Subgroups — C₅×#22693 #11945413

Order 1280.

850 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#444	C₂	1	1	yes	maximal, characteristic
2	C₅×#2952	C₂	1	1	yes	maximal, characteristic
3	C₅×#2951	C₂	1	1	yes	maximal, characteristic
4	C₅×#2913	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2912	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1952	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1951	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1860	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1860	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1859	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1859	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1847	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1816	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1815	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1773	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	C₅×#520	C₂²	1	1	yes	characteristic
20	C₅×#520	C₂²	1	1	yes	characteristic
21	C₅×#520	C₂²	1	1	yes	characteristic
22	C₅×#520	C₂²	1	1	yes	characteristic
23	C₅×#444	C₄	1	8	yes	complemented
24	C₅×#442	—	2	1	no	—
25	C₅×#441	—	2	1	no	—
26	C₅×#440	—	2	1	no	—
27	C₅×#440	—	2	1	no	—
28	C₄×C₅×Q₁₆	—	2	1	no	—
29	C₄×C₅×SD₁₆	—	2	1	no	—
30	C₄×C₅×SD₁₆	—	2	1	no	—
31	C₄×C₅×D₈	—	2	1	no	—
32	C₂×C₅×#108	C₂²	1	1	yes	characteristic
33	C₂×C₅×#108	C₂²	1	1	yes	characteristic
34	C₅×#428	—	2	1	no	—
35	C₅×#428	—	2	1	no	—
36	C₅×#428	—	2	1	no	—
37	C₅×#428	—	2	1	no	—
38	C₅×#428	C₂²	1	1	yes	characteristic
39	C₅×#428	C₂²	1	1	yes	characteristic
40	C₅×#428	C₂²	1	1	yes	characteristic
41	C₅×#428	C₂²	1	1	yes	characteristic
42	C₅×#427	—	2	1	no	—
43	C₅×#427	—	2	1	no	—
44	C₅×#427	C₂²	1	1	yes	characteristic
45	C₂×C₅×#107	—	2	1	no	—
46	C₂×C₅×#107	C₂²	1	1	yes	characteristic
47	C₂×C₅×#107	C₂²	1	1	yes	characteristic
48	C₂×C₅×#106	—	2	1	no	—
49	C₂×C₅×#106	C₂²	1	1	yes	characteristic
50	C₂×C₅×#106	C₂²	1	1	yes	characteristic
51	C₂×C₅×#104	C₂²	1	1	yes	characteristic
52	C₂×C₅×#104	C₂²	1	1	yes	characteristic
53	C₅×#417	C₂²	1	1	yes	characteristic
54	C₅×#417	C₂²	1	1	yes	characteristic
55	C₅×#417	C₂²	1	1	yes	characteristic
56	C₅×#417	C₂²	1	1	yes	characteristic
57	C₅×#405	C₂²	1	1	yes	characteristic
58	C₅×#405	C₂²	1	1	yes	characteristic
59	C₂×C₅×#97	C₂²	1	1	yes	characteristic
60	C₅×#384	C₂²	1	1	yes	characteristic
61	C₅×#382	C₂²	1	1	yes	characteristic
62	C₅×#343	C₂²	1	1	yes	characteristic
63	C₅×#343	C₂²	1	1	yes	characteristic
64	C₅×#343	C₂²	1	1	yes	characteristic
65	C₅×#343	C₂²	1	1	yes	characteristic
66	C₅×#339	C₂²	1	1	yes	characteristic
67	C₅×#339	C₂²	1	1	yes	characteristic
68	#22693	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
69	C₂×C₅×#41	C₂³	1	1	yes	characteristic
70	C₂×C₅×#41	C₂³	1	1	yes	characteristic
71	C₅×#135	C₂×C₄	1	4	yes	—
72	C₅×#135	Q₈	1	4	yes	—
73	C₂×C₅×Q₁₆	D₄	1	1	yes	characteristic
74	C₂×C₅×SD₁₆	D₄	1	1	yes	characteristic
75	C₂×C₅×SD₁₆	D₄	1	1	yes	characteristic
76	C₂×C₅×D₈	D₄	1	1	yes	characteristic
77	C₅×#131	—	2	2	no	—
78	C₅×#131	—	2	2	no	—
79	C₅×#131	C₂×C₄	1	4	yes	complemented
80	C₅×#131	C₂×C₄	1	4	yes	complemented
81	C₂×C₅×M₁₆	—	2	1	no	—
82	C₂×C₅×M₁₆	—	2	1	no	—
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	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
87	C₂²×C₅×C₈	—	2	1	no	—
88	C₂²×C₅×C₈	—	2	1	no	—
89	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
90	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
91	C₄×C₅×Q₈	—	2	1	no	—
92	C₄×C₅×Q₈	—	2	1	no	—
93	C₄×C₅×Q₈	—	2	1	no	—
94	C₄×C₅×Q₈	—	2	1	no	—
95	C₄×C₅×D₄	—	2	1	no	—
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	—	4	1	no	—
100	C₄×C₅×D₄	—	4	1	no	—
101	C₄×C₅×D₄	—	4	1	no	—
102	C₄×C₅×D₄	—	4	1	no	—
103	C₅×#117	—	2	1	no	—
104	C₅×#117	—	2	1	no	—
105	C₅×#117	—	2	1	no	—
106	C₅×#117	—	2	1	no	—
107	C₅×#117	C₂³	1	1	yes	characteristic
108	C₅×#117	C₂³	1	1	yes	characteristic
109	C₂×C₅×C₄⋊C₄	—	2	1	no	—
110	C₂×C₅×C₄⋊C₄	—	2	1	no	—
111	C₂×C₅×C₄⋊C₄	—	2	1	no	—
112	C₂×C₅×C₄⋊C₄	—	2	1	no	—
113	C₂×C₅×C₄⋊C₄	—	4	1	no	—
114	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
115	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
117	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
119	C₅×#108	—	2	2	no	—
120	C₅×#108	C₂×C₄	1	4	yes	complemented
121	C₅×#107	—	2	1	no	—
122	C₅×#107	—	2	1	no	—
123	C₅×#107	—	2	1	no	—
124	C₅×#107	—	2	1	no	—
125	C₅×#107	—	2	1	no	—
126	C₅×#107	—	2	1	no	—
127	C₅×#107	—	2	1	no	—
128	C₅×#107	—	2	1	no	—
129	C₅×#107	D₄	1	1	yes	characteristic
130	C₅×#107	D₄	1	1	yes	characteristic
131	C₅×#106	—	2	1	no	—
132	C₅×#106	—	2	1	no	—
133	C₅×#106	—	2	1	no	—
134	C₅×#106	—	2	1	no	—
135	C₅×#106	—	2	1	no	—
136	C₅×#106	—	2	1	no	—
137	C₅×#106	—	2	1	no	—
138	C₅×#106	—	2	1	no	—
139	C₅×#106	D₄	1	1	yes	characteristic
140	C₅×#106	D₄	1	1	yes	characteristic
141	C₅×#104	C₂×C₄	1	4	yes	complemented
142	C₅×#104	C₂×C₄	1	4	yes	complemented
143	C₅×#103	—	2	1	no	—
144	C₅×#103	—	2	1	no	—
145	C₅×#103	—	2	1	no	—
146	C₅×#103	—	2	1	no	—
147	C₅×#102	—	2	1	no	—
148	C₅×#102	—	2	1	no	—
149	C₅×#102	—	2	1	no	—
150	C₅×#102	—	2	1	no	—
151	C₅×#97	—	2	1	no	—
152	C₅×#97	—	2	1	no	—
153	C₅×#97	C₂×C₄	1	4	yes	complemented
154	C₄×C₅×C₈	—	2	1	no	—
155	C₄×C₅×C₈	—	2	1	no	—
156	C₅×#95	—	4	1	no	—
157	C₂×#444	C₂×C₅	1	1	yes	characteristic
158	#2952	C₂×C₅	1	1	yes	characteristic
159	#2951	C₂×C₅	1	1	yes	characteristic
160	#2913	C₂×C₅	1	1	yes	characteristic, complemented
161	#2912	C₂×C₅	1	1	yes	characteristic, complemented
162	#1952	C₂×C₅	1	1	yes	characteristic, complemented
163	#1951	C₂×C₅	1	1	yes	characteristic, complemented
164	#1860	C₂×C₅	1	1	yes	characteristic, complemented
165	#1860	C₂×C₅	1	1	yes	characteristic, complemented
166	#1859	C₂×C₅	1	1	yes	characteristic, complemented
167	#1859	C₂×C₅	1	1	yes	characteristic, complemented
168	#1847	C₂×C₅	1	1	yes	characteristic, complemented
169	#1816	C₂×C₅	1	1	yes	characteristic, complemented
170	#1815	C₂×C₅	1	1	yes	characteristic, complemented
171	#1773	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	C₂²×C₄	1	2	yes	—
177	C₅×#41	C₂²×C₄	1	2	yes	—
178	C₅×#41	C₂×Q₈	1	2	yes	—
179	C₅×#41	C₂×Q₈	1	2	yes	—
180	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
181	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
182	C₂×C₅×D₄	—	2	1	no	—
183	C₂×C₅×D₄	—	2	1	no	—
184	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
185	C₂×C₅×D₄	C₂×D₄	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	—	4	1	no	—
194	C₂²×C₄×C₅	—	4	1	no	—
195	C₂²×C₄×C₅	—	4	1	no	—
196	C₂²×C₄×C₅	—	4	1	no	—
197	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
198	C₅×Q₁₆	C₄⋊C₄	1	4	yes	complemented
199	C₅×SD₁₆	C₄⋊C₄	1	4	yes	complemented
200	C₅×SD₁₆	C₄⋊C₄	1	4	yes	complemented
201	C₅×D₈	C₄⋊C₄	1	4	yes	complemented
202	C₅×M₁₆	—	2	1	no	—
203	C₅×M₁₆	—	2	1	no	—
204	C₅×M₁₆	—	2	4	no	—
205	C₅×M₁₆	—	2	4	no	—
206	C₅×M₁₆	—	2	1	no	—
207	C₅×M₁₆	—	2	1	no	—
208	C₅×M₁₆	—	2	1	no	—
209	C₅×M₁₆	—	2	1	no	—
210	C₅×M₁₆	C₂²×C₄	1	2	yes	—
211	C₅×M₁₆	C₂²×C₄	1	2	yes	—
212	C₂×C₅×C₈	—	2	1	no	—
213	C₂×C₅×C₈	—	2	1	no	—
214	C₂×C₅×C₈	—	2	4	no	—
215	C₂×C₅×C₈	—	2	4	no	—
216	C₂×C₅×C₈	—	2	1	no	—
217	C₂×C₅×C₈	—	2	1	no	—
218	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
219	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
220	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
221	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
222	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
223	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
224	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
225	C₂×C₅×C₈	#41	1	2	yes	—
226	C₅×C₄⋊C₄	—	2	1	no	—
227	C₅×C₄⋊C₄	—	2	1	no	—
228	C₅×C₄⋊C₄	—	2	1	no	—
229	C₅×C₄⋊C₄	—	2	1	no	—
230	C₅×C₄⋊C₄	—	2	1	no	—
231	C₅×C₄⋊C₄	—	2	1	no	—
232	C₅×C₄⋊C₄	—	2	1	no	—
233	C₅×C₄⋊C₄	—	2	1	no	—
234	C₅×C₄⋊C₄	—	4	1	no	—
235	C₅×C₄⋊C₄	—	4	1	no	—
236	C₅×C₄⋊C₄	—	4	1	no	—
237	C₅×C₄⋊C₄	—	4	1	no	—
238	C₅×C₄⋊C₄	—	8	2	no	—
239	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
240	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
241	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
242	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
243	C₅×C₂²⋊C₄	—	2	1	no	—
244	C₅×C₂²⋊C₄	—	2	1	no	—
245	C₅×C₂²⋊C₄	—	4	1	no	—
246	C₅×C₂²⋊C₄	—	4	1	no	—
247	C₅×C₂²⋊C₄	—	4	1	no	—
248	C₅×C₂²⋊C₄	—	4	1	no	—
249	C₄²×C₅	—	2	1	no	—
250	C₄²×C₅	—	2	1	no	—
251	C₄²×C₅	—	2	1	no	—
252	C₄²×C₅	—	4	1	no	—
253	C₄²×C₅	—	4	1	no	—
254	C₄²×C₅	—	4	1	no	—
255	C₄²×C₅	—	4	1	no	—
256	C₄²×C₅	C₂²×C₄	1	2	yes	—
257	C₂×#135	C₂²×C₅	1	1	yes	characteristic
258	C₂×#131	C₂²×C₅	1	1	yes	characteristic
259	C₂×#131	C₂²×C₅	1	1	yes	characteristic
260	#520	C₂²×C₅	1	1	yes	characteristic
261	#520	C₂²×C₅	1	1	yes	characteristic
262	#520	C₂²×C₅	1	1	yes	characteristic
263	#520	C₂²×C₅	1	1	yes	characteristic
264	#444	C₄×C₅	1	8	yes	complemented
265	#442	—	2	1	no	—
266	#441	—	2	1	no	—
267	#440	—	2	1	no	—
268	#440	—	2	1	no	—
269	C₄×Q₁₆	—	2	1	no	—
270	C₄×SD₁₆	—	2	1	no	—
271	C₄×SD₁₆	—	2	1	no	—
272	C₄×D₈	—	2	1	no	—
273	C₂×#108	C₂²×C₅	1	1	yes	characteristic
274	C₂×#108	C₂²×C₅	1	1	yes	characteristic
275	#428	—	2	1	no	—
276	#428	—	2	1	no	—
277	#428	—	2	1	no	—
278	#428	—	2	1	no	—
279	#428	C₂²×C₅	1	1	yes	characteristic
280	#428	C₂²×C₅	1	1	yes	characteristic
281	#428	C₂²×C₅	1	1	yes	characteristic
282	#428	C₂²×C₅	1	1	yes	characteristic
283	#427	—	2	1	no	—
284	#427	—	2	1	no	—
285	#427	C₂²×C₅	1	1	yes	characteristic
286	C₂×#107	—	2	1	no	—
287	C₂×#107	C₂²×C₅	1	1	yes	characteristic
288	C₂×#107	C₂²×C₅	1	1	yes	characteristic
289	C₂×#106	—	2	1	no	—
290	C₂×#106	C₂²×C₅	1	1	yes	characteristic
291	C₂×#106	C₂²×C₅	1	1	yes	characteristic
292	C₂×#104	C₂²×C₅	1	1	yes	characteristic
293	C₂×#104	C₂²×C₅	1	1	yes	characteristic
294	#417	C₂²×C₅	1	1	yes	characteristic
295	#417	C₂²×C₅	1	1	yes	characteristic
296	#417	C₂²×C₅	1	1	yes	characteristic
297	#417	C₂²×C₅	1	1	yes	characteristic
298	#405	C₂²×C₅	1	1	yes	characteristic
299	#405	C₂²×C₅	1	1	yes	characteristic
300	C₂×#97	C₂²×C₅	1	1	yes	characteristic
301	#384	C₂²×C₅	1	1	yes	characteristic
302	#382	C₂²×C₅	1	1	yes	characteristic
303	#343	C₂²×C₅	1	1	yes	characteristic
304	#343	C₂²×C₅	1	1	yes	characteristic
305	#343	C₂²×C₅	1	1	yes	characteristic
306	#343	C₂²×C₅	1	1	yes	characteristic
307	#339	C₂²×C₅	1	1	yes	characteristic
308	#339	C₂²×C₅	1	1	yes	characteristic
309	C₂³×C₅	—	2	1	no	—
310	C₂³×C₅	—	2	1	no	—
311	C₂³×C₅	H(5,𝔽₂)	1	1	yes	characteristic
312	C₅×Q₈	—	2	1	no	—
313	C₅×Q₈	—	2	1	no	—
314	C₅×Q₈	C₂×C₄⋊C₄	1	2	yes	—
315	C₅×Q₈	C₂×C₄⋊C₄	1	2	yes	—
316	C₅×D₄	—	2	2	no	—
317	C₅×D₄	—	2	2	no	—
318	C₅×D₄	—	2	2	no	—
319	C₅×D₄	—	2	2	no	—
320	C₅×D₄	—	2	1	no	—
321	C₅×D₄	—	2	1	no	—
322	C₅×D₄	C₂×C₄⋊C₄	1	2	yes	—
323	C₅×D₄	C₂×C₄⋊C₄	1	2	yes	—
324	C₂×C₄×C₅	—	2	1	no	—
325	C₂×C₄×C₅	—	2	1	no	—
326	C₂×C₄×C₅	—	2	2	no	—
327	C₂×C₄×C₅	—	2	2	no	—
328	C₂×C₄×C₅	—	2	2	no	—
329	C₂×C₄×C₅	—	2	2	no	—
330	C₂×C₄×C₅	—	2	2	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	—	4	1	no	—
336	C₂×C₄×C₅	—	4	1	no	—
337	C₂×C₄×C₅	—	4	1	no	—
338	C₂×C₄×C₅	—	4	1	no	—
339	C₂×C₄×C₅	—	4	1	no	—
340	C₂×C₄×C₅	—	4	1	no	—
341	C₂×C₄×C₅	—	8	1	no	—
342	C₂×C₄×C₅	—	8	1	no	—
343	C₂×C₄×C₅	—	8	1	no	—
344	C₂×C₄×C₅	—	8	1	no	—
345	C₂×C₄×C₅	—	16	1	no	—
346	C₂×C₄×C₅	—	16	1	no	—
347	C₂×C₄×C₅	—	16	1	no	—
348	C₂×C₄×C₅	—	16	1	no	—
349	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
350	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
351	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
352	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
353	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
354	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
355	C₅×C₈	—	2	2	no	—
356	C₅×C₈	—	2	2	no	—
357	C₅×C₈	—	4	1	no	—
358	C₅×C₈	—	4	1	no	—
359	C₅×C₈	C₂×C₄⋊C₄	1	2	yes	—
360	C₅×C₈	C₂×C₄⋊C₄	1	2	yes	—
361	C₅×C₈	C₄×D₄	1	2	yes	—
362	C₅×C₈	C₄×D₄	1	2	yes	—
363	C₂×#41	C₂³×C₅	1	1	yes	characteristic
364	C₂×#41	C₂³×C₅	1	1	yes	characteristic
365	#135	C₂×C₄×C₅	1	4	yes	—
366	#135	C₅×Q₈	1	4	yes	—
367	C₂×Q₁₆	C₅×D₄	1	1	yes	characteristic
368	C₂×SD₁₆	C₅×D₄	1	1	yes	characteristic
369	C₂×SD₁₆	C₅×D₄	1	1	yes	characteristic
370	C₂×D₈	C₅×D₄	1	1	yes	characteristic
371	#131	—	2	2	no	—
372	#131	—	2	2	no	—
373	#131	C₂×C₄×C₅	1	4	yes	complemented
374	#131	C₂×C₄×C₅	1	4	yes	complemented
375	C₂×M₁₆	—	2	1	no	—
376	C₂×M₁₆	—	2	1	no	—
377	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
378	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
379	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
380	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
381	C₂²×C₈	—	2	1	no	—
382	C₂²×C₈	—	2	1	no	—
383	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
384	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
385	C₄×Q₈	—	2	1	no	—
386	C₄×Q₈	—	2	1	no	—
387	C₄×Q₈	—	2	1	no	—
388	C₄×Q₈	—	2	1	no	—
389	C₄×D₄	—	2	1	no	—
390	C₄×D₄	—	2	1	no	—
391	C₄×D₄	—	2	1	no	—
392	C₄×D₄	—	2	1	no	—
393	C₄×D₄	—	4	1	no	—
394	C₄×D₄	—	4	1	no	—
395	C₄×D₄	—	4	1	no	—
396	C₄×D₄	—	4	1	no	—
397	#117	—	2	1	no	—
398	#117	—	2	1	no	—
399	#117	—	2	1	no	—
400	#117	—	2	1	no	—
401	#117	C₂³×C₅	1	1	yes	characteristic
402	#117	C₂³×C₅	1	1	yes	characteristic
403	C₂×C₄⋊C₄	—	2	1	no	—
404	C₂×C₄⋊C₄	—	2	1	no	—
405	C₂×C₄⋊C₄	—	2	1	no	—
406	C₂×C₄⋊C₄	—	2	1	no	—
407	C₂×C₄⋊C₄	—	4	1	no	—
408	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
409	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
410	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
411	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
412	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
413	#108	—	2	2	no	—
414	#108	C₂×C₄×C₅	1	4	yes	complemented
415	#107	—	2	1	no	—
416	#107	—	2	1	no	—
417	#107	—	2	1	no	—
418	#107	—	2	1	no	—
419	#107	—	2	1	no	—
420	#107	—	2	1	no	—
421	#107	—	2	1	no	—
422	#107	—	2	1	no	—
423	#107	C₅×D₄	1	1	yes	characteristic
424	#107	C₅×D₄	1	1	yes	characteristic
425	#106	—	2	1	no	—
426	#106	—	2	1	no	—
427	#106	—	2	1	no	—
428	#106	—	2	1	no	—
429	#106	—	2	1	no	—
430	#106	—	2	1	no	—
431	#106	—	2	1	no	—
432	#106	—	2	1	no	—
433	#106	C₅×D₄	1	1	yes	characteristic
434	#106	C₅×D₄	1	1	yes	characteristic
435	#104	C₂×C₄×C₅	1	4	yes	complemented
436	#104	C₂×C₄×C₅	1	4	yes	complemented
437	#103	—	2	1	no	—
438	#103	—	2	1	no	—
439	#103	—	2	1	no	—
440	#103	—	2	1	no	—
441	#102	—	2	1	no	—
442	#102	—	2	1	no	—
443	#102	—	2	1	no	—
444	#102	—	2	1	no	—
445	#97	—	2	1	no	—
446	#97	—	2	1	no	—
447	#97	C₂×C₄×C₅	1	4	yes	complemented
448	C₄×C₈	—	2	1	no	—
449	C₄×C₈	—	2	1	no	—
450	#95	—	4	1	no	—
451	C₂²×C₅	—	2	1	no	—
452	C₂²×C₅	—	2	1	no	—
453	C₂²×C₅	—	2	2	no	—
454	C₂²×C₅	—	2	2	no	—
455	C₂²×C₅	—	4	1	no	—
456	C₂²×C₅	—	4	1	no	—
457	C₂²×C₅	—	4	1	no	—
458	C₂²×C₅	—	4	1	no	—
459	C₂²×C₅	#520	1	1	yes	characteristic
460	C₂²×C₅	D₄²	1	1	yes	characteristic
461	C₂²×C₅	#554	1	1	yes	characteristic
462	C₄×C₅	—	2	2	no	—
463	C₄×C₅	—	2	2	no	—
464	C₄×C₅	—	4	2	no	—
465	C₄×C₅	—	4	1	no	—
466	C₄×C₅	—	4	1	no	—
467	C₄×C₅	—	4	1	no	—
468	C₄×C₅	—	4	1	no	—
469	C₄×C₅	—	8	1	no	—
470	C₄×C₅	—	8	1	no	—
471	C₄×C₅	—	8	1	no	—
472	C₄×C₅	—	8	1	no	—
473	C₄×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
474	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
475	C₄×C₅	#547	1	1	yes	characteristic
476	C₄×C₅	D₄×Q₈	1	1	yes	characteristic
477	#41	—	2	1	no	—
478	#41	—	2	1	no	—
479	#41	—	2	1	no	—
480	#41	—	2	1	no	—
481	#41	C₂²×C₄×C₅	1	2	yes	—
482	#41	C₂²×C₄×C₅	1	2	yes	—
483	#41	C₂×C₅×Q₈	1	2	yes	—
484	#41	C₂×C₅×Q₈	1	2	yes	—
485	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
486	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
487	C₂×D₄	—	2	1	no	—
488	C₂×D₄	—	2	1	no	—
489	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
490	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	4	1	no	—
499	C₂²×C₄	—	4	1	no	—
500	C₂²×C₄	—	4	1	no	—
501	C₂²×C₄	—	4	1	no	—
502	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
503	Q₁₆	C₅×C₄⋊C₄	1	4	yes	complemented
504	SD₁₆	C₅×C₄⋊C₄	1	4	yes	complemented
505	SD₁₆	C₅×C₄⋊C₄	1	4	yes	complemented
506	D₈	C₅×C₄⋊C₄	1	4	yes	complemented
507	M₁₆	—	2	1	no	—
508	M₁₆	—	2	1	no	—
509	M₁₆	—	2	4	no	—
510	M₁₆	—	2	4	no	—
511	M₁₆	—	2	1	no	—
512	M₁₆	—	2	1	no	—
513	M₁₆	—	2	1	no	—
514	M₁₆	—	2	1	no	—
515	M₁₆	C₂²×C₄×C₅	1	2	yes	—
516	M₁₆	C₂²×C₄×C₅	1	2	yes	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	—	2	4	no	—
520	C₂×C₈	—	2	4	no	—
521	C₂×C₈	—	2	1	no	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
524	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
525	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
526	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
527	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
528	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
529	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
530	C₂×C₈	C₅×#41	1	2	yes	—
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	—	2	1	no	—
533	C₄⋊C₄	—	2	1	no	—
534	C₄⋊C₄	—	2	1	no	—
535	C₄⋊C₄	—	2	1	no	—
536	C₄⋊C₄	—	2	1	no	—
537	C₄⋊C₄	—	2	1	no	—
538	C₄⋊C₄	—	2	1	no	—
539	C₄⋊C₄	—	4	1	no	—
540	C₄⋊C₄	—	4	1	no	—
541	C₄⋊C₄	—	4	1	no	—
542	C₄⋊C₄	—	4	1	no	—
543	C₄⋊C₄	—	8	2	no	—
544	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
545	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
546	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
547	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
548	C₂²⋊C₄	—	2	1	no	—
549	C₂²⋊C₄	—	2	1	no	—
550	C₂²⋊C₄	—	4	1	no	—
551	C₂²⋊C₄	—	4	1	no	—
552	C₂²⋊C₄	—	4	1	no	—
553	C₂²⋊C₄	—	4	1	no	—
554	C₄²	—	2	1	no	—
555	C₄²	—	2	1	no	—
556	C₄²	—	2	1	no	—
557	C₄²	—	4	1	no	—
558	C₄²	—	4	1	no	—
559	C₄²	—	4	1	no	—
560	C₄²	—	4	1	no	—
561	C₄²	C₂²×C₄×C₅	1	2	yes	—
562	C₂×C₅	—	2	1	no	—
563	C₂×C₅	—	2	1	no	—
564	C₂×C₅	—	4	2	no	—
565	C₂×C₅	—	4	2	no	—
566	C₂×C₅	D₄×C₄⋊C₄	1	1	yes	characteristic
567	C₂×C₅	#3288	1	1	yes	characteristic
568	C₂×C₅	#3289	1	1	yes	characteristic
569	C₂³	—	2	1	no	—
570	C₂³	—	2	1	no	—
571	C₂³	C₅×H(5,𝔽₂)	1	1	yes	characteristic
572	Q₈	—	2	1	no	—
573	Q₈	—	2	1	no	—
574	Q₈	C₂×C₅×C₄⋊C₄	1	2	yes	—
575	Q₈	C₂×C₅×C₄⋊C₄	1	2	yes	—
576	D₄	—	2	2	no	—
577	D₄	—	2	2	no	—
578	D₄	—	2	2	no	—
579	D₄	—	2	2	no	—
580	D₄	—	2	1	no	—
581	D₄	—	2	1	no	—
582	D₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
583	D₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	8	1	no	—
602	C₂×C₄	—	8	1	no	—
603	C₂×C₄	—	8	1	no	—
604	C₂×C₄	—	8	1	no	—
605	C₂×C₄	—	16	1	no	—
606	C₂×C₄	—	16	1	no	—
607	C₂×C₄	—	16	1	no	—
608	C₂×C₄	—	16	1	no	—
609	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
610	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
611	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
612	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
613	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
614	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
615	C₈	—	2	2	no	—
616	C₈	—	2	2	no	—
617	C₈	—	4	1	no	—
618	C₈	—	4	1	no	—
619	C₈	C₂×C₅×C₄⋊C₄	1	2	yes	—
620	C₈	C₂×C₅×C₄⋊C₄	1	2	yes	—
621	C₈	C₄×C₅×D₄	1	2	yes	—
622	C₈	C₄×C₅×D₄	1	2	yes	—
623	C₅	#22693	1	1	yes	characteristic, direct product factor, Sylow
624	C₂²	—	2	1	no	—
625	C₂²	—	2	1	no	—
626	C₂²	—	2	2	no	—
627	C₂²	—	2	2	no	—
628	C₂²	—	4	1	no	—
629	C₂²	—	4	1	no	—
630	C₂²	—	4	1	no	—
631	C₂²	—	4	1	no	—
632	C₂²	C₅×#520	1	1	yes	characteristic
633	C₂²	C₅×D₄²	1	1	yes	characteristic
634	C₂²	C₅×#554	1	1	yes	characteristic
635	C₄	—	2	2	no	—
636	C₄	—	2	2	no	—
637	C₄	—	4	2	no	—
638	C₄	—	4	1	no	—
639	C₄	—	4	1	no	—
640	C₄	—	4	1	no	—
641	C₄	—	4	1	no	—
642	C₄	—	8	1	no	—
643	C₄	—	8	1	no	—
644	C₄	—	8	1	no	—
645	C₄	—	8	1	no	—
646	C₄	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
647	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
648	C₄	C₅×#547	1	1	yes	characteristic
649	C₄	C₅×D₄×Q₈	1	1	yes	characteristic
650	C₂	—	2	1	no	—
651	C₂	—	2	1	no	—
652	C₂	—	4	2	no	—
653	C₂	—	4	2	no	—
654	C₂	C₅×D₄×C₄⋊C₄	1	1	yes	characteristic
655	C₂	C₅×#3288	1	1	yes	characteristic
656	C₂	C₅×#3289	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	D₄²
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂×C₅×#135	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×#2913	C₂	semidirect
5. C₅×#2912	C₂	semidirect
6. C₅×#1952	C₂	semidirect
7. C₅×#1951	C₂	semidirect
8. C₅×#1860	C₂	semidirect
9. C₅×#1860	C₂	semidirect
10. C₅×#1859	C₂	semidirect
11. C₅×#1859	C₂	semidirect
12. C₅×#1847	C₂	semidirect
13. C₅×#1816	C₂	semidirect
14. C₅×#1815	C₂	semidirect
15. C₅×#1773	C₂	semidirect
23. C₅×#444	C₄	semidirect
68. #22693	C₅	direct (N × H)
79. C₅×#131	C₂×C₄	semidirect
80. C₅×#131	C₂×C₄	semidirect
120. C₅×#108	C₂×C₄	semidirect
141. C₅×#104	C₂×C₄	semidirect
142. C₅×#104	C₂×C₄	semidirect
153. C₅×#97	C₂×C₄	semidirect
160. #2913	C₂×C₅	semidirect
161. #2912	C₂×C₅	semidirect
162. #1952	C₂×C₅	semidirect
163. #1951	C₂×C₅	semidirect
164. #1860	C₂×C₅	semidirect
165. #1860	C₂×C₅	semidirect
166. #1859	C₂×C₅	semidirect
167. #1859	C₂×C₅	semidirect
168. #1847	C₂×C₅	semidirect
169. #1816	C₂×C₅	semidirect
170. #1815	C₂×C₅	semidirect
171. #1773	C₂×C₅	semidirect
198. C₅×Q₁₆	C₄⋊C₄	semidirect
199. C₅×SD₁₆	C₄⋊C₄	semidirect
200. C₅×SD₁₆	C₄⋊C₄	semidirect
201. C₅×D₈	C₄⋊C₄	semidirect
264. #444	C₄×C₅	semidirect
373. #131	C₂×C₄×C₅	semidirect
374. #131	C₂×C₄×C₅	semidirect
414. #108	C₂×C₄×C₅	semidirect
435. #104	C₂×C₄×C₅	semidirect
436. #104	C₂×C₄×C₅	semidirect
447. #97	C₂×C₄×C₅	semidirect
503. Q₁₆	C₅×C₄⋊C₄	semidirect
504. SD₁₆	C₅×C₄⋊C₄	semidirect
505. SD₁₆	C₅×C₄⋊C₄	semidirect
506. D₈	C₅×C₄⋊C₄	semidirect
623. C₅	#22693	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×#444	2
C₅×#2952	2
C₅×#2951	2
C₅×#2913	2
C₅×#2912	2
C₅×#1952	2
C₅×#1951	2
C₅×#1860	2
C₅×#1859	2
C₅×#1847	2
C₅×#1816	2
C₅×#1815	2
C₅×#1773	2
#22693	5

Subgroups — C5×#22693 #11945413

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22693 #11945413