Subgroups — C₅×#22273 #11944993

Order 1280.

906 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#497	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₅×#124	C₂	1	1	yes	maximal, characteristic
4	C₅×#1960	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1959	C₂	1	1	yes	maximal, characteristic
6	C₅×#1880	C₂	1	2	yes	maximal
7	C₅×#1878	C₂	1	2	yes	maximal, complemented
8	C₅×#1878	C₂	1	2	yes	maximal, complemented
9	C₅×#1877	C₂	1	2	yes	maximal
10	C₅×#1836	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1745	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₅×Q₁₆	C₂²	1	2	yes	—
13	C₂²×C₅×SD₁₆	C₂²	1	2	yes	—
14	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₅×#124	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
18	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₅×#497	C₄	1	8	yes	complemented
20	C₂×C₅×#103	C₂²	1	2	yes	—
21	C₂×C₅×#103	C₂²	1	2	yes	—
22	C₂×C₅×#103	C₂²	1	2	yes	—
23	C₂×C₅×#102	C₂²	1	2	yes	—
24	C₂×C₅×#97	C₂²	1	1	yes	characteristic
25	C₂×C₅×#97	C₂²	1	1	yes	characteristic
26	C₅×#391	C₂²	1	1	yes	characteristic
27	C₅×#391	C₂²	1	2	yes	—
28	C₅×#390	C₂²	1	1	yes	characteristic
29	C₅×#389	—	2	1	no	—
30	C₅×#389	—	2	1	no	—
31	C₅×#388	—	2	1	no	—
32	C₅×#388	—	2	1	no	—
33	C₅×#384	C₂²	1	1	yes	characteristic
34	C₅×#382	C₂²	1	1	yes	characteristic
35	C₄×C₅×C₄⋊C₄	—	2	1	no	—
36	C₄×C₅×C₄⋊C₄	—	2	1	no	—
37	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
38	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
39	C₄³×C₅	C₂²	1	1	yes	characteristic
40	C₅×#340	C₂²	1	2	yes	—
41	C₅×#340	C₂²	1	2	yes	—
42	C₅×#336	C₂²	1	2	yes	—
43	C₅×#336	C₂²	1	2	yes	—
44	#22273	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
46	C₂²×C₅×Q₈	C₂³	1	2	yes	—
47	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₅	—	2	1	no	—
49	C₂×C₅×Q₁₆	—	4	2	no	—
50	C₂×C₅×Q₁₆	—	4	2	no	—
51	C₂×C₅×Q₁₆	C₂×C₄	1	8	yes	complemented
52	C₂×C₅×SD₁₆	—	4	2	no	—
53	C₂×C₅×SD₁₆	—	4	2	no	—
54	C₂×C₅×SD₁₆	C₂×C₄	1	8	yes	—
55	C₂²×C₅×C₈	C₂³	1	2	yes	—
56	C₂²×C₅×C₈	C₂³	1	2	yes	—
57	C₅×C₄⋊Q₈	—	2	2	no	—
58	C₅×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
59	C₅×#124	—	2	2	no	—
60	C₅×#124	C₂×C₄	1	4	yes	—
61	C₄×C₅×Q₈	—	4	2	no	—
62	C₄×C₅×Q₈	—	4	2	no	—
63	C₄×C₅×Q₈	—	4	2	no	—
64	C₄×C₅×D₄	—	4	2	no	—
65	C₂×C₅×C₄⋊C₄	—	2	1	no	—
66	C₂×C₅×C₄⋊C₄	—	2	1	no	—
67	C₂×C₅×C₄⋊C₄	—	2	1	no	—
68	C₂×C₅×C₄⋊C₄	—	2	1	no	—
69	C₂×C₅×C₄⋊C₄	—	2	1	no	—
70	C₂×C₅×C₄⋊C₄	—	2	2	no	—
71	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
72	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
73	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
74	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
75	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
76	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
77	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
78	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
79	C₂×C₄²×C₅	—	2	1	no	—
80	C₂×C₄²×C₅	—	2	2	no	—
81	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
82	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
84	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
85	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
88	C₅×#103	—	4	2	no	—
89	C₅×#103	—	4	2	no	—
90	C₅×#103	—	4	2	no	—
91	C₅×#102	—	4	2	no	—
92	C₅×#97	—	2	2	no	—
93	C₅×#97	C₂×C₄	1	4	yes	complemented
94	C₅×#95	—	2	1	no	—
95	C₅×#95	—	2	1	no	—
96	C₅×#95	—	2	1	no	—
97	C₅×#95	—	2	1	no	—
98	C₅×#95	—	2	2	no	—
99	C₅×#95	—	2	2	no	—
100	C₂×#497	C₂×C₅	1	1	yes	characteristic
101	C₄×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
102	C₄×#124	C₂×C₅	1	1	yes	characteristic
103	#1960	C₂×C₅	1	1	yes	characteristic, complemented
104	#1959	C₂×C₅	1	1	yes	characteristic
105	#1880	C₂×C₅	1	2	yes	—
106	#1878	C₂×C₅	1	2	yes	complemented
107	#1878	C₂×C₅	1	2	yes	complemented
108	#1877	C₂×C₅	1	2	yes	—
109	#1836	C₂×C₅	1	1	yes	characteristic, complemented
110	#1745	C₂×C₅	1	1	yes	characteristic, complemented
111	C₂⁴×C₅	—	2	1	no	—
112	C₂×C₅×Q₈	—	2	1	no	—
113	C₂×C₅×Q₈	—	2	2	no	—
114	C₂×C₅×Q₈	—	2	2	no	—
115	C₂×C₅×Q₈	—	2	2	no	—
116	C₂×C₅×Q₈	—	2	2	no	—
117	C₂×C₅×Q₈	—	2	2	no	—
118	C₂×C₅×Q₈	—	2	2	no	—
119	C₂×C₅×Q₈	—	2	2	no	—
120	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
121	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
122	C₂×C₅×D₄	—	2	1	no	—
123	C₂×C₅×D₄	—	2	2	no	—
124	C₂×C₅×D₄	—	2	2	no	—
125	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
126	C₂²×C₄×C₅	—	2	1	no	—
127	C₂²×C₄×C₅	—	2	2	no	—
128	C₂²×C₄×C₅	—	2	1	no	—
129	C₂²×C₄×C₅	—	2	2	no	—
130	C₂²×C₄×C₅	—	2	1	no	—
131	C₂²×C₄×C₅	—	4	2	no	—
132	C₂²×C₄×C₅	—	4	2	no	—
133	C₂²×C₄×C₅	—	4	2	no	—
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	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
141	C₅×Q₁₆	—	4	8	no	—
142	C₅×SD₁₆	—	4	8	no	—
143	C₂×C₅×C₈	—	2	2	no	—
144	C₂×C₅×C₈	—	2	2	no	—
145	C₂×C₅×C₈	—	2	2	no	—
146	C₂×C₅×C₈	—	2	2	no	—
147	C₂×C₅×C₈	—	2	2	no	—
148	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
149	C₅×C₄⋊C₄	—	2	4	no	—
150	C₅×C₄⋊C₄	—	2	4	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	—	4	2	no	—
156	C₅×C₄⋊C₄	—	4	2	no	—
157	C₅×C₄⋊C₄	—	4	2	no	—
158	C₅×C₄⋊C₄	—	4	4	no	—
159	C₅×C₂²⋊C₄	—	2	4	no	—
160	C₅×C₂²⋊C₄	—	2	4	no	—
161	C₅×C₂²⋊C₄	—	4	2	no	—
162	C₅×C₂²⋊C₄	—	4	2	no	—
163	C₅×C₂²⋊C₄	—	4	2	no	—
164	C₄²×C₅	—	2	2	no	—
165	C₄²×C₅	—	2	2	no	—
166	C₄²×C₅	—	2	2	no	—
167	C₄²×C₅	—	2	2	no	—
168	C₄²×C₅	—	4	1	no	—
169	C₄²×C₅	—	4	1	no	—
170	C₄²×C₅	—	4	4	no	—
171	C₄²×C₅	—	4	2	no	—
172	C₄²×C₅	C₂²×C₄	1	2	yes	—
173	C₄²×C₅	#41	1	2	yes	—
174	C₂²×Q₁₆	C₂²×C₅	1	2	yes	—
175	C₂²×SD₁₆	C₂²×C₅	1	2	yes	—
176	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
177	C₂×#124	C₂²×C₅	1	1	yes	characteristic
178	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
179	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
180	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
181	#497	C₄×C₅	1	8	yes	complemented
182	C₂×#103	C₂²×C₅	1	2	yes	—
183	C₂×#103	C₂²×C₅	1	2	yes	—
184	C₂×#103	C₂²×C₅	1	2	yes	—
185	C₂×#102	C₂²×C₅	1	2	yes	—
186	C₂×#97	C₂²×C₅	1	1	yes	characteristic
187	C₂×#97	C₂²×C₅	1	1	yes	characteristic
188	#391	C₂²×C₅	1	2	yes	—
189	#391	C₂²×C₅	1	1	yes	characteristic
190	#390	C₂²×C₅	1	1	yes	characteristic
191	#389	—	2	1	no	—
192	#389	—	2	1	no	—
193	#388	—	2	1	no	—
194	#388	—	2	1	no	—
195	#384	C₂²×C₅	1	1	yes	characteristic
196	#382	C₂²×C₅	1	1	yes	characteristic
197	C₄×C₄⋊C₄	—	2	1	no	—
198	C₄×C₄⋊C₄	—	2	1	no	—
199	C₄×C₂²⋊C₄	—	2	1	no	—
200	C₄×C₂²⋊C₄	—	2	1	no	—
201	C₄³	C₂²×C₅	1	1	yes	characteristic
202	#340	C₂²×C₅	1	2	yes	—
203	#340	C₂²×C₅	1	2	yes	—
204	#336	C₂²×C₅	1	2	yes	—
205	#336	C₂²×C₅	1	2	yes	—
206	C₂³×C₅	—	2	2	no	—
207	C₂³×C₅	—	4	1	no	—
208	C₂³×C₅	—	4	1	no	—
209	C₂³×C₅	—	4	1	no	—
210	C₂³×C₅	—	4	1	no	—
211	C₂³×C₅	—	4	1	no	—
212	C₂³×C₅	—	4	1	no	—
213	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
214	C₅×Q₈	—	2	4	no	—
215	C₅×Q₈	—	2	4	no	—
216	C₅×Q₈	—	2	4	no	—
217	C₅×Q₈	—	4	2	no	—
218	C₅×Q₈	—	4	2	no	—
219	C₅×Q₈	—	4	2	no	—
220	C₅×D₄	—	2	4	no	—
221	C₅×D₄	—	4	2	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	1	no	—
228	C₂×C₄×C₅	—	2	1	no	—
229	C₂×C₄×C₅	—	2	1	no	—
230	C₂×C₄×C₅	—	2	2	no	—
231	C₂×C₄×C₅	—	2	4	no	—
232	C₂×C₄×C₅	—	2	1	no	—
233	C₂×C₄×C₅	—	2	1	no	—
234	C₂×C₄×C₅	—	2	1	no	—
235	C₂×C₄×C₅	—	2	1	no	—
236	C₂×C₄×C₅	—	2	1	no	—
237	C₂×C₄×C₅	—	2	1	no	—
238	C₂×C₄×C₅	—	4	1	no	—
239	C₂×C₄×C₅	—	4	2	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	2	no	—
244	C₂×C₄×C₅	—	4	1	no	—
245	C₂×C₄×C₅	—	4	1	no	—
246	C₂×C₄×C₅	—	4	1	no	—
247	C₂×C₄×C₅	—	4	1	no	—
248	C₂×C₄×C₅	—	4	2	no	—
249	C₂×C₄×C₅	—	4	2	no	—
250	C₂×C₄×C₅	—	4	1	no	—
251	C₂×C₄×C₅	—	8	4	no	—
252	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
253	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
254	C₂×C₄×C₅	#137	1	2	yes	—
255	C₂×C₄×C₅	#137	1	2	yes	—
256	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
257	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
258	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
259	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
260	C₅×C₈	—	2	4	no	—
261	C₅×C₈	—	4	2	no	—
262	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
263	C₂²×Q₈	C₂³×C₅	1	2	yes	—
264	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
265	C₂³×C₄	—	2	1	no	—
266	C₂×Q₁₆	—	4	2	no	—
267	C₂×Q₁₆	—	4	2	no	—
268	C₂×Q₁₆	C₂×C₄×C₅	1	8	yes	complemented
269	C₂×SD₁₆	—	4	2	no	—
270	C₂×SD₁₆	—	4	2	no	—
271	C₂×SD₁₆	C₂×C₄×C₅	1	8	yes	—
272	C₂²×C₈	C₂³×C₅	1	2	yes	—
273	C₂²×C₈	C₂³×C₅	1	2	yes	—
274	C₄⋊Q₈	—	2	2	no	—
275	C₄⋊Q₈	C₂×C₄×C₅	1	4	yes	complemented
276	#124	—	2	2	no	—
277	#124	C₂×C₄×C₅	1	4	yes	—
278	C₄×Q₈	—	4	2	no	—
279	C₄×Q₈	—	4	2	no	—
280	C₄×Q₈	—	4	2	no	—
281	C₄×D₄	—	4	2	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
291	C₂×C₂²⋊C₄	—	2	1	no	—
292	C₂×C₂²⋊C₄	—	2	1	no	—
293	C₂×C₂²⋊C₄	—	2	1	no	—
294	C₂×C₂²⋊C₄	—	2	1	no	—
295	C₂×C₂²⋊C₄	—	2	1	no	—
296	C₂×C₄²	—	2	1	no	—
297	C₂×C₄²	—	2	2	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	#103	—	4	2	no	—
306	#103	—	4	2	no	—
307	#103	—	4	2	no	—
308	#102	—	4	2	no	—
309	#97	—	2	2	no	—
310	#97	C₂×C₄×C₅	1	4	yes	complemented
311	#95	—	2	1	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	—	4	2	no	—
318	C₂²×C₅	—	4	2	no	—
319	C₂²×C₅	—	4	2	no	—
320	C₂²×C₅	—	8	1	no	—
321	C₂²×C₅	—	8	1	no	—
322	C₂²×C₅	—	8	1	no	—
323	C₂²×C₅	—	8	1	no	—
324	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
325	C₂²×C₅	#535	1	1	yes	characteristic
326	C₂²×C₅	#535	1	1	yes	characteristic
327	C₂²×C₅	C₂×#137	1	1	yes	characteristic
328	C₂²×C₅	C₂×#137	1	1	yes	characteristic
329	C₂²×C₅	#575	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	—	2	2	no	—
335	C₄×C₅	—	4	2	no	—
336	C₄×C₅	—	4	4	no	—
337	C₄×C₅	—	4	1	no	—
338	C₄×C₅	—	4	1	no	—
339	C₄×C₅	—	8	1	no	—
340	C₄×C₅	—	8	1	no	—
341	C₄×C₅	—	8	2	no	—
342	C₄×C₅	#518	1	2	yes	—
343	C₄×C₅	#540	1	2	yes	—
344	C₂⁴	—	2	1	no	—
345	C₂×Q₈	—	2	1	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	—	2	2	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	—	2	2	no	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
354	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	1	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	C₂×C₅×D₄	1	1	yes	characteristic
368	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
369	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
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	C₂⁴×C₅	1	1	yes	characteristic
374	Q₁₆	—	4	8	no	—
375	SD₁₆	—	4	8	no	—
376	C₂×C₈	—	2	2	no	—
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	C₂²×C₄×C₅	1	4	yes	—
382	C₄⋊C₄	—	2	4	no	—
383	C₄⋊C₄	—	2	4	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	4	2	no	—
389	C₄⋊C₄	—	4	4	no	—
390	C₄⋊C₄	—	4	2	no	—
391	C₄⋊C₄	—	4	2	no	—
392	C₂²⋊C₄	—	2	4	no	—
393	C₂²⋊C₄	—	2	4	no	—
394	C₂²⋊C₄	—	4	2	no	—
395	C₂²⋊C₄	—	4	2	no	—
396	C₂²⋊C₄	—	4	2	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	2	2	no	—
399	C₄²	—	2	2	no	—
400	C₄²	—	2	2	no	—
401	C₄²	—	4	1	no	—
402	C₄²	—	4	1	no	—
403	C₄²	—	4	4	no	—
404	C₄²	—	4	2	no	—
405	C₄²	C₂²×C₄×C₅	1	2	yes	—
406	C₄²	C₅×#41	1	2	yes	—
407	C₂×C₅	—	8	2	no	—
408	C₂×C₅	#2328	1	1	yes	characteristic
409	C₂×C₅	C₄×#137	1	1	yes	characteristic
410	C₂×C₅	C₄×#137	1	1	yes	characteristic
411	C₂×C₅	#3215	1	1	yes	characteristic
412	C₂×C₅	#3216	1	1	yes	characteristic
413	C₂×C₅	#3218	1	1	yes	characteristic
414	C₂×C₅	#3219	1	1	yes	characteristic
415	C₂³	—	2	2	no	—
416	C₂³	—	4	1	no	—
417	C₂³	—	4	1	no	—
418	C₂³	—	4	1	no	—
419	C₂³	—	4	1	no	—
420	C₂³	—	4	1	no	—
421	C₂³	—	4	1	no	—
422	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
423	Q₈	—	2	4	no	—
424	Q₈	—	2	4	no	—
425	Q₈	—	2	4	no	—
426	Q₈	—	4	2	no	—
427	Q₈	—	4	2	no	—
428	Q₈	—	4	2	no	—
429	D₄	—	2	4	no	—
430	D₄	—	4	2	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
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	2	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	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	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	8	4	no	—
461	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
462	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
463	C₂×C₄	C₅×#137	1	2	yes	—
464	C₂×C₄	C₅×#137	1	2	yes	—
465	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
466	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
467	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
468	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
469	C₈	—	2	4	no	—
470	C₈	—	4	2	no	—
471	C₅	#22273	1	1	yes	characteristic, direct product factor, Sylow
472	C₂²	—	4	2	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	4	2	no	—
475	C₂²	—	8	1	no	—
476	C₂²	—	8	1	no	—
477	C₂²	—	8	1	no	—
478	C₂²	—	8	1	no	—
479	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
480	C₂²	C₅×#535	1	1	yes	characteristic
481	C₂²	C₅×#535	1	1	yes	characteristic
482	C₂²	C₂×C₅×#137	1	1	yes	characteristic
483	C₂²	C₂×C₅×#137	1	1	yes	characteristic
484	C₂²	C₅×#575	1	1	yes	characteristic
485	C₂²	C₅×#575	1	1	yes	characteristic
486	C₄	—	2	2	no	—
487	C₄	—	2	2	no	—
488	C₄	—	2	2	no	—
489	C₄	—	2	2	no	—
490	C₄	—	4	2	no	—
491	C₄	—	4	4	no	—
492	C₄	—	4	1	no	—
493	C₄	—	4	1	no	—
494	C₄	—	8	1	no	—
495	C₄	—	8	1	no	—
496	C₄	—	8	2	no	—
497	C₄	C₅×#518	1	2	yes	—
498	C₄	C₅×#540	1	2	yes	—
499	C₂	—	8	2	no	—
500	C₂	C₅×#2328	1	1	yes	characteristic
501	C₂	C₄×C₅×#137	1	1	yes	characteristic
502	C₂	C₄×C₅×#137	1	1	yes	characteristic
503	C₂	C₅×#3215	1	1	yes	characteristic
504	C₂	C₅×#3216	1	1	yes	characteristic
505	C₂	C₅×#3218	1	1	yes	characteristic
506	C₂	C₅×#3219	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂²×C₅×D₄	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×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×#1960	C₂	semidirect
7. C₅×#1878	C₂	semidirect
8. C₅×#1878	C₂	semidirect
10. C₅×#1836	C₂	semidirect
11. C₅×#1745	C₂	semidirect
19. C₅×#497	C₄	semidirect
44. #22273	C₅	direct (N × H)
51. C₂×C₅×Q₁₆	C₂×C₄	semidirect
58. C₅×C₄⋊Q₈	C₂×C₄	semidirect
93. C₅×#97	C₂×C₄	semidirect
101. C₄×C₄⋊Q₈	C₂×C₅	semidirect
103. #1960	C₂×C₅	semidirect
106. #1878	C₂×C₅	semidirect
107. #1878	C₂×C₅	semidirect
109. #1836	C₂×C₅	semidirect
110. #1745	C₂×C₅	semidirect
181. #497	C₄×C₅	semidirect
268. C₂×Q₁₆	C₂×C₄×C₅	semidirect
275. C₄⋊Q₈	C₂×C₄×C₅	semidirect
310. #97	C₂×C₄×C₅	semidirect
471. C₅	#22273	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×#497	2
C₄×C₅×C₄⋊Q₈	2
C₄×C₅×#124	2
C₅×#1960	2
C₅×#1959	2
C₅×#1880	2
C₅×#1878	2
C₅×#1877	2
C₅×#1836	2
C₅×#1745	2
#22273	5

Subgroups — C5×#22273 #11944993

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22273 #11944993