Subgroups — C₅×#22984 #11945704

Order 1280.

692 conjugacy classes of subgroups.

The subgroup lattice has 636 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×#2906	C₂	1	1	yes	maximal, characteristic
4	C₅×#1995	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1950	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1946	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1945	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×#1866	C₂	1	1	yes	maximal, characteristic
11	C₅×#1866	C₂	1	1	yes	maximal, characteristic
12	C₅×#1768	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1765	C₂	1	1	yes	maximal, characteristic
14	C₅×#1764	C₂	1	1	yes	maximal, characteristic
15	C₅×#1759	C₂	1	1	yes	maximal, characteristic
16	C₂×C₅×#131	C₂²	1	1	yes	characteristic
17	C₂×C₅×#131	C₂²	1	1	yes	characteristic
18	C₅×#533	C₂²	1	1	yes	characteristic
19	C₄×C₅×#41	C₂²	1	1	yes	characteristic
20	C₅×#479	C₄	1	1	yes	characteristic, complemented
21	C₅×#479	C₄	1	1	yes	characteristic, complemented
22	C₅×#478	C₄	1	1	yes	characteristic, complemented
23	C₅×#478	C₄	1	1	yes	characteristic, complemented
24	C₅×#477	C₄	1	1	yes	characteristic, complemented
25	C₅×#476	C₄	1	1	yes	characteristic, complemented
26	C₅×#475	C₄	1	1	yes	characteristic, complemented
27	C₅×#474	C₄	1	1	yes	characteristic, complemented
28	C₅×#446	—	2	1	no	—
29	C₅×#446	—	2	1	no	—
30	C₅×#446	—	2	1	no	—
31	C₅×C₈×Q₈	—	2	1	no	—
32	C₂×C₅×#108	C₂²	1	1	yes	characteristic
33	C₂×C₅×#108	C₂²	1	1	yes	characteristic
34	C₅×#427	C₂²	1	1	yes	characteristic
35	C₅×#427	C₂²	1	1	yes	characteristic
36	C₅×#424	—	2	1	no	—
37	C₅×#424	—	2	1	no	—
38	C₅×#424	C₂²	1	1	yes	characteristic
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×#423	—	2	1	no	—
43	C₅×#423	C₂²	1	1	yes	characteristic
44	C₂×C₅×C₄⋊C₈	—	2	1	no	—
45	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
46	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
47	C₂×C₅×#104	C₂²	1	1	yes	characteristic
48	C₂×C₅×#104	C₂²	1	1	yes	characteristic
49	C₅×#416	C₂²	1	1	yes	characteristic
50	C₅×#416	C₂²	1	1	yes	characteristic
51	C₅×#405	C₂²	1	1	yes	characteristic
52	C₅×#405	C₂²	1	1	yes	characteristic
53	C₄×C₅×M₁₆	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	C₅×#376	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	#22984	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂×C₅×#41	C₂³	1	1	yes	characteristic
69	C₅×#131	—	2	2	no	—
70	C₅×#131	—	2	2	no	—
71	C₅×#131	—	4	1	no	—
72	C₅×#131	—	4	1	no	—
73	C₂×C₅×M₁₆	—	2	1	no	—
74	C₂×C₅×M₁₆	—	2	1	no	—
75	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
76	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
77	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
78	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
79	C₂²×C₅×C₈	—	2	1	no	—
80	C₂²×C₅×C₈	—	2	1	no	—
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×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
86	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
87	C₅×#125	C₂×C₄	1	1	yes	characteristic
88	C₅×#125	C₂×C₄	1	1	yes	characteristic
89	C₅×C₂²⋊Q₈	—	2	1	no	—
90	C₅×C₂²⋊Q₈	—	2	1	no	—
91	C₄×C₅×Q₈	—	2	1	no	—
92	C₄×C₅×Q₈	—	2	1	no	—
93	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
94	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
95	C₄×C₅×D₄	—	2	1	no	—
96	C₄×C₅×D₄	—	2	1	no	—
97	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
98	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
99	C₅×#117	—	2	1	no	—
100	C₅×#117	C₂³	1	1	yes	characteristic
101	C₅×#117	C₂³	1	1	yes	characteristic
102	C₅×#117	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₅	—	2	1	no	—
104	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
107	C₅×#108	—	4	1	no	—
108	C₅×#108	—	4	1	no	—
109	C₅×#107	C₂×C₄	1	1	yes	characteristic
110	C₅×#107	C₂×C₄	1	1	yes	characteristic
111	C₅×#107	C₂×C₄	1	1	yes	characteristic
112	C₅×#107	C₂×C₄	1	1	yes	characteristic
113	C₅×#106	C₂×C₄	1	1	yes	characteristic
114	C₅×#106	C₂×C₄	1	1	yes	characteristic
115	C₅×#106	C₂×C₄	1	1	yes	characteristic
116	C₅×#106	C₂×C₄	1	1	yes	characteristic
117	C₅×C₄⋊C₈	—	2	1	no	—
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	—	2	1	no	—
127	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
128	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
129	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
130	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
131	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
132	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
133	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
134	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
135	C₅×#104	—	2	2	no	—
136	C₅×#104	Q₈	1	4	yes	complemented
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×#103	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×#102	C₂×C₄	1	1	yes	characteristic
145	C₅×#97	—	2	1	no	—
146	C₅×#97	—	2	1	no	—
147	C₅×#97	—	2	1	no	—
148	C₅×#97	—	4	1	no	—
149	C₄×C₅×C₈	—	2	1	no	—
150	C₄×C₅×C₈	—	2	1	no	—
151	C₄×C₅×C₈	—	2	1	no	—
152	C₄×C₅×C₈	—	4	1	no	—
153	C₅×#95	—	2	1	no	—
154	C₅×#95	—	2	1	no	—
155	#3076	C₂×C₅	1	1	yes	characteristic
156	#2962	C₂×C₅	1	1	yes	characteristic, complemented
157	#2906	C₂×C₅	1	1	yes	characteristic
158	#1995	C₂×C₅	1	1	yes	characteristic, complemented
159	#1950	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	#1922	C₂×C₅	1	1	yes	characteristic, complemented
163	#1922	C₂×C₅	1	1	yes	characteristic, complemented
164	#1866	C₂×C₅	1	1	yes	characteristic
165	#1866	C₂×C₅	1	1	yes	characteristic
166	#1768	C₂×C₅	1	1	yes	characteristic, complemented
167	#1765	C₂×C₅	1	1	yes	characteristic
168	#1764	C₂×C₅	1	1	yes	characteristic
169	#1759	C₂×C₅	1	1	yes	characteristic
170	C₅×#41	—	2	1	no	—
171	C₅×#41	—	2	1	no	—
172	C₅×#41	C₂×Q₈	1	2	yes	—
173	C₅×#41	#41	1	2	yes	—
174	C₂×C₅×Q₈	—	2	1	no	—
175	C₂×C₅×Q₈	—	2	1	no	—
176	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
177	C₂×C₅×D₄	—	2	1	no	—
178	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
179	C₂²×C₄×C₅	—	2	1	no	—
180	C₂²×C₄×C₅	—	2	1	no	—
181	C₂²×C₄×C₅	—	2	1	no	—
182	C₂²×C₄×C₅	—	2	1	no	—
183	C₂²×C₄×C₅	—	2	1	no	—
184	C₂²×C₄×C₅	#41	1	1	yes	characteristic
185	C₂²×C₄×C₅	#41	1	1	yes	characteristic
186	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
187	C₅×M₁₆	—	2	1	no	—
188	C₅×M₁₆	—	2	1	no	—
189	C₅×M₁₆	—	2	1	no	—
190	C₅×M₁₆	—	2	1	no	—
191	C₅×M₁₆	—	2	1	no	—
192	C₅×M₁₆	—	2	1	no	—
193	C₅×M₁₆	—	2	1	no	—
194	C₅×M₁₆	—	4	2	no	—
195	C₅×M₁₆	—	4	2	no	—
196	C₅×M₁₆	C₂×Q₈	1	2	yes	—
197	C₂×C₅×C₈	—	2	1	no	—
198	C₂×C₅×C₈	—	2	1	no	—
199	C₂×C₅×C₈	—	2	1	no	—
200	C₂×C₅×C₈	—	2	1	no	—
201	C₂×C₅×C₈	—	2	1	no	—
202	C₂×C₅×C₈	—	2	1	no	—
203	C₂×C₅×C₈	—	2	1	no	—
204	C₂×C₅×C₈	—	2	1	no	—
205	C₂×C₅×C₈	—	2	1	no	—
206	C₂×C₅×C₈	—	2	1	no	—
207	C₂×C₅×C₈	—	2	1	no	—
208	C₂×C₅×C₈	—	2	1	no	—
209	C₂×C₅×C₈	—	4	2	no	—
210	C₂×C₅×C₈	—	4	2	no	—
211	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
212	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
213	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
214	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
215	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
216	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
217	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
218	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
219	C₅×C₄⋊C₄	—	2	1	no	—
220	C₅×C₄⋊C₄	—	2	1	no	—
221	C₅×C₄⋊C₄	—	2	1	no	—
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	C₂²×C₄	1	1	yes	characteristic
228	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
229	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
230	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
231	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
232	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
233	C₅×C₂²⋊C₄	—	2	1	no	—
234	C₅×C₂²⋊C₄	—	2	1	no	—
235	C₅×C₂²⋊C₄	—	2	1	no	—
236	C₅×C₂²⋊C₄	—	2	1	no	—
237	C₅×C₂²⋊C₄	—	2	1	no	—
238	C₄²×C₅	—	2	1	no	—
239	C₄²×C₅	—	2	1	no	—
240	C₄²×C₅	—	2	1	no	—
241	C₄²×C₅	—	2	1	no	—
242	C₄²×C₅	—	2	1	no	—
243	C₄²×C₅	—	2	1	no	—
244	C₄²×C₅	—	2	1	no	—
245	C₄²×C₅	—	2	1	no	—
246	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
247	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
248	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
249	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
250	C₄²×C₅	C₂×Q₈	1	2	yes	—
251	C₂×#131	C₂²×C₅	1	1	yes	characteristic
252	C₂×#131	C₂²×C₅	1	1	yes	characteristic
253	#533	C₂²×C₅	1	1	yes	characteristic
254	C₄×#41	C₂²×C₅	1	1	yes	characteristic
255	#479	C₄×C₅	1	1	yes	characteristic, complemented
256	#479	C₄×C₅	1	1	yes	characteristic, complemented
257	#478	C₄×C₅	1	1	yes	characteristic, complemented
258	#478	C₄×C₅	1	1	yes	characteristic, complemented
259	#477	C₄×C₅	1	1	yes	characteristic, complemented
260	#476	C₄×C₅	1	1	yes	characteristic, complemented
261	#475	C₄×C₅	1	1	yes	characteristic, complemented
262	#474	C₄×C₅	1	1	yes	characteristic, complemented
263	#446	—	2	1	no	—
264	#446	—	2	1	no	—
265	#446	—	2	1	no	—
266	C₈×Q₈	—	2	1	no	—
267	C₂×#108	C₂²×C₅	1	1	yes	characteristic
268	C₂×#108	C₂²×C₅	1	1	yes	characteristic
269	#427	C₂²×C₅	1	1	yes	characteristic
270	#427	C₂²×C₅	1	1	yes	characteristic
271	#424	—	2	1	no	—
272	#424	—	2	1	no	—
273	#424	C₂²×C₅	1	1	yes	characteristic
274	#424	C₂²×C₅	1	1	yes	characteristic
275	#424	C₂²×C₅	1	1	yes	characteristic
276	#424	C₂²×C₅	1	1	yes	characteristic
277	#423	—	2	1	no	—
278	#423	C₂²×C₅	1	1	yes	characteristic
279	C₂×C₄⋊C₈	—	2	1	no	—
280	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
281	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
282	C₂×#104	C₂²×C₅	1	1	yes	characteristic
283	C₂×#104	C₂²×C₅	1	1	yes	characteristic
284	#416	C₂²×C₅	1	1	yes	characteristic
285	#416	C₂²×C₅	1	1	yes	characteristic
286	#405	C₂²×C₅	1	1	yes	characteristic
287	#405	C₂²×C₅	1	1	yes	characteristic
288	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
289	C₂×#97	C₂²×C₅	1	1	yes	characteristic
290	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
291	#376	C₂²×C₅	1	1	yes	characteristic
292	#341	C₂²×C₅	1	1	yes	characteristic
293	#341	C₂²×C₅	1	1	yes	characteristic
294	#339	C₂²×C₅	1	1	yes	characteristic
295	#339	C₂²×C₅	1	1	yes	characteristic
296	#339	C₂²×C₅	1	1	yes	characteristic
297	#339	C₂²×C₅	1	1	yes	characteristic
298	#339	C₂²×C₅	1	1	yes	characteristic
299	#339	C₂²×C₅	1	1	yes	characteristic
300	#336	C₂²×C₅	1	1	yes	characteristic
301	#336	C₂²×C₅	1	1	yes	characteristic
302	C₂³×C₅	—	2	1	no	—
303	C₂³×C₅	C₂×#41	1	1	yes	characteristic
304	C₅×Q₈	—	2	1	no	—
305	C₅×Q₈	—	4	2	no	—
306	C₅×Q₈	—	8	1	no	—
307	C₅×Q₈	C₄×Q₈	1	2	yes	—
308	C₅×D₄	—	2	2	no	—
309	C₅×D₄	—	2	2	no	—
310	C₅×D₄	—	2	1	no	—
311	C₅×D₄	C₄×Q₈	1	2	yes	—
312	C₂×C₄×C₅	—	2	1	no	—
313	C₂×C₄×C₅	—	2	2	no	—
314	C₂×C₄×C₅	—	2	2	no	—
315	C₂×C₄×C₅	—	2	1	no	—
316	C₂×C₄×C₅	—	2	1	no	—
317	C₂×C₄×C₅	—	2	1	no	—
318	C₂×C₄×C₅	—	2	1	no	—
319	C₂×C₄×C₅	—	2	1	no	—
320	C₂×C₄×C₅	—	2	1	no	—
321	C₂×C₄×C₅	—	2	2	no	—
322	C₂×C₄×C₅	—	4	1	no	—
323	C₂×C₄×C₅	—	4	1	no	—
324	C₂×C₄×C₅	—	4	2	no	—
325	C₂×C₄×C₅	—	4	1	no	—
326	C₂×C₄×C₅	—	4	1	no	—
327	C₂×C₄×C₅	—	4	1	no	—
328	C₂×C₄×C₅	—	4	1	no	—
329	C₂×C₄×C₅	—	4	1	no	—
330	C₂×C₄×C₅	—	8	1	no	—
331	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
332	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
333	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
334	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
335	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
336	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
338	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
339	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
340	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
341	C₅×C₈	—	2	1	no	—
342	C₅×C₈	—	2	1	no	—
343	C₅×C₈	—	2	1	no	—
344	C₅×C₈	—	2	1	no	—
345	C₅×C₈	—	2	1	no	—
346	C₅×C₈	—	2	1	no	—
347	C₅×C₈	—	2	1	no	—
348	C₅×C₈	—	2	1	no	—
349	C₅×C₈	—	2	2	no	—
350	C₅×C₈	—	4	1	no	—
351	C₅×C₈	—	4	1	no	—
352	C₅×C₈	—	4	1	no	—
353	C₂×#41	C₂³×C₅	1	1	yes	characteristic
354	#131	—	2	2	no	—
355	#131	—	2	2	no	—
356	#131	—	4	1	no	—
357	#131	—	4	1	no	—
358	C₂×M₁₆	—	2	1	no	—
359	C₂×M₁₆	—	2	1	no	—
360	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
361	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
362	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
363	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
364	C₂²×C₈	—	2	1	no	—
365	C₂²×C₈	—	2	1	no	—
366	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
367	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
368	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
369	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
370	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
371	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
372	#125	C₂×C₄×C₅	1	1	yes	characteristic
373	#125	C₂×C₄×C₅	1	1	yes	characteristic
374	C₂²⋊Q₈	—	2	1	no	—
375	C₂²⋊Q₈	—	2	1	no	—
376	C₄×Q₈	—	2	1	no	—
377	C₄×Q₈	—	2	1	no	—
378	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
379	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
380	C₄×D₄	—	2	1	no	—
381	C₄×D₄	—	2	1	no	—
382	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
383	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
384	#117	—	2	1	no	—
385	#117	C₂³×C₅	1	1	yes	characteristic
386	#117	C₂³×C₅	1	1	yes	characteristic
387	#117	C₂³×C₅	1	1	yes	characteristic
388	C₂×C₄²	—	2	1	no	—
389	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
390	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
391	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
392	#108	—	4	1	no	—
393	#108	—	4	1	no	—
394	#107	C₂×C₄×C₅	1	1	yes	characteristic
395	#107	C₂×C₄×C₅	1	1	yes	characteristic
396	#107	C₂×C₄×C₅	1	1	yes	characteristic
397	#107	C₂×C₄×C₅	1	1	yes	characteristic
398	#106	C₂×C₄×C₅	1	1	yes	characteristic
399	#106	C₂×C₄×C₅	1	1	yes	characteristic
400	#106	C₂×C₄×C₅	1	1	yes	characteristic
401	#106	C₂×C₄×C₅	1	1	yes	characteristic
402	C₄⋊C₈	—	2	1	no	—
403	C₄⋊C₈	—	2	1	no	—
404	C₄⋊C₈	—	2	1	no	—
405	C₄⋊C₈	—	2	1	no	—
406	C₄⋊C₈	—	2	1	no	—
407	C₄⋊C₈	—	2	1	no	—
408	C₄⋊C₈	—	2	1	no	—
409	C₄⋊C₈	—	2	1	no	—
410	C₄⋊C₈	—	2	1	no	—
411	C₄⋊C₈	—	2	1	no	—
412	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
413	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
414	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
415	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
416	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
417	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
418	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
419	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
420	#104	—	2	2	no	—
421	#104	C₅×Q₈	1	4	yes	complemented
422	#103	C₂×C₄×C₅	1	1	yes	characteristic
423	#103	C₂×C₄×C₅	1	1	yes	characteristic
424	#103	C₂×C₄×C₅	1	1	yes	characteristic
425	#103	C₂×C₄×C₅	1	1	yes	characteristic
426	#102	C₂×C₄×C₅	1	1	yes	characteristic
427	#102	C₂×C₄×C₅	1	1	yes	characteristic
428	#102	C₂×C₄×C₅	1	1	yes	characteristic
429	#102	C₂×C₄×C₅	1	1	yes	characteristic
430	#97	—	2	1	no	—
431	#97	—	2	1	no	—
432	#97	—	2	1	no	—
433	#97	—	4	1	no	—
434	C₄×C₈	—	2	1	no	—
435	C₄×C₈	—	2	1	no	—
436	C₄×C₈	—	2	1	no	—
437	C₄×C₈	—	4	1	no	—
438	#95	—	2	1	no	—
439	#95	—	2	1	no	—
440	C₂²×C₅	—	2	1	no	—
441	C₂²×C₅	—	2	1	no	—
442	C₂²×C₅	—	2	2	no	—
443	C₂²×C₅	—	4	1	no	—
444	C₂²×C₅	—	4	1	no	—
445	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
446	C₂²×C₅	#552	1	1	yes	characteristic
447	C₂²×C₅	#554	1	1	yes	characteristic
448	C₄×C₅	—	2	2	no	—
449	C₄×C₅	—	2	1	no	—
450	C₄×C₅	—	2	1	no	—
451	C₄×C₅	—	2	1	no	—
452	C₄×C₅	—	2	1	no	—
453	C₄×C₅	—	4	2	no	—
454	C₄×C₅	—	4	1	no	—
455	C₄×C₅	—	4	1	no	—
456	C₄×C₅	—	4	1	no	—
457	C₄×C₅	—	4	1	no	—
458	C₄×C₅	—	4	1	no	—
459	C₄×C₅	—	4	1	no	—
460	C₄×C₅	—	8	1	no	—
461	C₄×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
462	C₄×C₅	#520	1	1	yes	characteristic
463	C₄×C₅	#546	1	1	yes	characteristic
464	C₄×C₅	D₄×Q₈	1	1	yes	characteristic
465	#41	—	2	1	no	—
466	#41	—	2	1	no	—
467	#41	C₂×C₅×Q₈	1	2	yes	—
468	#41	C₅×#41	1	2	yes	—
469	C₂×Q₈	—	2	1	no	—
470	C₂×Q₈	—	2	1	no	—
471	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
472	C₂×D₄	—	2	1	no	—
473	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	C₅×#41	1	1	yes	characteristic
480	C₂²×C₄	C₅×#41	1	1	yes	characteristic
481	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
482	M₁₆	—	2	1	no	—
483	M₁₆	—	2	1	no	—
484	M₁₆	—	2	1	no	—
485	M₁₆	—	2	1	no	—
486	M₁₆	—	2	1	no	—
487	M₁₆	—	2	1	no	—
488	M₁₆	—	2	1	no	—
489	M₁₆	—	4	2	no	—
490	M₁₆	—	4	2	no	—
491	M₁₆	C₂×C₅×Q₈	1	2	yes	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	2	1	no	—
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	2	1	no	—
500	C₂×C₈	—	2	1	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	4	2	no	—
505	C₂×C₈	—	4	2	no	—
506	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
507	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
508	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
509	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
510	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
511	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
512	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
513	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
523	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
524	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
525	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
526	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
527	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
528	C₂²⋊C₄	—	2	1	no	—
529	C₂²⋊C₄	—	2	1	no	—
530	C₂²⋊C₄	—	2	1	no	—
531	C₂²⋊C₄	—	2	1	no	—
532	C₂²⋊C₄	—	2	1	no	—
533	C₄²	—	2	1	no	—
534	C₄²	—	2	1	no	—
535	C₄²	—	2	1	no	—
536	C₄²	—	2	1	no	—
537	C₄²	—	2	1	no	—
538	C₄²	—	2	1	no	—
539	C₄²	—	2	1	no	—
540	C₄²	—	2	1	no	—
541	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
542	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
543	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
544	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
545	C₄²	C₂×C₅×Q₈	1	2	yes	—
546	C₂×C₅	—	2	1	no	—
547	C₂×C₅	—	2	1	no	—
548	C₂×C₅	—	4	2	no	—
549	C₂×C₅	#2360	1	1	yes	characteristic
550	C₂×C₅	#2955	1	1	yes	characteristic
551	C₂×C₅	#2957	1	1	yes	characteristic
552	C₂³	—	2	1	no	—
553	C₂³	C₂×C₅×#41	1	1	yes	characteristic
554	Q₈	—	2	1	no	—
555	Q₈	—	4	2	no	—
556	Q₈	—	8	1	no	—
557	Q₈	C₄×C₅×Q₈	1	2	yes	—
558	D₄	—	2	2	no	—
559	D₄	—	2	2	no	—
560	D₄	—	2	1	no	—
561	D₄	C₄×C₅×Q₈	1	2	yes	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	2	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	8	1	no	—
581	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
582	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
583	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
584	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
585	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
586	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
587	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
588	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
589	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
590	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
591	C₈	—	2	1	no	—
592	C₈	—	2	1	no	—
593	C₈	—	2	1	no	—
594	C₈	—	2	1	no	—
595	C₈	—	2	1	no	—
596	C₈	—	2	1	no	—
597	C₈	—	2	1	no	—
598	C₈	—	2	1	no	—
599	C₈	—	2	2	no	—
600	C₈	—	4	1	no	—
601	C₈	—	4	1	no	—
602	C₈	—	4	1	no	—
603	C₅	#22984	1	1	yes	characteristic, direct product factor, Sylow
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	4	1	no	—
608	C₂²	—	4	1	no	—
609	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
610	C₂²	C₅×#552	1	1	yes	characteristic
611	C₂²	C₅×#554	1	1	yes	characteristic
612	C₄	—	2	2	no	—
613	C₄	—	2	1	no	—
614	C₄	—	2	1	no	—
615	C₄	—	2	1	no	—
616	C₄	—	2	1	no	—
617	C₄	—	4	2	no	—
618	C₄	—	4	1	no	—
619	C₄	—	4	1	no	—
620	C₄	—	4	1	no	—
621	C₄	—	4	1	no	—
622	C₄	—	4	1	no	—
623	C₄	—	4	1	no	—
624	C₄	—	8	1	no	—
625	C₄	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
626	C₄	C₅×#520	1	1	yes	characteristic
627	C₄	C₅×#546	1	1	yes	characteristic
628	C₄	C₅×D₄×Q₈	1	1	yes	characteristic
629	C₂	—	2	1	no	—
630	C₂	—	2	1	no	—
631	C₂	—	4	2	no	—
632	C₂	C₅×#2360	1	1	yes	characteristic
633	C₂	C₅×#2955	1	1	yes	characteristic
634	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	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×#1995	C₂	semidirect
5. C₅×#1950	C₂	semidirect
6. C₅×#1946	C₂	semidirect
7. C₅×#1945	C₂	semidirect
8. C₅×#1922	C₂	semidirect
9. C₅×#1922	C₂	semidirect
12. C₅×#1768	C₂	semidirect
20. C₅×#479	C₄	semidirect
21. C₅×#479	C₄	semidirect
22. C₅×#478	C₄	semidirect
23. C₅×#478	C₄	semidirect
24. C₅×#477	C₄	semidirect
25. C₅×#476	C₄	semidirect
26. C₅×#475	C₄	semidirect
27. C₅×#474	C₄	semidirect
67. #22984	C₅	direct (N × H)
136. C₅×#104	Q₈	semidirect
156. #2962	C₂×C₅	semidirect
158. #1995	C₂×C₅	semidirect
159. #1950	C₂×C₅	semidirect
160. #1946	C₂×C₅	semidirect
161. #1945	C₂×C₅	semidirect
162. #1922	C₂×C₅	semidirect
163. #1922	C₂×C₅	semidirect
166. #1768	C₂×C₅	semidirect
255. #479	C₄×C₅	semidirect
256. #479	C₄×C₅	semidirect
257. #478	C₄×C₅	semidirect
258. #478	C₄×C₅	semidirect
259. #477	C₄×C₅	semidirect
260. #476	C₄×C₅	semidirect
261. #475	C₄×C₅	semidirect
262. #474	C₄×C₅	semidirect
421. #104	C₅×Q₈	semidirect
603. C₅	#22984	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×#2906	2
C₅×#1995	2
C₅×#1950	2
C₅×#1946	2
C₅×#1945	2
C₅×#1922	2
C₅×#1866	2
C₅×#1768	2
C₅×#1765	2
C₅×#1764	2
C₅×#1759	2
#22984	5

Subgroups — C5×#22984 #11945704

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22984 #11945704