Subgroups — C₅×#61319 #11984039

Order 1280.

1836 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3480	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×Q₈²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3375	C₂	1	6	yes	maximal, complemented
4	C₅×#3369	C₂	1	6	yes	maximal, complemented
5	C₅×#3363	C₂	1	2	yes	maximal, complemented
6	C₅×#3362	C₂	1	2	yes	maximal, complemented
7	C₅×#3141	C₂	1	3	yes	maximal, complemented
8	C₅×#3079	C₂	1	3	yes	maximal, complemented
9	C₅×#3037	C₂	1	3	yes	maximal, complemented
10	C₅×Q₈×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×#137	C₂	1	3	yes	maximal, complemented
12	C₂×C₅×#137	C₂²	1	3	yes	—
13	C₅×#559	C₂²	1	3	yes	—
14	C₅×Q₈²	—	2	1	no	—
15	C₅×Q₈²	—	2	3	no	—
16	C₅×Q₈²	C₂²	1	2	yes	—
17	C₅×Q₈²	C₂²	1	6	yes	—
18	C₅×#557	C₂²	1	1	yes	characteristic
19	C₅×#556	C₂²	1	3	yes	—
20	C₅×#553	—	2	3	no	—
21	C₅×#550	C₂²	1	1	yes	characteristic
22	C₅×#548	—	2	1	no	—
23	C₅×#532	C₂²	1	3	yes	—
24	C₂×C₅×C₄⋊Q₈	—	2	3	no	—
25	C₂×C₅×C₄⋊Q₈	C₂²	1	3	yes	—
26	C₅×#529	—	2	3	no	—
27	C₄×C₅×#41	—	2	1	no	—
28	C₄×C₅×#41	C₂²	1	3	yes	—
29	C₂×C₄×C₅×Q₈	—	2	1	no	—
30	C₂×C₄×C₅×Q₈	C₂²	1	3	yes	—
31	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
32	C₅×#489	C₂²	1	12	yes	—
33	C₅×#487	C₂²	1	6	yes	—
34	C₅×#486	C₂²	1	6	yes	—
35	C₅×#477	C₂²	1	6	yes	—
36	C₅×#476	C₂²	1	6	yes	—
37	C₅×#475	C₂²	1	6	yes	—
38	C₅×#474	C₂²	1	6	yes	—
39	C₅×#464	C₂²	1	12	yes	—
40	C₅×#462	C₂²	1	6	yes	—
41	C₅×#460	C₂²	1	6	yes	—
42	C₅×#446	C₂²	1	6	yes	—
43	C₅×C₈×Q₈	C₂²	1	2	yes	—
44	C₅×#441	C₂²	1	6	yes	—
45	C₅×#440	C₂²	1	6	yes	—
46	C₄×C₅×Q₁₆	C₂²	1	6	yes	—
47	C₄×C₅×SD₁₆	C₂²	1	6	yes	—
48	C₅×#428	C₂²	1	3	yes	—
49	C₅×#423	C₂²	1	3	yes	—
50	C₅×#419	C₂²	1	1	yes	characteristic
51	C₅×#417	C₂²	1	6	yes	—
52	C₅×#417	C₂²	1	3	yes	—
53	C₄×C₅×M₁₆	C₂²	1	3	yes	—
54	#61319	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
55	C₂×C₅×#41	—	2	1	no	—
56	C₂×C₅×#41	C₂³	1	3	yes	—
57	C₂²×C₅×Q₈	—	2	3	no	—
58	C₂²×C₅×Q₈	D₄	1	1	yes	characteristic
59	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
60	C₅×#137	—	2	12	no	—
61	C₂×C₅×Q₁₆	C₂³	1	6	yes	—
62	C₂×C₅×SD₁₆	C₂³	1	6	yes	—
63	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
64	C₂×C₅×M₁₆	C₂³	1	3	yes	—
65	C₅×C₄⋊Q₈	—	2	6	no	—
66	C₅×C₄⋊Q₈	—	2	6	no	—
67	C₅×C₄⋊Q₈	—	2	12	no	—
68	C₅×C₄⋊Q₈	—	2	3	no	—
69	C₅×C₄⋊Q₈	—	2	3	no	—
70	C₅×C₄⋊Q₈	C₂³	1	3	yes	—
71	C₅×C₄⋊Q₈	C₂³	1	6	yes	—
72	C₅×C₄⋊Q₈	C₂³	1	6	yes	—
73	C₅×#127	C₂³	1	3	yes	—
74	C₅×#126	—	2	6	no	—
75	C₅×#125	—	2	3	no	—
76	C₅×#124	—	2	3	no	—
77	C₅×#124	C₂³	1	6	yes	—
78	C₅×#123	—	2	6	no	—
79	C₅×C₂²⋊Q₈	—	2	3	no	—
80	C₅×#121	—	2	3	no	—
81	C₅×#121	—	2	3	no	—
82	C₅×#121	—	2	3	no	—
83	C₄×C₅×Q₈	—	2	6	no	—
84	C₄×C₅×Q₈	—	2	2	no	—
85	C₄×C₅×Q₈	—	2	1	no	—
86	C₄×C₅×Q₈	—	2	3	no	—
87	C₄×C₅×Q₈	—	2	3	no	—
88	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
89	C₄×C₅×Q₈	D₄	1	3	yes	—
90	C₄×C₅×Q₈	C₂³	1	6	yes	—
91	C₄×C₅×Q₈	C₂³	1	3	yes	—
92	C₄×C₅×Q₈	C₂³	1	6	yes	—
93	C₄×C₅×Q₈	C₂³	1	3	yes	—
94	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
95	C₄×C₅×Q₈	C₂³	1	3	yes	—
96	C₄×C₅×D₄	—	2	3	no	—
97	C₄×C₅×D₄	—	2	3	no	—
98	C₄×C₅×D₄	—	2	3	no	—
99	C₄×C₅×D₄	—	2	3	no	—
100	C₄×C₅×D₄	—	2	3	no	—
101	C₄×C₅×D₄	C₂³	1	3	yes	—
102	C₄×C₅×D₄	C₂³	1	3	yes	—
103	C₅×#117	—	2	3	no	—
104	C₅×#117	—	2	3	no	—
105	C₅×#117	C₂³	1	1	yes	characteristic
106	C₂×C₅×C₄⋊C₄	—	2	3	no	—
107	C₂×C₅×C₄⋊C₄	—	2	3	no	—
108	C₂×C₅×C₄⋊C₄	D₄	1	3	yes	—
109	C₂×C₅×C₄⋊C₄	C₂³	1	3	yes	—
110	C₂×C₄²×C₅	—	2	3	no	—
111	C₂×C₄²×C₅	—	2	3	no	—
112	C₂×C₄²×C₅	C₂³	1	3	yes	—
113	C₅×#107	C₂³	1	6	yes	—
114	C₅×#106	C₂³	1	6	yes	—
115	C₅×C₄⋊C₈	C₂³	1	6	yes	—
116	C₅×C₄⋊C₈	C₂³	1	6	yes	—
117	C₅×#103	C₂³	1	6	yes	—
118	C₅×#103	C₂³	1	12	yes	—
119	C₅×#103	C₂³	1	2	yes	—
120	C₅×#103	C₂³	1	2	yes	—
121	C₅×#102	C₂³	1	6	yes	—
122	C₅×#102	C₂³	1	12	yes	—
123	C₅×#97	C₂³	1	6	yes	—
124	C₄×C₅×C₈	C₂³	1	6	yes	—
125	#3480	C₂×C₅	1	1	yes	characteristic
126	C₂×Q₈²	C₂×C₅	1	1	yes	characteristic, complemented
127	#3375	C₂×C₅	1	6	yes	complemented
128	#3369	C₂×C₅	1	6	yes	complemented
129	#3363	C₂×C₅	1	2	yes	complemented
130	#3362	C₂×C₅	1	2	yes	complemented
131	#3141	C₂×C₅	1	3	yes	complemented
132	#3079	C₂×C₅	1	3	yes	complemented
133	#3037	C₂×C₅	1	3	yes	complemented
134	Q₈×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
135	C₄×#137	C₂×C₅	1	3	yes	complemented
136	C₅×#41	—	2	6	no	—
137	C₅×#41	—	2	6	no	—
138	C₅×#41	—	4	4	no	—
139	C₂×C₅×Q₈	—	2	4	no	—
140	C₂×C₅×Q₈	—	2	1	no	—
141	C₂×C₅×Q₈	—	2	6	no	—
142	C₂×C₅×Q₈	—	2	6	no	—
143	C₂×C₅×Q₈	—	2	2	no	—
144	C₂×C₅×Q₈	—	8	6	no	—
145	C₂×C₅×Q₈	C₂×D₄	1	3	yes	—
146	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
147	C₂×C₅×Q₈	#41	1	4	yes	complemented
148	C₂×C₅×Q₈	C₂⁴	1	3	yes	—
149	C₂×C₅×Q₈	C₂⁴	1	2	yes	—
150	C₂×C₅×D₄	—	2	3	no	—
151	C₂×C₅×D₄	—	2	3	no	—
152	C₂×C₅×D₄	—	2	3	no	—
153	C₂×C₅×D₄	C₂⁴	1	3	yes	—
154	C₂²×C₄×C₅	—	2	1	no	—
155	C₂²×C₄×C₅	—	2	3	no	—
156	C₂²×C₄×C₅	—	2	3	no	—
157	C₂²×C₄×C₅	—	2	3	no	—
158	C₂²×C₄×C₅	—	2	3	no	—
159	C₂²×C₄×C₅	C₂×D₄	1	3	yes	—
160	C₂²×C₄×C₅	C₂×D₄	1	3	yes	—
161	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
162	C₅×Q₁₆	—	2	12	no	—
163	C₅×SD₁₆	—	2	12	no	—
164	C₅×M₁₆	—	2	6	no	—
165	C₅×M₁₆	—	2	2	no	—
166	C₂×C₅×C₈	C₂⁴	1	6	yes	—
167	C₂×C₅×C₈	C₂⁴	1	2	yes	—
168	C₅×C₄⋊C₄	—	2	6	no	—
169	C₅×C₄⋊C₄	—	2	6	no	—
170	C₅×C₄⋊C₄	—	2	6	no	—
171	C₅×C₄⋊C₄	—	2	6	no	—
172	C₅×C₄⋊C₄	—	2	3	no	—
173	C₅×C₄⋊C₄	—	2	3	no	—
174	C₅×C₄⋊C₄	—	2	3	no	—
175	C₅×C₄⋊C₄	—	2	3	no	—
176	C₅×C₄⋊C₄	—	2	3	no	—
177	C₅×C₄⋊C₄	C₂×D₄	1	3	yes	—
178	C₅×C₄⋊C₄	C₂×D₄	1	3	yes	—
179	C₅×C₄⋊C₄	C₂×D₄	1	6	yes	—
180	C₅×C₄⋊C₄	C₂⁴	1	6	yes	—
181	C₅×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
182	C₅×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
183	C₅×C₂²⋊C₄	—	2	1	no	—
184	C₅×C₂²⋊C₄	—	2	6	no	—
185	C₅×C₂²⋊C₄	—	2	3	no	—
186	C₅×C₂²⋊C₄	—	2	3	no	—
187	C₅×C₂²⋊C₄	—	2	6	no	—
188	C₄²×C₅	—	2	1	no	—
189	C₄²×C₅	—	2	3	no	—
190	C₄²×C₅	—	2	3	no	—
191	C₄²×C₅	—	2	6	no	—
192	C₄²×C₅	—	2	6	no	—
193	C₄²×C₅	C₂×D₄	1	3	yes	—
194	C₄²×C₅	C₂×D₄	1	3	yes	—
195	C₄²×C₅	C₂⁴	1	3	yes	—
196	C₄²×C₅	C₂⁴	1	3	yes	—
197	C₂×#137	C₂²×C₅	1	3	yes	—
198	#559	C₂²×C₅	1	3	yes	—
199	Q₈²	—	2	1	no	—
200	Q₈²	—	2	3	no	—
201	Q₈²	C₂²×C₅	1	2	yes	—
202	Q₈²	C₂²×C₅	1	6	yes	—
203	#557	C₂²×C₅	1	1	yes	characteristic
204	#556	C₂²×C₅	1	3	yes	—
205	#553	—	2	3	no	—
206	#550	C₂²×C₅	1	1	yes	characteristic
207	#548	—	2	1	no	—
208	#532	C₂²×C₅	1	3	yes	—
209	C₂×C₄⋊Q₈	—	2	3	no	—
210	C₂×C₄⋊Q₈	C₂²×C₅	1	3	yes	—
211	#529	—	2	3	no	—
212	C₄×#41	—	2	1	no	—
213	C₄×#41	C₂²×C₅	1	3	yes	—
214	C₂×C₄×Q₈	—	2	1	no	—
215	C₂×C₄×Q₈	C₂²×C₅	1	3	yes	—
216	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
217	#489	C₂²×C₅	1	12	yes	—
218	#487	C₂²×C₅	1	6	yes	—
219	#486	C₂²×C₅	1	6	yes	—
220	#477	C₂²×C₅	1	6	yes	—
221	#476	C₂²×C₅	1	6	yes	—
222	#475	C₂²×C₅	1	6	yes	—
223	#474	C₂²×C₅	1	6	yes	—
224	#464	C₂²×C₅	1	12	yes	—
225	#462	C₂²×C₅	1	6	yes	—
226	#460	C₂²×C₅	1	6	yes	—
227	#446	C₂²×C₅	1	6	yes	—
228	C₈×Q₈	C₂²×C₅	1	2	yes	—
229	#441	C₂²×C₅	1	6	yes	—
230	#440	C₂²×C₅	1	6	yes	—
231	C₄×Q₁₆	C₂²×C₅	1	6	yes	—
232	C₄×SD₁₆	C₂²×C₅	1	6	yes	—
233	#428	C₂²×C₅	1	3	yes	—
234	#423	C₂²×C₅	1	3	yes	—
235	#419	C₂²×C₅	1	1	yes	characteristic
236	#417	C₂²×C₅	1	6	yes	—
237	#417	C₂²×C₅	1	3	yes	—
238	C₄×M₁₆	C₂²×C₅	1	3	yes	—
239	C₂³×C₅	—	2	3	no	—
240	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
241	C₅×Q₈	—	2	4	no	—
242	C₅×Q₈	—	2	6	no	—
243	C₅×Q₈	—	2	2	no	—
244	C₅×Q₈	—	2	3	no	—
245	C₅×Q₈	—	2	3	no	—
246	C₅×Q₈	—	8	6	no	—
247	C₅×Q₈	—	8	6	no	—
248	C₅×Q₈	#137	1	4	yes	complemented
249	C₅×Q₈	C₂×#41	1	4	yes	—
250	C₅×D₄	—	2	3	no	—
251	C₅×D₄	—	2	3	no	—
252	C₅×D₄	—	4	6	no	—
253	C₅×D₄	—	4	6	no	—
254	C₅×D₄	—	8	3	no	—
255	C₂×C₄×C₅	—	2	4	no	—
256	C₂×C₄×C₅	—	2	2	no	—
257	C₂×C₄×C₅	—	2	6	no	—
258	C₂×C₄×C₅	—	2	1	no	—
259	C₂×C₄×C₅	—	2	1	no	—
260	C₂×C₄×C₅	—	2	3	no	—
261	C₂×C₄×C₅	—	2	6	no	—
262	C₂×C₄×C₅	—	4	3	no	—
263	C₂×C₄×C₅	—	4	6	no	—
264	C₂×C₄×C₅	—	4	6	no	—
265	C₂×C₄×C₅	—	4	6	no	—
266	C₂×C₄×C₅	—	8	3	no	—
267	C₂×C₄×C₅	C₂²×D₄	1	3	yes	—
268	C₂×C₄×C₅	C₂²×D₄	1	3	yes	—
269	C₂×C₄×C₅	C₂²×D₄	1	3	yes	—
270	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
271	C₂×C₄×C₅	C₂²×D₄	1	3	yes	—
272	C₂×C₄×C₅	C₂×#41	1	2	yes	—
273	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
274	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
275	C₅×C₈	—	2	6	no	—
276	C₅×C₈	—	2	2	no	—
277	C₂×#41	—	2	1	no	—
278	C₂×#41	C₂³×C₅	1	3	yes	—
279	C₂²×Q₈	—	2	3	no	—
280	C₂²×Q₈	C₅×D₄	1	1	yes	characteristic
281	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
282	#137	—	2	12	no	—
283	C₂×Q₁₆	C₂³×C₅	1	6	yes	—
284	C₂×SD₁₆	C₂³×C₅	1	6	yes	—
285	C₂×M₁₆	C₂³×C₅	1	3	yes	—
286	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
287	C₄⋊Q₈	—	2	6	no	—
288	C₄⋊Q₈	—	2	6	no	—
289	C₄⋊Q₈	—	2	12	no	—
290	C₄⋊Q₈	—	2	3	no	—
291	C₄⋊Q₈	—	2	3	no	—
292	C₄⋊Q₈	C₂³×C₅	1	3	yes	—
293	C₄⋊Q₈	C₂³×C₅	1	6	yes	—
294	C₄⋊Q₈	C₂³×C₅	1	6	yes	—
295	#127	C₂³×C₅	1	3	yes	—
296	#126	—	2	6	no	—
297	#125	—	2	3	no	—
298	#124	—	2	3	no	—
299	#124	C₂³×C₅	1	6	yes	—
300	#123	—	2	6	no	—
301	C₂²⋊Q₈	—	2	3	no	—
302	#121	—	2	3	no	—
303	#121	—	2	3	no	—
304	#121	—	2	3	no	—
305	C₄×Q₈	—	2	6	no	—
306	C₄×Q₈	—	2	2	no	—
307	C₄×Q₈	—	2	1	no	—
308	C₄×Q₈	—	2	3	no	—
309	C₄×Q₈	—	2	3	no	—
310	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
311	C₄×Q₈	C₅×D₄	1	3	yes	—
312	C₄×Q₈	C₂³×C₅	1	6	yes	—
313	C₄×Q₈	C₂³×C₅	1	6	yes	—
314	C₄×Q₈	C₂³×C₅	1	3	yes	—
315	C₄×Q₈	C₂³×C₅	1	3	yes	—
316	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
317	C₄×Q₈	C₂³×C₅	1	3	yes	—
318	C₄×D₄	—	2	3	no	—
319	C₄×D₄	—	2	3	no	—
320	C₄×D₄	—	2	3	no	—
321	C₄×D₄	—	2	3	no	—
322	C₄×D₄	—	2	3	no	—
323	C₄×D₄	C₂³×C₅	1	3	yes	—
324	C₄×D₄	C₂³×C₅	1	3	yes	—
325	#117	—	2	3	no	—
326	#117	—	2	3	no	—
327	#117	C₂³×C₅	1	1	yes	characteristic
328	C₂×C₄⋊C₄	—	2	3	no	—
329	C₂×C₄⋊C₄	—	2	3	no	—
330	C₂×C₄⋊C₄	C₅×D₄	1	3	yes	—
331	C₂×C₄⋊C₄	C₂³×C₅	1	3	yes	—
332	C₂×C₄²	—	2	3	no	—
333	C₂×C₄²	—	2	3	no	—
334	C₂×C₄²	C₂³×C₅	1	3	yes	—
335	#107	C₂³×C₅	1	6	yes	—
336	#106	C₂³×C₅	1	6	yes	—
337	C₄⋊C₈	C₂³×C₅	1	6	yes	—
338	C₄⋊C₈	C₂³×C₅	1	6	yes	—
339	#103	C₂³×C₅	1	6	yes	—
340	#103	C₂³×C₅	1	12	yes	—
341	#103	C₂³×C₅	1	2	yes	—
342	#103	C₂³×C₅	1	2	yes	—
343	#102	C₂³×C₅	1	6	yes	—
344	#102	C₂³×C₅	1	12	yes	—
345	#97	C₂³×C₅	1	6	yes	—
346	C₄×C₈	C₂³×C₅	1	6	yes	—
347	C₂²×C₅	—	2	1	no	—
348	C₂²×C₅	—	2	1	no	—
349	C₂²×C₅	—	4	3	no	—
350	C₂²×C₅	—	4	3	no	—
351	C₂²×C₅	—	4	3	no	—
352	C₂²×C₅	#548	1	2	yes	—
353	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
354	C₄×C₅	—	2	3	no	—
355	C₄×C₅	—	2	3	no	—
356	C₄×C₅	—	2	4	no	—
357	C₄×C₅	—	2	3	no	—
358	C₄×C₅	—	4	6	no	—
359	C₄×C₅	—	4	1	no	—
360	C₄×C₅	—	4	3	no	—
361	C₄×C₅	—	4	1	no	—
362	C₄×C₅	#548	1	2	yes	—
363	C₄×C₅	C₂×#137	1	6	yes	—
364	C₄×C₅	C₂²×#41	1	1	yes	characteristic
365	C₄×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
366	#41	—	2	6	no	—
367	#41	—	2	6	no	—
368	#41	—	4	4	no	—
369	C₂×Q₈	—	2	4	no	—
370	C₂×Q₈	—	2	1	no	—
371	C₂×Q₈	—	2	6	no	—
372	C₂×Q₈	—	2	6	no	—
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	—	8	6	no	—
375	C₂×Q₈	C₂×C₅×D₄	1	3	yes	—
376	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
377	C₂×Q₈	C₅×#41	1	4	yes	complemented
378	C₂×Q₈	C₂⁴×C₅	1	3	yes	—
379	C₂×Q₈	C₂⁴×C₅	1	2	yes	—
380	C₂×D₄	—	2	3	no	—
381	C₂×D₄	—	2	3	no	—
382	C₂×D₄	—	2	3	no	—
383	C₂×D₄	C₂⁴×C₅	1	3	yes	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	3	no	—
386	C₂²×C₄	—	2	3	no	—
387	C₂²×C₄	—	2	3	no	—
388	C₂²×C₄	—	2	3	no	—
389	C₂²×C₄	C₂×C₅×D₄	1	3	yes	—
390	C₂²×C₄	C₂×C₅×D₄	1	3	yes	—
391	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
392	Q₁₆	—	2	12	no	—
393	SD₁₆	—	2	12	no	—
394	M₁₆	—	2	6	no	—
395	M₁₆	—	2	2	no	—
396	C₂×C₈	C₂⁴×C₅	1	2	yes	—
397	C₂×C₈	C₂⁴×C₅	1	6	yes	—
398	C₄⋊C₄	—	2	6	no	—
399	C₄⋊C₄	—	2	6	no	—
400	C₄⋊C₄	—	2	6	no	—
401	C₄⋊C₄	—	2	6	no	—
402	C₄⋊C₄	—	2	3	no	—
403	C₄⋊C₄	—	2	3	no	—
404	C₄⋊C₄	—	2	3	no	—
405	C₄⋊C₄	—	2	3	no	—
406	C₄⋊C₄	—	2	3	no	—
407	C₄⋊C₄	C₂×C₅×D₄	1	3	yes	—
408	C₄⋊C₄	C₂×C₅×D₄	1	3	yes	—
409	C₄⋊C₄	C₂×C₅×D₄	1	6	yes	—
410	C₄⋊C₄	C₂⁴×C₅	1	6	yes	—
411	C₄⋊C₄	C₂⁴×C₅	1	1	yes	characteristic
412	C₄⋊C₄	C₂⁴×C₅	1	1	yes	characteristic
413	C₂²⋊C₄	—	2	1	no	—
414	C₂²⋊C₄	—	2	6	no	—
415	C₂²⋊C₄	—	2	3	no	—
416	C₂²⋊C₄	—	2	3	no	—
417	C₂²⋊C₄	—	2	6	no	—
418	C₄²	—	2	1	no	—
419	C₄²	—	2	3	no	—
420	C₄²	—	2	3	no	—
421	C₄²	—	2	6	no	—
422	C₄²	—	2	6	no	—
423	C₄²	C₂×C₅×D₄	1	3	yes	—
424	C₄²	C₂×C₅×D₄	1	3	yes	—
425	C₄²	C₂⁴×C₅	1	3	yes	—
426	C₄²	C₂⁴×C₅	1	3	yes	—
427	C₂×C₅	—	2	2	no	—
428	C₂×C₅	—	8	3	no	—
429	C₂×C₅	C₂×#548	1	1	yes	characteristic
430	C₂×C₅	C₂²×#137	1	1	yes	characteristic
431	C₂×C₅	#3585	1	1	yes	characteristic
432	C₂³	—	2	3	no	—
433	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
434	Q₈	—	2	4	no	—
435	Q₈	—	2	6	no	—
436	Q₈	—	2	2	no	—
437	Q₈	—	2	3	no	—
438	Q₈	—	2	3	no	—
439	Q₈	—	8	6	no	—
440	Q₈	—	8	6	no	—
441	Q₈	C₅×#137	1	4	yes	complemented
442	Q₈	C₂×C₅×#41	1	4	yes	—
443	D₄	—	2	3	no	—
444	D₄	—	2	3	no	—
445	D₄	—	4	6	no	—
446	D₄	—	4	6	no	—
447	D₄	—	8	3	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	6	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	3	no	—
454	C₂×C₄	—	2	6	no	—
455	C₂×C₄	—	4	3	no	—
456	C₂×C₄	—	4	6	no	—
457	C₂×C₄	—	4	6	no	—
458	C₂×C₄	—	4	6	no	—
459	C₂×C₄	—	8	3	no	—
460	C₂×C₄	C₂²×C₅×D₄	1	3	yes	—
461	C₂×C₄	C₂²×C₅×D₄	1	3	yes	—
462	C₂×C₄	C₂²×C₅×D₄	1	3	yes	—
463	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
464	C₂×C₄	C₂²×C₅×D₄	1	3	yes	—
465	C₂×C₄	C₂×C₅×#41	1	2	yes	—
466	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
467	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
468	C₈	—	2	6	no	—
469	C₈	—	2	2	no	—
470	C₅	#61319	1	1	yes	characteristic, direct product factor, Sylow
471	C₂²	—	2	1	no	—
472	C₂²	—	2	1	no	—
473	C₂²	—	4	3	no	—
474	C₂²	—	4	3	no	—
475	C₂²	—	4	3	no	—
476	C₂²	C₅×#548	1	2	yes	—
477	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
478	C₄	—	2	4	no	—
479	C₄	—	2	3	no	—
480	C₄	—	2	3	no	—
481	C₄	—	2	3	no	—
482	C₄	—	4	3	no	—
483	C₄	—	4	1	no	—
484	C₄	—	4	6	no	—
485	C₄	—	4	1	no	—
486	C₄	C₅×#548	1	2	yes	—
487	C₄	C₂×C₅×#137	1	6	yes	—
488	C₄	C₂²×C₅×#41	1	1	yes	characteristic
489	C₄	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
490	C₂	—	2	2	no	—
491	C₂	—	8	3	no	—
492	C₂	C₂×C₅×#548	1	1	yes	characteristic
493	C₂	C₂²×C₅×#137	1	1	yes	characteristic
494	C₂	C₅×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅
prime radical	C₅×#3480	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄×C₅×Q₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×Q₈²	C₂	semidirect
3. C₅×#3375	C₂	semidirect
4. C₅×#3369	C₂	semidirect
5. C₅×#3363	C₂	semidirect
6. C₅×#3362	C₂	semidirect
7. C₅×#3141	C₂	semidirect
8. C₅×#3079	C₂	semidirect
9. C₅×#3037	C₂	semidirect
10. C₅×Q₈×M₁₆	C₂	semidirect
11. C₄×C₅×#137	C₂	semidirect
54. #61319	C₅	direct (N × H)
126. C₂×Q₈²	C₂×C₅	semidirect
127. #3375	C₂×C₅	semidirect
128. #3369	C₂×C₅	semidirect
129. #3363	C₂×C₅	semidirect
130. #3362	C₂×C₅	semidirect
131. #3141	C₂×C₅	semidirect
132. #3079	C₂×C₅	semidirect
133. #3037	C₂×C₅	semidirect
134. Q₈×M₁₆	C₂×C₅	semidirect
135. C₄×#137	C₂×C₅	semidirect
147. C₂×C₅×Q₈	#41	semidirect
248. C₅×Q₈	#137	semidirect
377. C₂×Q₈	C₅×#41	semidirect
441. Q₈	C₅×#137	semidirect
470. C₅	#61319	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×#3480	2
C₂×C₅×Q₈²	2
C₅×#3375	2
C₅×#3369	2
C₅×#3363	2
C₅×#3362	2
C₅×#3141	2
C₅×#3079	2
C₅×#3037	2
C₅×Q₈×M₁₆	2
C₄×C₅×#137	2
#61319	5

Subgroups — C5×#61319 #11984039

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#61319 #11984039