Subgroups — C₂×C₅×#5542 #14483994

Order 1920.

2224 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	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#936	C₂	1	2	yes	maximal
3	C₂×C₅×#926	C₂	1	2	yes	maximal, complemented
4	C₂×C₅×#924	C₂	1	2	yes	maximal, complemented
5	C₅×#5542	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₅×#887	C₂	1	2	yes	maximal, complemented
7	C₂×C₅×#879	C₂	1	4	yes	maximal, complemented
8	C₂×C₅×#869	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄×C₅×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#556	—	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×Dic₆	C₂²	1	1	yes	characteristic
14	C₂²×C₅×Dic₆	C₂²	1	2	yes	—
15	C₃×C₄×C₅×D₄	C₂²	1	8	yes	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
18	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
19	C₂×C₅×#217	C₂²	1	4	yes	—
20	C₂×C₅×#217	C₂²	1	4	yes	—
21	C₅×#936	C₂²	1	16	yes	—
22	C₅×#926	C₂²	1	16	yes	complemented
23	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
24	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
25	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
26	C₅×#924	C₂²	1	16	yes	complemented
27	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
28	C₂×C₅×Dic₃⋊C₄	C₂²	1	4	yes	—
29	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
30	C₂×C₄×C₅×Dic₃	C₂²	1	4	yes	—
31	C₅×#887	C₂²	1	16	yes	complemented
32	C₅×#879	C₂²	1	32	yes	complemented
33	C₅×#869	C₂²	1	8	yes	complemented
34	C₄×C₅×Dic₆	C₂²	1	8	yes	complemented
35	C₂×#5542	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
36	C₅×#556	—	3	16	no	—
37	C₂×C₅×C₄⋊Q₈	—	3	1	no	—
38	C₂×C₅×#126	—	3	4	no	—
39	C₂×C₅×#124	—	3	2	no	—
40	C₂×C₅×C₂²⋊Q₈	—	3	2	no	—
41	C₂×C₄×C₅×Q₈	—	3	2	no	—
42	C₂×C₄×C₅×Q₈	—	3	1	no	—
43	C₂×C₄×C₅×D₄	D₃	1	1	yes	characteristic
44	C₂×C₅×#117	—	3	2	no	—
45	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
46	C₂×C₃×C₅×D₄	—	2	4	no	—
47	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
48	C₂²×C₃×C₄×C₅	—	2	8	no	—
49	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂²×C₃×C₄×C₅	C₂³	1	8	yes	—
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
55	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
56	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
57	C₂×C₅×Dic₆	—	2	8	no	—
58	C₂×C₅×Dic₆	—	2	4	no	—
59	C₂×C₅×Dic₆	C₂³	1	4	yes	—
60	C₂×C₅×Dic₆	C₂³	1	8	yes	—
61	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
62	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
63	C₃×C₄²×C₅	C₂³	1	4	yes	—
64	C₅×#217	C₂³	1	16	yes	—
65	C₅×#217	C₂³	1	16	yes	—
66	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
67	C₅×C₄⋊Dic₃	C₂³	1	8	yes	—
68	C₅×C₄⋊Dic₃	C₂³	1	8	yes	—
69	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
70	C₅×Dic₃⋊C₄	C₂³	1	16	yes	—
71	C₄×C₅×Dic₃	C₂³	1	8	yes	—
72	C₄×C₅×Dic₃	C₂³	1	16	yes	—
73	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic
74	C₂×#936	C₂×C₅	1	2	yes	—
75	C₂×#926	C₂×C₅	1	2	yes	complemented
76	C₂×#924	C₂×C₅	1	2	yes	complemented
77	#5542	C₂×C₅	1	16	yes	direct product factor
78	C₂×#887	C₂×C₅	1	2	yes	complemented
79	C₂×#879	C₂×C₅	1	4	yes	complemented
80	C₂×#869	C₂×C₅	1	1	yes	characteristic, complemented
81	C₂×C₄×Dic₆	C₂×C₅	1	1	yes	characteristic, complemented
82	C₂²×C₅×Q₈	—	3	1	no	—
83	C₂²×C₅×Q₈	—	3	2	no	—
84	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
85	C₂³×C₄×C₅	C₂×D₃	1	2	yes	—
86	C₅×C₄⋊Q₈	—	3	8	no	—
87	C₅×#126	—	3	32	no	—
88	C₅×#124	—	3	16	no	—
89	C₅×C₂²⋊Q₈	—	3	16	no	—
90	C₄×C₅×Q₈	—	3	16	no	—
91	C₄×C₅×Q₈	—	3	8	no	—
92	C₄×C₅×D₄	C₂×D₃	1	8	yes	—
93	C₅×#117	—	3	16	no	—
94	C₂×C₅×C₄⋊C₄	—	3	4	no	—
95	C₂×C₅×C₄⋊C₄	—	3	2	no	—
96	C₂×C₅×C₄⋊C₄	—	3	1	no	—
97	C₂×C₅×C₄⋊C₄	—	3	2	no	—
98	C₂×C₅×C₄⋊C₄	—	3	2	no	—
99	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
100	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
101	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
102	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
103	C₂×C₄²×C₅	—	3	4	no	—
104	C₂×C₄²×C₅	—	3	2	no	—
105	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
106	C₂×#556	—	3	1	no	Sylow
107	C₂³×C₃×C₅	—	2	4	no	—
108	C₂³×C₃×C₅	—	2	4	no	—
109	C₂³×C₃×C₅	—	2	4	no	—
110	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
111	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
112	C₃×C₅×D₄	—	2	8	no	—
113	C₂×C₃×C₄×C₅	—	2	4	no	—
114	C₂×C₃×C₄×C₅	—	2	2	no	—
115	C₂×C₃×C₄×C₅	—	2	16	no	—
116	C₂×C₃×C₄×C₅	#41	1	4	yes	—
117	C₂×C₃×C₄×C₅	#41	1	4	yes	—
118	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
119	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
120	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
121	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
122	C₂×C₅×Dic₃	—	2	8	no	—
123	C₂×C₅×Dic₃	—	2	4	no	—
124	C₂×C₅×Dic₃	—	2	4	no	—
125	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
126	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
127	C₂×C₅×Dic₃	C₂⁴	1	8	yes	—
128	C₅×Dic₆	—	2	16	no	—
129	C₅×Dic₆	—	2	8	no	—
130	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
131	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
132	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
133	C₂²×Dic₆	C₂²×C₅	1	2	yes	—
134	C₃×C₄×D₄	C₂²×C₅	1	8	yes	—
135	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
136	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
137	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
138	C₂×#217	C₂²×C₅	1	4	yes	—
139	C₂×#217	C₂²×C₅	1	4	yes	—
140	#936	C₂²×C₅	1	16	yes	—
141	#926	C₂²×C₅	1	16	yes	complemented
142	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
143	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
144	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
145	#924	C₂²×C₅	1	16	yes	complemented
146	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
147	C₂×Dic₃⋊C₄	C₂²×C₅	1	4	yes	—
148	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
149	C₂×C₄×Dic₃	C₂²×C₅	1	4	yes	—
150	#887	C₂²×C₅	1	16	yes	complemented
151	#879	C₂²×C₅	1	32	yes	complemented
152	#869	C₂²×C₅	1	8	yes	complemented
153	C₄×Dic₆	C₂²×C₅	1	8	yes	complemented
154	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
155	C₂×C₅×Q₈	—	3	4	no	—
156	C₂×C₅×Q₈	—	3	8	no	—
157	C₂×C₅×Q₈	—	6	8	no	—
158	C₂×C₅×Q₈	—	6	4	no	—
159	C₂×C₅×D₄	—	2	4	no	—
160	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
161	C₂²×C₄×C₅	—	2	8	no	—
162	C₂²×C₄×C₅	—	3	2	no	—
163	C₂²×C₄×C₅	—	3	4	no	—
164	C₂²×C₄×C₅	—	3	2	no	—
165	C₂²×C₄×C₅	C₂²×D₃	1	8	yes	—
166	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
167	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
168	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
169	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
170	C₅×C₄⋊C₄	—	3	4	no	—
171	C₅×C₄⋊C₄	—	3	8	no	—
172	C₅×C₄⋊C₄	—	3	16	no	—
173	C₅×C₄⋊C₄	—	3	8	no	—
174	C₅×C₄⋊C₄	—	3	8	no	—
175	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
176	C₅×C₂²⋊C₄	—	3	16	no	—
177	C₅×C₂²⋊C₄	—	3	16	no	—
178	C₅×C₂²⋊C₄	C₂²×D₃	1	8	yes	—
179	C₄²×C₅	—	3	16	no	—
180	C₄²×C₅	—	3	8	no	—
181	C₄²×C₅	C₂²×D₃	1	4	yes	—
182	#556	—	3	16	no	—
183	C₂×C₄⋊Q₈	—	3	1	no	—
184	C₂×#126	—	3	4	no	—
185	C₂×#124	—	3	2	no	—
186	C₂×C₂²⋊Q₈	—	3	2	no	—
187	C₂×C₄×Q₈	—	3	2	no	—
188	C₂×C₄×Q₈	—	3	1	no	—
189	C₂×C₄×D₄	C₅×D₃	1	1	yes	characteristic
190	C₂×#117	—	3	2	no	—
191	C₂²×C₃×C₅	—	2	4	no	—
192	C₂²×C₃×C₅	—	2	4	no	—
193	C₂²×C₃×C₅	—	2	4	no	—
194	C₂²×C₃×C₅	—	4	8	no	—
195	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
196	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
197	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
198	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
199	C₃×C₄×C₅	—	2	4	no	—
200	C₃×C₄×C₅	—	2	2	no	—
201	C₃×C₄×C₅	C₂×#41	1	4	yes	—
202	C₃×C₄×C₅	C₂×#41	1	4	yes	—
203	C₅×Dic₃	—	2	8	no	—
204	C₅×Dic₃	—	2	4	no	—
205	C₅×Dic₃	—	2	4	no	—
206	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
207	C₂×C₃×D₄	—	2	4	no	—
208	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
209	C₂²×C₃×C₄	—	2	8	no	—
210	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
211	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
212	C₂²×C₃×C₄	C₂³×C₅	1	8	yes	—
213	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
214	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
215	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
216	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
217	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
218	C₂×Dic₆	—	2	8	no	—
219	C₂×Dic₆	—	2	4	no	—
220	C₂×Dic₆	C₂³×C₅	1	4	yes	—
221	C₂×Dic₆	C₂³×C₅	1	8	yes	—
222	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
223	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
224	C₃×C₄²	C₂³×C₅	1	4	yes	—
225	#217	C₂³×C₅	1	16	yes	—
226	#217	C₂³×C₅	1	16	yes	—
227	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
228	C₄⋊Dic₃	C₂³×C₅	1	8	yes	—
229	C₄⋊Dic₃	C₂³×C₅	1	8	yes	—
230	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
231	Dic₃⋊C₄	C₂³×C₅	1	16	yes	—
232	C₄×Dic₃	C₂³×C₅	1	8	yes	—
233	C₄×Dic₃	C₂³×C₅	1	16	yes	—
234	C₂³×C₅	—	2	4	no	—
235	C₂³×C₅	—	2	4	no	—
236	C₂³×C₅	—	2	4	no	—
237	C₂³×C₅	C₂³×D₃	1	4	yes	—
238	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
239	C₅×Q₈	—	6	16	no	—
240	C₅×Q₈	—	6	8	no	—
241	C₅×D₄	—	2	8	no	—
242	C₂×C₄×C₅	—	2	4	no	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	—	2	16	no	—
245	C₂×C₄×C₅	—	3	4	no	—
246	C₂×C₄×C₅	—	3	8	no	—
247	C₂×C₄×C₅	—	3	4	no	—
248	C₂×C₄×C₅	—	6	8	no	—
249	C₂×C₄×C₅	—	6	4	no	—
250	C₂×C₄×C₅	—	6	4	no	—
251	C₂×C₄×C₅	#235	1	4	yes	—
252	C₂×C₄×C₅	#237	1	4	yes	—
253	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
254	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
255	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
256	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
257	C₂²×Q₈	—	3	1	no	—
258	C₂²×Q₈	—	3	2	no	—
259	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
260	C₂³×C₄	C₂×C₅×D₃	1	2	yes	—
261	C₄⋊Q₈	—	3	8	no	—
262	#126	—	3	32	no	—
263	#124	—	3	16	no	—
264	C₂²⋊Q₈	—	3	16	no	—
265	C₄×Q₈	—	3	16	no	—
266	C₄×Q₈	—	3	8	no	—
267	C₄×D₄	C₂×C₅×D₃	1	8	yes	—
268	#117	—	3	16	no	—
269	C₂×C₄⋊C₄	—	3	1	no	—
270	C₂×C₄⋊C₄	—	3	2	no	—
271	C₂×C₄⋊C₄	—	3	4	no	—
272	C₂×C₄⋊C₄	—	3	2	no	—
273	C₂×C₄⋊C₄	—	3	2	no	—
274	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
275	C₂×C₂²⋊C₄	—	3	4	no	—
276	C₂×C₂²⋊C₄	—	3	4	no	—
277	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
278	C₂×C₄²	—	3	4	no	—
279	C₂×C₄²	—	3	2	no	—
280	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
281	C₂×C₃×C₅	—	4	4	no	—
282	C₂×C₃×C₅	#556	1	4	yes	complemented
283	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
284	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
285	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
286	C₂³×C₃	—	2	4	no	—
287	C₂³×C₃	—	2	4	no	—
288	C₂³×C₃	—	2	4	no	—
289	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
290	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
291	C₃×D₄	—	2	8	no	—
292	C₂×C₃×C₄	—	2	4	no	—
293	C₂×C₃×C₄	—	2	2	no	—
294	C₂×C₃×C₄	—	2	16	no	—
295	C₂×C₃×C₄	C₅×#41	1	4	yes	—
296	C₂×C₃×C₄	C₅×#41	1	4	yes	—
297	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
298	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
299	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
300	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
301	C₂×Dic₃	—	2	8	no	—
302	C₂×Dic₃	—	2	4	no	—
303	C₂×Dic₃	—	2	4	no	—
304	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
305	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
306	C₂×Dic₃	C₂⁴×C₅	1	8	yes	—
307	Dic₆	—	2	16	no	—
308	Dic₆	—	2	8	no	—
309	C₂²×C₅	—	2	4	no	—
310	C₂²×C₅	—	2	4	no	—
311	C₂²×C₅	—	2	4	no	—
312	C₂²×C₅	—	4	8	no	—
313	C₂²×C₅	C₂×#235	1	2	yes	—
314	C₂²×C₅	C₂×#237	1	2	yes	—
315	C₂²×C₅	#1010	1	2	yes	—
316	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
317	C₄×C₅	—	2	4	no	—
318	C₄×C₅	—	2	2	no	—
319	C₄×C₅	—	6	8	no	—
320	C₄×C₅	—	6	4	no	—
321	C₄×C₅	—	6	4	no	—
322	C₄×C₅	C₂×#235	1	4	yes	—
323	C₄×C₅	C₂×#237	1	4	yes	—
324	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
325	C₂×Q₈	—	3	4	no	—
326	C₂×Q₈	—	3	8	no	—
327	C₂×Q₈	—	6	8	no	—
328	C₂×Q₈	—	6	4	no	—
329	C₂×D₄	—	2	4	no	—
330	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
331	C₂²×C₄	—	2	8	no	—
332	C₂²×C₄	—	3	2	no	—
333	C₂²×C₄	—	3	4	no	—
334	C₂²×C₄	—	3	2	no	—
335	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
336	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
337	C₂²×C₄	C₂²×C₅×D₃	1	8	yes	—
338	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
339	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
340	C₄⋊C₄	—	3	4	no	—
341	C₄⋊C₄	—	3	8	no	—
342	C₄⋊C₄	—	3	16	no	—
343	C₄⋊C₄	—	3	8	no	—
344	C₄⋊C₄	—	3	8	no	—
345	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
346	C₂²⋊C₄	—	3	16	no	—
347	C₂²⋊C₄	—	3	16	no	—
348	C₂²⋊C₄	C₂²×C₅×D₃	1	8	yes	—
349	C₄²	—	3	16	no	—
350	C₄²	—	3	8	no	—
351	C₄²	C₂²×C₅×D₃	1	4	yes	—
352	C₃×C₅	C₂×#556	1	1	yes	characteristic, complemented, Hall
353	C₂²×C₃	—	2	4	no	—
354	C₂²×C₃	—	2	4	no	—
355	C₂²×C₃	—	2	4	no	—
356	C₂²×C₃	—	4	8	no	—
357	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
358	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
359	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
360	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
361	C₃×C₄	—	2	4	no	—
362	C₃×C₄	—	2	2	no	—
363	C₃×C₄	C₂×C₅×#41	1	4	yes	—
364	C₃×C₄	C₂×C₅×#41	1	4	yes	—
365	Dic₃	—	2	8	no	—
366	Dic₃	—	2	4	no	—
367	Dic₃	—	2	4	no	—
368	C₂×C₅	—	4	4	no	—
369	C₂×C₅	#5542	1	4	yes	direct product factor
370	C₂×C₅	C₂²×#235	1	1	yes	characteristic
371	C₂×C₅	C₂²×#237	1	1	yes	characteristic
372	C₂×C₅	C₂×#1010	1	1	yes	characteristic
373	C₂³	—	2	4	no	—
374	C₂³	—	2	4	no	—
375	C₂³	—	2	4	no	—
376	C₂³	C₂³×C₅×D₃	1	4	yes	—
377	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
378	Q₈	—	6	16	no	—
379	Q₈	—	6	8	no	—
380	D₄	—	2	8	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	16	no	—
384	C₂×C₄	—	3	4	no	—
385	C₂×C₄	—	3	8	no	—
386	C₂×C₄	—	3	4	no	—
387	C₂×C₄	—	6	8	no	—
388	C₂×C₄	—	6	4	no	—
389	C₂×C₄	—	6	4	no	—
390	C₂×C₄	C₅×#235	1	4	yes	—
391	C₂×C₄	C₅×#237	1	4	yes	—
392	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
393	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
394	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
395	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
396	C₂×C₃	—	4	4	no	—
397	C₂×C₃	C₅×#556	1	4	yes	complemented
398	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
399	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
400	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
401	C₅	C₂×#5542	1	1	yes	characteristic, direct product factor, Sylow
402	C₂²	—	2	4	no	—
403	C₂²	—	2	4	no	—
404	C₂²	—	2	4	no	—
405	C₂²	—	4	8	no	—
406	C₂²	C₂×C₅×#235	1	2	yes	—
407	C₂²	C₂×C₅×#237	1	2	yes	—
408	C₂²	C₅×#1010	1	2	yes	—
409	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
410	C₄	—	2	4	no	—
411	C₄	—	2	2	no	—
412	C₄	—	6	8	no	—
413	C₄	—	6	4	no	—
414	C₄	—	6	4	no	—
415	C₄	C₂×C₅×#235	1	4	yes	—
416	C₄	C₂×C₅×#237	1	4	yes	—
417	C₃	C₂×C₅×#556	1	1	yes	characteristic, complemented, Sylow
418	C₂	—	4	4	no	—
419	C₂	C₅×#5542	1	4	yes	direct product factor
420	C₂	C₂²×C₅×#235	1	1	yes	characteristic
421	C₂	C₂²×C₅×#237	1	1	yes	characteristic
422	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
prime radical	C₂²×C₃×C₅×D₄	C₂²
hypercenter	C₂×C₄×C₅×D₄	D₃
hypocenter	C₃	C₂×C₅×#556
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
3. C₂×C₅×#926	C₂	semidirect
4. C₂×C₅×#924	C₂	semidirect
5. C₅×#5542	C₂	direct (N × H)
6. C₂×C₅×#887	C₂	semidirect
7. C₂×C₅×#879	C₂	semidirect
8. C₂×C₅×#869	C₂	semidirect
9. C₂×C₄×C₅×Dic₆	C₂	semidirect
22. C₅×#926	C₂²	semidirect
26. C₅×#924	C₂²	semidirect
31. C₅×#887	C₂²	semidirect
32. C₅×#879	C₂²	semidirect
33. C₅×#869	C₂²	semidirect
34. C₄×C₅×Dic₆	C₂²	semidirect
35. C₂×#5542	C₅	direct (N × H)
75. C₂×#926	C₂×C₅	semidirect
76. C₂×#924	C₂×C₅	semidirect
77. #5542	C₂×C₅	direct (N × H)
78. C₂×#887	C₂×C₅	semidirect
79. C₂×#879	C₂×C₅	semidirect
80. C₂×#869	C₂×C₅	semidirect
81. C₂×C₄×Dic₆	C₂×C₅	semidirect
141. #926	C₂²×C₅	semidirect
145. #924	C₂²×C₅	semidirect
150. #887	C₂²×C₅	semidirect
151. #879	C₂²×C₅	semidirect
152. #869	C₂²×C₅	semidirect
153. C₄×Dic₆	C₂²×C₅	semidirect
282. C₂×C₃×C₅	#556	semidirect
352. C₃×C₅	C₂×#556	semidirect
369. C₂×C₅	#5542	direct (N × H)
397. C₂×C₃	C₅×#556	semidirect
401. C₅	C₂×#5542	direct (N × H)
417. C₃	C₂×C₅×#556	semidirect
419. C₂	C₅×#5542	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×D₄	2
C₂×C₅×#936	2
C₂×C₅×#926	2
C₂×C₅×#924	2
C₅×#5542	2
C₂×C₅×#887	2
C₂×C₅×#879	2
C₂×C₅×#869	2
C₂×C₄×C₅×Dic₆	2
C₂×C₅×#556	3
C₂×#5542	5

Subgroups — C2×C5×#5542 #14483994

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5542 #14483994