Subgroups — C₅×#23081 #11945801

Order 1280.

662 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3076	C₂	1	1	yes	maximal, characteristic
2	C₅×#2962	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2925	C₂	1	1	yes	maximal, characteristic
4	C₅×#1994	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1950	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1938	C₂	1	2	yes	maximal
7	C₅×#1929	C₂	1	2	yes	maximal
8	C₅×#1922	C₂	1	2	yes	maximal, complemented
9	C₅×#1773	C₂	1	2	yes	maximal, complemented
10	C₅×#1767	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×#104	C₂	1	1	yes	maximal, characteristic
12	C₅×#533	C₂²	1	1	yes	characteristic
13	C₄×C₅×#41	C₂²	1	1	yes	characteristic
14	C₅×#479	C₄	1	2	yes	complemented
15	C₅×#478	C₄	1	2	yes	complemented
16	C₅×#477	C₄	1	1	yes	characteristic, complemented
17	C₅×#476	C₄	1	1	yes	characteristic, complemented
18	C₅×#475	C₄	1	1	yes	characteristic, complemented
19	C₅×#474	C₄	1	1	yes	characteristic, complemented
20	C₅×#446	—	2	1	no	—
21	C₅×#446	—	2	2	no	—
22	C₅×C₈×Q₈	—	2	1	no	—
23	C₅×#433	—	2	2	no	—
24	C₅×#432	—	2	1	no	—
25	C₅×#431	—	2	1	no	—
26	C₂×C₅×#108	C₂²	1	2	yes	—
27	C₅×#427	C₂²	1	2	yes	—
28	C₅×#424	C₂²	1	2	yes	—
29	C₅×#423	C₂²	1	1	yes	characteristic
30	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₅×#104	C₂²	1	1	yes	characteristic
33	C₂×C₅×#104	C₂²	1	1	yes	characteristic
34	C₅×#416	C₂²	1	2	yes	—
35	C₅×#408	C₂²	1	2	yes	—
36	C₅×#405	C₂²	1	2	yes	—
37	C₅×#405	C₂²	1	2	yes	—
38	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
39	C₂×C₅×#97	C₂²	1	2	yes	—
40	C₄³×C₅	C₂²	1	1	yes	characteristic
41	C₅×#341	C₂²	1	2	yes	—
42	C₅×#339	C₂²	1	1	yes	characteristic
43	C₅×#339	C₂²	1	1	yes	characteristic
44	C₅×#339	C₂²	1	2	yes	—
45	C₅×#339	C₂²	1	2	yes	—
46	C₅×#336	C₂²	1	2	yes	—
47	#23081	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂×C₅×#41	C₂³	1	1	yes	characteristic
49	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
50	C₂×C₅×M₁₆	C₂³	1	2	yes	—
51	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
52	C₂²×C₅×C₈	C₂³	1	2	yes	—
53	C₂²×C₅×C₈	C₂³	1	2	yes	—
54	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
55	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
56	C₅×#125	C₂×C₄	1	2	yes	—
57	C₅×C₂²⋊Q₈	—	2	1	no	—
58	C₅×C₂²⋊Q₈	—	2	1	no	—
59	C₄×C₅×Q₈	—	2	1	no	—
60	C₄×C₅×Q₈	—	2	1	no	—
61	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
62	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
63	C₄×C₅×D₄	—	2	1	no	—
64	C₄×C₅×D₄	—	2	1	no	—
65	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
66	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
67	C₅×#117	—	2	1	no	—
68	C₅×#117	C₂³	1	1	yes	characteristic
69	C₅×#117	C₂³	1	2	yes	—
70	C₂×C₄²×C₅	—	2	1	no	—
71	C₂×C₄²×C₅	—	2	1	no	—
72	C₂×C₄²×C₅	—	2	1	no	—
73	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
76	C₅×#108	—	2	4	no	—
77	C₅×#107	C₂×C₄	1	2	yes	—
78	C₅×#107	C₂×C₄	1	2	yes	—
79	C₅×#106	C₂×C₄	1	2	yes	—
80	C₅×#106	C₂×C₄	1	2	yes	—
81	C₅×C₄⋊C₈	—	2	2	no	—
82	C₅×C₄⋊C₈	—	2	2	no	—
83	C₅×C₄⋊C₈	—	2	1	no	—
84	C₅×C₄⋊C₈	—	2	1	no	—
85	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
86	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
87	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
88	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
89	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
90	C₅×C₄⋊C₈	D₄	1	2	yes	—
91	C₅×#104	—	2	2	no	—
92	C₅×#104	—	2	2	no	—
93	C₅×#103	C₂×C₄	1	2	yes	—
94	C₅×#103	C₂×C₄	1	2	yes	—
95	C₅×#102	C₂×C₄	1	2	yes	—
96	C₅×#102	C₂×C₄	1	2	yes	—
97	C₅×C₂²⋊C₈	—	2	2	no	—
98	C₅×C₂²⋊C₈	—	2	2	no	—
99	C₅×#97	—	2	2	no	—
100	C₅×#97	—	2	2	no	—
101	C₅×#97	—	2	1	no	—
102	C₅×#97	—	2	4	no	—
103	C₄×C₅×C₈	—	2	2	no	—
104	C₄×C₅×C₈	—	2	2	no	—
105	C₄×C₅×C₈	—	2	1	no	—
106	#3076	C₂×C₅	1	1	yes	characteristic
107	#2962	C₂×C₅	1	1	yes	characteristic, complemented
108	#2925	C₂×C₅	1	1	yes	characteristic
109	#1994	C₂×C₅	1	1	yes	characteristic, complemented
110	#1950	C₂×C₅	1	1	yes	characteristic, complemented
111	#1938	C₂×C₅	1	2	yes	—
112	#1929	C₂×C₅	1	2	yes	—
113	#1922	C₂×C₅	1	2	yes	complemented
114	#1773	C₂×C₅	1	2	yes	complemented
115	#1767	C₂×C₅	1	1	yes	characteristic, complemented
116	C₄×#104	C₂×C₅	1	1	yes	characteristic
117	C₅×#41	—	2	1	no	—
118	C₅×#41	—	2	1	no	—
119	C₅×#41	—	2	1	no	—
120	C₅×#41	—	2	1	no	—
121	C₂×C₅×Q₈	—	2	1	no	—
122	C₂×C₅×Q₈	—	2	1	no	—
123	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₅×D₄	—	2	1	no	—
125	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₅	—	2	1	no	—
127	C₂²×C₄×C₅	—	2	1	no	—
128	C₂²×C₄×C₅	—	2	1	no	—
129	C₂²×C₄×C₅	—	2	1	no	—
130	C₂²×C₄×C₅	—	2	1	no	—
131	C₂²×C₄×C₅	#41	1	1	yes	characteristic
132	C₂²×C₄×C₅	#41	1	1	yes	characteristic
133	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
134	C₅×M₁₆	—	2	1	no	—
135	C₅×M₁₆	—	2	1	no	—
136	C₅×M₁₆	—	2	2	no	—
137	C₅×M₁₆	—	2	1	no	—
138	C₅×M₁₆	—	2	2	no	—
139	C₅×M₁₆	#41	1	2	yes	—
140	C₂×C₅×C₈	—	2	1	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	—	2	2	no	—
145	C₂×C₅×C₈	—	2	2	no	—
146	C₂×C₅×C₈	—	2	1	no	—
147	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
148	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
149	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
150	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
151	C₅×C₄⋊C₄	—	2	1	no	—
152	C₅×C₄⋊C₄	—	2	1	no	—
153	C₅×C₄⋊C₄	—	2	2	no	—
154	C₅×C₄⋊C₄	—	2	2	no	—
155	C₅×C₄⋊C₄	—	2	1	no	—
156	C₅×C₄⋊C₄	—	2	1	no	—
157	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
158	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
159	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
160	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
161	C₅×C₂²⋊C₄	—	2	1	no	—
162	C₅×C₂²⋊C₄	—	2	2	no	—
163	C₅×C₂²⋊C₄	—	2	1	no	—
164	C₅×C₂²⋊C₄	—	2	1	no	—
165	C₄²×C₅	—	2	1	no	—
166	C₄²×C₅	—	2	1	no	—
167	C₄²×C₅	—	2	1	no	—
168	C₄²×C₅	—	2	2	no	—
169	C₄²×C₅	—	2	1	no	—
170	C₄²×C₅	—	2	1	no	—
171	C₄²×C₅	—	2	1	no	—
172	C₄²×C₅	—	4	2	no	—
173	C₄²×C₅	—	4	2	no	—
174	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
175	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
176	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₅	#41	1	2	yes	—
179	#533	C₂²×C₅	1	1	yes	characteristic
180	C₄×#41	C₂²×C₅	1	1	yes	characteristic
181	#479	C₄×C₅	1	2	yes	complemented
182	#478	C₄×C₅	1	2	yes	complemented
183	#477	C₄×C₅	1	1	yes	characteristic, complemented
184	#476	C₄×C₅	1	1	yes	characteristic, complemented
185	#475	C₄×C₅	1	1	yes	characteristic, complemented
186	#474	C₄×C₅	1	1	yes	characteristic, complemented
187	#446	—	2	2	no	—
188	#446	—	2	1	no	—
189	C₈×Q₈	—	2	1	no	—
190	#433	—	2	2	no	—
191	#432	—	2	1	no	—
192	#431	—	2	1	no	—
193	C₂×#108	C₂²×C₅	1	2	yes	—
194	#427	C₂²×C₅	1	2	yes	—
195	#424	C₂²×C₅	1	2	yes	—
196	#423	C₂²×C₅	1	1	yes	characteristic
197	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
198	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
199	C₂×#104	C₂²×C₅	1	1	yes	characteristic
200	C₂×#104	C₂²×C₅	1	1	yes	characteristic
201	#416	C₂²×C₅	1	2	yes	—
202	#408	C₂²×C₅	1	2	yes	—
203	#405	C₂²×C₅	1	2	yes	—
204	#405	C₂²×C₅	1	2	yes	—
205	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
206	C₂×#97	C₂²×C₅	1	2	yes	—
207	C₄³	C₂²×C₅	1	1	yes	characteristic
208	#341	C₂²×C₅	1	2	yes	—
209	#339	C₂²×C₅	1	1	yes	characteristic
210	#339	C₂²×C₅	1	2	yes	—
211	#339	C₂²×C₅	1	2	yes	—
212	#339	C₂²×C₅	1	1	yes	characteristic
213	#336	C₂²×C₅	1	2	yes	—
214	C₂³×C₅	—	2	1	no	—
215	C₂³×C₅	C₂×#41	1	1	yes	characteristic
216	C₅×Q₈	—	2	1	no	—
217	C₅×Q₈	—	2	1	no	—
218	C₅×Q₈	—	4	2	no	—
219	C₅×Q₈	—	8	1	no	—
220	C₅×D₄	—	2	1	no	—
221	C₅×D₄	—	2	1	no	—
222	C₅×D₄	—	4	1	no	—
223	C₅×D₄	—	4	1	no	—
224	C₂×C₄×C₅	—	2	2	no	—
225	C₂×C₄×C₅	—	2	2	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	2	no	—
230	C₂×C₄×C₅	—	2	2	no	—
231	C₂×C₄×C₅	—	2	2	no	—
232	C₂×C₄×C₅	—	4	1	no	—
233	C₂×C₄×C₅	—	4	1	no	—
234	C₂×C₄×C₅	—	4	1	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	1	no	—
239	C₂×C₄×C₅	—	4	2	no	—
240	C₂×C₄×C₅	—	8	1	no	—
241	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
242	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
243	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
244	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
245	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
246	C₂×C₄×C₅	C₂²×D₄	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	2₋¹⁺⁴	1	1	yes	characteristic
250	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
251	C₅×C₈	—	2	2	no	—
252	C₅×C₈	—	2	2	no	—
253	C₅×C₈	—	2	2	no	—
254	C₅×C₈	—	2	2	no	—
255	C₅×C₈	—	2	2	no	—
256	C₅×C₈	—	4	1	no	—
257	C₅×C₈	—	4	2	no	—
258	C₂×#41	C₂³×C₅	1	1	yes	characteristic
259	C₂×M₁₆	C₂³×C₅	1	2	yes	—
260	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
261	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
262	C₂²×C₈	C₂³×C₅	1	2	yes	—
263	C₂²×C₈	C₂³×C₅	1	2	yes	—
264	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
265	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
266	#125	C₂×C₄×C₅	1	2	yes	—
267	C₂²⋊Q₈	—	2	1	no	—
268	C₂²⋊Q₈	—	2	1	no	—
269	C₄×Q₈	—	2	1	no	—
270	C₄×Q₈	—	2	1	no	—
271	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
272	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
273	C₄×D₄	—	2	1	no	—
274	C₄×D₄	—	2	1	no	—
275	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
276	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
277	#117	—	2	1	no	—
278	#117	C₂³×C₅	1	1	yes	characteristic
279	#117	C₂³×C₅	1	2	yes	—
280	C₂×C₄²	—	2	1	no	—
281	C₂×C₄²	—	2	1	no	—
282	C₂×C₄²	—	2	1	no	—
283	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
284	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
285	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
286	#108	—	2	4	no	—
287	#107	C₂×C₄×C₅	1	2	yes	—
288	#107	C₂×C₄×C₅	1	2	yes	—
289	#106	C₂×C₄×C₅	1	2	yes	—
290	#106	C₂×C₄×C₅	1	2	yes	—
291	C₄⋊C₈	—	2	2	no	—
292	C₄⋊C₈	—	2	2	no	—
293	C₄⋊C₈	—	2	1	no	—
294	C₄⋊C₈	—	2	1	no	—
295	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
296	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
297	C₄⋊C₈	C₂×C₄×C₅	1	2	yes	—
298	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
299	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
300	C₄⋊C₈	C₅×D₄	1	2	yes	—
301	#104	—	2	2	no	—
302	#104	—	2	2	no	—
303	#103	C₂×C₄×C₅	1	2	yes	—
304	#103	C₂×C₄×C₅	1	2	yes	—
305	#102	C₂×C₄×C₅	1	2	yes	—
306	#102	C₂×C₄×C₅	1	2	yes	—
307	C₂²⋊C₈	—	2	2	no	—
308	C₂²⋊C₈	—	2	2	no	—
309	#97	—	2	2	no	—
310	#97	—	2	2	no	—
311	#97	—	2	1	no	—
312	#97	—	2	4	no	—
313	C₄×C₈	—	2	2	no	—
314	C₄×C₈	—	2	2	no	—
315	C₄×C₈	—	2	1	no	—
316	C₂²×C₅	—	2	1	no	—
317	C₂²×C₅	—	2	1	no	—
318	C₂²×C₅	—	4	1	no	—
319	C₂²×C₅	—	4	1	no	—
320	C₂²×C₅	—	4	1	no	—
321	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
322	C₂²×C₅	#552	1	1	yes	characteristic
323	C₂²×C₅	#556	1	1	yes	characteristic
324	C₄×C₅	—	2	1	no	—
325	C₄×C₅	—	2	1	no	—
326	C₄×C₅	—	2	1	no	—
327	C₄×C₅	—	4	2	no	—
328	C₄×C₅	—	4	2	no	—
329	C₄×C₅	—	4	1	no	—
330	C₄×C₅	—	4	1	no	—
331	C₄×C₅	—	4	2	no	—
332	C₄×C₅	—	4	1	no	—
333	C₄×C₅	—	4	2	no	—
334	C₄×C₅	#444	1	2	yes	—
335	C₄×C₅	C₄×#41	1	1	yes	characteristic
336	C₄×C₅	#519	1	1	yes	characteristic
337	C₄×C₅	#547	1	1	yes	characteristic
338	C₄×C₅	#548	1	1	yes	characteristic
339	#41	—	2	1	no	—
340	#41	—	2	1	no	—
341	#41	—	2	1	no	—
342	#41	—	2	1	no	—
343	C₂×Q₈	—	2	1	no	—
344	C₂×Q₈	—	2	1	no	—
345	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	C₅×#41	1	1	yes	characteristic
354	C₂²×C₄	C₅×#41	1	1	yes	characteristic
355	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
356	M₁₆	—	2	1	no	—
357	M₁₆	—	2	1	no	—
358	M₁₆	—	2	2	no	—
359	M₁₆	—	2	1	no	—
360	M₁₆	—	2	2	no	—
361	M₁₆	C₅×#41	1	2	yes	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
370	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
371	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
372	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
380	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
381	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
382	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
383	C₂²⋊C₄	—	2	1	no	—
384	C₂²⋊C₄	—	2	2	no	—
385	C₂²⋊C₄	—	2	1	no	—
386	C₂²⋊C₄	—	2	1	no	—
387	C₄²	—	2	1	no	—
388	C₄²	—	2	1	no	—
389	C₄²	—	2	1	no	—
390	C₄²	—	2	2	no	—
391	C₄²	—	2	1	no	—
392	C₄²	—	2	1	no	—
393	C₄²	—	2	1	no	—
394	C₄²	—	4	2	no	—
395	C₄²	—	4	2	no	—
396	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
397	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
398	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
399	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
400	C₄²	C₅×#41	1	2	yes	—
401	C₂×C₅	—	2	1	no	—
402	C₂×C₅	—	2	1	no	—
403	C₂×C₅	—	8	1	no	—
404	C₂×C₅	#2362	1	1	yes	characteristic
405	C₂×C₅	C₂×#444	1	1	yes	characteristic
406	C₂×C₅	#2956	1	1	yes	characteristic
407	C₂³	—	2	1	no	—
408	C₂³	C₂×C₅×#41	1	1	yes	characteristic
409	Q₈	—	2	1	no	—
410	Q₈	—	2	1	no	—
411	Q₈	—	4	2	no	—
412	Q₈	—	8	1	no	—
413	D₄	—	2	1	no	—
414	D₄	—	2	1	no	—
415	D₄	—	4	1	no	—
416	D₄	—	4	1	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	8	1	no	—
434	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
435	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
436	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
437	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
438	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
439	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
440	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
441	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
442	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
443	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
444	C₈	—	2	2	no	—
445	C₈	—	2	2	no	—
446	C₈	—	2	2	no	—
447	C₈	—	2	2	no	—
448	C₈	—	2	2	no	—
449	C₈	—	4	1	no	—
450	C₈	—	4	2	no	—
451	C₅	#23081	1	1	yes	characteristic, direct product factor, Sylow
452	C₂²	—	2	1	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	4	1	no	—
455	C₂²	—	4	1	no	—
456	C₂²	—	4	1	no	—
457	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
458	C₂²	C₅×#552	1	1	yes	characteristic
459	C₂²	C₅×#556	1	1	yes	characteristic
460	C₄	—	2	1	no	—
461	C₄	—	2	1	no	—
462	C₄	—	2	1	no	—
463	C₄	—	4	2	no	—
464	C₄	—	4	2	no	—
465	C₄	—	4	1	no	—
466	C₄	—	4	1	no	—
467	C₄	—	4	2	no	—
468	C₄	—	4	1	no	—
469	C₄	—	4	2	no	—
470	C₄	C₅×#444	1	2	yes	—
471	C₄	C₄×C₅×#41	1	1	yes	characteristic
472	C₄	C₅×#519	1	1	yes	characteristic
473	C₄	C₅×#547	1	1	yes	characteristic
474	C₄	C₅×#548	1	1	yes	characteristic
475	C₂	—	2	1	no	—
476	C₂	—	2	1	no	—
477	C₂	—	8	1	no	—
478	C₂	C₅×#2362	1	1	yes	characteristic
479	C₂	C₂×C₅×#444	1	1	yes	characteristic
480	C₂	C₅×#2956	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₂×C₅×#41	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₅×C₄⋊C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2962	C₂	semidirect
4. C₅×#1994	C₂	semidirect
5. C₅×#1950	C₂	semidirect
8. C₅×#1922	C₂	semidirect
9. C₅×#1773	C₂	semidirect
10. C₅×#1767	C₂	semidirect
14. C₅×#479	C₄	semidirect
15. C₅×#478	C₄	semidirect
16. C₅×#477	C₄	semidirect
17. C₅×#476	C₄	semidirect
18. C₅×#475	C₄	semidirect
19. C₅×#474	C₄	semidirect
47. #23081	C₅	direct (N × H)
107. #2962	C₂×C₅	semidirect
109. #1994	C₂×C₅	semidirect
110. #1950	C₂×C₅	semidirect
113. #1922	C₂×C₅	semidirect
114. #1773	C₂×C₅	semidirect
115. #1767	C₂×C₅	semidirect
181. #479	C₄×C₅	semidirect
182. #478	C₄×C₅	semidirect
183. #477	C₄×C₅	semidirect
184. #476	C₄×C₅	semidirect
185. #475	C₄×C₅	semidirect
186. #474	C₄×C₅	semidirect
451. C₅	#23081	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅×#3076	2
C₅×#2962	2
C₅×#2925	2
C₅×#1994	2
C₅×#1950	2
C₅×#1938	2
C₅×#1929	2
C₅×#1922	2
C₅×#1773	2
C₅×#1767	2
C₄×C₅×#104	2
#23081	5

Subgroups — C5×#23081 #11945801

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#23081 #11945801