Subgroups — C₄×C₅×#467 #11944242

Order 1280.

1054 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#467	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic
4	C₄×C₅×C₂²⋊Q₈	C₂	1	2	yes	maximal
5	C₅×#1969	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1942	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1933	C₂	1	2	yes	maximal, complemented
8	C₅×#1892	C₂	1	2	yes	maximal
9	C₅×#1808	C₂	1	1	yes	maximal, characteristic
10	C₄×C₅×#107	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×#103	C₂	1	2	yes	maximal, complemented
12	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
17	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₅×#467	C₄	1	8	yes	direct product factor
19	C₄×C₅×Q₁₆	—	2	4	no	—
20	C₂×C₅×#107	C₂²	1	1	yes	characteristic
21	C₂×C₅×#107	C₂²	1	1	yes	characteristic
22	C₂×C₅×#107	C₂²	1	1	yes	characteristic
23	C₂×C₅×#103	C₂²	1	2	yes	—
24	C₂×C₅×#103	C₂²	1	2	yes	—
25	C₂×C₅×#103	C₂²	1	2	yes	—
26	C₂×C₄×C₅×C₈	—	2	4	no	—
27	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
31	C₅×#391	C₂²	1	2	yes	—
32	C₅×#389	C₂²	1	2	yes	—
33	C₅×#387	—	2	2	no	—
34	C₅×#385	—	2	2	no	—
35	C₅×#380	C₂²	1	2	yes	—
36	C₄×C₅×C₄⋊C₄	—	2	2	no	—
37	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
38	C₄×C₅×C₂²⋊C₄	—	2	2	no	—
39	C₅×#340	C₂²	1	2	yes	—
40	C₅×#340	C₂²	1	2	yes	—
41	C₅×#340	C₂²	1	2	yes	—
42	C₄×#467	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₅×Q₈	C₂³	1	2	yes	—
44	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₂×C₅×Q₁₆	—	2	2	no	—
48	C₂×C₅×Q₁₆	—	2	2	no	—
49	C₂×C₅×Q₁₆	C₂×C₄	1	4	yes	complemented
50	C₂²×C₅×C₈	—	2	2	no	—
51	C₂²×C₅×C₈	—	2	2	no	—
52	C₂²×C₅×C₈	—	2	2	no	—
53	C₂²×C₅×C₈	—	2	2	no	—
54	C₂²×C₅×C₈	—	2	2	no	—
55	C₂²×C₅×C₈	C₂×C₄	1	4	yes	—
56	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
57	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
58	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
59	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
60	C₅×C₂²⋊Q₈	—	2	4	no	—
61	C₅×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
62	C₄×C₅×Q₈	—	2	4	no	—
63	C₄×C₅×Q₈	—	2	4	no	—
64	C₂×C₅×C₄⋊C₄	—	2	2	no	—
65	C₂×C₅×C₄⋊C₄	—	2	2	no	—
66	C₂×C₅×C₄⋊C₄	—	2	2	no	—
67	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
69	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
70	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
71	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
72	C₂×C₄²×C₅	—	2	2	no	—
73	C₂×C₄²×C₅	—	2	2	no	—
74	C₂×C₄²×C₅	—	2	2	no	—
75	C₂×C₄²×C₅	—	2	2	no	—
76	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
80	C₅×#107	—	2	2	no	—
81	C₅×#107	—	2	2	no	—
82	C₅×#107	C₂×C₄	1	4	yes	complemented
83	C₅×#103	—	2	4	no	—
84	C₅×#103	—	2	4	no	—
85	C₅×#103	C₂×C₄	1	8	yes	complemented
86	C₄×C₅×C₈	—	2	2	no	—
87	C₄×C₅×C₈	—	2	2	no	—
88	C₄×C₅×C₈	—	2	2	no	—
89	C₄×C₅×C₈	D₄	1	4	yes	—
90	C₅×#95	—	2	2	no	—
91	C₅×#95	—	2	2	no	—
92	C₅×#95	—	2	2	no	—
93	C₅×#95	—	2	2	no	—
94	C₅×#95	—	2	2	no	—
95	C₂×#467	C₂×C₅	1	1	yes	characteristic
96	C₂×C₄×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
97	C₂²×C₄×C₈	C₂×C₅	1	1	yes	characteristic
98	C₄×C₂²⋊Q₈	C₂×C₅	1	2	yes	—
99	#1969	C₂×C₅	1	1	yes	characteristic, complemented
100	#1942	C₂×C₅	1	1	yes	characteristic, complemented
101	#1933	C₂×C₅	1	2	yes	complemented
102	#1892	C₂×C₅	1	2	yes	—
103	#1808	C₂×C₅	1	1	yes	characteristic
104	C₄×#107	C₂×C₅	1	1	yes	characteristic, complemented
105	C₄×#103	C₂×C₅	1	2	yes	complemented
106	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
107	C₂×C₅×Q₈	—	2	2	no	—
108	C₂×C₅×Q₈	—	2	2	no	—
109	C₂×C₅×Q₈	—	2	2	no	—
110	C₂×C₅×Q₈	—	2	2	no	—
111	C₂×C₅×Q₈	—	2	2	no	—
112	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
113	C₂²×C₄×C₅	—	2	2	no	—
114	C₂²×C₄×C₅	—	2	2	no	—
115	C₂²×C₄×C₅	—	2	2	no	—
116	C₂²×C₄×C₅	—	2	2	no	—
117	C₂²×C₄×C₅	—	2	2	no	—
118	C₂²×C₄×C₅	—	2	1	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	2	no	—
124	C₂²×C₄×C₅	—	2	2	no	—
125	C₂²×C₄×C₅	—	2	2	no	—
126	C₂²×C₄×C₅	Q₁₆	1	4	yes	complemented
127	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
128	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₅	#41	1	2	yes	—
134	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
135	C₅×Q₁₆	—	2	8	no	—
136	C₂×C₅×C₈	—	2	8	no	—
137	C₂×C₅×C₈	—	2	1	no	—
138	C₂×C₅×C₈	—	2	1	no	—
139	C₂×C₅×C₈	—	2	1	no	—
140	C₂×C₅×C₈	—	2	1	no	—
141	C₂×C₅×C₈	—	2	1	no	—
142	C₂×C₅×C₈	—	2	1	no	—
143	C₂×C₅×C₈	—	2	8	no	—
144	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
145	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
146	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
147	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
148	C₂×C₅×C₈	#41	1	2	yes	—
149	C₂×C₅×C₈	#41	1	2	yes	—
150	C₅×C₄⋊C₄	—	2	8	no	—
151	C₅×C₄⋊C₄	—	2	2	no	—
152	C₅×C₄⋊C₄	—	2	2	no	—
153	C₅×C₄⋊C₄	—	2	2	no	—
154	C₅×C₄⋊C₄	—	2	2	no	—
155	C₅×C₄⋊C₄	—	2	2	no	—
156	C₅×C₄⋊C₄	—	4	4	no	—
157	C₅×C₄⋊C₄	—	4	4	no	—
158	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
159	C₅×C₂²⋊C₄	—	2	8	no	—
160	C₅×C₂²⋊C₄	—	4	4	no	—
161	C₄²×C₅	—	2	2	no	—
162	C₄²×C₅	—	2	2	no	—
163	C₄²×C₅	—	2	1	no	—
164	C₄²×C₅	—	2	1	no	—
165	C₄²×C₅	—	4	4	no	—
166	C₄²×C₅	—	4	4	no	—
167	C₄²×C₅	C₂×D₄	1	2	yes	—
168	C₄²×C₅	#41	1	2	yes	—
169	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
170	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
171	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
172	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
173	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
174	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
175	#467	C₄×C₅	1	8	yes	direct product factor
176	C₄×Q₁₆	—	2	4	no	—
177	C₂×#107	C₂²×C₅	1	1	yes	characteristic
178	C₂×#107	C₂²×C₅	1	1	yes	characteristic
179	C₂×#107	C₂²×C₅	1	1	yes	characteristic
180	C₂×#103	C₂²×C₅	1	2	yes	—
181	C₂×#103	C₂²×C₅	1	2	yes	—
182	C₂×#103	C₂²×C₅	1	2	yes	—
183	C₂×C₄×C₈	—	2	4	no	—
184	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
185	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
186	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
187	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
188	#391	C₂²×C₅	1	2	yes	—
189	#389	C₂²×C₅	1	2	yes	—
190	#387	—	2	2	no	—
191	#385	—	2	2	no	—
192	#380	C₂²×C₅	1	2	yes	—
193	C₄×C₄⋊C₄	—	2	2	no	—
194	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
195	C₄×C₂²⋊C₄	—	2	2	no	—
196	#340	C₂²×C₅	1	2	yes	—
197	#340	C₂²×C₅	1	2	yes	—
198	#340	C₂²×C₅	1	2	yes	—
199	C₂³×C₅	—	2	1	no	—
200	C₂³×C₅	—	2	1	no	—
201	C₂³×C₅	—	2	1	no	—
202	C₂³×C₅	—	2	1	no	—
203	C₂³×C₅	C₄×D₄	1	2	yes	—
204	C₂³×C₅	C₂×Q₁₆	1	2	yes	—
205	C₂³×C₅	#135	1	2	yes	—
206	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
207	C₅×Q₈	—	2	4	no	—
208	C₅×Q₈	—	2	4	no	—
209	C₅×Q₈	—	4	2	no	—
210	C₅×Q₈	—	4	2	no	—
211	C₂×C₄×C₅	—	2	8	no	—
212	C₂×C₄×C₅	—	2	1	no	—
213	C₂×C₄×C₅	—	2	1	no	—
214	C₂×C₄×C₅	—	2	1	no	—
215	C₂×C₄×C₅	—	2	1	no	—
216	C₂×C₄×C₅	—	2	1	no	—
217	C₂×C₄×C₅	—	2	1	no	—
218	C₂×C₄×C₅	—	2	1	no	—
219	C₂×C₄×C₅	—	2	1	no	—
220	C₂×C₄×C₅	—	2	2	no	—
221	C₂×C₄×C₅	—	2	2	no	—
222	C₂×C₄×C₅	—	2	2	no	—
223	C₂×C₄×C₅	—	2	2	no	—
224	C₂×C₄×C₅	—	2	8	no	—
225	C₂×C₄×C₅	—	2	4	no	—
226	C₂×C₄×C₅	—	2	4	no	—
227	C₂×C₄×C₅	—	4	2	no	—
228	C₂×C₄×C₅	—	4	2	no	—
229	C₂×C₄×C₅	—	4	2	no	—
230	C₂×C₄×C₅	—	4	2	no	—
231	C₂×C₄×C₅	—	4	2	no	—
232	C₂×C₄×C₅	—	4	2	no	—
233	C₂×C₄×C₅	—	4	2	no	—
234	C₂×C₄×C₅	—	4	2	no	—
235	C₂×C₄×C₅	—	4	2	no	—
236	C₂×C₄×C₅	—	4	2	no	—
237	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
238	C₂×C₄×C₅	#121	1	2	yes	—
239	C₂×C₄×C₅	#121	1	2	yes	—
240	C₂×C₄×C₅	C₂×Q₁₆	1	2	yes	—
241	C₂×C₄×C₅	C₂×Q₁₆	1	2	yes	—
242	C₂×C₄×C₅	#135	1	2	yes	—
243	C₂×C₄×C₅	#135	1	2	yes	—
244	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
245	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
247	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
248	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
249	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
250	C₅×C₈	—	2	2	no	—
251	C₅×C₈	—	2	2	no	—
252	C₅×C₈	—	2	2	no	—
253	C₅×C₈	C₄×D₄	1	4	yes	—
254	C₂²×Q₈	C₂³×C₅	1	2	yes	—
255	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
256	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
257	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
258	C₂×Q₁₆	—	2	2	no	—
259	C₂×Q₁₆	—	2	2	no	—
260	C₂×Q₁₆	C₂×C₄×C₅	1	4	yes	complemented
261	C₂²×C₈	—	2	2	no	—
262	C₂²×C₈	—	2	2	no	—
263	C₂²×C₈	—	2	2	no	—
264	C₂²×C₈	—	2	2	no	—
265	C₂²×C₈	—	2	2	no	—
266	C₂²×C₈	C₂×C₄×C₅	1	4	yes	—
267	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
268	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
269	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
270	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
271	C₂²⋊Q₈	—	2	4	no	—
272	C₂²⋊Q₈	C₂×C₄×C₅	1	8	yes	—
273	C₄×Q₈	—	2	4	no	—
274	C₄×Q₈	—	2	4	no	—
275	C₂×C₄⋊C₄	—	2	2	no	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
279	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
280	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
281	C₂×C₂²⋊C₄	—	2	2	no	—
282	C₂×C₂²⋊C₄	—	2	2	no	—
283	C₂×C₄²	—	2	2	no	—
284	C₂×C₄²	—	2	2	no	—
285	C₂×C₄²	—	2	2	no	—
286	C₂×C₄²	—	2	2	no	—
287	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
288	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
289	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
290	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
291	#107	—	2	2	no	—
292	#107	—	2	2	no	—
293	#107	C₂×C₄×C₅	1	4	yes	complemented
294	#103	—	2	4	no	—
295	#103	—	2	4	no	—
296	#103	C₂×C₄×C₅	1	8	yes	complemented
297	C₄×C₈	—	2	2	no	—
298	C₄×C₈	—	2	2	no	—
299	C₄×C₈	—	2	2	no	—
300	C₄×C₈	C₅×D₄	1	4	yes	—
301	#95	—	2	2	no	—
302	#95	—	2	2	no	—
303	#95	—	2	2	no	—
304	#95	—	2	2	no	—
305	#95	—	2	2	no	—
306	C₂²×C₅	—	2	2	no	—
307	C₂²×C₅	—	2	2	no	—
308	C₂²×C₅	—	2	2	no	—
309	C₂²×C₅	—	2	2	no	—
310	C₂²×C₅	—	2	2	no	—
311	C₂²×C₅	—	2	2	no	—
312	C₂²×C₅	C₄×Q₁₆	1	4	yes	complemented
313	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
314	C₂²×C₅	C₂×#121	1	1	yes	characteristic
315	C₂²×C₅	#532	1	1	yes	characteristic
316	C₂²×C₅	C₂²×Q₁₆	1	1	yes	characteristic
317	C₂²×C₅	C₂×#135	1	1	yes	characteristic
318	C₂²×C₅	C₂×#135	1	1	yes	characteristic
319	C₂²×C₅	C₂×#135	1	1	yes	characteristic
320	C₄×C₅	—	2	2	no	—
321	C₄×C₅	—	2	2	no	—
322	C₄×C₅	—	2	2	no	—
323	C₄×C₅	—	2	2	no	—
324	C₄×C₅	—	4	4	no	—
325	C₄×C₅	—	4	4	no	—
326	C₄×C₅	—	8	2	no	—
327	C₄×C₅	—	8	2	no	—
328	C₄×C₅	#467	1	4	yes	direct product factor
329	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
330	C₄×C₅	C₄×#41	1	1	yes	characteristic
331	C₄×C₅	#525	1	1	yes	characteristic
332	C₄×C₅	#529	1	1	yes	characteristic
333	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	C₅×Q₁₆	1	4	yes	complemented
354	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
355	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
356	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
357	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
358	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
359	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
360	C₂²×C₄	C₅×#41	1	2	yes	—
361	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
362	Q₁₆	—	2	8	no	—
363	C₂×C₈	—	2	8	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	8	no	—
371	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
372	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
373	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
374	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
375	C₂×C₈	C₅×#41	1	2	yes	—
376	C₂×C₈	C₅×#41	1	2	yes	—
377	C₄⋊C₄	—	2	8	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	4	4	no	—
384	C₄⋊C₄	—	4	4	no	—
385	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
386	C₂²⋊C₄	—	2	8	no	—
387	C₂²⋊C₄	—	4	4	no	—
388	C₄²	—	2	2	no	—
389	C₄²	—	2	2	no	—
390	C₄²	—	2	1	no	—
391	C₄²	—	2	1	no	—
392	C₄²	—	4	4	no	—
393	C₄²	—	4	4	no	—
394	C₄²	C₂×C₅×D₄	1	2	yes	—
395	C₄²	C₅×#41	1	2	yes	—
396	C₂×C₅	—	2	4	no	—
397	C₂×C₅	C₄×#121	1	1	yes	characteristic
398	C₂×C₅	C₂×C₄×Q₁₆	1	1	yes	characteristic
399	C₂×C₅	C₄×#135	1	1	yes	characteristic
400	C₂×C₅	C₂×#467	1	1	yes	characteristic
401	C₂×C₅	#3050	1	1	yes	characteristic
402	C₂×C₅	#3168	1	1	yes	characteristic
403	C₂×C₅	#3170	1	1	yes	characteristic
404	C₂³	—	2	1	no	—
405	C₂³	—	2	1	no	—
406	C₂³	—	2	1	no	—
407	C₂³	—	2	1	no	—
408	C₂³	C₄×C₅×D₄	1	2	yes	—
409	C₂³	C₂×C₅×Q₁₆	1	2	yes	—
410	C₂³	C₅×#135	1	2	yes	—
411	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
412	Q₈	—	2	4	no	—
413	Q₈	—	2	4	no	—
414	Q₈	—	4	2	no	—
415	Q₈	—	4	2	no	—
416	C₂×C₄	—	2	8	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	8	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
443	C₂×C₄	C₅×#121	1	2	yes	—
444	C₂×C₄	C₅×#121	1	2	yes	—
445	C₂×C₄	C₂×C₅×Q₁₆	1	2	yes	—
446	C₂×C₄	C₂×C₅×Q₁₆	1	2	yes	—
447	C₂×C₄	C₅×#135	1	2	yes	—
448	C₂×C₄	C₅×#135	1	2	yes	—
449	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
450	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
451	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
452	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
453	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
454	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
455	C₈	—	2	2	no	—
456	C₈	—	2	2	no	—
457	C₈	—	2	2	no	—
458	C₈	C₄×C₅×D₄	1	4	yes	—
459	C₅	C₄×#467	1	1	yes	characteristic, direct product factor, Sylow
460	C₂²	—	2	2	no	—
461	C₂²	—	2	2	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	2	2	no	—
464	C₂²	—	2	2	no	—
465	C₂²	—	2	2	no	—
466	C₂²	C₄×C₅×Q₁₆	1	4	yes	complemented
467	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
468	C₂²	C₂×C₅×#121	1	1	yes	characteristic
469	C₂²	C₅×#532	1	1	yes	characteristic
470	C₂²	C₂²×C₅×Q₁₆	1	1	yes	characteristic
471	C₂²	C₂×C₅×#135	1	1	yes	characteristic
472	C₂²	C₂×C₅×#135	1	1	yes	characteristic
473	C₂²	C₂×C₅×#135	1	1	yes	characteristic
474	C₄	—	2	2	no	—
475	C₄	—	2	2	no	—
476	C₄	—	2	2	no	—
477	C₄	—	2	2	no	—
478	C₄	—	4	4	no	—
479	C₄	—	4	4	no	—
480	C₄	—	8	2	no	—
481	C₄	—	8	2	no	—
482	C₄	C₅×#467	1	4	yes	direct product factor
483	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
484	C₄	C₄×C₅×#41	1	1	yes	characteristic
485	C₄	C₅×#525	1	1	yes	characteristic
486	C₄	C₅×#529	1	1	yes	characteristic
487	C₂	—	2	4	no	—
488	C₂	C₄×C₅×#121	1	1	yes	characteristic
489	C₂	C₂×C₄×C₅×Q₁₆	1	1	yes	characteristic
490	C₂	C₄×C₅×#135	1	1	yes	characteristic
491	C₂	C₂×C₅×#467	1	1	yes	characteristic
492	C₂	C₅×#3050	1	1	yes	characteristic
493	C₂	C₅×#3168	1	1	yes	characteristic
494	C₂	C₅×#3170	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	C₂⁴×C₅	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂²×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₅×Q₁₆	C₂	semidirect
5. C₅×#1969	C₂	semidirect
6. C₅×#1942	C₂	semidirect
7. C₅×#1933	C₂	semidirect
10. C₄×C₅×#107	C₂	semidirect
11. C₄×C₅×#103	C₂	semidirect
18. C₅×#467	C₄	direct (N × H)
42. C₄×#467	C₅	direct (N × H)
49. C₂×C₅×Q₁₆	C₂×C₄	semidirect
82. C₅×#107	C₂×C₄	semidirect
85. C₅×#103	C₂×C₄	semidirect
96. C₂×C₄×Q₁₆	C₂×C₅	semidirect
99. #1969	C₂×C₅	semidirect
100. #1942	C₂×C₅	semidirect
101. #1933	C₂×C₅	semidirect
104. C₄×#107	C₂×C₅	semidirect
105. C₄×#103	C₂×C₅	semidirect
126. C₂²×C₄×C₅	Q₁₆	semidirect
175. #467	C₄×C₅	direct (N × H)
260. C₂×Q₁₆	C₂×C₄×C₅	semidirect
293. #107	C₂×C₄×C₅	semidirect
296. #103	C₂×C₄×C₅	semidirect
312. C₂²×C₅	C₄×Q₁₆	semidirect
328. C₄×C₅	#467	direct (N × H)
353. C₂²×C₄	C₅×Q₁₆	semidirect
459. C₅	C₄×#467	direct (N × H)
466. C₂²	C₄×C₅×Q₁₆	semidirect
482. C₄	C₅×#467	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×#467	2
C₂×C₄×C₅×Q₁₆	2
C₂²×C₄×C₅×C₈	2
C₄×C₅×C₂²⋊Q₈	2
C₅×#1969	2
C₅×#1942	2
C₅×#1933	2
C₅×#1892	2
C₅×#1808	2
C₄×C₅×#107	2
C₄×C₅×#103	2
C₄×#467	5

Subgroups — C4×C5×#467 #11944242

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×#467 #11944242