Subgroups — C₅×#22058 #11944778

Order 1280.

976 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#448	C₂	1	1	yes	maximal, characteristic
2	C₅×#2324	C₂	1	1	yes	maximal, characteristic
3	C₅×#2310	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1973	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1968	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1935	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1933	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1928	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1927	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1877	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1877	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1875	C₂	1	1	yes	maximal, characteristic
13	C₅×#1854	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1787	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1750	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×C₅×Q₈	C₂²	1	1	yes	characteristic
17	C₂²×C₅×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₅×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₅×#121	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
21	C₂×C₅×#117	C₂²	1	1	yes	characteristic
22	C₂×C₅×#117	C₂²	1	1	yes	characteristic
23	C₅×#448	C₄	1	8	yes	complemented
24	C₂×C₅×#107	C₂²	1	1	yes	characteristic
25	C₂×C₅×#106	C₂²	1	1	yes	characteristic
26	C₂×C₅×#103	C₂²	1	1	yes	characteristic
27	C₂×C₅×#103	C₂²	1	1	yes	characteristic
28	C₂×C₅×#103	C₂²	1	1	yes	characteristic
29	C₂×C₅×#103	C₂²	1	1	yes	characteristic
30	C₂×C₅×#103	C₂²	1	1	yes	characteristic
31	C₂×C₅×#103	C₂²	1	1	yes	characteristic
32	C₂×C₅×#102	C₂²	1	1	yes	characteristic
33	C₂×C₅×#102	C₂²	1	1	yes	characteristic
34	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₅×#97	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
38	C₅×#391	—	2	1	no	—
39	C₅×#391	—	2	1	no	—
40	C₅×#391	C₂²	1	1	yes	characteristic
41	C₅×#391	C₂²	1	1	yes	characteristic
42	C₅×#391	C₂²	1	1	yes	characteristic
43	C₅×#391	C₂²	1	1	yes	characteristic
44	C₅×#390	—	2	1	no	—
45	C₅×#390	C₂²	1	1	yes	characteristic
46	C₅×#389	C₂²	1	1	yes	characteristic
47	C₅×#388	—	2	1	no	—
48	C₅×#386	—	2	1	no	—
49	C₅×#385	—	2	1	no	—
50	C₅×#381	—	2	1	no	—
51	C₅×#381	—	2	1	no	—
52	C₅×#380	C₂²	1	1	yes	characteristic
53	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
54	C₅×#340	C₂²	1	1	yes	characteristic
55	C₅×#340	C₂²	1	1	yes	characteristic
56	C₅×#340	C₂²	1	1	yes	characteristic
57	C₅×#340	C₂²	1	1	yes	characteristic
58	C₅×#336	C₂²	1	1	yes	characteristic
59	C₅×#336	C₂²	1	1	yes	characteristic
60	#22058	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
61	C₂²×C₅×Q₈	—	2	1	no	—
62	C₂²×C₅×Q₈	—	2	2	no	—
63	C₂²×C₅×Q₈	—	4	1	no	—
64	C₂²×C₅×Q₈	—	4	1	no	—
65	C₂²×C₅×Q₈	—	4	1	no	—
66	C₂²×C₅×Q₈	—	4	1	no	—
67	C₂²×C₅×Q₈	C₂×C₄	1	4	yes	complemented
68	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
69	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
70	C₂²×C₅×D₄	—	2	1	no	—
71	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₅	—	2	1	no	—
73	C₂³×C₄×C₅	—	2	1	no	—
74	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
75	C₂×C₅×SD₁₆	—	4	1	no	—
76	C₂×C₅×SD₁₆	—	4	1	no	—
77	C₂×C₅×SD₁₆	—	4	1	no	—
78	C₂×C₅×SD₁₆	—	4	1	no	—
79	C₂×C₅×SD₁₆	C₂×C₄	1	4	yes	—
80	C₂×C₅×SD₁₆	C₂×C₄	1	4	yes	—
81	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
82	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
83	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
84	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
85	C₅×#121	—	2	2	no	—
86	C₅×#121	C₂×C₄	1	4	yes	—
87	C₄×C₅×D₄	—	4	1	no	—
88	C₄×C₅×D₄	—	4	1	no	—
89	C₅×#117	—	4	1	no	—
90	C₅×#117	—	4	1	no	—
91	C₅×#117	—	4	1	no	—
92	C₅×#117	—	4	1	no	—
93	C₂×C₅×C₄⋊C₄	—	2	1	no	—
94	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
95	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
96	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
98	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
99	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
100	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
102	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
103	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
104	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
105	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
106	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
107	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
108	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
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	C₅×#107	—	4	1	no	—
114	C₅×#106	—	4	1	no	—
115	C₅×#103	—	4	1	no	—
116	C₅×#103	—	4	1	no	—
117	C₅×#103	—	4	1	no	—
118	C₅×#103	—	4	1	no	—
119	C₅×#103	C₂×C₄	1	4	yes	complemented
120	C₅×#103	C₂×C₄	1	4	yes	complemented
121	C₅×#102	—	4	1	no	—
122	C₅×#102	—	4	1	no	—
123	C₅×C₂²⋊C₈	—	2	2	no	—
124	C₅×C₂²⋊C₈	C₂×C₄	1	4	yes	complemented
125	C₅×#97	—	4	1	no	—
126	C₄×C₅×C₈	—	4	1	no	—
127	C₅×#95	—	2	1	no	—
128	C₅×#95	—	2	1	no	—
129	C₅×#95	—	2	1	no	—
130	C₅×#95	—	2	1	no	—
131	C₅×#95	—	2	1	no	—
132	C₅×#95	—	2	1	no	—
133	C₅×#95	—	2	1	no	—
134	C₅×#95	—	2	1	no	—
135	C₅×#95	—	2	1	no	—
136	C₅×#95	—	2	1	no	—
137	C₅×#95	—	2	1	no	—
138	C₂×#448	C₂×C₅	1	1	yes	characteristic
139	#2324	C₂×C₅	1	1	yes	characteristic
140	#2310	C₂×C₅	1	1	yes	characteristic, complemented
141	#1973	C₂×C₅	1	1	yes	characteristic, complemented
142	#1968	C₂×C₅	1	1	yes	characteristic, complemented
143	#1935	C₂×C₅	1	1	yes	characteristic, complemented
144	#1933	C₂×C₅	1	1	yes	characteristic, complemented
145	#1928	C₂×C₅	1	1	yes	characteristic, complemented
146	#1927	C₂×C₅	1	1	yes	characteristic, complemented
147	#1877	C₂×C₅	1	1	yes	characteristic, complemented
148	#1877	C₂×C₅	1	1	yes	characteristic, complemented
149	#1875	C₂×C₅	1	1	yes	characteristic
150	#1854	C₂×C₅	1	1	yes	characteristic, complemented
151	#1787	C₂×C₅	1	1	yes	characteristic, complemented
152	#1750	C₂×C₅	1	1	yes	characteristic, complemented
153	C₂⁴×C₅	—	2	1	no	—
154	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
155	C₂×C₅×Q₈	—	2	4	no	—
156	C₂×C₅×Q₈	—	2	1	no	—
157	C₂×C₅×Q₈	—	2	1	no	—
158	C₂×C₅×Q₈	—	2	1	no	—
159	C₂×C₅×Q₈	—	2	1	no	—
160	C₂×C₅×Q₈	—	2	1	no	—
161	C₂×C₅×Q₈	—	2	1	no	—
162	C₂×C₅×Q₈	—	2	1	no	—
163	C₂×C₅×Q₈	—	2	1	no	—
164	C₂×C₅×Q₈	—	2	1	no	—
165	C₂×C₅×Q₈	—	2	1	no	—
166	C₂×C₅×Q₈	—	4	4	no	—
167	C₂×C₅×Q₈	—	4	4	no	—
168	C₂×C₅×Q₈	—	4	2	no	—
169	C₂×C₅×Q₈	—	4	2	no	—
170	C₂×C₅×Q₈	—	4	4	no	—
171	C₂×C₅×Q₈	—	4	4	no	—
172	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
173	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
174	C₂×C₅×D₄	—	2	4	no	—
175	C₂×C₅×D₄	—	2	1	no	—
176	C₂×C₅×D₄	—	2	1	no	—
177	C₂×C₅×D₄	—	2	1	no	—
178	C₂×C₅×D₄	—	2	1	no	—
179	C₂×C₅×D₄	—	2	1	no	—
180	C₂×C₅×D₄	—	8	1	no	—
181	C₂×C₅×D₄	—	8	1	no	—
182	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
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	4	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	—	2	1	no	—
195	C₂²×C₄×C₅	—	4	2	no	—
196	C₂²×C₄×C₅	—	4	2	no	—
197	C₂²×C₄×C₅	—	4	2	no	—
198	C₂²×C₄×C₅	—	8	1	no	—
199	C₂²×C₄×C₅	—	8	1	no	—
200	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
201	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₅	#41	1	2	yes	—
207	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
208	C₅×SD₁₆	—	4	4	no	—
209	C₅×SD₁₆	—	4	4	no	—
210	C₂×C₅×C₈	—	2	1	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	C₂²×C₄	1	2	yes	—
221	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
222	C₅×C₄⋊C₄	—	2	1	no	—
223	C₅×C₄⋊C₄	—	2	1	no	—
224	C₅×C₄⋊C₄	—	2	1	no	—
225	C₅×C₄⋊C₄	—	2	1	no	—
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	—	4	1	no	—
232	C₅×C₄⋊C₄	—	4	1	no	—
233	C₅×C₄⋊C₄	—	8	1	no	—
234	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
235	C₅×C₂²⋊C₄	—	2	4	no	—
236	C₅×C₂²⋊C₄	—	4	1	no	—
237	C₅×C₂²⋊C₄	—	4	1	no	—
238	C₅×C₂²⋊C₄	—	4	2	no	—
239	C₅×C₂²⋊C₄	—	4	2	no	—
240	C₅×C₂²⋊C₄	—	8	1	no	—
241	C₅×C₂²⋊C₄	—	8	1	no	—
242	C₅×C₂²⋊C₄	—	8	1	no	—
243	C₄²×C₅	—	2	1	no	—
244	C₄²×C₅	—	2	1	no	—
245	C₄²×C₅	—	2	1	no	—
246	C₄²×C₅	—	2	1	no	—
247	C₄²×C₅	—	4	2	no	—
248	C₄²×C₅	—	8	1	no	—
249	C₂³×Q₈	C₂²×C₅	1	1	yes	characteristic
250	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
251	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
252	C₂×#121	C₂²×C₅	1	1	yes	characteristic
253	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
254	C₂×#117	C₂²×C₅	1	1	yes	characteristic
255	C₂×#117	C₂²×C₅	1	1	yes	characteristic
256	#448	C₄×C₅	1	8	yes	complemented
257	C₂×#107	C₂²×C₅	1	1	yes	characteristic
258	C₂×#106	C₂²×C₅	1	1	yes	characteristic
259	C₂×#103	C₂²×C₅	1	1	yes	characteristic
260	C₂×#103	C₂²×C₅	1	1	yes	characteristic
261	C₂×#103	C₂²×C₅	1	1	yes	characteristic
262	C₂×#103	C₂²×C₅	1	1	yes	characteristic
263	C₂×#103	C₂²×C₅	1	1	yes	characteristic
264	C₂×#103	C₂²×C₅	1	1	yes	characteristic
265	C₂×#102	C₂²×C₅	1	1	yes	characteristic
266	C₂×#102	C₂²×C₅	1	1	yes	characteristic
267	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
268	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
269	C₂×#97	C₂²×C₅	1	1	yes	characteristic
270	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
271	#391	—	2	1	no	—
272	#391	—	2	1	no	—
273	#391	C₂²×C₅	1	1	yes	characteristic
274	#391	C₂²×C₅	1	1	yes	characteristic
275	#391	C₂²×C₅	1	1	yes	characteristic
276	#391	C₂²×C₅	1	1	yes	characteristic
277	#390	—	2	1	no	—
278	#390	C₂²×C₅	1	1	yes	characteristic
279	#389	C₂²×C₅	1	1	yes	characteristic
280	#388	—	2	1	no	—
281	#386	—	2	1	no	—
282	#385	—	2	1	no	—
283	#381	—	2	1	no	—
284	#381	—	2	1	no	—
285	#380	C₂²×C₅	1	1	yes	characteristic
286	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
287	#340	C₂²×C₅	1	1	yes	characteristic
288	#340	C₂²×C₅	1	1	yes	characteristic
289	#340	C₂²×C₅	1	1	yes	characteristic
290	#340	C₂²×C₅	1	1	yes	characteristic
291	#336	C₂²×C₅	1	1	yes	characteristic
292	#336	C₂²×C₅	1	1	yes	characteristic
293	C₂³×C₅	—	2	1	no	—
294	C₂³×C₅	—	2	1	no	—
295	C₂³×C₅	—	2	1	no	—
296	C₂³×C₅	—	2	1	no	—
297	C₂³×C₅	—	2	1	no	—
298	C₂³×C₅	—	2	1	no	—
299	C₂³×C₅	—	2	2	no	—
300	C₂³×C₅	—	4	1	no	—
301	C₂³×C₅	—	4	1	no	—
302	C₂³×C₅	—	4	1	no	—
303	C₂³×C₅	—	4	1	no	—
304	C₂³×C₅	—	4	1	no	—
305	C₂³×C₅	—	4	1	no	—
306	C₂³×C₅	C₄×D₄	1	2	yes	—
307	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
308	C₅×Q₈	—	2	2	no	—
309	C₅×Q₈	—	2	2	no	—
310	C₅×Q₈	—	2	2	no	—
311	C₅×Q₈	—	2	2	no	—
312	C₅×Q₈	—	4	8	no	—
313	C₅×Q₈	—	4	1	no	—
314	C₅×Q₈	—	4	1	no	—
315	C₅×Q₈	—	4	1	no	—
316	C₅×Q₈	—	4	1	no	—
317	C₅×D₄	—	2	2	no	—
318	C₅×D₄	—	2	2	no	—
319	C₅×D₄	—	4	1	no	—
320	C₅×D₄	—	4	1	no	—
321	C₅×D₄	—	8	4	no	—
322	C₂×C₄×C₅	—	2	1	no	—
323	C₂×C₄×C₅	—	2	1	no	—
324	C₂×C₄×C₅	—	2	2	no	—
325	C₂×C₄×C₅	—	2	2	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	—	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	1	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	—	4	8	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	—	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	—	4	1	no	—
355	C₂×C₄×C₅	—	4	1	no	—
356	C₂×C₄×C₅	—	4	1	no	—
357	C₂×C₄×C₅	—	4	1	no	—
358	C₂×C₄×C₅	—	4	1	no	—
359	C₂×C₄×C₅	—	4	1	no	—
360	C₂×C₄×C₅	—	4	1	no	—
361	C₂×C₄×C₅	—	4	1	no	—
362	C₂×C₄×C₅	—	8	4	no	—
363	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
364	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
365	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
366	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
367	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
368	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
369	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
370	C₅×C₈	—	2	2	no	—
371	C₅×C₈	—	2	2	no	—
372	C₅×C₈	—	4	1	no	—
373	C₅×C₈	—	4	1	no	—
374	C₂²×Q₈	—	2	1	no	—
375	C₂²×Q₈	—	2	2	no	—
376	C₂²×Q₈	—	4	1	no	—
377	C₂²×Q₈	—	4	1	no	—
378	C₂²×Q₈	—	4	1	no	—
379	C₂²×Q₈	—	4	1	no	—
380	C₂²×Q₈	C₂×C₄×C₅	1	4	yes	complemented
381	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
382	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
383	C₂²×D₄	—	2	1	no	—
384	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
385	C₂³×C₄	—	2	1	no	—
386	C₂³×C₄	—	2	1	no	—
387	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
388	C₂×SD₁₆	—	4	1	no	—
389	C₂×SD₁₆	—	4	1	no	—
390	C₂×SD₁₆	—	4	1	no	—
391	C₂×SD₁₆	—	4	1	no	—
392	C₂×SD₁₆	C₂×C₄×C₅	1	4	yes	—
393	C₂×SD₁₆	C₂×C₄×C₅	1	4	yes	—
394	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
395	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
396	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
397	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
398	#121	—	2	2	no	—
399	#121	C₂×C₄×C₅	1	4	yes	—
400	C₄×D₄	—	4	1	no	—
401	C₄×D₄	—	4	1	no	—
402	#117	—	4	1	no	—
403	#117	—	4	1	no	—
404	#117	—	4	1	no	—
405	#117	—	4	1	no	—
406	C₂×C₄⋊C₄	—	2	1	no	—
407	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
408	C₂×C₄⋊C₄	C₅×D₄	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×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
413	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
414	C₂×C₂²⋊C₄	—	2	1	no	—
415	C₂×C₂²⋊C₄	—	2	1	no	—
416	C₂×C₂²⋊C₄	—	2	1	no	—
417	C₂×C₂²⋊C₄	—	2	1	no	—
418	C₂×C₂²⋊C₄	—	2	1	no	—
419	C₂×C₂²⋊C₄	—	2	1	no	—
420	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
421	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
422	C₂×C₄²	—	2	1	no	—
423	C₂×C₄²	—	2	1	no	—
424	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
425	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
426	#107	—	4	1	no	—
427	#106	—	4	1	no	—
428	#103	—	4	1	no	—
429	#103	—	4	1	no	—
430	#103	—	4	1	no	—
431	#103	—	4	1	no	—
432	#103	C₂×C₄×C₅	1	4	yes	complemented
433	#103	C₂×C₄×C₅	1	4	yes	complemented
434	#102	—	4	1	no	—
435	#102	—	4	1	no	—
436	C₂²⋊C₈	—	2	2	no	—
437	C₂²⋊C₈	C₂×C₄×C₅	1	4	yes	complemented
438	#97	—	4	1	no	—
439	C₄×C₈	—	4	1	no	—
440	#95	—	2	1	no	—
441	#95	—	2	1	no	—
442	#95	—	2	1	no	—
443	#95	—	2	1	no	—
444	#95	—	2	1	no	—
445	#95	—	2	1	no	—
446	#95	—	2	1	no	—
447	#95	—	2	1	no	—
448	#95	—	2	1	no	—
449	#95	—	2	1	no	—
450	#95	—	2	1	no	—
451	C₂²×C₅	—	2	2	no	—
452	C₂²×C₅	—	2	2	no	—
453	C₂²×C₅	—	2	2	no	—
454	C₂²×C₅	—	4	1	no	—
455	C₂²×C₅	—	4	1	no	—
456	C₂²×C₅	—	4	1	no	—
457	C₂²×C₅	—	4	1	no	—
458	C₂²×C₅	—	4	2	no	—
459	C₂²×C₅	—	4	2	no	—
460	C₂²×C₅	—	4	2	no	—
461	C₂²×C₅	—	8	1	no	—
462	C₂²×C₅	—	8	1	no	—
463	C₂²×C₅	—	8	1	no	—
464	C₂²×C₅	—	8	1	no	—
465	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
466	C₂²×C₅	#534	1	1	yes	characteristic
467	C₂²×C₅	#535	1	1	yes	characteristic
468	C₂²×C₅	#577	1	1	yes	characteristic
469	C₂²×C₅	#577	1	1	yes	characteristic
470	C₂²×C₅	#577	1	1	yes	characteristic
471	C₂²×C₅	#578	1	1	yes	characteristic
472	C₄×C₅	—	2	2	no	—
473	C₄×C₅	—	4	2	no	—
474	C₄×C₅	—	4	2	no	—
475	C₄×C₅	—	4	1	no	—
476	C₄×C₅	—	4	1	no	—
477	C₄×C₅	—	4	1	no	—
478	C₄×C₅	—	4	1	no	—
479	C₄×C₅	—	4	2	no	—
480	C₄×C₅	—	8	1	no	—
481	C₄×C₅	—	8	1	no	—
482	C₄×C₅	—	8	1	no	—
483	C₄×C₅	—	8	1	no	—
484	C₄×C₅	#518	1	1	yes	characteristic
485	C₄×C₅	#518	1	1	yes	characteristic
486	C₄×C₅	#538	1	1	yes	characteristic
487	C₄×C₅	#538	1	1	yes	characteristic
488	C₂⁴	—	2	1	no	—
489	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
490	C₂×Q₈	—	2	4	no	—
491	C₂×Q₈	—	2	1	no	—
492	C₂×Q₈	—	2	1	no	—
493	C₂×Q₈	—	2	1	no	—
494	C₂×Q₈	—	2	1	no	—
495	C₂×Q₈	—	2	1	no	—
496	C₂×Q₈	—	2	1	no	—
497	C₂×Q₈	—	2	1	no	—
498	C₂×Q₈	—	2	1	no	—
499	C₂×Q₈	—	2	1	no	—
500	C₂×Q₈	—	2	1	no	—
501	C₂×Q₈	—	4	4	no	—
502	C₂×Q₈	—	4	4	no	—
503	C₂×Q₈	—	4	2	no	—
504	C₂×Q₈	—	4	2	no	—
505	C₂×Q₈	—	4	4	no	—
506	C₂×Q₈	—	4	4	no	—
507	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
508	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
509	C₂×D₄	—	2	4	no	—
510	C₂×D₄	—	2	1	no	—
511	C₂×D₄	—	2	1	no	—
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	—	2	1	no	—
514	C₂×D₄	—	2	1	no	—
515	C₂×D₄	—	8	1	no	—
516	C₂×D₄	—	8	1	no	—
517	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	4	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	4	2	no	—
531	C₂²×C₄	—	4	2	no	—
532	C₂²×C₄	—	4	2	no	—
533	C₂²×C₄	—	8	1	no	—
534	C₂²×C₄	—	8	1	no	—
535	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
536	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
537	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
538	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
539	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
540	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
541	C₂²×C₄	C₅×#41	1	2	yes	—
542	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
543	SD₁₆	—	4	4	no	—
544	SD₁₆	—	4	4	no	—
545	C₂×C₈	—	2	1	no	—
546	C₂×C₈	—	2	1	no	—
547	C₂×C₈	—	2	1	no	—
548	C₂×C₈	—	2	1	no	—
549	C₂×C₈	—	2	1	no	—
550	C₂×C₈	—	2	1	no	—
551	C₂×C₈	—	2	1	no	—
552	C₂×C₈	—	2	1	no	—
553	C₂×C₈	—	2	1	no	—
554	C₂×C₈	—	2	1	no	—
555	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
556	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
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	—	2	1	no	—
562	C₄⋊C₄	—	2	1	no	—
563	C₄⋊C₄	—	2	1	no	—
564	C₄⋊C₄	—	2	1	no	—
565	C₄⋊C₄	—	2	1	no	—
566	C₄⋊C₄	—	4	1	no	—
567	C₄⋊C₄	—	4	1	no	—
568	C₄⋊C₄	—	8	1	no	—
569	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
570	C₂²⋊C₄	—	2	4	no	—
571	C₂²⋊C₄	—	4	1	no	—
572	C₂²⋊C₄	—	4	1	no	—
573	C₂²⋊C₄	—	4	2	no	—
574	C₂²⋊C₄	—	4	2	no	—
575	C₂²⋊C₄	—	8	1	no	—
576	C₂²⋊C₄	—	8	1	no	—
577	C₂²⋊C₄	—	8	1	no	—
578	C₄²	—	2	1	no	—
579	C₄²	—	2	1	no	—
580	C₄²	—	2	1	no	—
581	C₄²	—	2	1	no	—
582	C₄²	—	4	2	no	—
583	C₄²	—	8	1	no	—
584	C₂×C₅	—	4	2	no	—
585	C₂×C₅	—	8	2	no	—
586	C₂×C₅	#2321	1	1	yes	characteristic
587	C₂×C₅	#2947	1	1	yes	characteristic
588	C₂×C₅	#2949	1	1	yes	characteristic
589	C₂×C₅	#3200	1	1	yes	characteristic
590	C₂×C₅	#3201	1	1	yes	characteristic
591	C₂×C₅	#3221	1	1	yes	characteristic
592	C₂×C₅	#3225	1	1	yes	characteristic
593	C₂³	—	2	1	no	—
594	C₂³	—	2	1	no	—
595	C₂³	—	2	1	no	—
596	C₂³	—	2	1	no	—
597	C₂³	—	2	1	no	—
598	C₂³	—	2	1	no	—
599	C₂³	—	2	2	no	—
600	C₂³	—	4	1	no	—
601	C₂³	—	4	1	no	—
602	C₂³	—	4	1	no	—
603	C₂³	—	4	1	no	—
604	C₂³	—	4	1	no	—
605	C₂³	—	4	1	no	—
606	C₂³	C₄×C₅×D₄	1	2	yes	—
607	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
608	Q₈	—	2	2	no	—
609	Q₈	—	2	2	no	—
610	Q₈	—	2	2	no	—
611	Q₈	—	2	2	no	—
612	Q₈	—	4	8	no	—
613	Q₈	—	4	1	no	—
614	Q₈	—	4	1	no	—
615	Q₈	—	4	1	no	—
616	Q₈	—	4	1	no	—
617	D₄	—	2	2	no	—
618	D₄	—	2	2	no	—
619	D₄	—	4	1	no	—
620	D₄	—	4	1	no	—
621	D₄	—	8	4	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	4	8	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	4	1	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	4	1	no	—
662	C₂×C₄	—	8	4	no	—
663	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
664	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
665	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
666	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
667	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
668	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
669	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
670	C₈	—	2	2	no	—
671	C₈	—	2	2	no	—
672	C₈	—	4	1	no	—
673	C₈	—	4	1	no	—
674	C₅	#22058	1	1	yes	characteristic, direct product factor, Sylow
675	C₂²	—	2	2	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	4	1	no	—
679	C₂²	—	4	1	no	—
680	C₂²	—	4	1	no	—
681	C₂²	—	4	1	no	—
682	C₂²	—	4	2	no	—
683	C₂²	—	4	2	no	—
684	C₂²	—	4	2	no	—
685	C₂²	—	8	1	no	—
686	C₂²	—	8	1	no	—
687	C₂²	—	8	1	no	—
688	C₂²	—	8	1	no	—
689	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
690	C₂²	C₅×#534	1	1	yes	characteristic
691	C₂²	C₅×#535	1	1	yes	characteristic
692	C₂²	C₅×#577	1	1	yes	characteristic
693	C₂²	C₅×#577	1	1	yes	characteristic
694	C₂²	C₅×#577	1	1	yes	characteristic
695	C₂²	C₅×#578	1	1	yes	characteristic
696	C₄	—	2	2	no	—
697	C₄	—	4	2	no	—
698	C₄	—	4	2	no	—
699	C₄	—	4	1	no	—
700	C₄	—	4	1	no	—
701	C₄	—	4	1	no	—
702	C₄	—	4	1	no	—
703	C₄	—	4	2	no	—
704	C₄	—	8	1	no	—
705	C₄	—	8	1	no	—
706	C₄	—	8	1	no	—
707	C₄	—	8	1	no	—
708	C₄	C₅×#518	1	1	yes	characteristic
709	C₄	C₅×#518	1	1	yes	characteristic
710	C₄	C₅×#538	1	1	yes	characteristic
711	C₄	C₅×#538	1	1	yes	characteristic
712	C₂	—	4	2	no	—
713	C₂	—	8	2	no	—
714	C₂	C₅×#2321	1	1	yes	characteristic
715	C₂	C₅×#2947	1	1	yes	characteristic
716	C₂	C₅×#2949	1	1	yes	characteristic
717	C₂	C₅×#3200	1	1	yes	characteristic
718	C₂	C₅×#3201	1	1	yes	characteristic
719	C₂	C₅×#3221	1	1	yes	characteristic
720	C₂	C₅×#3225	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	C₂×C₅×#121	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#117 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₅×#2310	C₂	semidirect
4. C₅×#1973	C₂	semidirect
5. C₅×#1968	C₂	semidirect
6. C₅×#1935	C₂	semidirect
7. C₅×#1933	C₂	semidirect
8. C₅×#1928	C₂	semidirect
9. C₅×#1927	C₂	semidirect
10. C₅×#1877	C₂	semidirect
11. C₅×#1877	C₂	semidirect
13. C₅×#1854	C₂	semidirect
14. C₅×#1787	C₂	semidirect
15. C₅×#1750	C₂	semidirect
23. C₅×#448	C₄	semidirect
60. #22058	C₅	direct (N × H)
67. C₂²×C₅×Q₈	C₂×C₄	semidirect
119. C₅×#103	C₂×C₄	semidirect
120. C₅×#103	C₂×C₄	semidirect
124. C₅×C₂²⋊C₈	C₂×C₄	semidirect
140. #2310	C₂×C₅	semidirect
141. #1973	C₂×C₅	semidirect
142. #1968	C₂×C₅	semidirect
143. #1935	C₂×C₅	semidirect
144. #1933	C₂×C₅	semidirect
145. #1928	C₂×C₅	semidirect
146. #1927	C₂×C₅	semidirect
147. #1877	C₂×C₅	semidirect
148. #1877	C₂×C₅	semidirect
150. #1854	C₂×C₅	semidirect
151. #1787	C₂×C₅	semidirect
152. #1750	C₂×C₅	semidirect
256. #448	C₄×C₅	semidirect
380. C₂²×Q₈	C₂×C₄×C₅	semidirect
432. #103	C₂×C₄×C₅	semidirect
433. #103	C₂×C₄×C₅	semidirect
437. C₂²⋊C₈	C₂×C₄×C₅	semidirect
674. C₅	#22058	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×#448	2
C₅×#2324	2
C₅×#2310	2
C₅×#1973	2
C₅×#1968	2
C₅×#1935	2
C₅×#1933	2
C₅×#1928	2
C₅×#1927	2
C₅×#1877	2
C₅×#1875	2
C₅×#1854	2
C₅×#1787	2
C₅×#1750	2
#22058	5

Subgroups — C5×#22058 #11944778

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22058 #11944778