Subgroups — C₅×#19285 #11942005

Order 1280.

636 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3167	C₂	1	1	yes	maximal, characteristic
2	C₅×#3078	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3037	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#446	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1700	C₂	1	2	yes	maximal, complemented
6	C₅×#1698	C₂	1	2	yes	maximal, complemented
7	C₅×#1692	C₂	1	2	yes	maximal, complemented
8	C₅×#1686	C₂	1	2	yes	maximal, complemented
9	C₅×#1567	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1550	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1547	C₂	1	1	yes	maximal, characteristic
12	C₂×C₅×#137	—	2	1	no	—
13	C₅×#533	C₂²	1	1	yes	characteristic
14	C₅×#532	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
16	C₅×#498	C₂²	1	1	yes	characteristic
17	C₅×#492	C₂²	1	1	yes	characteristic
18	C₅×#487	C₂²	1	1	yes	characteristic
19	C₅×#486	C₂²	1	1	yes	characteristic
20	C₅×#479	—	2	2	no	—
21	C₅×#477	C₂²	1	2	yes	—
22	C₅×#475	C₂²	1	2	yes	—
23	C₅×#465	—	2	1	no	—
24	C₅×#465	—	2	1	no	—
25	C₅×#464	—	2	2	no	—
26	C₅×#462	C₂²	1	2	yes	—
27	C₅×#460	C₂²	1	2	yes	—
28	C₅×#446	—	2	1	no	—
29	C₅×#446	—	2	1	no	—
30	C₅×#446	C₂²	1	2	yes	—
31	C₅×#446	C₂²	1	2	yes	—
32	C₄×C₅×SD₁₆	—	2	1	no	—
33	C₄×C₅×SD₁₆	—	2	1	no	—
34	C₅×#428	—	2	1	no	—
35	C₅×#423	C₂²	1	1	yes	characteristic
36	C₅×#423	C₂²	1	1	yes	characteristic
37	C₂×C₅×C₄⋊C₈	—	2	1	no	—
38	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	C₅×#419	—	2	1	no	—
40	C₅×#417	—	2	1	no	—
41	C₂×C₅×#97	—	2	1	no	—
42	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
43	C₅×#335	C₂²	1	2	yes	—
44	C₅×#335	C₂²	1	2	yes	—
45	C₅×#333	C₂²	1	2	yes	—
46	C₅×#332	C₂²	1	2	yes	—
47	C₅×#332	C₂²	1	2	yes	—
48	C₅×#331	C₂²	1	2	yes	—
49	#19285	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂×C₅×#41	—	2	1	no	—
51	C₂²×C₅×Q₈	D₄	1	1	yes	characteristic
52	C₅×#137	—	4	4	no	—
53	C₂×C₅×Q₁₆	—	2	2	no	—
54	C₂×C₅×SD₁₆	—	2	2	no	—
55	C₂×C₅×SD₁₆	—	2	1	no	—
56	C₂×C₅×SD₁₆	—	2	1	no	—
57	C₂×C₅×M₁₆	—	2	1	no	—
58	C₂×C₅×M₁₆	—	2	1	no	—
59	C₂²×C₅×C₈	—	2	1	no	—
60	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
61	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
62	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
63	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
64	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
65	C₅×#127	C₂³	1	1	yes	characteristic
66	C₅×#125	—	2	1	no	—
67	C₅×#124	—	2	1	no	—
68	C₅×C₂²⋊Q₈	—	2	1	no	—
69	C₅×C₂²⋊Q₈	—	2	1	no	—
70	C₅×#121	—	2	1	no	—
71	C₅×#121	—	2	1	no	—
72	C₄×C₅×Q₈	—	2	1	no	—
73	C₄×C₅×Q₈	—	2	1	no	—
74	C₄×C₅×Q₈	—	2	1	no	—
75	C₄×C₅×Q₈	—	2	1	no	—
76	C₄×C₅×Q₈	D₄	1	2	yes	—
77	C₄×C₅×Q₈	C₂³	1	2	yes	—
78	C₄×C₅×D₄	—	2	1	no	—
79	C₄×C₅×D₄	—	2	1	no	—
80	C₅×#117	—	2	1	no	—
81	C₂×C₅×C₄⋊C₄	—	2	1	no	—
82	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₅	—	2	1	no	—
84	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
85	C₅×#107	—	2	2	no	—
86	C₅×#106	—	2	1	no	—
87	C₅×#106	—	2	1	no	—
88	C₅×#106	—	2	2	no	—
89	C₅×C₄⋊C₈	—	2	2	no	—
90	C₅×C₄⋊C₈	—	2	2	no	—
91	C₅×C₄⋊C₈	—	2	1	no	—
92	C₅×C₄⋊C₈	—	2	1	no	—
93	C₅×C₄⋊C₈	—	2	1	no	—
94	C₅×C₄⋊C₈	C₂³	1	2	yes	—
95	C₅×C₄⋊C₈	C₂³	1	2	yes	—
96	C₅×C₄⋊C₈	C₂³	1	2	yes	—
97	C₅×#103	—	2	2	no	—
98	C₅×#103	—	2	2	no	—
99	C₅×#103	—	2	1	no	—
100	C₅×#103	—	2	1	no	—
101	C₅×#103	—	2	2	no	—
102	C₅×#102	—	2	1	no	—
103	C₅×#102	—	2	1	no	—
104	C₅×#102	—	2	2	no	—
105	C₅×#97	—	2	2	no	—
106	C₅×#97	—	2	2	no	—
107	C₄×C₅×C₈	D₄	1	1	yes	characteristic
108	C₄×C₅×C₈	D₄	1	1	yes	characteristic
109	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
110	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
111	#3167	C₂×C₅	1	1	yes	characteristic
112	#3078	C₂×C₅	1	1	yes	characteristic, complemented
113	#3037	C₂×C₅	1	1	yes	characteristic
114	C₂×#446	C₂×C₅	1	1	yes	characteristic, complemented
115	#1700	C₂×C₅	1	2	yes	complemented
116	#1698	C₂×C₅	1	2	yes	complemented
117	#1692	C₂×C₅	1	2	yes	complemented
118	#1686	C₂×C₅	1	2	yes	complemented
119	#1567	C₂×C₅	1	1	yes	characteristic, complemented
120	#1550	C₂×C₅	1	1	yes	characteristic, complemented
121	#1547	C₂×C₅	1	1	yes	characteristic
122	C₅×#41	—	4	2	no	—
123	C₅×#41	—	4	2	no	—
124	C₂×C₅×Q₈	—	2	1	no	—
125	C₂×C₅×Q₈	—	2	2	no	—
126	C₂×C₅×Q₈	—	2	2	no	—
127	C₂×C₅×Q₈	—	2	1	no	—
128	C₂×C₅×Q₈	—	2	1	no	—
129	C₂×C₅×Q₈	—	2	1	no	—
130	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
131	C₂×C₅×D₄	—	2	1	no	—
132	C₂×C₅×D₄	—	2	1	no	—
133	C₂×C₅×D₄	—	2	1	no	—
134	C₂×C₅×D₄	—	4	1	no	—
135	C₂²×C₄×C₅	—	2	1	no	—
136	C₂²×C₄×C₅	—	2	1	no	—
137	C₂²×C₄×C₅	—	4	1	no	—
138	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₅	#41	1	1	yes	characteristic
141	C₅×Q₁₆	—	4	4	no	—
142	C₅×SD₁₆	—	4	2	no	—
143	C₅×SD₁₆	—	4	4	no	—
144	C₅×SD₁₆	—	4	2	no	—
145	C₅×M₁₆	—	4	2	no	—
146	C₅×M₁₆	—	4	2	no	—
147	C₂×C₅×C₈	—	2	2	no	—
148	C₂×C₅×C₈	—	2	2	no	—
149	C₂×C₅×C₈	—	2	2	no	—
150	C₂×C₅×C₈	—	2	2	no	—
151	C₂×C₅×C₈	—	4	1	no	—
152	C₂×C₅×C₈	—	4	2	no	—
153	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
154	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
155	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
156	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
157	C₅×C₄⋊C₄	—	2	2	no	—
158	C₅×C₄⋊C₄	—	2	1	no	—
159	C₅×C₄⋊C₄	—	2	2	no	—
160	C₅×C₄⋊C₄	—	2	1	no	—
161	C₅×C₄⋊C₄	—	2	1	no	—
162	C₅×C₄⋊C₄	—	2	1	no	—
163	C₅×C₄⋊C₄	—	2	1	no	—
164	C₅×C₄⋊C₄	—	2	1	no	—
165	C₅×C₄⋊C₄	—	2	1	no	—
166	C₅×C₄⋊C₄	—	4	1	no	—
167	C₅×C₄⋊C₄	—	4	1	no	—
168	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
169	C₅×C₂²⋊C₄	—	4	1	no	—
170	C₅×C₂²⋊C₄	—	4	1	no	—
171	C₅×C₂²⋊C₄	—	4	1	no	—
172	C₄²×C₅	—	2	2	no	—
173	C₄²×C₅	—	2	2	no	—
174	C₄²×C₅	—	4	1	no	—
175	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₅	#41	1	1	yes	characteristic
178	C₄²×C₅	C₂⁴	1	1	yes	characteristic
179	C₂×#137	—	2	1	no	—
180	#533	C₂²×C₅	1	1	yes	characteristic
181	#532	C₂²×C₅	1	1	yes	characteristic
182	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
183	#498	C₂²×C₅	1	1	yes	characteristic
184	#492	C₂²×C₅	1	1	yes	characteristic
185	#487	C₂²×C₅	1	1	yes	characteristic
186	#486	C₂²×C₅	1	1	yes	characteristic
187	#479	—	2	2	no	—
188	#477	C₂²×C₅	1	2	yes	—
189	#475	C₂²×C₅	1	2	yes	—
190	#465	—	2	1	no	—
191	#465	—	2	1	no	—
192	#464	—	2	2	no	—
193	#462	C₂²×C₅	1	2	yes	—
194	#460	C₂²×C₅	1	2	yes	—
195	#446	—	2	1	no	—
196	#446	—	2	1	no	—
197	#446	C₂²×C₅	1	2	yes	—
198	#446	C₂²×C₅	1	2	yes	—
199	C₄×SD₁₆	—	2	1	no	—
200	C₄×SD₁₆	—	2	1	no	—
201	#428	—	2	1	no	—
202	#423	C₂²×C₅	1	1	yes	characteristic
203	#423	C₂²×C₅	1	1	yes	characteristic
204	C₂×C₄⋊C₈	—	2	1	no	—
205	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
206	#419	—	2	1	no	—
207	#417	—	2	1	no	—
208	C₂×#97	—	2	1	no	—
209	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
210	#335	C₂²×C₅	1	2	yes	—
211	#335	C₂²×C₅	1	2	yes	—
212	#333	C₂²×C₅	1	2	yes	—
213	#332	C₂²×C₅	1	2	yes	—
214	#332	C₂²×C₅	1	2	yes	—
215	#331	C₂²×C₅	1	2	yes	—
216	C₂³×C₅	—	4	1	no	—
217	C₂³×C₅	#121	1	1	yes	characteristic
218	C₅×Q₈	—	2	2	no	—
219	C₅×Q₈	—	2	2	no	—
220	C₅×Q₈	—	4	2	no	—
221	C₅×Q₈	—	4	1	no	—
222	C₅×Q₈	—	4	1	no	—
223	C₅×Q₈	—	4	1	no	—
224	C₅×Q₈	—	4	1	no	—
225	C₅×Q₈	—	8	1	no	—
226	C₅×D₄	—	4	1	no	—
227	C₅×D₄	—	4	1	no	—
228	C₅×D₄	—	4	1	no	—
229	C₅×D₄	—	4	1	no	—
230	C₅×D₄	—	8	1	no	—
231	C₅×D₄	—	8	2	no	—
232	C₂×C₄×C₅	—	2	1	no	—
233	C₂×C₄×C₅	—	2	1	no	—
234	C₂×C₄×C₅	—	2	2	no	—
235	C₂×C₄×C₅	—	2	2	no	—
236	C₂×C₄×C₅	—	4	1	no	—
237	C₂×C₄×C₅	—	4	2	no	—
238	C₂×C₄×C₅	—	4	2	no	—
239	C₂×C₄×C₅	—	4	1	no	—
240	C₂×C₄×C₅	—	4	1	no	—
241	C₂×C₄×C₅	—	4	1	no	—
242	C₂×C₄×C₅	—	8	2	no	—
243	C₂×C₄×C₅	#121	1	1	yes	characteristic
244	C₂×C₄×C₅	#121	1	1	yes	characteristic
245	C₂×C₄×C₅	#121	1	1	yes	characteristic
246	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
247	C₂×C₄×C₅	#137	1	2	yes	—
248	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₅	C₂×#41	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	—	4	2	no	—
255	C₅×C₈	—	4	2	no	—
256	C₅×C₈	—	4	2	no	—
257	C₅×C₈	#137	1	2	yes	complemented
258	C₂×#41	—	2	1	no	—
259	C₂²×Q₈	C₅×D₄	1	1	yes	characteristic
260	#137	—	4	4	no	—
261	C₂×Q₁₆	—	2	2	no	—
262	C₂×SD₁₆	—	2	2	no	—
263	C₂×SD₁₆	—	2	1	no	—
264	C₂×SD₁₆	—	2	1	no	—
265	C₂×M₁₆	—	2	1	no	—
266	C₂×M₁₆	—	2	1	no	—
267	C₂²×C₈	—	2	1	no	—
268	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
269	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
270	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
271	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
272	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
273	#127	C₂³×C₅	1	1	yes	characteristic
274	#125	—	2	1	no	—
275	#124	—	2	1	no	—
276	C₂²⋊Q₈	—	2	1	no	—
277	C₂²⋊Q₈	—	2	1	no	—
278	#121	—	2	1	no	—
279	#121	—	2	1	no	—
280	C₄×Q₈	—	2	1	no	—
281	C₄×Q₈	—	2	1	no	—
282	C₄×Q₈	—	2	1	no	—
283	C₄×Q₈	—	2	1	no	—
284	C₄×Q₈	C₅×D₄	1	2	yes	—
285	C₄×Q₈	C₂³×C₅	1	2	yes	—
286	C₄×D₄	—	2	1	no	—
287	C₄×D₄	—	2	1	no	—
288	#117	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
291	C₂×C₄²	—	2	1	no	—
292	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
293	#107	—	2	2	no	—
294	#106	—	2	1	no	—
295	#106	—	2	1	no	—
296	#106	—	2	2	no	—
297	C₄⋊C₈	—	2	2	no	—
298	C₄⋊C₈	—	2	2	no	—
299	C₄⋊C₈	—	2	1	no	—
300	C₄⋊C₈	—	2	1	no	—
301	C₄⋊C₈	—	2	1	no	—
302	C₄⋊C₈	C₂³×C₅	1	2	yes	—
303	C₄⋊C₈	C₂³×C₅	1	2	yes	—
304	C₄⋊C₈	C₂³×C₅	1	2	yes	—
305	#103	—	2	2	no	—
306	#103	—	2	2	no	—
307	#103	—	2	1	no	—
308	#103	—	2	1	no	—
309	#103	—	2	2	no	—
310	#102	—	2	1	no	—
311	#102	—	2	1	no	—
312	#102	—	2	2	no	—
313	#97	—	2	2	no	—
314	#97	—	2	2	no	—
315	C₄×C₈	C₅×D₄	1	1	yes	characteristic
316	C₄×C₈	C₅×D₄	1	1	yes	characteristic
317	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
318	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
319	C₂²×C₅	—	2	1	no	—
320	C₂²×C₅	—	2	1	no	—
321	C₂²×C₅	—	8	1	no	—
322	C₂²×C₅	—	8	1	no	—
323	C₂²×C₅	—	8	1	no	—
324	C₂²×C₅	#468	1	2	yes	—
325	C₂²×C₅	C₂×#121	1	1	yes	characteristic
326	C₄×C₅	—	2	1	no	—
327	C₄×C₅	—	2	1	no	—
328	C₄×C₅	—	2	1	no	—
329	C₄×C₅	—	4	2	no	—
330	C₄×C₅	—	4	2	no	—
331	C₄×C₅	—	8	1	no	—
332	C₄×C₅	—	8	1	no	—
333	C₄×C₅	—	8	1	no	—
334	C₄×C₅	#468	1	2	yes	—
335	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
336	C₄×C₅	C₂×#137	1	1	yes	characteristic
337	C₄×C₅	C₂×#137	1	1	yes	characteristic
338	C₄×C₅	#575	1	1	yes	characteristic
339	#41	—	4	2	no	—
340	#41	—	4	2	no	—
341	C₂×Q₈	—	2	1	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	1	no	—
345	C₂×Q₈	—	2	1	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
348	C₂×D₄	—	2	1	no	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	—	4	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	4	1	no	—
355	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
356	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
357	C₂²×C₄	C₅×#41	1	1	yes	characteristic
358	Q₁₆	—	4	4	no	—
359	SD₁₆	—	4	2	no	—
360	SD₁₆	—	4	4	no	—
361	SD₁₆	—	4	2	no	—
362	M₁₆	—	4	2	no	—
363	M₁₆	—	4	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	4	1	no	—
369	C₂×C₈	—	4	2	no	—
370	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
371	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
372	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
373	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	4	1	no	—
384	C₄⋊C₄	—	4	1	no	—
385	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
386	C₂²⋊C₄	—	4	1	no	—
387	C₂²⋊C₄	—	4	1	no	—
388	C₂²⋊C₄	—	4	1	no	—
389	C₄²	—	2	2	no	—
390	C₄²	—	2	2	no	—
391	C₄²	—	4	1	no	—
392	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
393	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
394	C₄²	C₅×#41	1	1	yes	characteristic
395	C₄²	C₂⁴×C₅	1	1	yes	characteristic
396	C₂×C₅	—	2	2	no	—
397	C₂×C₅	—	16	1	no	—
398	C₂×C₅	#3037	1	1	yes	characteristic
399	C₂×C₅	C₂×#468	1	1	yes	characteristic
400	C₂×C₅	#3067	1	1	yes	characteristic
401	C₂³	—	4	1	no	—
402	C₂³	C₅×#121	1	1	yes	characteristic
403	Q₈	—	2	2	no	—
404	Q₈	—	2	2	no	—
405	Q₈	—	4	2	no	—
406	Q₈	—	4	1	no	—
407	Q₈	—	4	1	no	—
408	Q₈	—	4	1	no	—
409	Q₈	—	4	1	no	—
410	Q₈	—	8	1	no	—
411	D₄	—	4	1	no	—
412	D₄	—	4	1	no	—
413	D₄	—	4	1	no	—
414	D₄	—	4	1	no	—
415	D₄	—	8	1	no	—
416	D₄	—	8	2	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	8	2	no	—
428	C₂×C₄	C₅×#121	1	1	yes	characteristic
429	C₂×C₄	C₅×#121	1	1	yes	characteristic
430	C₂×C₄	C₅×#121	1	1	yes	characteristic
431	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
432	C₂×C₄	C₅×#137	1	2	yes	—
433	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
434	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
435	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
436	C₈	—	2	1	no	—
437	C₈	—	2	1	no	—
438	C₈	—	2	1	no	—
439	C₈	—	4	2	no	—
440	C₈	—	4	2	no	—
441	C₈	—	4	2	no	—
442	C₈	C₅×#137	1	2	yes	complemented
443	C₅	#19285	1	1	yes	characteristic, direct product factor, Sylow
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	8	1	no	—
447	C₂²	—	8	1	no	—
448	C₂²	—	8	1	no	—
449	C₂²	C₅×#468	1	2	yes	—
450	C₂²	C₂×C₅×#121	1	1	yes	characteristic
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	4	2	no	—
455	C₄	—	4	2	no	—
456	C₄	—	8	1	no	—
457	C₄	—	8	1	no	—
458	C₄	—	8	1	no	—
459	C₄	C₅×#468	1	2	yes	—
460	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
461	C₄	C₂×C₅×#137	1	1	yes	characteristic
462	C₄	C₂×C₅×#137	1	1	yes	characteristic
463	C₄	C₅×#575	1	1	yes	characteristic
464	C₂	—	2	2	no	—
465	C₂	—	16	1	no	—
466	C₂	C₅×#3037	1	1	yes	characteristic
467	C₂	C₂×C₅×#468	1	1	yes	characteristic
468	C₂	C₅×#3067	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₅×#532	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#3078	C₂	semidirect
4. C₂×C₅×#446	C₂	semidirect
5. C₅×#1700	C₂	semidirect
6. C₅×#1698	C₂	semidirect
7. C₅×#1692	C₂	semidirect
8. C₅×#1686	C₂	semidirect
9. C₅×#1567	C₂	semidirect
10. C₅×#1550	C₂	semidirect
49. #19285	C₅	direct (N × H)
112. #3078	C₂×C₅	semidirect
114. C₂×#446	C₂×C₅	semidirect
115. #1700	C₂×C₅	semidirect
116. #1698	C₂×C₅	semidirect
117. #1692	C₂×C₅	semidirect
118. #1686	C₂×C₅	semidirect
119. #1567	C₂×C₅	semidirect
120. #1550	C₂×C₅	semidirect
257. C₅×C₈	#137	semidirect
442. C₈	C₅×#137	semidirect
443. C₅	#19285	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×#3167	2
C₅×#3078	2
C₅×#3037	2
C₂×C₅×#446	2
C₅×#1700	2
C₅×#1698	2
C₅×#1692	2
C₅×#1686	2
C₅×#1567	2
C₅×#1550	2
C₅×#1547	2
#19285	5

Subgroups — C5×#19285 #11942005

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19285 #11942005