Subgroups — C₂×C₅×#5511 #14483790

Order 1920.

2400 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	C₂²×C₃×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×C₅×#67	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₅×#67	C₂	1	2	yes	maximal
4	C₂×C₅×#924	C₂	1	2	yes	maximal, complemented
5	C₂×C₅×#924	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5511	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×D₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#889	C₂	1	2	yes	maximal, complemented
11	C₂×C₅×#888	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#887	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅×#554	—	3	1	no	maximal, Hall
14	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
15	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
16	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
17	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
19	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
20	C₂²×C₅×Dic₆	C₂²	1	2	yes	—
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
24	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	8	yes	complemented
25	C₂×C₅×#217	C₂²	1	2	yes	—
26	C₂×C₅×#217	C₂²	1	1	yes	characteristic
27	C₄×C₅×#67	C₂²	1	8	yes	—
28	C₄×C₅×#67	C₂²	1	16	yes	—
29	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
31	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
32	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
33	C₅×#924	C₂²	1	16	yes	complemented
34	C₅×#924	C₂²	1	8	yes	complemented
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	1	yes	characteristic
38	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
39	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
40	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
42	C₅×#897	C₂²	1	8	yes	complemented
43	C₅×#896	C₂²	1	16	yes	complemented
44	C₅×D₃×C₄⋊C₄	C₂²	1	8	yes	complemented
45	C₅×#889	C₂²	1	16	yes	complemented
46	C₅×#888	C₂²	1	8	yes	complemented
47	C₅×#887	C₂²	1	8	yes	complemented
48	C₂×#5511	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
49	C₅×#554	—	3	16	no	—
50	C₂×C₅×C₄⋊Q₈	—	3	1	no	—
51	C₂×C₅×#125	—	3	2	no	—
52	C₂×C₅×C₂²⋊Q₈	—	3	2	no	—
53	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
54	C₂×C₅×C₂²⋊Q₈	—	3	2	no	—
55	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
56	C₂×C₄×C₅×Q₈	—	3	1	no	—
57	C₂×C₄×C₅×D₄	—	3	2	no	—
58	C₂×C₄×C₅×D₄	—	3	1	no	—
59	C₂²×C₅×C₄⋊C₄	—	3	1	no	—
60	C₂²×C₅×C₄⋊C₄	D₃	1	1	yes	characteristic, complemented
61	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
62	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
63	C₂²×C₃×C₄×C₅	—	2	4	no	—
64	C₂²×C₃×C₄×C₅	—	4	4	no	—
65	C₂²×C₃×C₄×C₅	C₂³	1	2	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	4	yes	—
69	C₂²×C₃×C₄×C₅	C₂³	1	8	yes	—
70	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
71	C₂×C₅×#67	Q₈	1	8	yes	complemented
72	C₂×C₅×#67	C₂³	1	4	yes	—
73	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
74	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
75	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
76	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
77	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
78	C₂×C₄×C₅×D₃	—	2	4	no	—
79	C₂×C₄×C₅×D₃	—	4	4	no	—
80	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
81	C₂×C₄×C₅×D₃	C₂³	1	8	yes	—
82	C₂×C₅×Dic₆	—	2	4	no	—
83	C₂×C₅×Dic₆	—	4	4	no	—
84	C₂×C₅×Dic₆	C₂³	1	4	yes	—
85	C₂×C₅×Dic₆	C₂³	1	8	yes	—
86	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
87	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
88	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
89	C₅×#217	C₂³	1	8	yes	—
90	C₅×#217	C₂³	1	4	yes	—
91	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
92	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
93	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
94	C₅×C₄⋊Dic₃	C₂³	1	8	yes	—
95	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
96	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
97	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
98	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
99	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
100	C₄×C₅×Dic₃	C₂³	1	4	yes	—
101	C₄×C₅×Dic₃	C₂³	1	8	yes	—
102	C₂²×C₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
103	C₂×C₄×#67	C₂×C₅	1	1	yes	characteristic
104	C₂×C₄×#67	C₂×C₅	1	2	yes	—
105	C₂×#924	C₂×C₅	1	2	yes	complemented
106	C₂×#924	C₂×C₅	1	1	yes	characteristic, complemented
107	#5511	C₂×C₅	1	16	yes	direct product factor
108	C₂×#897	C₂×C₅	1	1	yes	characteristic, complemented
109	C₂×#896	C₂×C₅	1	2	yes	complemented
110	C₂×D₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
111	C₂×#889	C₂×C₅	1	2	yes	complemented
112	C₂×#888	C₂×C₅	1	1	yes	characteristic, complemented
113	C₂×#887	C₂×C₅	1	1	yes	characteristic, complemented
114	C₂²×C₅×Q₈	—	3	1	no	—
115	C₂²×C₅×Q₈	—	3	2	no	—
116	C₂²×C₅×D₄	—	3	1	no	—
117	C₂³×C₄×C₅	—	3	1	no	—
118	C₂³×C₄×C₅	—	3	2	no	—
119	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
120	C₂³×C₄×C₅	C₂×D₃	1	2	yes	—
121	C₅×C₄⋊Q₈	—	3	8	no	—
122	C₅×#125	—	3	16	no	—
123	C₅×C₂²⋊Q₈	—	3	16	no	—
124	C₅×C₂²⋊Q₈	—	3	8	no	—
125	C₅×C₂²⋊Q₈	—	3	16	no	—
126	C₅×C₂²⋊Q₈	—	3	8	no	—
127	C₄×C₅×Q₈	—	3	8	no	—
128	C₄×C₅×D₄	—	3	16	no	—
129	C₄×C₅×D₄	—	3	8	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	2	no	—
134	C₂×C₅×C₄⋊C₄	—	3	2	no	—
135	C₂×C₅×C₄⋊C₄	—	3	1	no	—
136	C₂×C₅×C₄⋊C₄	—	3	2	no	—
137	C₂×C₅×C₄⋊C₄	—	3	8	no	—
138	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
139	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
140	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
141	C₂×C₅×C₄⋊C₄	C₂×D₃	1	8	yes	complemented
142	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
143	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
144	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
145	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
146	C₂×C₄²×C₅	—	3	2	no	—
147	C₂×C₄²×C₅	—	3	1	no	—
148	C₂×#554	—	3	1	no	Sylow
149	C₂³×C₃×C₅	—	2	2	no	—
150	C₂³×C₃×C₅	—	2	2	no	—
151	C₂³×C₃×C₅	C₂×Q₈	1	4	yes	—
152	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
153	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
154	C₂²×C₅×D₃	—	2	2	no	—
155	C₂²×C₅×D₃	—	2	2	no	—
156	C₂²×C₅×D₃	C₂×Q₈	1	4	yes	—
157	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
158	C₂×C₃×C₄×C₅	—	2	2	no	—
159	C₂×C₃×C₄×C₅	—	2	4	no	—
160	C₂×C₃×C₄×C₅	—	2	4	no	—
161	C₂×C₃×C₄×C₅	—	2	8	no	—
162	C₂×C₃×C₄×C₅	—	4	8	no	—
163	C₂×C₃×C₄×C₅	#41	1	4	yes	—
164	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
165	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
166	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
167	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
168	C₅×#67	C₂×Q₈	1	16	yes	complemented
169	C₂×C₅×Dic₃	—	2	4	no	—
170	C₂×C₅×Dic₃	—	2	2	no	—
171	C₂×C₅×Dic₃	—	2	2	no	—
172	C₂×C₅×Dic₃	—	2	4	no	—
173	C₂×C₅×Dic₃	C₂×Q₈	1	4	yes	—
174	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
175	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
176	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
177	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
178	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
179	C₄×C₅×D₃	—	2	8	no	—
180	C₄×C₅×D₃	—	4	8	no	—
181	C₅×Dic₆	—	2	8	no	—
182	C₅×Dic₆	—	4	8	no	—
183	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
184	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
185	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
186	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
187	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
188	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
189	C₂²×Dic₆	C₂²×C₅	1	2	yes	—
190	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
191	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
192	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
193	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	8	yes	complemented
194	C₂×#217	C₂²×C₅	1	2	yes	—
195	C₂×#217	C₂²×C₅	1	1	yes	characteristic
196	C₄×#67	C₂²×C₅	1	8	yes	—
197	C₄×#67	C₂²×C₅	1	16	yes	—
198	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
199	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
200	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
201	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
202	#924	C₂²×C₅	1	16	yes	complemented
203	#924	C₂²×C₅	1	8	yes	complemented
204	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
205	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
206	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
207	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
208	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
209	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
210	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
211	#897	C₂²×C₅	1	8	yes	complemented
212	#896	C₂²×C₅	1	16	yes	complemented
213	D₃×C₄⋊C₄	C₂²×C₅	1	8	yes	complemented
214	#889	C₂²×C₅	1	16	yes	complemented
215	#888	C₂²×C₅	1	8	yes	complemented
216	#887	C₂²×C₅	1	8	yes	complemented
217	C₂⁴×C₅	—	3	1	no	—
218	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
219	C₂×C₅×Q₈	—	3	4	no	—
220	C₂×C₅×Q₈	—	3	8	no	—
221	C₂×C₅×Q₈	—	6	4	no	—
222	C₂×C₅×Q₈	—	12	4	no	—
223	C₂×C₅×D₄	—	3	8	no	—
224	C₂×C₅×D₄	—	3	4	no	—
225	C₂²×C₄×C₅	—	2	4	no	—
226	C₂²×C₄×C₅	—	3	1	no	—
227	C₂²×C₄×C₅	—	3	2	no	—
228	C₂²×C₄×C₅	—	3	1	no	—
229	C₂²×C₄×C₅	—	3	1	no	—
230	C₂²×C₄×C₅	—	3	2	no	—
231	C₂²×C₄×C₅	—	3	4	no	—
232	C₂²×C₄×C₅	—	3	8	no	—
233	C₂²×C₄×C₅	—	4	4	no	—
234	C₂²×C₄×C₅	—	6	4	no	—
235	C₂²×C₄×C₅	—	12	4	no	—
236	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
237	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
238	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
239	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
240	C₂²×C₄×C₅	C₂²×D₃	1	8	yes	—
241	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
242	C₅×C₄⋊C₄	—	3	8	no	—
243	C₅×C₄⋊C₄	—	3	4	no	—
244	C₅×C₄⋊C₄	—	3	4	no	—
245	C₅×C₄⋊C₄	—	3	8	no	—
246	C₅×C₄⋊C₄	—	3	8	no	—
247	C₅×C₄⋊C₄	—	3	8	no	—
248	C₅×C₄⋊C₄	—	3	8	no	—
249	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
250	C₅×C₄⋊C₄	C₂²×D₃	1	8	yes	—
251	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
252	C₅×C₂²⋊C₄	—	3	8	no	—
253	C₅×C₂²⋊C₄	—	3	4	no	—
254	C₅×C₂²⋊C₄	—	3	8	no	—
255	C₅×C₂²⋊C₄	—	3	4	no	—
256	C₄²×C₅	—	3	8	no	—
257	C₄²×C₅	—	3	4	no	—
258	#554	—	3	16	no	—
259	C₂×C₄⋊Q₈	—	3	1	no	—
260	C₂×#125	—	3	2	no	—
261	C₂×C₂²⋊Q₈	—	3	2	no	—
262	C₂×C₂²⋊Q₈	—	3	1	no	—
263	C₂×C₂²⋊Q₈	—	3	2	no	—
264	C₂×C₂²⋊Q₈	—	3	1	no	—
265	C₂×C₄×Q₈	—	3	1	no	—
266	C₂×C₄×D₄	—	3	2	no	—
267	C₂×C₄×D₄	—	3	1	no	—
268	C₂²×C₄⋊C₄	—	3	1	no	—
269	C₂²×C₄⋊C₄	C₅×D₃	1	1	yes	characteristic, complemented
270	C₂²×C₃×C₅	—	2	8	no	—
271	C₂²×C₃×C₅	—	2	2	no	—
272	C₂²×C₃×C₅	—	2	2	no	—
273	C₂²×C₃×C₅	C₂²×Q₈	1	4	yes	—
274	C₂²×C₃×C₅	C₂²×Q₈	1	2	yes	—
275	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
276	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
277	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
278	C₂×C₅×D₃	—	2	8	no	—
279	C₂×C₅×D₃	—	2	2	no	—
280	C₂×C₅×D₃	—	2	2	no	—
281	C₂×C₅×D₃	C₂²×Q₈	1	4	yes	—
282	C₃×C₄×C₅	—	2	2	no	—
283	C₃×C₄×C₅	—	2	4	no	—
284	C₃×C₄×C₅	—	2	4	no	—
285	C₃×C₄×C₅	C₂×#41	1	4	yes	—
286	C₅×Dic₃	—	2	4	no	—
287	C₅×Dic₃	—	2	2	no	—
288	C₅×Dic₃	—	2	2	no	—
289	C₅×Dic₃	—	2	4	no	—
290	C₅×Dic₃	C₂²×Q₈	1	4	yes	—
291	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
292	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
293	C₂²×C₃×C₄	—	2	4	no	—
294	C₂²×C₃×C₄	—	4	4	no	—
295	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
296	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
297	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
298	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
299	C₂²×C₃×C₄	C₂³×C₅	1	8	yes	—
300	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
301	C₂×#67	C₅×Q₈	1	8	yes	complemented
302	C₂×#67	C₂³×C₅	1	4	yes	—
303	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
304	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
305	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
306	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
307	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
308	C₂×C₄×D₃	—	2	4	no	—
309	C₂×C₄×D₃	—	4	4	no	—
310	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
311	C₂×C₄×D₃	C₂³×C₅	1	8	yes	—
312	C₂×Dic₆	—	2	4	no	—
313	C₂×Dic₆	—	4	4	no	—
314	C₂×Dic₆	C₂³×C₅	1	4	yes	—
315	C₂×Dic₆	C₂³×C₅	1	8	yes	—
316	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
317	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
318	C₃×C₄⋊C₄	C₂³×C₅	1	8	yes	—
319	#217	C₂³×C₅	1	8	yes	—
320	#217	C₂³×C₅	1	4	yes	—
321	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
322	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
323	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
324	C₄⋊Dic₃	C₂³×C₅	1	8	yes	—
325	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
326	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
327	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
328	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
329	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
330	C₄×Dic₃	C₂³×C₅	1	4	yes	—
331	C₄×Dic₃	C₂³×C₅	1	8	yes	—
332	C₂³×C₅	—	2	2	no	—
333	C₂³×C₅	—	2	2	no	—
334	C₂³×C₅	—	3	4	no	—
335	C₂³×C₅	—	3	2	no	—
336	C₂³×C₅	—	6	2	no	—
337	C₂³×C₅	—	6	2	no	—
338	C₂³×C₅	D₃×Q₈	1	4	yes	—
339	C₂³×C₅	C₂³×D₃	1	2	yes	—
340	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
341	C₅×Q₈	—	6	8	no	—
342	C₅×Q₈	—	12	8	no	—
343	C₅×D₄	—	3	16	no	—
344	C₂×C₄×C₅	—	2	2	no	—
345	C₂×C₄×C₅	—	2	4	no	—
346	C₂×C₄×C₅	—	2	4	no	—
347	C₂×C₄×C₅	—	2	8	no	—
348	C₂×C₄×C₅	—	3	4	no	—
349	C₂×C₄×C₅	—	3	2	no	—
350	C₂×C₄×C₅	—	3	4	no	—
351	C₂×C₄×C₅	—	3	2	no	—
352	C₂×C₄×C₅	—	3	2	no	—
353	C₂×C₄×C₅	—	3	4	no	—
354	C₂×C₄×C₅	—	4	8	no	—
355	C₂×C₄×C₅	—	6	2	no	—
356	C₂×C₄×C₅	—	6	4	no	—
357	C₂×C₄×C₅	—	6	4	no	—
358	C₂×C₄×C₅	—	6	2	no	—
359	C₂×C₄×C₅	—	6	8	no	—
360	C₂×C₄×C₅	—	12	8	no	—
361	C₂×C₄×C₅	#235	1	4	yes	—
362	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
363	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
364	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
365	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
366	C₂²×Q₈	—	3	1	no	—
367	C₂²×Q₈	—	3	2	no	—
368	C₂²×D₄	—	3	1	no	—
369	C₂³×C₄	—	3	1	no	—
370	C₂³×C₄	—	3	2	no	—
371	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
372	C₂³×C₄	C₂×C₅×D₃	1	2	yes	—
373	C₄⋊Q₈	—	3	8	no	—
374	#125	—	3	16	no	—
375	C₂²⋊Q₈	—	3	16	no	—
376	C₂²⋊Q₈	—	3	8	no	—
377	C₂²⋊Q₈	—	3	16	no	—
378	C₂²⋊Q₈	—	3	8	no	—
379	C₄×Q₈	—	3	8	no	—
380	C₄×D₄	—	3	16	no	—
381	C₄×D₄	—	3	8	no	—
382	C₂×C₄⋊C₄	—	3	2	no	—
383	C₂×C₄⋊C₄	—	3	1	no	—
384	C₂×C₄⋊C₄	—	3	1	no	—
385	C₂×C₄⋊C₄	—	3	2	no	—
386	C₂×C₄⋊C₄	—	3	2	no	—
387	C₂×C₄⋊C₄	—	3	2	no	—
388	C₂×C₄⋊C₄	—	3	2	no	—
389	C₂×C₄⋊C₄	—	3	8	no	—
390	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
391	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
392	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
393	C₂×C₄⋊C₄	C₂×C₅×D₃	1	8	yes	complemented
394	C₂×C₂²⋊C₄	—	3	2	no	—
395	C₂×C₂²⋊C₄	—	3	1	no	—
396	C₂×C₂²⋊C₄	—	3	2	no	—
397	C₂×C₂²⋊C₄	—	3	1	no	—
398	C₂×C₄²	—	3	2	no	—
399	C₂×C₄²	—	3	1	no	—
400	C₂×C₃×C₅	—	2	4	no	—
401	C₂×C₃×C₅	#554	1	4	yes	complemented
402	C₂×C₃×C₅	C₂³×Q₈	1	1	yes	characteristic
403	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
404	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
405	C₅×D₃	—	2	4	no	—
406	C₂³×C₃	—	2	2	no	—
407	C₂³×C₃	—	2	2	no	—
408	C₂³×C₃	C₂×C₅×Q₈	1	4	yes	—
409	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
410	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
411	C₂²×D₃	—	2	2	no	—
412	C₂²×D₃	—	2	2	no	—
413	C₂²×D₃	C₂×C₅×Q₈	1	4	yes	—
414	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
415	C₂×C₃×C₄	—	2	2	no	—
416	C₂×C₃×C₄	—	2	4	no	—
417	C₂×C₃×C₄	—	2	4	no	—
418	C₂×C₃×C₄	—	2	8	no	—
419	C₂×C₃×C₄	—	4	8	no	—
420	C₂×C₃×C₄	C₅×#41	1	4	yes	—
421	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
422	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
423	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
424	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
425	#67	C₂×C₅×Q₈	1	16	yes	complemented
426	C₂×Dic₃	—	2	4	no	—
427	C₂×Dic₃	—	2	2	no	—
428	C₂×Dic₃	—	2	2	no	—
429	C₂×Dic₃	—	2	4	no	—
430	C₂×Dic₃	C₂×C₅×Q₈	1	4	yes	—
431	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
432	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
433	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
434	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
435	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
436	C₄×D₃	—	2	8	no	—
437	C₄×D₃	—	4	8	no	—
438	Dic₆	—	2	8	no	—
439	Dic₆	—	4	8	no	—
440	C₂²×C₅	—	2	2	no	—
441	C₂²×C₅	—	2	2	no	—
442	C₂²×C₅	—	2	8	no	—
443	C₂²×C₅	—	3	4	no	—
444	C₂²×C₅	—	6	2	no	—
445	C₂²×C₅	—	6	2	no	—
446	C₂²×C₅	—	6	8	no	—
447	C₂²×C₅	C₂×#235	1	2	yes	—
448	C₂²×C₅	#1004	1	2	yes	—
449	C₂²×C₅	C₂×D₃×Q₈	1	4	yes	—
450	C₂²×C₅	C₂×D₃×Q₈	1	2	yes	—
451	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
452	C₄×C₅	—	2	2	no	—
453	C₄×C₅	—	2	4	no	—
454	C₄×C₅	—	2	4	no	—
455	C₄×C₅	—	3	4	no	—
456	C₄×C₅	—	6	2	no	—
457	C₄×C₅	—	6	4	no	—
458	C₄×C₅	—	6	4	no	—
459	C₄×C₅	—	6	2	no	—
460	C₄×C₅	C₂×#235	1	4	yes	—
461	C₂⁴	—	3	1	no	—
462	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
463	C₂×Q₈	—	3	4	no	—
464	C₂×Q₈	—	3	8	no	—
465	C₂×Q₈	—	6	4	no	—
466	C₂×Q₈	—	12	4	no	—
467	C₂×D₄	—	3	8	no	—
468	C₂×D₄	—	3	4	no	—
469	C₂²×C₄	—	2	4	no	—
470	C₂²×C₄	—	3	1	no	—
471	C₂²×C₄	—	3	2	no	—
472	C₂²×C₄	—	3	1	no	—
473	C₂²×C₄	—	3	1	no	—
474	C₂²×C₄	—	3	2	no	—
475	C₂²×C₄	—	3	4	no	—
476	C₂²×C₄	—	3	8	no	—
477	C₂²×C₄	—	4	4	no	—
478	C₂²×C₄	—	6	4	no	—
479	C₂²×C₄	—	12	4	no	—
480	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
481	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
482	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
483	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
484	C₂²×C₄	C₂²×C₅×D₃	1	8	yes	—
485	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
486	C₄⋊C₄	—	3	8	no	—
487	C₄⋊C₄	—	3	4	no	—
488	C₄⋊C₄	—	3	4	no	—
489	C₄⋊C₄	—	3	8	no	—
490	C₄⋊C₄	—	3	8	no	—
491	C₄⋊C₄	—	3	8	no	—
492	C₄⋊C₄	—	3	8	no	—
493	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
494	C₄⋊C₄	C₂²×C₅×D₃	1	8	yes	—
495	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
496	C₂²⋊C₄	—	3	8	no	—
497	C₂²⋊C₄	—	3	4	no	—
498	C₂²⋊C₄	—	3	8	no	—
499	C₂²⋊C₄	—	3	4	no	—
500	C₄²	—	3	8	no	—
501	C₄²	—	3	4	no	—
502	C₃×C₅	C₂×#554	1	1	yes	characteristic, complemented, Hall
503	C₂²×C₃	—	2	8	no	—
504	C₂²×C₃	—	2	2	no	—
505	C₂²×C₃	—	2	2	no	—
506	C₂²×C₃	C₂²×C₅×Q₈	1	4	yes	—
507	C₂²×C₃	C₂²×C₅×Q₈	1	2	yes	—
508	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
509	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
510	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
511	C₂×D₃	—	2	8	no	—
512	C₂×D₃	—	2	2	no	—
513	C₂×D₃	—	2	2	no	—
514	C₂×D₃	C₂²×C₅×Q₈	1	4	yes	—
515	C₃×C₄	—	2	2	no	—
516	C₃×C₄	—	2	4	no	—
517	C₃×C₄	—	2	4	no	—
518	C₃×C₄	C₂×C₅×#41	1	4	yes	—
519	Dic₃	—	2	4	no	—
520	Dic₃	—	2	2	no	—
521	Dic₃	—	2	2	no	—
522	Dic₃	—	2	4	no	—
523	Dic₃	C₂²×C₅×Q₈	1	4	yes	—
524	C₂×C₅	—	2	4	no	—
525	C₂×C₅	—	6	4	no	—
526	C₂×C₅	#5511	1	4	yes	direct product factor
527	C₂×C₅	C₂²×#235	1	1	yes	characteristic
528	C₂×C₅	C₂×#1004	1	1	yes	characteristic
529	C₂×C₅	C₂²×D₃×Q₈	1	1	yes	characteristic
530	C₂³	—	2	2	no	—
531	C₂³	—	2	2	no	—
532	C₂³	—	3	4	no	—
533	C₂³	—	3	2	no	—
534	C₂³	—	6	2	no	—
535	C₂³	—	6	2	no	—
536	C₂³	C₅×D₃×Q₈	1	4	yes	—
537	C₂³	C₂³×C₅×D₃	1	2	yes	—
538	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
539	Q₈	—	6	8	no	—
540	Q₈	—	12	8	no	—
541	D₄	—	3	16	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	2	8	no	—
546	C₂×C₄	—	3	4	no	—
547	C₂×C₄	—	3	2	no	—
548	C₂×C₄	—	3	4	no	—
549	C₂×C₄	—	3	2	no	—
550	C₂×C₄	—	3	2	no	—
551	C₂×C₄	—	3	4	no	—
552	C₂×C₄	—	4	8	no	—
553	C₂×C₄	—	6	2	no	—
554	C₂×C₄	—	6	4	no	—
555	C₂×C₄	—	6	4	no	—
556	C₂×C₄	—	6	2	no	—
557	C₂×C₄	—	6	8	no	—
558	C₂×C₄	—	12	8	no	—
559	C₂×C₄	C₅×#235	1	4	yes	—
560	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
561	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
562	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
563	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
564	C₂×C₃	—	2	4	no	—
565	C₂×C₃	C₅×#554	1	4	yes	complemented
566	C₂×C₃	C₂³×C₅×Q₈	1	1	yes	characteristic
567	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
568	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
569	D₃	—	2	4	no	—
570	C₅	C₂×#5511	1	1	yes	characteristic, direct product factor, Sylow
571	C₂²	—	2	2	no	—
572	C₂²	—	2	2	no	—
573	C₂²	—	2	8	no	—
574	C₂²	—	3	4	no	—
575	C₂²	—	6	2	no	—
576	C₂²	—	6	2	no	—
577	C₂²	—	6	8	no	—
578	C₂²	C₂×C₅×#235	1	2	yes	—
579	C₂²	C₅×#1004	1	2	yes	—
580	C₂²	C₂×C₅×D₃×Q₈	1	4	yes	—
581	C₂²	C₂×C₅×D₃×Q₈	1	2	yes	—
582	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
583	C₄	—	2	2	no	—
584	C₄	—	2	4	no	—
585	C₄	—	2	4	no	—
586	C₄	—	3	4	no	—
587	C₄	—	6	2	no	—
588	C₄	—	6	4	no	—
589	C₄	—	6	4	no	—
590	C₄	—	6	2	no	—
591	C₄	C₂×C₅×#235	1	4	yes	—
592	C₃	C₂×C₅×#554	1	1	yes	characteristic, complemented, Sylow
593	C₂	—	2	4	no	—
594	C₂	—	6	4	no	—
595	C₂	C₅×#5511	1	4	yes	direct product factor
596	C₂	C₂²×C₅×#235	1	1	yes	characteristic
597	C₂	C₂×C₅×#1004	1	1	yes	characteristic
598	C₂	C₂²×C₅×D₃×Q₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂²×C₃×C₅×C₄⋊C₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₅×#67	C₂²
hypercenter	C₂²×C₅×C₄⋊C₄	D₃
hypocenter	C₃	C₂×C₅×#554
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₅×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×C₄⋊C₄	C₂	semidirect
4. C₂×C₅×#924	C₂	semidirect
5. C₂×C₅×#924	C₂	semidirect
6. C₅×#5511	C₂	direct (N × H)
7. C₂×C₅×#897	C₂	semidirect
8. C₂×C₅×#896	C₂	semidirect
9. C₂×C₅×D₃×C₄⋊C₄	C₂	semidirect
10. C₂×C₅×#889	C₂	semidirect
11. C₂×C₅×#888	C₂	semidirect
12. C₂×C₅×#887	C₂	semidirect
24. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
33. C₅×#924	C₂²	semidirect
34. C₅×#924	C₂²	semidirect
42. C₅×#897	C₂²	semidirect
43. C₅×#896	C₂²	semidirect
44. C₅×D₃×C₄⋊C₄	C₂²	semidirect
45. C₅×#889	C₂²	semidirect
46. C₅×#888	C₂²	semidirect
47. C₅×#887	C₂²	semidirect
48. C₂×#5511	C₅	direct (N × H)
60. C₂²×C₅×C₄⋊C₄	D₃	semidirect
71. C₂×C₅×#67	Q₈	semidirect
102. C₂²×C₃×C₄⋊C₄	C₂×C₅	semidirect
105. C₂×#924	C₂×C₅	semidirect
106. C₂×#924	C₂×C₅	semidirect
107. #5511	C₂×C₅	direct (N × H)
108. C₂×#897	C₂×C₅	semidirect
109. C₂×#896	C₂×C₅	semidirect
110. C₂×D₃×C₄⋊C₄	C₂×C₅	semidirect
111. C₂×#889	C₂×C₅	semidirect
112. C₂×#888	C₂×C₅	semidirect
113. C₂×#887	C₂×C₅	semidirect
141. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
168. C₅×#67	C₂×Q₈	semidirect
193. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
202. #924	C₂²×C₅	semidirect
203. #924	C₂²×C₅	semidirect
211. #897	C₂²×C₅	semidirect
212. #896	C₂²×C₅	semidirect
213. D₃×C₄⋊C₄	C₂²×C₅	semidirect
214. #889	C₂²×C₅	semidirect
215. #888	C₂²×C₅	semidirect
216. #887	C₂²×C₅	semidirect
269. C₂²×C₄⋊C₄	C₅×D₃	semidirect
301. C₂×#67	C₅×Q₈	semidirect
393. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
401. C₂×C₃×C₅	#554	semidirect
425. #67	C₂×C₅×Q₈	semidirect
502. C₃×C₅	C₂×#554	semidirect
526. C₂×C₅	#5511	direct (N × H)
565. C₂×C₃	C₅×#554	semidirect
570. C₅	C₂×#5511	direct (N × H)
592. C₃	C₂×C₅×#554	semidirect
595. C₂	C₅×#5511	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×C₃×C₅×C₄⋊C₄	2
C₂×C₄×C₅×#67	2
C₂×C₅×#924	2
C₅×#5511	2
C₂×C₅×#897	2
C₂×C₅×#896	2
C₂×C₅×D₃×C₄⋊C₄	2
C₂×C₅×#889	2
C₂×C₅×#888	2
C₂×C₅×#887	2
C₂×C₅×#554	3
C₂×#5511	5

Subgroups — C2×C5×#5511 #14483790

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5511 #14483790