	1	2	yes	—
424	C₂²×C₅	D₃×#41	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	4	no	—
429	C₄×C₅	—	2	2	no	—
430	C₄×C₅	—	3	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×#235	1	4	yes	—
436	C₂⁴	—	3	2	no	—
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	—	3	4	no	—
444	C₂×D₄	—	6	4	no	—
445	C₂²×C₄	—	3	1	no	—
446	C₂²×C₄	—	3	1	no	—
447	C₂²×C₄	—	3	1	no	—
448	C₂²×C₄	—	3	2	no	—
449	C₂²×C₄	—	3	1	no	—
450	C₂²×C₄	—	3	8	no	—
451	C₂²×C₄	—	6	8	no	—
452	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
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	8	no	—
460	C₄⋊C₄	—	3	4	no	—
461	C₄⋊C₄	—	3	4	no	—
462	C₄⋊C₄	—	3	8	no	—
463	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
464	C₄⋊C₄	C₂²×C₅×D₃	1	8	yes	—
465	C₂²⋊C₄	—	3	8	no	—
466	C₂²⋊C₄	—	3	8	no	—
467	C₂²⋊C₄	—	3	8	no	—
468	C₂²⋊C₄	—	3	8	no	—
469	C₂²⋊C₄	—	3	8	no	—
470	C₄²	—	3	8	no	—
471	C₄²	—	3	4	no	—
472	C₄²	—	3	4	no	—
473	C₄²	C₂²×C₅×D₃	1	8	yes	—
474	C₄²	C₂²×C₅×D₃	1	4	yes	—
475	C₃×C₅	C₂×#556	1	1	yes	characteristic, complemented, Hall
476	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
477	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
478	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
479	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
480	C₂×D₃	—	2	4	no	—
481	C₂×D₃	—	2	4	no	—
482	C₂×D₃	—	2	4	no	—
483	C₂×D₃	—	4	8	no	—
484	C₃×C₄	—	2	2	no	—
485	C₃×C₄	—	2	4	no	—
486	C₃×C₄	—	2	4	no	—
487	C₃×C₄	—	2	2	no	—
488	C₃×C₄	C₂×C₅×#41	1	4	yes	—
489	Dic₃	—	2	4	no	—
490	Dic₃	—	2	2	no	—
491	Dic₃	—	2	2	no	—
492	Dic₃	—	2	2	no	—
493	Dic₃	C₂×C₅×#41	1	4	yes	—
494	C₂×C₅	—	12	4	no	—
495	C₂×C₅	#5568	1	4	yes	direct product factor
496	C₂×C₅	C₂²×#235	1	1	yes	characteristic
497	C₂×C₅	C₂×#1007	1	1	yes	characteristic
498	C₂×C₅	C₂×D₃×#41	1	1	yes	characteristic
499	C₂³	—	3	4	no	—
500	C₂³	—	6	4	no	—
501	C₂³	—	6	4	no	—
502	C₂³	—	6	4	no	—
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	—	6	8	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	3	4	no	—
513	C₂×C₄	—	3	2	no	—
514	C₂×C₄	—	3	2	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	2	no	—
521	C₂×C₄	—	6	2	no	—
522	C₂×C₄	—	6	2	no	—
523	C₂×C₄	C₅×#235	1	4	yes	—
524	C₂×C₄	C₂³×C₅×D₃	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	C₅×#556	1	4	yes	complemented
530	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
531	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
532	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
533	D₃	—	4	4	no	—
534	C₅	C₂×#5568	1	1	yes	characteristic, direct product factor, Sylow
535	C₂²	—	6	4	no	—
536	C₂²	—	6	4	no	—
537	C₂²	—	6	4	no	—
538	C₂²	—	12	8	no	—
539	C₂²	C₂×C₅×#235	1	2	yes	—
540	C₂²	C₅×#1007	1	2	yes	—
541	C₂²	C₅×D₃×#41	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	4	no	—
546	C₄	—	2	2	no	—
547	C₄	—	3	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×#235	1	4	yes	—
553	C₃	C₂×C₅×#556	1	1	yes	characteristic, complemented, Sylow
554	C₂	—	12	4	no	—
555	C₂	C₅×#5568	1	4	yes	direct product factor
556	C₂	C₂²×C₅×#235	1	1	yes	characteristic
557	C₂	C₂×C₅×#1007	1	1	yes	characteristic
558	C₂	C₂×C₅×D₃×#41	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×C₄×C₅×Q₈	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₅×D₁₂	C₂²
hypercenter	C₂×C₄×C₅×Q₈	D₃
hypocenter	C₃	C₂×C₅×#556
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄×C₅×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₄×C₅×Q₈	C₂	semidirect
3. C₂×C₅×#944	C₂	semidirect
4. C₅×#5568	C₂	direct (N × H)
5. C₂×C₅×#898	C₂	semidirect
6. C₂×C₅×#896	C₂	semidirect
8. C₂×C₅×#887	C₂	semidirect
9. C₂×C₅×#876	C₂	semidirect
11. C₂×C₅×#872	C₂	semidirect
12. C₂×C₄×C₅×Dic₆	C₂	semidirect
19. C₃×C₄×C₅×Q₈	C₂²	semidirect
25. C₅×#944	C₂²	semidirect
40. C₅×#898	C₂²	semidirect
41. C₅×#896	C₂²	semidirect
43. C₅×#887	C₂²	semidirect
44. C₅×#876	C₂²	semidirect
46. C₅×#872	C₂²	semidirect
47. C₄×C₅×Dic₆	C₂²	semidirect
48. C₂×#5568	C₅	direct (N × H)
58. C₂×C₄×C₅×Q₈	D₃	semidirect
100. C₂×C₃×C₄×Q₈	C₂×C₅	semidirect
102. C₂×#944	C₂×C₅	semidirect
103. #5568	C₂×C₅	direct (N × H)
104. C₂×#898	C₂×C₅	semidirect
105. C₂×#896	C₂×C₅	semidirect
107. C₂×#887	C₂×C₅	semidirect
108. C₂×#876	C₂×C₅	semidirect
110. C₂×#872	C₂×C₅	semidirect
111. C₂×C₄×Dic₆	C₂×C₅	semidirect
125. C₄×C₅×Q₈	C₂×D₃	semidirect
182. C₃×C₄×Q₈	C₂²×C₅	semidirect
188. #944	C₂²×C₅	semidirect
203. #898	C₂²×C₅	semidirect
204. #896	C₂²×C₅	semidirect
206. #887	C₂²×C₅	semidirect
207. #876	C₂²×C₅	semidirect
209. #872	C₂²×C₅	semidirect
210. C₄×Dic₆	C₂²×C₅	semidirect
259. C₂×C₄×Q₈	C₅×D₃	semidirect
362. C₄×Q₈	C₂×C₅×D₃	semidirect
383. C₂×C₃×C₅	#556	semidirect
475. C₃×C₅	C₂×#556	semidirect
495. C₂×C₅	#5568	direct (N × H)
529. C₂×C₃	C₅×#556	semidirect
534. C₅	C₂×#5568	direct (N × H)
553. C₃	C₂×C₅×#556	semidirect
555. C₂	C₅×#5568	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×C₄×C₅×Q₈	2
C₂×C₅×#947	2
C₂×C₅×#944	2
C₅×#5568	2
C₂×C₅×#898	2
C₂×C₅×#896	2
C₂×C₅×#893	2
C₂×C₅×#887	2
C₂×C₅×#876	2
C₂×C₅×#875	2
C₂×C₅×#872	2
C₂×C₄×C₅×Dic₆	2
C₂×C₅×#556	3
C₂×#5568	5

Subgroups — C2×C5×#5568 #14484000

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5568 #14484000