Subgroups — C₅×#22207 #11944927

Order 1280.

806 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3054	C₂	1	1	yes	maximal, characteristic
2	C₅×#2930	C₂	1	2	yes	maximal, complemented
3	C₅×#1929	C₂	1	2	yes	maximal, complemented
4	C₅×#1922	C₂	1	2	yes	maximal, complemented
5	C₅×#1896	C₂	1	2	yes	maximal, complemented
6	C₅×#1876	C₂	1	2	yes	maximal, complemented
7	C₅×#1866	C₂	1	2	yes	maximal, complemented
8	C₅×#1811	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1728	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#135	C₂²	1	1	yes	characteristic
11	C₂×C₅×#131	C₂²	1	2	yes	—
12	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
14	C₅×#525	C₂²	1	2	yes	—
15	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₅×#470	C₄	1	1	yes	characteristic, complemented
17	C₅×#470	C₄	1	1	yes	characteristic, complemented
18	C₅×#469	C₄	1	1	yes	characteristic, complemented
19	C₅×#469	C₄	1	1	yes	characteristic, complemented
20	C₅×#468	C₄	1	2	yes	complemented
21	C₅×#468	C₄	1	2	yes	complemented
22	C₅×#436	—	2	2	no	—
23	C₅×#436	—	2	2	no	—
24	C₅×#435	—	2	2	no	—
25	C₅×#435	—	2	2	no	—
26	C₂×C₅×#108	C₂²	1	1	yes	characteristic
27	C₂×C₅×#108	C₂²	1	1	yes	characteristic
28	C₅×#427	C₂²	1	1	yes	characteristic
29	C₅×#424	C₂²	1	2	yes	—
30	C₂×C₅×#104	C₂²	1	2	yes	—
31	C₂×C₅×#104	C₂²	1	2	yes	—
32	C₅×#416	C₂²	1	2	yes	—
33	C₅×#408	C₂²	1	2	yes	—
34	C₅×#407	C₂²	1	2	yes	—
35	C₅×#405	C₂²	1	2	yes	—
36	C₅×#341	C₂²	1	2	yes	—
37	C₅×#339	C₂²	1	2	yes	—
38	C₅×#339	C₂²	1	2	yes	—
39	C₅×#336	C₂²	1	2	yes	—
40	C₅×#336	C₂²	1	2	yes	—
41	#22207	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂×C₅×#41	C₂³	1	2	yes	—
43	C₂³×C₄×C₅	—	2	1	no	—
44	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₅×#135	—	4	1	no	—
46	C₅×#135	—	4	1	no	—
47	C₂×C₅×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
48	C₂×C₅×SD₁₆	C₂×C₄	1	2	yes	complemented
49	C₂×C₅×D₈	C₂×C₄	1	1	yes	characteristic, complemented
50	C₅×#131	—	4	2	no	—
51	C₅×#131	—	4	2	no	—
52	C₂×C₅×M₁₆	—	2	2	no	—
53	C₂×C₅×M₁₆	—	4	1	no	—
54	C₂×C₅×M₁₆	—	4	1	no	—
55	C₂×C₅×M₁₆	—	4	1	no	—
56	C₂×C₅×M₁₆	—	4	1	no	—
57	C₂×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
58	C₂×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
59	C₂×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
60	C₂×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
61	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
62	C₂×C₅×M₁₆	D₄	1	2	yes	—
63	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
64	C₂×C₅×M₁₆	C₂³	1	2	yes	—
65	C₂×C₅×M₁₆	C₂³	1	2	yes	—
66	C₂²×C₅×C₈	—	2	2	no	—
67	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₅×C₈	C₂³	1	2	yes	—
70	C₅×#123	—	2	2	no	—
71	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
72	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
73	C₅×#121	C₂×C₄	1	2	yes	—
74	C₅×#121	C₂×C₄	1	2	yes	—
75	C₅×#120	—	2	2	no	—
76	C₄×C₅×D₄	—	2	2	no	—
77	C₄×C₅×D₄	—	2	2	no	—
78	C₅×#117	C₂³	1	2	yes	—
79	C₂×C₄²×C₅	—	2	1	no	—
80	C₂×C₄²×C₅	—	4	1	no	—
81	C₂×C₄²×C₅	—	4	1	no	—
82	C₂×C₄²×C₅	C₂³	1	2	yes	—
83	C₅×#108	—	4	1	no	—
84	C₅×#108	—	4	1	no	—
85	C₅×#107	C₂×C₄	1	2	yes	complemented
86	C₅×#106	C₂×C₄	1	1	yes	characteristic, complemented
87	C₅×#106	C₂×C₄	1	1	yes	characteristic, complemented
88	C₅×C₄⋊C₈	—	2	2	no	—
89	C₅×C₄⋊C₈	—	2	2	no	—
90	C₅×#104	—	4	2	no	—
91	C₅×#104	—	4	2	no	—
92	C₅×#103	C₂×C₄	1	2	yes	complemented
93	C₅×#103	C₂×C₄	1	2	yes	complemented
94	C₅×#102	C₂×C₄	1	2	yes	complemented
95	C₅×#102	C₂×C₄	1	2	yes	complemented
96	C₅×C₂²⋊C₈	—	2	2	no	—
97	C₅×C₂²⋊C₈	—	2	2	no	—
98	C₅×C₂²⋊C₈	—	2	2	no	—
99	C₅×C₂²⋊C₈	—	2	2	no	—
100	C₅×#97	—	2	2	no	—
101	C₄×C₅×C₈	—	2	2	no	—
102	#3054	C₂×C₅	1	1	yes	characteristic
103	#2930	C₂×C₅	1	2	yes	complemented
104	#1929	C₂×C₅	1	2	yes	complemented
105	#1922	C₂×C₅	1	2	yes	complemented
106	#1896	C₂×C₅	1	2	yes	complemented
107	#1876	C₂×C₅	1	2	yes	complemented
108	#1866	C₂×C₅	1	2	yes	complemented
109	#1811	C₂×C₅	1	1	yes	characteristic, complemented
110	#1728	C₂×C₅	1	1	yes	characteristic, complemented
111	C₂⁴×C₅	#41	1	1	yes	characteristic
112	C₅×#41	—	2	2	no	—
113	C₅×#41	—	2	2	no	—
114	C₅×#41	—	2	2	no	—
115	C₅×#41	—	2	2	no	—
116	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
117	C₂×C₅×D₄	—	2	2	no	—
118	C₂×C₅×D₄	—	2	2	no	—
119	C₂×C₅×D₄	—	2	2	no	—
120	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₅	—	2	1	no	—
122	C₂²×C₄×C₅	—	2	1	no	—
123	C₂²×C₄×C₅	—	2	1	no	—
124	C₂²×C₄×C₅	—	2	1	no	—
125	C₂²×C₄×C₅	—	2	2	no	—
126	C₂²×C₄×C₅	—	2	2	no	—
127	C₂²×C₄×C₅	—	4	4	no	—
128	C₂²×C₄×C₅	—	4	2	no	—
129	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₅	#41	1	1	yes	characteristic
134	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
135	C₅×Q₁₆	—	4	1	no	—
136	C₅×SD₁₆	—	4	2	no	—
137	C₅×D₈	—	4	1	no	—
138	C₅×M₁₆	—	2	2	no	—
139	C₅×M₁₆	—	2	2	no	—
140	C₅×M₁₆	—	2	2	no	—
141	C₅×M₁₆	—	2	2	no	—
142	C₅×M₁₆	—	4	1	no	—
143	C₅×M₁₆	—	4	1	no	—
144	C₅×M₁₆	—	4	1	no	—
145	C₅×M₁₆	—	4	1	no	—
146	C₅×M₁₆	—	4	1	no	—
147	C₅×M₁₆	—	4	2	no	—
148	C₅×M₁₆	—	4	1	no	—
149	C₅×M₁₆	—	4	4	no	—
150	C₂×C₅×C₈	—	2	2	no	—
151	C₂×C₅×C₈	—	2	2	no	—
152	C₂×C₅×C₈	—	2	1	no	—
153	C₂×C₅×C₈	—	2	1	no	—
154	C₂×C₅×C₈	—	2	1	no	—
155	C₂×C₅×C₈	—	2	1	no	—
156	C₂×C₅×C₈	—	2	2	no	—
157	C₂×C₅×C₈	—	2	2	no	—
158	C₂×C₅×C₈	—	4	4	no	—
159	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
164	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
165	C₅×C₄⋊C₄	—	2	2	no	—
166	C₅×C₄⋊C₄	—	2	2	no	—
167	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
168	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
169	C₅×C₂²⋊C₄	—	2	2	no	—
170	C₅×C₂²⋊C₄	—	2	2	no	—
171	C₅×C₂²⋊C₄	—	2	2	no	—
172	C₅×C₂²⋊C₄	—	2	2	no	—
173	C₅×C₂²⋊C₄	—	2	2	no	—
174	C₄²×C₅	—	2	2	no	—
175	C₄²×C₅	—	2	2	no	—
176	C₄²×C₅	—	2	2	no	—
177	C₄²×C₅	—	4	2	no	—
178	C₂×#135	C₂²×C₅	1	1	yes	characteristic
179	C₂×#131	C₂²×C₅	1	2	yes	—
180	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
181	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
182	#525	C₂²×C₅	1	2	yes	—
183	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
184	#470	C₄×C₅	1	1	yes	characteristic, complemented
185	#470	C₄×C₅	1	1	yes	characteristic, complemented
186	#469	C₄×C₅	1	1	yes	characteristic, complemented
187	#469	C₄×C₅	1	1	yes	characteristic, complemented
188	#468	C₄×C₅	1	2	yes	complemented
189	#468	C₄×C₅	1	2	yes	complemented
190	#436	—	2	2	no	—
191	#436	—	2	2	no	—
192	#435	—	2	2	no	—
193	#435	—	2	2	no	—
194	C₂×#108	C₂²×C₅	1	1	yes	characteristic
195	C₂×#108	C₂²×C₅	1	1	yes	characteristic
196	#427	C₂²×C₅	1	1	yes	characteristic
197	#424	C₂²×C₅	1	2	yes	—
198	C₂×#104	C₂²×C₅	1	2	yes	—
199	C₂×#104	C₂²×C₅	1	2	yes	—
200	#416	C₂²×C₅	1	2	yes	—
201	#408	C₂²×C₅	1	2	yes	—
202	#407	C₂²×C₅	1	2	yes	—
203	#405	C₂²×C₅	1	2	yes	—
204	#341	C₂²×C₅	1	2	yes	—
205	#339	C₂²×C₅	1	2	yes	—
206	#339	C₂²×C₅	1	2	yes	—
207	#336	C₂²×C₅	1	2	yes	—
208	#336	C₂²×C₅	1	2	yes	—
209	C₂³×C₅	—	2	1	no	—
210	C₂³×C₅	—	2	1	no	—
211	C₂³×C₅	—	2	2	no	—
212	C₂³×C₅	—	4	2	no	—
213	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
214	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
215	C₂³×C₅	C₂×#41	1	1	yes	characteristic
216	C₅×Q₈	—	2	2	no	—
217	C₅×Q₈	—	2	2	no	—
218	C₅×D₄	—	2	2	no	—
219	C₅×D₄	—	2	2	no	—
220	C₅×D₄	—	4	2	no	—
221	C₅×D₄	—	4	2	no	—
222	C₅×D₄	—	8	2	no	—
223	C₅×D₄	—	8	2	no	—
224	C₂×C₄×C₅	—	2	1	no	—
225	C₂×C₄×C₅	—	2	1	no	—
226	C₂×C₄×C₅	—	2	1	no	—
227	C₂×C₄×C₅	—	2	1	no	—
228	C₂×C₄×C₅	—	2	1	no	—
229	C₂×C₄×C₅	—	2	1	no	—
230	C₂×C₄×C₅	—	2	1	no	—
231	C₂×C₄×C₅	—	2	1	no	—
232	C₂×C₄×C₅	—	2	1	no	—
233	C₂×C₄×C₅	—	2	1	no	—
234	C₂×C₄×C₅	—	2	4	no	—
235	C₂×C₄×C₅	—	2	2	no	—
236	C₂×C₄×C₅	—	2	2	no	—
237	C₂×C₄×C₅	—	2	2	no	—
238	C₂×C₄×C₅	—	4	2	no	—
239	C₂×C₄×C₅	—	4	8	no	—
240	C₂×C₄×C₅	—	4	2	no	—
241	C₂×C₄×C₅	—	4	2	no	—
242	C₂×C₄×C₅	—	4	2	no	—
243	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
244	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
245	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
246	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
248	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
249	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
250	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
251	C₅×C₈	—	2	1	no	—
252	C₅×C₈	—	2	1	no	—
253	C₅×C₈	—	2	1	no	—
254	C₅×C₈	—	2	1	no	—
255	C₅×C₈	—	2	2	no	—
256	C₅×C₈	—	2	2	no	—
257	C₅×C₈	—	4	2	no	—
258	C₅×C₈	—	4	2	no	—
259	C₂×#41	C₂³×C₅	1	2	yes	—
260	C₂³×C₄	—	2	1	no	—
261	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
262	#135	—	4	1	no	—
263	#135	—	4	1	no	—
264	C₂×Q₁₆	C₂×C₄×C₅	1	1	yes	characteristic, complemented
265	C₂×SD₁₆	C₂×C₄×C₅	1	2	yes	complemented
266	C₂×D₈	C₂×C₄×C₅	1	1	yes	characteristic, complemented
267	#131	—	4	2	no	—
268	#131	—	4	2	no	—
269	C₂×M₁₆	—	2	2	no	—
270	C₂×M₁₆	—	4	1	no	—
271	C₂×M₁₆	—	4	1	no	—
272	C₂×M₁₆	—	4	1	no	—
273	C₂×M₁₆	—	4	1	no	—
274	C₂×M₁₆	C₂×C₄×C₅	1	1	yes	characteristic
275	C₂×M₁₆	C₂×C₄×C₅	1	1	yes	characteristic
276	C₂×M₁₆	C₂×C₄×C₅	1	1	yes	characteristic
277	C₂×M₁₆	C₂×C₄×C₅	1	1	yes	characteristic
278	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
279	C₂×M₁₆	C₅×D₄	1	2	yes	—
280	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
281	C₂×M₁₆	C₂³×C₅	1	2	yes	—
282	C₂×M₁₆	C₂³×C₅	1	2	yes	—
283	C₂²×C₈	—	2	2	no	—
284	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
285	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
286	C₂²×C₈	C₂³×C₅	1	2	yes	—
287	#123	—	2	2	no	—
288	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
289	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
290	#121	C₂×C₄×C₅	1	2	yes	—
291	#121	C₂×C₄×C₅	1	2	yes	—
292	#120	—	2	2	no	—
293	C₄×D₄	—	2	2	no	—
294	C₄×D₄	—	2	2	no	—
295	#117	C₂³×C₅	1	2	yes	—
296	C₂×C₄²	—	2	1	no	—
297	C₂×C₄²	—	4	1	no	—
298	C₂×C₄²	—	4	1	no	—
299	C₂×C₄²	C₂³×C₅	1	2	yes	—
300	#108	—	4	1	no	—
301	#108	—	4	1	no	—
302	#107	C₂×C₄×C₅	1	2	yes	complemented
303	#106	C₂×C₄×C₅	1	1	yes	characteristic, complemented
304	#106	C₂×C₄×C₅	1	1	yes	characteristic, complemented
305	C₄⋊C₈	—	2	2	no	—
306	C₄⋊C₈	—	2	2	no	—
307	#104	—	4	2	no	—
308	#104	—	4	2	no	—
309	#103	C₂×C₄×C₅	1	2	yes	complemented
310	#103	C₂×C₄×C₅	1	2	yes	complemented
311	#102	C₂×C₄×C₅	1	2	yes	complemented
312	#102	C₂×C₄×C₅	1	2	yes	complemented
313	C₂²⋊C₈	—	2	2	no	—
314	C₂²⋊C₈	—	2	2	no	—
315	C₂²⋊C₈	—	2	2	no	—
316	C₂²⋊C₈	—	2	2	no	—
317	#97	—	2	2	no	—
318	C₄×C₈	—	2	2	no	—
319	C₂²×C₅	—	2	2	no	—
320	C₂²×C₅	—	2	1	no	—
321	C₂²×C₅	—	2	1	no	—
322	C₂²×C₅	—	2	2	no	—
323	C₂²×C₅	—	2	2	no	—
324	C₂²×C₅	—	4	2	no	—
325	C₂²×C₅	—	4	2	no	—
326	C₂²×C₅	—	4	2	no	—
327	C₂²×C₅	—	4	2	no	—
328	C₂²×C₅	—	4	2	no	—
329	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
330	C₂²×C₅	#538	1	1	yes	characteristic
331	C₂²×C₅	#539	1	1	yes	characteristic
332	C₄×C₅	—	2	1	no	—
333	C₄×C₅	—	2	1	no	—
334	C₄×C₅	—	4	4	no	—
335	C₄×C₅	—	4	2	no	—
336	C₄×C₅	—	4	2	no	—
337	C₄×C₅	—	4	2	no	—
338	C₄×C₅	#518	1	1	yes	characteristic
339	C₄×C₅	#520	1	1	yes	characteristic
340	C₄×C₅	#534	1	1	yes	characteristic
341	C₄×C₅	#537	1	1	yes	characteristic
342	C₂⁴	C₅×#41	1	1	yes	characteristic
343	#41	—	2	2	no	—
344	#41	—	2	2	no	—
345	#41	—	2	2	no	—
346	#41	—	2	2	no	—
347	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	4	4	no	—
359	C₂²×C₄	—	4	2	no	—
360	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
361	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
362	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
363	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
364	C₂²×C₄	C₅×#41	1	1	yes	characteristic
365	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
366	Q₁₆	—	4	1	no	—
367	SD₁₆	—	4	2	no	—
368	D₈	—	4	1	no	—
369	M₁₆	—	2	2	no	—
370	M₁₆	—	2	2	no	—
371	M₁₆	—	2	2	no	—
372	M₁₆	—	2	2	no	—
373	M₁₆	—	4	1	no	—
374	M₁₆	—	4	1	no	—
375	M₁₆	—	4	1	no	—
376	M₁₆	—	4	1	no	—
377	M₁₆	—	4	1	no	—
378	M₁₆	—	4	2	no	—
379	M₁₆	—	4	1	no	—
380	M₁₆	—	4	4	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	4	4	no	—
390	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
391	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
392	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
393	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
394	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
395	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
399	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
400	C₂²⋊C₄	—	2	2	no	—
401	C₂²⋊C₄	—	2	2	no	—
402	C₂²⋊C₄	—	2	2	no	—
403	C₂²⋊C₄	—	2	2	no	—
404	C₂²⋊C₄	—	2	2	no	—
405	C₄²	—	2	2	no	—
406	C₄²	—	2	2	no	—
407	C₄²	—	2	2	no	—
408	C₄²	—	4	2	no	—
409	C₂×C₅	—	2	1	no	—
410	C₂×C₅	—	2	1	no	—
411	C₂×C₅	—	4	1	no	—
412	C₂×C₅	—	4	1	no	—
413	C₂×C₅	—	8	2	no	—
414	C₂×C₅	#2325	1	1	yes	characteristic
415	C₂×C₅	#2956	1	2	yes	—
416	C₂³	—	2	1	no	—
417	C₂³	—	2	1	no	—
418	C₂³	—	2	2	no	—
419	C₂³	—	4	2	no	—
420	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
421	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
422	C₂³	C₂×C₅×#41	1	1	yes	characteristic
423	Q₈	—	2	2	no	—
424	Q₈	—	2	2	no	—
425	D₄	—	2	2	no	—
426	D₄	—	2	2	no	—
427	D₄	—	4	2	no	—
428	D₄	—	4	2	no	—
429	D₄	—	8	2	no	—
430	D₄	—	8	2	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	8	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
451	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
452	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
453	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
454	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
455	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
456	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
457	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
458	C₈	—	2	1	no	—
459	C₈	—	2	1	no	—
460	C₈	—	2	1	no	—
461	C₈	—	2	1	no	—
462	C₈	—	2	2	no	—
463	C₈	—	2	2	no	—
464	C₈	—	4	2	no	—
465	C₈	—	4	2	no	—
466	C₅	#22207	1	1	yes	characteristic, direct product factor, Sylow
467	C₂²	—	2	2	no	—
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	4	2	no	—
475	C₂²	—	4	2	no	—
476	C₂²	—	4	2	no	—
477	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
478	C₂²	C₅×#538	1	1	yes	characteristic
479	C₂²	C₅×#539	1	1	yes	characteristic
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	4	4	no	—
483	C₄	—	4	2	no	—
484	C₄	—	4	2	no	—
485	C₄	—	4	2	no	—
486	C₄	C₅×#518	1	1	yes	characteristic
487	C₄	C₅×#520	1	1	yes	characteristic
488	C₄	C₅×#534	1	1	yes	characteristic
489	C₄	C₅×#537	1	1	yes	characteristic
490	C₂	—	2	1	no	—
491	C₂	—	2	1	no	—
492	C₂	—	4	1	no	—
493	C₂	—	4	1	no	—
494	C₂	—	8	2	no	—
495	C₂	C₅×#2325	1	1	yes	characteristic
496	C₂	C₅×#2956	1	2	yes	—

	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	C₅×#3054	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₅×M₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2930	C₂	semidirect
3. C₅×#1929	C₂	semidirect
4. C₅×#1922	C₂	semidirect
5. C₅×#1896	C₂	semidirect
6. C₅×#1876	C₂	semidirect
7. C₅×#1866	C₂	semidirect
8. C₅×#1811	C₂	semidirect
9. C₅×#1728	C₂	semidirect
16. C₅×#470	C₄	semidirect
17. C₅×#470	C₄	semidirect
18. C₅×#469	C₄	semidirect
19. C₅×#469	C₄	semidirect
20. C₅×#468	C₄	semidirect
21. C₅×#468	C₄	semidirect
41. #22207	C₅	direct (N × H)
47. C₂×C₅×Q₁₆	C₂×C₄	semidirect
48. C₂×C₅×SD₁₆	C₂×C₄	semidirect
49. C₂×C₅×D₈	C₂×C₄	semidirect
85. C₅×#107	C₂×C₄	semidirect
86. C₅×#106	C₂×C₄	semidirect
87. C₅×#106	C₂×C₄	semidirect
92. C₅×#103	C₂×C₄	semidirect
93. C₅×#103	C₂×C₄	semidirect
94. C₅×#102	C₂×C₄	semidirect
95. C₅×#102	C₂×C₄	semidirect
103. #2930	C₂×C₅	semidirect
104. #1929	C₂×C₅	semidirect
105. #1922	C₂×C₅	semidirect
106. #1896	C₂×C₅	semidirect
107. #1876	C₂×C₅	semidirect
108. #1866	C₂×C₅	semidirect
109. #1811	C₂×C₅	semidirect
110. #1728	C₂×C₅	semidirect
184. #470	C₄×C₅	semidirect
185. #470	C₄×C₅	semidirect
186. #469	C₄×C₅	semidirect
187. #469	C₄×C₅	semidirect
188. #468	C₄×C₅	semidirect
189. #468	C₄×C₅	semidirect
264. C₂×Q₁₆	C₂×C₄×C₅	semidirect
265. C₂×SD₁₆	C₂×C₄×C₅	semidirect
266. C₂×D₈	C₂×C₄×C₅	semidirect
302. #107	C₂×C₄×C₅	semidirect
303. #106	C₂×C₄×C₅	semidirect
304. #106	C₂×C₄×C₅	semidirect
309. #103	C₂×C₄×C₅	semidirect
310. #103	C₂×C₄×C₅	semidirect
311. #102	C₂×C₄×C₅	semidirect
312. #102	C₂×C₄×C₅	semidirect
466. C₅	#22207	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×#3054	2
C₅×#2930	2
C₅×#1929	2
C₅×#1922	2
C₅×#1896	2
C₅×#1876	2
C₅×#1866	2
C₅×#1811	2
C₅×#1728	2
#22207	5

Subgroups — C5×#22207 #11944927

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22207 #11944927