Subgroups — C₂×C₅×#5555 #14482688

Order 1920.

3264 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#237	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#930	C₂	1	2	yes	maximal, complemented
4	C₂²×C₅×C₄⋊Dic₃	C₂	1	2	yes	maximal, complemented
5	C₅×#5555	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₅×#897	C₂	1	2	yes	maximal, complemented
7	C₂×C₅×#886	C₂	1	4	yes	maximal, complemented
8	C₂×C₄×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#869	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#547	—	3	1	no	maximal, Hall
11	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
12	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
13	C₂²×C₅×#67	C₂²	1	4	yes	—
14	C₂³×C₅×Dic₃	C₂²	1	4	yes	—
15	C₂×C₅×#237	—	2	16	no	—
16	C₂×C₅×#237	C₂²	1	16	yes	complemented
17	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
18	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
19	C₂²×C₅×Dic₆	C₂²	1	2	yes	—
20	C₃×C₄×C₅×D₄	C₂²	1	8	yes	complemented
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
24	C₅×#930	C₂²	1	16	yes	complemented
25	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
26	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
27	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
28	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
29	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
30	C₂×C₅×C₄⋊Dic₃	C₂²	1	4	yes	—
31	C₂×C₅×C₄⋊Dic₃	C₂²	1	16	yes	complemented
32	C₅×#897	C₂²	1	16	yes	complemented
33	C₅×#886	C₂²	1	32	yes	complemented
34	C₄×C₅×D₁₂	C₂²	1	8	yes	complemented
35	C₅×#869	C₂²	1	8	yes	complemented
36	C₂×#5555	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
37	C₂²×C₅×#41	—	3	2	no	—
38	C₅×#547	—	3	16	no	—
39	C₂×C₅×C₄⋊Q₈	—	3	1	no	—
40	C₂×C₅×#123	—	3	4	no	—
41	C₂×C₅×C₂²⋊Q₈	—	3	2	no	—
42	C₂×C₅×#121	—	3	2	no	—
43	C₂×C₄×C₅×D₄	—	3	1	no	—
44	C₂×C₄×C₅×D₄	D₃	1	1	yes	characteristic, complemented
45	C₂²×C₅×C₄⋊C₄	—	3	2	no	—
46	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
47	C₂³×C₅×D₃	C₂³	1	2	yes	—
48	C₂×C₃×C₅×D₄	D₄	1	8	yes	complemented
49	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
50	C₂²×C₃×C₄×C₅	—	2	8	no	—
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
53	C₂²×C₃×C₄×C₅	C₂³	1	8	yes	—
54	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
56	C₂×C₅×#67	—	2	16	no	—
57	C₂×C₅×#67	C₂³	1	16	yes	—
58	C₂²×C₅×Dic₃	—	2	16	no	—
59	C₂²×C₅×Dic₃	C₂³	1	16	yes	—
60	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
61	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
62	C₅×#237	—	2	64	no	—
63	C₂×C₅×D₁₂	—	2	4	no	—
64	C₂×C₅×D₁₂	C₂³	1	4	yes	—
65	C₂×C₄×C₅×D₃	—	2	8	no	—
66	C₂×C₄×C₅×D₃	C₂³	1	8	yes	—
67	C₂×C₅×Dic₆	—	2	8	no	—
68	C₂×C₅×Dic₆	C₂³	1	8	yes	—
69	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
70	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
71	C₃×C₄²×C₅	C₂³	1	4	yes	—
72	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
73	C₅×(C₂×D₃)⋊C₄	C₂³	1	16	yes	—
74	C₅×C₄⋊Dic₃	C₂³	1	8	yes	—
75	C₅×C₄⋊Dic₃	C₂³	1	8	yes	—
76	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
77	C₅×C₄⋊Dic₃	C₂³	1	16	yes	—
78	C₂²×#237	C₂×C₅	1	2	yes	complemented
79	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic, complemented
80	C₂×#930	C₂×C₅	1	2	yes	complemented
81	C₂²×C₄⋊Dic₃	C₂×C₅	1	2	yes	complemented
82	#5555	C₂×C₅	1	16	yes	direct product factor
83	C₂×#897	C₂×C₅	1	2	yes	complemented
84	C₂×#886	C₂×C₅	1	4	yes	complemented
85	C₂×C₄×D₁₂	C₂×C₅	1	1	yes	characteristic, complemented
86	C₂×#869	C₂×C₅	1	1	yes	characteristic, complemented
87	C₂×C₅×#41	—	3	16	no	—
88	C₂×C₅×#41	—	6	16	no	—
89	C₂²×C₅×Q₈	—	3	2	no	—
90	C₂²×C₅×D₄	—	3	4	no	—
91	C₂²×C₅×D₄	—	3	1	no	—
92	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
93	C₂³×C₄×C₅	—	3	4	no	—
94	C₂³×C₄×C₅	—	3	2	no	—
95	C₂³×C₄×C₅	C₂×D₃	1	2	yes	—
96	C₅×C₄⋊Q₈	—	3	8	no	—
97	C₅×#123	—	3	32	no	—
98	C₅×C₂²⋊Q₈	—	3	16	no	—
99	C₅×#121	—	3	16	no	—
100	C₄×C₅×D₄	—	3	8	no	—
101	C₄×C₅×D₄	C₂×D₃	1	8	yes	complemented
102	C₂×C₅×C₄⋊C₄	—	3	1	no	—
103	C₂×C₅×C₄⋊C₄	—	3	2	no	—
104	C₂×C₅×C₄⋊C₄	—	3	4	no	—
105	C₂×C₅×C₄⋊C₄	—	3	2	no	—
106	C₂×C₅×C₄⋊C₄	—	3	16	no	—
107	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
108	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
109	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
110	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
111	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
112	C₂×#547	—	3	1	no	Sylow
113	C₂³×C₃×C₅	—	2	4	no	—
114	C₂³×C₃×C₅	—	2	4	no	—
115	C₂³×C₃×C₅	C₂×D₄	1	8	yes	—
116	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
117	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
118	C₂²×C₅×D₃	—	2	4	no	—
119	C₂²×C₅×D₃	—	2	4	no	—
120	C₂²×C₅×D₃	—	2	4	no	—
121	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
122	C₃×C₅×D₄	C₂×D₄	1	16	yes	complemented
123	C₂×C₃×C₄×C₅	—	2	4	no	—
124	C₂×C₃×C₄×C₅	—	2	2	no	—
125	C₂×C₃×C₄×C₅	—	2	16	no	—
126	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
127	C₂×C₃×C₄×C₅	#41	1	4	yes	complemented
128	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
129	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
130	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
131	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
132	C₅×#67	—	2	32	no	—
133	C₂×C₅×Dic₃	—	2	8	no	—
134	C₂×C₅×Dic₃	—	2	4	no	—
135	C₂×C₅×Dic₃	—	2	32	no	—
136	C₂×C₅×Dic₃	C₂⁴	1	8	yes	—
137	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
138	C₅×D₁₂	—	2	8	no	—
139	C₄×C₅×D₃	—	2	16	no	—
140	C₅×Dic₆	—	2	16	no	—
141	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
142	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
143	C₂²×#67	C₂²×C₅	1	4	yes	—
144	C₂³×Dic₃	C₂²×C₅	1	4	yes	—
145	C₂×#237	—	2	16	no	—
146	C₂×#237	C₂²×C₅	1	16	yes	complemented
147	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
148	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
149	C₂²×Dic₆	C₂²×C₅	1	2	yes	—
150	C₃×C₄×D₄	C₂²×C₅	1	8	yes	complemented
151	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
152	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
153	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
154	#930	C₂²×C₅	1	16	yes	complemented
155	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
156	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	—
157	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
158	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
159	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
160	C₂×C₄⋊Dic₃	C₂²×C₅	1	4	yes	—
161	C₂×C₄⋊Dic₃	C₂²×C₅	1	16	yes	complemented
162	#897	C₂²×C₅	1	16	yes	complemented
163	#886	C₂²×C₅	1	32	yes	complemented
164	C₄×D₁₂	C₂²×C₅	1	8	yes	complemented
165	#869	C₂²×C₅	1	8	yes	complemented
166	C₂⁴×C₅	—	3	2	no	—
167	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
168	C₅×#41	—	6	64	no	—
169	C₂×C₅×Q₈	—	3	8	no	—
170	C₂×C₅×Q₈	—	6	8	no	—
171	C₂×C₅×D₄	—	3	16	no	—
172	C₂×C₅×D₄	—	3	4	no	—
173	C₂×C₅×D₄	—	6	16	no	—
174	C₂×C₅×D₄	—	6	4	no	—
175	C₂×C₅×D₄	D₁₂	1	8	yes	complemented
176	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
177	C₂²×C₄×C₅	—	2	8	no	—
178	C₂²×C₄×C₅	—	3	16	no	—
179	C₂²×C₄×C₅	—	3	2	no	—
180	C₂²×C₄×C₅	—	3	4	no	—
181	C₂²×C₄×C₅	—	3	8	no	—
182	C₂²×C₄×C₅	—	6	16	no	—
183	C₂²×C₄×C₅	—	6	8	no	—
184	C₂²×C₄×C₅	C₂²×D₃	1	8	yes	—
185	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
186	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
187	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
188	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
189	C₅×C₄⋊C₄	—	3	4	no	—
190	C₅×C₄⋊C₄	—	3	8	no	—
191	C₅×C₄⋊C₄	—	3	16	no	—
192	C₅×C₄⋊C₄	—	3	8	no	—
193	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
194	C₅×C₂²⋊C₄	—	3	8	no	—
195	C₅×C₂²⋊C₄	—	3	16	no	—
196	C₅×C₂²⋊C₄	C₂²×D₃	1	8	yes	—
197	C₄²×C₅	C₂²×D₃	1	4	yes	—
198	C₂²×#41	—	3	2	no	—
199	#547	—	3	16	no	—
200	C₂×C₄⋊Q₈	—	3	1	no	—
201	C₂×#123	—	3	4	no	—
202	C₂×C₂²⋊Q₈	—	3	2	no	—
203	C₂×#121	—	3	2	no	—
204	C₂×C₄×D₄	—	3	1	no	—
205	C₂×C₄×D₄	C₅×D₃	1	1	yes	characteristic, complemented
206	C₂²×C₄⋊C₄	—	3	2	no	—
207	C₂²×C₃×C₅	—	2	16	no	—
208	C₂²×C₃×C₅	—	2	4	no	—
209	C₂²×C₃×C₅	—	2	4	no	—
210	C₂²×C₃×C₅	C₂²×D₄	1	8	yes	—
211	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
212	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
213	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
214	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
215	C₂×C₅×D₃	—	2	4	no	—
216	C₂×C₅×D₃	—	2	4	no	—
217	C₂×C₅×D₃	—	2	4	no	—
218	C₂×C₅×D₃	—	4	8	no	—
219	C₃×C₄×C₅	—	2	4	no	—
220	C₃×C₄×C₅	—	2	2	no	—
221	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
222	C₃×C₄×C₅	C₂×#41	1	4	yes	complemented
223	C₅×Dic₃	—	2	8	no	—
224	C₅×Dic₃	—	2	4	no	—
225	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
226	C₂³×D₃	C₂³×C₅	1	2	yes	—
227	C₂×C₃×D₄	C₅×D₄	1	8	yes	complemented
228	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
229	C₂²×C₃×C₄	—	2	8	no	—
230	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
231	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
232	C₂²×C₃×C₄	C₂³×C₅	1	8	yes	—
233	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
234	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
235	C₂×#67	—	2	16	no	—
236	C₂×#67	C₂³×C₅	1	16	yes	—
237	C₂²×Dic₃	—	2	16	no	—
238	C₂²×Dic₃	C₂³×C₅	1	16	yes	—
239	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
240	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
241	#237	—	2	64	no	—
242	C₂×D₁₂	—	2	4	no	—
243	C₂×D₁₂	C₂³×C₅	1	4	yes	—
244	C₂×C₄×D₃	—	2	8	no	—
245	C₂×C₄×D₃	C₂³×C₅	1	8	yes	—
246	C₂×Dic₆	—	2	8	no	—
247	C₂×Dic₆	C₂³×C₅	1	8	yes	—
248	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
249	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
250	C₃×C₄²	C₂³×C₅	1	4	yes	—
251	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
252	(C₂×D₃)⋊C₄	C₂³×C₅	1	16	yes	—
253	C₄⋊Dic₃	C₂³×C₅	1	8	yes	—
254	C₄⋊Dic₃	C₂³×C₅	1	8	yes	—
255	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
256	C₄⋊Dic₃	C₂³×C₅	1	16	yes	—
257	C₂³×C₅	—	2	4	no	—
258	C₂³×C₅	—	2	4	no	—
259	C₂³×C₅	—	3	4	no	—
260	C₂³×C₅	—	6	4	no	—
261	C₂³×C₅	—	6	4	no	—
262	C₂³×C₅	—	6	4	no	—
263	C₂³×C₅	C₂×D₁₂	1	8	yes	—
264	C₂³×C₅	C₂³×D₃	1	4	yes	—
265	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
266	C₅×Q₈	—	6	16	no	—
267	C₅×D₄	—	6	32	no	—
268	C₅×D₄	—	6	8	no	—
269	C₅×D₄	C₂×D₁₂	1	16	yes	complemented
270	C₂×C₄×C₅	—	2	4	no	—
271	C₂×C₄×C₅	—	2	2	no	—
272	C₂×C₄×C₅	—	2	16	no	—
273	C₂×C₄×C₅	—	3	4	no	—
274	C₂×C₄×C₅	—	3	8	no	—
275	C₂×C₄×C₅	—	6	4	no	—
276	C₂×C₄×C₅	—	6	8	no	—
277	C₂×C₄×C₅	—	6	32	no	—
278	C₂×C₄×C₅	—	6	16	no	—
279	C₂×C₄×C₅	C₂×D₁₂	1	4	yes	—
280	C₂×C₄×C₅	#237	1	4	yes	complemented
281	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
282	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
283	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
284	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
285	C₂×#41	—	3	16	no	—
286	C₂×#41	—	6	16	no	—
287	C₂²×Q₈	—	3	2	no	—
288	C₂²×D₄	—	3	4	no	—
289	C₂²×D₄	—	3	1	no	—
290	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
291	C₂³×C₄	—	3	4	no	—
292	C₂³×C₄	—	3	2	no	—
293	C₂³×C₄	C₂×C₅×D₃	1	2	yes	—
294	C₄⋊Q₈	—	3	8	no	—
295	#123	—	3	32	no	—
296	C₂²⋊Q₈	—	3	16	no	—
297	#121	—	3	16	no	—
298	C₄×D₄	—	3	8	no	—
299	C₄×D₄	C₂×C₅×D₃	1	8	yes	complemented
300	C₂×C₄⋊C₄	—	3	1	no	—
301	C₂×C₄⋊C₄	—	3	2	no	—
302	C₂×C₄⋊C₄	—	3	4	no	—
303	C₂×C₄⋊C₄	—	3	16	no	—
304	C₂×C₄⋊C₄	—	3	2	no	—
305	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
306	C₂×C₂²⋊C₄	—	3	2	no	—
307	C₂×C₂²⋊C₄	—	3	4	no	—
308	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
309	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
310	C₂×C₃×C₅	—	2	8	no	—
311	C₂×C₃×C₅	#547	1	4	yes	complemented
312	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
313	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
314	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
315	C₅×D₃	—	4	4	no	—
316	C₂³×C₃	—	2	4	no	—
317	C₂³×C₃	—	2	4	no	—
318	C₂³×C₃	C₂×C₅×D₄	1	8	yes	—
319	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
320	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
321	C₂²×D₃	—	2	4	no	—
322	C₂²×D₃	—	2	4	no	—
323	C₂²×D₃	—	2	4	no	—
324	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
325	C₃×D₄	C₂×C₅×D₄	1	16	yes	complemented
326	C₂×C₃×C₄	—	2	4	no	—
327	C₂×C₃×C₄	—	2	2	no	—
328	C₂×C₃×C₄	—	2	16	no	—
329	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
330	C₂×C₃×C₄	C₅×#41	1	4	yes	complemented
331	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
332	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
333	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
334	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
335	#67	—	2	32	no	—
336	C₂×Dic₃	—	2	8	no	—
337	C₂×Dic₃	—	2	4	no	—
338	C₂×Dic₃	—	2	32	no	—
339	C₂×Dic₃	C₂⁴×C₅	1	8	yes	—
340	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
341	D₁₂	—	2	8	no	—
342	C₄×D₃	—	2	16	no	—
343	Dic₆	—	2	16	no	—
344	C₂²×C₅	—	2	4	no	—
345	C₂²×C₅	—	2	4	no	—
346	C₂²×C₅	—	2	16	no	—
347	C₂²×C₅	—	6	4	no	—
348	C₂²×C₅	—	6	4	no	—
349	C₂²×C₅	—	6	4	no	—
350	C₂²×C₅	—	12	8	no	—
351	C₂²×C₅	C₂²×D₁₂	1	8	yes	—
352	C₂²×C₅	C₂²×D₁₂	1	2	yes	—
353	C₂²×C₅	C₂×#237	1	2	yes	—
354	C₂²×C₅	#1010	1	2	yes	—
355	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
356	C₄×C₅	—	2	4	no	—
357	C₄×C₅	—	2	2	no	—
358	C₄×C₅	—	6	4	no	—
359	C₄×C₅	—	6	8	no	—
360	C₄×C₅	C₂²×D₁₂	1	4	yes	—
361	C₄×C₅	C₂×#237	1	4	yes	complemented
362	C₂⁴	—	3	2	no	—
363	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
364	#41	—	6	64	no	—
365	C₂×Q₈	—	3	8	no	—
366	C₂×Q₈	—	6	8	no	—
367	C₂×D₄	—	3	16	no	—
368	C₂×D₄	—	3	4	no	—
369	C₂×D₄	—	6	16	no	—
370	C₂×D₄	—	6	4	no	—
371	C₂×D₄	C₅×D₁₂	1	8	yes	complemented
372	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
373	C₂²×C₄	—	2	8	no	—
374	C₂²×C₄	—	3	2	no	—
375	C₂²×C₄	—	3	4	no	—
376	C₂²×C₄	—	3	16	no	—
377	C₂²×C₄	—	3	8	no	—
378	C₂²×C₄	—	6	16	no	—
379	C₂²×C₄	—	6	8	no	—
380	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
381	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
382	C₂²×C₄	C₂²×C₅×D₃	1	8	yes	—
383	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
384	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
385	C₄⋊C₄	—	3	4	no	—
386	C₄⋊C₄	—	3	8	no	—
387	C₄⋊C₄	—	3	16	no	—
388	C₄⋊C₄	—	3	8	no	—
389	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
390	C₂²⋊C₄	—	3	8	no	—
391	C₂²⋊C₄	—	3	16	no	—
392	C₂²⋊C₄	C₂²×C₅×D₃	1	8	yes	—
393	C₄²	C₂²×C₅×D₃	1	4	yes	—
394	C₃×C₅	C₂×#547	1	1	yes	characteristic, complemented, Hall
395	C₂²×C₃	—	2	16	no	—
396	C₂²×C₃	—	2	4	no	—
397	C₂²×C₃	—	2	4	no	—
398	C₂²×C₃	C₂²×C₅×D₄	1	8	yes	—
399	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
400	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
401	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
402	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
403	C₂×D₃	—	2	4	no	—
404	C₂×D₃	—	2	4	no	—
405	C₂×D₃	—	2	4	no	—
406	C₂×D₃	—	4	8	no	—
407	C₃×C₄	—	2	4	no	—
408	C₃×C₄	—	2	2	no	—
409	C₃×C₄	C₂²×C₅×D₄	1	4	yes	—
410	C₃×C₄	C₂×C₅×#41	1	4	yes	complemented
411	Dic₃	—	2	8	no	—
412	Dic₃	—	2	4	no	—
413	C₂×C₅	—	2	8	no	—
414	C₂×C₅	—	12	4	no	—
415	C₂×C₅	#5555	1	4	yes	direct product factor
416	C₂×C₅	C₂³×D₁₂	1	1	yes	characteristic
417	C₂×C₅	C₂²×#237	1	1	yes	characteristic
418	C₂×C₅	C₂×#1010	1	1	yes	characteristic
419	C₂³	—	2	4	no	—
420	C₂³	—	2	4	no	—
421	C₂³	—	3	4	no	—
422	C₂³	—	6	4	no	—
423	C₂³	—	6	4	no	—
424	C₂³	—	6	4	no	—
425	C₂³	C₂×C₅×D₁₂	1	8	yes	—
426	C₂³	C₂³×C₅×D₃	1	4	yes	—
427	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
428	Q₈	—	6	16	no	—
429	D₄	—	6	32	no	—
430	D₄	—	6	8	no	—
431	D₄	C₂×C₅×D₁₂	1	16	yes	complemented
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	16	no	—
435	C₂×C₄	—	3	4	no	—
436	C₂×C₄	—	3	8	no	—
437	C₂×C₄	—	6	4	no	—
438	C₂×C₄	—	6	8	no	—
439	C₂×C₄	—	6	32	no	—
440	C₂×C₄	—	6	16	no	—
441	C₂×C₄	C₂×C₅×D₁₂	1	4	yes	—
442	C₂×C₄	C₅×#237	1	4	yes	complemented
443	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
444	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
445	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
446	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
447	C₂×C₃	—	2	8	no	—
448	C₂×C₃	C₅×#547	1	4	yes	complemented
449	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
450	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
451	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
452	D₃	—	4	4	no	—
453	C₅	C₂×#5555	1	1	yes	characteristic, direct product factor, Sylow
454	C₂²	—	2	4	no	—
455	C₂²	—	2	4	no	—
456	C₂²	—	2	16	no	—
457	C₂²	—	6	4	no	—
458	C₂²	—	6	4	no	—
459	C₂²	—	6	4	no	—
460	C₂²	—	12	8	no	—
461	C₂²	C₂²×C₅×D₁₂	1	8	yes	—
462	C₂²	C₂²×C₅×D₁₂	1	2	yes	—
463	C₂²	C₂×C₅×#237	1	2	yes	—
464	C₂²	C₅×#1010	1	2	yes	—
465	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
466	C₄	—	2	4	no	—
467	C₄	—	2	2	no	—
468	C₄	—	6	4	no	—
469	C₄	—	6	8	no	—
470	C₄	C₂²×C₅×D₁₂	1	4	yes	—
471	C₄	C₂×C₅×#237	1	4	yes	complemented
472	C₃	C₂×C₅×#547	1	1	yes	characteristic, complemented, Sylow
473	C₂	—	2	8	no	—
474	C₂	—	12	4	no	—
475	C₂	C₅×#5555	1	4	yes	direct product factor
476	C₂	C₂³×C₅×D₁₂	1	1	yes	characteristic
477	C₂	C₂²×C₅×#237	1	1	yes	characteristic
478	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×C₄×C₅×D₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₄×C₅×D₄	D₃
hypocenter	C₃	C₂×C₅×#547
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄×C₅×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×#237	C₂	semidirect
2. C₂×C₃×C₄×C₅×D₄	C₂	semidirect
3. C₂×C₅×#930	C₂	semidirect
4. C₂²×C₅×C₄⋊Dic₃	C₂	semidirect
5. C₅×#5555	C₂	direct (N × H)
6. C₂×C₅×#897	C₂	semidirect
7. C₂×C₅×#886	C₂	semidirect
8. C₂×C₄×C₅×D₁₂	C₂	semidirect
9. C₂×C₅×#869	C₂	semidirect
16. C₂×C₅×#237	C₂²	semidirect
20. C₃×C₄×C₅×D₄	C₂²	semidirect
24. C₅×#930	C₂²	semidirect
31. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
32. C₅×#897	C₂²	semidirect
33. C₅×#886	C₂²	semidirect
34. C₄×C₅×D₁₂	C₂²	semidirect
35. C₅×#869	C₂²	semidirect
36. C₂×#5555	C₅	direct (N × H)
44. C₂×C₄×C₅×D₄	D₃	semidirect
48. C₂×C₃×C₅×D₄	D₄	semidirect
78. C₂²×#237	C₂×C₅	semidirect
79. C₂×C₃×C₄×D₄	C₂×C₅	semidirect
80. C₂×#930	C₂×C₅	semidirect
81. C₂²×C₄⋊Dic₃	C₂×C₅	semidirect
82. #5555	C₂×C₅	direct (N × H)
83. C₂×#897	C₂×C₅	semidirect
84. C₂×#886	C₂×C₅	semidirect
85. C₂×C₄×D₁₂	C₂×C₅	semidirect
86. C₂×#869	C₂×C₅	semidirect
101. C₄×C₅×D₄	C₂×D₃	semidirect
122. C₃×C₅×D₄	C₂×D₄	semidirect
127. C₂×C₃×C₄×C₅	#41	semidirect
146. C₂×#237	C₂²×C₅	semidirect
150. C₃×C₄×D₄	C₂²×C₅	semidirect
154. #930	C₂²×C₅	semidirect
161. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
162. #897	C₂²×C₅	semidirect
163. #886	C₂²×C₅	semidirect
164. C₄×D₁₂	C₂²×C₅	semidirect
165. #869	C₂²×C₅	semidirect
175. C₂×C₅×D₄	D₁₂	semidirect
205. C₂×C₄×D₄	C₅×D₃	semidirect
222. C₃×C₄×C₅	C₂×#41	semidirect
227. C₂×C₃×D₄	C₅×D₄	semidirect
269. C₅×D₄	C₂×D₁₂	semidirect
280. C₂×C₄×C₅	#237	semidirect
299. C₄×D₄	C₂×C₅×D₃	semidirect
311. C₂×C₃×C₅	#547	semidirect
325. C₃×D₄	C₂×C₅×D₄	semidirect
330. C₂×C₃×C₄	C₅×#41	semidirect
361. C₄×C₅	C₂×#237	semidirect
371. C₂×D₄	C₅×D₁₂	semidirect
394. C₃×C₅	C₂×#547	semidirect
410. C₃×C₄	C₂×C₅×#41	semidirect
415. C₂×C₅	#5555	direct (N × H)
431. D₄	C₂×C₅×D₁₂	semidirect
442. C₂×C₄	C₅×#237	semidirect
448. C₂×C₃	C₅×#547	semidirect
453. C₅	C₂×#5555	direct (N × H)
471. C₄	C₂×C₅×#237	semidirect
472. C₃	C₂×C₅×#547	semidirect
475. C₂	C₅×#5555	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×#237	2
C₂×C₃×C₄×C₅×D₄	2
C₂×C₅×#930	2
C₂²×C₅×C₄⋊Dic₃	2
C₅×#5555	2
C₂×C₅×#897	2
C₂×C₅×#886	2
C₂×C₄×C₅×D₁₂	2
C₂×C₅×#869	2
C₂×C₅×#547	3
C₂×#5555	5

Subgroups — C2×C5×#5555 #14482688

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5555 #14482688