Subgroups — C₅×#22784 #11945504

Order 1280.

740 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2943	C₂	1	1	yes	maximal, characteristic
2	C₅×#2925	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2906	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1938	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1937	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1922	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1922	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1876	C₂	1	1	yes	maximal, characteristic
9	C₅×#1876	C₂	1	1	yes	maximal, characteristic
10	C₅×#1838	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1806	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1806	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1771	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1765	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1764	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#135	C₂²	1	1	yes	characteristic
17	C₂×C₅×#131	C₂²	1	1	yes	characteristic
18	C₂×C₅×#131	C₂²	1	1	yes	characteristic
19	C₄×C₅×#41	C₂²	1	1	yes	characteristic
20	C₄×C₅×#41	C₂²	1	1	yes	characteristic
21	C₅×#442	C₄	1	1	yes	characteristic, complemented
22	C₅×#442	C₄	1	1	yes	characteristic, complemented
23	C₅×#441	C₄	1	1	yes	characteristic, complemented
24	C₅×#441	C₄	1	1	yes	characteristic, complemented
25	C₅×#440	C₄	1	1	yes	characteristic, complemented
26	C₅×#440	C₄	1	1	yes	characteristic, complemented
27	C₅×#440	C₄	1	1	yes	characteristic, complemented
28	C₅×#440	C₄	1	1	yes	characteristic, complemented
29	C₅×#433	—	2	1	no	—
30	C₅×#433	—	2	1	no	—
31	C₅×#432	—	2	1	no	—
32	C₅×#431	—	2	1	no	—
33	C₅×#427	C₂²	1	1	yes	characteristic
34	C₅×#424	—	2	1	no	—
35	C₅×#424	—	2	1	no	—
36	C₅×#424	C₂²	1	1	yes	characteristic
37	C₅×#424	C₂²	1	1	yes	characteristic
38	C₅×#423	—	2	1	no	—
39	C₅×#423	C₂²	1	1	yes	characteristic
40	C₅×#423	C₂²	1	1	yes	characteristic
41	C₂×C₅×C₄⋊C₈	—	2	1	no	—
42	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
43	C₂×C₅×#104	C₂²	1	1	yes	characteristic
44	C₂×C₅×#104	C₂²	1	1	yes	characteristic
45	C₂×C₅×#104	C₂²	1	1	yes	characteristic
46	C₂×C₅×#104	C₂²	1	1	yes	characteristic
47	C₅×#416	C₂²	1	1	yes	characteristic
48	C₅×#416	C₂²	1	1	yes	characteristic
49	C₅×#408	C₂²	1	1	yes	characteristic
50	C₅×#408	C₂²	1	1	yes	characteristic
51	C₅×#405	C₂²	1	1	yes	characteristic
52	C₅×#405	C₂²	1	1	yes	characteristic
53	C₂×C₅×#97	C₂²	1	1	yes	characteristic
54	C₂×C₅×#97	C₂²	1	1	yes	characteristic
55	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
56	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
57	C₅×#341	C₂²	1	1	yes	characteristic
58	C₅×#341	C₂²	1	1	yes	characteristic
59	C₅×#341	C₂²	1	1	yes	characteristic
60	C₅×#341	C₂²	1	1	yes	characteristic
61	C₅×#339	C₂²	1	1	yes	characteristic
62	C₅×#339	C₂²	1	1	yes	characteristic
63	C₅×#339	C₂²	1	1	yes	characteristic
64	C₅×#339	C₂²	1	1	yes	characteristic
65	C₅×#336	C₂²	1	1	yes	characteristic
66	C₅×#336	C₂²	1	1	yes	characteristic
67	#22784	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂×C₅×#41	C₂³	1	1	yes	characteristic
69	C₂×C₅×#41	C₂³	1	1	yes	characteristic
70	C₅×#135	—	2	2	no	—
71	C₅×#135	—	2	2	no	—
72	C₂×C₅×Q₁₆	C₂×C₄	1	1	yes	characteristic
73	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic
74	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic
75	C₂×C₅×D₈	C₂×C₄	1	1	yes	characteristic
76	C₅×#131	—	2	2	no	—
77	C₅×#131	—	2	2	no	—
78	C₅×#131	—	4	1	no	—
79	C₅×#131	—	4	1	no	—
80	C₂×C₅×M₁₆	—	2	1	no	—
81	C₂×C₅×M₁₆	—	2	1	no	—
82	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
83	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
84	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
85	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
86	C₂²×C₅×C₈	—	2	1	no	—
87	C₂²×C₅×C₈	—	2	1	no	—
88	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
89	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
90	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
91	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
92	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
93	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
94	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
95	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
96	C₄×C₅×D₄	—	2	1	no	—
97	C₄×C₅×D₄	—	2	1	no	—
98	C₄×C₅×D₄	—	2	1	no	—
99	C₄×C₅×D₄	—	2	1	no	—
100	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
101	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
102	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
103	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
104	C₅×#117	—	2	1	no	—
105	C₅×#117	—	2	1	no	—
106	C₅×#117	C₂³	1	1	yes	characteristic
107	C₅×#117	C₂³	1	1	yes	characteristic
108	C₂×C₅×C₄⋊C₄	—	2	1	no	—
109	C₂×C₄²×C₅	—	2	1	no	—
110	C₂×C₄²×C₅	—	2	1	no	—
111	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
114	C₅×#107	C₂×C₄	1	1	yes	characteristic
115	C₅×#107	C₂×C₄	1	1	yes	characteristic
116	C₅×#106	C₂×C₄	1	1	yes	characteristic
117	C₅×#106	C₂×C₄	1	1	yes	characteristic
118	C₅×C₄⋊C₈	—	2	1	no	—
119	C₅×C₄⋊C₈	—	2	1	no	—
120	C₅×C₄⋊C₈	—	2	1	no	—
121	C₅×C₄⋊C₈	—	2	1	no	—
122	C₅×C₄⋊C₈	—	2	1	no	—
123	C₅×C₄⋊C₈	—	2	1	no	—
124	C₅×C₄⋊C₈	—	2	1	no	—
125	C₅×C₄⋊C₈	—	2	1	no	—
126	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
127	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
128	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
129	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
130	C₅×#104	—	2	2	no	—
131	C₅×#104	—	2	2	no	—
132	C₅×#104	—	4	1	no	—
133	C₅×#104	—	4	1	no	—
134	C₅×#103	C₂×C₄	1	1	yes	characteristic
135	C₅×#103	C₂×C₄	1	1	yes	characteristic
136	C₅×#103	C₂×C₄	1	1	yes	characteristic
137	C₅×#103	C₂×C₄	1	1	yes	characteristic
138	C₅×#102	C₂×C₄	1	1	yes	characteristic
139	C₅×#102	C₂×C₄	1	1	yes	characteristic
140	C₅×#102	C₂×C₄	1	1	yes	characteristic
141	C₅×#102	C₂×C₄	1	1	yes	characteristic
142	C₅×C₂²⋊C₈	—	2	1	no	—
143	C₅×C₂²⋊C₈	—	2	1	no	—
144	C₅×C₂²⋊C₈	—	2	1	no	—
145	C₅×C₂²⋊C₈	—	2	1	no	—
146	C₅×#97	—	2	1	no	—
147	C₅×#97	—	2	1	no	—
148	C₅×#97	—	4	1	no	—
149	C₅×#97	C₂×C₄	1	1	yes	characteristic
150	C₅×#97	C₂×C₄	1	1	yes	characteristic
151	C₅×#97	C₂×C₄	1	1	yes	characteristic
152	C₅×#97	C₂×C₄	1	1	yes	characteristic
153	C₄×C₅×C₈	—	2	1	no	—
154	C₄×C₅×C₈	—	2	1	no	—
155	C₄×C₅×C₈	—	4	1	no	—
156	C₅×#95	—	2	1	no	—
157	#2943	C₂×C₅	1	1	yes	characteristic
158	#2925	C₂×C₅	1	1	yes	characteristic, complemented
159	#2906	C₂×C₅	1	1	yes	characteristic, complemented
160	#1938	C₂×C₅	1	1	yes	characteristic, complemented
161	#1937	C₂×C₅	1	1	yes	characteristic, complemented
162	#1922	C₂×C₅	1	1	yes	characteristic, complemented
163	#1922	C₂×C₅	1	1	yes	characteristic, complemented
164	#1876	C₂×C₅	1	1	yes	characteristic
165	#1876	C₂×C₅	1	1	yes	characteristic
166	#1838	C₂×C₅	1	1	yes	characteristic, complemented
167	#1806	C₂×C₅	1	1	yes	characteristic, complemented
168	#1806	C₂×C₅	1	1	yes	characteristic, complemented
169	#1771	C₂×C₅	1	1	yes	characteristic, complemented
170	#1765	C₂×C₅	1	1	yes	characteristic, complemented
171	#1764	C₂×C₅	1	1	yes	characteristic, complemented
172	C₅×#41	—	2	1	no	—
173	C₅×#41	—	2	1	no	—
174	C₅×#41	—	2	1	no	—
175	C₅×#41	—	2	1	no	—
176	C₅×#41	—	2	1	no	—
177	C₅×#41	—	2	1	no	—
178	C₅×#41	#41	1	2	yes	—
179	C₅×#41	#41	1	2	yes	—
180	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
181	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
182	C₂×C₅×D₄	—	2	1	no	—
183	C₂×C₅×D₄	—	2	1	no	—
184	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
185	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
186	C₂²×C₄×C₅	—	2	1	no	—
187	C₂²×C₄×C₅	—	2	1	no	—
188	C₂²×C₄×C₅	—	2	1	no	—
189	C₂²×C₄×C₅	—	2	1	no	—
190	C₂²×C₄×C₅	—	2	1	no	—
191	C₂²×C₄×C₅	—	2	1	no	—
192	C₂²×C₄×C₅	—	2	1	no	—
193	C₂²×C₄×C₅	—	2	1	no	—
194	C₂²×C₄×C₅	#41	1	1	yes	characteristic
195	C₂²×C₄×C₅	#41	1	1	yes	characteristic
196	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
197	C₅×Q₁₆	—	2	2	no	—
198	C₅×SD₁₆	—	2	2	no	—
199	C₅×SD₁₆	—	2	2	no	—
200	C₅×D₈	—	2	2	no	—
201	C₅×M₁₆	—	2	1	no	—
202	C₅×M₁₆	—	2	1	no	—
203	C₅×M₁₆	—	2	1	no	—
204	C₅×M₁₆	—	2	1	no	—
205	C₅×M₁₆	—	2	1	no	—
206	C₅×M₁₆	—	2	1	no	—
207	C₅×M₁₆	—	2	1	no	—
208	C₅×M₁₆	—	2	1	no	—
209	C₅×M₁₆	—	4	2	no	—
210	C₅×M₁₆	—	4	2	no	—
211	C₂×C₅×C₈	—	2	1	no	—
212	C₂×C₅×C₈	—	2	1	no	—
213	C₂×C₅×C₈	—	2	1	no	—
214	C₂×C₅×C₈	—	2	1	no	—
215	C₂×C₅×C₈	—	2	1	no	—
216	C₂×C₅×C₈	—	2	1	no	—
217	C₂×C₅×C₈	—	2	1	no	—
218	C₂×C₅×C₈	—	2	1	no	—
219	C₂×C₅×C₈	—	2	1	no	—
220	C₂×C₅×C₈	—	2	1	no	—
221	C₂×C₅×C₈	—	2	1	no	—
222	C₂×C₅×C₈	—	2	1	no	—
223	C₂×C₅×C₈	—	4	2	no	—
224	C₂×C₅×C₈	—	4	2	no	—
225	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
226	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
227	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
228	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
229	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
230	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
231	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
232	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
233	C₅×C₄⋊C₄	—	2	1	no	—
234	C₅×C₄⋊C₄	—	2	1	no	—
235	C₅×C₄⋊C₄	—	2	1	no	—
236	C₅×C₄⋊C₄	—	2	1	no	—
237	C₅×C₄⋊C₄	—	4	2	no	—
238	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
239	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
240	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
241	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
242	C₅×C₂²⋊C₄	—	2	1	no	—
243	C₅×C₂²⋊C₄	—	2	1	no	—
244	C₅×C₂²⋊C₄	—	2	1	no	—
245	C₅×C₂²⋊C₄	—	2	1	no	—
246	C₅×C₂²⋊C₄	—	2	1	no	—
247	C₅×C₂²⋊C₄	—	2	1	no	—
248	C₄²×C₅	—	2	1	no	—
249	C₄²×C₅	—	2	1	no	—
250	C₄²×C₅	—	2	1	no	—
251	C₄²×C₅	—	2	1	no	—
252	C₄²×C₅	—	2	1	no	—
253	C₄²×C₅	—	2	1	no	—
254	C₄²×C₅	—	2	1	no	—
255	C₄²×C₅	—	2	1	no	—
256	C₄²×C₅	—	2	1	no	—
257	C₄²×C₅	—	2	1	no	—
258	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
259	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
260	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
261	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
262	C₂×#135	C₂²×C₅	1	1	yes	characteristic
263	C₂×#131	C₂²×C₅	1	1	yes	characteristic
264	C₂×#131	C₂²×C₅	1	1	yes	characteristic
265	C₄×#41	C₂²×C₅	1	1	yes	characteristic
266	C₄×#41	C₂²×C₅	1	1	yes	characteristic
267	#442	C₄×C₅	1	1	yes	characteristic, complemented
268	#442	C₄×C₅	1	1	yes	characteristic, complemented
269	#441	C₄×C₅	1	1	yes	characteristic, complemented
270	#441	C₄×C₅	1	1	yes	characteristic, complemented
271	#440	C₄×C₅	1	1	yes	characteristic, complemented
272	#440	C₄×C₅	1	1	yes	characteristic, complemented
273	#440	C₄×C₅	1	1	yes	characteristic, complemented
274	#440	C₄×C₅	1	1	yes	characteristic, complemented
275	#433	—	2	1	no	—
276	#433	—	2	1	no	—
277	#432	—	2	1	no	—
278	#431	—	2	1	no	—
279	#427	C₂²×C₅	1	1	yes	characteristic
280	#424	—	2	1	no	—
281	#424	—	2	1	no	—
282	#424	C₂²×C₅	1	1	yes	characteristic
283	#424	C₂²×C₅	1	1	yes	characteristic
284	#423	—	2	1	no	—
285	#423	C₂²×C₅	1	1	yes	characteristic
286	#423	C₂²×C₅	1	1	yes	characteristic
287	C₂×C₄⋊C₈	—	2	1	no	—
288	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
289	C₂×#104	C₂²×C₅	1	1	yes	characteristic
290	C₂×#104	C₂²×C₅	1	1	yes	characteristic
291	C₂×#104	C₂²×C₅	1	1	yes	characteristic
292	C₂×#104	C₂²×C₅	1	1	yes	characteristic
293	#416	C₂²×C₅	1	1	yes	characteristic
294	#416	C₂²×C₅	1	1	yes	characteristic
295	#408	C₂²×C₅	1	1	yes	characteristic
296	#408	C₂²×C₅	1	1	yes	characteristic
297	#405	C₂²×C₅	1	1	yes	characteristic
298	#405	C₂²×C₅	1	1	yes	characteristic
299	C₂×#97	C₂²×C₅	1	1	yes	characteristic
300	C₂×#97	C₂²×C₅	1	1	yes	characteristic
301	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
302	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
303	#341	C₂²×C₅	1	1	yes	characteristic
304	#341	C₂²×C₅	1	1	yes	characteristic
305	#341	C₂²×C₅	1	1	yes	characteristic
306	#341	C₂²×C₅	1	1	yes	characteristic
307	#339	C₂²×C₅	1	1	yes	characteristic
308	#339	C₂²×C₅	1	1	yes	characteristic
309	#339	C₂²×C₅	1	1	yes	characteristic
310	#339	C₂²×C₅	1	1	yes	characteristic
311	#336	C₂²×C₅	1	1	yes	characteristic
312	#336	C₂²×C₅	1	1	yes	characteristic
313	C₂³×C₅	—	2	1	no	—
314	C₂³×C₅	—	2	1	no	—
315	C₂³×C₅	C₂×#41	1	1	yes	characteristic
316	C₅×Q₈	—	2	1	no	—
317	C₅×Q₈	—	2	1	no	—
318	C₅×Q₈	—	2	1	no	—
319	C₅×Q₈	#117	1	2	yes	—
320	C₅×D₄	—	2	2	no	—
321	C₅×D₄	—	2	2	no	—
322	C₅×D₄	—	2	1	no	—
323	C₅×D₄	—	2	1	no	—
324	C₅×D₄	—	2	1	no	—
325	C₅×D₄	—	4	1	no	—
326	C₅×D₄	—	4	1	no	—
327	C₅×D₄	#117	1	2	yes	—
328	C₂×C₄×C₅	—	2	1	no	—
329	C₂×C₄×C₅	—	2	2	no	—
330	C₂×C₄×C₅	—	2	2	no	—
331	C₂×C₄×C₅	—	2	2	no	—
332	C₂×C₄×C₅	—	2	1	no	—
333	C₂×C₄×C₅	—	2	1	no	—
334	C₂×C₄×C₅	—	2	1	no	—
335	C₂×C₄×C₅	—	2	1	no	—
336	C₂×C₄×C₅	—	2	1	no	—
337	C₂×C₄×C₅	—	4	1	no	—
338	C₂×C₄×C₅	—	4	1	no	—
339	C₂×C₄×C₅	—	4	2	no	—
340	C₂×C₄×C₅	—	4	2	no	—
341	C₂×C₄×C₅	—	4	1	no	—
342	C₂×C₄×C₅	—	4	1	no	—
343	C₂×C₄×C₅	—	4	1	no	—
344	C₂×C₄×C₅	—	4	1	no	—
345	C₂×C₄×C₅	—	4	1	no	—
346	C₂×C₄×C₅	—	4	1	no	—
347	C₂×C₄×C₅	—	4	1	no	—
348	C₂×C₄×C₅	—	8	1	no	—
349	C₂×C₄×C₅	—	8	1	no	—
350	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
351	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
352	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
353	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
354	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
355	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
356	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
357	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
358	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
359	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
360	C₅×C₈	—	2	1	no	—
361	C₅×C₈	—	2	1	no	—
362	C₅×C₈	—	2	1	no	—
363	C₅×C₈	—	2	1	no	—
364	C₅×C₈	—	2	1	no	—
365	C₅×C₈	—	2	1	no	—
366	C₅×C₈	—	2	1	no	—
367	C₅×C₈	—	2	1	no	—
368	C₅×C₈	—	4	1	no	—
369	C₅×C₈	—	4	1	no	—
370	C₅×C₈	—	4	1	no	—
371	C₅×C₈	—	4	1	no	—
372	C₂×#41	C₂³×C₅	1	1	yes	characteristic
373	C₂×#41	C₂³×C₅	1	1	yes	characteristic
374	#135	—	2	2	no	—
375	#135	—	2	2	no	—
376	C₂×Q₁₆	C₂×C₄×C₅	1	1	yes	characteristic
377	C₂×SD₁₆	C₂×C₄×C₅	1	1	yes	characteristic
378	C₂×SD₁₆	C₂×C₄×C₅	1	1	yes	characteristic
379	C₂×D₈	C₂×C₄×C₅	1	1	yes	characteristic
380	#131	—	2	2	no	—
381	#131	—	2	2	no	—
382	#131	—	4	1	no	—
383	#131	—	4	1	no	—
384	C₂×M₁₆	—	2	1	no	—
385	C₂×M₁₆	—	2	1	no	—
386	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
387	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
388	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
389	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
390	C₂²×C₈	—	2	1	no	—
391	C₂²×C₈	—	2	1	no	—
392	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
393	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
394	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
395	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
396	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
397	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
398	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
399	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
400	C₄×D₄	—	2	1	no	—
401	C₄×D₄	—	2	1	no	—
402	C₄×D₄	—	2	1	no	—
403	C₄×D₄	—	2	1	no	—
404	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
405	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
406	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
407	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
408	#117	—	2	1	no	—
409	#117	—	2	1	no	—
410	#117	C₂³×C₅	1	1	yes	characteristic
411	#117	C₂³×C₅	1	1	yes	characteristic
412	C₂×C₄⋊C₄	—	2	1	no	—
413	C₂×C₄²	—	2	1	no	—
414	C₂×C₄²	—	2	1	no	—
415	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
416	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
417	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
418	#107	C₂×C₄×C₅	1	1	yes	characteristic
419	#107	C₂×C₄×C₅	1	1	yes	characteristic
420	#106	C₂×C₄×C₅	1	1	yes	characteristic
421	#106	C₂×C₄×C₅	1	1	yes	characteristic
422	C₄⋊C₈	—	2	1	no	—
423	C₄⋊C₈	—	2	1	no	—
424	C₄⋊C₈	—	2	1	no	—
425	C₄⋊C₈	—	2	1	no	—
426	C₄⋊C₈	—	2	1	no	—
427	C₄⋊C₈	—	2	1	no	—
428	C₄⋊C₈	—	2	1	no	—
429	C₄⋊C₈	—	2	1	no	—
430	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
431	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
432	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
433	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
434	#104	—	2	2	no	—
435	#104	—	2	2	no	—
436	#104	—	4	1	no	—
437	#104	—	4	1	no	—
438	#103	C₂×C₄×C₅	1	1	yes	characteristic
439	#103	C₂×C₄×C₅	1	1	yes	characteristic
440	#103	C₂×C₄×C₅	1	1	yes	characteristic
441	#103	C₂×C₄×C₅	1	1	yes	characteristic
442	#102	C₂×C₄×C₅	1	1	yes	characteristic
443	#102	C₂×C₄×C₅	1	1	yes	characteristic
444	#102	C₂×C₄×C₅	1	1	yes	characteristic
445	#102	C₂×C₄×C₅	1	1	yes	characteristic
446	C₂²⋊C₈	—	2	1	no	—
447	C₂²⋊C₈	—	2	1	no	—
448	C₂²⋊C₈	—	2	1	no	—
449	C₂²⋊C₈	—	2	1	no	—
450	#97	—	2	1	no	—
451	#97	—	2	1	no	—
452	#97	—	4	1	no	—
453	#97	C₂×C₄×C₅	1	1	yes	characteristic
454	#97	C₂×C₄×C₅	1	1	yes	characteristic
455	#97	C₂×C₄×C₅	1	1	yes	characteristic
456	#97	C₂×C₄×C₅	1	1	yes	characteristic
457	C₄×C₈	—	2	1	no	—
458	C₄×C₈	—	2	1	no	—
459	C₄×C₈	—	4	1	no	—
460	#95	—	2	1	no	—
461	C₂²×C₅	—	2	1	no	—
462	C₂²×C₅	—	2	1	no	—
463	C₂²×C₅	—	2	2	no	—
464	C₂²×C₅	—	4	1	no	—
465	C₂²×C₅	—	4	1	no	—
466	C₂²×C₅	—	4	1	no	—
467	C₂²×C₅	—	4	1	no	—
468	C₂²×C₅	—	4	1	no	—
469	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
470	C₂²×C₅	#552	1	1	yes	characteristic
471	C₂²×C₅	#553	1	1	yes	characteristic
472	C₄×C₅	—	2	2	no	—
473	C₄×C₅	—	2	1	no	—
474	C₄×C₅	—	2	1	no	—
475	C₄×C₅	—	2	1	no	—
476	C₄×C₅	—	2	1	no	—
477	C₄×C₅	—	4	2	no	—
478	C₄×C₅	—	4	1	no	—
479	C₄×C₅	—	4	1	no	—
480	C₄×C₅	—	4	1	no	—
481	C₄×C₅	—	4	1	no	—
482	C₄×C₅	—	4	1	no	—
483	C₄×C₅	—	8	1	no	—
484	C₄×C₅	C₂×#117	1	1	yes	characteristic
485	C₄×C₅	#520	1	1	yes	characteristic
486	C₄×C₅	#546	1	1	yes	characteristic
487	C₄×C₅	#548	1	1	yes	characteristic
488	#41	—	2	1	no	—
489	#41	—	2	1	no	—
490	#41	—	2	1	no	—
491	#41	—	2	1	no	—
492	#41	—	2	1	no	—
493	#41	—	2	1	no	—
494	#41	C₅×#41	1	2	yes	—
495	#41	C₅×#41	1	2	yes	—
496	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
497	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
498	C₂×D₄	—	2	1	no	—
499	C₂×D₄	—	2	1	no	—
500	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
501	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	C₅×#41	1	1	yes	characteristic
511	C₂²×C₄	C₅×#41	1	1	yes	characteristic
512	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
513	Q₁₆	—	2	2	no	—
514	SD₁₆	—	2	2	no	—
515	SD₁₆	—	2	2	no	—
516	D₈	—	2	2	no	—
517	M₁₆	—	2	1	no	—
518	M₁₆	—	2	1	no	—
519	M₁₆	—	2	1	no	—
520	M₁₆	—	2	1	no	—
521	M₁₆	—	2	1	no	—
522	M₁₆	—	2	1	no	—
523	M₁₆	—	2	1	no	—
524	M₁₆	—	2	1	no	—
525	M₁₆	—	4	2	no	—
526	M₁₆	—	4	2	no	—
527	C₂×C₈	—	2	1	no	—
528	C₂×C₈	—	2	1	no	—
529	C₂×C₈	—	2	1	no	—
530	C₂×C₈	—	2	1	no	—
531	C₂×C₈	—	2	1	no	—
532	C₂×C₈	—	2	1	no	—
533	C₂×C₈	—	2	1	no	—
534	C₂×C₈	—	2	1	no	—
535	C₂×C₈	—	2	1	no	—
536	C₂×C₈	—	2	1	no	—
537	C₂×C₈	—	2	1	no	—
538	C₂×C₈	—	2	1	no	—
539	C₂×C₈	—	4	2	no	—
540	C₂×C₈	—	4	2	no	—
541	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
542	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
543	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
544	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
545	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
546	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
547	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
548	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
549	C₄⋊C₄	—	2	1	no	—
550	C₄⋊C₄	—	2	1	no	—
551	C₄⋊C₄	—	2	1	no	—
552	C₄⋊C₄	—	2	1	no	—
553	C₄⋊C₄	—	4	2	no	—
554	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
555	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
556	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
557	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
558	C₂²⋊C₄	—	2	1	no	—
559	C₂²⋊C₄	—	2	1	no	—
560	C₂²⋊C₄	—	2	1	no	—
561	C₂²⋊C₄	—	2	1	no	—
562	C₂²⋊C₄	—	2	1	no	—
563	C₂²⋊C₄	—	2	1	no	—
564	C₄²	—	2	1	no	—
565	C₄²	—	2	1	no	—
566	C₄²	—	2	1	no	—
567	C₄²	—	2	1	no	—
568	C₄²	—	2	1	no	—
569	C₄²	—	2	1	no	—
570	C₄²	—	2	1	no	—
571	C₄²	—	2	1	no	—
572	C₄²	—	2	1	no	—
573	C₄²	—	2	1	no	—
574	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
575	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
576	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
577	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
578	C₂×C₅	—	2	1	no	—
579	C₂×C₅	—	2	1	no	—
580	C₂×C₅	—	4	2	no	—
581	C₂×C₅	—	8	1	no	—
582	C₂×C₅	#2352	1	1	yes	characteristic
583	C₂×C₅	#2955	1	1	yes	characteristic
584	C₂×C₅	#2956	1	1	yes	characteristic
585	C₂³	—	2	1	no	—
586	C₂³	—	2	1	no	—
587	C₂³	C₂×C₅×#41	1	1	yes	characteristic
588	Q₈	—	2	1	no	—
589	Q₈	—	2	1	no	—
590	Q₈	—	2	1	no	—
591	Q₈	C₅×#117	1	2	yes	—
592	D₄	—	2	2	no	—
593	D₄	—	2	2	no	—
594	D₄	—	2	1	no	—
595	D₄	—	2	1	no	—
596	D₄	—	2	1	no	—
597	D₄	—	4	1	no	—
598	D₄	—	4	1	no	—
599	D₄	C₅×#117	1	2	yes	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	2	no	—
612	C₂×C₄	—	4	2	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	8	1	no	—
621	C₂×C₄	—	8	1	no	—
622	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
623	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
624	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
625	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
626	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
627	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
628	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
629	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
630	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
631	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
632	C₈	—	2	1	no	—
633	C₈	—	2	1	no	—
634	C₈	—	2	1	no	—
635	C₈	—	2	1	no	—
636	C₈	—	2	1	no	—
637	C₈	—	2	1	no	—
638	C₈	—	2	1	no	—
639	C₈	—	2	1	no	—
640	C₈	—	4	1	no	—
641	C₈	—	4	1	no	—
642	C₈	—	4	1	no	—
643	C₈	—	4	1	no	—
644	C₅	#22784	1	1	yes	characteristic, direct product factor, Sylow
645	C₂²	—	2	1	no	—
646	C₂²	—	2	1	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	4	1	no	—
649	C₂²	—	4	1	no	—
650	C₂²	—	4	1	no	—
651	C₂²	—	4	1	no	—
652	C₂²	—	4	1	no	—
653	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
654	C₂²	C₅×#552	1	1	yes	characteristic
655	C₂²	C₅×#553	1	1	yes	characteristic
656	C₄	—	2	2	no	—
657	C₄	—	2	1	no	—
658	C₄	—	2	1	no	—
659	C₄	—	2	1	no	—
660	C₄	—	2	1	no	—
661	C₄	—	4	2	no	—
662	C₄	—	4	1	no	—
663	C₄	—	4	1	no	—
664	C₄	—	4	1	no	—
665	C₄	—	4	1	no	—
666	C₄	—	4	1	no	—
667	C₄	—	8	1	no	—
668	C₄	C₂×C₅×#117	1	1	yes	characteristic
669	C₄	C₅×#520	1	1	yes	characteristic
670	C₄	C₅×#546	1	1	yes	characteristic
671	C₄	C₅×#548	1	1	yes	characteristic
672	C₂	—	2	1	no	—
673	C₂	—	2	1	no	—
674	C₂	—	4	2	no	—
675	C₂	—	8	1	no	—
676	C₂	C₅×#2352	1	1	yes	characteristic
677	C₂	C₅×#2955	1	1	yes	characteristic
678	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×#135	C₂²
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×#2925	C₂	semidirect
3. C₅×#2906	C₂	semidirect
4. C₅×#1938	C₂	semidirect
5. C₅×#1937	C₂	semidirect
6. C₅×#1922	C₂	semidirect
7. C₅×#1922	C₂	semidirect
10. C₅×#1838	C₂	semidirect
11. C₅×#1806	C₂	semidirect
12. C₅×#1806	C₂	semidirect
13. C₅×#1771	C₂	semidirect
14. C₅×#1765	C₂	semidirect
15. C₅×#1764	C₂	semidirect
21. C₅×#442	C₄	semidirect
22. C₅×#442	C₄	semidirect
23. C₅×#441	C₄	semidirect
24. C₅×#441	C₄	semidirect
25. C₅×#440	C₄	semidirect
26. C₅×#440	C₄	semidirect
27. C₅×#440	C₄	semidirect
28. C₅×#440	C₄	semidirect
67. #22784	C₅	direct (N × H)
158. #2925	C₂×C₅	semidirect
159. #2906	C₂×C₅	semidirect
160. #1938	C₂×C₅	semidirect
161. #1937	C₂×C₅	semidirect
162. #1922	C₂×C₅	semidirect
163. #1922	C₂×C₅	semidirect
166. #1838	C₂×C₅	semidirect
167. #1806	C₂×C₅	semidirect
168. #1806	C₂×C₅	semidirect
169. #1771	C₂×C₅	semidirect
170. #1765	C₂×C₅	semidirect
171. #1764	C₂×C₅	semidirect
267. #442	C₄×C₅	semidirect
268. #442	C₄×C₅	semidirect
269. #441	C₄×C₅	semidirect
270. #441	C₄×C₅	semidirect
271. #440	C₄×C₅	semidirect
272. #440	C₄×C₅	semidirect
273. #440	C₄×C₅	semidirect
274. #440	C₄×C₅	semidirect
644. C₅	#22784	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×#2943	2
C₅×#2925	2
C₅×#2906	2
C₅×#1938	2
C₅×#1937	2
C₅×#1922	2
C₅×#1876	2
C₅×#1838	2
C₅×#1806	2
C₅×#1771	2
C₅×#1765	2
C₅×#1764	2
#22784	5

Subgroups — C5×#22784 #11945504

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22784 #11945504