Subgroups — C₄×C₅×#474 #11944327

Order 1280.

1000 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#474	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄²×C₅×D₄	C₂	1	1	yes	maximal, characteristic
4	C₅×#1988	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1947	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1918	C₂	1	2	yes	maximal, complemented
7	C₅×#1862	C₂	1	2	yes	maximal
8	C₅×#1802	C₂	1	1	yes	maximal, characteristic
9	C₄×C₅×#107	C₂	1	2	yes	maximal, complemented
10	C₄×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×#102	C₂	1	2	yes	maximal
12	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₅×Q₈	—	2	1	no	—
14	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₅	—	2	1	no	—
18	C₅×#474	C₄	1	8	yes	direct product factor
19	C₂×C₅×#107	C₂²	1	2	yes	—
20	C₂×C₅×#107	C₂²	1	2	yes	—
21	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₅×#102	C₂²	1	2	yes	—
24	C₂×C₅×#102	C₂²	1	2	yes	—
25	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
26	C₅×#391	—	2	1	no	—
27	C₅×#389	—	2	1	no	—
28	C₅×#389	C₂²	1	2	yes	—
29	C₅×#384	C₂²	1	1	yes	characteristic
30	C₄×C₅×C₄⋊C₄	—	2	1	no	—
31	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
32	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
36	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
37	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
38	C₄³×C₅	C₂²	1	1	yes	characteristic
39	C₅×#340	C₂²	1	2	yes	—
40	C₅×#340	C₂²	1	2	yes	—
41	C₅×#340	C₂²	1	2	yes	—
42	C₅×#340	C₂²	1	2	yes	—
43	C₅×#336	C₂²	1	2	yes	—
44	C₄×#474	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂²×C₅×Q₈	—	2	1	no	—
46	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₅	—	2	1	no	—
48	C₂³×C₄×C₅	—	2	1	no	—
49	C₂³×C₄×C₅	—	2	1	no	—
50	C₂²×C₅×C₈	C₂³	1	2	yes	—
51	C₂²×C₅×C₈	C₂³	1	2	yes	—
52	C₅×C₄⋊Q₈	—	2	2	no	—
53	C₅×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
54	C₄×C₅×Q₈	—	4	4	no	—
55	C₄×C₅×D₄	—	2	2	no	—
56	C₄×C₅×D₄	—	2	2	no	—
57	C₄×C₅×D₄	—	2	2	no	—
58	C₄×C₅×D₄	—	2	2	no	—
59	C₄×C₅×D₄	C₂×C₄	1	4	yes	—
60	C₄×C₅×D₄	Q₈	1	4	yes	complemented
61	C₂×C₅×C₄⋊C₄	—	2	1	no	—
62	C₂×C₅×C₄⋊C₄	—	2	1	no	—
63	C₂×C₅×C₄⋊C₄	—	2	1	no	—
64	C₂×C₅×C₄⋊C₄	—	2	2	no	—
65	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
66	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
67	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
69	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
71	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
72	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
73	C₂×C₄²×C₅	—	2	1	no	—
74	C₂×C₄²×C₅	—	2	1	no	—
75	C₂×C₄²×C₅	—	2	1	no	—
76	C₂×C₄²×C₅	—	2	2	no	—
77	C₂×C₄²×C₅	—	4	4	no	—
78	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
79	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
81	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
82	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
85	C₅×#107	—	2	4	no	—
86	C₅×#107	C₂×C₄	1	8	yes	complemented
87	C₅×C₄⋊C₈	—	2	2	no	—
88	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
89	C₅×#102	—	2	4	no	—
90	C₅×#102	C₂×C₄	1	8	yes	—
91	C₄×C₅×C₈	—	2	4	no	—
92	C₅×#95	—	2	1	no	—
93	C₅×#95	—	2	1	no	—
94	C₅×#95	—	2	1	no	—
95	C₅×#95	—	2	2	no	—
96	C₅×#95	—	2	2	no	—
97	C₂×#474	C₂×C₅	1	1	yes	characteristic
98	C₄×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
99	C₄²×D₄	C₂×C₅	1	1	yes	characteristic
100	#1988	C₂×C₅	1	1	yes	characteristic, complemented
101	#1947	C₂×C₅	1	1	yes	characteristic, complemented
102	#1918	C₂×C₅	1	2	yes	complemented
103	#1862	C₂×C₅	1	2	yes	—
104	#1802	C₂×C₅	1	1	yes	characteristic
105	C₄×#107	C₂×C₅	1	2	yes	complemented
106	C₄×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
107	C₄×#102	C₂×C₅	1	2	yes	—
108	C₂⁴×C₅	—	2	1	no	—
109	C₂×C₅×Q₈	—	2	4	no	—
110	C₂×C₅×Q₈	—	4	2	no	—
111	C₂×C₅×Q₈	—	4	2	no	—
112	C₂×C₅×D₄	—	2	1	no	—
113	C₂×C₅×D₄	—	2	1	no	—
114	C₂×C₅×D₄	—	2	1	no	—
115	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
116	C₂×C₅×D₄	C₂×Q₈	1	2	yes	—
117	C₂×C₅×D₄	#41	1	2	yes	—
118	C₂²×C₄×C₅	—	2	4	no	—
119	C₂²×C₄×C₅	—	2	1	no	—
120	C₂²×C₄×C₅	—	2	1	no	—
121	C₂²×C₄×C₅	—	2	1	no	—
122	C₂²×C₄×C₅	—	2	2	no	—
123	C₂²×C₄×C₅	—	2	4	no	—
124	C₂²×C₄×C₅	—	2	4	no	—
125	C₂²×C₄×C₅	—	2	2	no	—
126	C₂²×C₄×C₅	—	4	2	no	—
127	C₂²×C₄×C₅	—	4	2	no	—
128	C₂²×C₄×C₅	—	4	2	no	—
129	C₂²×C₄×C₅	—	4	2	no	—
130	C₂²×C₄×C₅	—	4	2	no	—
131	C₂²×C₄×C₅	—	4	2	no	—
132	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
139	C₂×C₅×C₈	—	2	2	no	—
140	C₂×C₅×C₈	—	2	2	no	—
141	C₂×C₅×C₈	—	2	2	no	—
142	C₂×C₅×C₈	—	2	2	no	—
143	C₂×C₅×C₈	—	2	2	no	—
144	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
145	C₅×C₄⋊C₄	—	2	4	no	—
146	C₅×C₄⋊C₄	—	2	1	no	—
147	C₅×C₄⋊C₄	—	2	1	no	—
148	C₅×C₄⋊C₄	—	2	1	no	—
149	C₅×C₄⋊C₄	—	2	2	no	—
150	C₅×C₄⋊C₄	—	2	2	no	—
151	C₅×C₄⋊C₄	—	2	2	no	—
152	C₅×C₄⋊C₄	—	4	2	no	—
153	C₅×C₄⋊C₄	—	4	4	no	—
154	C₅×C₄⋊C₄	—	4	2	no	—
155	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
156	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
157	C₅×C₄⋊C₄	C₂×Q₈	1	2	yes	—
158	C₅×C₄⋊C₄	#41	1	2	yes	—
159	C₅×C₂²⋊C₄	—	2	4	no	—
160	C₅×C₂²⋊C₄	—	2	4	no	—
161	C₅×C₂²⋊C₄	—	2	4	no	—
162	C₄²×C₅	—	2	2	no	—
163	C₄²×C₅	—	2	2	no	—
164	C₄²×C₅	—	2	1	no	—
165	C₄²×C₅	—	2	1	no	—
166	C₄²×C₅	—	4	1	no	—
167	C₄²×C₅	—	4	2	no	—
168	C₄²×C₅	—	4	2	no	—
169	C₄²×C₅	—	4	2	no	—
170	C₄²×C₅	—	4	4	no	—
171	C₄²×C₅	D₈	1	4	yes	—
172	C₄²×C₅	C₂²×C₄	1	2	yes	—
173	C₄²×C₅	C₂×Q₈	1	2	yes	—
174	C₄²×C₅	#41	1	2	yes	—
175	C₄²×C₅	#41	1	2	yes	—
176	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
177	C₂×C₄×Q₈	—	2	1	no	—
178	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
179	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
180	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
181	C₂²×C₄²	—	2	1	no	—
182	#474	C₄×C₅	1	8	yes	direct product factor
183	C₂×#107	C₂²×C₅	1	2	yes	—
184	C₂×#107	C₂²×C₅	1	2	yes	—
185	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
186	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
187	C₂×#102	C₂²×C₅	1	2	yes	—
188	C₂×#102	C₂²×C₅	1	2	yes	—
189	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
190	#391	—	2	1	no	—
191	#389	—	2	1	no	—
192	#389	C₂²×C₅	1	2	yes	—
193	#384	C₂²×C₅	1	1	yes	characteristic
194	C₄×C₄⋊C₄	—	2	1	no	—
195	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
196	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
197	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
198	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
199	C₄×C₂²⋊C₄	—	2	1	no	—
200	C₄×C₂²⋊C₄	—	2	1	no	—
201	C₄×C₂²⋊C₄	—	2	1	no	—
202	C₄³	C₂²×C₅	1	1	yes	characteristic
203	#340	C₂²×C₅	1	2	yes	—
204	#340	C₂²×C₅	1	2	yes	—
205	#340	C₂²×C₅	1	2	yes	—
206	#340	C₂²×C₅	1	2	yes	—
207	#336	C₂²×C₅	1	2	yes	—
208	C₂³×C₅	—	2	2	no	—
209	C₂³×C₅	—	2	2	no	—
210	C₂³×C₅	—	2	2	no	—
211	C₂³×C₅	—	4	1	no	—
212	C₂³×C₅	—	4	1	no	—
213	C₂³×C₅	—	4	1	no	—
214	C₂³×C₅	—	4	1	no	—
215	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
216	C₅×Q₈	—	4	8	no	—
217	C₅×D₄	—	2	2	no	—
218	C₅×D₄	—	2	2	no	—
219	C₅×D₄	—	2	2	no	—
220	C₅×D₄	C₄×Q₈	1	4	yes	complemented
221	C₂×C₄×C₅	—	2	1	no	—
222	C₂×C₄×C₅	—	2	1	no	—
223	C₂×C₄×C₅	—	2	1	no	—
224	C₂×C₄×C₅	—	2	1	no	—
225	C₂×C₄×C₅	—	2	1	no	—
226	C₂×C₄×C₅	—	2	1	no	—
227	C₂×C₄×C₅	—	2	2	no	—
228	C₂×C₄×C₅	—	2	4	no	—
229	C₂×C₄×C₅	—	2	2	no	—
230	C₂×C₄×C₅	—	2	1	no	—
231	C₂×C₄×C₅	—	2	2	no	—
232	C₂×C₄×C₅	—	2	1	no	—
233	C₂×C₄×C₅	—	2	1	no	—
234	C₂×C₄×C₅	—	4	8	no	—
235	C₂×C₄×C₅	—	4	1	no	—
236	C₂×C₄×C₅	—	4	1	no	—
237	C₂×C₄×C₅	—	4	1	no	—
238	C₂×C₄×C₅	—	4	2	no	—
239	C₂×C₄×C₅	—	4	1	no	—
240	C₂×C₄×C₅	—	4	2	no	—
241	C₂×C₄×C₅	—	4	1	no	—
242	C₂×C₄×C₅	—	4	1	no	—
243	C₂×C₄×C₅	—	4	8	no	—
244	C₂×C₄×C₅	—	4	8	no	—
245	C₂×C₄×C₅	—	4	2	no	—
246	C₂×C₄×C₅	—	4	2	no	—
247	C₂×C₄×C₅	—	4	2	no	—
248	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
249	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
250	C₂×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
251	C₂×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
252	C₂×C₄×C₅	C₂×D₈	1	2	yes	—
253	C₂×C₄×C₅	C₂×D₈	1	2	yes	—
254	C₂×C₄×C₅	C₂×D₈	1	2	yes	—
255	C₂×C₄×C₅	#135	1	2	yes	—
256	C₂×C₄×C₅	#137	1	2	yes	—
257	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
258	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
259	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
260	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
261	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
262	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
263	C₅×C₈	—	2	4	no	—
264	C₅×C₈	—	4	2	no	—
265	C₂²×Q₈	—	2	1	no	—
266	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
267	C₂³×C₄	—	2	1	no	—
268	C₂³×C₄	—	2	1	no	—
269	C₂³×C₄	—	2	1	no	—
270	C₂²×C₈	C₂³×C₅	1	2	yes	—
271	C₂²×C₈	C₂³×C₅	1	2	yes	—
272	C₄⋊Q₈	—	2	2	no	—
273	C₄⋊Q₈	C₂×C₄×C₅	1	4	yes	complemented
274	C₄×Q₈	—	4	4	no	—
275	C₄×D₄	—	2	2	no	—
276	C₄×D₄	—	2	2	no	—
277	C₄×D₄	—	2	2	no	—
278	C₄×D₄	—	2	2	no	—
279	C₄×D₄	C₂×C₄×C₅	1	4	yes	—
280	C₄×D₄	C₅×Q₈	1	4	yes	complemented
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
286	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
288	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
290	C₂×C₂²⋊C₄	—	2	1	no	—
291	C₂×C₂²⋊C₄	—	2	1	no	—
292	C₂×C₂²⋊C₄	—	2	1	no	—
293	C₂×C₄²	—	2	2	no	—
294	C₂×C₄²	—	2	1	no	—
295	C₂×C₄²	—	2	1	no	—
296	C₂×C₄²	—	2	1	no	—
297	C₂×C₄²	—	4	4	no	—
298	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
299	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
300	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
301	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
302	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
303	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
304	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
305	#107	—	2	4	no	—
306	#107	C₂×C₄×C₅	1	8	yes	complemented
307	C₄⋊C₈	—	2	2	no	—
308	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	complemented
309	#102	—	2	4	no	—
310	#102	C₂×C₄×C₅	1	8	yes	—
311	C₄×C₈	—	2	4	no	—
312	#95	—	2	1	no	—
313	#95	—	2	1	no	—
314	#95	—	2	1	no	—
315	#95	—	2	2	no	—
316	#95	—	2	2	no	—
317	C₂²×C₅	—	2	4	no	—
318	C₂²×C₅	—	4	2	no	—
319	C₂²×C₅	—	4	2	no	—
320	C₂²×C₅	—	4	2	no	—
321	C₂²×C₅	—	4	2	no	—
322	C₂²×C₅	—	4	2	no	—
323	C₂²×C₅	—	4	2	no	—
324	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
325	C₂²×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
326	C₂²×C₅	#525	1	1	yes	characteristic
327	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
328	C₂²×C₅	C₂×#135	1	1	yes	characteristic
329	C₂²×C₅	C₂×#137	1	1	yes	characteristic
330	C₂²×C₅	#575	1	1	yes	characteristic
331	C₄×C₅	—	2	2	no	—
332	C₄×C₅	—	2	2	no	—
333	C₄×C₅	—	2	2	no	—
334	C₄×C₅	—	4	2	no	—
335	C₄×C₅	—	4	1	no	—
336	C₄×C₅	—	4	2	no	—
337	C₄×C₅	—	4	4	no	—
338	C₄×C₅	—	4	2	no	—
339	C₄×C₅	—	8	2	no	—
340	C₄×C₅	C₄×D₈	1	4	yes	—
341	C₄×C₅	#474	1	4	yes	direct product factor
342	C₄×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
343	C₄×C₅	C₄×#41	1	1	yes	characteristic
344	C₄×C₅	#529	1	1	yes	characteristic
345	C₄×C₅	#533	1	1	yes	characteristic
346	C₂⁴	—	2	1	no	—
347	C₂×Q₈	—	2	4	no	—
348	C₂×Q₈	—	4	2	no	—
349	C₂×Q₈	—	4	2	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
354	C₂×D₄	C₂×C₅×Q₈	1	2	yes	—
355	C₂×D₄	C₅×#41	1	2	yes	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	4	no	—
362	C₂²×C₄	—	2	4	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	4	2	no	—
365	C₂²×C₄	—	4	2	no	—
366	C₂²×C₄	—	4	2	no	—
367	C₂²×C₄	—	4	2	no	—
368	C₂²×C₄	—	4	2	no	—
369	C₂²×C₄	—	4	2	no	—
370	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
371	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
372	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
373	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
374	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
375	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
376	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
383	C₄⋊C₄	—	2	4	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	4	2	no	—
391	C₄⋊C₄	—	4	4	no	—
392	C₄⋊C₄	—	4	2	no	—
393	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
394	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
395	C₄⋊C₄	C₂×C₅×Q₈	1	2	yes	—
396	C₄⋊C₄	C₅×#41	1	2	yes	—
397	C₂²⋊C₄	—	2	4	no	—
398	C₂²⋊C₄	—	2	4	no	—
399	C₂²⋊C₄	—	2	4	no	—
400	C₄²	—	2	2	no	—
401	C₄²	—	2	2	no	—
402	C₄²	—	2	1	no	—
403	C₄²	—	2	1	no	—
404	C₄²	—	4	1	no	—
405	C₄²	—	4	2	no	—
406	C₄²	—	4	2	no	—
407	C₄²	—	4	2	no	—
408	C₄²	—	4	4	no	—
409	C₄²	C₅×D₈	1	4	yes	—
410	C₄²	C₂²×C₄×C₅	1	2	yes	—
411	C₄²	C₂×C₅×Q₈	1	2	yes	—
412	C₄²	C₅×#41	1	2	yes	—
413	C₄²	C₅×#41	1	2	yes	—
414	C₂×C₅	—	4	4	no	—
415	C₂×C₅	C₄×C₂²⋊Q₈	1	1	yes	characteristic
416	C₂×C₅	C₂×C₄×D₈	1	1	yes	characteristic
417	C₂×C₅	C₄×#137	1	1	yes	characteristic
418	C₂×C₅	C₂×#474	1	1	yes	characteristic
419	C₂×C₅	#3076	1	1	yes	characteristic
420	C₂×C₅	#3100	1	1	yes	characteristic
421	C₂×C₅	#3107	1	1	yes	characteristic
422	C₂³	—	2	2	no	—
423	C₂³	—	2	2	no	—
424	C₂³	—	2	2	no	—
425	C₂³	—	4	1	no	—
426	C₂³	—	4	1	no	—
427	C₂³	—	4	1	no	—
428	C₂³	—	4	1	no	—
429	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
430	Q₈	—	4	8	no	—
431	D₄	—	2	2	no	—
432	D₄	—	2	2	no	—
433	D₄	—	2	2	no	—
434	D₄	C₄×C₅×Q₈	1	4	yes	complemented
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	4	8	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	8	no	—
458	C₂×C₄	—	4	8	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
463	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
464	C₂×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
465	C₂×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
466	C₂×C₄	C₂×C₅×D₈	1	2	yes	—
467	C₂×C₄	C₂×C₅×D₈	1	2	yes	—
468	C₂×C₄	C₂×C₅×D₈	1	2	yes	—
469	C₂×C₄	C₅×#135	1	2	yes	—
470	C₂×C₄	C₅×#137	1	2	yes	—
471	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
472	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
473	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
474	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
475	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
476	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
477	C₈	—	2	4	no	—
478	C₈	—	4	2	no	—
479	C₅	C₄×#474	1	1	yes	characteristic, direct product factor, Sylow
480	C₂²	—	2	4	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	4	2	no	—
483	C₂²	—	4	2	no	—
484	C₂²	—	4	2	no	—
485	C₂²	—	4	2	no	—
486	C₂²	—	4	2	no	—
487	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
488	C₂²	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
489	C₂²	C₅×#525	1	1	yes	characteristic
490	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
491	C₂²	C₂×C₅×#135	1	1	yes	characteristic
492	C₂²	C₂×C₅×#137	1	1	yes	characteristic
493	C₂²	C₅×#575	1	1	yes	characteristic
494	C₄	—	2	2	no	—
495	C₄	—	2	2	no	—
496	C₄	—	2	2	no	—
497	C₄	—	4	2	no	—
498	C₄	—	4	2	no	—
499	C₄	—	4	1	no	—
500	C₄	—	4	2	no	—
501	C₄	—	4	4	no	—
502	C₄	—	8	2	no	—
503	C₄	C₄×C₅×D₈	1	4	yes	—
504	C₄	C₅×#474	1	4	yes	direct product factor
505	C₄	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
506	C₄	C₄×C₅×#41	1	1	yes	characteristic
507	C₄	C₅×#529	1	1	yes	characteristic
508	C₄	C₅×#533	1	1	yes	characteristic
509	C₂	—	4	4	no	—
510	C₂	C₄×C₅×C₂²⋊Q₈	1	1	yes	characteristic
511	C₂	C₂×C₄×C₅×D₈	1	1	yes	characteristic
512	C₂	C₄×C₅×#137	1	1	yes	characteristic
513	C₂	C₂×C₅×#474	1	1	yes	characteristic
514	C₂	C₅×#3076	1	1	yes	characteristic
515	C₂	C₅×#3100	1	1	yes	characteristic
516	C₂	C₅×#3107	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂³×C₅	C₂²×D₄
prime radical	C₂²×C₅×D₄	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₄³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₅×C₄⋊Q₈	C₂	semidirect
4. C₅×#1988	C₂	semidirect
5. C₅×#1947	C₂	semidirect
6. C₅×#1918	C₂	semidirect
9. C₄×C₅×#107	C₂	semidirect
10. C₄×C₅×C₄⋊C₈	C₂	semidirect
18. C₅×#474	C₄	direct (N × H)
44. C₄×#474	C₅	direct (N × H)
53. C₅×C₄⋊Q₈	C₂×C₄	semidirect
60. C₄×C₅×D₄	Q₈	semidirect
86. C₅×#107	C₂×C₄	semidirect
88. C₅×C₄⋊C₈	C₂×C₄	semidirect
98. C₄×C₄⋊Q₈	C₂×C₅	semidirect
100. #1988	C₂×C₅	semidirect
101. #1947	C₂×C₅	semidirect
102. #1918	C₂×C₅	semidirect
105. C₄×#107	C₂×C₅	semidirect
106. C₄×C₄⋊C₈	C₂×C₅	semidirect
182. #474	C₄×C₅	direct (N × H)
220. C₅×D₄	C₄×Q₈	semidirect
273. C₄⋊Q₈	C₂×C₄×C₅	semidirect
280. C₄×D₄	C₅×Q₈	semidirect
306. #107	C₂×C₄×C₅	semidirect
308. C₄⋊C₈	C₂×C₄×C₅	semidirect
341. C₄×C₅	#474	direct (N × H)
434. D₄	C₄×C₅×Q₈	semidirect
479. C₅	C₄×#474	direct (N × H)
504. C₄	C₅×#474	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×#474	2
C₄×C₅×C₄⋊Q₈	2
C₄²×C₅×D₄	2
C₅×#1988	2
C₅×#1947	2
C₅×#1918	2
C₅×#1862	2
C₅×#1802	2
C₄×C₅×#107	2
C₄×C₅×C₄⋊C₈	2
C₄×C₅×#102	2
C₄×#474	5

Subgroups — C4×C5×#474 #11944327

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×#474 #11944327