Subgroups — C₂×C₅×#5644 #14480773

Order 1920.

2672 conjugacy classes of subgroups.

The subgroup lattice has 600 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, complemented
2	C₂×C₅×#947	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×#930	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₅×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5644	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₅×#898	C₂	1	2	yes	maximal, complemented
7	C₂×C₅×#895	C₂	1	2	yes	maximal, complemented
8	C₂×C₅×#894	C₂	1	2	yes	maximal, complemented
9	C₂×C₅×#882	C₂	1	2	yes	maximal, complemented
10	C₂×C₅×#67⋊C₄	C₂	1	2	yes	maximal, complemented
11	C₂×C₅×#538	—	3	1	no	maximal, Hall
12	C₂⁴×C₅×D₃	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
14	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
15	C₂²×C₅×#67	C₂²	1	2	yes	—
16	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
17	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
18	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
19	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	complemented
21	C₃×C₅×C₂²⋊Q₈	C₂²	1	8	yes	complemented
22	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
24	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₅×#947	C₂²	1	16	yes	complemented
26	C₅×#930	C₂²	1	8	yes	complemented
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×(C₂×D₃)⋊C₄	C₂²	1	8	yes	complemented
32	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
33	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
34	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	complemented
36	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	complemented
37	C₅×#898	C₂²	1	16	yes	complemented
38	C₅×#895	C₂²	1	16	yes	complemented
39	C₅×#894	C₂²	1	16	yes	complemented
40	C₅×#882	C₂²	1	16	yes	complemented
41	C₅×#67⋊C₄	C₂²	1	16	yes	complemented
42	C₂×#5644	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×#538	—	3	16	no	—
44	C₂×C₅×#126	—	3	2	no	—
45	C₂×C₅×#124	—	3	2	no	—
46	C₂×C₅×#123	—	3	2	no	—
47	C₂×C₅×C₂²⋊Q₈	D₃	1	1	yes	characteristic, complemented
48	C₂×C₅×#121	—	3	1	no	—
49	C₂×C₅×#121	—	3	2	no	—
50	C₂×C₅×#120	—	3	2	no	—
51	C₂×C₄×C₅×D₄	—	3	2	no	—
52	C₂²×C₅×C₂²⋊C₄	—	3	1	no	—
53	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
54	C₂³×C₅×D₃	—	2	4	no	—
55	C₂³×C₅×D₃	—	4	2	no	—
56	C₂³×C₅×D₃	—	4	2	no	—
57	C₂³×C₅×D₃	C₂³	1	2	yes	—
58	C₂³×C₅×D₃	C₂³	1	2	yes	—
59	C₂³×C₅×D₃	C₂³	1	4	yes	—
60	C₂×C₃×C₅×Q₈	—	4	2	no	—
61	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	complemented
62	C₂²×C₃×C₄×C₅	—	4	2	no	—
63	C₂²×C₃×C₄×C₅	C₂³	1	2	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	1	yes	characteristic
67	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
68	C₂×C₅×#67	—	2	8	no	—
69	C₂×C₅×#67	C₂³	1	8	yes	—
70	C₂²×C₅×Dic₃	—	4	2	no	—
71	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
72	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
73	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
74	C₂×C₅×D₁₂	—	4	4	no	—
75	C₂×C₅×D₁₂	—	4	4	no	—
76	C₂×C₅×D₁₂	—	4	2	no	—
77	C₂×C₅×D₁₂	C₂³	1	8	yes	—
78	C₂×C₅×D₁₂	C₂³	1	8	yes	—
79	C₂×C₅×D₁₂	C₂³	1	4	yes	complemented
80	C₂×C₄×C₅×D₃	—	4	4	no	—
81	C₂×C₄×C₅×D₃	C₂³	1	8	yes	complemented
82	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	complemented
83	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	complemented
84	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
85	C₅×(C₂×D₃)⋊C₄	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	complemented
90	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	complemented
91	C₅×C₄⋊Dic₃	C₂³	1	4	yes	complemented
92	C₅×Dic₃⋊C₄	C₂³	1	8	yes	complemented
93	C₄×C₅×Dic₃	C₂³	1	8	yes	complemented
94	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
95	C₂×#947	C₂×C₅	1	2	yes	complemented
96	C₂×#930	C₂×C₅	1	1	yes	characteristic, complemented
97	C₂²×(C₂×D₃)⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
98	#5644	C₂×C₅	1	16	yes	direct product factor
99	C₂×#898	C₂×C₅	1	2	yes	complemented
100	C₂×#895	C₂×C₅	1	2	yes	complemented
101	C₂×#894	C₂×C₅	1	2	yes	complemented
102	C₂×#882	C₂×C₅	1	2	yes	complemented
103	C₂×#67⋊C₄	C₂×C₅	1	2	yes	complemented
104	C₂⁵×C₅	—	3	1	no	—
105	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
106	C₂²×C₅×D₄	—	3	2	no	—
107	C₂²×C₅×D₄	—	3	2	no	—
108	C₂²×C₅×D₄	—	3	2	no	—
109	C₂²×C₅×D₄	—	3	1	no	—
110	C₂³×C₄×C₅	—	3	1	no	—
111	C₂³×C₄×C₅	—	3	2	no	—
112	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
113	C₅×#126	—	3	16	no	—
114	C₅×#124	—	3	16	no	—
115	C₅×#123	—	3	16	no	—
116	C₅×C₂²⋊Q₈	C₂×D₃	1	8	yes	complemented
117	C₅×#121	—	3	8	no	—
118	C₅×#121	—	3	16	no	—
119	C₅×#120	—	3	16	no	—
120	C₄×C₅×D₄	—	3	16	no	—
121	C₂×C₅×C₄⋊C₄	—	3	2	no	—
122	C₂×C₅×C₄⋊C₄	—	3	1	no	—
123	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	complemented
124	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
125	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
126	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
127	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
128	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
129	C₂×C₅×C₂²⋊C₄	—	3	8	no	—
130	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
131	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
132	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
133	C₂×C₄²×C₅	—	3	2	no	—
134	C₂×#538	—	3	1	no	Sylow
135	C₂³×C₃×C₅	—	2	2	no	—
136	C₂³×C₃×C₅	—	2	2	no	—
137	C₂³×C₃×C₅	#41	1	4	yes	—
138	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
139	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
140	C₂²×C₅×D₃	—	2	4	no	—
141	C₂²×C₅×D₃	—	2	8	no	—
142	C₂²×C₅×D₃	—	2	4	no	—
143	C₂²×C₅×D₃	—	2	4	no	—
144	C₂²×C₅×D₃	—	2	4	no	—
145	C₂²×C₅×D₃	—	2	4	no	—
146	C₂²×C₅×D₃	—	2	4	no	—
147	C₂²×C₅×D₃	—	4	4	no	—
148	C₂²×C₅×D₃	—	4	4	no	—
149	C₂²×C₅×D₃	—	4	16	no	—
150	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
151	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
152	C₃×C₅×Q₈	—	4	4	no	—
153	C₂×C₃×C₄×C₅	—	2	4	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	—	4	4	no	—
158	C₂×C₃×C₄×C₅	C₂⁴	1	4	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	C₅×#67	—	2	16	no	—
163	C₂×C₅×Dic₃	—	2	4	no	—
164	C₂×C₅×Dic₃	—	2	4	no	—
165	C₂×C₅×Dic₃	—	4	4	no	—
166	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
167	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
168	C₅×D₁₂	—	4	8	no	—
169	C₅×D₁₂	—	4	8	no	—
170	C₅×D₁₂	—	4	4	no	—
171	C₄×C₅×D₃	—	4	8	no	—
172	C₂⁴×D₃	C₂²×C₅	1	1	yes	characteristic
173	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
174	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
175	C₂²×#67	C₂²×C₅	1	2	yes	—
176	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
177	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
178	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
179	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
180	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	complemented
181	C₃×C₂²⋊Q₈	C₂²×C₅	1	8	yes	complemented
182	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
183	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
184	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
185	#947	C₂²×C₅	1	16	yes	complemented
186	#930	C₂²×C₅	1	8	yes	complemented
187	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
188	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
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	8	yes	complemented
192	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
193	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
194	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
195	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	complemented
196	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	complemented
197	#898	C₂²×C₅	1	16	yes	complemented
198	#895	C₂²×C₅	1	16	yes	complemented
199	#894	C₂²×C₅	1	16	yes	complemented
200	#882	C₂²×C₅	1	16	yes	complemented
201	#67⋊C₄	C₂²×C₅	1	16	yes	complemented
202	C₂⁴×C₅	—	3	2	no	—
203	C₂⁴×C₅	—	3	2	no	—
204	C₂⁴×C₅	—	3	4	no	—
205	C₂⁴×C₅	—	6	4	no	—
206	C₂⁴×C₅	—	12	2	no	—
207	C₂⁴×C₅	—	12	2	no	—
208	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
209	C₂×C₅×Q₈	—	4	2	no	—
210	C₂×C₅×Q₈	C₂²×D₃	1	4	yes	complemented
211	C₂×C₅×D₄	—	3	8	no	—
212	C₂×C₅×D₄	—	3	8	no	—
213	C₂×C₅×D₄	—	3	8	no	—
214	C₂×C₅×D₄	—	3	4	no	—
215	C₂×C₅×D₄	—	6	8	no	—
216	C₂×C₅×D₄	—	12	2	no	—
217	C₂×C₅×D₄	—	12	4	no	—
218	C₂×C₅×D₄	—	12	4	no	—
219	C₂²×C₄×C₅	—	3	2	no	—
220	C₂²×C₄×C₅	—	3	2	no	—
221	C₂²×C₄×C₅	—	3	4	no	—
222	C₂²×C₄×C₅	—	3	8	no	—
223	C₂²×C₄×C₅	—	4	2	no	—
224	C₂²×C₄×C₅	—	12	4	no	—
225	C₂²×C₄×C₅	—	12	2	no	—
226	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
227	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
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	4	yes	—
231	C₅×C₄⋊C₄	—	3	8	no	—
232	C₅×C₄⋊C₄	—	3	4	no	—
233	C₅×C₄⋊C₄	C₂²×D₃	1	8	yes	complemented
234	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	complemented
235	C₅×C₂²⋊C₄	—	3	8	no	—
236	C₅×C₂²⋊C₄	—	3	8	no	—
237	C₅×C₂²⋊C₄	—	3	8	no	—
238	C₅×C₂²⋊C₄	—	3	8	no	—
239	C₅×C₂²⋊C₄	—	3	8	no	—
240	C₅×C₂²⋊C₄	—	3	8	no	—
241	C₅×C₂²⋊C₄	C₂²×D₃	1	8	yes	—
242	C₄²×C₅	—	3	8	no	—
243	#538	—	3	16	no	—
244	C₂×#126	—	3	2	no	—
245	C₂×#124	—	3	2	no	—
246	C₂×#123	—	3	2	no	—
247	C₂×C₂²⋊Q₈	C₅×D₃	1	1	yes	characteristic, complemented
248	C₂×#121	—	3	1	no	—
249	C₂×#121	—	3	2	no	—
250	C₂×#120	—	3	2	no	—
251	C₂×C₄×D₄	—	3	2	no	—
252	C₂²×C₂²⋊C₄	—	3	1	no	—
253	C₂²×C₃×C₅	—	2	8	no	—
254	C₂²×C₃×C₅	—	2	2	no	—
255	C₂²×C₃×C₅	—	2	2	no	—
256	C₂²×C₃×C₅	C₂×#41	1	4	yes	—
257	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
258	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
259	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
260	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
261	C₂×C₅×D₃	—	2	4	no	—
262	C₂×C₅×D₃	—	2	4	no	—
263	C₂×C₅×D₃	—	2	4	no	—
264	C₂×C₅×D₃	—	2	4	no	—
265	C₂×C₅×D₃	—	2	4	no	—
266	C₂×C₅×D₃	—	2	4	no	—
267	C₂×C₅×D₃	—	4	16	no	—
268	C₂×C₅×D₃	—	4	8	no	—
269	C₂×C₅×D₃	—	4	8	no	—
270	C₃×C₄×C₅	—	2	4	no	—
271	C₃×C₄×C₅	—	2	2	no	—
272	C₃×C₄×C₅	—	2	4	no	—
273	C₃×C₄×C₅	—	2	2	no	—
274	C₅×Dic₃	—	2	4	no	—
275	C₅×Dic₃	—	2	4	no	—
276	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
277	C₂³×D₃	—	2	4	no	—
278	C₂³×D₃	—	4	2	no	—
279	C₂³×D₃	—	4	2	no	—
280	C₂³×D₃	C₂³×C₅	1	2	yes	—
281	C₂³×D₃	C₂³×C₅	1	2	yes	—
282	C₂³×D₃	C₂³×C₅	1	4	yes	—
283	C₂×C₃×Q₈	—	4	2	no	—
284	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	complemented
285	C₂²×C₃×C₄	—	4	2	no	—
286	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
287	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
288	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
289	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
290	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
291	C₂×#67	—	2	8	no	—
292	C₂×#67	C₂³×C₅	1	8	yes	—
293	C₂²×Dic₃	—	4	2	no	—
294	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
295	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
296	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
297	C₂×D₁₂	—	4	4	no	—
298	C₂×D₁₂	—	4	4	no	—
299	C₂×D₁₂	—	4	2	no	—
300	C₂×D₁₂	C₂³×C₅	1	8	yes	—
301	C₂×D₁₂	C₂³×C₅	1	8	yes	—
302	C₂×D₁₂	C₂³×C₅	1	4	yes	complemented
303	C₂×C₄×D₃	—	4	4	no	—
304	C₂×C₄×D₃	C₂³×C₅	1	8	yes	complemented
305	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	complemented
306	C₃×C₄⋊C₄	C₂³×C₅	1	8	yes	complemented
307	C₃×C₂²⋊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	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
311	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
312	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	complemented
313	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	complemented
314	C₄⋊Dic₃	C₂³×C₅	1	4	yes	complemented
315	Dic₃⋊C₄	C₂³×C₅	1	8	yes	complemented
316	C₄×Dic₃	C₂³×C₅	1	8	yes	complemented
317	C₂³×C₅	—	2	2	no	—
318	C₂³×C₅	—	2	2	no	—
319	C₂³×C₅	—	3	4	no	—
320	C₂³×C₅	—	3	4	no	—
321	C₂³×C₅	—	6	4	no	—
322	C₂³×C₅	—	6	4	no	—
323	C₂³×C₅	—	6	4	no	—
324	C₂³×C₅	—	6	8	no	—
325	C₂³×C₅	—	6	4	no	—
326	C₂³×C₅	—	6	4	no	—
327	C₂³×C₅	—	6	4	no	—
328	C₂³×C₅	—	12	4	no	—
329	C₂³×C₅	—	12	4	no	—
330	C₂³×C₅	—	12	16	no	—
331	C₂³×C₅	#239	1	4	yes	—
332	C₂³×C₅	C₂³×D₃	1	2	yes	—
333	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
334	C₅×Q₈	—	4	4	no	—
335	C₅×D₄	—	6	16	no	—
336	C₅×D₄	—	12	4	no	—
337	C₅×D₄	—	12	8	no	—
338	C₅×D₄	—	12	8	no	—
339	C₂×C₄×C₅	—	2	2	no	—
340	C₂×C₄×C₅	—	2	2	no	—
341	C₂×C₄×C₅	—	2	4	no	—
342	C₂×C₄×C₅	—	2	4	no	—
343	C₂×C₄×C₅	—	3	4	no	—
344	C₂×C₄×C₅	—	3	4	no	—
345	C₂×C₄×C₅	—	4	4	no	—
346	C₂×C₄×C₅	—	6	4	no	—
347	C₂×C₄×C₅	—	6	4	no	—
348	C₂×C₄×C₅	—	12	8	no	—
349	C₂×C₄×C₅	—	12	4	no	—
350	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
351	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
352	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
353	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
354	C₂⁵	—	3	1	no	—
355	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
356	C₂²×D₄	—	3	2	no	—
357	C₂²×D₄	—	3	2	no	—
358	C₂²×D₄	—	3	2	no	—
359	C₂²×D₄	—	3	1	no	—
360	C₂³×C₄	—	3	1	no	—
361	C₂³×C₄	—	3	2	no	—
362	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
363	#126	—	3	16	no	—
364	#124	—	3	16	no	—
365	#123	—	3	16	no	—
366	C₂²⋊Q₈	C₂×C₅×D₃	1	8	yes	complemented
367	#121	—	3	8	no	—
368	#121	—	3	16	no	—
369	#120	—	3	16	no	—
370	C₄×D₄	—	3	16	no	—
371	C₂×C₄⋊C₄	—	3	2	no	—
372	C₂×C₄⋊C₄	—	3	1	no	—
373	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	complemented
374	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
375	C₂×C₂²⋊C₄	—	3	2	no	—
376	C₂×C₂²⋊C₄	—	3	2	no	—
377	C₂×C₂²⋊C₄	—	3	8	no	—
378	C₂×C₂²⋊C₄	—	3	2	no	—
379	C₂×C₂²⋊C₄	—	3	2	no	—
380	C₂×C₂²⋊C₄	—	3	2	no	—
381	C₂×C₂²⋊C₄	—	3	2	no	—
382	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
383	C₂×C₄²	—	3	2	no	—
384	C₂×C₃×C₅	—	2	4	no	—
385	C₂×C₃×C₅	#538	1	4	yes	complemented
386	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
387	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
388	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
389	C₅×D₃	—	4	4	no	—
390	C₅×D₃	—	4	4	no	—
391	C₂³×C₃	—	2	2	no	—
392	C₂³×C₃	—	2	2	no	—
393	C₂³×C₃	C₅×#41	1	4	yes	—
394	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
395	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
396	C₂²×D₃	—	2	4	no	—
397	C₂²×D₃	—	2	8	no	—
398	C₂²×D₃	—	2	4	no	—
399	C₂²×D₃	—	2	4	no	—
400	C₂²×D₃	—	2	4	no	—
401	C₂²×D₃	—	2	4	no	—
402	C₂²×D₃	—	2	4	no	—
403	C₂²×D₃	—	4	4	no	—
404	C₂²×D₃	—	4	4	no	—
405	C₂²×D₃	—	4	16	no	—
406	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
407	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
408	C₃×Q₈	—	4	4	no	—
409	C₂×C₃×C₄	—	2	4	no	—
410	C₂×C₃×C₄	—	2	2	no	—
411	C₂×C₃×C₄	—	2	4	no	—
412	C₂×C₃×C₄	—	2	2	no	—
413	C₂×C₃×C₄	—	4	4	no	—
414	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
415	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
416	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
417	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
418	#67	—	2	16	no	—
419	C₂×Dic₃	—	2	4	no	—
420	C₂×Dic₃	—	2	4	no	—
421	C₂×Dic₃	—	4	4	no	—
422	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
423	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
424	D₁₂	—	4	8	no	—
425	D₁₂	—	4	8	no	—
426	D₁₂	—	4	4	no	—
427	C₄×D₃	—	4	8	no	—
428	C₂²×C₅	—	2	8	no	—
429	C₂²×C₅	—	2	2	no	—
430	C₂²×C₅	—	2	2	no	—
431	C₂²×C₅	—	6	4	no	—
432	C₂²×C₅	—	6	4	no	—
433	C₂²×C₅	—	6	4	no	—
434	C₂²×C₅	—	6	4	no	—
435	C₂²×C₅	—	6	4	no	—
436	C₂²×C₅	—	6	4	no	—
437	C₂²×C₅	—	12	16	no	—
438	C₂²×C₅	—	12	8	no	—
439	C₂²×C₅	—	12	8	no	—
440	C₂²×C₅	#1004	1	2	yes	—
441	C₂²×C₅	C₂×#239	1	4	yes	—
442	C₂²×C₅	C₂×#239	1	2	yes	—
443	C₂²×C₅	#1009	1	2	yes	—
444	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
445	C₄×C₅	—	2	2	no	—
446	C₄×C₅	—	2	2	no	—
447	C₄×C₅	—	2	4	no	—
448	C₄×C₅	—	2	4	no	—
449	C₄×C₅	—	6	4	no	—
450	C₄×C₅	—	6	4	no	—
451	C₂⁴	—	3	2	no	—
452	C₂⁴	—	3	2	no	—
453	C₂⁴	—	3	4	no	—
454	C₂⁴	—	6	4	no	—
455	C₂⁴	—	12	2	no	—
456	C₂⁴	—	12	2	no	—
457	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
458	C₂×Q₈	—	4	2	no	—
459	C₂×Q₈	C₂²×C₅×D₃	1	4	yes	complemented
460	C₂×D₄	—	3	8	no	—
461	C₂×D₄	—	3	8	no	—
462	C₂×D₄	—	3	8	no	—
463	C₂×D₄	—	3	4	no	—
464	C₂×D₄	—	6	8	no	—
465	C₂×D₄	—	12	2	no	—
466	C₂×D₄	—	12	4	no	—
467	C₂×D₄	—	12	4	no	—
468	C₂²×C₄	—	3	2	no	—
469	C₂²×C₄	—	3	2	no	—
470	C₂²×C₄	—	3	4	no	—
471	C₂²×C₄	—	3	8	no	—
472	C₂²×C₄	—	4	2	no	—
473	C₂²×C₄	—	12	4	no	—
474	C₂²×C₄	—	12	2	no	—
475	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
476	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
477	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
478	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
479	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
480	C₄⋊C₄	—	3	8	no	—
481	C₄⋊C₄	—	3	4	no	—
482	C₄⋊C₄	C₂²×C₅×D₃	1	8	yes	complemented
483	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	complemented
484	C₂²⋊C₄	—	3	8	no	—
485	C₂²⋊C₄	—	3	8	no	—
486	C₂²⋊C₄	—	3	8	no	—
487	C₂²⋊C₄	—	3	8	no	—
488	C₂²⋊C₄	—	3	8	no	—
489	C₂²⋊C₄	—	3	8	no	—
490	C₂²⋊C₄	C₂²×C₅×D₃	1	8	yes	—
491	C₄²	—	3	8	no	—
492	C₃×C₅	C₂×#538	1	1	yes	characteristic, complemented, Hall
493	C₂²×C₃	—	2	8	no	—
494	C₂²×C₃	—	2	2	no	—
495	C₂²×C₃	—	2	2	no	—
496	C₂²×C₃	C₂×C₅×#41	1	4	yes	—
497	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
498	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
499	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
500	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
501	C₂×D₃	—	2	4	no	—
502	C₂×D₃	—	2	4	no	—
503	C₂×D₃	—	2	4	no	—
504	C₂×D₃	—	2	4	no	—
505	C₂×D₃	—	2	4	no	—
506	C₂×D₃	—	2	4	no	—
507	C₂×D₃	—	4	16	no	—
508	C₂×D₃	—	4	8	no	—
509	C₂×D₃	—	4	8	no	—
510	C₃×C₄	—	2	4	no	—
511	C₃×C₄	—	2	2	no	—
512	C₃×C₄	—	2	4	no	—
513	C₃×C₄	—	2	2	no	—
514	Dic₃	—	2	4	no	—
515	Dic₃	—	2	4	no	—
516	C₂×C₅	—	2	4	no	—
517	C₂×C₅	—	12	4	no	—
518	C₂×C₅	—	12	4	no	—
519	C₂×C₅	#5644	1	4	yes	direct product factor
520	C₂×C₅	C₂×#1004	1	1	yes	characteristic
521	C₂×C₅	C₂²×#239	1	1	yes	characteristic
522	C₂×C₅	C₂×#1009	1	1	yes	characteristic
523	C₂³	—	2	2	no	—
524	C₂³	—	2	2	no	—
525	C₂³	—	3	4	no	—
526	C₂³	—	3	4	no	—
527	C₂³	—	6	4	no	—
528	C₂³	—	6	4	no	—
529	C₂³	—	6	4	no	—
530	C₂³	—	6	8	no	—
531	C₂³	—	6	4	no	—
532	C₂³	—	6	4	no	—
533	C₂³	—	6	4	no	—
534	C₂³	—	12	4	no	—
535	C₂³	—	12	4	no	—
536	C₂³	—	12	16	no	—
537	C₂³	C₅×#239	1	4	yes	—
538	C₂³	C₂³×C₅×D₃	1	2	yes	—
539	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
540	Q₈	—	4	4	no	—
541	D₄	—	6	16	no	—
542	D₄	—	12	4	no	—
543	D₄	—	12	8	no	—
544	D₄	—	12	8	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	4	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	3	4	no	—
550	C₂×C₄	—	3	4	no	—
551	C₂×C₄	—	4	4	no	—
552	C₂×C₄	—	6	4	no	—
553	C₂×C₄	—	6	4	no	—
554	C₂×C₄	—	12	8	no	—
555	C₂×C₄	—	12	4	no	—
556	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
557	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
558	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
559	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
560	C₂×C₃	—	2	4	no	—
561	C₂×C₃	C₅×#538	1	4	yes	complemented
562	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
563	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
564	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
565	D₃	—	4	4	no	—
566	D₃	—	4	4	no	—
567	C₅	C₂×#5644	1	1	yes	characteristic, direct product factor, Sylow
568	C₂²	—	2	2	no	—
569	C₂²	—	2	2	no	—
570	C₂²	—	2	8	no	—
571	C₂²	—	6	4	no	—
572	C₂²	—	6	4	no	—
573	C₂²	—	6	4	no	—
574	C₂²	—	6	4	no	—
575	C₂²	—	6	4	no	—
576	C₂²	—	6	4	no	—
577	C₂²	—	12	16	no	—
578	C₂²	—	12	8	no	—
579	C₂²	—	12	8	no	—
580	C₂²	C₅×#1004	1	2	yes	—
581	C₂²	C₂×C₅×#239	1	4	yes	—
582	C₂²	C₂×C₅×#239	1	2	yes	—
583	C₂²	C₅×#1009	1	2	yes	—
584	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
585	C₄	—	2	2	no	—
586	C₄	—	2	2	no	—
587	C₄	—	2	4	no	—
588	C₄	—	2	4	no	—
589	C₄	—	6	4	no	—
590	C₄	—	6	4	no	—
591	C₃	C₂×C₅×#538	1	1	yes	characteristic, complemented, Sylow
592	C₂	—	2	4	no	—
593	C₂	—	12	4	no	—
594	C₂	—	12	4	no	—
595	C₂	C₅×#5644	1	4	yes	direct product factor
596	C₂	C₂×C₅×#1004	1	1	yes	characteristic
597	C₂	C₂²×C₅×#239	1	1	yes	characteristic
598	C₂	C₂×C₅×#1009	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
hypercenter	C₂×C₅×C₂²⋊Q₈	D₃
hypocenter	C₃	C₂×C₅×#538
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. C₂×C₃×C₅×C₂²⋊Q₈	C₂	semidirect
2. C₂×C₅×#947	C₂	semidirect
3. C₂×C₅×#930	C₂	semidirect
4. C₂²×C₅×(C₂×D₃)⋊C₄	C₂	semidirect
5. C₅×#5644	C₂	direct (N × H)
6. C₂×C₅×#898	C₂	semidirect
7. C₂×C₅×#895	C₂	semidirect
8. C₂×C₅×#894	C₂	semidirect
9. C₂×C₅×#882	C₂	semidirect
10. C₂×C₅×#67⋊C₄	C₂	semidirect
13. C₂²×C₃×C₅×Q₈	C₂²	semidirect
19. C₂²×C₅×D₁₂	C₂²	semidirect
20. C₂²×C₄×C₅×D₃	C₂²	semidirect
21. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
22. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
23. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
25. C₅×#947	C₂²	semidirect
26. C₅×#930	C₂²	semidirect
31. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
32. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
33. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
34. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
35. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
36. C₂×C₄×C₅×Dic₃	C₂²	semidirect
37. C₅×#898	C₂²	semidirect
38. C₅×#895	C₂²	semidirect
39. C₅×#894	C₂²	semidirect
40. C₅×#882	C₂²	semidirect
41. C₅×#67⋊C₄	C₂²	semidirect
42. C₂×#5644	C₅	direct (N × H)
47. C₂×C₅×C₂²⋊Q₈	D₃	semidirect
61. C₂×C₃×C₅×Q₈	C₂³	semidirect
79. C₂×C₅×D₁₂	C₂³	semidirect
81. C₂×C₄×C₅×D₃	C₂³	semidirect
82. C₃×C₅×C₄⋊C₄	C₂³	semidirect
83. C₃×C₅×C₄⋊C₄	C₂³	semidirect
89. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
90. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
91. C₅×C₄⋊Dic₃	C₂³	semidirect
92. C₅×Dic₃⋊C₄	C₂³	semidirect
93. C₄×C₅×Dic₃	C₂³	semidirect
94. C₂×C₃×C₂²⋊Q₈	C₂×C₅	semidirect
95. C₂×#947	C₂×C₅	semidirect
96. C₂×#930	C₂×C₅	semidirect
97. C₂²×(C₂×D₃)⋊C₄	C₂×C₅	semidirect
98. #5644	C₂×C₅	direct (N × H)
99. C₂×#898	C₂×C₅	semidirect
100. C₂×#895	C₂×C₅	semidirect
101. C₂×#894	C₂×C₅	semidirect
102. C₂×#882	C₂×C₅	semidirect
103. C₂×#67⋊C₄	C₂×C₅	semidirect
105. C₂²×C₅×Q₈	C₂×D₃	semidirect
116. C₅×C₂²⋊Q₈	C₂×D₃	semidirect
123. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
124. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
173. C₂²×C₃×Q₈	C₂²×C₅	semidirect
179. C₂²×D₁₂	C₂²×C₅	semidirect
180. C₂²×C₄×D₃	C₂²×C₅	semidirect
181. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
182. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
183. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
185. #947	C₂²×C₅	semidirect
186. #930	C₂²×C₅	semidirect
191. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
192. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
193. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
194. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
195. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
196. C₂×C₄×Dic₃	C₂²×C₅	semidirect
197. #898	C₂²×C₅	semidirect
198. #895	C₂²×C₅	semidirect
199. #894	C₂²×C₅	semidirect
200. #882	C₂²×C₅	semidirect
201. #67⋊C₄	C₂²×C₅	semidirect
210. C₂×C₅×Q₈	C₂²×D₃	semidirect
233. C₅×C₄⋊C₄	C₂²×D₃	semidirect
234. C₅×C₄⋊C₄	C₂²×D₃	semidirect
247. C₂×C₂²⋊Q₈	C₅×D₃	semidirect
284. C₂×C₃×Q₈	C₂³×C₅	semidirect
302. C₂×D₁₂	C₂³×C₅	semidirect
304. C₂×C₄×D₃	C₂³×C₅	semidirect
305. C₃×C₄⋊C₄	C₂³×C₅	semidirect
306. C₃×C₄⋊C₄	C₂³×C₅	semidirect
312. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
313. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
314. C₄⋊Dic₃	C₂³×C₅	semidirect
315. Dic₃⋊C₄	C₂³×C₅	semidirect
316. C₄×Dic₃	C₂³×C₅	semidirect
355. C₂²×Q₈	C₂×C₅×D₃	semidirect
366. C₂²⋊Q₈	C₂×C₅×D₃	semidirect
373. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
374. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
385. C₂×C₃×C₅	#538	semidirect
459. C₂×Q₈	C₂²×C₅×D₃	semidirect
482. C₄⋊C₄	C₂²×C₅×D₃	semidirect
483. C₄⋊C₄	C₂²×C₅×D₃	semidirect
492. C₃×C₅	C₂×#538	semidirect
519. C₂×C₅	#5644	direct (N × H)
561. C₂×C₃	C₅×#538	semidirect
567. C₅	C₂×#5644	direct (N × H)
591. C₃	C₂×C₅×#538	semidirect
595. C₂	C₅×#5644	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×#947	2
C₂×C₅×#930	2
C₂²×C₅×(C₂×D₃)⋊C₄	2
C₅×#5644	2
C₂×C₅×#898	2
C₂×C₅×#895	2
C₂×C₅×#894	2
C₂×C₅×#882	2
C₂×C₅×#67⋊C₄	2
C₂×C₅×#538	3
C₂×#5644	5

Subgroups — C2×C5×#5644 #14480773

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5644 #14480773