Subgroups — C₂×C₅×#5246 #14425134

Order 1920.

1416 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#951	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×#944	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5246	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₅×#837	C₂	1	2	yes	maximal, complemented
6	C₂×C₅×#836	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#456	—	3	1	no	maximal, Hall
8	C₃×C₅×2₋¹⁺⁴	—	2	4	no	—
9	C₃×C₅×2₋¹⁺⁴	—	2	2	no	—
10	C₃×C₅×2₋¹⁺⁴	C₂²	1	4	yes	—
11	C₂×C₃×C₅×#41	—	2	2	no	—
12	C₂×C₃×C₅×#41	—	2	2	no	—
13	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
14	C₂²×C₃×C₅×Q₈	—	2	2	no	—
15	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
16	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
17	C₅×#951	—	2	4	no	—
18	C₅×#951	C₂²	1	8	yes	complemented
19	C₅×#944	—	2	2	no	—
20	C₅×#944	C₂²	1	4	yes	complemented
21	C₂×C₅×#216	—	2	2	no	—
22	C₂×C₅×#214	—	2	2	no	—
23	C₂×C₅×Dic₃⋊C₄	—	2	2	no	—
24	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
25	C₂×C₅×#208	C₂²	1	2	yes	—
26	C₅×#837	C₂²	1	8	yes	complemented
27	C₅×#836	C₂²	1	4	yes	complemented
28	C₂×#5246	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₂×C₅×2₋¹⁺⁴	D₃	1	1	yes	characteristic
30	C₂×C₅×#137	—	3	2	no	—
31	C₂×C₅×C₄⋊Q₈	—	3	1	no	—
32	C₅×#456	—	3	8	no	—
33	C₂×C₅×#104	—	3	2	no	—
34	C₂×C₅×#101	—	3	1	no	—
35	C₃×C₅×#41	—	2	8	no	—
36	C₃×C₅×#41	—	2	8	no	—
37	C₃×C₅×#41	—	2	8	no	—
38	C₃×C₅×#41	—	2	8	no	—
39	C₃×C₅×#41	—	2	2	no	—
40	C₃×C₅×#41	—	2	2	no	—
41	C₃×C₅×#41	D₄	1	4	yes	—
42	C₃×C₅×#41	C₂³	1	4	yes	—
43	C₂×C₃×C₅×Q₈	—	2	2	no	—
44	C₂×C₃×C₅×Q₈	—	2	8	no	—
45	C₂×C₃×C₅×Q₈	—	2	8	no	—
46	C₂×C₃×C₅×Q₈	—	2	2	no	—
47	C₂×C₃×C₅×Q₈	—	2	2	no	—
48	C₂×C₃×C₅×Q₈	D₄	1	2	yes	—
49	C₂×C₃×C₅×Q₈	D₄	1	2	yes	—
50	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
51	C₂×C₃×C₅×D₄	—	2	2	no	—
52	C₂×C₃×C₅×D₄	—	2	2	no	—
53	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
54	C₂²×C₃×C₄×C₅	—	2	4	no	—
55	C₂²×C₃×C₄×C₅	—	2	2	no	—
56	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
57	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₂²×C₅×Dic₃	—	2	1	no	—
59	C₂²×C₅×Dic₃	—	2	1	no	—
60	C₂×C₅×Dic₆	—	2	2	no	—
61	C₂×C₅×Dic₆	—	2	2	no	—
62	C₂×C₅×Dic₆	—	2	1	no	—
63	C₂×C₅×Dic₆	C₂³	1	2	yes	—
64	C₅×#216	—	2	8	no	—
65	C₅×#214	—	2	8	no	—
66	C₅×Dic₃⋊C₄	—	2	8	no	—
67	C₄×C₅×Dic₃	—	2	1	no	—
68	C₄×C₅×Dic₃	C₂³	1	2	yes	—
69	C₅×#208	—	2	2	no	—
70	C₅×#208	C₂³	1	4	yes	—
71	C₂×C₅×C₃⋊C₈	—	2	2	no	—
72	C₂×C₃×2₋¹⁺⁴	C₂×C₅	1	1	yes	characteristic
73	C₂×#951	C₂×C₅	1	2	yes	complemented
74	C₂×#944	C₂×C₅	1	1	yes	characteristic, complemented
75	#5246	C₂×C₅	1	8	yes	direct product factor
76	C₂×#837	C₂×C₅	1	2	yes	complemented
77	C₂×#836	C₂×C₅	1	1	yes	characteristic, complemented
78	C₅×2₋¹⁺⁴	—	2	4	no	—
79	C₅×2₋¹⁺⁴	—	2	2	no	—
80	C₅×2₋¹⁺⁴	C₂×D₃	1	4	yes	—
81	C₂×C₅×#41	—	2	2	no	—
82	C₂×C₅×#41	—	2	2	no	—
83	C₂×C₅×#41	C₂×D₃	1	2	yes	—
84	C₂²×C₅×Q₈	—	2	2	no	—
85	C₂²×C₅×Q₈	—	3	1	no	—
86	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
87	C₅×#137	—	3	8	no	—
88	C₅×#137	—	6	4	no	—
89	C₂×C₅×Q₁₆	—	6	2	no	—
90	C₂×C₅×SD₁₆	—	6	2	no	—
91	C₂×C₅×M₁₆	—	3	2	no	—
92	C₅×C₄⋊Q₈	—	3	4	no	—
93	C₅×C₄⋊Q₈	—	6	2	no	—
94	C₂×C₅×C₄⋊C₄	—	6	2	no	—
95	C₂×C₄²×C₅	—	3	1	no	—
96	C₅×#104	—	3	8	no	—
97	C₅×#101	—	3	4	no	—
98	C₂×#456	—	3	1	no	Sylow
99	C₂³×C₃×C₅	—	2	2	no	—
100	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
101	C₃×C₅×Q₈	—	2	8	no	—
102	C₃×C₅×Q₈	—	2	2	no	—
103	C₃×C₅×Q₈	—	2	4	no	—
104	C₃×C₅×Q₈	—	2	4	no	—
105	C₃×C₅×Q₈	C₂×D₄	1	4	yes	—
106	C₃×C₅×D₄	—	2	8	no	—
107	C₃×C₅×D₄	—	2	4	no	—
108	C₃×C₅×D₄	—	2	4	no	—
109	C₃×C₅×D₄	—	2	2	no	—
110	C₃×C₅×D₄	C₂×D₄	1	4	yes	—
111	C₂×C₃×C₄×C₅	—	2	16	no	—
112	C₂×C₃×C₄×C₅	—	2	2	no	—
113	C₂×C₃×C₄×C₅	—	2	2	no	—
114	C₂×C₃×C₄×C₅	—	2	2	no	—
115	C₂×C₃×C₄×C₅	—	2	4	no	—
116	C₂×C₃×C₄×C₅	—	2	4	no	—
117	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
118	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
119	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
120	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
121	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
122	C₂×C₅×Dic₃	—	2	4	no	—
123	C₂×C₅×Dic₃	—	2	2	no	—
124	C₂×C₅×Dic₃	—	2	2	no	—
125	C₂×C₅×Dic₃	—	4	1	no	—
126	C₂×C₅×Dic₃	—	4	1	no	—
127	C₅×Dic₆	—	2	4	no	—
128	C₅×Dic₆	—	4	2	no	—
129	C₅×C₃⋊C₈	—	2	4	no	—
130	C₃×2₋¹⁺⁴	—	2	4	no	—
131	C₃×2₋¹⁺⁴	—	2	2	no	—
132	C₃×2₋¹⁺⁴	C₂²×C₅	1	4	yes	—
133	C₂×C₃×#41	—	2	2	no	—
134	C₂×C₃×#41	—	2	2	no	—
135	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
136	C₂²×C₃×Q₈	—	2	2	no	—
137	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
138	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
139	#951	—	2	4	no	—
140	#951	C₂²×C₅	1	8	yes	complemented
141	#944	—	2	2	no	—
142	#944	C₂²×C₅	1	4	yes	complemented
143	C₂×#216	—	2	2	no	—
144	C₂×#214	—	2	2	no	—
145	C₂×Dic₃⋊C₄	—	2	2	no	—
146	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
147	C₂×#208	C₂²×C₅	1	2	yes	—
148	#837	C₂²×C₅	1	8	yes	complemented
149	#836	C₂²×C₅	1	4	yes	complemented
150	C₅×#41	—	2	8	no	—
151	C₅×#41	—	2	8	no	—
152	C₅×#41	—	2	8	no	—
153	C₅×#41	—	2	8	no	—
154	C₅×#41	—	2	2	no	—
155	C₅×#41	—	2	2	no	—
156	C₅×#41	#67	1	4	yes	—
157	C₅×#41	C₂²×D₃	1	4	yes	—
158	C₂×C₅×Q₈	—	2	2	no	—
159	C₂×C₅×Q₈	—	2	8	no	—
160	C₂×C₅×Q₈	—	2	8	no	—
161	C₂×C₅×Q₈	—	2	2	no	—
162	C₂×C₅×Q₈	—	2	2	no	—
163	C₂×C₅×Q₈	—	3	2	no	—
164	C₂×C₅×Q₈	—	6	1	no	—
165	C₂×C₅×Q₈	—	6	2	no	—
166	C₂×C₅×Q₈	—	6	2	no	—
167	C₂×C₅×Q₈	#67	1	2	yes	—
168	C₂×C₅×Q₈	#67	1	2	yes	—
169	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
170	C₂×C₅×D₄	—	2	2	no	—
171	C₂×C₅×D₄	—	2	2	no	—
172	C₂×C₅×D₄	#67	1	2	yes	—
173	C₂²×C₄×C₅	—	2	4	no	—
174	C₂²×C₄×C₅	—	2	2	no	—
175	C₂²×C₄×C₅	—	6	1	no	—
176	C₂²×C₄×C₅	—	6	1	no	—
177	C₂²×C₄×C₅	#67	1	2	yes	—
178	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
179	C₅×Q₁₆	—	6	8	no	—
180	C₅×SD₁₆	—	6	8	no	—
181	C₅×M₁₆	—	3	4	no	—
182	C₅×M₁₆	—	6	2	no	—
183	C₂×C₅×C₈	—	6	2	no	—
184	C₅×C₄⋊C₄	—	6	8	no	—
185	C₄²×C₅	—	3	2	no	—
186	C₄²×C₅	—	6	1	no	—
187	C₂×2₋¹⁺⁴	C₅×D₃	1	1	yes	characteristic
188	C₂×#137	—	3	2	no	—
189	C₂×C₄⋊Q₈	—	3	1	no	—
190	#456	—	3	8	no	—
191	C₂×#104	—	3	2	no	—
192	C₂×#101	—	3	1	no	—
193	C₂²×C₃×C₅	—	2	2	no	—
194	C₂²×C₃×C₅	—	2	4	no	—
195	C₂²×C₃×C₅	—	4	4	no	—
196	C₂²×C₃×C₅	#120	1	1	yes	characteristic
197	C₂²×C₃×C₅	#120	1	1	yes	characteristic
198	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
199	C₃×C₄×C₅	—	2	4	no	—
200	C₃×C₄×C₅	—	2	4	no	—
201	C₃×C₄×C₅	#120	1	2	yes	—
202	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
203	C₅×Dic₃	—	2	4	no	—
204	C₅×Dic₃	—	4	2	no	—
205	C₃×#41	—	2	8	no	—
206	C₃×#41	—	2	8	no	—
207	C₃×#41	—	2	8	no	—
208	C₃×#41	—	2	8	no	—
209	C₃×#41	—	2	2	no	—
210	C₃×#41	—	2	2	no	—
211	C₃×#41	C₅×D₄	1	4	yes	—
212	C₃×#41	C₂³×C₅	1	4	yes	—
213	C₂×C₃×Q₈	—	2	2	no	—
214	C₂×C₃×Q₈	—	2	8	no	—
215	C₂×C₃×Q₈	—	2	8	no	—
216	C₂×C₃×Q₈	—	2	2	no	—
217	C₂×C₃×Q₈	—	2	2	no	—
218	C₂×C₃×Q₈	C₅×D₄	1	2	yes	—
219	C₂×C₃×Q₈	C₅×D₄	1	2	yes	—
220	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
221	C₂×C₃×D₄	—	2	2	no	—
222	C₂×C₃×D₄	—	2	2	no	—
223	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
224	C₂²×C₃×C₄	—	2	4	no	—
225	C₂²×C₃×C₄	—	2	2	no	—
226	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
227	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
228	C₂²×Dic₃	—	2	1	no	—
229	C₂²×Dic₃	—	2	1	no	—
230	C₂×Dic₆	—	2	2	no	—
231	C₂×Dic₆	—	2	2	no	—
232	C₂×Dic₆	—	2	1	no	—
233	C₂×Dic₆	C₂³×C₅	1	2	yes	—
234	#216	—	2	8	no	—
235	#214	—	2	8	no	—
236	Dic₃⋊C₄	—	2	8	no	—
237	C₄×Dic₃	—	2	1	no	—
238	C₄×Dic₃	C₂³×C₅	1	2	yes	—
239	#208	—	2	2	no	—
240	#208	C₂³×C₅	1	4	yes	—
241	C₂×C₃⋊C₈	—	2	2	no	—
242	C₂³×C₅	—	2	2	no	—
243	C₂³×C₅	C₂×#67	1	1	yes	characteristic
244	C₅×Q₈	—	2	8	no	—
245	C₅×Q₈	—	2	2	no	—
246	C₅×Q₈	—	2	4	no	—
247	C₅×Q₈	—	2	4	no	—
248	C₅×Q₈	—	6	4	no	—
249	C₅×Q₈	—	12	2	no	—
250	C₅×Q₈	C₂×#67	1	4	yes	—
251	C₅×D₄	—	2	8	no	—
252	C₅×D₄	—	2	4	no	—
253	C₅×D₄	—	2	4	no	—
254	C₅×D₄	—	2	2	no	—
255	C₅×D₄	C₂×#67	1	4	yes	—
256	C₂×C₄×C₅	—	2	16	no	—
257	C₂×C₄×C₅	—	2	2	no	—
258	C₂×C₄×C₅	—	2	2	no	—
259	C₂×C₄×C₅	—	2	2	no	—
260	C₂×C₄×C₅	—	2	4	no	—
261	C₂×C₄×C₅	—	2	4	no	—
262	C₂×C₄×C₅	—	6	4	no	—
263	C₂×C₄×C₅	—	6	2	no	—
264	C₂×C₄×C₅	—	6	2	no	—
265	C₂×C₄×C₅	—	12	1	no	—
266	C₂×C₄×C₅	—	12	1	no	—
267	C₂×C₄×C₅	C₂×#67	1	4	yes	—
268	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
269	C₂×C₄×C₅	C₂×#67	1	2	yes	—
270	C₂×C₄×C₅	C₂×#67	1	2	yes	—
271	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
272	C₅×C₈	—	6	4	no	—
273	2₋¹⁺⁴	—	2	4	no	—
274	2₋¹⁺⁴	—	2	2	no	—
275	2₋¹⁺⁴	C₂×C₅×D₃	1	4	yes	—
276	C₂×#41	—	2	2	no	—
277	C₂×#41	—	2	2	no	—
278	C₂×#41	C₂×C₅×D₃	1	2	yes	—
279	C₂²×Q₈	—	2	2	no	—
280	C₂²×Q₈	—	3	1	no	—
281	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
282	#137	—	3	8	no	—
283	#137	—	6	4	no	—
284	C₂×Q₁₆	—	6	2	no	—
285	C₂×SD₁₆	—	6	2	no	—
286	C₂×M₁₆	—	3	2	no	—
287	C₄⋊Q₈	—	3	4	no	—
288	C₄⋊Q₈	—	6	2	no	—
289	C₂×C₄⋊C₄	—	6	2	no	—
290	C₂×C₄²	—	3	1	no	—
291	#104	—	3	8	no	—
292	#101	—	3	4	no	—
293	C₂×C₃×C₅	—	2	1	no	—
294	C₂×C₃×C₅	—	2	1	no	—
295	C₂×C₃×C₅	—	4	4	no	—
296	C₂×C₃×C₅	#456	1	2	yes	complemented
297	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
298	C₂³×C₃	—	2	2	no	—
299	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
300	C₃×Q₈	—	2	8	no	—
301	C₃×Q₈	—	2	2	no	—
302	C₃×Q₈	—	2	4	no	—
303	C₃×Q₈	—	2	4	no	—
304	C₃×Q₈	C₂×C₅×D₄	1	4	yes	—
305	C₃×D₄	—	2	8	no	—
306	C₃×D₄	—	2	4	no	—
307	C₃×D₄	—	2	4	no	—
308	C₃×D₄	—	2	2	no	—
309	C₃×D₄	C₂×C₅×D₄	1	4	yes	—
310	C₂×C₃×C₄	—	2	16	no	—
311	C₂×C₃×C₄	—	2	2	no	—
312	C₂×C₃×C₄	—	2	2	no	—
313	C₂×C₃×C₄	—	2	2	no	—
314	C₂×C₃×C₄	—	2	4	no	—
315	C₂×C₃×C₄	—	2	4	no	—
316	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
317	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
318	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
319	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
320	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
321	C₂×Dic₃	—	2	4	no	—
322	C₂×Dic₃	—	2	2	no	—
323	C₂×Dic₃	—	2	2	no	—
324	C₂×Dic₃	—	4	1	no	—
325	C₂×Dic₃	—	4	1	no	—
326	Dic₆	—	2	4	no	—
327	Dic₆	—	4	2	no	—
328	C₃⋊C₈	—	2	4	no	—
329	C₂²×C₅	—	2	2	no	—
330	C₂²×C₅	—	2	4	no	—
331	C₂²×C₅	—	4	4	no	—
332	C₂²×C₅	#953	1	1	yes	characteristic
333	C₂²×C₅	#953	1	1	yes	characteristic
334	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
335	C₄×C₅	—	2	4	no	—
336	C₄×C₅	—	2	4	no	—
337	C₄×C₅	—	6	4	no	—
338	C₄×C₅	—	12	2	no	—
339	C₄×C₅	#953	1	2	yes	—
340	C₄×C₅	C₂²×#67	1	2	yes	—
341	#41	—	2	8	no	—
342	#41	—	2	8	no	—
343	#41	—	2	8	no	—
344	#41	—	2	8	no	—
345	#41	—	2	2	no	—
346	#41	—	2	2	no	—
347	#41	C₅×#67	1	4	yes	—
348	#41	C₂²×C₅×D₃	1	4	yes	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	—	2	8	no	—
351	C₂×Q₈	—	2	8	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	3	2	no	—
355	C₂×Q₈	—	6	1	no	—
356	C₂×Q₈	—	6	2	no	—
357	C₂×Q₈	—	6	2	no	—
358	C₂×Q₈	C₅×#67	1	2	yes	—
359	C₂×Q₈	C₅×#67	1	2	yes	—
360	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	C₅×#67	1	2	yes	—
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	6	1	no	—
367	C₂²×C₄	—	6	1	no	—
368	C₂²×C₄	C₅×#67	1	2	yes	—
369	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
370	Q₁₆	—	6	8	no	—
371	SD₁₆	—	6	8	no	—
372	M₁₆	—	3	4	no	—
373	M₁₆	—	6	2	no	—
374	C₂×C₈	—	6	2	no	—
375	C₄⋊C₄	—	6	8	no	—
376	C₄²	—	3	2	no	—
377	C₄²	—	6	1	no	—
378	C₃×C₅	C₂×#456	1	1	yes	characteristic, complemented, Hall
379	C₂²×C₃	—	2	2	no	—
380	C₂²×C₃	—	2	4	no	—
381	C₂²×C₃	—	4	4	no	—
382	C₂²×C₃	C₅×#120	1	1	yes	characteristic
383	C₂²×C₃	C₅×#120	1	1	yes	characteristic
384	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
385	C₃×C₄	—	2	4	no	—
386	C₃×C₄	—	2	4	no	—
387	C₃×C₄	C₅×#120	1	2	yes	—
388	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
389	Dic₃	—	2	4	no	—
390	Dic₃	—	4	2	no	—
391	C₂×C₅	—	2	1	no	—
392	C₂×C₅	—	2	1	no	—
393	C₂×C₅	—	4	4	no	—
394	C₂×C₅	#5246	1	2	yes	direct product factor
395	C₂×C₅	C₂×#953	1	1	yes	characteristic
396	C₂³	—	2	2	no	—
397	C₂³	C₂×C₅×#67	1	1	yes	characteristic
398	Q₈	—	2	8	no	—
399	Q₈	—	2	2	no	—
400	Q₈	—	2	4	no	—
401	Q₈	—	2	4	no	—
402	Q₈	—	6	4	no	—
403	Q₈	—	12	2	no	—
404	Q₈	C₂×C₅×#67	1	4	yes	—
405	D₄	—	2	8	no	—
406	D₄	—	2	4	no	—
407	D₄	—	2	4	no	—
408	D₄	—	2	2	no	—
409	D₄	C₂×C₅×#67	1	4	yes	—
410	C₂×C₄	—	2	16	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	6	4	no	—
417	C₂×C₄	—	6	2	no	—
418	C₂×C₄	—	6	2	no	—
419	C₂×C₄	—	12	1	no	—
420	C₂×C₄	—	12	1	no	—
421	C₂×C₄	C₂×C₅×#67	1	4	yes	—
422	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
423	C₂×C₄	C₂×C₅×#67	1	2	yes	—
424	C₂×C₄	C₂×C₅×#67	1	2	yes	—
425	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
426	C₈	—	6	4	no	—
427	C₂×C₃	—	2	1	no	—
428	C₂×C₃	—	2	1	no	—
429	C₂×C₃	—	4	4	no	—
430	C₂×C₃	C₅×#456	1	2	yes	complemented
431	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
432	C₅	C₂×#5246	1	1	yes	characteristic, direct product factor, Sylow
433	C₂²	—	2	2	no	—
434	C₂²	—	2	4	no	—
435	C₂²	—	4	4	no	—
436	C₂²	C₅×#953	1	1	yes	characteristic
437	C₂²	C₅×#953	1	1	yes	characteristic
438	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
439	C₄	—	2	4	no	—
440	C₄	—	2	4	no	—
441	C₄	—	6	4	no	—
442	C₄	—	12	2	no	—
443	C₄	C₅×#953	1	2	yes	—
444	C₄	C₂²×C₅×#67	1	2	yes	—
445	C₃	C₂×C₅×#456	1	1	yes	characteristic, complemented, Sylow
446	C₂	—	2	1	no	—
447	C₂	—	2	1	no	—
448	C₂	—	4	4	no	—
449	C₂	C₅×#5246	1	2	yes	direct product factor
450	C₂	C₂×C₅×#953	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	#953
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting, prime radical	C₂×C₃×C₅×2₋¹⁺⁴	C₂
socle	C₂²×C₃×C₅	#120
hypercenter	C₂×C₅×2₋¹⁺⁴	D₃
hypocenter	C₃	C₂×C₅×#456
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×2₋¹⁺⁴

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#951	C₂	semidirect
3. C₂×C₅×#944	C₂	semidirect
4. C₅×#5246	C₂	direct (N × H)
5. C₂×C₅×#837	C₂	semidirect
6. C₂×C₅×#836	C₂	semidirect
18. C₅×#951	C₂²	semidirect
20. C₅×#944	C₂²	semidirect
26. C₅×#837	C₂²	semidirect
27. C₅×#836	C₂²	semidirect
28. C₂×#5246	C₅	direct (N × H)
73. C₂×#951	C₂×C₅	semidirect
74. C₂×#944	C₂×C₅	semidirect
75. #5246	C₂×C₅	direct (N × H)
76. C₂×#837	C₂×C₅	semidirect
77. C₂×#836	C₂×C₅	semidirect
140. #951	C₂²×C₅	semidirect
142. #944	C₂²×C₅	semidirect
148. #837	C₂²×C₅	semidirect
149. #836	C₂²×C₅	semidirect
296. C₂×C₃×C₅	#456	semidirect
378. C₃×C₅	C₂×#456	semidirect
394. C₂×C₅	#5246	direct (N × H)
430. C₂×C₃	C₅×#456	semidirect
432. C₅	C₂×#5246	direct (N × H)
445. C₃	C₂×C₅×#456	semidirect
449. C₂	C₅×#5246	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×C₅×2₋¹⁺⁴	2
C₂×C₅×#951	2
C₂×C₅×#944	2
C₅×#5246	2
C₂×C₅×#837	2
C₂×C₅×#836	2
C₂×C₅×#456	3
C₂×#5246	5

Subgroups — C2×C5×#5246 #14425134

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5246 #14425134