Subgroups — C₂×C₅×#4794 #14437860

Order 1920.

872 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#947	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#888	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#103	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#835	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#821	C₂	1	1	yes	maximal, characteristic
6	C₂×C₅×#815	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#809	C₂	1	1	yes	maximal, characteristic
8	C₅×#4794	C₂	1	8	yes	maximal, direct product factor
9	C₂×C₅×#489	—	3	1	no	maximal, Hall
10	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
12	C₂²×C₅×Dic₆	—	2	1	no	—
13	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₅×#947	—	2	2	no	—
16	C₅×#947	C₂²	1	4	yes	—
17	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
18	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
19	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
20	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
21	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
22	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
23	C₅×#888	—	2	2	no	—
24	C₅×#888	C₂²	1	4	yes	complemented
25	C₃×C₅×#103	C₂²	1	4	yes	complemented
26	C₅×#835	C₂²	1	4	yes	complemented
27	C₅×#821	C₂²	1	4	yes	—
28	C₅×#815	C₂²	1	4	yes	complemented
29	C₅×#809	C₂²	1	4	yes	—
30	C₂×#4794	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₂×C₅×C₄⋊Q₈	—	3	1	no	—
32	C₂×C₅×#124	—	3	1	no	—
33	C₅×#489	—	3	8	no	—
34	C₂×C₅×#103	—	3	1	no	—
35	C₂×C₅×#103	D₃	1	1	yes	characteristic, complemented
36	C₂×C₅×#102	—	3	1	no	—
37	C₂×C₅×#102	—	3	1	no	—
38	C₂×C₅×#97	—	3	1	no	—
39	C₂³×C₅×D₃	—	2	1	no	—
40	C₂×C₃×C₅×Q₈	—	2	1	no	—
41	C₂×C₃×C₅×Q₈	—	2	2	no	—
42	C₂×C₃×C₅×Q₈	—	2	2	no	—
43	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
44	C₂²×C₃×C₄×C₅	—	2	1	no	—
45	C₂²×C₃×C₄×C₅	—	2	1	no	—
46	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₂²×C₅×Dic₃	—	2	1	no	—
48	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
49	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
50	C₂×C₅×D₁₂	—	2	2	no	—
51	C₂×C₅×D₁₂	—	2	2	no	—
52	C₂×C₅×D₁₂	—	2	1	no	—
53	C₂×C₅×D₁₂	C₂³	1	2	yes	—
54	C₂×C₅×Dic₆	—	2	4	no	—
55	C₂×C₅×Dic₆	—	4	4	no	—
56	C₂×C₃×C₅×C₈	—	2	2	no	—
57	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
58	C₃×C₅×C₄⋊C₄	—	2	1	no	—
59	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
60	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
61	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
62	C₅×C₄⋊Dic₃	—	2	1	no	—
63	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
64	C₅×Dic₃⋊C₄	—	2	4	no	—
65	C₄×C₅×Dic₃	D₄	1	2	yes	—
66	C₄×C₅×Dic₃	C₂³	1	2	yes	—
67	C₂×C₅×C₃⋊C₈	—	2	2	no	—
68	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
69	C₂×#947	C₂×C₅	1	1	yes	characteristic
70	C₂×#888	C₂×C₅	1	1	yes	characteristic, complemented
71	C₂×C₃×#103	C₂×C₅	1	1	yes	characteristic, complemented
72	C₂×#835	C₂×C₅	1	1	yes	characteristic, complemented
73	C₂×#821	C₂×C₅	1	1	yes	characteristic
74	C₂×#815	C₂×C₅	1	1	yes	characteristic, complemented
75	C₂×#809	C₂×C₅	1	1	yes	characteristic
76	#4794	C₂×C₅	1	8	yes	direct product factor
77	C₂²×C₅×Q₈	—	6	1	no	—
78	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
79	C₂²×C₅×D₄	—	3	1	no	—
80	C₂²×C₅×C₈	—	3	1	no	—
81	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
82	C₅×C₄⋊Q₈	—	3	4	no	—
83	C₅×C₄⋊Q₈	—	6	2	no	—
84	C₅×#124	—	3	4	no	—
85	C₅×#124	—	6	2	no	—
86	C₂×C₅×C₄⋊C₄	—	3	1	no	—
87	C₂×C₅×C₄⋊C₄	—	6	1	no	—
88	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
89	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
90	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
91	C₂×C₄²×C₅	—	3	1	no	—
92	C₅×#103	—	3	4	no	—
93	C₅×#103	C₂×D₃	1	4	yes	complemented
94	C₅×#102	—	3	4	no	—
95	C₅×#102	—	3	4	no	—
96	C₅×#97	—	3	4	no	—
97	C₂×#489	—	3	1	no	Sylow
98	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₅×D₃	—	2	2	no	—
100	C₂²×C₅×D₃	—	4	2	no	—
101	C₂²×C₅×D₃	—	4	2	no	—
102	C₂²×C₅×D₃	—	4	2	no	—
103	C₃×C₅×Q₈	—	2	2	no	—
104	C₃×C₅×Q₈	—	2	2	no	—
105	C₃×C₅×Q₈	—	4	2	no	—
106	C₂×C₃×C₄×C₅	—	2	2	no	—
107	C₂×C₃×C₄×C₅	—	2	2	no	—
108	C₂×C₃×C₄×C₅	—	4	2	no	—
109	C₂×C₃×C₄×C₅	—	4	2	no	—
110	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
111	C₂×C₃×C₄×C₅	#41	1	2	yes	—
112	C₂×C₃×C₄×C₅	#41	1	2	yes	—
113	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
114	C₂×C₅×Dic₃	—	2	2	no	—
115	C₂×C₅×Dic₃	—	2	2	no	—
116	C₂×C₅×Dic₃	—	2	2	no	—
117	C₂×C₅×Dic₃	—	4	2	no	—
118	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
119	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
120	C₅×D₁₂	—	2	2	no	—
121	C₅×D₁₂	—	2	2	no	—
122	C₅×D₁₂	—	4	2	no	—
123	C₅×Dic₆	—	4	8	no	—
124	C₃×C₅×C₈	—	2	2	no	—
125	C₅×C₃⋊C₈	—	2	2	no	—
126	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
127	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
128	C₂²×Dic₆	—	2	1	no	—
129	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
130	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
131	#947	—	2	2	no	—
132	#947	C₂²×C₅	1	4	yes	—
133	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
134	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
135	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
136	C₂×Dic₃⋊C₄	—	2	1	no	—
137	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
138	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
139	#888	—	2	2	no	—
140	#888	C₂²×C₅	1	4	yes	complemented
141	C₃×#103	C₂²×C₅	1	4	yes	complemented
142	#835	C₂²×C₅	1	4	yes	complemented
143	#821	C₂²×C₅	1	4	yes	—
144	#815	C₂²×C₅	1	4	yes	complemented
145	#809	C₂²×C₅	1	4	yes	—
146	C₂⁴×C₅	—	6	1	no	—
147	C₂×C₅×Q₈	—	2	1	no	—
148	C₂×C₅×Q₈	—	2	2	no	—
149	C₂×C₅×Q₈	—	2	2	no	—
150	C₂×C₅×Q₈	—	6	4	no	—
151	C₂×C₅×Q₈	—	12	4	no	—
152	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
153	C₂×C₅×D₄	—	3	2	no	—
154	C₂×C₅×D₄	—	6	2	no	—
155	C₂×C₅×D₄	—	6	1	no	—
156	C₂×C₅×D₄	—	6	2	no	—
157	C₂²×C₄×C₅	—	2	1	no	—
158	C₂²×C₄×C₅	—	2	1	no	—
159	C₂²×C₄×C₅	—	3	1	no	—
160	C₂²×C₄×C₅	—	3	1	no	—
161	C₂²×C₄×C₅	—	6	1	no	—
162	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
163	C₂×C₅×C₈	—	2	2	no	—
164	C₂×C₅×C₈	—	3	2	no	—
165	C₂×C₅×C₈	—	6	2	no	—
166	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
167	C₅×C₄⋊C₄	—	2	1	no	—
168	C₅×C₄⋊C₄	—	3	2	no	—
169	C₅×C₄⋊C₄	—	6	4	no	—
170	C₅×C₄⋊C₄	—	6	1	no	—
171	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
172	C₅×C₂²⋊C₄	—	6	4	no	—
173	C₅×C₂²⋊C₄	—	6	4	no	—
174	C₄²×C₅	—	3	2	no	—
175	C₄²×C₅	—	3	2	no	—
176	C₂×C₄⋊Q₈	—	3	1	no	—
177	C₂×#124	—	3	1	no	—
178	#489	—	3	8	no	—
179	C₂×#103	—	3	1	no	—
180	C₂×#103	C₅×D₃	1	1	yes	characteristic, complemented
181	C₂×#102	—	3	1	no	—
182	C₂×#102	—	3	1	no	—
183	C₂×#97	—	3	1	no	—
184	C₂²×C₃×C₅	#124	1	2	yes	—
185	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
186	C₂²×C₃×C₅	#137	1	2	yes	—
187	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₅×D₃	—	4	2	no	—
189	C₂×C₅×D₃	—	4	2	no	—
190	C₂×C₅×D₃	—	4	2	no	—
191	C₂×C₅×D₃	—	8	4	no	—
192	C₃×C₄×C₅	—	4	2	no	—
193	C₃×C₄×C₅	—	4	2	no	—
194	C₃×C₄×C₅	#124	1	2	yes	—
195	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
196	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
197	C₅×Dic₃	—	2	2	no	—
198	C₅×Dic₃	—	2	2	no	—
199	C₅×Dic₃	—	4	2	no	—
200	C₂³×D₃	—	2	1	no	—
201	C₂×C₃×Q₈	—	2	1	no	—
202	C₂×C₃×Q₈	—	2	2	no	—
203	C₂×C₃×Q₈	—	2	2	no	—
204	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
205	C₂²×C₃×C₄	—	2	1	no	—
206	C₂²×C₃×C₄	—	2	1	no	—
207	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
208	C₂²×Dic₃	—	2	1	no	—
209	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
210	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
211	C₂×D₁₂	—	2	2	no	—
212	C₂×D₁₂	—	2	2	no	—
213	C₂×D₁₂	—	2	1	no	—
214	C₂×D₁₂	C₂³×C₅	1	2	yes	—
215	C₂×Dic₆	—	2	4	no	—
216	C₂×Dic₆	—	4	4	no	—
217	C₂×C₃×C₈	—	2	2	no	—
218	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
219	C₃×C₄⋊C₄	—	2	1	no	—
220	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
221	(C₂×D₃)⋊C₄	—	2	4	no	—
222	(C₂×D₃)⋊C₄	—	2	4	no	—
223	C₄⋊Dic₃	—	2	1	no	—
224	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
225	Dic₃⋊C₄	—	2	4	no	—
226	C₄×Dic₃	C₅×D₄	1	2	yes	—
227	C₄×Dic₃	C₂³×C₅	1	2	yes	—
228	C₂×C₃⋊C₈	—	2	2	no	—
229	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
230	C₂³×C₅	—	6	2	no	—
231	C₂³×C₅	—	12	2	no	—
232	C₂³×C₅	—	12	2	no	—
233	C₂³×C₅	—	12	2	no	—
234	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
235	C₅×Q₈	—	2	2	no	—
236	C₅×Q₈	—	2	2	no	—
237	C₅×Q₈	—	4	2	no	—
238	C₅×Q₈	—	12	8	no	—
239	C₅×D₄	—	6	2	no	—
240	C₅×D₄	—	6	2	no	—
241	C₅×D₄	—	12	2	no	—
242	C₂×C₄×C₅	—	2	2	no	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	—	3	2	no	—
245	C₂×C₄×C₅	—	3	2	no	—
246	C₂×C₄×C₅	—	4	2	no	—
247	C₂×C₄×C₅	—	4	2	no	—
248	C₂×C₄×C₅	—	6	2	no	—
249	C₂×C₄×C₅	—	6	2	no	—
250	C₂×C₄×C₅	—	6	2	no	—
251	C₂×C₄×C₅	—	12	2	no	—
252	C₂×C₄×C₅	#235	1	2	yes	—
253	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
254	C₂×C₄×C₅	#237	1	2	yes	—
255	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
256	C₅×C₈	—	2	2	no	—
257	C₅×C₈	—	6	2	no	—
258	C₂²×Q₈	—	6	1	no	—
259	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
260	C₂²×D₄	—	3	1	no	—
261	C₂²×C₈	—	3	1	no	—
262	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
263	C₄⋊Q₈	—	3	4	no	—
264	C₄⋊Q₈	—	6	2	no	—
265	#124	—	3	4	no	—
266	#124	—	6	2	no	—
267	C₂×C₄⋊C₄	—	3	1	no	—
268	C₂×C₄⋊C₄	—	6	1	no	—
269	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
270	C₂×C₂²⋊C₄	—	6	1	no	—
271	C₂×C₂²⋊C₄	—	6	1	no	—
272	C₂×C₄²	—	3	1	no	—
273	#103	—	3	4	no	—
274	#103	C₂×C₅×D₃	1	4	yes	complemented
275	#102	—	3	4	no	—
276	#102	—	3	4	no	—
277	#97	—	3	4	no	—
278	C₂×C₃×C₅	#489	1	4	yes	complemented
279	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
280	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
281	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
282	C₅×D₃	—	8	2	no	—
283	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
284	C₂²×D₃	—	2	2	no	—
285	C₂²×D₃	—	4	2	no	—
286	C₂²×D₃	—	4	2	no	—
287	C₂²×D₃	—	4	2	no	—
288	C₃×Q₈	—	2	2	no	—
289	C₃×Q₈	—	2	2	no	—
290	C₃×Q₈	—	4	2	no	—
291	C₂×C₃×C₄	—	2	2	no	—
292	C₂×C₃×C₄	—	2	2	no	—
293	C₂×C₃×C₄	—	4	2	no	—
294	C₂×C₃×C₄	—	4	2	no	—
295	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
296	C₂×C₃×C₄	C₅×#41	1	2	yes	—
297	C₂×C₃×C₄	C₅×#41	1	2	yes	—
298	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
299	C₂×Dic₃	—	2	2	no	—
300	C₂×Dic₃	—	2	2	no	—
301	C₂×Dic₃	—	2	2	no	—
302	C₂×Dic₃	—	4	2	no	—
303	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
304	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
305	D₁₂	—	2	2	no	—
306	D₁₂	—	2	2	no	—
307	D₁₂	—	4	2	no	—
308	Dic₆	—	4	8	no	—
309	C₃×C₈	—	2	2	no	—
310	C₃⋊C₈	—	2	2	no	—
311	C₂²×C₅	—	12	2	no	—
312	C₂²×C₅	—	12	2	no	—
313	C₂²×C₅	—	12	2	no	—
314	C₂²×C₅	—	24	4	no	—
315	C₂²×C₅	#885	1	2	yes	—
316	C₂²×C₅	#914	1	2	yes	—
317	C₂²×C₅	#918	1	2	yes	—
318	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
319	C₄×C₅	—	4	2	no	—
320	C₄×C₅	—	4	2	no	—
321	C₄×C₅	—	6	2	no	—
322	C₄×C₅	—	6	2	no	—
323	C₄×C₅	—	12	2	no	—
324	C₄×C₅	#885	1	2	yes	—
325	C₄×C₅	C₂×#235	1	1	yes	characteristic
326	C₄×C₅	C₂×#237	1	1	yes	characteristic
327	C₂⁴	—	6	1	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	6	4	no	—
332	C₂×Q₈	—	12	4	no	—
333	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
334	C₂×D₄	—	3	2	no	—
335	C₂×D₄	—	6	2	no	—
336	C₂×D₄	—	6	1	no	—
337	C₂×D₄	—	6	2	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	3	1	no	—
341	C₂²×C₄	—	3	1	no	—
342	C₂²×C₄	—	6	1	no	—
343	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	3	2	no	—
346	C₂×C₈	—	6	2	no	—
347	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	3	2	no	—
350	C₄⋊C₄	—	6	4	no	—
351	C₄⋊C₄	—	6	1	no	—
352	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
353	C₂²⋊C₄	—	6	4	no	—
354	C₂²⋊C₄	—	6	4	no	—
355	C₄²	—	3	2	no	—
356	C₄²	—	3	2	no	—
357	C₃×C₅	C₂×#489	1	1	yes	characteristic, complemented, Hall
358	C₂²×C₃	C₅×#124	1	2	yes	—
359	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
360	C₂²×C₃	C₅×#137	1	2	yes	—
361	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
362	C₂×D₃	—	4	2	no	—
363	C₂×D₃	—	4	2	no	—
364	C₂×D₃	—	4	2	no	—
365	C₂×D₃	—	8	4	no	—
366	C₃×C₄	—	4	2	no	—
367	C₃×C₄	—	4	2	no	—
368	C₃×C₄	C₅×#124	1	2	yes	—
369	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
370	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
371	Dic₃	—	2	2	no	—
372	Dic₃	—	2	2	no	—
373	Dic₃	—	4	2	no	—
374	C₂×C₅	—	24	2	no	—
375	C₂×C₅	#4794	1	4	yes	direct product factor
376	C₂×C₅	C₂×#885	1	1	yes	characteristic
377	C₂×C₅	C₂×#914	1	1	yes	characteristic
378	C₂×C₅	C₂×#918	1	1	yes	characteristic
379	C₂³	—	6	2	no	—
380	C₂³	—	12	2	no	—
381	C₂³	—	12	2	no	—
382	C₂³	—	12	2	no	—
383	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
384	Q₈	—	2	2	no	—
385	Q₈	—	2	2	no	—
386	Q₈	—	4	2	no	—
387	Q₈	—	12	8	no	—
388	D₄	—	6	2	no	—
389	D₄	—	6	2	no	—
390	D₄	—	12	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	3	2	no	—
394	C₂×C₄	—	3	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	6	2	no	—
398	C₂×C₄	—	6	2	no	—
399	C₂×C₄	—	6	2	no	—
400	C₂×C₄	—	12	2	no	—
401	C₂×C₄	C₅×#235	1	2	yes	—
402	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
403	C₂×C₄	C₅×#237	1	2	yes	—
404	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
405	C₈	—	2	2	no	—
406	C₈	—	6	2	no	—
407	C₂×C₃	C₅×#489	1	4	yes	complemented
408	C₂×C₃	C₂×C₅×#124	1	1	yes	characteristic
409	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
410	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
411	D₃	—	8	2	no	—
412	C₅	C₂×#4794	1	1	yes	characteristic, direct product factor, Sylow
413	C₂²	—	12	2	no	—
414	C₂²	—	12	2	no	—
415	C₂²	—	12	2	no	—
416	C₂²	—	24	4	no	—
417	C₂²	C₅×#885	1	2	yes	—
418	C₂²	C₅×#914	1	2	yes	—
419	C₂²	C₅×#918	1	2	yes	—
420	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
421	C₄	—	4	2	no	—
422	C₄	—	4	2	no	—
423	C₄	—	6	2	no	—
424	C₄	—	6	2	no	—
425	C₄	—	12	2	no	—
426	C₄	C₅×#885	1	2	yes	—
427	C₄	C₂×C₅×#235	1	1	yes	characteristic
428	C₄	C₂×C₅×#237	1	1	yes	characteristic
429	C₃	C₂×C₅×#489	1	1	yes	characteristic, complemented, Sylow
430	C₂	—	24	2	no	—
431	C₂	C₅×#4794	1	4	yes	direct product factor
432	C₂	C₂×C₅×#885	1	1	yes	characteristic
433	C₂	C₂×C₅×#914	1	1	yes	characteristic
434	C₂	C₂×C₅×#918	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×#103	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₅×D₁₂	C₂²
hypercenter	C₂×C₅×#103	D₃
hypocenter	C₃	C₂×C₅×#489
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#103

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#888	C₂	semidirect
3. C₂×C₃×C₅×#103	C₂	semidirect
4. C₂×C₅×#835	C₂	semidirect
6. C₂×C₅×#815	C₂	semidirect
8. C₅×#4794	C₂	direct (N × H)
24. C₅×#888	C₂²	semidirect
25. C₃×C₅×#103	C₂²	semidirect
26. C₅×#835	C₂²	semidirect
28. C₅×#815	C₂²	semidirect
30. C₂×#4794	C₅	direct (N × H)
35. C₂×C₅×#103	D₃	semidirect
70. C₂×#888	C₂×C₅	semidirect
71. C₂×C₃×#103	C₂×C₅	semidirect
72. C₂×#835	C₂×C₅	semidirect
74. C₂×#815	C₂×C₅	semidirect
76. #4794	C₂×C₅	direct (N × H)
93. C₅×#103	C₂×D₃	semidirect
140. #888	C₂²×C₅	semidirect
141. C₃×#103	C₂²×C₅	semidirect
142. #835	C₂²×C₅	semidirect
144. #815	C₂²×C₅	semidirect
180. C₂×#103	C₅×D₃	semidirect
274. #103	C₂×C₅×D₃	semidirect
278. C₂×C₃×C₅	#489	semidirect
357. C₃×C₅	C₂×#489	semidirect
375. C₂×C₅	#4794	direct (N × H)
407. C₂×C₃	C₅×#489	semidirect
412. C₅	C₂×#4794	direct (N × H)
429. C₃	C₂×C₅×#489	semidirect
431. C₂	C₅×#4794	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×C₅×#947	2
C₂×C₅×#888	2
C₂×C₃×C₅×#103	2
C₂×C₅×#835	2
C₂×C₅×#821	2
C₂×C₅×#815	2
C₂×C₅×#809	2
C₅×#4794	2
C₂×C₅×#489	3
C₂×#4794	5

Subgroups — C2×C5×#4794 #14437860

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4794 #14437860