Subgroups — C₅×#33516 #11956236

Order 1280.

1150 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#135	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#508	C₂	1	2	yes	maximal, complemented
3	C₅×#3050	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2189	C₂	1	2	yes	maximal, complemented
5	C₅×#2188	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2187	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2186	C₂	1	2	yes	maximal, complemented
8	C₅×#2185	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2184	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2138	C₂	1	2	yes	maximal, complemented
11	C₂×C₅×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₅×#41	—	2	1	no	—
13	C₂×C₅×#135	—	2	8	no	—
14	C₂×C₅×#135	—	2	1	no	—
15	C₂×C₅×#135	—	2	1	no	—
16	C₂×C₅×#135	C₂²	1	2	yes	—
17	C₂×C₅×#135	C₂²	1	2	yes	—
18	C₂×C₅×#135	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₅×SD₁₆	—	2	1	no	—
21	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
22	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
23	C₅×#525	—	2	1	no	—
24	C₅×#508	—	2	8	no	—
25	C₂×C₅×Q₃₂	C₂²	1	2	yes	complemented
26	C₂×C₅×SD₃₂	C₂²	1	2	yes	complemented
27	C₂×C₅×SD₃₂	C₂²	1	2	yes	complemented
28	C₂×C₅×D₁₆	C₂²	1	2	yes	complemented
29	C₂²×C₅×C₁₆	C₂²	1	2	yes	complemented
30	C₅×#467	C₂²	1	1	yes	characteristic
31	C₅×#467	C₂²	1	1	yes	characteristic, complemented
32	C₅×#466	C₂²	1	1	yes	characteristic
33	C₅×#466	C₂²	1	1	yes	characteristic, complemented
34	C₅×#465	—	2	1	no	—
35	C₅×#465	—	2	1	no	—
36	C₅×#427	C₂²	1	1	yes	characteristic, complemented
37	C₅×#416	—	2	1	no	—
38	C₅×#358	C₂²	1	2	yes	complemented
39	C₅×#358	C₂²	1	2	yes	complemented
40	C₅×#357	C₂²	1	2	yes	complemented
41	C₅×#357	C₂²	1	2	yes	complemented
42	C₅×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
43	C₅×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
44	C₅×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
45	#33516	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂×C₅×#41	—	2	8	no	—
47	C₂×C₅×#41	—	2	2	no	—
48	C₂×C₅×#41	—	2	2	no	—
49	C₂×C₅×#41	—	2	1	no	—
50	C₂×C₅×#41	—	4	4	no	—
51	C₂×C₅×#41	—	4	1	no	—
52	C₂×C₅×#41	—	4	1	no	—
53	C₂²×C₅×Q₈	—	2	1	no	—
54	C₂²×C₅×D₄	—	2	1	no	—
55	C₂²×C₅×D₄	—	4	1	no	—
56	C₂³×C₄×C₅	—	4	1	no	—
57	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
58	C₅×#135	—	2	8	no	—
59	C₅×#135	—	2	8	no	—
60	C₅×#135	—	2	4	no	—
61	C₅×#135	—	2	4	no	—
62	C₅×#135	—	2	4	no	—
63	C₅×#135	—	2	4	no	—
64	C₅×#135	D₄	1	8	yes	complemented
65	C₂×C₅×Q₁₆	—	2	4	no	—
66	C₂×C₅×Q₁₆	—	2	1	no	—
67	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
68	C₂×C₅×Q₁₆	C₂³	1	2	yes	—
69	C₂×C₅×SD₁₆	—	2	8	no	—
70	C₂×C₅×SD₁₆	—	2	2	no	—
71	C₂×C₅×SD₁₆	—	2	2	no	—
72	C₂×C₅×SD₁₆	—	2	1	no	—
73	C₂×C₅×D₈	—	2	4	no	—
74	C₂×C₅×D₈	—	2	1	no	—
75	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
76	C₂×C₅×D₈	C₂³	1	2	yes	—
77	C₂²×C₅×C₈	—	2	4	no	—
78	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
79	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
80	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
81	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
82	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
83	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
84	C₅×#123	—	4	1	no	—
85	C₅×C₂²⋊Q₈	—	2	1	no	—
86	C₅×C₂²⋊Q₈	—	2	1	no	—
87	C₅×#121	—	2	1	no	—
88	C₅×#121	—	2	1	no	—
89	C₅×#120	—	4	1	no	—
90	C₄×C₅×D₄	—	4	1	no	—
91	C₄×C₅×D₄	—	4	1	no	—
92	C₅×#117	—	2	1	no	—
93	C₅×Q₃₂	—	2	4	no	—
94	C₅×SD₃₂	—	2	4	no	—
95	C₅×SD₃₂	—	2	4	no	—
96	C₅×D₁₆	—	2	4	no	—
97	C₂×C₅×C₁₆	—	2	4	no	—
98	C₂×C₅×C₁₆	C₂³	1	2	yes	—
99	C₂×C₅×C₁₆	C₂³	1	2	yes	—
100	C₅×#107	C₂³	1	1	yes	characteristic
101	C₅×#107	C₂³	1	1	yes	characteristic
102	C₅×#106	—	2	1	no	—
103	C₅×#103	—	2	1	no	—
104	C₅×#103	—	2	1	no	—
105	C₅×#102	—	2	1	no	—
106	C₅×#102	—	2	1	no	—
107	C₂²×#135	C₂×C₅	1	1	yes	characteristic, complemented
108	C₂×#508	C₂×C₅	1	2	yes	complemented
109	#3050	C₂×C₅	1	1	yes	characteristic, complemented
110	#2189	C₂×C₅	1	2	yes	complemented
111	#2188	C₂×C₅	1	1	yes	characteristic, complemented
112	#2187	C₂×C₅	1	1	yes	characteristic, complemented
113	#2186	C₂×C₅	1	2	yes	complemented
114	#2185	C₂×C₅	1	1	yes	characteristic, complemented
115	#2184	C₂×C₅	1	1	yes	characteristic, complemented
116	#2138	C₂×C₅	1	2	yes	complemented
117	C₂×C₂²⋊C₁₆	C₂×C₅	1	1	yes	characteristic, complemented
118	C₂⁴×C₅	—	4	1	no	—
119	C₂⁴×C₅	D₈	1	1	yes	characteristic
120	C₅×#41	—	2	8	no	—
121	C₅×#41	—	2	8	no	—
122	C₅×#41	—	4	8	no	—
123	C₅×#41	—	4	4	no	—
124	C₅×#41	—	4	8	no	—
125	C₅×#41	—	4	4	no	—
126	C₅×#41	—	4	2	no	—
127	C₅×#41	—	4	2	no	—
128	C₂×C₅×Q₈	—	2	4	no	—
129	C₂×C₅×Q₈	—	2	2	no	—
130	C₂×C₅×Q₈	—	2	1	no	—
131	C₂×C₅×Q₈	—	4	2	no	—
132	C₂×C₅×Q₈	—	4	1	no	—
133	C₂×C₅×D₄	—	2	4	no	—
134	C₂×C₅×D₄	—	2	2	no	—
135	C₂×C₅×D₄	—	2	1	no	—
136	C₂×C₅×D₄	—	4	2	no	—
137	C₂×C₅×D₄	—	4	8	no	—
138	C₂×C₅×D₄	—	4	2	no	—
139	C₂×C₅×D₄	—	4	2	no	—
140	C₂×C₅×D₄	—	4	1	no	—
141	C₂×C₅×D₄	—	4	1	no	—
142	C₂×C₅×D₄	—	4	1	no	—
143	C₂×C₅×D₄	—	4	1	no	—
144	C₂²×C₄×C₅	—	2	2	no	—
145	C₂²×C₄×C₅	—	2	2	no	—
146	C₂²×C₄×C₅	—	4	8	no	—
147	C₂²×C₄×C₅	—	4	1	no	—
148	C₂²×C₄×C₅	—	4	2	no	—
149	C₂²×C₄×C₅	—	4	2	no	—
150	C₂²×C₄×C₅	—	4	1	no	—
151	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
152	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
153	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
154	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
157	C₅×Q₁₆	—	2	4	no	—
158	C₅×Q₁₆	—	2	2	no	—
159	C₅×Q₁₆	—	2	2	no	—
160	C₅×Q₁₆	C₂×D₄	1	4	yes	—
161	C₅×SD₁₆	—	2	8	no	—
162	C₅×SD₁₆	—	2	8	no	—
163	C₅×SD₁₆	—	4	2	no	—
164	C₅×D₈	—	2	4	no	—
165	C₅×D₈	—	2	2	no	—
166	C₅×D₈	—	2	2	no	—
167	C₅×D₈	C₂×D₄	1	4	yes	—
168	C₂×C₅×C₈	—	2	2	no	—
169	C₂×C₅×C₈	—	2	2	no	—
170	C₂×C₅×C₈	—	2	2	no	—
171	C₂×C₅×C₈	—	2	2	no	—
172	C₂×C₅×C₈	—	2	2	no	—
173	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
174	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
175	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
176	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
177	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
178	C₅×C₄⋊C₄	—	2	1	no	—
179	C₅×C₄⋊C₄	—	2	1	no	—
180	C₅×C₄⋊C₄	—	4	1	no	—
181	C₅×C₄⋊C₄	—	4	1	no	—
182	C₅×C₂²⋊C₄	—	4	1	no	—
183	C₅×C₂²⋊C₄	—	4	1	no	—
184	C₅×C₂²⋊C₄	—	4	1	no	—
185	C₅×C₂²⋊C₄	—	4	1	no	—
186	C₅×C₂²⋊C₄	—	4	1	no	—
187	C₄²×C₅	—	4	1	no	—
188	C₅×C₁₆	—	2	2	no	—
189	C₅×C₁₆	—	2	2	no	—
190	C₂²×#41	—	2	1	no	—
191	C₂×#135	—	2	8	no	—
192	C₂×#135	—	2	1	no	—
193	C₂×#135	—	2	1	no	—
194	C₂×#135	C₂²×C₅	1	2	yes	—
195	C₂×#135	C₂²×C₅	1	2	yes	—
196	C₂×#135	C₂²×C₅	1	1	yes	characteristic, complemented
197	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
198	C₂²×SD₁₆	—	2	1	no	—
199	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
200	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
201	#525	—	2	1	no	—
202	#508	—	2	8	no	—
203	C₂×Q₃₂	C₂²×C₅	1	2	yes	complemented
204	C₂×SD₃₂	C₂²×C₅	1	2	yes	complemented
205	C₂×SD₃₂	C₂²×C₅	1	2	yes	complemented
206	C₂×D₁₆	C₂²×C₅	1	2	yes	complemented
207	C₂²×C₁₆	C₂²×C₅	1	2	yes	complemented
208	#467	C₂²×C₅	1	1	yes	characteristic
209	#467	C₂²×C₅	1	1	yes	characteristic, complemented
210	#466	C₂²×C₅	1	1	yes	characteristic
211	#466	C₂²×C₅	1	1	yes	characteristic, complemented
212	#465	—	2	1	no	—
213	#465	—	2	1	no	—
214	#427	C₂²×C₅	1	1	yes	characteristic, complemented
215	#416	—	2	1	no	—
216	#358	C₂²×C₅	1	2	yes	complemented
217	#358	C₂²×C₅	1	2	yes	complemented
218	#357	C₂²×C₅	1	2	yes	complemented
219	#357	C₂²×C₅	1	2	yes	complemented
220	C₂²⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
221	C₂²⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
222	C₂²⋊C₁₆	C₂²×C₅	1	2	yes	complemented
223	C₂³×C₅	—	2	2	no	—
224	C₂³×C₅	—	2	2	no	—
225	C₂³×C₅	—	4	1	no	—
226	C₂³×C₅	—	4	4	no	—
227	C₂³×C₅	—	4	2	no	—
228	C₂³×C₅	—	4	1	no	—
229	C₂³×C₅	—	8	2	no	—
230	C₂³×C₅	—	8	2	no	—
231	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
232	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
233	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
234	C₅×Q₈	—	2	4	no	—
235	C₅×Q₈	—	4	4	no	—
236	C₅×Q₈	—	4	2	no	—
237	C₅×Q₈	—	4	1	no	—
238	C₅×Q₈	—	4	1	no	—
239	C₅×D₄	—	2	4	no	—
240	C₅×D₄	—	4	4	no	—
241	C₅×D₄	—	4	8	no	—
242	C₅×D₄	—	4	8	no	—
243	C₅×D₄	—	4	1	no	—
244	C₅×D₄	—	4	2	no	—
245	C₅×D₄	—	4	1	no	—
246	C₅×D₄	—	8	2	no	—
247	C₅×D₄	—	8	2	no	—
248	C₅×D₄	—	8	2	no	—
249	C₂×C₄×C₅	—	2	2	no	—
250	C₂×C₄×C₅	—	2	1	no	—
251	C₂×C₄×C₅	—	2	1	no	—
252	C₂×C₄×C₅	—	2	1	no	—
253	C₂×C₄×C₅	—	2	1	no	—
254	C₂×C₄×C₅	—	2	2	no	—
255	C₂×C₄×C₅	—	2	2	no	—
256	C₂×C₄×C₅	—	4	8	no	—
257	C₂×C₄×C₅	—	4	4	no	—
258	C₂×C₄×C₅	—	4	2	no	—
259	C₂×C₄×C₅	—	4	8	no	—
260	C₂×C₄×C₅	—	4	1	no	—
261	C₂×C₄×C₅	—	4	1	no	—
262	C₂×C₄×C₅	—	4	1	no	—
263	C₂×C₄×C₅	—	8	2	no	—
264	C₂×C₄×C₅	#120	1	2	yes	—
265	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
266	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
267	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
268	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
269	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
270	C₅×C₈	—	2	1	no	—
271	C₅×C₈	—	2	1	no	—
272	C₅×C₈	#120	1	2	yes	—
273	C₅×C₈	C₂²×D₄	1	2	yes	—
274	C₂×#41	—	2	8	no	—
275	C₂×#41	—	2	2	no	—
276	C₂×#41	—	2	2	no	—
277	C₂×#41	—	2	1	no	—
278	C₂×#41	—	4	4	no	—
279	C₂×#41	—	4	1	no	—
280	C₂×#41	—	4	1	no	—
281	C₂²×Q₈	—	2	1	no	—
282	C₂²×D₄	—	2	1	no	—
283	C₂²×D₄	—	4	1	no	—
284	C₂³×C₄	—	4	1	no	—
285	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
286	#135	—	2	8	no	—
287	#135	—	2	8	no	—
288	#135	—	2	4	no	—
289	#135	—	2	4	no	—
290	#135	—	2	4	no	—
291	#135	—	2	4	no	—
292	#135	C₅×D₄	1	8	yes	complemented
293	C₂×Q₁₆	—	2	4	no	—
294	C₂×Q₁₆	—	2	1	no	—
295	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
296	C₂×Q₁₆	C₂³×C₅	1	2	yes	—
297	C₂×SD₁₆	—	2	8	no	—
298	C₂×SD₁₆	—	2	2	no	—
299	C₂×SD₁₆	—	2	2	no	—
300	C₂×SD₁₆	—	2	1	no	—
301	C₂×D₈	—	2	4	no	—
302	C₂×D₈	—	2	1	no	—
303	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
304	C₂×D₈	C₂³×C₅	1	2	yes	—
305	C₂²×C₈	—	2	4	no	—
306	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
307	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
308	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
309	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
310	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
311	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
312	#123	—	4	1	no	—
313	C₂²⋊Q₈	—	2	1	no	—
314	C₂²⋊Q₈	—	2	1	no	—
315	#121	—	2	1	no	—
316	#121	—	2	1	no	—
317	#120	—	4	1	no	—
318	C₄×D₄	—	4	1	no	—
319	C₄×D₄	—	4	1	no	—
320	#117	—	2	1	no	—
321	Q₃₂	—	2	4	no	—
322	SD₃₂	—	2	4	no	—
323	SD₃₂	—	2	4	no	—
324	D₁₆	—	2	4	no	—
325	C₂×C₁₆	—	2	4	no	—
326	C₂×C₁₆	C₂³×C₅	1	2	yes	—
327	C₂×C₁₆	C₂³×C₅	1	2	yes	—
328	#107	C₂³×C₅	1	1	yes	characteristic
329	#107	C₂³×C₅	1	1	yes	characteristic
330	#106	—	2	1	no	—
331	#103	—	2	1	no	—
332	#103	—	2	1	no	—
333	#102	—	2	1	no	—
334	#102	—	2	1	no	—
335	C₂²×C₅	—	2	1	no	—
336	C₂²×C₅	—	2	1	no	—
337	C₂²×C₅	—	2	1	no	—
338	C₂²×C₅	—	2	1	no	—
339	C₂²×C₅	—	2	1	no	—
340	C₂²×C₅	—	2	1	no	—
341	C₂²×C₅	—	2	1	no	—
342	C₂²×C₅	—	4	4	no	—
343	C₂²×C₅	—	4	4	no	—
344	C₂²×C₅	—	8	8	no	—
345	C₂²×C₅	—	8	2	no	—
346	C₂²×C₅	—	8	2	no	—
347	C₂²×C₅	—	8	1	no	—
348	C₂²×C₅	—	8	1	no	—
349	C₂²×C₅	—	8	1	no	—
350	C₂²×C₅	#447	1	2	yes	—
351	C₂²×C₅	#508	1	2	yes	complemented
352	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
353	C₄×C₅	—	2	1	no	—
354	C₄×C₅	—	2	1	no	—
355	C₄×C₅	—	4	4	no	—
356	C₄×C₅	—	8	1	no	—
357	C₄×C₅	—	8	1	no	—
358	C₄×C₅	—	8	1	no	—
359	C₄×C₅	#447	1	2	yes	—
360	C₄×C₅	C₂×#120	1	1	yes	characteristic
361	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
362	C₂⁴	—	4	1	no	—
363	C₂⁴	C₅×D₈	1	1	yes	characteristic
364	#41	—	2	8	no	—
365	#41	—	2	8	no	—
366	#41	—	4	8	no	—
367	#41	—	4	8	no	—
368	#41	—	4	4	no	—
369	#41	—	4	4	no	—
370	#41	—	4	2	no	—
371	#41	—	4	2	no	—
372	C₂×Q₈	—	2	4	no	—
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	—	2	1	no	—
375	C₂×Q₈	—	4	2	no	—
376	C₂×Q₈	—	4	1	no	—
377	C₂×D₄	—	2	4	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	1	no	—
380	C₂×D₄	—	4	2	no	—
381	C₂×D₄	—	4	8	no	—
382	C₂×D₄	—	4	2	no	—
383	C₂×D₄	—	4	2	no	—
384	C₂×D₄	—	4	1	no	—
385	C₂×D₄	—	4	1	no	—
386	C₂×D₄	—	4	1	no	—
387	C₂×D₄	—	4	1	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	4	8	no	—
391	C₂²×C₄	—	4	1	no	—
392	C₂²×C₄	—	4	2	no	—
393	C₂²×C₄	—	4	2	no	—
394	C₂²×C₄	—	4	1	no	—
395	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
396	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
397	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
398	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
399	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
400	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
401	Q₁₆	—	2	4	no	—
402	Q₁₆	—	2	2	no	—
403	Q₁₆	—	2	2	no	—
404	Q₁₆	C₂×C₅×D₄	1	4	yes	—
405	SD₁₆	—	2	8	no	—
406	SD₁₆	—	2	8	no	—
407	SD₁₆	—	4	2	no	—
408	D₈	—	2	4	no	—
409	D₈	—	2	2	no	—
410	D₈	—	2	2	no	—
411	D₈	C₂×C₅×D₄	1	4	yes	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
418	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
419	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
420	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
421	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	4	1	no	—
425	C₄⋊C₄	—	4	1	no	—
426	C₂²⋊C₄	—	4	1	no	—
427	C₂²⋊C₄	—	4	1	no	—
428	C₂²⋊C₄	—	4	1	no	—
429	C₂²⋊C₄	—	4	1	no	—
430	C₂²⋊C₄	—	4	1	no	—
431	C₄²	—	4	1	no	—
432	C₁₆	—	2	2	no	—
433	C₁₆	—	2	2	no	—
434	C₂×C₅	—	2	2	no	—
435	C₂×C₅	—	2	2	no	—
436	C₂×C₅	—	4	1	no	—
437	C₂×C₅	—	8	4	no	—
438	C₂×C₅	—	16	1	no	—
439	C₂×C₅	C₂×#447	1	1	yes	characteristic
440	C₂×C₅	C₂×#508	1	1	yes	characteristic
441	C₂×C₅	#3414	1	1	yes	characteristic
442	C₂³	—	2	2	no	—
443	C₂³	—	2	2	no	—
444	C₂³	—	4	1	no	—
445	C₂³	—	4	4	no	—
446	C₂³	—	4	2	no	—
447	C₂³	—	4	1	no	—
448	C₂³	—	8	2	no	—
449	C₂³	—	8	2	no	—
450	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
451	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
452	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
453	Q₈	—	2	4	no	—
454	Q₈	—	4	4	no	—
455	Q₈	—	4	2	no	—
456	Q₈	—	4	1	no	—
457	Q₈	—	4	1	no	—
458	D₄	—	2	4	no	—
459	D₄	—	4	4	no	—
460	D₄	—	4	8	no	—
461	D₄	—	4	8	no	—
462	D₄	—	4	1	no	—
463	D₄	—	4	2	no	—
464	D₄	—	4	1	no	—
465	D₄	—	8	2	no	—
466	D₄	—	8	2	no	—
467	D₄	—	8	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	4	8	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	8	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	8	2	no	—
483	C₂×C₄	C₅×#120	1	2	yes	—
484	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
485	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
486	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
487	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
488	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
489	C₈	—	2	1	no	—
490	C₈	—	2	1	no	—
491	C₈	C₅×#120	1	2	yes	—
492	C₈	C₂²×C₅×D₄	1	2	yes	—
493	C₅	#33516	1	1	yes	characteristic, direct product factor, Sylow
494	C₂²	—	2	1	no	—
495	C₂²	—	2	1	no	—
496	C₂²	—	2	1	no	—
497	C₂²	—	2	1	no	—
498	C₂²	—	2	1	no	—
499	C₂²	—	2	1	no	—
500	C₂²	—	2	1	no	—
501	C₂²	—	4	4	no	—
502	C₂²	—	4	4	no	—
503	C₂²	—	8	8	no	—
504	C₂²	—	8	2	no	—
505	C₂²	—	8	2	no	—
506	C₂²	—	8	1	no	—
507	C₂²	—	8	1	no	—
508	C₂²	—	8	1	no	—
509	C₂²	C₅×#447	1	2	yes	—
510	C₂²	C₅×#508	1	2	yes	complemented
511	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
512	C₄	—	2	1	no	—
513	C₄	—	2	1	no	—
514	C₄	—	4	4	no	—
515	C₄	—	8	1	no	—
516	C₄	—	8	1	no	—
517	C₄	—	8	1	no	—
518	C₄	C₅×#447	1	2	yes	—
519	C₄	C₂×C₅×#120	1	1	yes	characteristic
520	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
521	C₂	—	2	2	no	—
522	C₂	—	2	2	no	—
523	C₂	—	4	1	no	—
524	C₂	—	8	4	no	—
525	C₂	—	16	1	no	—
526	C₂	C₂×C₅×#447	1	1	yes	characteristic
527	C₂	C₂×C₅×#508	1	1	yes	characteristic
528	C₂	C₅×#3414	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₅
socle	C₂²×C₅	C₂²×D₈
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×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. C₂²×C₅×#135	C₂	semidirect
2. C₂×C₅×#508	C₂	semidirect
3. C₅×#3050	C₂	semidirect
4. C₅×#2189	C₂	semidirect
5. C₅×#2188	C₂	semidirect
6. C₅×#2187	C₂	semidirect
7. C₅×#2186	C₂	semidirect
8. C₅×#2185	C₂	semidirect
9. C₅×#2184	C₂	semidirect
10. C₅×#2138	C₂	semidirect
11. C₂×C₅×C₂²⋊C₁₆	C₂	semidirect
18. C₂×C₅×#135	C₂²	semidirect
25. C₂×C₅×Q₃₂	C₂²	semidirect
26. C₂×C₅×SD₃₂	C₂²	semidirect
27. C₂×C₅×SD₃₂	C₂²	semidirect
28. C₂×C₅×D₁₆	C₂²	semidirect
29. C₂²×C₅×C₁₆	C₂²	semidirect
31. C₅×#467	C₂²	semidirect
33. C₅×#466	C₂²	semidirect
36. C₅×#427	C₂²	semidirect
38. C₅×#358	C₂²	semidirect
39. C₅×#358	C₂²	semidirect
40. C₅×#357	C₂²	semidirect
41. C₅×#357	C₂²	semidirect
44. C₅×C₂²⋊C₁₆	C₂²	semidirect
45. #33516	C₅	direct (N × H)
64. C₅×#135	D₄	semidirect
107. C₂²×#135	C₂×C₅	semidirect
108. C₂×#508	C₂×C₅	semidirect
109. #3050	C₂×C₅	semidirect
110. #2189	C₂×C₅	semidirect
111. #2188	C₂×C₅	semidirect
112. #2187	C₂×C₅	semidirect
113. #2186	C₂×C₅	semidirect
114. #2185	C₂×C₅	semidirect
115. #2184	C₂×C₅	semidirect
116. #2138	C₂×C₅	semidirect
117. C₂×C₂²⋊C₁₆	C₂×C₅	semidirect
196. C₂×#135	C₂²×C₅	semidirect
203. C₂×Q₃₂	C₂²×C₅	semidirect
204. C₂×SD₃₂	C₂²×C₅	semidirect
205. C₂×SD₃₂	C₂²×C₅	semidirect
206. C₂×D₁₆	C₂²×C₅	semidirect
207. C₂²×C₁₆	C₂²×C₅	semidirect
209. #467	C₂²×C₅	semidirect
211. #466	C₂²×C₅	semidirect
214. #427	C₂²×C₅	semidirect
216. #358	C₂²×C₅	semidirect
217. #358	C₂²×C₅	semidirect
218. #357	C₂²×C₅	semidirect
219. #357	C₂²×C₅	semidirect
222. C₂²⋊C₁₆	C₂²×C₅	semidirect
292. #135	C₅×D₄	semidirect
351. C₂²×C₅	#508	semidirect
493. C₅	#33516	direct (N × H)
510. C₂²	C₅×#508	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×#135	2
C₂×C₅×#508	2
C₅×#3050	2
C₅×#2189	2
C₅×#2188	2
C₅×#2187	2
C₅×#2186	2
C₅×#2185	2
C₅×#2184	2
C₅×#2138	2
C₂×C₅×C₂²⋊C₁₆	2
#33516	5

Subgroups — C5×#33516 #11956236

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33516 #11956236