Subgroups — C₅×#26082 #11948802

Order 1280.

674 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3164	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3084	C₂	1	2	yes	maximal
3	C₅×#2913	C₂	1	1	yes	maximal, characteristic
4	C₅×#2090	C₂	1	2	yes	maximal, complemented
5	C₅×#2061	C₂	1	2	yes	maximal, complemented
6	C₅×#1952	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1945	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1860	C₂	1	2	yes	maximal
9	C₅×#1846	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1816	C₂	1	1	yes	maximal, characteristic
11	C₅×#1764	C₂	1	1	yes	maximal, characteristic
12	C₂×C₅×#131	C₂²	1	1	yes	characteristic
13	C₅×#544	C₂²	1	2	yes	—
14	C₅×#520	C₂²	1	2	yes	—
15	C₅×#501	—	2	2	no	—
16	C₅×#500	—	2	1	no	—
17	C₅×#499	—	2	1	no	—
18	C₅×#479	—	2	2	no	—
19	C₅×#478	—	2	2	no	—
20	C₅×#476	—	2	2	no	—
21	C₅×#475	—	2	2	no	—
22	C₂×C₅×#108	C₂²	1	1	yes	characteristic
23	C₅×#428	—	2	2	no	—
24	C₅×#428	C₂²	1	2	yes	—
25	C₅×#428	C₂²	1	2	yes	—
26	C₅×#428	C₂²	1	2	yes	—
27	C₅×#427	—	2	1	no	—
28	C₅×#427	C₂²	1	1	yes	characteristic
29	C₂×C₅×#107	—	2	1	no	—
30	C₂×C₅×#107	C₂²	1	1	yes	characteristic
31	C₂×C₅×#107	C₂²	1	1	yes	characteristic
32	C₂×C₅×#106	C₂²	1	2	yes	—
33	C₅×#424	C₂²	1	2	yes	—
34	C₂×C₅×#104	C₂²	1	1	yes	characteristic
35	C₅×#417	C₂²	1	2	yes	—
36	C₅×#416	C₂²	1	1	yes	characteristic
37	C₅×#405	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
39	C₅×#382	C₂²	1	2	yes	—
40	C₅×#343	C₂²	1	2	yes	—
41	C₅×#343	C₂²	1	2	yes	—
42	C₅×#341	C₂²	1	1	yes	characteristic
43	C₅×#339	C₂²	1	1	yes	characteristic
44	C₅×#339	C₂²	1	2	yes	—
45	#26082	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂×C₅×#41	C₂³	1	1	yes	characteristic
47	C₅×#131	—	2	2	no	—
48	C₅×#131	Q₈	1	4	yes	complemented
49	C₂×C₅×M₁₆	—	2	1	no	—
50	C₂×C₅×M₁₆	C₂³	1	2	yes	—
51	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
52	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
53	C₂²×C₅×C₈	—	2	1	no	—
54	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
55	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
56	C₅×C₄⋊Q₈	—	2	2	no	—
57	C₅×C₄⋊Q₈	—	2	2	no	—
58	C₅×#125	—	2	2	no	—
59	C₅×#125	—	2	2	no	—
60	C₅×C₂²⋊Q₈	—	4	2	no	—
61	C₄×C₅×Q₈	—	2	2	no	—
62	C₄×C₅×D₄	—	2	2	no	—
63	C₄×C₅×D₄	—	4	2	no	—
64	C₅×#117	—	2	2	no	—
65	C₅×#117	C₂³	1	1	yes	characteristic
66	C₅×#117	C₂³	1	2	yes	—
67	C₂×C₅×C₄⋊C₄	—	2	2	no	—
68	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
69	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
70	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
71	C₅×#108	—	2	2	no	—
72	C₅×#107	—	2	1	no	—
73	C₅×#107	—	2	1	no	—
74	C₅×#107	—	2	1	no	—
75	C₅×#107	—	2	1	no	—
76	C₅×#107	—	2	2	no	—
77	C₅×#107	—	2	2	no	—
78	C₅×#107	—	2	2	no	—
79	C₅×#107	D₄	1	1	yes	characteristic
80	C₅×#107	D₄	1	1	yes	characteristic
81	C₅×#106	—	2	2	no	—
82	C₅×#106	—	2	2	no	—
83	C₅×#106	—	2	2	no	—
84	C₅×#106	—	2	2	no	—
85	C₅×#106	—	2	2	no	—
86	C₅×#106	D₄	1	2	yes	—
87	C₅×C₄⋊C₈	—	2	2	no	—
88	C₅×C₄⋊C₈	—	2	2	no	—
89	C₅×#104	Q₈	1	4	yes	complemented
90	C₅×#103	—	2	2	no	—
91	C₅×#103	D₄	1	1	yes	characteristic
92	C₅×#103	D₄	1	1	yes	characteristic
93	C₅×#102	—	2	2	no	—
94	C₅×#102	D₄	1	1	yes	characteristic
95	C₅×#102	D₄	1	1	yes	characteristic
96	C₅×#97	—	2	1	no	—
97	C₄×C₅×C₈	—	2	1	no	—
98	C₄×C₅×C₈	—	2	2	no	—
99	C₅×#95	—	4	2	no	—
100	#3164	C₂×C₅	1	1	yes	characteristic, complemented
101	#3084	C₂×C₅	1	2	yes	—
102	#2913	C₂×C₅	1	1	yes	characteristic
103	#2090	C₂×C₅	1	2	yes	complemented
104	#2061	C₂×C₅	1	2	yes	complemented
105	#1952	C₂×C₅	1	1	yes	characteristic, complemented
106	#1945	C₂×C₅	1	1	yes	characteristic, complemented
107	#1860	C₂×C₅	1	2	yes	—
108	#1846	C₂×C₅	1	1	yes	characteristic, complemented
109	#1816	C₂×C₅	1	1	yes	characteristic
110	#1764	C₂×C₅	1	1	yes	characteristic
111	C₅×#41	—	2	1	no	—
112	C₅×#41	—	2	1	no	—
113	C₅×#41	C₂×Q₈	1	2	yes	—
114	C₅×#41	C₂×Q₈	1	2	yes	—
115	C₂×C₅×Q₈	—	4	2	no	—
116	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
117	C₂×C₅×D₄	—	2	1	no	—
118	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₅	—	2	1	no	—
120	C₂²×C₄×C₅	—	2	1	no	—
121	C₂²×C₄×C₅	—	2	2	no	—
122	C₂²×C₄×C₅	—	2	2	no	—
123	C₂²×C₄×C₅	—	4	2	no	—
124	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
125	C₅×M₁₆	—	2	1	no	—
126	C₅×M₁₆	—	2	1	no	—
127	C₅×M₁₆	—	2	4	no	—
128	C₅×M₁₆	—	2	2	no	—
129	C₅×M₁₆	—	2	2	no	—
130	C₅×M₁₆	C₂×Q₈	1	2	yes	—
131	C₅×M₁₆	C₂×Q₈	1	2	yes	—
132	C₂×C₅×C₈	—	2	1	no	—
133	C₂×C₅×C₈	—	2	1	no	—
134	C₂×C₅×C₈	—	2	1	no	—
135	C₂×C₅×C₈	—	2	1	no	—
136	C₂×C₅×C₈	—	2	4	no	—
137	C₂×C₅×C₈	—	2	2	no	—
138	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
139	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
140	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
141	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
142	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
143	C₂×C₅×C₈	#41	1	2	yes	—
144	C₅×C₄⋊C₄	—	2	2	no	—
145	C₅×C₄⋊C₄	—	2	2	no	—
146	C₅×C₄⋊C₄	—	2	2	no	—
147	C₅×C₄⋊C₄	—	2	2	no	—
148	C₅×C₄⋊C₄	—	4	2	no	—
149	C₅×C₄⋊C₄	—	4	2	no	—
150	C₅×C₄⋊C₄	—	4	2	no	—
151	C₅×C₄⋊C₄	—	4	2	no	—
152	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
153	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
154	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
155	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
156	C₅×C₂²⋊C₄	—	2	2	no	—
157	C₅×C₂²⋊C₄	—	2	1	no	—
158	C₅×C₂²⋊C₄	—	4	2	no	—
159	C₄²×C₅	—	2	2	no	—
160	C₄²×C₅	—	2	1	no	—
161	C₄²×C₅	—	2	1	no	—
162	C₄²×C₅	—	4	2	no	—
163	C₄²×C₅	C₂×Q₈	1	2	yes	—
164	C₂×#131	C₂²×C₅	1	1	yes	characteristic
165	#544	C₂²×C₅	1	2	yes	—
166	#520	C₂²×C₅	1	2	yes	—
167	#501	—	2	2	no	—
168	#500	—	2	1	no	—
169	#499	—	2	1	no	—
170	#479	—	2	2	no	—
171	#478	—	2	2	no	—
172	#476	—	2	2	no	—
173	#475	—	2	2	no	—
174	C₂×#108	C₂²×C₅	1	1	yes	characteristic
175	#428	—	2	2	no	—
176	#428	C₂²×C₅	1	2	yes	—
177	#428	C₂²×C₅	1	2	yes	—
178	#428	C₂²×C₅	1	2	yes	—
179	#427	—	2	1	no	—
180	#427	C₂²×C₅	1	1	yes	characteristic
181	C₂×#107	—	2	1	no	—
182	C₂×#107	C₂²×C₅	1	1	yes	characteristic
183	C₂×#107	C₂²×C₅	1	1	yes	characteristic
184	C₂×#106	C₂²×C₅	1	2	yes	—
185	#424	C₂²×C₅	1	2	yes	—
186	C₂×#104	C₂²×C₅	1	1	yes	characteristic
187	#417	C₂²×C₅	1	2	yes	—
188	#416	C₂²×C₅	1	1	yes	characteristic
189	#405	C₂²×C₅	1	1	yes	characteristic
190	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
191	#382	C₂²×C₅	1	2	yes	—
192	#343	C₂²×C₅	1	2	yes	—
193	#343	C₂²×C₅	1	2	yes	—
194	#341	C₂²×C₅	1	1	yes	characteristic
195	#339	C₂²×C₅	1	1	yes	characteristic
196	#339	C₂²×C₅	1	2	yes	—
197	C₂³×C₅	—	2	1	no	—
198	C₂³×C₅	H(5,𝔽₂)	1	1	yes	characteristic
199	C₅×Q₈	—	2	1	no	—
200	C₅×Q₈	—	16	2	no	—
201	C₅×Q₈	C₄⋊Q₈	1	2	yes	—
202	C₅×D₄	—	2	2	no	—
203	C₅×D₄	—	2	2	no	—
204	C₅×D₄	—	2	1	no	—
205	C₅×D₄	C₄⋊Q₈	1	2	yes	—
206	C₂×C₄×C₅	—	2	1	no	—
207	C₂×C₄×C₅	—	2	2	no	—
208	C₂×C₄×C₅	—	2	2	no	—
209	C₂×C₄×C₅	—	2	2	no	—
210	C₂×C₄×C₅	—	2	1	no	—
211	C₂×C₄×C₅	—	2	2	no	—
212	C₂×C₄×C₅	—	2	1	no	—
213	C₂×C₄×C₅	—	2	2	no	—
214	C₂×C₄×C₅	—	4	1	no	—
215	C₂×C₄×C₅	—	4	1	no	—
216	C₂×C₄×C₅	—	4	2	no	—
217	C₂×C₄×C₅	—	4	2	no	—
218	C₂×C₄×C₅	—	8	2	no	—
219	C₂×C₄×C₅	—	8	2	no	—
220	C₂×C₄×C₅	—	16	2	no	—
221	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
224	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
225	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
226	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
227	C₅×C₈	—	2	2	no	—
228	C₅×C₈	—	2	1	no	—
229	C₅×C₈	—	2	1	no	—
230	C₅×C₈	—	2	2	no	—
231	C₅×C₈	—	4	2	no	—
232	C₅×C₈	C₂²⋊Q₈	1	2	yes	—
233	C₅×C₈	C₂²⋊Q₈	1	2	yes	—
234	C₂×#41	C₂³×C₅	1	1	yes	characteristic
235	#131	—	2	2	no	—
236	#131	C₅×Q₈	1	4	yes	complemented
237	C₂×M₁₆	—	2	1	no	—
238	C₂×M₁₆	C₂³×C₅	1	2	yes	—
239	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
240	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
241	C₂²×C₈	—	2	1	no	—
242	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
243	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
244	C₄⋊Q₈	—	2	2	no	—
245	C₄⋊Q₈	—	2	2	no	—
246	#125	—	2	2	no	—
247	#125	—	2	2	no	—
248	C₂²⋊Q₈	—	4	2	no	—
249	C₄×Q₈	—	2	2	no	—
250	C₄×D₄	—	2	2	no	—
251	C₄×D₄	—	4	2	no	—
252	#117	—	2	2	no	—
253	#117	C₂³×C₅	1	2	yes	—
254	#117	C₂³×C₅	1	1	yes	characteristic
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
257	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
258	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
259	#108	—	2	2	no	—
260	#107	—	2	1	no	—
261	#107	—	2	1	no	—
262	#107	—	2	1	no	—
263	#107	—	2	1	no	—
264	#107	—	2	2	no	—
265	#107	—	2	2	no	—
266	#107	—	2	2	no	—
267	#107	C₅×D₄	1	1	yes	characteristic
268	#107	C₅×D₄	1	1	yes	characteristic
269	#106	—	2	2	no	—
270	#106	—	2	2	no	—
271	#106	—	2	2	no	—
272	#106	—	2	2	no	—
273	#106	—	2	2	no	—
274	#106	C₅×D₄	1	2	yes	—
275	C₄⋊C₈	—	2	2	no	—
276	C₄⋊C₈	—	2	2	no	—
277	#104	C₅×Q₈	1	4	yes	complemented
278	#103	—	2	2	no	—
279	#103	C₅×D₄	1	1	yes	characteristic
280	#103	C₅×D₄	1	1	yes	characteristic
281	#102	—	2	2	no	—
282	#102	C₅×D₄	1	1	yes	characteristic
283	#102	C₅×D₄	1	1	yes	characteristic
284	#97	—	2	1	no	—
285	C₄×C₈	—	2	1	no	—
286	C₄×C₈	—	2	2	no	—
287	#95	—	4	2	no	—
288	C₂²×C₅	—	2	1	no	—
289	C₂²×C₅	—	2	1	no	—
290	C₂²×C₅	—	2	2	no	—
291	C₂²×C₅	—	4	1	no	—
292	C₂²×C₅	—	4	1	no	—
293	C₂²×C₅	#544	1	1	yes	characteristic
294	C₂²×C₅	D₄²	1	1	yes	characteristic
295	C₂²×C₅	#554	1	1	yes	characteristic
296	C₄×C₅	—	2	2	no	—
297	C₄×C₅	—	4	2	no	—
298	C₄×C₅	—	4	1	no	—
299	C₄×C₅	—	4	2	no	—
300	C₄×C₅	—	4	2	no	—
301	C₄×C₅	—	4	1	no	—
302	C₄×C₅	—	8	2	no	—
303	C₄×C₅	—	8	2	no	—
304	C₄×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
305	C₄×C₅	C₂×C₄⋊Q₈	1	1	yes	characteristic
306	C₄×C₅	#547	1	1	yes	characteristic
307	C₄×C₅	D₄×Q₈	1	1	yes	characteristic
308	#41	—	2	1	no	—
309	#41	—	2	1	no	—
310	#41	C₂×C₅×Q₈	1	2	yes	—
311	#41	C₂×C₅×Q₈	1	2	yes	—
312	C₂×Q₈	—	4	2	no	—
313	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
314	C₂×D₄	—	2	1	no	—
315	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	4	2	no	—
321	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
322	M₁₆	—	2	1	no	—
323	M₁₆	—	2	1	no	—
324	M₁₆	—	2	4	no	—
325	M₁₆	—	2	2	no	—
326	M₁₆	—	2	2	no	—
327	M₁₆	C₂×C₅×Q₈	1	2	yes	—
328	M₁₆	C₂×C₅×Q₈	1	2	yes	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	4	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
336	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
337	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
338	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
339	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
340	C₂×C₈	C₅×#41	1	2	yes	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	4	2	no	—
346	C₄⋊C₄	—	4	2	no	—
347	C₄⋊C₄	—	4	2	no	—
348	C₄⋊C₄	—	4	2	no	—
349	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
350	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
351	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
352	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
353	C₂²⋊C₄	—	2	2	no	—
354	C₂²⋊C₄	—	2	1	no	—
355	C₂²⋊C₄	—	4	2	no	—
356	C₄²	—	2	1	no	—
357	C₄²	—	2	2	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	4	2	no	—
360	C₄²	C₂×C₅×Q₈	1	2	yes	—
361	C₂×C₅	—	2	1	no	—
362	C₂×C₅	—	2	1	no	—
363	C₂×C₅	—	4	2	no	—
364	C₂×C₅	#2440	1	1	yes	characteristic
365	C₂×C₅	#3290	1	1	yes	characteristic
366	C₂×C₅	#3290	1	1	yes	characteristic
367	C₂³	—	2	1	no	—
368	C₂³	C₅×H(5,𝔽₂)	1	1	yes	characteristic
369	Q₈	—	2	1	no	—
370	Q₈	—	16	2	no	—
371	Q₈	C₅×C₄⋊Q₈	1	2	yes	—
372	D₄	—	2	2	no	—
373	D₄	—	2	2	no	—
374	D₄	—	2	1	no	—
375	D₄	C₅×C₄⋊Q₈	1	2	yes	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	8	2	no	—
389	C₂×C₄	—	8	2	no	—
390	C₂×C₄	—	16	2	no	—
391	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
392	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
393	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
394	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
395	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
396	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
397	C₈	—	2	2	no	—
398	C₈	—	2	1	no	—
399	C₈	—	2	1	no	—
400	C₈	—	2	2	no	—
401	C₈	—	4	2	no	—
402	C₈	C₅×C₂²⋊Q₈	1	2	yes	—
403	C₈	C₅×C₂²⋊Q₈	1	2	yes	—
404	C₅	#26082	1	1	yes	characteristic, direct product factor, Sylow
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	4	1	no	—
410	C₂²	C₅×#544	1	1	yes	characteristic
411	C₂²	C₅×D₄²	1	1	yes	characteristic
412	C₂²	C₅×#554	1	1	yes	characteristic
413	C₄	—	2	2	no	—
414	C₄	—	4	2	no	—
415	C₄	—	4	2	no	—
416	C₄	—	4	1	no	—
417	C₄	—	4	2	no	—
418	C₄	—	4	1	no	—
419	C₄	—	8	2	no	—
420	C₄	—	8	2	no	—
421	C₄	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
422	C₄	C₂×C₅×C₄⋊Q₈	1	1	yes	characteristic
423	C₄	C₅×#547	1	1	yes	characteristic
424	C₄	C₅×D₄×Q₈	1	1	yes	characteristic
425	C₂	—	2	1	no	—
426	C₂	—	2	1	no	—
427	C₂	—	4	2	no	—
428	C₂	C₅×#2440	1	1	yes	characteristic
429	C₂	C₅×#3290	1	1	yes	characteristic
430	C₂	C₅×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂×C₅×#41	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3164	C₂	semidirect
4. C₅×#2090	C₂	semidirect
5. C₅×#2061	C₂	semidirect
6. C₅×#1952	C₂	semidirect
7. C₅×#1945	C₂	semidirect
9. C₅×#1846	C₂	semidirect
45. #26082	C₅	direct (N × H)
48. C₅×#131	Q₈	semidirect
89. C₅×#104	Q₈	semidirect
100. #3164	C₂×C₅	semidirect
103. #2090	C₂×C₅	semidirect
104. #2061	C₂×C₅	semidirect
105. #1952	C₂×C₅	semidirect
106. #1945	C₂×C₅	semidirect
108. #1846	C₂×C₅	semidirect
236. #131	C₅×Q₈	semidirect
277. #104	C₅×Q₈	semidirect
404. C₅	#26082	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×#3164	2
C₅×#3084	2
C₅×#2913	2
C₅×#2090	2
C₅×#2061	2
C₅×#1952	2
C₅×#1945	2
C₅×#1860	2
C₅×#1846	2
C₅×#1816	2
C₅×#1764	2
#26082	5

Subgroups — C5×#26082 #11948802

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#26082 #11948802