Subgroups — C₂×C₅×#5526 #14480479

Order 1920.

3024 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#235	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₅×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5526	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₅×#897	C₂	1	4	yes	maximal, complemented
6	C₂×C₅×#886	C₂	1	4	yes	maximal, complemented
7	C₂×C₅×#875	C₂	1	2	yes	maximal, complemented
8	C₂×C₅×#869	C₂	1	2	yes	maximal, complemented
9	C₂×C₅×#536	—	3	1	no	maximal, Hall
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂²×C₅×#67	C₂²	1	2	yes	—
12	C₂³×C₅×Dic₃	C₂²	1	2	yes	—
13	C₂×C₅×#235	—	2	8	no	—
14	C₂×C₅×#235	C₂²	1	8	yes	—
15	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
16	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
17	C₂²×C₅×Dic₆	—	2	8	no	—
18	C₂²×C₅×Dic₆	C₂²	1	2	yes	—
19	C₂²×C₅×Dic₆	C₂²	1	2	yes	—
20	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
21	C₂²×C₅×Dic₆	C₂²	1	8	yes	complemented
22	C₃×C₅×#117	C₂²	1	8	yes	complemented
23	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
24	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
26	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	8	yes	—
27	C₂×C₅×C₄⋊Dic₃	C₂²	1	8	yes	—
28	C₅×#897	C₂²	1	32	yes	complemented
29	C₅×#886	C₂²	1	32	yes	complemented
30	C₅×#875	C₂²	1	16	yes	complemented
31	C₅×#869	C₂²	1	16	yes	complemented
32	C₂×#5526	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
33	C₂²×C₅×#41	—	3	1	no	—
34	C₂³×C₅×Q₈	—	3	1	no	—
35	C₅×#536	—	3	16	no	—
36	C₂×C₅×C₄⋊Q₈	—	3	2	no	—
37	C₂×C₅×#124	—	3	2	no	—
38	C₂×C₅×#123	—	3	4	no	—
39	C₂×C₅×C₂²⋊Q₈	—	3	4	no	—
40	C₂×C₅×#117	D₃	1	1	yes	characteristic, complemented
41	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
42	C₂³×C₅×D₃	C₂³	1	2	yes	—
43	C₂²×C₃×C₄×C₅	D₄	1	8	yes	—
44	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
48	C₂×C₅×#67	—	2	8	no	—
49	C₂×C₅×#67	C₂³	1	8	yes	—
50	C₂²×C₅×Dic₃	—	2	8	no	—
51	C₂²×C₅×Dic₃	C₂³	1	8	yes	—
52	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
53	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
54	C₅×#235	—	2	32	no	—
55	C₂×C₅×D₁₂	—	2	4	no	—
56	C₂×C₅×D₁₂	C₂³	1	4	yes	—
57	C₂×C₄×C₅×D₃	—	2	8	no	—
58	C₂×C₄×C₅×D₃	C₂³	1	8	yes	—
59	C₂×C₅×Dic₆	—	2	8	no	—
60	C₂×C₅×Dic₆	—	2	8	no	—
61	C₂×C₅×Dic₆	—	2	32	no	—
62	C₂×C₅×Dic₆	—	2	4	no	—
63	C₂×C₅×Dic₆	C₂³	1	4	yes	—
64	C₂×C₅×Dic₆	C₂³	1	8	yes	—
65	C₂×C₅×Dic₆	C₂³	1	8	yes	—
66	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
67	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
68	C₃×C₄²×C₅	C₂³	1	8	yes	—
69	C₅×(C₂×D₃)⋊C₄	C₂³	1	32	yes	—
70	C₅×C₄⋊Dic₃	C₂³	1	32	yes	—
71	C₂²×#235	C₂×C₅	1	1	yes	characteristic
72	C₂³×Dic₆	C₂×C₅	1	1	yes	characteristic, complemented
73	C₂×C₃×#117	C₂×C₅	1	1	yes	characteristic, complemented
74	#5526	C₂×C₅	1	16	yes	direct product factor
75	C₂×#897	C₂×C₅	1	4	yes	complemented
76	C₂×#886	C₂×C₅	1	4	yes	complemented
77	C₂×#875	C₂×C₅	1	2	yes	complemented
78	C₂×#869	C₂×C₅	1	2	yes	complemented
79	C₂×C₅×#41	—	3	8	no	—
80	C₂×C₅×#41	—	6	8	no	—
81	C₂²×C₅×Q₈	—	3	2	no	—
82	C₂²×C₅×Q₈	—	3	2	no	—
83	C₂²×C₅×Q₈	—	3	1	no	—
84	C₂²×C₅×Q₈	—	3	8	no	—
85	C₂²×C₅×Q₈	—	6	8	no	—
86	C₂²×C₅×D₄	—	3	2	no	—
87	C₂²×C₅×D₄	—	3	1	no	—
88	C₂³×C₄×C₅	—	3	2	no	—
89	C₂³×C₄×C₅	—	3	2	no	—
90	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
91	C₅×C₄⋊Q₈	—	3	16	no	—
92	C₅×#124	—	3	16	no	—
93	C₅×#123	—	3	32	no	—
94	C₅×C₂²⋊Q₈	—	3	32	no	—
95	C₅×#117	C₂×D₃	1	8	yes	complemented
96	C₂×C₅×C₄⋊C₄	—	3	8	no	—
97	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
98	C₂×C₅×C₂²⋊C₄	—	3	8	no	—
99	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
100	C₂×C₄²×C₅	C₂×D₃	1	2	yes	—
101	C₂×#536	—	3	1	no	Sylow
102	C₂³×C₃×C₅	—	2	4	no	—
103	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
104	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
105	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
106	C₂²×C₅×D₃	—	2	4	no	—
107	C₂²×C₅×D₃	—	2	8	no	—
108	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
109	C₂×C₃×C₄×C₅	—	2	8	no	—
110	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
111	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
112	C₂×C₃×C₄×C₅	C₂×D₄	1	16	yes	—
113	C₂×C₃×C₄×C₅	C₂⁴	1	8	yes	—
114	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
115	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
116	C₅×#67	—	2	16	no	—
117	C₂×C₅×Dic₃	—	2	16	no	—
118	C₂×C₅×Dic₃	—	2	8	no	—
119	C₂×C₅×Dic₃	—	2	4	no	—
120	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
121	C₂×C₅×Dic₃	C₂⁴	1	8	yes	—
122	C₅×D₁₂	—	2	8	no	—
123	C₄×C₅×D₃	—	2	16	no	—
124	C₅×Dic₆	—	2	16	no	—
125	C₅×Dic₆	—	2	16	no	—
126	C₅×Dic₆	—	2	8	no	—
127	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
128	C₂²×#67	C₂²×C₅	1	2	yes	—
129	C₂³×Dic₃	C₂²×C₅	1	2	yes	—
130	C₂×#235	—	2	8	no	—
131	C₂×#235	C₂²×C₅	1	8	yes	—
132	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
133	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
134	C₂²×Dic₆	—	2	8	no	—
135	C₂²×Dic₆	C₂²×C₅	1	2	yes	—
136	C₂²×Dic₆	C₂²×C₅	1	2	yes	—
137	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
138	C₂²×Dic₆	C₂²×C₅	1	8	yes	complemented
139	C₃×#117	C₂²×C₅	1	8	yes	complemented
140	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
141	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
142	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
143	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	8	yes	—
144	C₂×C₄⋊Dic₃	C₂²×C₅	1	8	yes	—
145	#897	C₂²×C₅	1	32	yes	complemented
146	#886	C₂²×C₅	1	32	yes	complemented
147	#875	C₂²×C₅	1	16	yes	complemented
148	#869	C₂²×C₅	1	16	yes	complemented
149	C₂⁴×C₅	—	3	2	no	—
150	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
151	C₅×#41	—	6	32	no	—
152	C₂×C₅×Q₈	—	3	8	no	—
153	C₂×C₅×Q₈	—	3	8	no	—
154	C₂×C₅×Q₈	—	3	4	no	—
155	C₂×C₅×Q₈	—	6	8	no	—
156	C₂×C₅×Q₈	—	6	8	no	—
157	C₂×C₅×Q₈	—	6	32	no	—
158	C₂×C₅×Q₈	—	6	4	no	—
159	C₂×C₅×D₄	—	3	8	no	—
160	C₂×C₅×D₄	—	3	4	no	—
161	C₂×C₅×D₄	—	6	8	no	—
162	C₂×C₅×D₄	—	6	4	no	—
163	C₂²×C₄×C₅	—	3	8	no	—
164	C₂²×C₄×C₅	—	3	4	no	—
165	C₂²×C₄×C₅	—	3	2	no	—
166	C₂²×C₄×C₅	—	3	8	no	—
167	C₂²×C₄×C₅	—	6	8	no	—
168	C₂²×C₄×C₅	—	6	8	no	—
169	C₂²×C₄×C₅	D₁₂	1	8	yes	—
170	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
171	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
172	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
173	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
174	C₅×C₄⋊C₄	—	3	32	no	—
175	C₅×C₄⋊C₄	C₂²×D₃	1	8	yes	—
176	C₅×C₂²⋊C₄	—	3	32	no	—
177	C₅×C₂²⋊C₄	C₂²×D₃	1	8	yes	—
178	C₄²×C₅	C₂²×D₃	1	8	yes	—
179	C₂²×#41	—	3	1	no	—
180	C₂³×Q₈	—	3	1	no	—
181	#536	—	3	16	no	—
182	C₂×C₄⋊Q₈	—	3	2	no	—
183	C₂×#124	—	3	2	no	—
184	C₂×#123	—	3	4	no	—
185	C₂×C₂²⋊Q₈	—	3	4	no	—
186	C₂×#117	C₅×D₃	1	1	yes	characteristic, complemented
187	C₂²×C₃×C₅	—	2	8	no	—
188	C₂²×C₃×C₅	—	2	4	no	—
189	C₂²×C₃×C₅	C₂²×D₄	1	4	yes	—
190	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
191	C₂²×C₃×C₅	2₋¹⁺⁴	1	4	yes	—
192	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
193	C₂×C₅×D₃	—	2	4	no	—
194	C₂×C₅×D₃	—	2	8	no	—
195	C₂×C₅×D₃	—	4	8	no	—
196	C₃×C₄×C₅	—	2	8	no	—
197	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
198	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
199	C₅×Dic₃	—	2	8	no	—
200	C₅×Dic₃	—	2	4	no	—
201	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
202	C₂³×D₃	C₂³×C₅	1	2	yes	—
203	C₂²×C₃×C₄	C₅×D₄	1	8	yes	—
204	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
205	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
206	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
207	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
208	C₂×#67	—	2	8	no	—
209	C₂×#67	C₂³×C₅	1	8	yes	—
210	C₂²×Dic₃	—	2	8	no	—
211	C₂²×Dic₃	C₂³×C₅	1	8	yes	—
212	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
213	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
214	#235	—	2	32	no	—
215	C₂×D₁₂	—	2	4	no	—
216	C₂×D₁₂	C₂³×C₅	1	4	yes	—
217	C₂×C₄×D₃	—	2	8	no	—
218	C₂×C₄×D₃	C₂³×C₅	1	8	yes	—
219	C₂×Dic₆	—	2	8	no	—
220	C₂×Dic₆	—	2	8	no	—
221	C₂×Dic₆	—	2	32	no	—
222	C₂×Dic₆	—	2	4	no	—
223	C₂×Dic₆	C₂³×C₅	1	4	yes	—
224	C₂×Dic₆	C₂³×C₅	1	8	yes	—
225	C₂×Dic₆	C₂³×C₅	1	8	yes	—
226	C₃×C₄⋊C₄	C₂³×C₅	1	8	yes	—
227	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
228	C₃×C₄²	C₂³×C₅	1	8	yes	—
229	(C₂×D₃)⋊C₄	C₂³×C₅	1	32	yes	—
230	C₄⋊Dic₃	C₂³×C₅	1	32	yes	—
231	C₂³×C₅	—	2	4	no	—
232	C₂³×C₅	—	3	4	no	—
233	C₂³×C₅	—	6	4	no	—
234	C₂³×C₅	—	6	8	no	—
235	C₂³×C₅	C₂×D₁₂	1	4	yes	—
236	C₂³×C₅	C₂³×D₃	1	2	yes	—
237	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
238	C₅×Q₈	—	6	16	no	—
239	C₅×Q₈	—	6	16	no	—
240	C₅×Q₈	—	6	8	no	—
241	C₅×D₄	—	6	16	no	—
242	C₅×D₄	—	6	8	no	—
243	C₂×C₄×C₅	—	2	8	no	—
244	C₂×C₄×C₅	—	3	8	no	—
245	C₂×C₄×C₅	—	3	4	no	—
246	C₂×C₄×C₅	—	6	4	no	—
247	C₂×C₄×C₅	—	6	16	no	—
248	C₂×C₄×C₅	—	6	8	no	—
249	C₂×C₄×C₅	—	6	16	no	—
250	C₂×C₄×C₅	C₂×D₁₂	1	4	yes	—
251	C₂×C₄×C₅	C₂×D₁₂	1	4	yes	—
252	C₂×C₄×C₅	C₂×D₁₂	1	16	yes	—
253	C₂×C₄×C₅	C₂³×D₃	1	8	yes	—
254	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
255	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
256	C₂×#41	—	3	8	no	—
257	C₂×#41	—	6	8	no	—
258	C₂²×Q₈	—	3	2	no	—
259	C₂²×Q₈	—	3	2	no	—
260	C₂²×Q₈	—	3	1	no	—
261	C₂²×Q₈	—	3	8	no	—
262	C₂²×Q₈	—	6	8	no	—
263	C₂²×D₄	—	3	2	no	—
264	C₂²×D₄	—	3	1	no	—
265	C₂³×C₄	—	3	2	no	—
266	C₂³×C₄	—	3	2	no	—
267	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
268	C₄⋊Q₈	—	3	16	no	—
269	#124	—	3	16	no	—
270	#123	—	3	32	no	—
271	C₂²⋊Q₈	—	3	32	no	—
272	#117	C₂×C₅×D₃	1	8	yes	complemented
273	C₂×C₄⋊C₄	—	3	8	no	—
274	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
275	C₂×C₂²⋊C₄	—	3	8	no	—
276	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
277	C₂×C₄²	C₂×C₅×D₃	1	2	yes	—
278	C₂×C₃×C₅	—	2	4	no	—
279	C₂×C₃×C₅	#536	1	4	yes	complemented
280	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
281	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	2	yes	—
282	C₅×D₃	—	4	4	no	—
283	C₂³×C₃	—	2	4	no	—
284	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
285	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
286	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
287	C₂²×D₃	—	2	4	no	—
288	C₂²×D₃	—	2	8	no	—
289	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
290	C₂×C₃×C₄	—	2	8	no	—
291	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
292	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
293	C₂×C₃×C₄	C₂×C₅×D₄	1	16	yes	—
294	C₂×C₃×C₄	C₂⁴×C₅	1	8	yes	—
295	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
296	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
297	#67	—	2	16	no	—
298	C₂×Dic₃	—	2	16	no	—
299	C₂×Dic₃	—	2	8	no	—
300	C₂×Dic₃	—	2	4	no	—
301	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
302	C₂×Dic₃	C₂⁴×C₅	1	8	yes	—
303	D₁₂	—	2	8	no	—
304	C₄×D₃	—	2	16	no	—
305	Dic₆	—	2	16	no	—
306	Dic₆	—	2	16	no	—
307	Dic₆	—	2	8	no	—
308	C₂²×C₅	—	2	4	no	—
309	C₂²×C₅	—	2	8	no	—
310	C₂²×C₅	—	6	4	no	—
311	C₂²×C₅	—	6	8	no	—
312	C₂²×C₅	—	12	8	no	—
313	C₂²×C₅	C₂²×D₁₂	1	4	yes	—
314	C₂²×C₅	C₂²×D₁₂	1	2	yes	—
315	C₂²×C₅	#1010	1	4	yes	—
316	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
317	C₄×C₅	—	2	8	no	—
318	C₄×C₅	—	6	4	no	—
319	C₄×C₅	—	6	8	no	—
320	C₄×C₅	C₂²×D₁₂	1	4	yes	—
321	C₄×C₅	C₂²×D₁₂	1	4	yes	—
322	C₂⁴	—	3	2	no	—
323	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
324	#41	—	6	32	no	—
325	C₂×Q₈	—	3	8	no	—
326	C₂×Q₈	—	3	8	no	—
327	C₂×Q₈	—	3	4	no	—
328	C₂×Q₈	—	6	8	no	—
329	C₂×Q₈	—	6	8	no	—
330	C₂×Q₈	—	6	32	no	—
331	C₂×Q₈	—	6	4	no	—
332	C₂×D₄	—	3	8	no	—
333	C₂×D₄	—	3	4	no	—
334	C₂×D₄	—	6	8	no	—
335	C₂×D₄	—	6	4	no	—
336	C₂²×C₄	—	3	4	no	—
337	C₂²×C₄	—	3	2	no	—
338	C₂²×C₄	—	3	8	no	—
339	C₂²×C₄	—	3	8	no	—
340	C₂²×C₄	—	6	8	no	—
341	C₂²×C₄	—	6	8	no	—
342	C₂²×C₄	C₅×D₁₂	1	8	yes	—
343	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
344	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
345	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
346	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
347	C₄⋊C₄	—	3	32	no	—
348	C₄⋊C₄	C₂²×C₅×D₃	1	8	yes	—
349	C₂²⋊C₄	—	3	32	no	—
350	C₂²⋊C₄	C₂²×C₅×D₃	1	8	yes	—
351	C₄²	C₂²×C₅×D₃	1	8	yes	—
352	C₃×C₅	C₂×#536	1	1	yes	characteristic, complemented, Hall
353	C₂²×C₃	—	2	8	no	—
354	C₂²×C₃	—	2	4	no	—
355	C₂²×C₃	C₂²×C₅×D₄	1	4	yes	—
356	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
357	C₂²×C₃	C₅×2₋¹⁺⁴	1	4	yes	—
358	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
359	C₂×D₃	—	2	4	no	—
360	C₂×D₃	—	2	8	no	—
361	C₂×D₃	—	4	8	no	—
362	C₃×C₄	—	2	8	no	—
363	C₃×C₄	C₂²×C₅×D₄	1	4	yes	—
364	C₃×C₄	C₂²×C₅×D₄	1	4	yes	—
365	Dic₃	—	2	8	no	—
366	Dic₃	—	2	4	no	—
367	C₂×C₅	—	2	4	no	—
368	C₂×C₅	—	12	4	no	—
369	C₂×C₅	#5526	1	4	yes	direct product factor
370	C₂×C₅	C₂³×D₁₂	1	1	yes	characteristic
371	C₂×C₅	C₂×#1010	1	2	yes	—
372	C₂³	—	2	4	no	—
373	C₂³	—	3	4	no	—
374	C₂³	—	6	4	no	—
375	C₂³	—	6	8	no	—
376	C₂³	C₂×C₅×D₁₂	1	4	yes	—
377	C₂³	C₂³×C₅×D₃	1	2	yes	—
378	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
379	Q₈	—	6	16	no	—
380	Q₈	—	6	16	no	—
381	Q₈	—	6	8	no	—
382	D₄	—	6	16	no	—
383	D₄	—	6	8	no	—
384	C₂×C₄	—	2	8	no	—
385	C₂×C₄	—	3	8	no	—
386	C₂×C₄	—	3	4	no	—
387	C₂×C₄	—	6	4	no	—
388	C₂×C₄	—	6	16	no	—
389	C₂×C₄	—	6	8	no	—
390	C₂×C₄	—	6	16	no	—
391	C₂×C₄	C₂×C₅×D₁₂	1	4	yes	—
392	C₂×C₄	C₂×C₅×D₁₂	1	4	yes	—
393	C₂×C₄	C₂×C₅×D₁₂	1	16	yes	—
394	C₂×C₄	C₂³×C₅×D₃	1	8	yes	—
395	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
396	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
397	C₂×C₃	—	2	4	no	—
398	C₂×C₃	C₅×#536	1	4	yes	complemented
399	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
400	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	2	yes	—
401	D₃	—	4	4	no	—
402	C₅	C₂×#5526	1	1	yes	characteristic, direct product factor, Sylow
403	C₂²	—	2	4	no	—
404	C₂²	—	2	8	no	—
405	C₂²	—	6	4	no	—
406	C₂²	—	6	8	no	—
407	C₂²	—	12	8	no	—
408	C₂²	C₂²×C₅×D₁₂	1	4	yes	—
409	C₂²	C₂²×C₅×D₁₂	1	2	yes	—
410	C₂²	C₅×#1010	1	4	yes	—
411	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
412	C₄	—	2	8	no	—
413	C₄	—	6	4	no	—
414	C₄	—	6	8	no	—
415	C₄	C₂²×C₅×D₁₂	1	4	yes	—
416	C₄	C₂²×C₅×D₁₂	1	4	yes	—
417	C₃	C₂×C₅×#536	1	1	yes	characteristic, complemented, Sylow
418	C₂	—	2	4	no	—
419	C₂	—	12	4	no	—
420	C₂	C₅×#5526	1	4	yes	direct product factor
421	C₂	C₂³×C₅×D₁₂	1	1	yes	characteristic
422	C₂	C₂×C₅×#1010	1	2	yes	—

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂×C₃×C₅×#117	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₅×#235	C₂
hypercenter	C₂×C₅×#117	D₃
hypocenter	C₃	C₂×C₅×#536
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#117

Complements

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

N	H ≅ G/N	type
2. C₂³×C₅×Dic₆	C₂	semidirect
3. C₂×C₃×C₅×#117	C₂	semidirect
4. C₅×#5526	C₂	direct (N × H)
5. C₂×C₅×#897	C₂	semidirect
6. C₂×C₅×#886	C₂	semidirect
7. C₂×C₅×#875	C₂	semidirect
8. C₂×C₅×#869	C₂	semidirect
21. C₂²×C₅×Dic₆	C₂²	semidirect
22. C₃×C₅×#117	C₂²	semidirect
28. C₅×#897	C₂²	semidirect
29. C₅×#886	C₂²	semidirect
30. C₅×#875	C₂²	semidirect
31. C₅×#869	C₂²	semidirect
32. C₂×#5526	C₅	direct (N × H)
40. C₂×C₅×#117	D₃	semidirect
72. C₂³×Dic₆	C₂×C₅	semidirect
73. C₂×C₃×#117	C₂×C₅	semidirect
74. #5526	C₂×C₅	direct (N × H)
75. C₂×#897	C₂×C₅	semidirect
76. C₂×#886	C₂×C₅	semidirect
77. C₂×#875	C₂×C₅	semidirect
78. C₂×#869	C₂×C₅	semidirect
95. C₅×#117	C₂×D₃	semidirect
138. C₂²×Dic₆	C₂²×C₅	semidirect
139. C₃×#117	C₂²×C₅	semidirect
145. #897	C₂²×C₅	semidirect
146. #886	C₂²×C₅	semidirect
147. #875	C₂²×C₅	semidirect
148. #869	C₂²×C₅	semidirect
186. C₂×#117	C₅×D₃	semidirect
272. #117	C₂×C₅×D₃	semidirect
279. C₂×C₃×C₅	#536	semidirect
352. C₃×C₅	C₂×#536	semidirect
369. C₂×C₅	#5526	direct (N × H)
398. C₂×C₃	C₅×#536	semidirect
402. C₅	C₂×#5526	direct (N × H)
417. C₃	C₂×C₅×#536	semidirect
420. C₂	C₅×#5526	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×#235	2
C₂³×C₅×Dic₆	2
C₂×C₃×C₅×#117	2
C₅×#5526	2
C₂×C₅×#897	2
C₂×C₅×#886	2
C₂×C₅×#875	2
C₂×C₅×#869	2
C₂×C₅×#536	3
C₂×#5526	5

Subgroups — C2×C5×#5526 #14480479

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5526 #14480479