Subgroups — C₅×#33605 #11956325

Order 1280.

738 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3050	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#466	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2220	C₂	1	2	yes	maximal, complemented
6	C₅×#2218	C₂	1	2	yes	maximal, complemented
7	C₅×#2217	C₂	1	2	yes	maximal, complemented
8	C₅×#2215	C₂	1	2	yes	maximal, complemented
9	C₅×#2159	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2140	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#2139	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#135	C₂²	1	1	yes	characteristic
13	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
14	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₅×#525	—	2	1	no	—
16	C₂×C₅×#121	—	2	1	no	—
17	C₅×#509	—	2	4	no	—
18	C₂×C₅×SD₃₂	C₂²	1	2	yes	complemented
19	C₂×C₅×D₁₆	C₂²	1	2	yes	complemented
20	C₂×C₅×M₃₂	—	2	4	no	—
21	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic
22	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic
23	C₂×C₅×M₃₂	C₂²	1	2	yes	complemented
24	C₂²×C₅×C₁₆	C₂²	1	2	yes	complemented
25	C₅×#467	C₂²	1	1	yes	characteristic, complemented
26	C₅×#467	C₂²	1	1	yes	characteristic, complemented
27	C₅×#466	—	2	1	no	—
28	C₅×#466	—	2	1	no	—
29	C₅×#466	C₂²	1	2	yes	—
30	C₅×#466	C₂²	1	2	yes	—
31	C₅×#466	C₂²	1	1	yes	characteristic, complemented
32	C₅×#466	C₂²	1	1	yes	characteristic, complemented
33	C₅×#465	—	2	1	no	—
34	C₅×#465	—	2	1	no	—
35	C₅×#427	C₂²	1	1	yes	characteristic
36	C₂×C₅×#107	C₂²	1	1	yes	characteristic
37	C₅×#416	—	2	1	no	—
38	C₂×C₅×#102	—	2	1	no	—
39	C₅×#367	C₂²	1	2	yes	complemented
40	C₅×#366	C₂²	1	2	yes	complemented
41	C₅×#358	C₂²	1	2	yes	complemented
42	C₅×#357	C₂²	1	2	yes	complemented
43	C₅×#357	C₂²	1	2	yes	complemented
44	C₅×#357	C₂²	1	2	yes	complemented
45	#33605	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂×C₅×#41	—	2	1	no	—
47	C₂²×C₅×D₄	—	2	1	no	—
48	C₂²×C₅×D₄	—	4	1	no	—
49	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
50	C₅×#135	—	2	2	no	—
51	C₅×#135	—	2	2	no	—
52	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
53	C₂×C₅×SD₁₆	—	2	1	no	—
54	C₂×C₅×D₈	—	2	2	no	—
55	C₂×C₅×D₈	—	2	1	no	—
56	C₂×C₅×D₈	—	2	2	no	—
57	C₂×C₅×D₈	C₂³	1	2	yes	—
58	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
59	C₂²×C₅×C₈	—	2	2	no	—
60	C₂²×C₅×C₈	—	2	2	no	—
61	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
62	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
63	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
64	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
67	C₅×#123	—	4	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	C₅×#121	—	2	2	no	—
73	C₅×#121	—	2	2	no	—
74	C₅×#121	—	4	1	no	—
75	C₅×#121	—	4	1	no	—
76	C₅×#120	—	4	1	no	—
77	C₄×C₅×D₄	—	4	1	no	—
78	C₄×C₅×D₄	—	4	1	no	—
79	C₅×#117	—	2	1	no	—
80	C₂×C₅×C₄⋊C₄	—	2	1	no	—
81	C₂×C₅×C₂²⋊C₄	—	4	1	no	—
82	C₅×SD₃₂	—	2	4	no	—
83	C₅×D₁₆	—	2	4	no	—
84	C₅×M₃₂	—	2	2	no	—
85	C₅×M₃₂	—	2	4	no	—
86	C₅×M₃₂	D₄	1	4	yes	complemented
87	C₂×C₅×C₁₆	—	2	4	no	—
88	C₂×C₅×C₁₆	C₂³	1	2	yes	—
89	C₂×C₅×C₁₆	C₂³	1	2	yes	—
90	C₅×#107	—	2	1	no	—
91	C₅×#107	C₂³	1	2	yes	—
92	C₅×#107	C₂³	1	1	yes	characteristic
93	C₅×#107	C₂³	1	1	yes	characteristic
94	C₅×#106	—	2	1	no	—
95	C₅×#103	—	2	1	no	—
96	C₅×#103	—	2	1	no	—
97	C₅×#102	—	2	2	no	—
98	C₅×#102	—	2	2	no	—
99	C₅×#102	—	2	1	no	—
100	C₅×#102	—	2	1	no	—
101	C₂×#509	C₂×C₅	1	1	yes	characteristic, complemented
102	C₂²×M₃₂	C₂×C₅	1	1	yes	characteristic, complemented
103	#3050	C₂×C₅	1	1	yes	characteristic, complemented
104	C₂×#466	C₂×C₅	1	1	yes	characteristic, complemented
105	#2220	C₂×C₅	1	2	yes	complemented
106	#2218	C₂×C₅	1	2	yes	complemented
107	#2217	C₂×C₅	1	2	yes	complemented
108	#2215	C₂×C₅	1	2	yes	complemented
109	#2159	C₂×C₅	1	1	yes	characteristic, complemented
110	#2140	C₂×C₅	1	1	yes	characteristic, complemented
111	#2139	C₂×C₅	1	1	yes	characteristic, complemented
112	C₂⁴×C₅	—	4	1	no	—
113	C₂⁴×C₅	D₈	1	1	yes	characteristic
114	C₅×#41	—	4	2	no	—
115	C₅×#41	—	4	2	no	—
116	C₂×C₅×Q₈	—	2	1	no	—
117	C₂×C₅×D₄	—	2	2	no	—
118	C₂×C₅×D₄	—	2	1	no	—
119	C₂×C₅×D₄	—	4	1	no	—
120	C₂×C₅×D₄	—	4	1	no	—
121	C₂×C₅×D₄	—	4	1	no	—
122	C₂×C₅×D₄	—	4	2	no	—
123	C₂×C₅×D₄	—	4	2	no	—
124	C₂×C₅×D₄	—	4	2	no	—
125	C₂×C₅×D₄	—	4	1	no	—
126	C₂×C₅×D₄	—	4	2	no	—
127	C₂×C₅×D₄	—	8	4	no	—
128	C₂²×C₄×C₅	—	2	2	no	—
129	C₂²×C₄×C₅	—	2	2	no	—
130	C₂²×C₄×C₅	—	4	1	no	—
131	C₂²×C₄×C₅	—	4	1	no	—
132	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
133	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
134	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
135	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
138	C₅×Q₁₆	—	2	1	no	—
139	C₅×Q₁₆	—	2	1	no	—
140	C₅×SD₁₆	—	4	2	no	—
141	C₅×D₈	—	2	2	no	—
142	C₅×D₈	—	2	1	no	—
143	C₅×D₈	—	2	2	no	—
144	C₅×D₈	—	2	1	no	—
145	C₅×D₈	—	4	2	no	—
146	C₂×C₅×C₈	—	2	2	no	—
147	C₂×C₅×C₈	—	2	2	no	—
148	C₂×C₅×C₈	—	2	2	no	—
149	C₂×C₅×C₈	—	2	1	no	—
150	C₂×C₅×C₈	—	2	1	no	—
151	C₂×C₅×C₈	—	2	1	no	—
152	C₂×C₅×C₈	—	2	1	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	2	yes	—
157	C₂×C₅×C₈	#41	1	2	yes	—
158	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
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	—	4	1	no	—
163	C₅×C₄⋊C₄	—	4	1	no	—
164	C₅×C₄⋊C₄	—	4	1	no	—
165	C₅×C₂²⋊C₄	—	4	1	no	—
166	C₅×C₂²⋊C₄	—	4	1	no	—
167	C₅×C₂²⋊C₄	—	4	1	no	—
168	C₅×C₂²⋊C₄	—	4	2	no	—
169	C₅×C₂²⋊C₄	—	4	2	no	—
170	C₅×C₂²⋊C₄	—	4	1	no	—
171	C₅×C₂²⋊C₄	—	4	1	no	—
172	C₄²×C₅	—	4	1	no	—
173	C₅×C₁₆	—	2	2	no	—
174	C₅×C₁₆	C₂×D₄	1	4	yes	complemented
175	C₂×#135	C₂²×C₅	1	1	yes	characteristic
176	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
177	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
178	#525	—	2	1	no	—
179	C₂×#121	—	2	1	no	—
180	#509	—	2	4	no	—
181	C₂×SD₃₂	C₂²×C₅	1	2	yes	complemented
182	C₂×D₁₆	C₂²×C₅	1	2	yes	complemented
183	C₂×M₃₂	—	2	4	no	—
184	C₂×M₃₂	C₂²×C₅	1	1	yes	characteristic
185	C₂×M₃₂	C₂²×C₅	1	1	yes	characteristic
186	C₂×M₃₂	C₂²×C₅	1	2	yes	complemented
187	C₂²×C₁₆	C₂²×C₅	1	2	yes	complemented
188	#467	C₂²×C₅	1	1	yes	characteristic, complemented
189	#467	C₂²×C₅	1	1	yes	characteristic, complemented
190	#466	—	2	1	no	—
191	#466	—	2	1	no	—
192	#466	C₂²×C₅	1	2	yes	—
193	#466	C₂²×C₅	1	2	yes	—
194	#466	C₂²×C₅	1	1	yes	characteristic, complemented
195	#466	C₂²×C₅	1	1	yes	characteristic, complemented
196	#465	—	2	1	no	—
197	#465	—	2	1	no	—
198	#427	C₂²×C₅	1	1	yes	characteristic
199	C₂×#107	C₂²×C₅	1	1	yes	characteristic
200	#416	—	2	1	no	—
201	C₂×#102	—	2	1	no	—
202	#367	C₂²×C₅	1	2	yes	complemented
203	#366	C₂²×C₅	1	2	yes	complemented
204	#358	C₂²×C₅	1	2	yes	complemented
205	#357	C₂²×C₅	1	2	yes	complemented
206	#357	C₂²×C₅	1	2	yes	complemented
207	#357	C₂²×C₅	1	2	yes	complemented
208	C₂³×C₅	—	2	2	no	—
209	C₂³×C₅	—	2	2	no	—
210	C₂³×C₅	—	4	1	no	—
211	C₂³×C₅	—	4	1	no	—
212	C₂³×C₅	—	4	2	no	—
213	C₂³×C₅	—	8	2	no	—
214	C₂³×C₅	—	8	2	no	—
215	C₂³×C₅	—	8	2	no	—
216	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
217	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
218	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
219	C₅×Q₈	—	4	1	no	—
220	C₅×Q₈	—	4	1	no	—
221	C₅×D₄	—	4	2	no	—
222	C₅×D₄	—	4	1	no	—
223	C₅×D₄	—	4	2	no	—
224	C₅×D₄	—	4	1	no	—
225	C₅×D₄	—	8	2	no	—
226	C₅×D₄	—	8	4	no	—
227	C₅×D₄	—	8	2	no	—
228	C₅×D₄	—	8	2	no	—
229	C₅×D₄	—	8	4	no	—
230	C₅×D₄	—	8	2	no	—
231	C₂×C₄×C₅	—	2	2	no	—
232	C₂×C₄×C₅	—	2	1	no	—
233	C₂×C₄×C₅	—	2	1	no	—
234	C₂×C₄×C₅	—	2	1	no	—
235	C₂×C₄×C₅	—	2	1	no	—
236	C₂×C₄×C₅	—	2	2	no	—
237	C₂×C₄×C₅	—	2	2	no	—
238	C₂×C₄×C₅	—	4	1	no	—
239	C₂×C₄×C₅	—	4	1	no	—
240	C₂×C₄×C₅	—	4	2	no	—
241	C₂×C₄×C₅	—	4	1	no	—
242	C₂×C₄×C₅	—	8	2	no	—
243	C₂×C₄×C₅	—	8	2	no	—
244	C₂×C₄×C₅	#121	1	2	yes	—
245	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
246	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
247	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
248	C₂×C₄×C₅	#135	1	2	yes	—
249	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
250	C₅×C₈	—	2	1	no	—
251	C₅×C₈	—	2	1	no	—
252	C₅×C₈	#121	1	2	yes	—
253	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
254	C₅×C₈	C₂×#41	1	1	yes	characteristic
255	C₂×#41	—	2	1	no	—
256	C₂²×D₄	—	2	1	no	—
257	C₂²×D₄	—	4	1	no	—
258	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
259	#135	—	2	2	no	—
260	#135	—	2	2	no	—
261	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
262	C₂×SD₁₆	—	2	1	no	—
263	C₂×D₈	—	2	2	no	—
264	C₂×D₈	—	2	1	no	—
265	C₂×D₈	—	2	2	no	—
266	C₂×D₈	C₂³×C₅	1	2	yes	—
267	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
268	C₂²×C₈	—	2	2	no	—
269	C₂²×C₈	—	2	2	no	—
270	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
271	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
272	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
273	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
274	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
275	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
276	#123	—	4	1	no	—
277	C₂²⋊Q₈	—	2	1	no	—
278	C₂²⋊Q₈	—	2	1	no	—
279	#121	—	2	2	no	—
280	#121	—	2	2	no	—
281	#121	—	2	1	no	—
282	#121	—	2	1	no	—
283	#121	—	4	1	no	—
284	#121	—	4	1	no	—
285	#120	—	4	1	no	—
286	C₄×D₄	—	4	1	no	—
287	C₄×D₄	—	4	1	no	—
288	#117	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₂²⋊C₄	—	4	1	no	—
291	SD₃₂	—	2	4	no	—
292	D₁₆	—	2	4	no	—
293	M₃₂	—	2	2	no	—
294	M₃₂	—	2	4	no	—
295	M₃₂	C₅×D₄	1	4	yes	complemented
296	C₂×C₁₆	—	2	4	no	—
297	C₂×C₁₆	C₂³×C₅	1	2	yes	—
298	C₂×C₁₆	C₂³×C₅	1	2	yes	—
299	#107	—	2	1	no	—
300	#107	C₂³×C₅	1	1	yes	characteristic
301	#107	C₂³×C₅	1	1	yes	characteristic
302	#107	C₂³×C₅	1	2	yes	—
303	#106	—	2	1	no	—
304	#103	—	2	1	no	—
305	#103	—	2	1	no	—
306	#102	—	2	2	no	—
307	#102	—	2	2	no	—
308	#102	—	2	1	no	—
309	#102	—	2	1	no	—
310	C₂²×C₅	—	2	1	no	—
311	C₂²×C₅	—	2	1	no	—
312	C₂²×C₅	—	2	1	no	—
313	C₂²×C₅	—	2	1	no	—
314	C₂²×C₅	—	2	1	no	—
315	C₂²×C₅	—	2	1	no	—
316	C₂²×C₅	—	2	1	no	—
317	C₂²×C₅	—	4	4	no	—
318	C₂²×C₅	—	8	2	no	—
319	C₂²×C₅	—	8	1	no	—
320	C₂²×C₅	—	8	1	no	—
321	C₂²×C₅	—	8	2	no	—
322	C₂²×C₅	—	8	1	no	—
323	C₂²×C₅	—	8	2	no	—
324	C₂²×C₅	—	16	4	no	—
325	C₂²×C₅	#466	1	2	yes	—
326	C₂²×C₅	#509	1	2	yes	complemented
327	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
328	C₄×C₅	—	2	1	no	—
329	C₄×C₅	—	2	1	no	—
330	C₄×C₅	—	8	2	no	—
331	C₄×C₅	—	8	1	no	—
332	C₄×C₅	—	8	1	no	—
333	C₄×C₅	—	8	1	no	—
334	C₄×C₅	#466	1	2	yes	—
335	C₄×C₅	C₂×#121	1	1	yes	characteristic
336	C₄×C₅	C₂×#135	1	1	yes	characteristic
337	C₂⁴	—	4	1	no	—
338	C₂⁴	C₅×D₈	1	1	yes	characteristic
339	#41	—	4	2	no	—
340	#41	—	4	2	no	—
341	C₂×Q₈	—	2	1	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	1	no	—
344	C₂×D₄	—	4	1	no	—
345	C₂×D₄	—	4	1	no	—
346	C₂×D₄	—	4	1	no	—
347	C₂×D₄	—	4	2	no	—
348	C₂×D₄	—	4	2	no	—
349	C₂×D₄	—	4	2	no	—
350	C₂×D₄	—	4	1	no	—
351	C₂×D₄	—	4	2	no	—
352	C₂×D₄	—	8	4	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	4	1	no	—
356	C₂²×C₄	—	4	1	no	—
357	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
358	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
359	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
360	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
361	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
362	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
363	Q₁₆	—	2	1	no	—
364	Q₁₆	—	2	1	no	—
365	SD₁₆	—	4	2	no	—
366	D₈	—	2	1	no	—
367	D₈	—	2	2	no	—
368	D₈	—	2	2	no	—
369	D₈	—	2	1	no	—
370	D₈	—	4	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
379	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
380	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
381	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
382	C₂×C₈	C₅×#41	1	2	yes	—
383	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	4	1	no	—
388	C₄⋊C₄	—	4	1	no	—
389	C₄⋊C₄	—	4	1	no	—
390	C₂²⋊C₄	—	4	1	no	—
391	C₂²⋊C₄	—	4	1	no	—
392	C₂²⋊C₄	—	4	1	no	—
393	C₂²⋊C₄	—	4	2	no	—
394	C₂²⋊C₄	—	4	2	no	—
395	C₂²⋊C₄	—	4	1	no	—
396	C₂²⋊C₄	—	4	1	no	—
397	C₄²	—	4	1	no	—
398	C₁₆	—	2	2	no	—
399	C₁₆	C₂×C₅×D₄	1	4	yes	complemented
400	C₂×C₅	—	2	2	no	—
401	C₂×C₅	—	2	2	no	—
402	C₂×C₅	—	4	1	no	—
403	C₂×C₅	—	16	1	no	—
404	C₂×C₅	—	16	2	no	—
405	C₂×C₅	C₂×#466	1	1	yes	characteristic
406	C₂×C₅	C₂×#509	1	1	yes	characteristic
407	C₂×C₅	#3414	1	1	yes	characteristic
408	C₂³	—	2	2	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	4	1	no	—
411	C₂³	—	4	1	no	—
412	C₂³	—	4	2	no	—
413	C₂³	—	8	2	no	—
414	C₂³	—	8	2	no	—
415	C₂³	—	8	2	no	—
416	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
417	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
418	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
419	Q₈	—	4	1	no	—
420	Q₈	—	4	1	no	—
421	D₄	—	4	2	no	—
422	D₄	—	4	1	no	—
423	D₄	—	4	2	no	—
424	D₄	—	4	1	no	—
425	D₄	—	8	4	no	—
426	D₄	—	8	2	no	—
427	D₄	—	8	2	no	—
428	D₄	—	8	4	no	—
429	D₄	—	8	2	no	—
430	D₄	—	8	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	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	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	8	2	no	—
443	C₂×C₄	—	8	2	no	—
444	C₂×C₄	C₅×#121	1	2	yes	—
445	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
446	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
447	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
448	C₂×C₄	C₅×#135	1	2	yes	—
449	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
450	C₈	—	2	1	no	—
451	C₈	—	2	1	no	—
452	C₈	C₅×#121	1	2	yes	—
453	C₈	C₂²×C₅×D₄	1	1	yes	characteristic
454	C₈	C₂×C₅×#41	1	1	yes	characteristic
455	C₅	#33605	1	1	yes	characteristic, direct product factor, Sylow
456	C₂²	—	2	1	no	—
457	C₂²	—	2	1	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	4	4	no	—
464	C₂²	—	8	1	no	—
465	C₂²	—	8	2	no	—
466	C₂²	—	8	2	no	—
467	C₂²	—	8	1	no	—
468	C₂²	—	8	1	no	—
469	C₂²	—	8	2	no	—
470	C₂²	—	16	4	no	—
471	C₂²	C₅×#466	1	2	yes	—
472	C₂²	C₅×#509	1	2	yes	complemented
473	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
474	C₄	—	2	1	no	—
475	C₄	—	2	1	no	—
476	C₄	—	8	1	no	—
477	C₄	—	8	2	no	—
478	C₄	—	8	1	no	—
479	C₄	—	8	1	no	—
480	C₄	C₅×#466	1	2	yes	—
481	C₄	C₂×C₅×#121	1	1	yes	characteristic
482	C₄	C₂×C₅×#135	1	1	yes	characteristic
483	C₂	—	2	2	no	—
484	C₂	—	2	2	no	—
485	C₂	—	4	1	no	—
486	C₂	—	16	2	no	—
487	C₂	—	16	1	no	—
488	C₂	C₂×C₅×#466	1	1	yes	characteristic
489	C₂	C₂×C₅×#509	1	1	yes	characteristic
490	C₂	C₅×#3414	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₅
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂³×C₄×C₅ ◁ C₂³×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#509	C₂	semidirect
2. C₂²×C₅×M₃₂	C₂	semidirect
3. C₅×#3050	C₂	semidirect
4. C₂×C₅×#466	C₂	semidirect
5. C₅×#2220	C₂	semidirect
6. C₅×#2218	C₂	semidirect
7. C₅×#2217	C₂	semidirect
8. C₅×#2215	C₂	semidirect
9. C₅×#2159	C₂	semidirect
10. C₅×#2140	C₂	semidirect
11. C₅×#2139	C₂	semidirect
18. C₂×C₅×SD₃₂	C₂²	semidirect
19. C₂×C₅×D₁₆	C₂²	semidirect
23. C₂×C₅×M₃₂	C₂²	semidirect
24. C₂²×C₅×C₁₆	C₂²	semidirect
25. C₅×#467	C₂²	semidirect
26. C₅×#467	C₂²	semidirect
31. C₅×#466	C₂²	semidirect
32. C₅×#466	C₂²	semidirect
39. C₅×#367	C₂²	semidirect
40. C₅×#366	C₂²	semidirect
41. C₅×#358	C₂²	semidirect
42. C₅×#357	C₂²	semidirect
43. C₅×#357	C₂²	semidirect
44. C₅×#357	C₂²	semidirect
45. #33605	C₅	direct (N × H)
86. C₅×M₃₂	D₄	semidirect
101. C₂×#509	C₂×C₅	semidirect
102. C₂²×M₃₂	C₂×C₅	semidirect
103. #3050	C₂×C₅	semidirect
104. C₂×#466	C₂×C₅	semidirect
105. #2220	C₂×C₅	semidirect
106. #2218	C₂×C₅	semidirect
107. #2217	C₂×C₅	semidirect
108. #2215	C₂×C₅	semidirect
109. #2159	C₂×C₅	semidirect
110. #2140	C₂×C₅	semidirect
111. #2139	C₂×C₅	semidirect
174. C₅×C₁₆	C₂×D₄	semidirect
181. C₂×SD₃₂	C₂²×C₅	semidirect
182. C₂×D₁₆	C₂²×C₅	semidirect
186. C₂×M₃₂	C₂²×C₅	semidirect
187. C₂²×C₁₆	C₂²×C₅	semidirect
188. #467	C₂²×C₅	semidirect
189. #467	C₂²×C₅	semidirect
194. #466	C₂²×C₅	semidirect
195. #466	C₂²×C₅	semidirect
202. #367	C₂²×C₅	semidirect
203. #366	C₂²×C₅	semidirect
204. #358	C₂²×C₅	semidirect
205. #357	C₂²×C₅	semidirect
206. #357	C₂²×C₅	semidirect
207. #357	C₂²×C₅	semidirect
295. M₃₂	C₅×D₄	semidirect
326. C₂²×C₅	#509	semidirect
399. C₁₆	C₂×C₅×D₄	semidirect
455. C₅	#33605	direct (N × H)
472. C₂²	C₅×#509	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#509	2
C₂²×C₅×M₃₂	2
C₅×#3050	2
C₂×C₅×#466	2
C₅×#2220	2
C₅×#2218	2
C₅×#2217	2
C₅×#2215	2
C₅×#2159	2
C₅×#2140	2
C₅×#2139	2
#33605	5

Subgroups — C5×#33605 #11956325

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33605 #11956325