Subgroups — C₅×#17760 #11940480

Order 1280.

896 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3503	C₂	1	1	yes	maximal, characteristic
2	C₅×#2989	C₂	1	1	yes	maximal, characteristic
3	C₅×#2925	C₂	1	1	yes	maximal, characteristic
4	C₅×#1559	C₂	1	2	yes	maximal, complemented
5	C₅×#1558	C₂	1	2	yes	maximal, complemented
6	C₅×#1554	C₂	1	2	yes	maximal, complemented
7	C₅×#1550	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1548	C₂	1	2	yes	maximal, complemented
9	C₅×#1548	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1542	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#333	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×Q₈²	—	2	1	no	—
13	C₅×#557	C₄	1	2	yes	—
14	C₅×#554	—	2	2	no	—
15	C₅×#554	—	2	1	no	—
16	C₅×D₄×Q₈	C₄	1	2	yes	—
17	C₅×D₄×Q₈	C₄	1	4	yes	—
18	C₅×#544	—	2	1	no	—
19	C₅×#544	—	2	2	no	—
20	C₅×#533	C₂²	1	1	yes	characteristic
21	C₅×#533	C₂²	1	2	yes	—
22	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
24	C₅×#520	—	2	1	no	—
25	C₄×C₅×#41	C₂²	1	1	yes	characteristic
26	C₅×#446	—	2	1	no	—
27	C₅×#436	—	2	1	no	—
28	C₅×#435	—	2	2	no	—
29	C₅×#433	—	2	2	no	—
30	C₅×#432	C₂²	1	2	yes	—
31	C₅×#432	C₂²	1	2	yes	—
32	C₅×#431	C₂²	1	1	yes	characteristic
33	C₅×#431	C₂²	1	2	yes	—
34	C₅×#423	C₂²	1	2	yes	—
35	C₅×#423	C₂²	1	1	yes	characteristic
36	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₅×#408	—	2	1	no	—
39	C₅×#405	—	2	1	no	—
40	C₅×#333	C₂²	1	2	yes	—
41	C₅×#333	C₂²	1	2	yes	—
42	C₅×#333	C₂²	1	1	yes	characteristic
43	C₅×#333	C₂²	1	1	yes	characteristic
44	C₅×#333	C₂²	1	2	yes	—
45	C₅×#333	C₂²	1	2	yes	—
46	C₅×#333	C₂²	1	2	yes	—
47	C₅×#332	C₂²	1	1	yes	characteristic
48	C₅×#332	C₂²	1	1	yes	characteristic
49	C₅×#332	C₂²	1	2	yes	—
50	#17760	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
51	C₂×C₅×#41	D₄	1	1	yes	characteristic
52	C₂²×C₅×Q₈	C₂×C₄	1	2	yes	—
53	C₂²×C₅×Q₈	C₂×C₄	1	4	yes	—
54	C₂×C₅×M₁₆	—	2	1	no	—
55	C₂×C₅×M₁₆	—	2	2	no	—
56	C₂²×C₅×C₈	—	2	1	no	—
57	C₂²×C₅×C₈	—	2	1	no	—
58	C₅×C₄⋊Q₈	—	2	4	no	—
59	C₅×C₄⋊Q₈	—	2	2	no	—
60	C₅×C₄⋊Q₈	—	2	2	no	—
61	C₅×C₄⋊Q₈	—	2	1	no	—
62	C₅×C₄⋊Q₈	—	2	1	no	—
63	C₅×C₄⋊Q₈	—	2	2	no	—
64	C₅×C₄⋊Q₈	C₂×C₄	1	2	yes	—
65	C₅×C₄⋊Q₈	C₂×C₄	1	4	yes	—
66	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
67	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
68	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
69	C₅×#125	—	2	4	no	—
70	C₅×#125	—	2	2	no	—
71	C₅×#125	—	2	2	no	—
72	C₅×#125	—	2	1	no	—
73	C₅×C₂²⋊Q₈	—	2	1	no	—
74	C₅×C₂²⋊Q₈	—	2	2	no	—
75	C₅×C₂²⋊Q₈	—	2	4	no	—
76	C₅×C₂²⋊Q₈	—	2	4	no	—
77	C₅×C₂²⋊Q₈	—	2	4	no	—
78	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
79	C₅×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
80	C₄×C₅×Q₈	—	2	2	no	—
81	C₄×C₅×Q₈	—	2	1	no	—
82	C₄×C₅×Q₈	—	2	2	no	—
83	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
84	C₄×C₅×Q₈	C₂×C₄	1	4	yes	—
85	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
86	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
87	C₄×C₅×D₄	—	2	4	no	—
88	C₄×C₅×D₄	—	2	2	no	—
89	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
90	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
91	C₄×C₅×D₄	D₄	1	2	yes	—
92	C₄×C₅×D₄	D₄	1	1	yes	characteristic
93	C₅×#117	—	2	2	no	—
94	C₅×#117	—	2	1	no	—
95	C₅×#117	D₄	1	1	yes	characteristic
96	C₅×#117	D₄	1	2	yes	—
97	C₂×C₅×C₄⋊C₄	—	2	2	no	—
98	C₂×C₅×C₄⋊C₄	—	2	1	no	—
99	C₂×C₅×C₄⋊C₄	—	2	1	no	—
100	C₂×C₅×C₄⋊C₄	—	2	2	no	—
101	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₅	C₂³	1	2	yes	—
103	C₅×C₄⋊C₈	—	2	1	no	—
104	C₅×C₄⋊C₈	—	2	1	no	—
105	C₅×C₄⋊C₈	—	2	1	no	—
106	C₅×C₄⋊C₈	—	2	2	no	—
107	C₅×C₄⋊C₈	C₂³	1	2	yes	—
108	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
109	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
110	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
111	C₅×C₄⋊C₈	C₂³	1	2	yes	—
112	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
113	C₅×C₂²⋊C₈	—	2	2	no	—
114	C₅×C₂²⋊C₈	—	2	2	no	—
115	C₅×C₂²⋊C₈	—	2	1	no	—
116	C₅×C₂²⋊C₈	—	2	2	no	—
117	C₅×#97	—	2	2	no	—
118	C₅×#97	—	2	2	no	—
119	C₄×C₅×C₈	—	2	2	no	—
120	C₄×C₅×C₈	—	2	1	no	—
121	#3503	C₂×C₅	1	1	yes	characteristic
122	#2989	C₂×C₅	1	1	yes	characteristic
123	#2925	C₂×C₅	1	1	yes	characteristic
124	#1559	C₂×C₅	1	2	yes	complemented
125	#1558	C₂×C₅	1	2	yes	complemented
126	#1554	C₂×C₅	1	2	yes	complemented
127	#1550	C₂×C₅	1	1	yes	characteristic, complemented
128	#1548	C₂×C₅	1	1	yes	characteristic, complemented
129	#1548	C₂×C₅	1	2	yes	complemented
130	#1542	C₂×C₅	1	1	yes	characteristic, complemented
131	C₂×#333	C₂×C₅	1	1	yes	characteristic, complemented
132	C₅×#41	—	2	2	no	—
133	C₅×#41	—	2	2	no	—
134	C₂×C₅×Q₈	—	2	4	no	—
135	C₂×C₅×Q₈	—	2	2	no	—
136	C₂×C₅×Q₈	—	2	1	no	—
137	C₂×C₅×Q₈	—	8	2	no	—
138	C₂×C₅×Q₈	—	8	4	no	—
139	C₂×C₅×Q₈	C₂²⋊C₄	1	1	yes	characteristic
140	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
141	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
142	C₂×C₅×D₄	C₂²⋊C₄	1	2	yes	—
143	C₂×C₅×D₄	C₂²⋊C₄	1	1	yes	characteristic
144	C₂²×C₄×C₅	—	2	4	no	—
145	C₂²×C₄×C₅	—	2	2	no	—
146	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
147	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
149	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
151	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
152	C₅×M₁₆	—	4	2	no	—
153	C₅×M₁₆	—	8	2	no	—
154	C₂×C₅×C₈	—	2	2	no	—
155	C₂×C₅×C₈	—	2	1	no	—
156	C₂×C₅×C₈	—	2	1	no	—
157	C₂×C₅×C₈	—	2	1	no	—
158	C₂×C₅×C₈	—	2	2	no	—
159	C₂×C₅×C₈	—	2	1	no	—
160	C₂×C₅×C₈	—	4	2	no	—
161	C₂×C₅×C₈	—	8	1	no	—
162	C₅×C₄⋊C₄	—	2	4	no	—
163	C₅×C₄⋊C₄	—	2	2	no	—
164	C₅×C₄⋊C₄	—	2	4	no	—
165	C₅×C₄⋊C₄	—	2	2	no	—
166	C₅×C₄⋊C₄	—	2	4	no	—
167	C₅×C₄⋊C₄	—	2	2	no	—
168	C₅×C₄⋊C₄	—	2	4	no	—
169	C₅×C₄⋊C₄	—	2	2	no	—
170	C₅×C₄⋊C₄	—	2	1	no	—
171	C₅×C₄⋊C₄	—	2	2	no	—
172	C₅×C₄⋊C₄	—	2	2	no	—
173	C₅×C₄⋊C₄	—	2	1	no	—
174	C₅×C₄⋊C₄	—	2	1	no	—
175	C₅×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
176	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
177	C₅×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
178	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
179	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
180	C₅×C₂²⋊C₄	—	2	4	no	—
181	C₅×C₂²⋊C₄	—	2	2	no	—
182	C₅×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
183	C₅×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
184	C₅×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
185	C₄²×C₅	—	2	4	no	—
186	C₄²×C₅	—	2	2	no	—
187	C₄²×C₅	C₂²×C₄	1	2	yes	—
188	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
189	C₄²×C₅	C₂×D₄	1	2	yes	—
190	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
191	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
192	C₄²×C₅	C₂×D₄	1	2	yes	—
193	C₄²×C₅	C₂⁴	1	1	yes	characteristic
194	Q₈²	—	2	1	no	—
195	#557	C₄×C₅	1	2	yes	—
196	#554	—	2	2	no	—
197	#554	—	2	1	no	—
198	D₄×Q₈	C₄×C₅	1	2	yes	—
199	D₄×Q₈	C₄×C₅	1	4	yes	—
200	#544	—	2	1	no	—
201	#544	—	2	2	no	—
202	#533	C₂²×C₅	1	1	yes	characteristic
203	#533	C₂²×C₅	1	2	yes	—
204	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
205	C₂×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
206	#520	—	2	1	no	—
207	C₄×#41	C₂²×C₅	1	1	yes	characteristic
208	#446	—	2	1	no	—
209	#436	—	2	1	no	—
210	#435	—	2	2	no	—
211	#433	—	2	2	no	—
212	#432	C₂²×C₅	1	2	yes	—
213	#432	C₂²×C₅	1	2	yes	—
214	#431	C₂²×C₅	1	1	yes	characteristic
215	#431	C₂²×C₅	1	2	yes	—
216	#423	C₂²×C₅	1	1	yes	characteristic
217	#423	C₂²×C₅	1	2	yes	—
218	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
219	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
220	#408	—	2	1	no	—
221	#405	—	2	1	no	—
222	#333	C₂²×C₅	1	2	yes	—
223	#333	C₂²×C₅	1	2	yes	—
224	#333	C₂²×C₅	1	1	yes	characteristic
225	#333	C₂²×C₅	1	1	yes	characteristic
226	#333	C₂²×C₅	1	2	yes	—
227	#333	C₂²×C₅	1	2	yes	—
228	#333	C₂²×C₅	1	2	yes	—
229	#332	C₂²×C₅	1	1	yes	characteristic
230	#332	C₂²×C₅	1	1	yes	characteristic
231	#332	C₂²×C₅	1	2	yes	—
232	C₂³×C₅	C₂×C₂²⋊C₄	1	2	yes	—
233	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
234	C₅×Q₈	—	2	2	no	—
235	C₅×Q₈	—	4	4	no	—
236	C₅×Q₈	—	4	2	no	—
237	C₅×Q₈	—	4	1	no	—
238	C₅×Q₈	—	4	1	no	—
239	C₅×Q₈	—	8	2	no	—
240	C₅×Q₈	—	8	4	no	—
241	C₅×D₄	—	2	4	no	—
242	C₅×D₄	—	2	2	no	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	—	2	2	no	—
245	C₂×C₄×C₅	—	2	1	no	—
246	C₂×C₄×C₅	—	2	2	no	—
247	C₂×C₄×C₅	—	2	1	no	—
248	C₂×C₄×C₅	—	2	2	no	—
249	C₂×C₄×C₅	—	2	2	no	—
250	C₂×C₄×C₅	—	2	4	no	—
251	C₂×C₄×C₅	—	2	2	no	—
252	C₂×C₄×C₅	—	4	1	no	—
253	C₂×C₄×C₅	—	4	2	no	—
254	C₂×C₄×C₅	—	8	2	no	—
255	C₂×C₄×C₅	—	8	4	no	—
256	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
257	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
258	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
259	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
260	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
261	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
262	C₂×C₄×C₅	#137	1	2	yes	—
263	C₂×C₄×C₅	#137	1	2	yes	—
264	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
265	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
267	C₅×C₈	—	4	1	no	—
268	C₅×C₈	—	4	1	no	—
269	C₅×C₈	—	4	2	no	—
270	C₅×C₈	—	4	2	no	—
271	C₅×C₈	—	4	1	no	—
272	C₅×C₈	—	4	1	no	—
273	C₂×#41	C₅×D₄	1	1	yes	characteristic
274	C₂²×Q₈	C₂×C₄×C₅	1	2	yes	—
275	C₂²×Q₈	C₂×C₄×C₅	1	4	yes	—
276	C₂×M₁₆	—	2	1	no	—
277	C₂×M₁₆	—	2	2	no	—
278	C₂²×C₈	—	2	1	no	—
279	C₂²×C₈	—	2	1	no	—
280	C₄⋊Q₈	—	2	4	no	—
281	C₄⋊Q₈	—	2	2	no	—
282	C₄⋊Q₈	—	2	2	no	—
283	C₄⋊Q₈	—	2	1	no	—
284	C₄⋊Q₈	—	2	1	no	—
285	C₄⋊Q₈	—	2	2	no	—
286	C₄⋊Q₈	C₂×C₄×C₅	1	2	yes	—
287	C₄⋊Q₈	C₂×C₄×C₅	1	4	yes	—
288	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
289	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
290	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
291	#125	—	2	4	no	—
292	#125	—	2	2	no	—
293	#125	—	2	2	no	—
294	#125	—	2	1	no	—
295	C₂²⋊Q₈	—	2	1	no	—
296	C₂²⋊Q₈	—	2	2	no	—
297	C₂²⋊Q₈	—	2	4	no	—
298	C₂²⋊Q₈	—	2	4	no	—
299	C₂²⋊Q₈	—	2	4	no	—
300	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
301	C₂²⋊Q₈	C₂×C₄×C₅	1	4	yes	—
302	C₄×Q₈	—	2	2	no	—
303	C₄×Q₈	—	2	1	no	—
304	C₄×Q₈	—	2	2	no	—
305	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
306	C₄×Q₈	C₂×C₄×C₅	1	4	yes	—
307	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
308	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
309	C₄×D₄	—	2	4	no	—
310	C₄×D₄	—	2	2	no	—
311	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
312	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
313	C₄×D₄	C₅×D₄	1	2	yes	—
314	C₄×D₄	C₅×D₄	1	1	yes	characteristic
315	#117	—	2	2	no	—
316	#117	—	2	1	no	—
317	#117	C₅×D₄	1	1	yes	characteristic
318	#117	C₅×D₄	1	2	yes	—
319	C₂×C₄⋊C₄	—	2	2	no	—
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄⋊C₄	—	2	1	no	—
322	C₂×C₄⋊C₄	—	2	2	no	—
323	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
324	C₂×C₄²	C₂³×C₅	1	2	yes	—
325	C₄⋊C₈	—	2	1	no	—
326	C₄⋊C₈	—	2	1	no	—
327	C₄⋊C₈	—	2	1	no	—
328	C₄⋊C₈	—	2	2	no	—
329	C₄⋊C₈	C₂³×C₅	1	2	yes	—
330	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
331	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
332	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
333	C₄⋊C₈	C₂³×C₅	1	2	yes	—
334	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
335	C₂²⋊C₈	—	2	2	no	—
336	C₂²⋊C₈	—	2	2	no	—
337	C₂²⋊C₈	—	2	1	no	—
338	C₂²⋊C₈	—	2	2	no	—
339	#97	—	2	2	no	—
340	#97	—	2	2	no	—
341	C₄×C₈	—	2	2	no	—
342	C₄×C₈	—	2	1	no	—
343	C₂²×C₅	—	2	1	no	—
344	C₂²×C₅	—	2	1	no	—
345	C₂²×C₅	—	2	2	no	—
346	C₂²×C₅	—	2	2	no	—
347	C₂²×C₅	—	2	2	no	—
348	C₂²×C₅	#419	1	2	yes	—
349	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
350	C₄×C₅	—	2	1	no	—
351	C₄×C₅	—	2	1	no	—
352	C₄×C₅	—	2	2	no	—
353	C₄×C₅	—	2	2	no	—
354	C₄×C₅	—	2	1	no	—
355	C₄×C₅	—	2	2	no	—
356	C₄×C₅	—	4	4	no	—
357	C₄×C₅	—	4	2	no	—
358	C₄×C₅	—	4	2	no	—
359	C₄×C₅	#419	1	2	yes	—
360	C₄×C₅	C₂×#137	1	1	yes	characteristic
361	C₄×C₅	C₂×#137	1	1	yes	characteristic
362	C₄×C₅	#577	1	1	yes	characteristic
363	C₄×C₅	#578	1	1	yes	characteristic
364	#41	—	2	2	no	—
365	#41	—	2	2	no	—
366	C₂×Q₈	—	2	4	no	—
367	C₂×Q₈	—	2	2	no	—
368	C₂×Q₈	—	2	1	no	—
369	C₂×Q₈	—	8	2	no	—
370	C₂×Q₈	—	8	4	no	—
371	C₂×Q₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
372	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
373	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
374	C₂×D₄	C₅×C₂²⋊C₄	1	2	yes	—
375	C₂×D₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
376	C₂²×C₄	—	2	4	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
379	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
380	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
381	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
382	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
383	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
384	M₁₆	—	4	2	no	—
385	M₁₆	—	8	2	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	4	2	no	—
393	C₂×C₈	—	8	1	no	—
394	C₄⋊C₄	—	2	4	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	4	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	4	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	4	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
408	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
409	C₄⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
410	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
411	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
412	C₂²⋊C₄	—	2	4	no	—
413	C₂²⋊C₄	—	2	2	no	—
414	C₂²⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
415	C₂²⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
416	C₂²⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
417	C₄²	—	2	4	no	—
418	C₄²	—	2	2	no	—
419	C₄²	C₂²×C₄×C₅	1	2	yes	—
420	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
421	C₄²	C₂×C₅×D₄	1	2	yes	—
422	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
423	C₄²	C₂×C₅×D₄	1	2	yes	—
424	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
425	C₄²	C₂⁴×C₅	1	1	yes	characteristic
426	C₂×C₅	—	2	2	no	—
427	C₂×C₅	—	4	2	no	—
428	C₂×C₅	#2888	1	1	yes	characteristic
429	C₂×C₅	C₂×#419	1	1	yes	characteristic
430	C₂×C₅	#2898	1	1	yes	characteristic
431	C₂³	C₂×C₅×C₂²⋊C₄	1	2	yes	—
432	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
433	Q₈	—	2	2	no	—
434	Q₈	—	4	4	no	—
435	Q₈	—	4	2	no	—
436	Q₈	—	4	1	no	—
437	Q₈	—	4	1	no	—
438	Q₈	—	8	2	no	—
439	Q₈	—	8	4	no	—
440	D₄	—	2	4	no	—
441	D₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	8	2	no	—
454	C₂×C₄	—	8	4	no	—
455	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
456	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
457	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
458	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
459	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
460	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
461	C₂×C₄	C₅×#137	1	2	yes	—
462	C₂×C₄	C₅×#137	1	2	yes	—
463	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
464	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
465	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
466	C₈	—	4	1	no	—
467	C₈	—	4	1	no	—
468	C₈	—	4	2	no	—
469	C₈	—	4	2	no	—
470	C₈	—	4	1	no	—
471	C₈	—	4	1	no	—
472	C₅	#17760	1	1	yes	characteristic, direct product factor, Sylow
473	C₂²	—	2	1	no	—
474	C₂²	—	2	1	no	—
475	C₂²	—	2	2	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	2	2	no	—
478	C₂²	C₅×#419	1	2	yes	—
479	C₂²	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	2	2	no	—
483	C₄	—	2	2	no	—
484	C₄	—	2	1	no	—
485	C₄	—	2	2	no	—
486	C₄	—	4	4	no	—
487	C₄	—	4	2	no	—
488	C₄	—	4	2	no	—
489	C₄	C₅×#419	1	2	yes	—
490	C₄	C₂×C₅×#137	1	1	yes	characteristic
491	C₄	C₂×C₅×#137	1	1	yes	characteristic
492	C₄	C₅×#577	1	1	yes	characteristic
493	C₄	C₅×#578	1	1	yes	characteristic
494	C₂	—	2	2	no	—
495	C₂	—	4	2	no	—
496	C₂	C₅×#2888	1	1	yes	characteristic
497	C₂	C₂×C₅×#419	1	1	yes	characteristic
498	C₂	C₅×#2898	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₂×C₅×#41	D₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₄×C₅×#41 ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×#1559	C₂	semidirect
5. C₅×#1558	C₂	semidirect
6. C₅×#1554	C₂	semidirect
7. C₅×#1550	C₂	semidirect
8. C₅×#1548	C₂	semidirect
9. C₅×#1548	C₂	semidirect
10. C₅×#1542	C₂	semidirect
11. C₂×C₅×#333	C₂	semidirect
50. #17760	C₅	direct (N × H)
124. #1559	C₂×C₅	semidirect
125. #1558	C₂×C₅	semidirect
126. #1554	C₂×C₅	semidirect
127. #1550	C₂×C₅	semidirect
128. #1548	C₂×C₅	semidirect
129. #1548	C₂×C₅	semidirect
130. #1542	C₂×C₅	semidirect
131. C₂×#333	C₂×C₅	semidirect
472. C₅	#17760	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×#3503	2
C₅×#2989	2
C₅×#2925	2
C₅×#1559	2
C₅×#1558	2
C₅×#1554	2
C₅×#1550	2
C₅×#1548	2
C₅×#1542	2
C₂×C₅×#333	2
#17760	5

Subgroups — C5×#17760 #11940480

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17760 #11940480