Subgroups — C₅×#22097 #11944817

Order 1280.

712 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3091	C₂	1	1	yes	maximal, characteristic
2	C₅×#2930	C₂	1	1	yes	maximal, characteristic
3	C₅×#2905	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1946	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1945	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1938	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1937	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1922	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1922	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1871	C₂	1	1	yes	maximal, characteristic
11	C₅×#1866	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1866	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1855	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1826	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1753	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#131	C₂²	1	1	yes	characteristic
17	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
19	C₅×#525	C₂²	1	1	yes	characteristic
20	C₂×C₅×#117	C₂²	1	1	yes	characteristic
21	C₅×#485	C₄	1	1	yes	characteristic, complemented
22	C₅×#485	C₄	1	1	yes	characteristic, complemented
23	C₅×#484	C₄	1	1	yes	characteristic, complemented
24	C₅×#483	C₄	1	1	yes	characteristic, complemented
25	C₅×#482	C₄	1	1	yes	characteristic, complemented
26	C₅×#482	C₄	1	1	yes	characteristic, complemented
27	C₅×#481	C₄	1	1	yes	characteristic, complemented
28	C₅×#480	C₄	1	1	yes	characteristic, complemented
29	C₅×#436	—	2	1	no	—
30	C₅×#436	—	2	1	no	—
31	C₅×#435	—	2	1	no	—
32	C₅×#435	—	2	1	no	—
33	C₂×C₅×#108	C₂²	1	1	yes	characteristic
34	C₂×C₅×#108	C₂²	1	1	yes	characteristic
35	C₅×#427	C₂²	1	1	yes	characteristic
36	C₅×#427	C₂²	1	1	yes	characteristic
37	C₅×#424	—	2	1	no	—
38	C₅×#424	—	2	1	no	—
39	C₅×#424	C₂²	1	1	yes	characteristic
40	C₅×#424	C₂²	1	1	yes	characteristic
41	C₅×#424	C₂²	1	1	yes	characteristic
42	C₅×#424	C₂²	1	1	yes	characteristic
43	C₅×#424	C₂²	1	1	yes	characteristic
44	C₅×#423	—	2	1	no	—
45	C₅×#423	—	2	1	no	—
46	C₂×C₅×#104	C₂²	1	1	yes	characteristic
47	C₂×C₅×#104	C₂²	1	1	yes	characteristic
48	C₅×#416	C₂²	1	1	yes	characteristic
49	C₅×#416	C₂²	1	1	yes	characteristic
50	C₅×#408	C₂²	1	1	yes	characteristic
51	C₅×#407	C₂²	1	1	yes	characteristic
52	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
53	C₅×#405	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×C₂²⋊C₄	C₂²	1	1	yes	characteristic
57	C₅×#341	C₂²	1	1	yes	characteristic
58	C₅×#341	C₂²	1	1	yes	characteristic
59	C₅×#339	C₂²	1	1	yes	characteristic
60	C₅×#339	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	#22097	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂×C₅×#41	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
70	C₅×#131	—	4	1	no	—
71	C₅×#131	—	4	1	no	—
72	C₂×C₅×M₁₆	—	2	1	no	—
73	C₂×C₅×M₁₆	—	2	1	no	—
74	C₂×C₅×M₁₆	—	4	1	no	—
75	C₂×C₅×M₁₆	—	4	1	no	—
76	C₂×C₅×M₁₆	—	4	1	no	—
77	C₂×C₅×M₁₆	—	4	1	no	—
78	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
79	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
80	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
81	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
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	C₅×#123	—	2	1	no	—
93	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
94	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
95	C₅×#121	C₂×C₄	1	1	yes	characteristic
96	C₅×#121	C₂×C₄	1	1	yes	characteristic
97	C₅×#120	—	2	1	no	—
98	C₄×C₅×D₄	—	2	1	no	—
99	C₄×C₅×D₄	—	2	1	no	—
100	C₅×#117	—	2	1	no	—
101	C₅×#117	—	2	1	no	—
102	C₅×#117	C₂×C₄	1	1	yes	characteristic
103	C₅×#117	C₂×C₄	1	1	yes	characteristic
104	C₅×#117	C₂³	1	1	yes	characteristic
105	C₅×#117	C₂³	1	1	yes	characteristic
106	C₅×#117	C₂³	1	1	yes	characteristic
107	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
108	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
109	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
110	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
111	C₂×C₄²×C₅	—	2	1	no	—
112	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
114	C₅×#108	—	4	1	no	—
115	C₅×#108	—	4	1	no	—
116	C₅×#107	C₂×C₄	1	1	yes	characteristic
117	C₅×#107	C₂×C₄	1	1	yes	characteristic
118	C₅×#107	C₂×C₄	1	1	yes	characteristic
119	C₅×#107	C₂×C₄	1	1	yes	characteristic
120	C₅×#106	C₂×C₄	1	1	yes	characteristic
121	C₅×#106	C₂×C₄	1	1	yes	characteristic
122	C₅×#106	C₂×C₄	1	1	yes	characteristic
123	C₅×#106	C₂×C₄	1	1	yes	characteristic
124	C₅×C₄⋊C₈	—	2	1	no	—
125	C₅×C₄⋊C₈	—	2	1	no	—
126	C₅×C₄⋊C₈	—	2	1	no	—
127	C₅×C₄⋊C₈	—	2	1	no	—
128	C₅×C₄⋊C₈	—	2	1	no	—
129	C₅×C₄⋊C₈	—	2	1	no	—
130	C₅×C₄⋊C₈	—	2	1	no	—
131	C₅×C₄⋊C₈	—	2	1	no	—
132	C₅×C₄⋊C₈	—	2	1	no	—
133	C₅×C₄⋊C₈	—	2	1	no	—
134	C₅×#104	—	4	1	no	—
135	C₅×#104	—	4	1	no	—
136	C₅×#103	C₂×C₄	1	1	yes	characteristic
137	C₅×#103	C₂×C₄	1	1	yes	characteristic
138	C₅×#103	C₂×C₄	1	1	yes	characteristic
139	C₅×#103	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×#102	C₂×C₄	1	1	yes	characteristic
143	C₅×#102	C₂×C₄	1	1	yes	characteristic
144	C₅×C₂²⋊C₈	—	2	1	no	—
145	C₅×C₂²⋊C₈	—	2	1	no	—
146	C₅×C₂²⋊C₈	—	2	1	no	—
147	C₅×C₂²⋊C₈	—	2	1	no	—
148	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
149	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
150	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
151	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
152	C₅×#97	—	2	1	no	—
153	C₅×#97	—	4	1	no	—
154	C₄×C₅×C₈	—	2	1	no	—
155	C₄×C₅×C₈	—	4	1	no	—
156	C₅×#95	—	2	1	no	—
157	#3091	C₂×C₅	1	1	yes	characteristic
158	#2930	C₂×C₅	1	1	yes	characteristic
159	#2905	C₂×C₅	1	1	yes	characteristic, complemented
160	#1946	C₂×C₅	1	1	yes	characteristic, complemented
161	#1945	C₂×C₅	1	1	yes	characteristic, complemented
162	#1938	C₂×C₅	1	1	yes	characteristic, complemented
163	#1937	C₂×C₅	1	1	yes	characteristic, complemented
164	#1922	C₂×C₅	1	1	yes	characteristic, complemented
165	#1922	C₂×C₅	1	1	yes	characteristic, complemented
166	#1871	C₂×C₅	1	1	yes	characteristic
167	#1866	C₂×C₅	1	1	yes	characteristic, complemented
168	#1866	C₂×C₅	1	1	yes	characteristic, complemented
169	#1855	C₂×C₅	1	1	yes	characteristic, complemented
170	#1826	C₂×C₅	1	1	yes	characteristic, complemented
171	#1753	C₂×C₅	1	1	yes	characteristic, complemented
172	C₂⁴×C₅	#41	1	1	yes	characteristic
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	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
178	C₂×C₅×D₄	—	2	1	no	—
179	C₂×C₅×D₄	—	2	1	no	—
180	C₂×C₅×D₄	—	2	1	no	—
181	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
182	C₂²×C₄×C₅	—	2	1	no	—
183	C₂²×C₄×C₅	—	2	1	no	—
184	C₂²×C₄×C₅	—	2	1	no	—
185	C₂²×C₄×C₅	—	2	1	no	—
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	C₂²×C₄	1	1	yes	characteristic
192	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
193	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₅	#41	1	1	yes	characteristic
196	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
197	C₅×M₁₆	—	2	1	no	—
198	C₅×M₁₆	—	2	1	no	—
199	C₅×M₁₆	—	2	1	no	—
200	C₅×M₁₆	—	2	1	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	—	4	1	no	—
206	C₅×M₁₆	—	4	1	no	—
207	C₅×M₁₆	—	4	1	no	—
208	C₅×M₁₆	—	4	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	C₂²×C₄	1	1	yes	characteristic
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×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
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	C₅×C₂²⋊C₄	—	2	1	no	—
249	C₅×C₂²⋊C₄	—	2	1	no	—
250	C₅×C₂²⋊C₄	—	2	1	no	—
251	C₅×C₂²⋊C₄	—	2	1	no	—
252	C₅×C₂²⋊C₄	—	4	2	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	—	2	1	no	—
259	C₄²×C₅	—	2	1	no	—
260	C₄²×C₅	—	2	1	no	—
261	C₄²×C₅	—	2	1	no	—
262	C₂×#131	C₂²×C₅	1	1	yes	characteristic
263	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
264	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
265	#525	C₂²×C₅	1	1	yes	characteristic
266	C₂×#117	C₂²×C₅	1	1	yes	characteristic
267	#485	C₄×C₅	1	1	yes	characteristic, complemented
268	#485	C₄×C₅	1	1	yes	characteristic, complemented
269	#484	C₄×C₅	1	1	yes	characteristic, complemented
270	#483	C₄×C₅	1	1	yes	characteristic, complemented
271	#482	C₄×C₅	1	1	yes	characteristic, complemented
272	#482	C₄×C₅	1	1	yes	characteristic, complemented
273	#481	C₄×C₅	1	1	yes	characteristic, complemented
274	#480	C₄×C₅	1	1	yes	characteristic, complemented
275	#436	—	2	1	no	—
276	#436	—	2	1	no	—
277	#435	—	2	1	no	—
278	#435	—	2	1	no	—
279	C₂×#108	C₂²×C₅	1	1	yes	characteristic
280	C₂×#108	C₂²×C₅	1	1	yes	characteristic
281	#427	C₂²×C₅	1	1	yes	characteristic
282	#427	C₂²×C₅	1	1	yes	characteristic
283	#424	—	2	1	no	—
284	#424	—	2	1	no	—
285	#424	C₂²×C₅	1	1	yes	characteristic
286	#424	C₂²×C₅	1	1	yes	characteristic
287	#424	C₂²×C₅	1	1	yes	characteristic
288	#424	C₂²×C₅	1	1	yes	characteristic
289	#424	C₂²×C₅	1	1	yes	characteristic
290	#423	—	2	1	no	—
291	#423	—	2	1	no	—
292	C₂×#104	C₂²×C₅	1	1	yes	characteristic
293	C₂×#104	C₂²×C₅	1	1	yes	characteristic
294	#416	C₂²×C₅	1	1	yes	characteristic
295	#416	C₂²×C₅	1	1	yes	characteristic
296	#408	C₂²×C₅	1	1	yes	characteristic
297	#407	C₂²×C₅	1	1	yes	characteristic
298	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
299	#405	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×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
303	#341	C₂²×C₅	1	1	yes	characteristic
304	#341	C₂²×C₅	1	1	yes	characteristic
305	#339	C₂²×C₅	1	1	yes	characteristic
306	#339	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	—	2	1	no	—
316	C₂³×C₅	—	4	1	no	—
317	C₂³×C₅	—	4	1	no	—
318	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
319	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
320	C₂³×C₅	C₂×#41	1	1	yes	characteristic
321	C₅×Q₈	—	2	1	no	—
322	C₅×Q₈	—	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	—	8	1	no	—
328	C₅×D₄	—	8	1	no	—
329	C₂×C₄×C₅	—	2	1	no	—
330	C₂×C₄×C₅	—	2	1	no	—
331	C₂×C₄×C₅	—	2	1	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	—	2	1	no	—
338	C₂×C₄×C₅	—	2	1	no	—
339	C₂×C₄×C₅	—	2	2	no	—
340	C₂×C₄×C₅	—	2	1	no	—
341	C₂×C₄×C₅	—	2	1	no	—
342	C₂×C₄×C₅	—	2	1	no	—
343	C₂×C₄×C₅	—	2	1	no	—
344	C₂×C₄×C₅	—	2	1	no	—
345	C₂×C₄×C₅	—	2	1	no	—
346	C₂×C₄×C₅	—	2	1	no	—
347	C₂×C₄×C₅	—	4	1	no	—
348	C₂×C₄×C₅	—	4	1	no	—
349	C₂×C₄×C₅	—	4	1	no	—
350	C₂×C₄×C₅	—	4	1	no	—
351	C₂×C₄×C₅	—	4	1	no	—
352	C₂×C₄×C₅	—	4	1	no	—
353	C₂×C₄×C₅	—	4	1	no	—
354	C₂×C₄×C₅	—	8	1	no	—
355	C₂×C₄×C₅	—	8	1	no	—
356	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
357	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
358	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
359	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
361	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
362	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
363	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
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	—	2	1	no	—
369	C₅×C₈	—	2	1	no	—
370	C₅×C₈	—	2	1	no	—
371	C₅×C₈	—	2	1	no	—
372	C₅×C₈	—	4	1	no	—
373	C₅×C₈	—	4	1	no	—
374	C₅×C₈	—	4	1	no	—
375	C₅×C₈	—	4	1	no	—
376	C₂×#41	C₂³×C₅	1	1	yes	characteristic
377	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
378	#131	—	4	1	no	—
379	#131	—	4	1	no	—
380	C₂×M₁₆	—	2	1	no	—
381	C₂×M₁₆	—	2	1	no	—
382	C₂×M₁₆	—	4	1	no	—
383	C₂×M₁₆	—	4	1	no	—
384	C₂×M₁₆	—	4	1	no	—
385	C₂×M₁₆	—	4	1	no	—
386	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
387	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
388	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
389	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
390	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
391	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
392	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
393	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
394	C₂²×C₈	—	2	1	no	—
395	C₂²×C₈	—	2	1	no	—
396	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
397	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
398	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
399	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
400	#123	—	2	1	no	—
401	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
402	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
403	#121	C₂×C₄×C₅	1	1	yes	characteristic
404	#121	C₂×C₄×C₅	1	1	yes	characteristic
405	#120	—	2	1	no	—
406	C₄×D₄	—	2	1	no	—
407	C₄×D₄	—	2	1	no	—
408	#117	—	2	1	no	—
409	#117	—	2	1	no	—
410	#117	C₂×C₄×C₅	1	1	yes	characteristic
411	#117	C₂×C₄×C₅	1	1	yes	characteristic
412	#117	C₂³×C₅	1	1	yes	characteristic
413	#117	C₂³×C₅	1	1	yes	characteristic
414	#117	C₂³×C₅	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
416	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
417	C₂×C₂²⋊C₄	—	2	1	no	—
418	C₂×C₂²⋊C₄	—	2	1	no	—
419	C₂×C₄²	—	2	1	no	—
420	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
421	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
422	#108	—	4	1	no	—
423	#108	—	4	1	no	—
424	#107	C₂×C₄×C₅	1	1	yes	characteristic
425	#107	C₂×C₄×C₅	1	1	yes	characteristic
426	#107	C₂×C₄×C₅	1	1	yes	characteristic
427	#107	C₂×C₄×C₅	1	1	yes	characteristic
428	#106	C₂×C₄×C₅	1	1	yes	characteristic
429	#106	C₂×C₄×C₅	1	1	yes	characteristic
430	#106	C₂×C₄×C₅	1	1	yes	characteristic
431	#106	C₂×C₄×C₅	1	1	yes	characteristic
432	C₄⋊C₈	—	2	1	no	—
433	C₄⋊C₈	—	2	1	no	—
434	C₄⋊C₈	—	2	1	no	—
435	C₄⋊C₈	—	2	1	no	—
436	C₄⋊C₈	—	2	1	no	—
437	C₄⋊C₈	—	2	1	no	—
438	C₄⋊C₈	—	2	1	no	—
439	C₄⋊C₈	—	2	1	no	—
440	C₄⋊C₈	—	2	1	no	—
441	C₄⋊C₈	—	2	1	no	—
442	#104	—	4	1	no	—
443	#104	—	4	1	no	—
444	#103	C₂×C₄×C₅	1	1	yes	characteristic
445	#103	C₂×C₄×C₅	1	1	yes	characteristic
446	#103	C₂×C₄×C₅	1	1	yes	characteristic
447	#103	C₂×C₄×C₅	1	1	yes	characteristic
448	#102	C₂×C₄×C₅	1	1	yes	characteristic
449	#102	C₂×C₄×C₅	1	1	yes	characteristic
450	#102	C₂×C₄×C₅	1	1	yes	characteristic
451	#102	C₂×C₄×C₅	1	1	yes	characteristic
452	C₂²⋊C₈	—	2	1	no	—
453	C₂²⋊C₈	—	2	1	no	—
454	C₂²⋊C₈	—	2	1	no	—
455	C₂²⋊C₈	—	2	1	no	—
456	C₂²⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
457	C₂²⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
458	C₂²⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
459	C₂²⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
460	#97	—	2	1	no	—
461	#97	—	4	1	no	—
462	C₄×C₈	—	2	1	no	—
463	C₄×C₈	—	4	1	no	—
464	#95	—	2	1	no	—
465	C₂²×C₅	—	2	1	no	—
466	C₂²×C₅	—	2	1	no	—
467	C₂²×C₅	—	2	1	no	—
468	C₂²×C₅	—	2	1	no	—
469	C₂²×C₅	—	2	1	no	—
470	C₂²×C₅	—	2	1	no	—
471	C₂²×C₅	—	2	1	no	—
472	C₂²×C₅	—	2	1	no	—
473	C₂²×C₅	—	4	1	no	—
474	C₂²×C₅	—	4	1	no	—
475	C₂²×C₅	—	4	1	no	—
476	C₂²×C₅	—	8	1	no	—
477	C₂²×C₅	—	8	1	no	—
478	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
479	C₂²×C₅	#539	1	1	yes	characteristic
480	C₂²×C₅	#539	1	1	yes	characteristic
481	C₄×C₅	—	2	1	no	—
482	C₄×C₅	—	2	1	no	—
483	C₄×C₅	—	4	2	no	—
484	C₄×C₅	—	4	1	no	—
485	C₄×C₅	—	4	1	no	—
486	C₄×C₅	—	4	1	no	—
487	C₄×C₅	—	4	1	no	—
488	C₄×C₅	—	4	1	no	—
489	C₄×C₅	—	4	1	no	—
490	C₄×C₅	—	4	1	no	—
491	C₄×C₅	—	8	1	no	—
492	C₄×C₅	#520	1	1	yes	characteristic
493	C₄×C₅	#520	1	1	yes	characteristic
494	C₄×C₅	#534	1	1	yes	characteristic
495	C₄×C₅	#536	1	1	yes	characteristic
496	C₂⁴	C₅×#41	1	1	yes	characteristic
497	#41	—	2	1	no	—
498	#41	—	2	1	no	—
499	#41	—	2	1	no	—
500	#41	—	2	1	no	—
501	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
502	C₂×D₄	—	2	1	no	—
503	C₂×D₄	—	2	1	no	—
504	C₂×D₄	—	2	1	no	—
505	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
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	—	2	1	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	—	2	1	no	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
516	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
517	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
518	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
519	C₂²×C₄	C₅×#41	1	1	yes	characteristic
520	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
521	M₁₆	—	2	1	no	—
522	M₁₆	—	2	1	no	—
523	M₁₆	—	2	1	no	—
524	M₁₆	—	2	1	no	—
525	M₁₆	—	2	1	no	—
526	M₁₆	—	2	1	no	—
527	M₁₆	—	2	1	no	—
528	M₁₆	—	2	1	no	—
529	M₁₆	—	4	1	no	—
530	M₁₆	—	4	1	no	—
531	M₁₆	—	4	1	no	—
532	M₁₆	—	4	1	no	—
533	M₁₆	—	4	2	no	—
534	M₁₆	—	4	2	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	—	2	1	no	—
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	—	2	1	no	—
543	C₂×C₈	—	2	1	no	—
544	C₂×C₈	—	2	1	no	—
545	C₂×C₈	—	2	1	no	—
546	C₂×C₈	—	2	1	no	—
547	C₂×C₈	—	4	2	no	—
548	C₂×C₈	—	4	2	no	—
549	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
550	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
551	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
552	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
553	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
554	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
555	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
556	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
557	C₄⋊C₄	—	2	1	no	—
558	C₄⋊C₄	—	2	1	no	—
559	C₄⋊C₄	—	2	1	no	—
560	C₄⋊C₄	—	2	1	no	—
561	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
562	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
563	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
564	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
565	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
566	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
567	C₂²⋊C₄	—	2	1	no	—
568	C₂²⋊C₄	—	2	1	no	—
569	C₂²⋊C₄	—	2	1	no	—
570	C₂²⋊C₄	—	2	1	no	—
571	C₂²⋊C₄	—	2	1	no	—
572	C₂²⋊C₄	—	2	1	no	—
573	C₂²⋊C₄	—	2	1	no	—
574	C₂²⋊C₄	—	2	1	no	—
575	C₂²⋊C₄	—	2	1	no	—
576	C₂²⋊C₄	—	4	2	no	—
577	C₄²	—	2	1	no	—
578	C₄²	—	2	1	no	—
579	C₄²	—	2	1	no	—
580	C₄²	—	2	1	no	—
581	C₄²	—	2	1	no	—
582	C₄²	—	2	1	no	—
583	C₄²	—	2	1	no	—
584	C₄²	—	2	1	no	—
585	C₄²	—	2	1	no	—
586	C₂×C₅	—	2	1	no	—
587	C₂×C₅	—	2	1	no	—
588	C₂×C₅	—	4	1	no	—
589	C₂×C₅	—	4	1	no	—
590	C₂×C₅	—	8	1	no	—
591	C₂×C₅	#2322	1	1	yes	characteristic
592	C₂×C₅	#2956	1	1	yes	characteristic
593	C₂×C₅	#2957	1	1	yes	characteristic
594	C₂³	—	2	1	no	—
595	C₂³	—	2	1	no	—
596	C₂³	—	2	1	no	—
597	C₂³	—	4	1	no	—
598	C₂³	—	4	1	no	—
599	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
600	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
601	C₂³	C₂×C₅×#41	1	1	yes	characteristic
602	Q₈	—	2	1	no	—
603	Q₈	—	2	1	no	—
604	D₄	—	2	1	no	—
605	D₄	—	2	1	no	—
606	D₄	—	4	1	no	—
607	D₄	—	4	1	no	—
608	D₄	—	8	1	no	—
609	D₄	—	8	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	8	1	no	—
636	C₂×C₄	—	8	1	no	—
637	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
638	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
639	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
640	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
641	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
642	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
643	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
644	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
645	C₈	—	2	1	no	—
646	C₈	—	2	1	no	—
647	C₈	—	2	1	no	—
648	C₈	—	2	1	no	—
649	C₈	—	2	1	no	—
650	C₈	—	2	1	no	—
651	C₈	—	2	1	no	—
652	C₈	—	2	1	no	—
653	C₈	—	4	1	no	—
654	C₈	—	4	1	no	—
655	C₈	—	4	1	no	—
656	C₈	—	4	1	no	—
657	C₅	#22097	1	1	yes	characteristic, direct product factor, Sylow
658	C₂²	—	2	1	no	—
659	C₂²	—	2	1	no	—
660	C₂²	—	2	1	no	—
661	C₂²	—	2	1	no	—
662	C₂²	—	2	1	no	—
663	C₂²	—	2	1	no	—
664	C₂²	—	2	1	no	—
665	C₂²	—	2	1	no	—
666	C₂²	—	4	1	no	—
667	C₂²	—	4	1	no	—
668	C₂²	—	4	1	no	—
669	C₂²	—	8	1	no	—
670	C₂²	—	8	1	no	—
671	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
672	C₂²	C₅×#539	1	1	yes	characteristic
673	C₂²	C₅×#539	1	1	yes	characteristic
674	C₄	—	2	1	no	—
675	C₄	—	2	1	no	—
676	C₄	—	4	2	no	—
677	C₄	—	4	1	no	—
678	C₄	—	4	1	no	—
679	C₄	—	4	1	no	—
680	C₄	—	4	1	no	—
681	C₄	—	4	1	no	—
682	C₄	—	4	1	no	—
683	C₄	—	4	1	no	—
684	C₄	—	8	1	no	—
685	C₄	C₅×#520	1	1	yes	characteristic
686	C₄	C₅×#520	1	1	yes	characteristic
687	C₄	C₅×#534	1	1	yes	characteristic
688	C₄	C₅×#536	1	1	yes	characteristic
689	C₂	—	2	1	no	—
690	C₂	—	2	1	no	—
691	C₂	—	4	1	no	—
692	C₂	—	4	1	no	—
693	C₂	—	8	1	no	—
694	C₂	C₅×#2322	1	1	yes	characteristic
695	C₂	C₅×#2956	1	1	yes	characteristic
696	C₂	C₅×#2957	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	C₅×#525	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₅×M₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₅×#2905	C₂	semidirect
4. C₅×#1946	C₂	semidirect
5. C₅×#1945	C₂	semidirect
6. C₅×#1938	C₂	semidirect
7. C₅×#1937	C₂	semidirect
8. C₅×#1922	C₂	semidirect
9. C₅×#1922	C₂	semidirect
11. C₅×#1866	C₂	semidirect
12. C₅×#1866	C₂	semidirect
13. C₅×#1855	C₂	semidirect
14. C₅×#1826	C₂	semidirect
15. C₅×#1753	C₂	semidirect
21. C₅×#485	C₄	semidirect
22. C₅×#485	C₄	semidirect
23. C₅×#484	C₄	semidirect
24. C₅×#483	C₄	semidirect
25. C₅×#482	C₄	semidirect
26. C₅×#482	C₄	semidirect
27. C₅×#481	C₄	semidirect
28. C₅×#480	C₄	semidirect
67. #22097	C₅	direct (N × H)
159. #2905	C₂×C₅	semidirect
160. #1946	C₂×C₅	semidirect
161. #1945	C₂×C₅	semidirect
162. #1938	C₂×C₅	semidirect
163. #1937	C₂×C₅	semidirect
164. #1922	C₂×C₅	semidirect
165. #1922	C₂×C₅	semidirect
167. #1866	C₂×C₅	semidirect
168. #1866	C₂×C₅	semidirect
169. #1855	C₂×C₅	semidirect
170. #1826	C₂×C₅	semidirect
171. #1753	C₂×C₅	semidirect
267. #485	C₄×C₅	semidirect
268. #485	C₄×C₅	semidirect
269. #484	C₄×C₅	semidirect
270. #483	C₄×C₅	semidirect
271. #482	C₄×C₅	semidirect
272. #482	C₄×C₅	semidirect
273. #481	C₄×C₅	semidirect
274. #480	C₄×C₅	semidirect
657. C₅	#22097	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×#3091	2
C₅×#2930	2
C₅×#2905	2
C₅×#1946	2
C₅×#1945	2
C₅×#1938	2
C₅×#1937	2
C₅×#1922	2
C₅×#1871	2
C₅×#1866	2
C₅×#1855	2
C₅×#1826	2
C₅×#1753	2
#22097	5

Subgroups — C5×#22097 #11944817

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22097 #11944817