Subgroups — C₅×#17766 #11940486

Order 1280.

982 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3508	C₂	1	1	yes	maximal, characteristic
2	C₅×#2989	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2925	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1560	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1559	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1557	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1555	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1554	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1553	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1551	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1551	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1547	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1545	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1543	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1540	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#559	—	2	1	no	—
17	C₅×#559	C₄	1	2	yes	—
18	C₅×#550	—	2	1	no	—
19	C₅×#550	C₄	1	2	yes	—
20	C₅×#546	—	2	1	no	—
21	C₅×#546	—	2	1	no	—
22	C₅×#546	C₄	1	2	yes	—
23	C₅×#546	C₄	1	2	yes	—
24	C₅×#540	—	2	1	no	—
25	C₅×#540	—	2	1	no	—
26	C₅×#535	—	2	1	no	—
27	C₅×#533	C₂²	1	1	yes	characteristic
28	C₅×#532	C₂²	1	1	yes	characteristic
29	C₅×#532	C₂²	1	1	yes	characteristic
30	C₅×#532	C₂²	1	1	yes	characteristic
31	C₅×#532	C₂²	1	1	yes	characteristic
32	C₂×C₅×#127	C₂²	1	1	yes	characteristic
33	C₅×#518	—	2	1	no	—
34	C₄×C₅×#41	C₂²	1	1	yes	characteristic
35	C₅×#446	—	2	1	no	—
36	C₅×#436	—	2	1	no	—
37	C₅×#435	—	2	1	no	—
38	C₅×#435	—	2	1	no	—
39	C₅×#433	—	2	1	no	—
40	C₅×#433	—	2	1	no	—
41	C₅×#432	C₂²	1	1	yes	characteristic
42	C₅×#432	C₂²	1	1	yes	characteristic
43	C₅×#432	C₂²	1	1	yes	characteristic, complemented
44	C₅×#432	C₂²	1	1	yes	characteristic, complemented
45	C₅×#431	C₂²	1	1	yes	characteristic
46	C₅×#431	C₂²	1	1	yes	characteristic, complemented
47	C₅×#431	C₂²	1	1	yes	characteristic, complemented
48	C₅×#423	C₂²	1	1	yes	characteristic
49	C₅×#423	C₂²	1	1	yes	characteristic, complemented
50	C₅×#423	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
53	C₅×#408	—	2	1	no	—
54	C₅×#405	—	2	1	no	—
55	C₅×#333	C₂²	1	1	yes	characteristic, complemented
56	C₅×#333	C₂²	1	1	yes	characteristic, complemented
57	C₅×#333	C₂²	1	1	yes	characteristic, complemented
58	C₅×#333	C₂²	1	1	yes	characteristic, complemented
59	C₅×#332	C₂²	1	1	yes	characteristic, complemented
60	C₅×#332	C₂²	1	1	yes	characteristic, complemented
61	C₅×#332	C₂²	1	1	yes	characteristic, complemented
62	C₅×#332	C₂²	1	1	yes	characteristic, complemented
63	C₅×#331	C₂²	1	1	yes	characteristic
64	C₅×#331	C₂²	1	1	yes	characteristic
65	C₅×#331	C₂²	1	1	yes	characteristic
66	C₅×#331	C₂²	1	1	yes	characteristic
67	C₅×#331	C₂²	1	1	yes	characteristic
68	C₅×#331	C₂²	1	1	yes	characteristic
69	C₅×#331	C₂²	1	1	yes	characteristic
70	C₅×#331	C₂²	1	1	yes	characteristic
71	#17766	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
72	C₂×C₅×#41	—	2	1	no	—
73	C₂×C₅×#41	—	2	1	no	—
74	C₂×C₅×#41	C₂×C₄	1	2	yes	—
75	C₂×C₅×#41	C₂×C₄	1	2	yes	—
76	C₂×C₅×#41	D₄	1	1	yes	characteristic
77	C₂²×C₅×D₄	—	2	1	no	—
78	C₂²×C₅×D₄	—	2	1	no	—
79	C₂²×C₅×D₄	C₂×C₄	1	2	yes	—
80	C₂×C₅×M₁₆	—	2	1	no	—
81	C₂×C₅×M₁₆	—	2	1	no	—
82	C₂×C₅×M₁₆	—	2	1	no	—
83	C₂²×C₅×C₈	—	2	1	no	—
84	C₂²×C₅×C₈	—	2	1	no	—
85	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
87	C₅×#127	—	2	2	no	—
88	C₅×#127	—	2	1	no	—
89	C₅×#127	—	2	1	no	—
90	C₅×#127	C₂×C₄	1	2	yes	—
91	C₅×#127	C₂³	1	1	yes	characteristic
92	C₅×#127	C₂³	1	1	yes	characteristic
93	C₅×#125	—	2	1	no	—
94	C₅×#124	—	2	2	no	—
95	C₅×#124	—	2	1	no	—
96	C₅×#124	—	2	1	no	—
97	C₅×#124	C₂×C₄	1	2	yes	—
98	C₅×#124	C₂×C₄	1	2	yes	—
99	C₅×#123	—	2	2	no	—
100	C₅×#123	—	2	2	no	—
101	C₅×#123	—	2	2	no	—
102	C₅×#123	—	2	2	no	—
103	C₅×C₂²⋊Q₈	—	2	1	no	—
104	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
105	C₅×#121	—	2	1	no	—
106	C₅×#121	—	2	1	no	—
107	C₅×#121	—	2	1	no	—
108	C₅×#121	—	2	1	no	—
109	C₅×#121	—	2	1	no	—
110	C₅×#121	—	2	1	no	—
111	C₅×#121	—	2	2	no	—
112	C₅×#121	—	2	2	no	—
113	C₅×#121	—	2	2	no	—
114	C₅×#121	—	2	2	no	—
115	C₅×#121	C₂×C₄	1	2	yes	—
116	C₅×#121	C₂×C₄	1	2	yes	—
117	C₅×#120	—	2	2	no	—
118	C₅×#120	—	2	2	no	—
119	C₄×C₅×Q₈	—	2	1	no	—
120	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
121	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
122	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
123	C₄×C₅×D₄	—	2	2	no	—
124	C₄×C₅×D₄	—	2	2	no	—
125	C₄×C₅×D₄	—	2	1	no	—
126	C₄×C₅×D₄	—	2	1	no	—
127	C₄×C₅×D₄	—	2	1	no	—
128	C₄×C₅×D₄	—	2	1	no	—
129	C₄×C₅×D₄	—	2	1	no	—
130	C₄×C₅×D₄	—	2	1	no	—
131	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
132	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
133	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
134	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
135	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
136	C₄×C₅×D₄	D₄	1	1	yes	characteristic
137	C₄×C₅×D₄	D₄	1	1	yes	characteristic
138	C₄×C₅×D₄	D₄	1	1	yes	characteristic
139	C₅×#117	—	2	1	no	—
140	C₅×#117	D₄	1	1	yes	characteristic
141	C₅×#117	D₄	1	1	yes	characteristic
142	C₅×#117	D₄	1	1	yes	characteristic
143	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
144	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
145	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
147	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
148	C₅×C₄⋊C₈	—	2	1	no	—
149	C₅×C₄⋊C₈	—	2	1	no	—
150	C₅×C₄⋊C₈	—	2	1	no	—
151	C₅×C₄⋊C₈	—	2	1	no	—
152	C₅×C₄⋊C₈	—	2	1	no	—
153	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
154	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
155	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
156	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
157	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
158	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
159	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
160	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
161	C₅×C₂²⋊C₈	—	2	1	no	—
162	C₅×C₂²⋊C₈	—	2	1	no	—
163	C₅×C₂²⋊C₈	—	2	1	no	—
164	C₅×C₂²⋊C₈	—	2	1	no	—
165	C₅×C₂²⋊C₈	—	2	1	no	—
166	C₅×C₂²⋊C₈	—	2	1	no	—
167	C₅×C₂²⋊C₈	—	2	1	no	—
168	C₅×#97	—	2	1	no	—
169	C₅×#97	—	2	1	no	—
170	C₅×#97	—	2	1	no	—
171	C₅×#97	—	2	1	no	—
172	C₄×C₅×C₈	—	2	1	no	—
173	C₄×C₅×C₈	—	2	1	no	—
174	C₄×C₅×C₈	—	2	1	no	—
175	#3508	C₂×C₅	1	1	yes	characteristic
176	#2989	C₂×C₅	1	1	yes	characteristic, complemented
177	#2925	C₂×C₅	1	1	yes	characteristic, complemented
178	#1560	C₂×C₅	1	1	yes	characteristic, complemented
179	#1559	C₂×C₅	1	1	yes	characteristic, complemented
180	#1557	C₂×C₅	1	1	yes	characteristic, complemented
181	#1555	C₂×C₅	1	1	yes	characteristic, complemented
182	#1554	C₂×C₅	1	1	yes	characteristic, complemented
183	#1553	C₂×C₅	1	1	yes	characteristic, complemented
184	#1551	C₂×C₅	1	1	yes	characteristic, complemented
185	#1551	C₂×C₅	1	1	yes	characteristic, complemented
186	#1547	C₂×C₅	1	1	yes	characteristic, complemented
187	#1545	C₂×C₅	1	1	yes	characteristic, complemented
188	#1543	C₂×C₅	1	1	yes	characteristic, complemented
189	#1540	C₂×C₅	1	1	yes	characteristic, complemented
190	C₂⁴×C₅	—	2	2	no	—
191	C₅×#41	—	4	1	no	—
192	C₅×#41	—	4	1	no	—
193	C₅×#41	—	8	1	no	—
194	C₅×#41	—	8	1	no	—
195	C₅×#41	—	8	1	no	—
196	C₅×#41	—	8	1	no	—
197	C₅×#41	—	8	2	no	—
198	C₅×#41	—	8	2	no	—
199	C₂×C₅×Q₈	—	2	1	no	—
200	C₂×C₅×Q₈	C₂²⋊C₄	1	1	yes	characteristic
201	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
202	C₂×C₅×D₄	—	2	2	no	—
203	C₂×C₅×D₄	—	2	2	no	—
204	C₂×C₅×D₄	—	2	2	no	—
205	C₂×C₅×D₄	—	2	2	no	—
206	C₂×C₅×D₄	—	2	2	no	—
207	C₂×C₅×D₄	—	2	2	no	—
208	C₂×C₅×D₄	—	2	2	no	—
209	C₂×C₅×D₄	—	2	1	no	—
210	C₂×C₅×D₄	—	2	1	no	—
211	C₂×C₅×D₄	—	2	1	no	—
212	C₂×C₅×D₄	—	2	1	no	—
213	C₂×C₅×D₄	—	4	2	no	—
214	C₂×C₅×D₄	—	4	2	no	—
215	C₂×C₅×D₄	—	8	1	no	—
216	C₂×C₅×D₄	—	8	1	no	—
217	C₂×C₅×D₄	—	8	2	no	—
218	C₂×C₅×D₄	C₂²⋊C₄	1	1	yes	characteristic
219	C₂×C₅×D₄	C₂²⋊C₄	1	1	yes	characteristic
220	C₂×C₅×D₄	C₂²⋊C₄	1	1	yes	characteristic
221	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
222	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
223	C₂²×C₄×C₅	—	2	2	no	—
224	C₂²×C₄×C₅	—	2	2	no	—
225	C₂²×C₄×C₅	—	2	2	no	—
226	C₂²×C₄×C₅	—	2	2	no	—
227	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
228	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
229	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
230	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
236	C₅×M₁₆	—	4	2	no	—
237	C₅×M₁₆	—	8	1	no	—
238	C₅×M₁₆	—	8	1	no	—
239	C₂×C₅×C₈	—	2	1	no	—
240	C₂×C₅×C₈	—	2	1	no	—
241	C₂×C₅×C₈	—	2	1	no	—
242	C₂×C₅×C₈	—	2	1	no	—
243	C₂×C₅×C₈	—	2	1	no	—
244	C₂×C₅×C₈	—	2	1	no	—
245	C₂×C₅×C₈	—	2	1	no	—
246	C₂×C₅×C₈	—	2	1	no	—
247	C₂×C₅×C₈	—	4	2	no	—
248	C₂×C₅×C₈	—	8	1	no	—
249	C₅×C₄⋊C₄	—	2	2	no	—
250	C₅×C₄⋊C₄	—	2	2	no	—
251	C₅×C₄⋊C₄	—	2	1	no	—
252	C₅×C₄⋊C₄	—	2	1	no	—
253	C₅×C₄⋊C₄	—	2	1	no	—
254	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
255	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
256	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
257	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
258	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
259	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
260	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
261	C₅×C₂²⋊C₄	—	2	2	no	—
262	C₅×C₂²⋊C₄	—	2	2	no	—
263	C₅×C₂²⋊C₄	—	2	2	no	—
264	C₅×C₂²⋊C₄	—	2	2	no	—
265	C₅×C₂²⋊C₄	—	2	2	no	—
266	C₅×C₂²⋊C₄	—	2	2	no	—
267	C₅×C₂²⋊C₄	—	2	2	no	—
268	C₅×C₂²⋊C₄	—	2	2	no	—
269	C₅×C₂²⋊C₄	—	2	2	no	—
270	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
271	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
272	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
273	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
274	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
275	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
276	C₄²×C₅	—	2	2	no	—
277	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
278	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
279	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
280	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
281	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
282	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
283	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
284	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
285	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
286	C₄²×C₅	C₂⁴	1	1	yes	characteristic
287	#559	—	2	1	no	—
288	#559	C₄×C₅	1	2	yes	—
289	#550	—	2	1	no	—
290	#550	C₄×C₅	1	2	yes	—
291	#546	—	2	1	no	—
292	#546	—	2	1	no	—
293	#546	C₄×C₅	1	2	yes	—
294	#546	C₄×C₅	1	2	yes	—
295	#540	—	2	1	no	—
296	#540	—	2	1	no	—
297	#535	—	2	1	no	—
298	#533	C₂²×C₅	1	1	yes	characteristic
299	#532	C₂²×C₅	1	1	yes	characteristic
300	#532	C₂²×C₅	1	1	yes	characteristic
301	#532	C₂²×C₅	1	1	yes	characteristic
302	#532	C₂²×C₅	1	1	yes	characteristic
303	C₂×#127	C₂²×C₅	1	1	yes	characteristic
304	#518	—	2	1	no	—
305	C₄×#41	C₂²×C₅	1	1	yes	characteristic
306	#446	—	2	1	no	—
307	#436	—	2	1	no	—
308	#435	—	2	1	no	—
309	#435	—	2	1	no	—
310	#433	—	2	1	no	—
311	#433	—	2	1	no	—
312	#432	C₂²×C₅	1	1	yes	characteristic
313	#432	C₂²×C₅	1	1	yes	characteristic
314	#432	C₂²×C₅	1	1	yes	characteristic, complemented
315	#432	C₂²×C₅	1	1	yes	characteristic, complemented
316	#431	C₂²×C₅	1	1	yes	characteristic
317	#431	C₂²×C₅	1	1	yes	characteristic, complemented
318	#431	C₂²×C₅	1	1	yes	characteristic, complemented
319	#423	C₂²×C₅	1	1	yes	characteristic
320	#423	C₂²×C₅	1	1	yes	characteristic, complemented
321	#423	C₂²×C₅	1	1	yes	characteristic, complemented
322	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
323	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
324	#408	—	2	1	no	—
325	#405	—	2	1	no	—
326	#333	C₂²×C₅	1	1	yes	characteristic, complemented
327	#333	C₂²×C₅	1	1	yes	characteristic, complemented
328	#333	C₂²×C₅	1	1	yes	characteristic, complemented
329	#333	C₂²×C₅	1	1	yes	characteristic, complemented
330	#332	C₂²×C₅	1	1	yes	characteristic, complemented
331	#332	C₂²×C₅	1	1	yes	characteristic, complemented
332	#332	C₂²×C₅	1	1	yes	characteristic, complemented
333	#332	C₂²×C₅	1	1	yes	characteristic, complemented
334	#331	C₂²×C₅	1	1	yes	characteristic
335	#331	C₂²×C₅	1	1	yes	characteristic
336	#331	C₂²×C₅	1	1	yes	characteristic
337	#331	C₂²×C₅	1	1	yes	characteristic
338	#331	C₂²×C₅	1	1	yes	characteristic
339	#331	C₂²×C₅	1	1	yes	characteristic
340	#331	C₂²×C₅	1	1	yes	characteristic
341	#331	C₂²×C₅	1	1	yes	characteristic
342	C₂³×C₅	—	2	2	no	—
343	C₂³×C₅	—	2	2	no	—
344	C₂³×C₅	—	4	4	no	—
345	C₂³×C₅	—	8	2	no	—
346	C₂³×C₅	—	8	2	no	—
347	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
348	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
349	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
350	C₅×Q₈	—	4	1	no	—
351	C₅×Q₈	—	4	2	no	—
352	C₅×Q₈	—	4	1	no	—
353	C₅×Q₈	—	4	1	no	—
354	C₅×D₄	—	4	1	no	—
355	C₅×D₄	—	4	1	no	—
356	C₅×D₄	—	4	1	no	—
357	C₅×D₄	—	4	2	no	—
358	C₅×D₄	—	4	2	no	—
359	C₅×D₄	—	4	4	no	—
360	C₅×D₄	—	4	1	no	—
361	C₅×D₄	—	4	1	no	—
362	C₅×D₄	—	4	1	no	—
363	C₅×D₄	—	4	1	no	—
364	C₅×D₄	—	4	1	no	—
365	C₅×D₄	—	4	1	no	—
366	C₅×D₄	—	4	1	no	—
367	C₅×D₄	—	4	1	no	—
368	C₅×D₄	—	8	2	no	—
369	C₅×D₄	—	8	2	no	—
370	C₅×D₄	—	8	2	no	—
371	C₅×D₄	—	8	2	no	—
372	C₅×D₄	—	8	2	no	—
373	C₅×D₄	—	8	2	no	—
374	C₂×C₄×C₅	—	2	1	no	—
375	C₂×C₄×C₅	—	2	1	no	—
376	C₂×C₄×C₅	—	2	1	no	—
377	C₂×C₄×C₅	—	2	1	no	—
378	C₂×C₄×C₅	—	2	1	no	—
379	C₂×C₄×C₅	—	2	1	no	—
380	C₂×C₄×C₅	—	2	1	no	—
381	C₂×C₄×C₅	—	2	1	no	—
382	C₂×C₄×C₅	—	2	1	no	—
383	C₂×C₄×C₅	—	2	1	no	—
384	C₂×C₄×C₅	—	2	1	no	—
385	C₂×C₄×C₅	—	2	1	no	—
386	C₂×C₄×C₅	—	2	2	no	—
387	C₂×C₄×C₅	—	2	2	no	—
388	C₂×C₄×C₅	—	4	1	no	—
389	C₂×C₄×C₅	—	4	1	no	—
390	C₂×C₄×C₅	—	4	1	no	—
391	C₂×C₄×C₅	—	8	2	no	—
392	C₂×C₄×C₅	—	8	2	no	—
393	C₂×C₄×C₅	—	8	2	no	—
394	C₂×C₄×C₅	—	8	2	no	—
395	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
396	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
397	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
398	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
399	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
400	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
401	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
402	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
403	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
404	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
405	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
406	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
407	C₅×C₈	—	4	1	no	—
408	C₅×C₈	—	4	1	no	—
409	C₅×C₈	—	4	1	no	—
410	C₅×C₈	—	4	1	no	—
411	C₅×C₈	—	4	1	no	—
412	C₅×C₈	—	4	1	no	—
413	C₅×C₈	—	4	1	no	—
414	C₅×C₈	—	4	1	no	—
415	C₂×#41	—	2	1	no	—
416	C₂×#41	—	2	1	no	—
417	C₂×#41	C₂×C₄×C₅	1	2	yes	—
418	C₂×#41	C₂×C₄×C₅	1	2	yes	—
419	C₂×#41	C₅×D₄	1	1	yes	characteristic
420	C₂²×D₄	—	2	1	no	—
421	C₂²×D₄	—	2	1	no	—
422	C₂²×D₄	C₂×C₄×C₅	1	2	yes	—
423	C₂×M₁₆	—	2	1	no	—
424	C₂×M₁₆	—	2	1	no	—
425	C₂×M₁₆	—	2	1	no	—
426	C₂²×C₈	—	2	1	no	—
427	C₂²×C₈	—	2	1	no	—
428	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
429	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
430	#127	—	2	2	no	—
431	#127	—	2	1	no	—
432	#127	—	2	1	no	—
433	#127	C₂×C₄×C₅	1	2	yes	—
434	#127	C₂³×C₅	1	1	yes	characteristic
435	#127	C₂³×C₅	1	1	yes	characteristic
436	#125	—	2	1	no	—
437	#124	—	2	2	no	—
438	#124	—	2	1	no	—
439	#124	—	2	1	no	—
440	#124	C₂×C₄×C₅	1	2	yes	—
441	#124	C₂×C₄×C₅	1	2	yes	—
442	#123	—	2	2	no	—
443	#123	—	2	2	no	—
444	#123	—	2	2	no	—
445	#123	—	2	2	no	—
446	C₂²⋊Q₈	—	2	1	no	—
447	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
448	#121	—	2	1	no	—
449	#121	—	2	1	no	—
450	#121	—	2	1	no	—
451	#121	—	2	1	no	—
452	#121	—	2	1	no	—
453	#121	—	2	1	no	—
454	#121	—	2	2	no	—
455	#121	—	2	2	no	—
456	#121	—	2	2	no	—
457	#121	—	2	2	no	—
458	#121	C₂×C₄×C₅	1	2	yes	—
459	#121	C₂×C₄×C₅	1	2	yes	—
460	#120	—	2	2	no	—
461	#120	—	2	2	no	—
462	C₄×Q₈	—	2	1	no	—
463	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
464	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
465	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
466	C₄×D₄	—	2	2	no	—
467	C₄×D₄	—	2	2	no	—
468	C₄×D₄	—	2	1	no	—
469	C₄×D₄	—	2	1	no	—
470	C₄×D₄	—	2	1	no	—
471	C₄×D₄	—	2	1	no	—
472	C₄×D₄	—	2	1	no	—
473	C₄×D₄	—	2	1	no	—
474	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
475	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
476	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
477	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
478	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
479	C₄×D₄	C₅×D₄	1	1	yes	characteristic
480	C₄×D₄	C₅×D₄	1	1	yes	characteristic
481	C₄×D₄	C₅×D₄	1	1	yes	characteristic
482	#117	—	2	1	no	—
483	#117	C₅×D₄	1	1	yes	characteristic
484	#117	C₅×D₄	1	1	yes	characteristic
485	#117	C₅×D₄	1	1	yes	characteristic
486	C₂×C₂²⋊C₄	—	2	2	no	—
487	C₂×C₂²⋊C₄	—	2	2	no	—
488	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
489	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
490	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
491	C₄⋊C₈	—	2	1	no	—
492	C₄⋊C₈	—	2	1	no	—
493	C₄⋊C₈	—	2	1	no	—
494	C₄⋊C₈	—	2	1	no	—
495	C₄⋊C₈	—	2	1	no	—
496	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
497	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
498	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
499	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
500	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
501	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
502	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
503	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
504	C₂²⋊C₈	—	2	1	no	—
505	C₂²⋊C₈	—	2	1	no	—
506	C₂²⋊C₈	—	2	1	no	—
507	C₂²⋊C₈	—	2	1	no	—
508	C₂²⋊C₈	—	2	1	no	—
509	C₂²⋊C₈	—	2	1	no	—
510	C₂²⋊C₈	—	2	1	no	—
511	#97	—	2	1	no	—
512	#97	—	2	1	no	—
513	#97	—	2	1	no	—
514	#97	—	2	1	no	—
515	C₄×C₈	—	2	1	no	—
516	C₄×C₈	—	2	1	no	—
517	C₄×C₈	—	2	1	no	—
518	C₂²×C₅	—	2	1	no	—
519	C₂²×C₅	—	2	1	no	—
520	C₂²×C₅	—	2	1	no	—
521	C₂²×C₅	—	2	1	no	—
522	C₂²×C₅	—	2	1	no	—
523	C₂²×C₅	—	2	1	no	—
524	C₂²×C₅	—	2	1	no	—
525	C₂²×C₅	—	2	1	no	—
526	C₂²×C₅	—	2	1	no	—
527	C₂²×C₅	—	4	2	no	—
528	C₂²×C₅	—	4	2	no	—
529	C₂²×C₅	—	4	2	no	—
530	C₂²×C₅	—	4	2	no	—
531	C₂²×C₅	—	4	2	no	—
532	C₂²×C₅	—	4	2	no	—
533	C₂²×C₅	—	16	4	no	—
534	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
535	C₄×C₅	—	2	1	no	—
536	C₄×C₅	—	2	1	no	—
537	C₄×C₅	—	2	1	no	—
538	C₄×C₅	—	2	1	no	—
539	C₄×C₅	—	2	1	no	—
540	C₄×C₅	—	2	1	no	—
541	C₄×C₅	—	2	1	no	—
542	C₄×C₅	—	2	1	no	—
543	C₄×C₅	—	2	1	no	—
544	C₄×C₅	—	2	1	no	—
545	C₄×C₅	—	4	2	no	—
546	C₄×C₅	—	4	2	no	—
547	C₄×C₅	#575	1	1	yes	characteristic
548	C₄×C₅	#575	1	1	yes	characteristic
549	C₄×C₅	#576	1	1	yes	characteristic
550	C₄×C₅	#577	1	1	yes	characteristic
551	C₂⁴	—	2	2	no	—
552	#41	—	4	1	no	—
553	#41	—	4	1	no	—
554	#41	—	8	1	no	—
555	#41	—	8	1	no	—
556	#41	—	8	1	no	—
557	#41	—	8	1	no	—
558	#41	—	8	2	no	—
559	#41	—	8	2	no	—
560	C₂×Q₈	—	2	1	no	—
561	C₂×Q₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
562	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
563	C₂×D₄	—	2	2	no	—
564	C₂×D₄	—	2	2	no	—
565	C₂×D₄	—	2	2	no	—
566	C₂×D₄	—	2	2	no	—
567	C₂×D₄	—	2	2	no	—
568	C₂×D₄	—	2	2	no	—
569	C₂×D₄	—	2	2	no	—
570	C₂×D₄	—	2	1	no	—
571	C₂×D₄	—	2	1	no	—
572	C₂×D₄	—	2	1	no	—
573	C₂×D₄	—	2	1	no	—
574	C₂×D₄	—	4	2	no	—
575	C₂×D₄	—	4	2	no	—
576	C₂×D₄	—	8	1	no	—
577	C₂×D₄	—	8	1	no	—
578	C₂×D₄	—	8	2	no	—
579	C₂×D₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
580	C₂×D₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
581	C₂×D₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
582	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
583	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	2	2	no	—
587	C₂²×C₄	—	2	2	no	—
588	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
589	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
590	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
591	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
592	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
593	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
594	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
595	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
596	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
597	M₁₆	—	4	2	no	—
598	M₁₆	—	8	1	no	—
599	M₁₆	—	8	1	no	—
600	C₂×C₈	—	2	1	no	—
601	C₂×C₈	—	2	1	no	—
602	C₂×C₈	—	2	1	no	—
603	C₂×C₈	—	2	1	no	—
604	C₂×C₈	—	2	1	no	—
605	C₂×C₈	—	2	1	no	—
606	C₂×C₈	—	2	1	no	—
607	C₂×C₈	—	2	1	no	—
608	C₂×C₈	—	4	2	no	—
609	C₂×C₈	—	8	1	no	—
610	C₄⋊C₄	—	2	2	no	—
611	C₄⋊C₄	—	2	2	no	—
612	C₄⋊C₄	—	2	1	no	—
613	C₄⋊C₄	—	2	1	no	—
614	C₄⋊C₄	—	2	1	no	—
615	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
616	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
617	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
618	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
619	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
620	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
621	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
622	C₂²⋊C₄	—	2	2	no	—
623	C₂²⋊C₄	—	2	2	no	—
624	C₂²⋊C₄	—	2	2	no	—
625	C₂²⋊C₄	—	2	2	no	—
626	C₂²⋊C₄	—	2	2	no	—
627	C₂²⋊C₄	—	2	2	no	—
628	C₂²⋊C₄	—	2	2	no	—
629	C₂²⋊C₄	—	2	2	no	—
630	C₂²⋊C₄	—	2	2	no	—
631	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
632	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
633	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
634	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
635	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
636	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
637	C₄²	—	2	2	no	—
638	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
639	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
640	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
641	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
642	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
643	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
644	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
645	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
646	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
647	C₄²	C₂⁴×C₅	1	1	yes	characteristic
648	C₂×C₅	—	4	1	no	—
649	C₂×C₅	—	4	1	no	—
650	C₂×C₅	—	4	1	no	—
651	C₂×C₅	—	8	2	no	—
652	C₂×C₅	—	8	2	no	—
653	C₂×C₅	#2888	1	1	yes	characteristic
654	C₂×C₅	#2896	1	1	yes	characteristic
655	C₂×C₅	#2897	1	1	yes	characteristic
656	C₂³	—	2	2	no	—
657	C₂³	—	2	2	no	—
658	C₂³	—	4	4	no	—
659	C₂³	—	8	2	no	—
660	C₂³	—	8	2	no	—
661	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
662	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
663	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
664	Q₈	—	4	1	no	—
665	Q₈	—	4	2	no	—
666	Q₈	—	4	1	no	—
667	Q₈	—	4	1	no	—
668	D₄	—	4	1	no	—
669	D₄	—	4	1	no	—
670	D₄	—	4	1	no	—
671	D₄	—	4	2	no	—
672	D₄	—	4	2	no	—
673	D₄	—	4	4	no	—
674	D₄	—	4	1	no	—
675	D₄	—	4	1	no	—
676	D₄	—	4	1	no	—
677	D₄	—	4	1	no	—
678	D₄	—	4	1	no	—
679	D₄	—	4	1	no	—
680	D₄	—	4	1	no	—
681	D₄	—	4	1	no	—
682	D₄	—	8	2	no	—
683	D₄	—	8	2	no	—
684	D₄	—	8	2	no	—
685	D₄	—	8	2	no	—
686	D₄	—	8	2	no	—
687	D₄	—	8	2	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	4	1	no	—
703	C₂×C₄	—	4	1	no	—
704	C₂×C₄	—	4	1	no	—
705	C₂×C₄	—	8	2	no	—
706	C₂×C₄	—	8	2	no	—
707	C₂×C₄	—	8	2	no	—
708	C₂×C₄	—	8	2	no	—
709	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
710	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
711	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
712	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
713	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
714	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
715	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
716	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
717	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
718	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
719	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
720	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
721	C₈	—	4	1	no	—
722	C₈	—	4	1	no	—
723	C₈	—	4	1	no	—
724	C₈	—	4	1	no	—
725	C₈	—	4	1	no	—
726	C₈	—	4	1	no	—
727	C₈	—	4	1	no	—
728	C₈	—	4	1	no	—
729	C₅	#17766	1	1	yes	characteristic, direct product factor, Sylow
730	C₂²	—	2	1	no	—
731	C₂²	—	2	1	no	—
732	C₂²	—	2	1	no	—
733	C₂²	—	2	1	no	—
734	C₂²	—	2	1	no	—
735	C₂²	—	2	1	no	—
736	C₂²	—	2	1	no	—
737	C₂²	—	2	1	no	—
738	C₂²	—	2	1	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	2	no	—
741	C₂²	—	4	2	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	16	4	no	—
746	C₂²	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
747	C₄	—	2	1	no	—
748	C₄	—	2	1	no	—
749	C₄	—	2	1	no	—
750	C₄	—	2	1	no	—
751	C₄	—	2	1	no	—
752	C₄	—	2	1	no	—
753	C₄	—	2	1	no	—
754	C₄	—	2	1	no	—
755	C₄	—	2	1	no	—
756	C₄	—	2	1	no	—
757	C₄	—	4	2	no	—
758	C₄	—	4	2	no	—
759	C₄	C₅×#575	1	1	yes	characteristic
760	C₄	C₅×#575	1	1	yes	characteristic
761	C₄	C₅×#576	1	1	yes	characteristic
762	C₄	C₅×#577	1	1	yes	characteristic
763	C₂	—	4	1	no	—
764	C₂	—	4	1	no	—
765	C₂	—	4	1	no	—
766	C₂	—	8	2	no	—
767	C₂	—	8	2	no	—
768	C₂	C₅×#2888	1	1	yes	characteristic
769	C₂	C₅×#2896	1	1	yes	characteristic
770	C₂	C₅×#2897	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	C₅×#3508	C₂
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
2. C₅×#2989	C₂	semidirect
3. C₅×#2925	C₂	semidirect
4. C₅×#1560	C₂	semidirect
5. C₅×#1559	C₂	semidirect
6. C₅×#1557	C₂	semidirect
7. C₅×#1555	C₂	semidirect
8. C₅×#1554	C₂	semidirect
9. C₅×#1553	C₂	semidirect
10. C₅×#1551	C₂	semidirect
11. C₅×#1551	C₂	semidirect
12. C₅×#1547	C₂	semidirect
13. C₅×#1545	C₂	semidirect
14. C₅×#1543	C₂	semidirect
15. C₅×#1540	C₂	semidirect
43. C₅×#432	C₂²	semidirect
44. C₅×#432	C₂²	semidirect
46. C₅×#431	C₂²	semidirect
47. C₅×#431	C₂²	semidirect
49. C₅×#423	C₂²	semidirect
50. C₅×#423	C₂²	semidirect
51. C₂×C₅×C₄⋊C₈	C₂²	semidirect
52. C₂×C₅×C₄⋊C₈	C₂²	semidirect
55. C₅×#333	C₂²	semidirect
56. C₅×#333	C₂²	semidirect
57. C₅×#333	C₂²	semidirect
58. C₅×#333	C₂²	semidirect
59. C₅×#332	C₂²	semidirect
60. C₅×#332	C₂²	semidirect
61. C₅×#332	C₂²	semidirect
62. C₅×#332	C₂²	semidirect
71. #17766	C₅	direct (N × H)
176. #2989	C₂×C₅	semidirect
177. #2925	C₂×C₅	semidirect
178. #1560	C₂×C₅	semidirect
179. #1559	C₂×C₅	semidirect
180. #1557	C₂×C₅	semidirect
181. #1555	C₂×C₅	semidirect
182. #1554	C₂×C₅	semidirect
183. #1553	C₂×C₅	semidirect
184. #1551	C₂×C₅	semidirect
185. #1551	C₂×C₅	semidirect
186. #1547	C₂×C₅	semidirect
187. #1545	C₂×C₅	semidirect
188. #1543	C₂×C₅	semidirect
189. #1540	C₂×C₅	semidirect
314. #432	C₂²×C₅	semidirect
315. #432	C₂²×C₅	semidirect
317. #431	C₂²×C₅	semidirect
318. #431	C₂²×C₅	semidirect
320. #423	C₂²×C₅	semidirect
321. #423	C₂²×C₅	semidirect
322. C₂×C₄⋊C₈	C₂²×C₅	semidirect
323. C₂×C₄⋊C₈	C₂²×C₅	semidirect
326. #333	C₂²×C₅	semidirect
327. #333	C₂²×C₅	semidirect
328. #333	C₂²×C₅	semidirect
329. #333	C₂²×C₅	semidirect
330. #332	C₂²×C₅	semidirect
331. #332	C₂²×C₅	semidirect
332. #332	C₂²×C₅	semidirect
333. #332	C₂²×C₅	semidirect
729. C₅	#17766	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×#3508	2
C₅×#2989	2
C₅×#2925	2
C₅×#1560	2
C₅×#1559	2
C₅×#1557	2
C₅×#1555	2
C₅×#1554	2
C₅×#1553	2
C₅×#1551	2
C₅×#1547	2
C₅×#1545	2
C₅×#1543	2
C₅×#1540	2
#17766	5

Subgroups — C5×#17766 #11940486

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17766 #11940486