Subgroups — C₅×#17681 #11940401

Order 1280.

940 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3514	C₂	1	1	yes	maximal, characteristic
2	C₅×#2971	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2923	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1535	C₂	1	2	yes	maximal, complemented
5	C₅×#1533	C₂	1	2	yes	maximal, complemented
6	C₅×#1530	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1529	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1529	C₂	1	2	yes	maximal, complemented
9	C₅×#1527	C₂	1	2	yes	maximal, complemented
10	C₅×#1525	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1524	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#559	C₄	1	1	yes	characteristic
13	C₅×#556	C₄	1	1	yes	characteristic
14	C₅×#555	—	2	1	no	—
15	C₅×#551	—	2	2	no	—
16	C₅×D₄×Q₈	C₄	1	1	yes	characteristic
17	C₅×#548	C₄	1	2	yes	—
18	C₅×#546	—	2	1	no	—
19	C₅×#546	C₄	1	2	yes	—
20	C₅×D₄²	C₄	1	1	yes	characteristic
21	C₅×#542	—	2	1	no	—
22	C₅×#538	—	2	2	no	—
23	C₅×#532	C₂²	1	1	yes	characteristic
24	C₅×#529	C₂²	1	1	yes	characteristic
25	C₅×#529	C₂²	1	2	yes	—
26	C₂×C₅×#124	C₂²	1	2	yes	—
27	C₅×#518	—	2	1	no	—
28	C₄×C₅×#41	C₂²	1	1	yes	characteristic
29	C₅×C₈×Q₈	—	2	1	no	—
30	C₅×#436	—	2	1	no	—
31	C₅×#436	—	2	2	no	—
32	C₅×#433	—	2	2	no	—
33	C₅×#432	C₂²	1	2	yes	complemented
34	C₅×#432	C₂²	1	1	yes	characteristic, complemented
35	C₅×#432	C₂²	1	2	yes	complemented
36	C₅×#432	C₂²	1	2	yes	complemented
37	C₅×#424	—	2	1	no	—
38	C₅×#408	—	2	1	no	—
39	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic, complemented
40	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic, complemented
41	C₄×C₅×M₁₆	C₂²	1	2	yes	complemented
42	C₂×C₅×#97	C₂²	1	1	yes	characteristic, complemented
43	C₅×#330	C₂²	1	1	yes	characteristic, complemented
44	C₅×#330	C₂²	1	1	yes	characteristic, complemented
45	C₅×#330	C₂²	1	2	yes	complemented
46	C₅×#329	C₂²	1	1	yes	characteristic
47	C₅×#329	C₂²	1	1	yes	characteristic
48	C₅×#329	C₂²	1	2	yes	—
49	C₅×#329	C₂²	1	2	yes	complemented
50	C₅×#329	C₂²	1	2	yes	complemented
51	C₅×#329	C₂²	1	2	yes	complemented
52	C₅×#329	C₂²	1	2	yes	complemented
53	#17681	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
54	C₂×C₅×#41	C₂×C₄	1	2	yes	—
55	C₂×C₅×#41	D₄	1	1	yes	characteristic
56	C₂²×C₅×Q₈	C₂×C₄	1	2	yes	—
57	C₂²×C₅×D₄	—	2	1	no	—
58	C₂²×C₅×D₄	C₂×C₄	1	2	yes	—
59	C₂×C₅×M₁₆	—	2	1	no	—
60	C₂×C₅×M₁₆	—	2	2	no	—
61	C₂×C₅×M₁₆	—	2	1	no	—
62	C₂²×C₅×C₈	—	2	1	no	—
63	C₅×C₄⋊Q₈	—	2	1	no	—
64	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
65	C₅×#127	C₂×C₄	1	1	yes	characteristic
66	C₅×#126	—	2	2	no	—
67	C₅×#126	—	2	2	no	—
68	C₅×#126	—	2	1	no	—
69	C₅×#125	C₂³	1	1	yes	characteristic
70	C₅×#124	—	2	1	no	—
71	C₅×#124	—	2	2	no	—
72	C₅×#124	—	2	2	no	—
73	C₅×#124	—	2	2	no	—
74	C₅×#124	C₂×C₄	1	2	yes	—
75	C₅×#124	C₂×C₄	1	2	yes	—
76	C₅×#124	C₂³	1	1	yes	characteristic
77	C₅×#124	C₂³	1	2	yes	—
78	C₅×#123	—	2	1	no	—
79	C₅×#123	—	2	2	no	—
80	C₅×#123	—	2	2	no	—
81	C₅×#123	—	2	2	no	—
82	C₅×C₂²⋊Q₈	—	2	1	no	—
83	C₅×C₂²⋊Q₈	—	2	2	no	—
84	C₅×C₂²⋊Q₈	—	2	2	no	—
85	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
86	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
87	C₅×#121	—	2	2	no	—
88	C₅×#121	—	2	1	no	—
89	C₅×#121	—	2	1	no	—
90	C₅×#121	—	2	1	no	—
91	C₅×#121	—	2	2	no	—
92	C₅×#121	C₂×C₄	1	2	yes	—
93	C₅×#121	C₂×C₄	1	1	yes	characteristic
94	C₅×#120	—	2	2	no	—
95	C₅×#120	—	2	2	no	—
96	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
97	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
98	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
99	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
100	C₄×C₅×D₄	—	2	1	no	—
101	C₄×C₅×D₄	—	2	2	no	—
102	C₄×C₅×D₄	—	2	1	no	—
103	C₄×C₅×D₄	—	2	1	no	—
104	C₄×C₅×D₄	—	2	2	no	—
105	C₄×C₅×D₄	—	2	1	no	—
106	C₄×C₅×D₄	—	2	1	no	—
107	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
108	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
109	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
110	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
111	C₄×C₅×D₄	D₄	1	1	yes	characteristic
112	C₄×C₅×D₄	D₄	1	2	yes	—
113	C₅×#117	—	2	1	no	—
114	C₅×#117	—	2	1	no	—
115	C₅×#117	—	2	2	no	—
116	C₅×#117	D₄	1	1	yes	characteristic
117	C₅×#117	D₄	1	2	yes	—
118	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
119	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
120	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
121	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₅	C₂³	1	2	yes	—
123	C₅×C₄⋊C₈	—	2	2	no	—
124	C₅×C₄⋊C₈	—	2	2	no	—
125	C₅×C₄⋊C₈	—	2	1	no	—
126	C₅×C₄⋊C₈	—	2	2	no	—
127	C₅×C₂²⋊C₈	—	2	2	no	—
128	C₅×C₂²⋊C₈	—	2	2	no	—
129	C₅×C₂²⋊C₈	—	2	2	no	—
130	C₅×C₂²⋊C₈	—	2	1	no	—
131	C₅×#97	—	2	1	no	—
132	C₅×#97	C₂³	1	1	yes	characteristic
133	C₅×#97	C₂³	1	1	yes	characteristic
134	C₅×#97	C₂³	1	1	yes	characteristic
135	C₅×#97	C₂³	1	1	yes	characteristic
136	C₅×#97	C₂³	1	2	yes	—
137	C₅×#97	C₂³	1	2	yes	—
138	C₄×C₅×C₈	—	2	1	no	—
139	C₄×C₅×C₈	—	2	1	no	—
140	C₄×C₅×C₈	—	2	2	no	—
141	#3514	C₂×C₅	1	1	yes	characteristic
142	#2971	C₂×C₅	1	1	yes	characteristic, complemented
143	#2923	C₂×C₅	1	1	yes	characteristic, complemented
144	#1535	C₂×C₅	1	2	yes	complemented
145	#1533	C₂×C₅	1	2	yes	complemented
146	#1530	C₂×C₅	1	1	yes	characteristic, complemented
147	#1529	C₂×C₅	1	1	yes	characteristic, complemented
148	#1529	C₂×C₅	1	2	yes	complemented
149	#1527	C₂×C₅	1	2	yes	complemented
150	#1525	C₂×C₅	1	1	yes	characteristic, complemented
151	#1524	C₂×C₅	1	1	yes	characteristic, complemented
152	C₂⁴×C₅	—	2	2	no	—
153	C₅×#41	—	4	2	no	—
154	C₅×#41	—	8	2	no	—
155	C₂×C₅×Q₈	—	2	2	no	—
156	C₂×C₅×Q₈	—	8	2	no	—
157	C₂×C₅×Q₈	C₂²⋊C₄	1	1	yes	characteristic
158	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
160	C₂×C₅×D₄	—	2	2	no	—
161	C₂×C₅×D₄	—	2	1	no	—
162	C₂×C₅×D₄	—	2	2	no	—
163	C₂×C₅×D₄	—	2	1	no	—
164	C₂×C₅×D₄	—	2	1	no	—
165	C₂×C₅×D₄	—	2	2	no	—
166	C₂×C₅×D₄	—	4	4	no	—
167	C₂×C₅×D₄	—	8	2	no	—
168	C₂×C₅×D₄	C₂²⋊C₄	1	1	yes	characteristic
169	C₂×C₅×D₄	C₂²⋊C₄	1	2	yes	—
170	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
172	C₂²×C₄×C₅	—	2	2	no	—
173	C₂²×C₄×C₅	—	2	1	no	—
174	C₂²×C₄×C₅	—	2	2	no	—
175	C₂²×C₄×C₅	—	2	2	no	—
176	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
177	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
178	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
180	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
181	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
182	C₅×M₁₆	—	4	4	no	—
183	C₅×M₁₆	—	4	2	no	—
184	C₅×M₁₆	—	4	2	no	—
185	C₂×C₅×C₈	—	2	1	no	—
186	C₂×C₅×C₈	—	2	1	no	—
187	C₂×C₅×C₈	—	2	1	no	—
188	C₂×C₅×C₈	—	2	2	no	—
189	C₂×C₅×C₈	—	2	2	no	—
190	C₂×C₅×C₈	—	2	1	no	—
191	C₂×C₅×C₈	—	4	2	no	—
192	C₅×C₄⋊C₄	—	2	1	no	—
193	C₅×C₄⋊C₄	—	2	1	no	—
194	C₅×C₄⋊C₄	—	2	2	no	—
195	C₅×C₄⋊C₄	—	2	1	no	—
196	C₅×C₄⋊C₄	—	2	2	no	—
197	C₅×C₄⋊C₄	—	2	1	no	—
198	C₅×C₄⋊C₄	—	2	1	no	—
199	C₅×C₄⋊C₄	—	2	1	no	—
200	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
201	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
202	C₅×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
203	C₅×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
204	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
205	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
206	C₅×C₂²⋊C₄	—	2	2	no	—
207	C₅×C₂²⋊C₄	—	2	1	no	—
208	C₅×C₂²⋊C₄	—	2	2	no	—
209	C₅×C₂²⋊C₄	—	2	1	no	—
210	C₅×C₂²⋊C₄	—	2	2	no	—
211	C₅×C₂²⋊C₄	—	2	2	no	—
212	C₅×C₂²⋊C₄	—	2	2	no	—
213	C₅×C₂²⋊C₄	—	2	2	no	—
214	C₅×C₂²⋊C₄	—	2	1	no	—
215	C₅×C₂²⋊C₄	—	2	2	no	—
216	C₅×C₂²⋊C₄	—	2	1	no	—
217	C₅×C₂²⋊C₄	—	2	1	no	—
218	C₅×C₂²⋊C₄	—	2	2	no	—
219	C₅×C₂²⋊C₄	—	2	2	no	—
220	C₅×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
221	C₅×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
222	C₅×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
223	C₄²×C₅	—	2	2	no	—
224	C₄²×C₅	—	2	1	no	—
225	C₄²×C₅	C₂²×C₄	1	2	yes	—
226	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
227	C₄²×C₅	C₂×D₄	1	2	yes	—
228	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
229	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
230	C₄²×C₅	C₂×D₄	1	2	yes	—
231	C₄²×C₅	C₂⁴	1	1	yes	characteristic
232	#559	C₄×C₅	1	1	yes	characteristic
233	#556	C₄×C₅	1	1	yes	characteristic
234	#555	—	2	1	no	—
235	#551	—	2	2	no	—
236	D₄×Q₈	C₄×C₅	1	1	yes	characteristic
237	#548	C₄×C₅	1	2	yes	—
238	#546	—	2	1	no	—
239	#546	C₄×C₅	1	2	yes	—
240	D₄²	C₄×C₅	1	1	yes	characteristic
241	#542	—	2	1	no	—
242	#538	—	2	2	no	—
243	#532	C₂²×C₅	1	1	yes	characteristic
244	#529	C₂²×C₅	1	1	yes	characteristic
245	#529	C₂²×C₅	1	2	yes	—
246	C₂×#124	C₂²×C₅	1	2	yes	—
247	#518	—	2	1	no	—
248	C₄×#41	C₂²×C₅	1	1	yes	characteristic
249	C₈×Q₈	—	2	1	no	—
250	#436	—	2	1	no	—
251	#436	—	2	2	no	—
252	#433	—	2	2	no	—
253	#432	C₂²×C₅	1	2	yes	complemented
254	#432	C₂²×C₅	1	2	yes	complemented
255	#432	C₂²×C₅	1	1	yes	characteristic, complemented
256	#432	C₂²×C₅	1	2	yes	complemented
257	#424	—	2	1	no	—
258	#408	—	2	1	no	—
259	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
260	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
261	C₄×M₁₆	C₂²×C₅	1	2	yes	complemented
262	C₂×#97	C₂²×C₅	1	1	yes	characteristic, complemented
263	#330	C₂²×C₅	1	1	yes	characteristic, complemented
264	#330	C₂²×C₅	1	1	yes	characteristic, complemented
265	#330	C₂²×C₅	1	2	yes	complemented
266	#329	C₂²×C₅	1	1	yes	characteristic
267	#329	C₂²×C₅	1	1	yes	characteristic
268	#329	C₂²×C₅	1	2	yes	—
269	#329	C₂²×C₅	1	2	yes	complemented
270	#329	C₂²×C₅	1	2	yes	complemented
271	#329	C₂²×C₅	1	2	yes	complemented
272	#329	C₂²×C₅	1	2	yes	complemented
273	C₂³×C₅	—	2	1	no	—
274	C₂³×C₅	—	2	2	no	—
275	C₂³×C₅	—	4	4	no	—
276	C₂³×C₅	—	8	2	no	—
277	C₂³×C₅	—	8	2	no	—
278	C₂³×C₅	C₂×C₂²⋊C₄	1	2	yes	—
279	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
280	C₅×Q₈	—	2	2	no	—
281	C₅×Q₈	—	4	1	no	—
282	C₅×Q₈	—	4	2	no	—
283	C₅×Q₈	—	8	2	no	—
284	C₅×D₄	—	2	2	no	—
285	C₅×D₄	—	4	2	no	—
286	C₅×D₄	—	4	1	no	—
287	C₅×D₄	—	4	2	no	—
288	C₅×D₄	—	4	4	no	—
289	C₅×D₄	—	4	2	no	—
290	C₅×D₄	—	8	1	no	—
291	C₅×D₄	—	8	2	no	—
292	C₅×D₄	—	8	1	no	—
293	C₅×D₄	—	8	2	no	—
294	C₂×C₄×C₅	—	2	2	no	—
295	C₂×C₄×C₅	—	2	1	no	—
296	C₂×C₄×C₅	—	2	1	no	—
297	C₂×C₄×C₅	—	2	1	no	—
298	C₂×C₄×C₅	—	2	2	no	—
299	C₂×C₄×C₅	—	4	2	no	—
300	C₂×C₄×C₅	—	4	1	no	—
301	C₂×C₄×C₅	—	4	2	no	—
302	C₂×C₄×C₅	—	4	1	no	—
303	C₂×C₄×C₅	—	4	2	no	—
304	C₂×C₄×C₅	—	4	2	no	—
305	C₂×C₄×C₅	—	8	2	no	—
306	C₂×C₄×C₅	—	8	2	no	—
307	C₂×C₄×C₅	—	8	2	no	—
308	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
309	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
310	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
311	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
312	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
313	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
314	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
315	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
316	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
317	C₅×C₈	—	2	2	no	—
318	C₅×C₈	—	4	1	no	—
319	C₅×C₈	—	4	1	no	—
320	C₅×C₈	—	4	2	no	—
321	C₅×C₈	—	4	2	no	—
322	C₅×C₈	—	4	1	no	—
323	C₂×#41	C₂×C₄×C₅	1	2	yes	—
324	C₂×#41	C₅×D₄	1	1	yes	characteristic
325	C₂²×Q₈	C₂×C₄×C₅	1	2	yes	—
326	C₂²×D₄	—	2	1	no	—
327	C₂²×D₄	C₂×C₄×C₅	1	2	yes	—
328	C₂×M₁₆	—	2	1	no	—
329	C₂×M₁₆	—	2	2	no	—
330	C₂×M₁₆	—	2	1	no	—
331	C₂²×C₈	—	2	1	no	—
332	C₄⋊Q₈	—	2	1	no	—
333	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
334	#127	C₂×C₄×C₅	1	1	yes	characteristic
335	#126	—	2	2	no	—
336	#126	—	2	2	no	—
337	#126	—	2	1	no	—
338	#125	C₂³×C₅	1	1	yes	characteristic
339	#124	—	2	1	no	—
340	#124	—	2	2	no	—
341	#124	—	2	2	no	—
342	#124	—	2	2	no	—
343	#124	C₂×C₄×C₅	1	2	yes	—
344	#124	C₂×C₄×C₅	1	2	yes	—
345	#124	C₂³×C₅	1	1	yes	characteristic
346	#124	C₂³×C₅	1	2	yes	—
347	#123	—	2	1	no	—
348	#123	—	2	2	no	—
349	#123	—	2	2	no	—
350	#123	—	2	2	no	—
351	C₂²⋊Q₈	—	2	1	no	—
352	C₂²⋊Q₈	—	2	2	no	—
353	C₂²⋊Q₈	—	2	2	no	—
354	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
355	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
356	#121	—	2	2	no	—
357	#121	—	2	1	no	—
358	#121	—	2	1	no	—
359	#121	—	2	1	no	—
360	#121	—	2	2	no	—
361	#121	C₂×C₄×C₅	1	2	yes	—
362	#121	C₂×C₄×C₅	1	1	yes	characteristic
363	#120	—	2	2	no	—
364	#120	—	2	2	no	—
365	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
366	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
367	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
368	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
369	C₄×D₄	—	2	1	no	—
370	C₄×D₄	—	2	2	no	—
371	C₄×D₄	—	2	1	no	—
372	C₄×D₄	—	2	1	no	—
373	C₄×D₄	—	2	2	no	—
374	C₄×D₄	—	2	1	no	—
375	C₄×D₄	—	2	1	no	—
376	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
377	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
378	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
379	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
380	C₄×D₄	C₅×D₄	1	1	yes	characteristic
381	C₄×D₄	C₅×D₄	1	2	yes	—
382	#117	—	2	1	no	—
383	#117	—	2	1	no	—
384	#117	—	2	2	no	—
385	#117	C₅×D₄	1	2	yes	—
386	#117	C₅×D₄	1	1	yes	characteristic
387	C₂×C₂²⋊C₄	—	2	2	no	—
388	C₂×C₂²⋊C₄	—	2	2	no	—
389	C₂×C₂²⋊C₄	—	2	2	no	—
390	C₂×C₄²	C₂³×C₅	1	2	yes	—
391	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
392	C₄⋊C₈	—	2	2	no	—
393	C₄⋊C₈	—	2	2	no	—
394	C₄⋊C₈	—	2	1	no	—
395	C₄⋊C₈	—	2	2	no	—
396	C₂²⋊C₈	—	2	2	no	—
397	C₂²⋊C₈	—	2	2	no	—
398	C₂²⋊C₈	—	2	2	no	—
399	C₂²⋊C₈	—	2	1	no	—
400	#97	—	2	1	no	—
401	#97	C₂³×C₅	1	1	yes	characteristic
402	#97	C₂³×C₅	1	1	yes	characteristic
403	#97	C₂³×C₅	1	1	yes	characteristic
404	#97	C₂³×C₅	1	1	yes	characteristic
405	#97	C₂³×C₅	1	2	yes	—
406	#97	C₂³×C₅	1	2	yes	—
407	C₄×C₈	—	2	1	no	—
408	C₄×C₈	—	2	1	no	—
409	C₄×C₈	—	2	2	no	—
410	C₂²×C₅	—	2	2	no	—
411	C₂²×C₅	—	2	1	no	—
412	C₂²×C₅	—	2	1	no	—
413	C₂²×C₅	—	2	2	no	—
414	C₂²×C₅	—	2	1	no	—
415	C₂²×C₅	—	2	2	no	—
416	C₂²×C₅	—	4	2	no	—
417	C₂²×C₅	—	4	1	no	—
418	C₂²×C₅	—	4	1	no	—
419	C₂²×C₅	—	4	2	no	—
420	C₂²×C₅	—	4	2	no	—
421	C₂²×C₅	—	4	1	no	—
422	C₂²×C₅	—	16	4	no	—
423	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
424	C₄×C₅	—	2	1	no	—
425	C₄×C₅	—	2	1	no	—
426	C₄×C₅	—	2	2	no	—
427	C₄×C₅	—	2	1	no	—
428	C₄×C₅	—	2	2	no	—
429	C₄×C₅	—	2	1	no	—
430	C₄×C₅	—	2	2	no	—
431	C₄×C₅	—	2	1	no	—
432	C₄×C₅	—	4	2	no	—
433	C₄×C₅	—	4	1	no	—
434	C₄×C₅	—	4	1	no	—
435	C₄×C₅	—	4	1	no	—
436	C₄×C₅	#421	1	2	yes	—
437	C₂⁴	—	2	2	no	—
438	#41	—	4	2	no	—
439	#41	—	8	2	no	—
440	C₂×Q₈	—	2	2	no	—
441	C₂×Q₈	—	8	2	no	—
442	C₂×Q₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
443	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
444	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
445	C₂×D₄	—	2	2	no	—
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	2	2	no	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	2	no	—
451	C₂×D₄	—	4	4	no	—
452	C₂×D₄	—	8	2	no	—
453	C₂×D₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
454	C₂×D₄	C₅×C₂²⋊C₄	1	2	yes	—
455	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
456	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
457	C₂²×C₄	—	2	2	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
462	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
463	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
464	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
465	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
466	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
467	M₁₆	—	4	4	no	—
468	M₁₆	—	4	2	no	—
469	M₁₆	—	4	2	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	2	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	4	2	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	2	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
486	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
487	C₄⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
488	C₄⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
489	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
490	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
491	C₂²⋊C₄	—	2	2	no	—
492	C₂²⋊C₄	—	2	1	no	—
493	C₂²⋊C₄	—	2	2	no	—
494	C₂²⋊C₄	—	2	1	no	—
495	C₂²⋊C₄	—	2	2	no	—
496	C₂²⋊C₄	—	2	2	no	—
497	C₂²⋊C₄	—	2	2	no	—
498	C₂²⋊C₄	—	2	2	no	—
499	C₂²⋊C₄	—	2	1	no	—
500	C₂²⋊C₄	—	2	2	no	—
501	C₂²⋊C₄	—	2	1	no	—
502	C₂²⋊C₄	—	2	1	no	—
503	C₂²⋊C₄	—	2	2	no	—
504	C₂²⋊C₄	—	2	2	no	—
505	C₂²⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
506	C₂²⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
507	C₂²⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
508	C₄²	—	2	2	no	—
509	C₄²	—	2	1	no	—
510	C₄²	C₂²×C₄×C₅	1	2	yes	—
511	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
512	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
513	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
514	C₄²	C₂×C₅×D₄	1	2	yes	—
515	C₄²	C₂×C₅×D₄	1	2	yes	—
516	C₄²	C₂⁴×C₅	1	1	yes	characteristic
517	C₂×C₅	—	4	1	no	—
518	C₂×C₅	—	4	2	no	—
519	C₂×C₅	—	8	2	no	—
520	C₂×C₅	—	8	1	no	—
521	C₂×C₅	#2888	1	1	yes	characteristic
522	C₂×C₅	C₂×#421	1	1	yes	characteristic
523	C₂×C₅	#2901	1	1	yes	characteristic
524	C₂³	—	2	1	no	—
525	C₂³	—	2	2	no	—
526	C₂³	—	4	4	no	—
527	C₂³	—	8	2	no	—
528	C₂³	—	8	2	no	—
529	C₂³	C₂×C₅×C₂²⋊C₄	1	2	yes	—
530	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
531	Q₈	—	2	2	no	—
532	Q₈	—	4	1	no	—
533	Q₈	—	4	2	no	—
534	Q₈	—	8	2	no	—
535	D₄	—	2	2	no	—
536	D₄	—	4	2	no	—
537	D₄	—	4	1	no	—
538	D₄	—	4	2	no	—
539	D₄	—	4	4	no	—
540	D₄	—	4	2	no	—
541	D₄	—	8	2	no	—
542	D₄	—	8	1	no	—
543	D₄	—	8	2	no	—
544	D₄	—	8	1	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	4	2	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	8	2	no	—
557	C₂×C₄	—	8	2	no	—
558	C₂×C₄	—	8	2	no	—
559	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
560	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
561	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
562	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
563	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
564	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
565	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
566	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
567	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
568	C₈	—	2	2	no	—
569	C₈	—	4	1	no	—
570	C₈	—	4	1	no	—
571	C₈	—	4	2	no	—
572	C₈	—	4	1	no	—
573	C₈	—	4	2	no	—
574	C₅	#17681	1	1	yes	characteristic, direct product factor, Sylow
575	C₂²	—	2	2	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	2	2	no	—
581	C₂²	—	4	2	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	2	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	16	4	no	—
588	C₂²	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	2	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	2	no	—
594	C₄	—	2	1	no	—
595	C₄	—	2	2	no	—
596	C₄	—	2	1	no	—
597	C₄	—	4	2	no	—
598	C₄	—	4	1	no	—
599	C₄	—	4	1	no	—
600	C₄	—	4	1	no	—
601	C₄	C₅×#421	1	2	yes	—
602	C₂	—	4	2	no	—
603	C₂	—	4	1	no	—
604	C₂	—	8	1	no	—
605	C₂	—	8	2	no	—
606	C₂	C₅×#2888	1	1	yes	characteristic
607	C₂	C₂×C₅×#421	1	1	yes	characteristic
608	C₂	C₅×#2901	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₅×#3514	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₄×C₅×#41 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2971	C₂	semidirect
3. C₅×#2923	C₂	semidirect
4. C₅×#1535	C₂	semidirect
5. C₅×#1533	C₂	semidirect
6. C₅×#1530	C₂	semidirect
7. C₅×#1529	C₂	semidirect
8. C₅×#1529	C₂	semidirect
9. C₅×#1527	C₂	semidirect
10. C₅×#1525	C₂	semidirect
11. C₅×#1524	C₂	semidirect
33. C₅×#432	C₂²	semidirect
34. C₅×#432	C₂²	semidirect
35. C₅×#432	C₂²	semidirect
36. C₅×#432	C₂²	semidirect
39. C₄×C₅×M₁₆	C₂²	semidirect
40. C₄×C₅×M₁₆	C₂²	semidirect
41. C₄×C₅×M₁₆	C₂²	semidirect
42. C₂×C₅×#97	C₂²	semidirect
43. C₅×#330	C₂²	semidirect
44. C₅×#330	C₂²	semidirect
45. C₅×#330	C₂²	semidirect
49. C₅×#329	C₂²	semidirect
50. C₅×#329	C₂²	semidirect
51. C₅×#329	C₂²	semidirect
52. C₅×#329	C₂²	semidirect
53. #17681	C₅	direct (N × H)
142. #2971	C₂×C₅	semidirect
143. #2923	C₂×C₅	semidirect
144. #1535	C₂×C₅	semidirect
145. #1533	C₂×C₅	semidirect
146. #1530	C₂×C₅	semidirect
147. #1529	C₂×C₅	semidirect
148. #1529	C₂×C₅	semidirect
149. #1527	C₂×C₅	semidirect
150. #1525	C₂×C₅	semidirect
151. #1524	C₂×C₅	semidirect
253. #432	C₂²×C₅	semidirect
254. #432	C₂²×C₅	semidirect
255. #432	C₂²×C₅	semidirect
256. #432	C₂²×C₅	semidirect
259. C₄×M₁₆	C₂²×C₅	semidirect
260. C₄×M₁₆	C₂²×C₅	semidirect
261. C₄×M₁₆	C₂²×C₅	semidirect
262. C₂×#97	C₂²×C₅	semidirect
263. #330	C₂²×C₅	semidirect
264. #330	C₂²×C₅	semidirect
265. #330	C₂²×C₅	semidirect
269. #329	C₂²×C₅	semidirect
270. #329	C₂²×C₅	semidirect
271. #329	C₂²×C₅	semidirect
272. #329	C₂²×C₅	semidirect
574. C₅	#17681	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×#3514	2
C₅×#2971	2
C₅×#2923	2
C₅×#1535	2
C₅×#1533	2
C₅×#1530	2
C₅×#1529	2
C₅×#1527	2
C₅×#1525	2
C₅×#1524	2
#17681	5

Subgroups — C5×#17681 #11940401

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17681 #11940401