Subgroups — C₅×#33830 #11956550

Order 1280.

760 conjugacy classes of subgroups.

The subgroup lattice has 624 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×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3280	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₄×D₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2250	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2218	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2217	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2210	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2206	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2187	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#2186	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2184	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#2184	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#2177	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#2168	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#135	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
18	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
20	C₅×#546	—	2	1	no	—
21	C₅×D₄²	—	2	1	no	—
22	C₅×#509	—	2	4	no	—
23	C₂×C₅×SD₃₂	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₅×SD₃₂	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₅×SD₃₂	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₅×D₁₆	—	2	4	no	—
27	C₂×C₅×D₁₆	C₂²	1	1	yes	characteristic
28	C₂×C₅×D₁₆	C₂²	1	1	yes	characteristic
29	C₂×C₅×D₁₆	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₅×D₁₆	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₅×D₁₆	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₅×D₁₆	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic, complemented
34	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic, complemented
35	C₅×#495	C₂²	1	1	yes	characteristic, complemented
36	C₅×#493	C₂²	1	1	yes	characteristic, complemented
37	C₅×#467	C₂²	1	1	yes	characteristic, complemented
38	C₅×#466	C₂²	1	1	yes	characteristic
39	C₅×#466	C₂²	1	1	yes	characteristic, complemented
40	C₅×#466	C₂²	1	1	yes	characteristic, complemented
41	C₅×#463	—	2	1	no	—
42	C₅×#459	—	2	1	no	—
43	C₅×#450	—	2	1	no	—
44	C₅×#449	—	2	1	no	—
45	C₅×#447	—	2	1	no	—
46	C₅×#447	—	2	1	no	—
47	C₄×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
48	C₄×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
49	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
50	C₅×#367	C₂²	1	1	yes	characteristic, complemented
51	C₅×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
52	C₅×#358	C₂²	1	1	yes	characteristic, complemented
53	C₅×#357	C₂²	1	1	yes	characteristic, complemented
54	C₅×#357	C₂²	1	1	yes	characteristic, complemented
55	C₅×#357	C₂²	1	1	yes	characteristic, complemented
56	C₅×#357	C₂²	1	1	yes	characteristic, complemented
57	C₅×#357	C₂²	1	1	yes	characteristic, complemented
58	C₅×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
59	C₅×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
60	C₅×#346	C₂²	1	1	yes	characteristic, complemented
61	#33830	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂×C₅×#41	—	2	1	no	—
63	C₂²×C₅×D₄	—	2	1	no	—
64	C₂²×C₅×D₄	—	2	1	no	—
65	C₂²×C₅×D₄	—	2	1	no	—
66	C₂²×C₅×D₄	—	4	1	no	—
67	C₅×#135	—	2	2	no	—
68	C₅×#135	—	4	1	no	—
69	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
70	C₂×C₅×SD₁₆	—	2	1	no	—
71	C₂×C₅×SD₁₆	—	2	1	no	—
72	C₂×C₅×D₈	—	2	2	no	—
73	C₂×C₅×D₈	—	2	2	no	—
74	C₂×C₅×D₈	—	2	2	no	—
75	C₂×C₅×D₈	—	2	1	no	—
76	C₂×C₅×D₈	—	2	1	no	—
77	C₂×C₅×D₈	—	2	1	no	—
78	C₂×C₅×D₈	—	2	1	no	—
79	C₂×C₅×D₈	—	4	1	no	—
80	C₂×C₅×D₈	—	4	1	no	—
81	C₂×C₅×D₈	—	4	1	no	—
82	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
83	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
84	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
85	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
86	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
87	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
88	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
89	C₅×#127	—	2	1	no	—
90	C₅×#124	—	2	1	no	—
91	C₅×#123	—	4	1	no	—
92	C₅×C₂²⋊Q₈	—	2	1	no	—
93	C₅×#121	—	2	1	no	—
94	C₅×#121	—	2	1	no	—
95	C₅×#121	—	2	1	no	—
96	C₅×#121	—	4	1	no	—
97	C₅×#121	—	4	1	no	—
98	C₅×#120	—	4	1	no	—
99	C₅×#120	—	4	1	no	—
100	C₅×#120	—	4	1	no	—
101	C₄×C₅×D₄	—	2	1	no	—
102	C₄×C₅×D₄	—	2	1	no	—
103	C₄×C₅×D₄	D₄	1	1	yes	characteristic
104	C₂×C₅×C₂²⋊C₄	—	4	1	no	—
105	C₅×SD₃₂	—	2	2	no	—
106	C₅×SD₃₂	—	2	2	no	—
107	C₅×SD₃₂	—	4	1	no	—
108	C₅×D₁₆	—	2	2	no	—
109	C₅×D₁₆	—	2	2	no	—
110	C₅×D₁₆	—	2	2	no	—
111	C₅×D₁₆	—	2	2	no	—
112	C₅×D₁₆	—	4	1	no	—
113	C₅×D₁₆	D₄	1	4	yes	complemented
114	C₅×M₃₂	—	2	2	no	—
115	C₂×C₅×C₁₆	—	2	2	no	—
116	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
117	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
118	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
119	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
120	C₅×#107	C₂³	1	1	yes	characteristic
121	C₅×#107	C₂³	1	1	yes	characteristic
122	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
123	C₅×#103	—	2	1	no	—
124	C₅×#102	—	2	1	no	—
125	C₅×#102	—	2	1	no	—
126	C₅×#102	—	2	1	no	—
127	C₅×#102	—	2	1	no	—
128	C₅×#102	—	2	1	no	—
129	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
130	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
131	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
132	C₂×#509	C₂×C₅	1	1	yes	characteristic, complemented
133	C₂²×D₁₆	C₂×C₅	1	1	yes	characteristic, complemented
134	#3280	C₂×C₅	1	1	yes	characteristic, complemented
135	D₄×D₈	C₂×C₅	1	1	yes	characteristic, complemented
136	#2250	C₂×C₅	1	1	yes	characteristic, complemented
137	#2218	C₂×C₅	1	1	yes	characteristic, complemented
138	#2217	C₂×C₅	1	1	yes	characteristic, complemented
139	#2210	C₂×C₅	1	1	yes	characteristic, complemented
140	#2206	C₂×C₅	1	1	yes	characteristic, complemented
141	#2187	C₂×C₅	1	1	yes	characteristic, complemented
142	#2186	C₂×C₅	1	1	yes	characteristic, complemented
143	#2184	C₂×C₅	1	1	yes	characteristic, complemented
144	#2184	C₂×C₅	1	1	yes	characteristic, complemented
145	#2177	C₂×C₅	1	1	yes	characteristic, complemented
146	#2168	C₂×C₅	1	1	yes	characteristic, complemented
147	C₂⁴×C₅	—	4	1	no	—
148	C₂⁴×C₅	—	4	1	no	—
149	C₂⁴×C₅	—	4	1	no	—
150	C₅×#41	—	4	2	no	—
151	C₅×#41	—	8	1	no	—
152	C₂×C₅×Q₈	—	2	1	no	—
153	C₂×C₅×D₄	—	2	1	no	—
154	C₂×C₅×D₄	—	2	1	no	—
155	C₂×C₅×D₄	—	2	1	no	—
156	C₂×C₅×D₄	—	2	1	no	—
157	C₂×C₅×D₄	—	2	1	no	—
158	C₂×C₅×D₄	—	4	2	no	—
159	C₂×C₅×D₄	—	4	2	no	—
160	C₂×C₅×D₄	—	4	2	no	—
161	C₂×C₅×D₄	—	4	1	no	—
162	C₂×C₅×D₄	—	4	1	no	—
163	C₂×C₅×D₄	—	4	1	no	—
164	C₂×C₅×D₄	—	4	1	no	—
165	C₂×C₅×D₄	—	4	1	no	—
166	C₂×C₅×D₄	—	4	1	no	—
167	C₂×C₅×D₄	—	4	1	no	—
168	C₂×C₅×D₄	—	4	1	no	—
169	C₂×C₅×D₄	—	4	1	no	—
170	C₂×C₅×D₄	—	8	1	no	—
171	C₂×C₅×D₄	—	8	1	no	—
172	C₂×C₅×D₄	—	8	1	no	—
173	C₂×C₅×D₄	—	8	4	no	—
174	C₂×C₅×D₄	D₈	1	1	yes	characteristic
175	C₂²×C₄×C₅	—	4	1	no	—
176	C₂²×C₄×C₅	—	4	1	no	—
177	C₂²×C₄×C₅	—	4	1	no	—
178	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
180	C₅×Q₁₆	—	2	1	no	—
181	C₅×Q₁₆	—	2	1	no	—
182	C₅×SD₁₆	—	4	2	no	—
183	C₅×SD₁₆	—	8	1	no	—
184	C₅×D₈	—	2	1	no	—
185	C₅×D₈	—	2	1	no	—
186	C₅×D₈	—	2	1	no	—
187	C₅×D₈	—	2	1	no	—
188	C₅×D₈	—	2	1	no	—
189	C₅×D₈	—	2	1	no	—
190	C₅×D₈	—	2	1	no	—
191	C₅×D₈	—	2	1	no	—
192	C₅×D₈	—	4	2	no	—
193	C₅×D₈	—	4	2	no	—
194	C₅×D₈	—	4	2	no	—
195	C₅×D₈	—	8	1	no	—
196	C₅×D₈	C₂×D₄	1	2	yes	—
197	C₅×D₈	C₂×D₄	1	2	yes	complemented
198	C₂×C₅×C₈	—	2	1	no	—
199	C₂×C₅×C₈	—	2	1	no	—
200	C₂×C₅×C₈	—	2	1	no	—
201	C₂×C₅×C₈	—	2	1	no	—
202	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
203	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
204	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
205	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
206	C₅×C₄⋊C₄	—	2	1	no	—
207	C₅×C₄⋊C₄	—	2	1	no	—
208	C₅×C₄⋊C₄	—	4	1	no	—
209	C₅×C₄⋊C₄	D₈	1	1	yes	characteristic
210	C₅×C₂²⋊C₄	—	4	1	no	—
211	C₅×C₂²⋊C₄	—	4	1	no	—
212	C₅×C₂²⋊C₄	—	4	1	no	—
213	C₅×C₂²⋊C₄	—	4	1	no	—
214	C₅×C₂²⋊C₄	—	4	1	no	—
215	C₅×C₂²⋊C₄	—	4	1	no	—
216	C₅×C₂²⋊C₄	—	4	1	no	—
217	C₅×C₂²⋊C₄	—	4	1	no	—
218	C₅×C₂²⋊C₄	D₈	1	1	yes	characteristic
219	C₅×C₂²⋊C₄	D₈	1	1	yes	characteristic
220	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
221	C₅×C₁₆	—	2	1	no	—
222	C₅×C₁₆	—	2	1	no	—
223	C₅×C₁₆	—	2	1	no	—
224	C₅×C₁₆	C₂×D₄	1	2	yes	complemented
225	C₂×#135	C₂²×C₅	1	1	yes	characteristic, complemented
226	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
227	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic, complemented
228	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic, complemented
229	#546	—	2	1	no	—
230	D₄²	—	2	1	no	—
231	#509	—	2	4	no	—
232	C₂×SD₃₂	C₂²×C₅	1	1	yes	characteristic, complemented
233	C₂×SD₃₂	C₂²×C₅	1	1	yes	characteristic, complemented
234	C₂×SD₃₂	C₂²×C₅	1	1	yes	characteristic, complemented
235	C₂×D₁₆	—	2	4	no	—
236	C₂×D₁₆	C₂²×C₅	1	1	yes	characteristic
237	C₂×D₁₆	C₂²×C₅	1	1	yes	characteristic
238	C₂×D₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
239	C₂×D₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
240	C₂×D₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
241	C₂×D₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
242	C₂×M₃₂	C₂²×C₅	1	1	yes	characteristic, complemented
243	C₂²×C₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
244	#495	C₂²×C₅	1	1	yes	characteristic, complemented
245	#493	C₂²×C₅	1	1	yes	characteristic, complemented
246	#467	C₂²×C₅	1	1	yes	characteristic, complemented
247	#466	C₂²×C₅	1	1	yes	characteristic
248	#466	C₂²×C₅	1	1	yes	characteristic, complemented
249	#466	C₂²×C₅	1	1	yes	characteristic, complemented
250	#463	—	2	1	no	—
251	#459	—	2	1	no	—
252	#450	—	2	1	no	—
253	#449	—	2	1	no	—
254	#447	—	2	1	no	—
255	#447	—	2	1	no	—
256	C₄×D₈	C₂²×C₅	1	1	yes	characteristic, complemented
257	C₄×D₈	C₂²×C₅	1	1	yes	characteristic, complemented
258	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
259	#367	C₂²×C₅	1	1	yes	characteristic, complemented
260	C₄⋊C₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
261	#358	C₂²×C₅	1	1	yes	characteristic, complemented
262	#357	C₂²×C₅	1	1	yes	characteristic, complemented
263	#357	C₂²×C₅	1	1	yes	characteristic, complemented
264	#357	C₂²×C₅	1	1	yes	characteristic, complemented
265	#357	C₂²×C₅	1	1	yes	characteristic, complemented
266	#357	C₂²×C₅	1	1	yes	characteristic, complemented
267	C₂²⋊C₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
268	C₂²⋊C₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
269	#346	C₂²×C₅	1	1	yes	characteristic, complemented
270	C₂³×C₅	—	4	1	no	—
271	C₂³×C₅	—	4	1	no	—
272	C₂³×C₅	—	4	1	no	—
273	C₂³×C₅	—	4	1	no	—
274	C₂³×C₅	—	4	1	no	—
275	C₂³×C₅	—	8	2	no	—
276	C₂³×C₅	—	8	2	no	—
277	C₂³×C₅	—	8	2	no	—
278	C₂³×C₅	—	8	2	no	—
279	C₂³×C₅	—	8	2	no	—
280	C₂³×C₅	—	8	2	no	—
281	C₂³×C₅	—	16	1	no	—
282	C₂³×C₅	—	16	1	no	—
283	C₂³×C₅	—	16	1	no	—
284	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
285	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
286	C₅×Q₈	—	4	1	no	—
287	C₅×Q₈	—	4	1	no	—
288	C₅×D₄	—	2	2	no	—
289	C₅×D₄	—	2	2	no	—
290	C₅×D₄	—	2	2	no	—
291	C₅×D₄	—	4	1	no	—
292	C₅×D₄	—	4	1	no	—
293	C₅×D₄	—	4	1	no	—
294	C₅×D₄	—	4	1	no	—
295	C₅×D₄	—	4	1	no	—
296	C₅×D₄	—	4	1	no	—
297	C₅×D₄	—	4	1	no	—
298	C₅×D₄	—	4	1	no	—
299	C₅×D₄	—	8	2	no	—
300	C₅×D₄	—	8	2	no	—
301	C₅×D₄	—	8	2	no	—
302	C₅×D₄	—	8	2	no	—
303	C₅×D₄	—	8	2	no	—
304	C₅×D₄	—	8	2	no	—
305	C₅×D₄	—	8	2	no	—
306	C₅×D₄	—	16	1	no	—
307	C₅×D₄	—	16	1	no	—
308	C₂×C₄×C₅	—	2	1	no	—
309	C₂×C₄×C₅	—	2	1	no	—
310	C₂×C₄×C₅	—	2	1	no	—
311	C₂×C₄×C₅	—	2	1	no	—
312	C₂×C₄×C₅	—	4	1	no	—
313	C₂×C₄×C₅	—	4	1	no	—
314	C₂×C₄×C₅	—	4	1	no	—
315	C₂×C₄×C₅	—	8	2	no	—
316	C₂×C₄×C₅	—	8	2	no	—
317	C₂×C₄×C₅	—	16	1	no	—
318	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
319	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
320	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
321	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
322	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
323	C₅×C₈	—	2	1	no	—
324	C₅×C₈	—	2	1	no	—
325	C₅×C₈	—	2	1	no	—
326	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
327	C₅×C₈	H(5,𝔽₂)	1	1	yes	characteristic
328	C₂×#41	—	2	1	no	—
329	C₂²×D₄	—	2	1	no	—
330	C₂²×D₄	—	2	1	no	—
331	C₂²×D₄	—	2	1	no	—
332	C₂²×D₄	—	4	1	no	—
333	#135	—	2	2	no	—
334	#135	—	4	1	no	—
335	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
336	C₂×SD₁₆	—	2	1	no	—
337	C₂×SD₁₆	—	2	1	no	—
338	C₂×D₈	—	2	2	no	—
339	C₂×D₈	—	2	2	no	—
340	C₂×D₈	—	2	2	no	—
341	C₂×D₈	—	2	1	no	—
342	C₂×D₈	—	2	1	no	—
343	C₂×D₈	—	2	1	no	—
344	C₂×D₈	—	2	1	no	—
345	C₂×D₈	—	4	1	no	—
346	C₂×D₈	—	4	1	no	—
347	C₂×D₈	—	4	1	no	—
348	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
349	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
350	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
351	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
352	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
353	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
354	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
355	#127	—	2	1	no	—
356	#124	—	2	1	no	—
357	#123	—	4	1	no	—
358	C₂²⋊Q₈	—	2	1	no	—
359	#121	—	2	1	no	—
360	#121	—	2	1	no	—
361	#121	—	2	1	no	—
362	#121	—	4	1	no	—
363	#121	—	4	1	no	—
364	#120	—	4	1	no	—
365	#120	—	4	1	no	—
366	#120	—	4	1	no	—
367	C₄×D₄	—	2	1	no	—
368	C₄×D₄	—	2	1	no	—
369	C₄×D₄	C₅×D₄	1	1	yes	characteristic
370	C₂×C₂²⋊C₄	—	4	1	no	—
371	SD₃₂	—	2	2	no	—
372	SD₃₂	—	2	2	no	—
373	SD₃₂	—	4	1	no	—
374	D₁₆	—	2	2	no	—
375	D₁₆	—	2	2	no	—
376	D₁₆	—	2	2	no	—
377	D₁₆	—	2	2	no	—
378	D₁₆	—	4	1	no	—
379	D₁₆	C₅×D₄	1	4	yes	complemented
380	M₃₂	—	2	2	no	—
381	C₂×C₁₆	—	2	2	no	—
382	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
383	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
384	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
385	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
386	#107	C₂³×C₅	1	1	yes	characteristic
387	#107	C₂³×C₅	1	1	yes	characteristic
388	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
389	#103	—	2	1	no	—
390	#102	—	2	1	no	—
391	#102	—	2	1	no	—
392	#102	—	2	1	no	—
393	#102	—	2	1	no	—
394	#102	—	2	1	no	—
395	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
396	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
397	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
398	C₂²×C₅	—	2	1	no	—
399	C₂²×C₅	—	2	1	no	—
400	C₂²×C₅	—	2	1	no	—
401	C₂²×C₅	—	2	1	no	—
402	C₂²×C₅	—	2	1	no	—
403	C₂²×C₅	—	4	2	no	—
404	C₂²×C₅	—	4	2	no	—
405	C₂²×C₅	—	8	1	no	—
406	C₂²×C₅	—	8	1	no	—
407	C₂²×C₅	—	8	1	no	—
408	C₂²×C₅	—	8	1	no	—
409	C₂²×C₅	—	8	1	no	—
410	C₂²×C₅	—	8	1	no	—
411	C₂²×C₅	—	8	1	no	—
412	C₂²×C₅	—	8	1	no	—
413	C₂²×C₅	—	8	1	no	—
414	C₂²×C₅	—	8	1	no	—
415	C₂²×C₅	—	8	1	no	—
416	C₂²×C₅	—	8	1	no	—
417	C₂²×C₅	—	8	1	no	—
418	C₂²×C₅	—	16	4	no	—
419	C₂²×C₅	—	16	4	no	—
420	C₂²×C₅	—	16	4	no	—
421	C₂²×C₅	#509	1	2	yes	complemented
422	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
423	C₄×C₅	—	2	1	no	—
424	C₄×C₅	—	2	1	no	—
425	C₄×C₅	—	2	1	no	—
426	C₄×C₅	—	2	1	no	—
427	C₄×C₅	—	8	1	no	—
428	C₄×C₅	—	8	1	no	—
429	C₄×C₅	—	8	1	no	—
430	C₄×C₅	D₄²	1	1	yes	characteristic
431	C₄×C₅	#576	1	1	yes	characteristic
432	C₂⁴	—	4	1	no	—
433	C₂⁴	—	4	1	no	—
434	C₂⁴	—	4	1	no	—
435	#41	—	4	2	no	—
436	#41	—	8	1	no	—
437	C₂×Q₈	—	2	1	no	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	4	2	no	—
444	C₂×D₄	—	4	2	no	—
445	C₂×D₄	—	4	2	no	—
446	C₂×D₄	—	4	1	no	—
447	C₂×D₄	—	4	1	no	—
448	C₂×D₄	—	4	1	no	—
449	C₂×D₄	—	4	1	no	—
450	C₂×D₄	—	4	1	no	—
451	C₂×D₄	—	4	1	no	—
452	C₂×D₄	—	4	1	no	—
453	C₂×D₄	—	4	1	no	—
454	C₂×D₄	—	4	1	no	—
455	C₂×D₄	—	8	1	no	—
456	C₂×D₄	—	8	1	no	—
457	C₂×D₄	—	8	1	no	—
458	C₂×D₄	—	8	4	no	—
459	C₂×D₄	C₅×D₈	1	1	yes	characteristic
460	C₂²×C₄	—	4	1	no	—
461	C₂²×C₄	—	4	1	no	—
462	C₂²×C₄	—	4	1	no	—
463	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
464	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
465	Q₁₆	—	2	1	no	—
466	Q₁₆	—	2	1	no	—
467	SD₁₆	—	4	2	no	—
468	SD₁₆	—	8	1	no	—
469	D₈	—	2	1	no	—
470	D₈	—	2	1	no	—
471	D₈	—	2	1	no	—
472	D₈	—	2	1	no	—
473	D₈	—	2	1	no	—
474	D₈	—	2	1	no	—
475	D₈	—	2	1	no	—
476	D₈	—	2	1	no	—
477	D₈	—	4	2	no	—
478	D₈	—	4	2	no	—
479	D₈	—	4	2	no	—
480	D₈	—	8	1	no	—
481	D₈	C₂×C₅×D₄	1	2	yes	—
482	D₈	C₂×C₅×D₄	1	2	yes	complemented
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
488	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
489	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
490	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	4	1	no	—
494	C₄⋊C₄	C₅×D₈	1	1	yes	characteristic
495	C₂²⋊C₄	—	4	1	no	—
496	C₂²⋊C₄	—	4	1	no	—
497	C₂²⋊C₄	—	4	1	no	—
498	C₂²⋊C₄	—	4	1	no	—
499	C₂²⋊C₄	—	4	1	no	—
500	C₂²⋊C₄	—	4	1	no	—
501	C₂²⋊C₄	—	4	1	no	—
502	C₂²⋊C₄	—	4	1	no	—
503	C₂²⋊C₄	C₅×D₈	1	1	yes	characteristic
504	C₂²⋊C₄	C₅×D₈	1	1	yes	characteristic
505	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
506	C₁₆	—	2	1	no	—
507	C₁₆	—	2	1	no	—
508	C₁₆	—	2	1	no	—
509	C₁₆	C₂×C₅×D₄	1	2	yes	complemented
510	C₂×C₅	—	2	2	no	—
511	C₂×C₅	—	4	1	no	—
512	C₂×C₅	—	8	2	no	—
513	C₂×C₅	—	8	2	no	—
514	C₂×C₅	—	16	1	no	—
515	C₂×C₅	—	16	1	no	—
516	C₂×C₅	—	16	1	no	—
517	C₂×C₅	D₄×D₈	1	1	yes	characteristic
518	C₂×C₅	C₂×#509	1	1	yes	characteristic
519	C₂×C₅	#3415	1	1	yes	characteristic
520	C₂³	—	4	1	no	—
521	C₂³	—	4	1	no	—
522	C₂³	—	4	1	no	—
523	C₂³	—	4	1	no	—
524	C₂³	—	4	1	no	—
525	C₂³	—	8	2	no	—
526	C₂³	—	8	2	no	—
527	C₂³	—	8	2	no	—
528	C₂³	—	8	2	no	—
529	C₂³	—	8	2	no	—
530	C₂³	—	8	2	no	—
531	C₂³	—	16	1	no	—
532	C₂³	—	16	1	no	—
533	C₂³	—	16	1	no	—
534	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
535	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
536	Q₈	—	4	1	no	—
537	Q₈	—	4	1	no	—
538	D₄	—	2	2	no	—
539	D₄	—	2	2	no	—
540	D₄	—	2	2	no	—
541	D₄	—	4	1	no	—
542	D₄	—	4	1	no	—
543	D₄	—	4	1	no	—
544	D₄	—	4	1	no	—
545	D₄	—	4	1	no	—
546	D₄	—	4	1	no	—
547	D₄	—	4	1	no	—
548	D₄	—	4	1	no	—
549	D₄	—	8	2	no	—
550	D₄	—	8	2	no	—
551	D₄	—	8	2	no	—
552	D₄	—	8	2	no	—
553	D₄	—	8	2	no	—
554	D₄	—	8	2	no	—
555	D₄	—	8	2	no	—
556	D₄	—	16	1	no	—
557	D₄	—	16	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	8	2	no	—
566	C₂×C₄	—	8	2	no	—
567	C₂×C₄	—	16	1	no	—
568	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
569	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
570	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
571	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
572	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
573	C₈	—	2	1	no	—
574	C₈	—	2	1	no	—
575	C₈	—	2	1	no	—
576	C₈	C₂²×C₅×D₄	1	1	yes	characteristic
577	C₈	C₅×H(5,𝔽₂)	1	1	yes	characteristic
578	C₅	#33830	1	1	yes	characteristic, direct product factor, Sylow
579	C₂²	—	2	1	no	—
580	C₂²	—	2	1	no	—
581	C₂²	—	2	1	no	—
582	C₂²	—	2	1	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	4	2	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	8	1	no	—
587	C₂²	—	8	1	no	—
588	C₂²	—	8	1	no	—
589	C₂²	—	8	1	no	—
590	C₂²	—	8	1	no	—
591	C₂²	—	8	1	no	—
592	C₂²	—	8	1	no	—
593	C₂²	—	8	1	no	—
594	C₂²	—	8	1	no	—
595	C₂²	—	8	1	no	—
596	C₂²	—	8	1	no	—
597	C₂²	—	8	1	no	—
598	C₂²	—	8	1	no	—
599	C₂²	—	16	4	no	—
600	C₂²	—	16	4	no	—
601	C₂²	—	16	4	no	—
602	C₂²	C₅×#509	1	2	yes	complemented
603	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
604	C₄	—	2	1	no	—
605	C₄	—	2	1	no	—
606	C₄	—	2	1	no	—
607	C₄	—	2	1	no	—
608	C₄	—	8	1	no	—
609	C₄	—	8	1	no	—
610	C₄	—	8	1	no	—
611	C₄	C₅×D₄²	1	1	yes	characteristic
612	C₄	C₅×#576	1	1	yes	characteristic
613	C₂	—	2	2	no	—
614	C₂	—	4	1	no	—
615	C₂	—	8	2	no	—
616	C₂	—	8	2	no	—
617	C₂	—	16	1	no	—
618	C₂	—	16	1	no	—
619	C₂	—	16	1	no	—
620	C₂	C₅×D₄×D₈	1	1	yes	characteristic
621	C₂	C₂×C₅×#509	1	1	yes	characteristic
622	C₂	C₅×#3415	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 ◁ C₄×C₅×D₄ ◁ C₅×C₈×D₄ ◁ 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×D₁₆	C₂	semidirect
3. C₅×#3280	C₂	semidirect
4. C₅×D₄×D₈	C₂	semidirect
5. C₅×#2250	C₂	semidirect
6. C₅×#2218	C₂	semidirect
7. C₅×#2217	C₂	semidirect
8. C₅×#2210	C₂	semidirect
9. C₅×#2206	C₂	semidirect
10. C₅×#2187	C₂	semidirect
11. C₅×#2186	C₂	semidirect
12. C₅×#2184	C₂	semidirect
13. C₅×#2184	C₂	semidirect
14. C₅×#2177	C₂	semidirect
15. C₅×#2168	C₂	semidirect
16. C₂×C₅×#135	C₂²	semidirect
18. C₂²×C₅×D₈	C₂²	semidirect
19. C₂²×C₅×D₈	C₂²	semidirect
23. C₂×C₅×SD₃₂	C₂²	semidirect
24. C₂×C₅×SD₃₂	C₂²	semidirect
25. C₂×C₅×SD₃₂	C₂²	semidirect
29. C₂×C₅×D₁₆	C₂²	semidirect
30. C₂×C₅×D₁₆	C₂²	semidirect
31. C₂×C₅×D₁₆	C₂²	semidirect
32. C₂×C₅×D₁₆	C₂²	semidirect
33. C₂×C₅×M₃₂	C₂²	semidirect
34. C₂²×C₅×C₁₆	C₂²	semidirect
35. C₅×#495	C₂²	semidirect
36. C₅×#493	C₂²	semidirect
37. C₅×#467	C₂²	semidirect
39. C₅×#466	C₂²	semidirect
40. C₅×#466	C₂²	semidirect
47. C₄×C₅×D₈	C₂²	semidirect
48. C₄×C₅×D₈	C₂²	semidirect
50. C₅×#367	C₂²	semidirect
51. C₅×C₄⋊C₁₆	C₂²	semidirect
52. C₅×#358	C₂²	semidirect
53. C₅×#357	C₂²	semidirect
54. C₅×#357	C₂²	semidirect
55. C₅×#357	C₂²	semidirect
56. C₅×#357	C₂²	semidirect
57. C₅×#357	C₂²	semidirect
58. C₅×C₂²⋊C₁₆	C₂²	semidirect
59. C₅×C₂²⋊C₁₆	C₂²	semidirect
60. C₅×#346	C₂²	semidirect
61. #33830	C₅	direct (N × H)
113. C₅×D₁₆	D₄	semidirect
132. C₂×#509	C₂×C₅	semidirect
133. C₂²×D₁₆	C₂×C₅	semidirect
134. #3280	C₂×C₅	semidirect
135. D₄×D₈	C₂×C₅	semidirect
136. #2250	C₂×C₅	semidirect
137. #2218	C₂×C₅	semidirect
138. #2217	C₂×C₅	semidirect
139. #2210	C₂×C₅	semidirect
140. #2206	C₂×C₅	semidirect
141. #2187	C₂×C₅	semidirect
142. #2186	C₂×C₅	semidirect
143. #2184	C₂×C₅	semidirect
144. #2184	C₂×C₅	semidirect
145. #2177	C₂×C₅	semidirect
146. #2168	C₂×C₅	semidirect
197. C₅×D₈	C₂×D₄	semidirect
224. C₅×C₁₆	C₂×D₄	semidirect
225. C₂×#135	C₂²×C₅	semidirect
227. C₂²×D₈	C₂²×C₅	semidirect
228. C₂²×D₈	C₂²×C₅	semidirect
232. C₂×SD₃₂	C₂²×C₅	semidirect
233. C₂×SD₃₂	C₂²×C₅	semidirect
234. C₂×SD₃₂	C₂²×C₅	semidirect
238. C₂×D₁₆	C₂²×C₅	semidirect
239. C₂×D₁₆	C₂²×C₅	semidirect
240. C₂×D₁₆	C₂²×C₅	semidirect
241. C₂×D₁₆	C₂²×C₅	semidirect
242. C₂×M₃₂	C₂²×C₅	semidirect
243. C₂²×C₁₆	C₂²×C₅	semidirect
244. #495	C₂²×C₅	semidirect
245. #493	C₂²×C₅	semidirect
246. #467	C₂²×C₅	semidirect
248. #466	C₂²×C₅	semidirect
249. #466	C₂²×C₅	semidirect
256. C₄×D₈	C₂²×C₅	semidirect
257. C₄×D₈	C₂²×C₅	semidirect
259. #367	C₂²×C₅	semidirect
260. C₄⋊C₁₆	C₂²×C₅	semidirect
261. #358	C₂²×C₅	semidirect
262. #357	C₂²×C₅	semidirect
263. #357	C₂²×C₅	semidirect
264. #357	C₂²×C₅	semidirect
265. #357	C₂²×C₅	semidirect
266. #357	C₂²×C₅	semidirect
267. C₂²⋊C₁₆	C₂²×C₅	semidirect
268. C₂²⋊C₁₆	C₂²×C₅	semidirect
269. #346	C₂²×C₅	semidirect
379. D₁₆	C₅×D₄	semidirect
421. C₂²×C₅	#509	semidirect
482. D₈	C₂×C₅×D₄	semidirect
509. C₁₆	C₂×C₅×D₄	semidirect
578. C₅	#33830	direct (N × H)
602. 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×D₁₆	2
C₅×#3280	2
C₅×D₄×D₈	2
C₅×#2250	2
C₅×#2218	2
C₅×#2217	2
C₅×#2210	2
C₅×#2206	2
C₅×#2187	2
C₅×#2186	2
C₅×#2184	2
C₅×#2177	2
C₅×#2168	2
#33830	5

Subgroups — C5×#33830 #11956550

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33830 #11956550