Subgroups — C₅×#19915 #11942635

Order 1280.

660 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3366	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3335	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3330	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#3284	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1708	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1700	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1697	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1671	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1665	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1644	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1642	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1635	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1625	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1590	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×C₈×D₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#135	—	2	1	no	—
17	C₅×#554	C₂²	1	1	yes	characteristic
18	C₅×#550	C₂²	1	1	yes	characteristic
19	C₅×#547	C₂²	1	1	yes	characteristic
20	C₅×#547	C₂²	1	1	yes	characteristic
21	C₅×#498	C₂²	1	1	yes	characteristic
22	C₅×#492	C₂²	1	1	yes	characteristic
23	C₅×#490	—	2	1	no	—
24	C₅×#487	C₂²	1	1	yes	characteristic
25	C₅×#487	C₂²	1	1	yes	characteristic
26	C₅×#486	C₂²	1	1	yes	characteristic
27	C₅×#486	C₂²	1	1	yes	characteristic
28	C₅×#484	—	2	1	no	—
29	C₅×#483	—	2	1	no	—
30	C₅×#481	—	2	1	no	—
31	C₅×#478	—	2	1	no	—
32	C₅×#476	C₂²	1	1	yes	characteristic
33	C₅×#476	C₂²	1	1	yes	characteristic
34	C₅×#475	C₂²	1	1	yes	characteristic
35	C₅×#474	C₂²	1	1	yes	characteristic
36	C₅×#468	—	2	1	no	—
37	C₅×#465	—	2	1	no	—
38	C₅×#465	—	2	1	no	—
39	C₅×#462	C₂²	1	1	yes	characteristic
40	C₅×#461	C₂²	1	1	yes	characteristic
41	C₅×#459	—	2	1	no	—
42	C₅×#459	C₂²	1	1	yes	characteristic
43	C₅×#459	C₂²	1	1	yes	characteristic
44	C₅×#452	—	2	1	no	—
45	C₅×#449	—	2	1	no	—
46	C₅×#449	—	2	1	no	—
47	C₅×#446	C₂²	1	1	yes	characteristic
48	C₅×#442	—	2	1	no	—
49	C₄×C₅×SD₁₆	C₂²	1	1	yes	characteristic
50	C₄×C₅×D₈	C₂²	1	1	yes	characteristic
51	C₅×#436	C₂²	1	1	yes	characteristic
52	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
53	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
54	C₂×C₅×#106	—	2	1	no	—
55	C₅×#417	—	2	1	no	—
56	C₅×#335	C₂²	1	1	yes	characteristic
57	C₅×#334	C₂²	1	1	yes	characteristic
58	C₅×#333	C₂²	1	1	yes	characteristic
59	C₅×#332	C₂²	1	1	yes	characteristic
60	C₅×#332	C₂²	1	1	yes	characteristic
61	C₅×#331	C₂²	1	1	yes	characteristic
62	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
63	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
64	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₅×C₈²	C₂²	1	1	yes	characteristic
67	#19915	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂×C₅×#41	—	2	1	no	—
69	C₂×C₅×#41	—	2	1	no	—
70	C₂×C₅×#41	—	2	1	no	—
71	C₅×#135	—	4	4	no	—
72	C₂×C₅×Q₁₆	—	2	1	no	—
73	C₂×C₅×SD₁₆	—	2	1	no	—
74	C₂×C₅×SD₁₆	—	2	1	no	—
75	C₂×C₅×SD₁₆	—	2	1	no	—
76	C₂×C₅×SD₁₆	D₄	1	1	yes	characteristic
77	C₂×C₅×D₈	—	2	1	no	—
78	C₂×C₅×D₈	—	2	1	no	—
79	C₂×C₅×D₈	D₄	1	1	yes	characteristic
80	C₂×C₅×M₁₆	—	2	1	no	—
81	C₂²×C₅×C₈	—	2	1	no	—
82	C₂²×C₅×C₈	—	2	1	no	—
83	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
84	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
85	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₅×#127	—	2	1	no	—
87	C₅×#127	C₂³	1	1	yes	characteristic
88	C₅×#125	—	2	1	no	—
89	C₅×#123	—	4	1	no	—
90	C₅×#123	—	4	1	no	—
91	C₅×C₂²⋊Q₈	—	2	1	no	—
92	C₅×C₂²⋊Q₈	—	2	1	no	—
93	C₅×C₂²⋊Q₈	—	2	1	no	—
94	C₅×C₂²⋊Q₈	—	4	1	no	—
95	C₅×#121	—	2	1	no	—
96	C₅×#121	—	2	1	no	—
97	C₅×#121	—	2	1	no	—
98	C₅×#121	—	4	1	no	—
99	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
100	C₄×C₅×D₄	—	2	1	no	—
101	C₄×C₅×D₄	—	2	1	no	—
102	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
103	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
104	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
105	C₂×C₅×C₄⋊C₄	—	2	1	no	—
106	C₂×C₅×C₄⋊C₄	—	2	1	no	—
107	C₂×C₅×C₄⋊C₄	—	2	1	no	—
108	C₅×#107	—	2	1	no	—
109	C₅×#107	D₄	1	1	yes	characteristic
110	C₅×#106	—	2	1	no	—
111	C₅×#106	—	2	1	no	—
112	C₅×#106	—	2	1	no	—
113	C₅×#106	—	2	1	no	—
114	C₅×#106	—	2	1	no	—
115	C₅×#106	D₄	1	1	yes	characteristic
116	C₅×C₄⋊C₈	—	2	1	no	—
117	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
118	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
119	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
120	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
121	C₅×#103	—	2	1	no	—
122	C₅×#103	—	2	1	no	—
123	C₅×#103	—	2	1	no	—
124	C₅×#103	—	2	1	no	—
125	C₅×#103	—	2	1	no	—
126	C₅×#103	—	4	1	no	—
127	C₅×#103	D₄	1	1	yes	characteristic
128	C₅×#102	—	2	1	no	—
129	C₅×#102	—	2	1	no	—
130	C₅×#102	—	2	1	no	—
131	C₅×#102	—	2	1	no	—
132	C₅×#102	—	2	1	no	—
133	C₅×#102	—	2	1	no	—
134	C₅×#102	—	2	1	no	—
135	C₅×#102	—	4	1	no	—
136	C₅×#102	D₄	1	1	yes	characteristic
137	C₅×#102	D₄	1	1	yes	characteristic
138	C₅×#102	D₄	1	1	yes	characteristic
139	C₅×C₂²⋊C₈	—	2	1	no	—
140	C₅×C₂²⋊C₈	—	2	1	no	—
141	C₅×C₂²⋊C₈	—	2	1	no	—
142	C₅×#97	—	2	1	no	—
143	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
144	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
145	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
146	#3366	C₂×C₅	1	1	yes	characteristic, complemented
147	#3335	C₂×C₅	1	1	yes	characteristic, complemented
148	#3330	C₂×C₅	1	1	yes	characteristic, complemented
149	#3284	C₂×C₅	1	1	yes	characteristic, complemented
150	#1708	C₂×C₅	1	1	yes	characteristic, complemented
151	#1700	C₂×C₅	1	1	yes	characteristic, complemented
152	#1697	C₂×C₅	1	1	yes	characteristic, complemented
153	#1671	C₂×C₅	1	1	yes	characteristic, complemented
154	#1665	C₂×C₅	1	1	yes	characteristic, complemented
155	#1644	C₂×C₅	1	1	yes	characteristic, complemented
156	#1642	C₂×C₅	1	1	yes	characteristic, complemented
157	#1635	C₂×C₅	1	1	yes	characteristic, complemented
158	#1625	C₂×C₅	1	1	yes	characteristic, complemented
159	#1590	C₂×C₅	1	1	yes	characteristic, complemented
160	C₈×D₈	C₂×C₅	1	1	yes	characteristic, complemented
161	C₅×#41	—	4	2	no	—
162	C₅×#41	—	4	2	no	—
163	C₅×#41	—	4	2	no	—
164	C₅×#41	—	8	1	no	—
165	C₅×#41	—	8	1	no	—
166	C₅×#41	—	8	1	no	—
167	C₂×C₅×Q₈	—	2	1	no	—
168	C₂×C₅×Q₈	—	2	1	no	—
169	C₂×C₅×Q₈	—	2	1	no	—
170	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
171	C₂×C₅×D₄	—	2	1	no	—
172	C₂×C₅×D₄	—	2	1	no	—
173	C₂×C₅×D₄	—	2	1	no	—
174	C₂×C₅×D₄	—	4	1	no	—
175	C₂×C₅×D₄	—	4	1	no	—
176	C₂×C₅×D₄	—	4	1	no	—
177	C₂×C₅×D₄	—	4	1	no	—
178	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
179	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
180	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
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	—	4	1	no	—
185	C₂²×C₄×C₅	—	4	1	no	—
186	C₂²×C₄×C₅	—	4	1	no	—
187	C₂²×C₄×C₅	—	4	1	no	—
188	C₅×Q₁₆	—	4	2	no	—
189	C₅×SD₁₆	—	2	2	no	—
190	C₅×SD₁₆	—	4	2	no	—
191	C₅×SD₁₆	—	8	1	no	—
192	C₅×SD₁₆	—	8	1	no	—
193	C₅×D₈	—	2	2	no	—
194	C₅×D₈	—	4	2	no	—
195	C₅×D₈	—	4	2	no	—
196	C₅×M₁₆	—	8	1	no	—
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	—	4	2	no	—
203	C₂×C₅×C₈	—	4	2	no	—
204	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
205	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
206	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
207	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
208	C₅×C₄⋊C₄	—	2	1	no	—
209	C₅×C₄⋊C₄	—	2	1	no	—
210	C₅×C₄⋊C₄	—	2	1	no	—
211	C₅×C₄⋊C₄	—	2	1	no	—
212	C₅×C₄⋊C₄	—	2	1	no	—
213	C₅×C₄⋊C₄	—	2	1	no	—
214	C₅×C₄⋊C₄	—	2	1	no	—
215	C₅×C₄⋊C₄	—	4	1	no	—
216	C₅×C₄⋊C₄	—	4	1	no	—
217	C₅×C₄⋊C₄	—	4	1	no	—
218	C₅×C₄⋊C₄	—	4	1	no	—
219	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
220	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
221	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
222	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
223	C₅×C₂²⋊C₄	—	2	1	no	—
224	C₅×C₂²⋊C₄	—	2	1	no	—
225	C₅×C₂²⋊C₄	—	2	1	no	—
226	C₅×C₂²⋊C₄	—	4	1	no	—
227	C₅×C₂²⋊C₄	—	4	1	no	—
228	C₅×C₂²⋊C₄	—	4	1	no	—
229	C₅×C₂²⋊C₄	—	4	1	no	—
230	C₄²×C₅	—	2	1	no	—
231	C₄²×C₅	C₂⁴	1	1	yes	characteristic
232	C₂×#135	—	2	1	no	—
233	#554	C₂²×C₅	1	1	yes	characteristic
234	#550	C₂²×C₅	1	1	yes	characteristic
235	#547	C₂²×C₅	1	1	yes	characteristic
236	#547	C₂²×C₅	1	1	yes	characteristic
237	#498	C₂²×C₅	1	1	yes	characteristic
238	#492	C₂²×C₅	1	1	yes	characteristic
239	#490	—	2	1	no	—
240	#487	C₂²×C₅	1	1	yes	characteristic
241	#487	C₂²×C₅	1	1	yes	characteristic
242	#486	C₂²×C₅	1	1	yes	characteristic
243	#486	C₂²×C₅	1	1	yes	characteristic
244	#484	—	2	1	no	—
245	#483	—	2	1	no	—
246	#481	—	2	1	no	—
247	#478	—	2	1	no	—
248	#476	C₂²×C₅	1	1	yes	characteristic
249	#476	C₂²×C₅	1	1	yes	characteristic
250	#475	C₂²×C₅	1	1	yes	characteristic
251	#474	C₂²×C₅	1	1	yes	characteristic
252	#468	—	2	1	no	—
253	#465	—	2	1	no	—
254	#465	—	2	1	no	—
255	#462	C₂²×C₅	1	1	yes	characteristic
256	#461	C₂²×C₅	1	1	yes	characteristic
257	#459	—	2	1	no	—
258	#459	C₂²×C₅	1	1	yes	characteristic
259	#459	C₂²×C₅	1	1	yes	characteristic
260	#452	—	2	1	no	—
261	#449	—	2	1	no	—
262	#449	—	2	1	no	—
263	#446	C₂²×C₅	1	1	yes	characteristic
264	#442	—	2	1	no	—
265	C₄×SD₁₆	C₂²×C₅	1	1	yes	characteristic
266	C₄×D₈	C₂²×C₅	1	1	yes	characteristic
267	#436	C₂²×C₅	1	1	yes	characteristic
268	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
269	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
270	C₂×#106	—	2	1	no	—
271	#417	—	2	1	no	—
272	#335	C₂²×C₅	1	1	yes	characteristic
273	#334	C₂²×C₅	1	1	yes	characteristic
274	#333	C₂²×C₅	1	1	yes	characteristic
275	#332	C₂²×C₅	1	1	yes	characteristic
276	#332	C₂²×C₅	1	1	yes	characteristic
277	#331	C₂²×C₅	1	1	yes	characteristic
278	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
279	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
280	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
281	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
282	C₈²	C₂²×C₅	1	1	yes	characteristic
283	C₂³×C₅	—	2	1	no	—
284	C₂³×C₅	—	2	1	no	—
285	C₂³×C₅	—	2	1	no	—
286	C₂³×C₅	—	4	1	no	—
287	C₅×Q₈	—	2	1	no	—
288	C₅×Q₈	—	2	1	no	—
289	C₅×Q₈	—	4	1	no	—
290	C₅×Q₈	—	4	1	no	—
291	C₅×Q₈	—	4	1	no	—
292	C₅×Q₈	—	4	1	no	—
293	C₅×Q₈	—	8	1	no	—
294	C₅×D₄	—	2	1	no	—
295	C₅×D₄	—	2	1	no	—
296	C₅×D₄	—	2	1	no	—
297	C₅×D₄	—	2	1	no	—
298	C₅×D₄	—	2	1	no	—
299	C₅×D₄	—	4	1	no	—
300	C₅×D₄	—	4	1	no	—
301	C₅×D₄	—	4	1	no	—
302	C₅×D₄	—	4	1	no	—
303	C₅×D₄	—	8	1	no	—
304	C₅×D₄	—	8	2	no	—
305	C₅×D₄	—	8	2	no	—
306	C₅×D₄	—	8	2	no	—
307	C₅×D₄	—	16	1	no	—
308	C₅×D₄	#135	1	2	yes	complemented
309	C₂×C₄×C₅	—	2	1	no	—
310	C₂×C₄×C₅	—	2	1	no	—
311	C₂×C₄×C₅	—	2	1	no	—
312	C₂×C₄×C₅	—	2	1	no	—
313	C₂×C₄×C₅	—	2	1	no	—
314	C₂×C₄×C₅	—	4	1	no	—
315	C₂×C₄×C₅	—	4	1	no	—
316	C₂×C₄×C₅	—	4	1	no	—
317	C₂×C₄×C₅	—	4	1	no	—
318	C₂×C₄×C₅	—	4	1	no	—
319	C₂×C₄×C₅	—	4	1	no	—
320	C₂×C₄×C₅	—	4	1	no	—
321	C₂×C₄×C₅	—	4	1	no	—
322	C₂×C₄×C₅	—	4	1	no	—
323	C₂×C₄×C₅	—	8	2	no	—
324	C₂×C₄×C₅	—	8	2	no	—
325	C₂×C₄×C₅	—	8	2	no	—
326	C₂×C₄×C₅	—	16	1	no	—
327	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
330	C₅×C₈	—	2	1	no	—
331	C₅×C₈	—	2	1	no	—
332	C₅×C₈	—	2	1	no	—
333	C₅×C₈	—	4	1	no	—
334	C₅×C₈	—	4	1	no	—
335	C₅×C₈	—	4	1	no	—
336	C₅×C₈	—	4	1	no	—
337	C₅×C₈	—	4	1	no	—
338	C₅×C₈	AGL(1,ℤ/8)	1	2	yes	—
339	C₂×#41	—	2	1	no	—
340	C₂×#41	—	2	1	no	—
341	C₂×#41	—	2	1	no	—
342	#135	—	4	4	no	—
343	C₂×Q₁₆	—	2	1	no	—
344	C₂×SD₁₆	—	2	1	no	—
345	C₂×SD₁₆	—	2	1	no	—
346	C₂×SD₁₆	—	2	1	no	—
347	C₂×SD₁₆	C₅×D₄	1	1	yes	characteristic
348	C₂×D₈	—	2	1	no	—
349	C₂×D₈	—	2	1	no	—
350	C₂×D₈	C₅×D₄	1	1	yes	characteristic
351	C₂×M₁₆	—	2	1	no	—
352	C₂²×C₈	—	2	1	no	—
353	C₂²×C₈	—	2	1	no	—
354	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
355	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
356	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
357	#127	—	2	1	no	—
358	#127	C₂³×C₅	1	1	yes	characteristic
359	#125	—	2	1	no	—
360	#123	—	4	1	no	—
361	#123	—	4	1	no	—
362	C₂²⋊Q₈	—	2	1	no	—
363	C₂²⋊Q₈	—	2	1	no	—
364	C₂²⋊Q₈	—	2	1	no	—
365	C₂²⋊Q₈	—	4	1	no	—
366	#121	—	2	1	no	—
367	#121	—	2	1	no	—
368	#121	—	2	1	no	—
369	#121	—	4	1	no	—
370	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
371	C₄×D₄	—	2	1	no	—
372	C₄×D₄	—	2	1	no	—
373	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
374	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
375	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
376	C₂×C₄⋊C₄	—	2	1	no	—
377	C₂×C₄⋊C₄	—	2	1	no	—
378	C₂×C₄⋊C₄	—	2	1	no	—
379	#107	—	2	1	no	—
380	#107	C₅×D₄	1	1	yes	characteristic
381	#106	—	2	1	no	—
382	#106	—	2	1	no	—
383	#106	—	2	1	no	—
384	#106	—	2	1	no	—
385	#106	—	2	1	no	—
386	#106	C₅×D₄	1	1	yes	characteristic
387	C₄⋊C₈	—	2	1	no	—
388	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
389	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
390	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
391	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
392	#103	—	2	1	no	—
393	#103	—	2	1	no	—
394	#103	—	2	1	no	—
395	#103	—	2	1	no	—
396	#103	—	2	1	no	—
397	#103	—	4	1	no	—
398	#103	C₅×D₄	1	1	yes	characteristic
399	#102	—	2	1	no	—
400	#102	—	2	1	no	—
401	#102	—	2	1	no	—
402	#102	—	2	1	no	—
403	#102	—	2	1	no	—
404	#102	—	2	1	no	—
405	#102	—	2	1	no	—
406	#102	—	4	1	no	—
407	#102	C₅×D₄	1	1	yes	characteristic
408	#102	C₅×D₄	1	1	yes	characteristic
409	#102	C₅×D₄	1	1	yes	characteristic
410	C₂²⋊C₈	—	2	1	no	—
411	C₂²⋊C₈	—	2	1	no	—
412	C₂²⋊C₈	—	2	1	no	—
413	#97	—	2	1	no	—
414	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
415	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
416	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
417	C₂²×C₅	—	2	2	no	—
418	C₂²×C₅	—	4	1	no	—
419	C₂²×C₅	—	4	1	no	—
420	C₂²×C₅	—	4	1	no	—
421	C₂²×C₅	—	4	1	no	—
422	C₂²×C₅	—	4	1	no	—
423	C₂²×C₅	—	4	1	no	—
424	C₂²×C₅	—	4	1	no	—
425	C₂²×C₅	—	4	1	no	—
426	C₂²×C₅	—	8	1	no	—
427	C₂²×C₅	—	8	1	no	—
428	C₂²×C₅	—	8	1	no	—
429	C₂²×C₅	D₄²	1	1	yes	characteristic
430	C₄×C₅	—	2	1	no	—
431	C₄×C₅	—	4	1	no	—
432	C₄×C₅	—	4	1	no	—
433	C₄×C₅	—	4	1	no	—
434	C₄×C₅	—	4	1	no	—
435	C₄×C₅	—	4	1	no	—
436	C₄×C₅	—	8	1	no	—
437	C₄×C₅	—	8	1	no	—
438	C₄×C₅	—	8	1	no	—
439	C₄×C₅	C₂×#135	1	1	yes	characteristic
440	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
441	C₄×C₅	#577	1	1	yes	characteristic
442	C₄×C₅	#577	1	1	yes	characteristic
443	#41	—	4	2	no	—
444	#41	—	4	2	no	—
445	#41	—	4	2	no	—
446	#41	—	8	1	no	—
447	#41	—	8	1	no	—
448	#41	—	8	1	no	—
449	C₂×Q₈	—	2	1	no	—
450	C₂×Q₈	—	2	1	no	—
451	C₂×Q₈	—	2	1	no	—
452	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	4	1	no	—
457	C₂×D₄	—	4	1	no	—
458	C₂×D₄	—	4	1	no	—
459	C₂×D₄	—	4	1	no	—
460	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
461	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
462	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	4	1	no	—
467	C₂²×C₄	—	4	1	no	—
468	C₂²×C₄	—	4	1	no	—
469	C₂²×C₄	—	4	1	no	—
470	Q₁₆	—	4	2	no	—
471	SD₁₆	—	2	2	no	—
472	SD₁₆	—	4	2	no	—
473	SD₁₆	—	8	1	no	—
474	SD₁₆	—	8	1	no	—
475	D₈	—	2	2	no	—
476	D₈	—	4	2	no	—
477	D₈	—	4	2	no	—
478	M₁₆	—	8	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	4	2	no	—
485	C₂×C₈	—	4	2	no	—
486	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
487	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
488	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
489	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	4	1	no	—
498	C₄⋊C₄	—	4	1	no	—
499	C₄⋊C₄	—	4	1	no	—
500	C₄⋊C₄	—	4	1	no	—
501	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
502	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
503	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
504	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
505	C₂²⋊C₄	—	2	1	no	—
506	C₂²⋊C₄	—	2	1	no	—
507	C₂²⋊C₄	—	2	1	no	—
508	C₂²⋊C₄	—	4	1	no	—
509	C₂²⋊C₄	—	4	1	no	—
510	C₂²⋊C₄	—	4	1	no	—
511	C₂²⋊C₄	—	4	1	no	—
512	C₄²	—	2	1	no	—
513	C₄²	C₂⁴×C₅	1	1	yes	characteristic
514	C₂×C₅	—	4	2	no	—
515	C₂×C₅	—	8	1	no	—
516	C₂×C₅	—	8	1	no	—
517	C₂×C₅	—	16	1	no	—
518	C₂×C₅	#3272	1	1	yes	characteristic
519	C₂×C₅	#3282	1	1	yes	characteristic
520	C₂×C₅	#3290	1	1	yes	characteristic
521	C₂³	—	2	1	no	—
522	C₂³	—	2	1	no	—
523	C₂³	—	2	1	no	—
524	C₂³	—	4	1	no	—
525	Q₈	—	2	1	no	—
526	Q₈	—	2	1	no	—
527	Q₈	—	4	1	no	—
528	Q₈	—	4	1	no	—
529	Q₈	—	4	1	no	—
530	Q₈	—	4	1	no	—
531	Q₈	—	8	1	no	—
532	D₄	—	2	1	no	—
533	D₄	—	2	1	no	—
534	D₄	—	2	1	no	—
535	D₄	—	2	1	no	—
536	D₄	—	2	1	no	—
537	D₄	—	4	1	no	—
538	D₄	—	4	1	no	—
539	D₄	—	4	1	no	—
540	D₄	—	4	1	no	—
541	D₄	—	8	1	no	—
542	D₄	—	8	2	no	—
543	D₄	—	8	2	no	—
544	D₄	—	8	2	no	—
545	D₄	—	16	1	no	—
546	D₄	C₅×#135	1	2	yes	complemented
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	8	2	no	—
562	C₂×C₄	—	8	2	no	—
563	C₂×C₄	—	8	2	no	—
564	C₂×C₄	—	16	1	no	—
565	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
566	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
567	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
568	C₈	—	2	1	no	—
569	C₈	—	2	1	no	—
570	C₈	—	2	1	no	—
571	C₈	—	4	1	no	—
572	C₈	—	4	1	no	—
573	C₈	—	4	1	no	—
574	C₈	—	4	1	no	—
575	C₈	—	4	1	no	—
576	C₈	C₅×AGL(1,ℤ/8)	1	2	yes	—
577	C₅	#19915	1	1	yes	characteristic, direct product factor, Sylow
578	C₂²	—	2	2	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	8	1	no	—
588	C₂²	—	8	1	no	—
589	C₂²	—	8	1	no	—
590	C₂²	C₅×D₄²	1	1	yes	characteristic
591	C₄	—	2	1	no	—
592	C₄	—	4	1	no	—
593	C₄	—	4	1	no	—
594	C₄	—	4	1	no	—
595	C₄	—	4	1	no	—
596	C₄	—	4	1	no	—
597	C₄	—	8	1	no	—
598	C₄	—	8	1	no	—
599	C₄	—	8	1	no	—
600	C₄	C₂×C₅×#135	1	1	yes	characteristic
601	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
602	C₄	C₅×#577	1	1	yes	characteristic
603	C₄	C₅×#577	1	1	yes	characteristic
604	C₂	—	4	2	no	—
605	C₂	—	8	1	no	—
606	C₂	—	8	1	no	—
607	C₂	—	16	1	no	—
608	C₂	C₅×#3272	1	1	yes	characteristic
609	C₂	C₅×#3282	1	1	yes	characteristic
610	C₂	C₅×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3366	C₂	semidirect
2. C₅×#3335	C₂	semidirect
3. C₅×#3330	C₂	semidirect
4. C₅×#3284	C₂	semidirect
5. C₅×#1708	C₂	semidirect
6. C₅×#1700	C₂	semidirect
7. C₅×#1697	C₂	semidirect
8. C₅×#1671	C₂	semidirect
9. C₅×#1665	C₂	semidirect
10. C₅×#1644	C₂	semidirect
11. C₅×#1642	C₂	semidirect
12. C₅×#1635	C₂	semidirect
13. C₅×#1625	C₂	semidirect
14. C₅×#1590	C₂	semidirect
15. C₅×C₈×D₈	C₂	semidirect
67. #19915	C₅	direct (N × H)
146. #3366	C₂×C₅	semidirect
147. #3335	C₂×C₅	semidirect
148. #3330	C₂×C₅	semidirect
149. #3284	C₂×C₅	semidirect
150. #1708	C₂×C₅	semidirect
151. #1700	C₂×C₅	semidirect
152. #1697	C₂×C₅	semidirect
153. #1671	C₂×C₅	semidirect
154. #1665	C₂×C₅	semidirect
155. #1644	C₂×C₅	semidirect
156. #1642	C₂×C₅	semidirect
157. #1635	C₂×C₅	semidirect
158. #1625	C₂×C₅	semidirect
159. #1590	C₂×C₅	semidirect
160. C₈×D₈	C₂×C₅	semidirect
308. C₅×D₄	#135	semidirect
546. D₄	C₅×#135	semidirect
577. C₅	#19915	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×#3366	2
C₅×#3335	2
C₅×#3330	2
C₅×#3284	2
C₅×#1708	2
C₅×#1700	2
C₅×#1697	2
C₅×#1671	2
C₅×#1665	2
C₅×#1644	2
C₅×#1642	2
C₅×#1635	2
C₅×#1625	2
C₅×#1590	2
C₅×C₈×D₈	2
#19915	5

Subgroups — C5×#19915 #11942635

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19915 #11942635