Subgroups — C₅×#22687 #11945407

Order 1280.

858 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#444	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#443	C₂	1	1	yes	maximal, characteristic
3	C₅×#2943	C₂	1	1	yes	maximal, characteristic
4	C₅×#2906	C₂	1	2	yes	maximal, complemented
5	C₅×#1946	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1945	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1866	C₂	1	2	yes	maximal, complemented
8	C₅×#1866	C₂	1	2	yes	maximal, complemented
9	C₅×#1849	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1806	C₂	1	2	yes	maximal, complemented
11	C₅×#1771	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#135	C₂²	1	1	yes	characteristic
13	C₂×C₅×#131	C₂²	1	2	yes	—
14	C₂×C₅×#131	C₂²	1	2	yes	—
15	C₄×C₅×#41	C₂²	1	2	yes	—
16	C₅×#444	—	2	4	no	—
17	C₅×#443	—	2	4	no	—
18	C₅×#442	C₄	1	2	yes	complemented
19	C₅×#441	C₄	1	2	yes	complemented
20	C₅×#440	C₄	1	2	yes	complemented
21	C₅×#440	C₄	1	2	yes	complemented
22	C₂×C₅×#108	C₂²	1	1	yes	characteristic
23	C₂×C₅×#108	C₂²	1	1	yes	characteristic
24	C₂×C₅×#108	C₂²	1	2	yes	—
25	C₅×#427	C₂²	1	1	yes	characteristic
26	C₅×#424	—	2	2	no	—
27	C₅×#424	—	2	2	no	—
28	C₅×#424	C₂²	1	2	yes	—
29	C₅×#424	C₂²	1	2	yes	—
30	C₅×#423	—	2	2	no	—
31	C₅×#423	C₂²	1	2	yes	—
32	C₂×C₅×C₄⋊C₈	—	2	2	no	—
33	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₅×#104	C₂²	1	2	yes	—
35	C₂×C₅×#104	C₂²	1	2	yes	—
36	C₅×#416	C₂²	1	2	yes	—
37	C₂×C₅×#97	C₂²	1	1	yes	characteristic
38	C₂×C₅×#97	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
40	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
41	C₅×#339	C₂²	1	2	yes	—
42	C₅×#339	C₂²	1	2	yes	—
43	C₅×#336	C₂²	1	1	yes	characteristic
44	C₅×#336	C₂²	1	1	yes	characteristic
45	#22687	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂×C₅×#41	C₂³	1	2	yes	—
47	C₅×#135	D₄	1	4	yes	—
48	C₅×#135	Q₈	1	4	yes	—
49	C₂×C₅×Q₁₆	C₂×C₄	1	1	yes	characteristic
50	C₂×C₅×SD₁₆	C₂×C₄	1	2	yes	—
51	C₂×C₅×D₈	C₂×C₄	1	1	yes	characteristic
52	C₅×#131	—	2	4	no	—
53	C₅×#131	—	2	4	no	—
54	C₅×#131	—	4	2	no	—
55	C₅×#131	—	4	2	no	—
56	C₂×C₅×M₁₆	—	2	2	no	—
57	C₂×C₅×M₁₆	—	2	2	no	—
58	C₂×C₅×M₁₆	C₂³	1	2	yes	—
59	C₂×C₅×M₁₆	C₂³	1	2	yes	—
60	C₂²×C₅×C₈	—	2	2	no	—
61	C₂²×C₅×C₈	—	2	2	no	—
62	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
63	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
64	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
67	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
68	C₄×C₅×D₄	—	2	2	no	—
69	C₄×C₅×D₄	—	2	2	no	—
70	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
71	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
72	C₅×#117	—	2	2	no	—
73	C₅×#117	C₂³	1	2	yes	—
74	C₂×C₅×C₄⋊C₄	—	2	1	no	—
75	C₂×C₄²×C₅	—	2	2	no	—
76	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
79	C₅×#108	—	2	2	no	—
80	C₅×#108	—	2	2	no	—
81	C₅×#108	—	4	2	no	—
82	C₅×#107	C₂×C₄	1	1	yes	characteristic
83	C₅×#107	C₂×C₄	1	1	yes	characteristic
84	C₅×#106	C₂×C₄	1	2	yes	—
85	C₅×C₄⋊C₈	—	2	2	no	—
86	C₅×C₄⋊C₈	—	2	2	no	—
87	C₅×C₄⋊C₈	—	2	2	no	—
88	C₅×C₄⋊C₈	—	2	2	no	—
89	C₅×C₄⋊C₈	—	2	2	no	—
90	C₅×C₄⋊C₈	—	2	2	no	—
91	C₅×C₄⋊C₈	D₄	1	2	yes	—
92	C₅×C₄⋊C₈	D₄	1	2	yes	—
93	C₅×#104	—	2	4	no	—
94	C₅×#104	—	2	4	no	—
95	C₅×#103	C₂×C₄	1	2	yes	—
96	C₅×#103	C₂×C₄	1	2	yes	—
97	C₅×#102	C₂×C₄	1	2	yes	—
98	C₅×#102	C₂×C₄	1	2	yes	—
99	C₅×#97	—	2	2	no	—
100	C₅×#97	C₂×C₄	1	2	yes	—
101	C₅×#97	C₂×C₄	1	2	yes	—
102	C₄×C₅×C₈	—	2	2	no	—
103	C₅×#95	—	2	1	no	—
104	C₂×#444	C₂×C₅	1	1	yes	characteristic
105	C₂×#443	C₂×C₅	1	1	yes	characteristic
106	#2943	C₂×C₅	1	1	yes	characteristic
107	#2906	C₂×C₅	1	2	yes	complemented
108	#1946	C₂×C₅	1	1	yes	characteristic, complemented
109	#1945	C₂×C₅	1	1	yes	characteristic, complemented
110	#1866	C₂×C₅	1	2	yes	complemented
111	#1866	C₂×C₅	1	2	yes	complemented
112	#1849	C₂×C₅	1	1	yes	characteristic, complemented
113	#1806	C₂×C₅	1	2	yes	complemented
114	#1771	C₂×C₅	1	1	yes	characteristic, complemented
115	C₅×#41	—	2	2	no	—
116	C₅×#41	—	2	2	no	—
117	C₅×#41	C₂×D₄	1	4	yes	—
118	C₅×#41	C₂×Q₈	1	4	yes	—
119	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
120	C₂×C₅×D₄	—	2	2	no	—
121	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₅	—	2	2	no	—
123	C₂²×C₄×C₅	—	2	1	no	—
124	C₂²×C₄×C₅	—	2	2	no	—
125	C₂²×C₄×C₅	—	2	2	no	—
126	C₂²×C₄×C₅	—	2	1	no	—
127	C₂²×C₄×C₅	#41	1	1	yes	characteristic
128	C₂²×C₄×C₅	#41	1	1	yes	characteristic
129	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
130	C₅×Q₁₆	C₄⋊C₄	1	4	yes	complemented
131	C₅×SD₁₆	C₄⋊C₄	1	8	yes	complemented
132	C₅×D₈	C₄⋊C₄	1	4	yes	complemented
133	C₅×M₁₆	—	2	2	no	—
134	C₅×M₁₆	—	2	2	no	—
135	C₅×M₁₆	—	2	2	no	—
136	C₅×M₁₆	—	2	2	no	—
137	C₅×M₁₆	—	4	4	no	—
138	C₅×M₁₆	—	4	4	no	—
139	C₂×C₅×C₈	—	2	1	no	—
140	C₂×C₅×C₈	—	2	1	no	—
141	C₂×C₅×C₈	—	2	1	no	—
142	C₂×C₅×C₈	—	2	1	no	—
143	C₂×C₅×C₈	—	2	1	no	—
144	C₂×C₅×C₈	—	2	1	no	—
145	C₂×C₅×C₈	—	2	2	no	—
146	C₂×C₅×C₈	—	2	2	no	—
147	C₂×C₅×C₈	—	4	4	no	—
148	C₂×C₅×C₈	—	4	4	no	—
149	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
150	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
153	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
154	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
155	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
156	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
157	C₅×C₄⋊C₄	—	2	2	no	—
158	C₅×C₄⋊C₄	—	2	2	no	—
159	C₅×C₄⋊C₄	—	4	2	no	—
160	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
161	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
162	C₅×C₂²⋊C₄	—	2	2	no	—
163	C₅×C₂²⋊C₄	—	2	2	no	—
164	C₅×C₂²⋊C₄	—	2	2	no	—
165	C₄²×C₅	—	2	2	no	—
166	C₄²×C₅	—	2	2	no	—
167	C₄²×C₅	—	2	2	no	—
168	C₄²×C₅	—	2	1	no	—
169	C₄²×C₅	—	2	1	no	—
170	C₄²×C₅	—	2	1	no	—
171	C₄²×C₅	—	2	1	no	—
172	C₄²×C₅	C₂²×C₄	1	2	yes	—
173	C₄²×C₅	C₂×D₄	1	2	yes	—
174	C₂×#135	C₂²×C₅	1	1	yes	characteristic
175	C₂×#131	C₂²×C₅	1	2	yes	—
176	C₂×#131	C₂²×C₅	1	2	yes	—
177	C₄×#41	C₂²×C₅	1	2	yes	—
178	#444	—	2	4	no	—
179	#443	—	2	4	no	—
180	#442	C₄×C₅	1	2	yes	complemented
181	#441	C₄×C₅	1	2	yes	complemented
182	#440	C₄×C₅	1	2	yes	complemented
183	#440	C₄×C₅	1	2	yes	complemented
184	C₂×#108	C₂²×C₅	1	1	yes	characteristic
185	C₂×#108	C₂²×C₅	1	1	yes	characteristic
186	C₂×#108	C₂²×C₅	1	2	yes	—
187	#427	C₂²×C₅	1	1	yes	characteristic
188	#424	—	2	2	no	—
189	#424	—	2	2	no	—
190	#424	C₂²×C₅	1	2	yes	—
191	#424	C₂²×C₅	1	2	yes	—
192	#423	—	2	2	no	—
193	#423	C₂²×C₅	1	2	yes	—
194	C₂×C₄⋊C₈	—	2	2	no	—
195	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
196	C₂×#104	C₂²×C₅	1	2	yes	—
197	C₂×#104	C₂²×C₅	1	2	yes	—
198	#416	C₂²×C₅	1	2	yes	—
199	C₂×#97	C₂²×C₅	1	1	yes	characteristic
200	C₂×#97	C₂²×C₅	1	1	yes	characteristic
201	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
202	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
203	#339	C₂²×C₅	1	2	yes	—
204	#339	C₂²×C₅	1	2	yes	—
205	#336	C₂²×C₅	1	1	yes	characteristic
206	#336	C₂²×C₅	1	1	yes	characteristic
207	C₂³×C₅	—	2	2	no	—
208	C₂³×C₅	C₂×#41	1	1	yes	characteristic
209	C₅×Q₈	—	2	2	no	—
210	C₅×Q₈	C₂×C₄⋊C₄	1	4	yes	—
211	C₅×D₄	—	2	4	no	—
212	C₅×D₄	—	2	4	no	—
213	C₅×D₄	—	2	2	no	—
214	C₅×D₄	C₂×C₄⋊C₄	1	4	yes	—
215	C₂×C₄×C₅	—	2	2	no	—
216	C₂×C₄×C₅	—	2	4	no	—
217	C₂×C₄×C₅	—	2	4	no	—
218	C₂×C₄×C₅	—	2	2	no	—
219	C₂×C₄×C₅	—	2	2	no	—
220	C₂×C₄×C₅	—	2	2	no	—
221	C₂×C₄×C₅	—	4	1	no	—
222	C₂×C₄×C₅	—	4	1	no	—
223	C₂×C₄×C₅	—	4	4	no	—
224	C₂×C₄×C₅	—	4	1	no	—
225	C₂×C₄×C₅	—	4	1	no	—
226	C₂×C₄×C₅	—	4	1	no	—
227	C₂×C₄×C₅	—	4	1	no	—
228	C₂×C₄×C₅	—	4	1	no	—
229	C₂×C₄×C₅	—	8	2	no	—
230	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
231	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
232	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
233	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
236	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
237	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
238	C₅×C₈	—	2	2	no	—
239	C₅×C₈	—	2	1	no	—
240	C₅×C₈	—	2	2	no	—
241	C₅×C₈	—	2	1	no	—
242	C₅×C₈	—	4	2	no	—
243	C₅×C₈	—	4	2	no	—
244	C₅×C₈	C₂×C₄⋊C₄	1	2	yes	—
245	C₅×C₈	C₂×C₄⋊C₄	1	2	yes	—
246	C₂×#41	C₂³×C₅	1	2	yes	—
247	#135	C₅×D₄	1	4	yes	—
248	#135	C₅×Q₈	1	4	yes	—
249	C₂×Q₁₆	C₂×C₄×C₅	1	1	yes	characteristic
250	C₂×SD₁₆	C₂×C₄×C₅	1	2	yes	—
251	C₂×D₈	C₂×C₄×C₅	1	1	yes	characteristic
252	#131	—	2	4	no	—
253	#131	—	2	4	no	—
254	#131	—	4	2	no	—
255	#131	—	4	2	no	—
256	C₂×M₁₆	—	2	2	no	—
257	C₂×M₁₆	—	2	2	no	—
258	C₂×M₁₆	C₂³×C₅	1	2	yes	—
259	C₂×M₁₆	C₂³×C₅	1	2	yes	—
260	C₂²×C₈	—	2	2	no	—
261	C₂²×C₈	—	2	2	no	—
262	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
263	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
264	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
265	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
266	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
267	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
268	C₄×D₄	—	2	2	no	—
269	C₄×D₄	—	2	2	no	—
270	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
271	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
272	#117	—	2	2	no	—
273	#117	C₂³×C₅	1	2	yes	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄²	—	2	2	no	—
276	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
277	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
278	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
279	#108	—	2	2	no	—
280	#108	—	2	2	no	—
281	#108	—	4	2	no	—
282	#107	C₂×C₄×C₅	1	1	yes	characteristic
283	#107	C₂×C₄×C₅	1	1	yes	characteristic
284	#106	C₂×C₄×C₅	1	2	yes	—
285	C₄⋊C₈	—	2	2	no	—
286	C₄⋊C₈	—	2	2	no	—
287	C₄⋊C₈	—	2	2	no	—
288	C₄⋊C₈	—	2	2	no	—
289	C₄⋊C₈	—	2	2	no	—
290	C₄⋊C₈	—	2	2	no	—
291	C₄⋊C₈	C₅×D₄	1	2	yes	—
292	C₄⋊C₈	C₅×D₄	1	2	yes	—
293	#104	—	2	4	no	—
294	#104	—	2	4	no	—
295	#103	C₂×C₄×C₅	1	2	yes	—
296	#103	C₂×C₄×C₅	1	2	yes	—
297	#102	C₂×C₄×C₅	1	2	yes	—
298	#102	C₂×C₄×C₅	1	2	yes	—
299	#97	—	2	2	no	—
300	#97	C₂×C₄×C₅	1	2	yes	—
301	#97	C₂×C₄×C₅	1	2	yes	—
302	C₄×C₈	—	2	2	no	—
303	#95	—	2	1	no	—
304	C₂²×C₅	—	2	1	no	—
305	C₂²×C₅	—	2	1	no	—
306	C₂²×C₅	—	2	4	no	—
307	C₂²×C₅	—	4	2	no	—
308	C₂²×C₅	—	4	2	no	—
309	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
310	C₂²×C₅	#547	1	1	yes	characteristic
311	C₂²×C₅	#554	1	1	yes	characteristic
312	C₄×C₅	—	2	4	no	—
313	C₄×C₅	—	2	2	no	—
314	C₄×C₅	—	2	2	no	—
315	C₄×C₅	—	4	2	no	—
316	C₄×C₅	—	4	2	no	—
317	C₄×C₅	—	4	2	no	—
318	C₄×C₅	—	8	1	no	—
319	C₄×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
320	C₄×C₅	#520	1	1	yes	characteristic
321	C₄×C₅	D₄²	1	1	yes	characteristic
322	C₄×C₅	D₄×Q₈	1	1	yes	characteristic
323	#41	—	2	2	no	—
324	#41	—	2	2	no	—
325	#41	C₂×C₅×D₄	1	4	yes	—
326	#41	C₂×C₅×Q₈	1	4	yes	—
327	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	C₅×#41	1	1	yes	characteristic
336	C₂²×C₄	C₅×#41	1	1	yes	characteristic
337	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
338	Q₁₆	C₅×C₄⋊C₄	1	4	yes	complemented
339	SD₁₆	C₅×C₄⋊C₄	1	8	yes	complemented
340	D₈	C₅×C₄⋊C₄	1	4	yes	complemented
341	M₁₆	—	2	2	no	—
342	M₁₆	—	2	2	no	—
343	M₁₆	—	2	2	no	—
344	M₁₆	—	2	2	no	—
345	M₁₆	—	4	4	no	—
346	M₁₆	—	4	4	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	4	4	no	—
356	C₂×C₈	—	4	4	no	—
357	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
358	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
359	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
360	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
361	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
362	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
363	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
364	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	4	2	no	—
368	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
369	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
370	C₂²⋊C₄	—	2	2	no	—
371	C₂²⋊C₄	—	2	2	no	—
372	C₂²⋊C₄	—	2	2	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	1	no	—
377	C₄²	—	2	1	no	—
378	C₄²	—	2	1	no	—
379	C₄²	—	2	1	no	—
380	C₄²	C₂²×C₄×C₅	1	2	yes	—
381	C₄²	C₂×C₅×D₄	1	2	yes	—
382	C₂×C₅	—	2	1	no	—
383	C₂×C₅	—	2	1	no	—
384	C₂×C₅	—	4	4	no	—
385	C₂×C₅	D₄×C₄⋊C₄	1	1	yes	characteristic
386	C₂×C₅	#2955	1	1	yes	characteristic
387	C₂×C₅	#2956	1	1	yes	characteristic
388	C₂³	—	2	2	no	—
389	C₂³	C₂×C₅×#41	1	1	yes	characteristic
390	Q₈	—	2	2	no	—
391	Q₈	C₂×C₅×C₄⋊C₄	1	4	yes	—
392	D₄	—	2	4	no	—
393	D₄	—	2	4	no	—
394	D₄	—	2	2	no	—
395	D₄	C₂×C₅×C₄⋊C₄	1	4	yes	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	8	2	no	—
411	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
412	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
413	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
414	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
415	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
416	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
417	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
418	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
419	C₈	—	2	2	no	—
420	C₈	—	2	1	no	—
421	C₈	—	2	2	no	—
422	C₈	—	2	1	no	—
423	C₈	—	4	2	no	—
424	C₈	—	4	2	no	—
425	C₈	C₂×C₅×C₄⋊C₄	1	2	yes	—
426	C₈	C₂×C₅×C₄⋊C₄	1	2	yes	—
427	C₅	#22687	1	1	yes	characteristic, direct product factor, Sylow
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	4	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	2	no	—
433	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
434	C₂²	C₅×#547	1	1	yes	characteristic
435	C₂²	C₅×#554	1	1	yes	characteristic
436	C₄	—	2	4	no	—
437	C₄	—	2	2	no	—
438	C₄	—	2	2	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	2	no	—
441	C₄	—	4	2	no	—
442	C₄	—	8	1	no	—
443	C₄	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
444	C₄	C₅×#520	1	1	yes	characteristic
445	C₄	C₅×D₄²	1	1	yes	characteristic
446	C₄	C₅×D₄×Q₈	1	1	yes	characteristic
447	C₂	—	2	1	no	—
448	C₂	—	2	1	no	—
449	C₂	—	4	4	no	—
450	C₂	C₅×D₄×C₄⋊C₄	1	1	yes	characteristic
451	C₂	C₅×#2955	1	1	yes	characteristic
452	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	C₂×C₅×#135	C₂²
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
4. C₅×#2906	C₂	semidirect
5. C₅×#1946	C₂	semidirect
6. C₅×#1945	C₂	semidirect
7. C₅×#1866	C₂	semidirect
8. C₅×#1866	C₂	semidirect
9. C₅×#1849	C₂	semidirect
10. C₅×#1806	C₂	semidirect
11. C₅×#1771	C₂	semidirect
18. C₅×#442	C₄	semidirect
19. C₅×#441	C₄	semidirect
20. C₅×#440	C₄	semidirect
21. C₅×#440	C₄	semidirect
45. #22687	C₅	direct (N × H)
107. #2906	C₂×C₅	semidirect
108. #1946	C₂×C₅	semidirect
109. #1945	C₂×C₅	semidirect
110. #1866	C₂×C₅	semidirect
111. #1866	C₂×C₅	semidirect
112. #1849	C₂×C₅	semidirect
113. #1806	C₂×C₅	semidirect
114. #1771	C₂×C₅	semidirect
130. C₅×Q₁₆	C₄⋊C₄	semidirect
131. C₅×SD₁₆	C₄⋊C₄	semidirect
132. C₅×D₈	C₄⋊C₄	semidirect
180. #442	C₄×C₅	semidirect
181. #441	C₄×C₅	semidirect
182. #440	C₄×C₅	semidirect
183. #440	C₄×C₅	semidirect
338. Q₁₆	C₅×C₄⋊C₄	semidirect
339. SD₁₆	C₅×C₄⋊C₄	semidirect
340. D₈	C₅×C₄⋊C₄	semidirect
427. C₅	#22687	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₅×#444	2
C₂×C₅×#443	2
C₅×#2943	2
C₅×#2906	2
C₅×#1946	2
C₅×#1945	2
C₅×#1866	2
C₅×#1849	2
C₅×#1806	2
C₅×#1771	2
#22687	5

Subgroups — C5×#22687 #11945407

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22687 #11945407