Subgroups — C₅×#22588 #11945308

Order 1280.

888 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2924	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#2896	C₂	1	1	yes	maximal, characteristic
3	C₅×#2880	C₂	1	1	yes	maximal, characteristic
4	C₅×#1938	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1937	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1929	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1929	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1866	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1866	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1826	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1811	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1789	C₂	1	1	yes	maximal, characteristic
13	C₅×#1765	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1764	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1753	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
17	C₂×C₅×#131	C₂²	1	1	yes	characteristic
18	C₂×C₅×#131	C₂²	1	1	yes	characteristic
19	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₅×#117	C₂²	1	1	yes	characteristic
21	C₅×#433	—	2	1	no	—
22	C₅×#433	—	2	1	no	—
23	C₅×#432	—	2	1	no	—
24	C₅×#431	—	2	1	no	—
25	C₂×C₅×#108	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₅×#108	C₂²	1	1	yes	characteristic, complemented
27	C₅×#424	C₂²	1	1	yes	characteristic, complemented
28	C₅×#424	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₅×#104	C₂²	1	1	yes	characteristic
30	C₂×C₅×#104	C₂²	1	1	yes	characteristic
31	C₂×C₅×#104	C₂²	1	1	yes	characteristic
32	C₂×C₅×#104	C₂²	1	1	yes	characteristic
33	C₅×#419	C₄	1	1	yes	characteristic, complemented
34	C₅×#419	C₄	1	1	yes	characteristic, complemented
35	C₅×#418	C₄	1	1	yes	characteristic, complemented
36	C₅×#418	C₄	1	1	yes	characteristic, complemented
37	C₅×#417	C₄	1	1	yes	characteristic, complemented
38	C₅×#417	C₄	1	1	yes	characteristic, complemented
39	C₅×#417	C₄	1	1	yes	characteristic, complemented
40	C₅×#417	C₄	1	1	yes	characteristic, complemented
41	C₅×#416	C₂²	1	1	yes	characteristic
42	C₅×#416	C₂²	1	1	yes	characteristic
43	C₅×#416	C₂²	1	1	yes	characteristic
44	C₅×#416	C₂²	1	1	yes	characteristic
45	C₅×#408	—	2	1	no	—
46	C₅×#408	—	2	1	no	—
47	C₅×#408	C₂²	1	1	yes	characteristic
48	C₅×#408	C₂²	1	1	yes	characteristic
49	C₅×#407	—	2	1	no	—
50	C₅×#407	C₂²	1	1	yes	characteristic
51	C₅×#407	C₂²	1	1	yes	characteristic
52	C₂×C₅×C₂²⋊C₈	—	2	1	no	—
53	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
54	C₅×#405	C₂²	1	1	yes	characteristic, complemented
55	C₅×#405	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₅×#97	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
58	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
59	C₅×#341	C₂²	1	1	yes	characteristic, complemented
60	C₅×#341	C₂²	1	1	yes	characteristic, complemented
61	C₅×#339	C₂²	1	1	yes	characteristic, complemented
62	C₅×#339	C₂²	1	1	yes	characteristic, complemented
63	C₅×#339	C₂²	1	1	yes	characteristic, complemented
64	C₅×#339	C₂²	1	1	yes	characteristic, complemented
65	C₅×#336	C₂²	1	1	yes	characteristic, complemented
66	C₅×#336	C₂²	1	1	yes	characteristic, complemented
67	#22588	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	2	no	—
71	C₂×C₅×#41	—	2	2	no	—
72	C₂×C₅×#41	—	4	1	no	—
73	C₂×C₅×#41	—	4	1	no	—
74	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
75	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
76	C₂×C₅×#41	C₂³	1	1	yes	characteristic
77	C₂×C₅×#41	C₂³	1	1	yes	characteristic
78	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
79	C₂²×C₅×D₄	—	2	1	no	—
80	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
81	C₂³×C₄×C₅	—	2	1	no	—
82	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
83	C₅×#131	—	2	2	no	—
84	C₅×#131	—	2	2	no	—
85	C₅×#131	—	4	1	no	—
86	C₅×#131	—	4	1	no	—
87	C₂×C₅×M₁₆	—	2	1	no	—
88	C₂×C₅×M₁₆	—	2	1	no	—
89	C₂×C₅×M₁₆	—	4	1	no	—
90	C₂×C₅×M₁₆	—	4	1	no	—
91	C₂×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
92	C₂×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
93	C₂×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
94	C₂×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
95	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
96	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
97	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
98	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
99	C₂²×C₅×C₈	—	2	1	no	—
100	C₂²×C₅×C₈	—	2	1	no	—
101	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
102	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
103	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
104	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
105	C₅×#117	—	2	1	no	—
106	C₅×#117	—	2	1	no	—
107	C₅×#117	C₂×C₄	1	1	yes	characteristic
108	C₅×#117	C₂×C₄	1	1	yes	characteristic
109	C₅×#117	C₂³	1	1	yes	characteristic
110	C₅×#117	C₂³	1	1	yes	characteristic
111	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
112	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
113	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
114	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
115	C₂×C₄²×C₅	—	2	1	no	—
116	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
118	C₅×#108	—	4	1	no	—
119	C₅×#108	—	4	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×#104	—	2	2	no	—
125	C₅×#104	—	2	2	no	—
126	C₅×#104	—	4	1	no	—
127	C₅×#104	—	4	1	no	—
128	C₅×#103	C₂×C₄	1	1	yes	characteristic
129	C₅×#103	C₂×C₄	1	1	yes	characteristic
130	C₅×#103	C₂×C₄	1	1	yes	characteristic
131	C₅×#103	C₂×C₄	1	1	yes	characteristic
132	C₅×#103	C₂×C₄	1	1	yes	characteristic
133	C₅×#103	C₂×C₄	1	1	yes	characteristic
134	C₅×#103	C₂×C₄	1	1	yes	characteristic
135	C₅×#103	C₂×C₄	1	1	yes	characteristic
136	C₅×#102	C₂×C₄	1	1	yes	characteristic
137	C₅×#102	C₂×C₄	1	1	yes	characteristic
138	C₅×#102	C₂×C₄	1	1	yes	characteristic
139	C₅×#102	C₂×C₄	1	1	yes	characteristic
140	C₅×#102	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×C₂²⋊C₈	—	2	1	no	—
145	C₅×C₂²⋊C₈	—	2	1	no	—
146	C₅×C₂²⋊C₈	—	2	1	no	—
147	C₅×C₂²⋊C₈	—	2	1	no	—
148	C₅×C₂²⋊C₈	—	2	1	no	—
149	C₅×C₂²⋊C₈	—	2	1	no	—
150	C₅×C₂²⋊C₈	—	2	1	no	—
151	C₅×C₂²⋊C₈	—	2	1	no	—
152	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
153	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
154	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
155	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
156	C₅×#97	—	2	1	no	—
157	C₅×#97	—	2	1	no	—
158	C₅×#97	—	4	1	no	—
159	C₄×C₅×C₈	—	2	1	no	—
160	C₄×C₅×C₈	—	2	1	no	—
161	C₄×C₅×C₈	—	4	1	no	—
162	C₅×#95	—	2	1	no	—
163	#2924	C₂×C₅	1	1	yes	characteristic, complemented
164	#2896	C₂×C₅	1	1	yes	characteristic
165	#2880	C₂×C₅	1	1	yes	characteristic
166	#1938	C₂×C₅	1	1	yes	characteristic, complemented
167	#1937	C₂×C₅	1	1	yes	characteristic, complemented
168	#1929	C₂×C₅	1	1	yes	characteristic, complemented
169	#1929	C₂×C₅	1	1	yes	characteristic, complemented
170	#1866	C₂×C₅	1	1	yes	characteristic, complemented
171	#1866	C₂×C₅	1	1	yes	characteristic, complemented
172	#1826	C₂×C₅	1	1	yes	characteristic, complemented
173	#1811	C₂×C₅	1	1	yes	characteristic, complemented
174	#1789	C₂×C₅	1	1	yes	characteristic
175	#1765	C₂×C₅	1	1	yes	characteristic, complemented
176	#1764	C₂×C₅	1	1	yes	characteristic, complemented
177	#1753	C₂×C₅	1	1	yes	characteristic, complemented
178	C₂⁴×C₅	—	2	1	no	—
179	C₂⁴×C₅	#41	1	1	yes	characteristic
180	C₅×#41	—	2	1	no	—
181	C₅×#41	—	2	1	no	—
182	C₅×#41	—	2	2	no	—
183	C₅×#41	—	2	2	no	—
184	C₅×#41	—	2	1	no	—
185	C₅×#41	—	2	1	no	—
186	C₅×#41	—	2	1	no	—
187	C₅×#41	—	2	1	no	—
188	C₅×#41	—	4	2	no	—
189	C₅×#41	—	4	2	no	—
190	C₅×#41	—	4	1	no	—
191	C₅×#41	—	4	1	no	—
192	C₅×#41	—	4	2	no	—
193	C₅×#41	—	4	2	no	—
194	C₅×#41	#41	1	2	yes	—
195	C₅×#41	#41	1	2	yes	—
196	C₂×C₅×Q₈	—	2	1	no	—
197	C₂×C₅×Q₈	—	2	2	no	—
198	C₂×C₅×Q₈	—	4	1	no	—
199	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
200	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
201	C₂×C₅×D₄	—	2	1	no	—
202	C₂×C₅×D₄	—	2	2	no	—
203	C₂×C₅×D₄	—	2	1	no	—
204	C₂×C₅×D₄	—	2	1	no	—
205	C₂×C₅×D₄	—	2	1	no	—
206	C₂×C₅×D₄	—	2	1	no	—
207	C₂×C₅×D₄	—	4	1	no	—
208	C₂×C₅×D₄	—	4	2	no	—
209	C₂×C₅×D₄	—	4	2	no	—
210	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
211	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
212	C₂²×C₄×C₅	—	2	1	no	—
213	C₂²×C₄×C₅	—	2	1	no	—
214	C₂²×C₄×C₅	—	2	1	no	—
215	C₂²×C₄×C₅	—	2	1	no	—
216	C₂²×C₄×C₅	—	2	1	no	—
217	C₂²×C₄×C₅	—	2	1	no	—
218	C₂²×C₄×C₅	—	2	1	no	—
219	C₂²×C₄×C₅	—	2	1	no	—
220	C₂²×C₄×C₅	—	2	1	no	—
221	C₂²×C₄×C₅	—	2	1	no	—
222	C₂²×C₄×C₅	—	2	1	no	—
223	C₂²×C₄×C₅	—	2	1	no	—
224	C₂²×C₄×C₅	—	2	1	no	—
225	C₂²×C₄×C₅	—	4	2	no	—
226	C₂²×C₄×C₅	—	4	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	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₅	#41	1	1	yes	characteristic
232	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
233	C₅×M₁₆	—	2	1	no	—
234	C₅×M₁₆	—	2	1	no	—
235	C₅×M₁₆	—	2	1	no	—
236	C₅×M₁₆	—	2	1	no	—
237	C₅×M₁₆	—	2	1	no	—
238	C₅×M₁₆	—	2	1	no	—
239	C₅×M₁₆	—	2	1	no	—
240	C₅×M₁₆	—	2	1	no	—
241	C₅×M₁₆	—	4	1	no	—
242	C₅×M₁₆	—	4	1	no	—
243	C₅×M₁₆	—	4	1	no	—
244	C₅×M₁₆	—	4	1	no	—
245	C₅×M₁₆	—	4	2	no	—
246	C₅×M₁₆	—	4	2	no	—
247	C₂×C₅×C₈	—	2	1	no	—
248	C₂×C₅×C₈	—	2	1	no	—
249	C₂×C₅×C₈	—	2	1	no	—
250	C₂×C₅×C₈	—	2	1	no	—
251	C₂×C₅×C₈	—	2	1	no	—
252	C₂×C₅×C₈	—	2	1	no	—
253	C₂×C₅×C₈	—	2	1	no	—
254	C₂×C₅×C₈	—	2	1	no	—
255	C₂×C₅×C₈	—	2	1	no	—
256	C₂×C₅×C₈	—	2	1	no	—
257	C₂×C₅×C₈	—	2	1	no	—
258	C₂×C₅×C₈	—	2	1	no	—
259	C₂×C₅×C₈	—	4	2	no	—
260	C₂×C₅×C₈	—	4	2	no	—
261	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
262	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
263	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
264	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
265	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
266	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
267	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
268	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
269	C₅×C₄⋊C₄	—	2	1	no	—
270	C₅×C₄⋊C₄	—	2	1	no	—
271	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
272	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
273	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
274	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
275	C₅×C₂²⋊C₄	—	2	1	no	—
276	C₅×C₂²⋊C₄	—	2	1	no	—
277	C₅×C₂²⋊C₄	—	2	1	no	—
278	C₅×C₂²⋊C₄	—	2	1	no	—
279	C₅×C₂²⋊C₄	—	4	2	no	—
280	C₄²×C₅	—	2	1	no	—
281	C₄²×C₅	—	2	1	no	—
282	C₄²×C₅	—	2	1	no	—
283	C₄²×C₅	—	2	1	no	—
284	C₄²×C₅	—	2	1	no	—
285	C₄²×C₅	—	2	1	no	—
286	C₄²×C₅	—	2	1	no	—
287	C₄²×C₅	—	2	1	no	—
288	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
289	C₂×#131	C₂²×C₅	1	1	yes	characteristic
290	C₂×#131	C₂²×C₅	1	1	yes	characteristic
291	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
292	C₂×#117	C₂²×C₅	1	1	yes	characteristic
293	#433	—	2	1	no	—
294	#433	—	2	1	no	—
295	#432	—	2	1	no	—
296	#431	—	2	1	no	—
297	C₂×#108	C₂²×C₅	1	1	yes	characteristic, complemented
298	C₂×#108	C₂²×C₅	1	1	yes	characteristic, complemented
299	#424	C₂²×C₅	1	1	yes	characteristic, complemented
300	#424	C₂²×C₅	1	1	yes	characteristic, complemented
301	C₂×#104	C₂²×C₅	1	1	yes	characteristic
302	C₂×#104	C₂²×C₅	1	1	yes	characteristic
303	C₂×#104	C₂²×C₅	1	1	yes	characteristic
304	C₂×#104	C₂²×C₅	1	1	yes	characteristic
305	#419	C₄×C₅	1	1	yes	characteristic, complemented
306	#419	C₄×C₅	1	1	yes	characteristic, complemented
307	#418	C₄×C₅	1	1	yes	characteristic, complemented
308	#418	C₄×C₅	1	1	yes	characteristic, complemented
309	#417	C₄×C₅	1	1	yes	characteristic, complemented
310	#417	C₄×C₅	1	1	yes	characteristic, complemented
311	#417	C₄×C₅	1	1	yes	characteristic, complemented
312	#417	C₄×C₅	1	1	yes	characteristic, complemented
313	#416	C₂²×C₅	1	1	yes	characteristic
314	#416	C₂²×C₅	1	1	yes	characteristic
315	#416	C₂²×C₅	1	1	yes	characteristic
316	#416	C₂²×C₅	1	1	yes	characteristic
317	#408	—	2	1	no	—
318	#408	—	2	1	no	—
319	#408	C₂²×C₅	1	1	yes	characteristic
320	#408	C₂²×C₅	1	1	yes	characteristic
321	#407	—	2	1	no	—
322	#407	C₂²×C₅	1	1	yes	characteristic
323	#407	C₂²×C₅	1	1	yes	characteristic
324	C₂×C₂²⋊C₈	—	2	1	no	—
325	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
326	#405	C₂²×C₅	1	1	yes	characteristic, complemented
327	#405	C₂²×C₅	1	1	yes	characteristic, complemented
328	C₂×#97	C₂²×C₅	1	1	yes	characteristic, complemented
329	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
330	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
331	#341	C₂²×C₅	1	1	yes	characteristic, complemented
332	#341	C₂²×C₅	1	1	yes	characteristic, complemented
333	#339	C₂²×C₅	1	1	yes	characteristic, complemented
334	#339	C₂²×C₅	1	1	yes	characteristic, complemented
335	#339	C₂²×C₅	1	1	yes	characteristic, complemented
336	#339	C₂²×C₅	1	1	yes	characteristic, complemented
337	#336	C₂²×C₅	1	1	yes	characteristic, complemented
338	#336	C₂²×C₅	1	1	yes	characteristic, complemented
339	C₂³×C₅	—	2	1	no	—
340	C₂³×C₅	—	2	1	no	—
341	C₂³×C₅	—	2	1	no	—
342	C₂³×C₅	—	2	1	no	—
343	C₂³×C₅	—	4	1	no	—
344	C₂³×C₅	—	4	1	no	—
345	C₂³×C₅	—	4	2	no	—
346	C₂³×C₅	—	4	2	no	—
347	C₂³×C₅	—	8	1	no	—
348	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
349	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
350	C₂³×C₅	C₂×#41	1	1	yes	characteristic
351	C₅×Q₈	—	2	1	no	—
352	C₅×Q₈	—	2	1	no	—
353	C₅×Q₈	—	2	1	no	—
354	C₅×Q₈	—	4	2	no	—
355	C₅×Q₈	#117	1	2	yes	—
356	C₅×D₄	—	2	2	no	—
357	C₅×D₄	—	2	2	no	—
358	C₅×D₄	—	2	1	no	—
359	C₅×D₄	—	2	1	no	—
360	C₅×D₄	—	2	1	no	—
361	C₅×D₄	—	4	2	no	—
362	C₅×D₄	—	4	2	no	—
363	C₅×D₄	—	4	2	no	—
364	C₅×D₄	—	4	1	no	—
365	C₅×D₄	—	4	1	no	—
366	C₅×D₄	#117	1	2	yes	—
367	C₂×C₄×C₅	—	2	1	no	—
368	C₂×C₄×C₅	—	2	1	no	—
369	C₂×C₄×C₅	—	2	1	no	—
370	C₂×C₄×C₅	—	2	1	no	—
371	C₂×C₄×C₅	—	2	1	no	—
372	C₂×C₄×C₅	—	2	1	no	—
373	C₂×C₄×C₅	—	2	1	no	—
374	C₂×C₄×C₅	—	2	2	no	—
375	C₂×C₄×C₅	—	2	2	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	2	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	—	4	2	no	—
387	C₂×C₄×C₅	—	4	2	no	—
388	C₂×C₄×C₅	—	4	2	no	—
389	C₂×C₄×C₅	—	4	1	no	—
390	C₂×C₄×C₅	—	4	2	no	—
391	C₂×C₄×C₅	—	4	1	no	—
392	C₂×C₄×C₅	—	4	1	no	—
393	C₂×C₄×C₅	—	4	1	no	—
394	C₂×C₄×C₅	—	4	1	no	—
395	C₂×C₄×C₅	—	4	1	no	—
396	C₂×C₄×C₅	—	4	1	no	—
397	C₂×C₄×C₅	—	8	1	no	—
398	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
399	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
400	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
401	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
403	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
404	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
405	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
406	C₅×C₈	—	2	1	no	—
407	C₅×C₈	—	2	1	no	—
408	C₅×C₈	—	2	1	no	—
409	C₅×C₈	—	2	1	no	—
410	C₅×C₈	—	2	1	no	—
411	C₅×C₈	—	2	1	no	—
412	C₅×C₈	—	2	1	no	—
413	C₅×C₈	—	2	1	no	—
414	C₅×C₈	—	4	1	no	—
415	C₅×C₈	—	4	1	no	—
416	C₅×C₈	—	4	1	no	—
417	C₅×C₈	—	4	1	no	—
418	C₂×#41	—	2	1	no	—
419	C₂×#41	—	2	1	no	—
420	C₂×#41	—	2	2	no	—
421	C₂×#41	—	2	2	no	—
422	C₂×#41	—	4	1	no	—
423	C₂×#41	—	4	1	no	—
424	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic
425	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic
426	C₂×#41	C₂³×C₅	1	1	yes	characteristic
427	C₂×#41	C₂³×C₅	1	1	yes	characteristic
428	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
429	C₂²×D₄	—	2	1	no	—
430	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
431	C₂³×C₄	—	2	1	no	—
432	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
433	#131	—	2	2	no	—
434	#131	—	2	2	no	—
435	#131	—	4	1	no	—
436	#131	—	4	1	no	—
437	C₂×M₁₆	—	2	1	no	—
438	C₂×M₁₆	—	2	1	no	—
439	C₂×M₁₆	—	4	1	no	—
440	C₂×M₁₆	—	4	1	no	—
441	C₂×M₁₆	C₂×C₄×C₅	1	1	yes	characteristic
442	C₂×M₁₆	C₂×C₄×C₅	1	1	yes	characteristic
443	C₂×M₁₆	C₂×C₄×C₅	1	1	yes	characteristic
444	C₂×M₁₆	C₂×C₄×C₅	1	1	yes	characteristic
445	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
446	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
447	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
448	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
449	C₂²×C₈	—	2	1	no	—
450	C₂²×C₈	—	2	1	no	—
451	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
452	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
453	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
454	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
455	#117	—	2	1	no	—
456	#117	—	2	1	no	—
457	#117	C₂×C₄×C₅	1	1	yes	characteristic
458	#117	C₂×C₄×C₅	1	1	yes	characteristic
459	#117	C₂³×C₅	1	1	yes	characteristic
460	#117	C₂³×C₅	1	1	yes	characteristic
461	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
462	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
463	C₂×C₂²⋊C₄	—	2	1	no	—
464	C₂×C₂²⋊C₄	—	2	1	no	—
465	C₂×C₄²	—	2	1	no	—
466	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
467	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
468	#108	—	4	1	no	—
469	#108	—	4	1	no	—
470	C₄⋊C₈	—	2	1	no	—
471	C₄⋊C₈	—	2	1	no	—
472	C₄⋊C₈	—	2	1	no	—
473	C₄⋊C₈	—	2	1	no	—
474	#104	—	2	2	no	—
475	#104	—	2	2	no	—
476	#104	—	4	1	no	—
477	#104	—	4	1	no	—
478	#103	C₂×C₄×C₅	1	1	yes	characteristic
479	#103	C₂×C₄×C₅	1	1	yes	characteristic
480	#103	C₂×C₄×C₅	1	1	yes	characteristic
481	#103	C₂×C₄×C₅	1	1	yes	characteristic
482	#103	C₂×C₄×C₅	1	1	yes	characteristic
483	#103	C₂×C₄×C₅	1	1	yes	characteristic
484	#103	C₂×C₄×C₅	1	1	yes	characteristic
485	#103	C₂×C₄×C₅	1	1	yes	characteristic
486	#102	C₂×C₄×C₅	1	1	yes	characteristic
487	#102	C₂×C₄×C₅	1	1	yes	characteristic
488	#102	C₂×C₄×C₅	1	1	yes	characteristic
489	#102	C₂×C₄×C₅	1	1	yes	characteristic
490	#102	C₂×C₄×C₅	1	1	yes	characteristic
491	#102	C₂×C₄×C₅	1	1	yes	characteristic
492	#102	C₂×C₄×C₅	1	1	yes	characteristic
493	#102	C₂×C₄×C₅	1	1	yes	characteristic
494	C₂²⋊C₈	—	2	1	no	—
495	C₂²⋊C₈	—	2	1	no	—
496	C₂²⋊C₈	—	2	1	no	—
497	C₂²⋊C₈	—	2	1	no	—
498	C₂²⋊C₈	—	2	1	no	—
499	C₂²⋊C₈	—	2	1	no	—
500	C₂²⋊C₈	—	2	1	no	—
501	C₂²⋊C₈	—	2	1	no	—
502	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
503	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
504	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
505	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
506	#97	—	2	1	no	—
507	#97	—	2	1	no	—
508	#97	—	4	1	no	—
509	C₄×C₈	—	2	1	no	—
510	C₄×C₈	—	2	1	no	—
511	C₄×C₈	—	4	1	no	—
512	#95	—	2	1	no	—
513	C₂²×C₅	—	2	1	no	—
514	C₂²×C₅	—	2	1	no	—
515	C₂²×C₅	—	2	1	no	—
516	C₂²×C₅	—	2	1	no	—
517	C₂²×C₅	—	2	2	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	—	4	1	no	—
523	C₂²×C₅	—	4	1	no	—
524	C₂²×C₅	—	4	1	no	—
525	C₂²×C₅	—	4	1	no	—
526	C₂²×C₅	—	4	1	no	—
527	C₂²×C₅	—	8	1	no	—
528	C₂²×C₅	—	8	1	no	—
529	C₂²×C₅	—	8	4	no	—
530	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
531	C₂²×C₅	#551	1	1	yes	characteristic
532	C₂²×C₅	#551	1	1	yes	characteristic
533	C₄×C₅	—	2	1	no	—
534	C₄×C₅	—	2	1	no	—
535	C₄×C₅	—	2	2	no	—
536	C₄×C₅	—	4	2	no	—
537	C₄×C₅	—	4	1	no	—
538	C₄×C₅	—	4	1	no	—
539	C₄×C₅	—	4	1	no	—
540	C₄×C₅	—	4	1	no	—
541	C₄×C₅	—	4	1	no	—
542	C₄×C₅	—	8	1	no	—
543	C₄×C₅	C₂×#117	1	1	yes	characteristic
544	C₄×C₅	#518	1	1	yes	characteristic
545	C₄×C₅	#546	1	1	yes	characteristic
546	C₄×C₅	#546	1	1	yes	characteristic
547	C₂⁴	—	2	1	no	—
548	C₂⁴	C₅×#41	1	1	yes	characteristic
549	#41	—	2	1	no	—
550	#41	—	2	1	no	—
551	#41	—	2	2	no	—
552	#41	—	2	2	no	—
553	#41	—	2	1	no	—
554	#41	—	2	1	no	—
555	#41	—	2	1	no	—
556	#41	—	2	1	no	—
557	#41	—	4	2	no	—
558	#41	—	4	2	no	—
559	#41	—	4	1	no	—
560	#41	—	4	1	no	—
561	#41	—	4	2	no	—
562	#41	—	4	2	no	—
563	#41	C₅×#41	1	2	yes	—
564	#41	C₅×#41	1	2	yes	—
565	C₂×Q₈	—	2	1	no	—
566	C₂×Q₈	—	2	2	no	—
567	C₂×Q₈	—	4	1	no	—
568	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
569	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
570	C₂×D₄	—	2	1	no	—
571	C₂×D₄	—	2	2	no	—
572	C₂×D₄	—	2	1	no	—
573	C₂×D₄	—	2	1	no	—
574	C₂×D₄	—	2	1	no	—
575	C₂×D₄	—	2	1	no	—
576	C₂×D₄	—	4	1	no	—
577	C₂×D₄	—	4	2	no	—
578	C₂×D₄	—	4	2	no	—
579	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
580	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	2	1	no	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	—	2	1	no	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	2	1	no	—
591	C₂²×C₄	—	2	1	no	—
592	C₂²×C₄	—	2	1	no	—
593	C₂²×C₄	—	2	1	no	—
594	C₂²×C₄	—	4	2	no	—
595	C₂²×C₄	—	4	2	no	—
596	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
597	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
598	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
599	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
600	C₂²×C₄	C₅×#41	1	1	yes	characteristic
601	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
602	M₁₆	—	2	1	no	—
603	M₁₆	—	2	1	no	—
604	M₁₆	—	2	1	no	—
605	M₁₆	—	2	1	no	—
606	M₁₆	—	2	1	no	—
607	M₁₆	—	2	1	no	—
608	M₁₆	—	2	1	no	—
609	M₁₆	—	2	1	no	—
610	M₁₆	—	4	1	no	—
611	M₁₆	—	4	1	no	—
612	M₁₆	—	4	1	no	—
613	M₁₆	—	4	1	no	—
614	M₁₆	—	4	2	no	—
615	M₁₆	—	4	2	no	—
616	C₂×C₈	—	2	1	no	—
617	C₂×C₈	—	2	1	no	—
618	C₂×C₈	—	2	1	no	—
619	C₂×C₈	—	2	1	no	—
620	C₂×C₈	—	2	1	no	—
621	C₂×C₈	—	2	1	no	—
622	C₂×C₈	—	2	1	no	—
623	C₂×C₈	—	2	1	no	—
624	C₂×C₈	—	2	1	no	—
625	C₂×C₈	—	2	1	no	—
626	C₂×C₈	—	2	1	no	—
627	C₂×C₈	—	2	1	no	—
628	C₂×C₈	—	4	2	no	—
629	C₂×C₈	—	4	2	no	—
630	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
631	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
632	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
633	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
634	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
635	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
636	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
637	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
638	C₄⋊C₄	—	2	1	no	—
639	C₄⋊C₄	—	2	1	no	—
640	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
641	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
642	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
643	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
644	C₂²⋊C₄	—	2	1	no	—
645	C₂²⋊C₄	—	2	1	no	—
646	C₂²⋊C₄	—	2	1	no	—
647	C₂²⋊C₄	—	2	1	no	—
648	C₂²⋊C₄	—	4	2	no	—
649	C₄²	—	2	1	no	—
650	C₄²	—	2	1	no	—
651	C₄²	—	2	1	no	—
652	C₄²	—	2	1	no	—
653	C₄²	—	2	1	no	—
654	C₄²	—	2	1	no	—
655	C₄²	—	2	1	no	—
656	C₄²	—	2	1	no	—
657	C₂×C₅	—	2	1	no	—
658	C₂×C₅	—	2	1	no	—
659	C₂×C₅	—	4	1	no	—
660	C₂×C₅	—	4	1	no	—
661	C₂×C₅	—	4	2	no	—
662	C₂×C₅	—	8	1	no	—
663	C₂×C₅	#2342	1	1	yes	characteristic
664	C₂×C₅	#2955	1	1	yes	characteristic
665	C₂×C₅	#2956	1	1	yes	characteristic
666	C₂³	—	2	1	no	—
667	C₂³	—	2	1	no	—
668	C₂³	—	2	1	no	—
669	C₂³	—	2	1	no	—
670	C₂³	—	4	1	no	—
671	C₂³	—	4	1	no	—
672	C₂³	—	4	2	no	—
673	C₂³	—	4	2	no	—
674	C₂³	—	8	1	no	—
675	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
676	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
677	C₂³	C₂×C₅×#41	1	1	yes	characteristic
678	Q₈	—	2	1	no	—
679	Q₈	—	2	1	no	—
680	Q₈	—	2	1	no	—
681	Q₈	—	4	2	no	—
682	Q₈	C₅×#117	1	2	yes	—
683	D₄	—	2	2	no	—
684	D₄	—	2	2	no	—
685	D₄	—	2	1	no	—
686	D₄	—	2	1	no	—
687	D₄	—	2	1	no	—
688	D₄	—	4	2	no	—
689	D₄	—	4	2	no	—
690	D₄	—	4	2	no	—
691	D₄	—	4	1	no	—
692	D₄	—	4	1	no	—
693	D₄	C₅×#117	1	2	yes	—
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	1	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	4	2	no	—
714	C₂×C₄	—	4	2	no	—
715	C₂×C₄	—	4	2	no	—
716	C₂×C₄	—	4	1	no	—
717	C₂×C₄	—	4	2	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	4	1	no	—
721	C₂×C₄	—	4	1	no	—
722	C₂×C₄	—	4	1	no	—
723	C₂×C₄	—	4	1	no	—
724	C₂×C₄	—	8	1	no	—
725	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
726	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
727	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
728	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
729	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
730	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
731	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
732	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
733	C₈	—	2	1	no	—
734	C₈	—	2	1	no	—
735	C₈	—	2	1	no	—
736	C₈	—	2	1	no	—
737	C₈	—	2	1	no	—
738	C₈	—	2	1	no	—
739	C₈	—	2	1	no	—
740	C₈	—	2	1	no	—
741	C₈	—	4	1	no	—
742	C₈	—	4	1	no	—
743	C₈	—	4	1	no	—
744	C₈	—	4	1	no	—
745	C₅	#22588	1	1	yes	characteristic, direct product factor, Sylow
746	C₂²	—	2	1	no	—
747	C₂²	—	2	1	no	—
748	C₂²	—	2	1	no	—
749	C₂²	—	2	1	no	—
750	C₂²	—	2	2	no	—
751	C₂²	—	2	1	no	—
752	C₂²	—	2	1	no	—
753	C₂²	—	2	1	no	—
754	C₂²	—	2	1	no	—
755	C₂²	—	4	1	no	—
756	C₂²	—	4	1	no	—
757	C₂²	—	4	1	no	—
758	C₂²	—	4	1	no	—
759	C₂²	—	4	1	no	—
760	C₂²	—	8	1	no	—
761	C₂²	—	8	1	no	—
762	C₂²	—	8	4	no	—
763	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
764	C₂²	C₅×#551	1	1	yes	characteristic
765	C₂²	C₅×#551	1	1	yes	characteristic
766	C₄	—	2	1	no	—
767	C₄	—	2	1	no	—
768	C₄	—	2	2	no	—
769	C₄	—	4	2	no	—
770	C₄	—	4	1	no	—
771	C₄	—	4	1	no	—
772	C₄	—	4	1	no	—
773	C₄	—	4	1	no	—
774	C₄	—	4	1	no	—
775	C₄	—	8	1	no	—
776	C₄	C₂×C₅×#117	1	1	yes	characteristic
777	C₄	C₅×#518	1	1	yes	characteristic
778	C₄	C₅×#546	1	1	yes	characteristic
779	C₄	C₅×#546	1	1	yes	characteristic
780	C₂	—	2	1	no	—
781	C₂	—	2	1	no	—
782	C₂	—	4	1	no	—
783	C₂	—	4	1	no	—
784	C₂	—	4	2	no	—
785	C₂	—	8	1	no	—
786	C₂	C₅×#2342	1	1	yes	characteristic
787	C₂	C₅×#2955	1	1	yes	characteristic
788	C₂	C₅×#2956	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	C₂²×C₅×#41	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₅×C₂²⋊C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#2924	C₂	semidirect
4. C₅×#1938	C₂	semidirect
5. C₅×#1937	C₂	semidirect
6. C₅×#1929	C₂	semidirect
7. C₅×#1929	C₂	semidirect
8. C₅×#1866	C₂	semidirect
9. C₅×#1866	C₂	semidirect
10. C₅×#1826	C₂	semidirect
11. C₅×#1811	C₂	semidirect
13. C₅×#1765	C₂	semidirect
14. C₅×#1764	C₂	semidirect
15. C₅×#1753	C₂	semidirect
25. C₂×C₅×#108	C₂²	semidirect
26. C₂×C₅×#108	C₂²	semidirect
27. C₅×#424	C₂²	semidirect
28. C₅×#424	C₂²	semidirect
33. C₅×#419	C₄	semidirect
34. C₅×#419	C₄	semidirect
35. C₅×#418	C₄	semidirect
36. C₅×#418	C₄	semidirect
37. C₅×#417	C₄	semidirect
38. C₅×#417	C₄	semidirect
39. C₅×#417	C₄	semidirect
40. C₅×#417	C₄	semidirect
54. C₅×#405	C₂²	semidirect
55. C₅×#405	C₂²	semidirect
56. C₂×C₅×#97	C₂²	semidirect
57. C₂×C₄×C₅×C₈	C₂²	semidirect
59. C₅×#341	C₂²	semidirect
60. C₅×#341	C₂²	semidirect
61. C₅×#339	C₂²	semidirect
62. C₅×#339	C₂²	semidirect
63. C₅×#339	C₂²	semidirect
64. C₅×#339	C₂²	semidirect
65. C₅×#336	C₂²	semidirect
66. C₅×#336	C₂²	semidirect
67. #22588	C₅	direct (N × H)
163. #2924	C₂×C₅	semidirect
166. #1938	C₂×C₅	semidirect
167. #1937	C₂×C₅	semidirect
168. #1929	C₂×C₅	semidirect
169. #1929	C₂×C₅	semidirect
170. #1866	C₂×C₅	semidirect
171. #1866	C₂×C₅	semidirect
172. #1826	C₂×C₅	semidirect
173. #1811	C₂×C₅	semidirect
175. #1765	C₂×C₅	semidirect
176. #1764	C₂×C₅	semidirect
177. #1753	C₂×C₅	semidirect
297. C₂×#108	C₂²×C₅	semidirect
298. C₂×#108	C₂²×C₅	semidirect
299. #424	C₂²×C₅	semidirect
300. #424	C₂²×C₅	semidirect
305. #419	C₄×C₅	semidirect
306. #419	C₄×C₅	semidirect
307. #418	C₄×C₅	semidirect
308. #418	C₄×C₅	semidirect
309. #417	C₄×C₅	semidirect
310. #417	C₄×C₅	semidirect
311. #417	C₄×C₅	semidirect
312. #417	C₄×C₅	semidirect
326. #405	C₂²×C₅	semidirect
327. #405	C₂²×C₅	semidirect
328. C₂×#97	C₂²×C₅	semidirect
329. C₂×C₄×C₈	C₂²×C₅	semidirect
331. #341	C₂²×C₅	semidirect
332. #341	C₂²×C₅	semidirect
333. #339	C₂²×C₅	semidirect
334. #339	C₂²×C₅	semidirect
335. #339	C₂²×C₅	semidirect
336. #339	C₂²×C₅	semidirect
337. #336	C₂²×C₅	semidirect
338. #336	C₂²×C₅	semidirect
745. C₅	#22588	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×#2924	2
C₅×#2896	2
C₅×#2880	2
C₅×#1938	2
C₅×#1937	2
C₅×#1929	2
C₅×#1866	2
C₅×#1826	2
C₅×#1811	2
C₅×#1789	2
C₅×#1765	2
C₅×#1764	2
C₅×#1753	2
#22588	5

Subgroups — C5×#22588 #11945308

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22588 #11945308