Subgroups — C₅×#26193 #11948913

Order 1280.

734 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3097	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3046	C₂	1	1	yes	maximal, characteristic
3	C₅×#2952	C₂	1	1	yes	maximal, characteristic
4	C₅×#2913	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2097	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2090	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2078	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2038	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1930	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1922	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1908	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1882	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1876	C₂	1	1	yes	maximal, characteristic
14	C₅×#1860	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1860	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#137	C₂²	1	1	yes	characteristic
17	C₂×C₅×#135	C₂²	1	1	yes	characteristic
18	C₂×C₅×#131	C₂²	1	1	yes	characteristic
19	C₅×#536	C₂²	1	1	yes	characteristic
20	C₅×#520	C₂²	1	1	yes	characteristic
21	C₅×#520	C₂²	1	1	yes	characteristic
22	C₅×#520	C₂²	1	1	yes	characteristic
23	C₅×#485	—	2	1	no	—
24	C₅×#485	—	2	1	no	—
25	C₅×#484	—	2	1	no	—
26	C₅×#483	—	2	1	no	—
27	C₅×#464	—	2	1	no	—
28	C₅×#463	—	2	1	no	—
29	C₅×#462	—	2	1	no	—
30	C₅×#461	—	2	1	no	—
31	C₅×#442	—	2	1	no	—
32	C₅×#441	—	2	1	no	—
33	C₄×C₅×SD₁₆	—	2	1	no	—
34	C₄×C₅×SD₁₆	—	2	1	no	—
35	C₅×#428	—	2	1	no	—
36	C₅×#428	—	2	1	no	—
37	C₅×#428	C₂²	1	1	yes	characteristic
38	C₅×#428	C₂²	1	1	yes	characteristic
39	C₅×#428	C₂²	1	1	yes	characteristic
40	C₅×#427	—	2	1	no	—
41	C₅×#427	C₂²	1	1	yes	characteristic
42	C₂×C₅×#107	—	2	1	no	—
43	C₂×C₅×#107	C₂²	1	1	yes	characteristic
44	C₂×C₅×#106	C₂²	1	1	yes	characteristic
45	C₅×#424	C₂²	1	1	yes	characteristic
46	C₂×C₅×#104	C₂²	1	1	yes	characteristic
47	C₂×C₅×#104	C₂²	1	1	yes	characteristic
48	C₅×#419	C₂²	1	1	yes	characteristic
49	C₅×#417	C₂²	1	1	yes	characteristic
50	C₅×#417	C₂²	1	1	yes	characteristic
51	C₅×#417	C₂²	1	1	yes	characteristic
52	C₂×C₅×#103	C₂²	1	1	yes	characteristic
53	C₂×C₅×#103	C₂²	1	1	yes	characteristic
54	C₂×C₅×#101	C₂²	1	1	yes	characteristic
55	C₅×#408	C₂²	1	1	yes	characteristic
56	C₅×#405	C₂²	1	1	yes	characteristic
57	C₅×#391	C₂²	1	1	yes	characteristic
58	C₅×#382	C₂²	1	1	yes	characteristic
59	C₅×#343	C₂²	1	1	yes	characteristic
60	C₅×#343	C₂²	1	1	yes	characteristic
61	C₅×#343	C₂²	1	1	yes	characteristic
62	C₅×#341	C₂²	1	1	yes	characteristic
63	C₅×#341	C₂²	1	1	yes	characteristic
64	C₅×#339	C₂²	1	1	yes	characteristic
65	C₅×#339	C₂²	1	1	yes	characteristic
66	C₅×#336	C₂²	1	1	yes	characteristic
67	#26193	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂×C₅×#41	C₂³	1	1	yes	characteristic
69	C₂×C₅×#41	C₂³	1	1	yes	characteristic
70	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
71	C₅×#137	—	2	2	no	—
72	C₅×#137	—	2	2	no	—
73	C₅×#135	—	2	2	no	—
74	C₅×#135	—	2	2	no	—
75	C₂×C₅×Q₁₆	—	2	1	no	—
76	C₂×C₅×Q₁₆	D₄	1	1	yes	characteristic
77	C₂×C₅×SD₁₆	—	2	1	no	—
78	C₂×C₅×SD₁₆	D₄	1	1	yes	characteristic
79	C₂×C₅×SD₁₆	D₄	1	1	yes	characteristic
80	C₂×C₅×D₈	D₄	1	1	yes	characteristic
81	C₅×#131	—	2	2	no	—
82	C₅×#131	—	2	2	no	—
83	C₂×C₅×M₁₆	—	2	1	no	—
84	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
85	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
86	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
87	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
88	C₂²×C₅×C₈	—	2	1	no	—
89	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
90	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
91	C₅×C₄⋊Q₈	—	2	1	no	—
92	C₅×#124	—	2	1	no	—
93	C₅×#123	—	4	1	no	—
94	C₅×C₂²⋊Q₈	—	2	1	no	—
95	C₅×C₂²⋊Q₈	—	2	1	no	—
96	C₄×C₅×Q₈	—	2	1	no	—
97	C₄×C₅×Q₈	—	2	1	no	—
98	C₄×C₅×Q₈	—	2	1	no	—
99	C₄×C₅×D₄	—	2	1	no	—
100	C₄×C₅×D₄	—	2	1	no	—
101	C₄×C₅×D₄	—	2	1	no	—
102	C₄×C₅×D₄	—	4	1	no	—
103	C₄×C₅×D₄	—	4	1	no	—
104	C₄×C₅×D₄	—	4	1	no	—
105	C₅×#117	—	2	1	no	—
106	C₅×#117	—	2	1	no	—
107	C₅×#117	—	2	1	no	—
108	C₅×#117	C₂³	1	1	yes	characteristic
109	C₅×#117	C₂³	1	1	yes	characteristic
110	C₂×C₅×C₄⋊C₄	—	2	1	no	—
111	C₂×C₅×C₄⋊C₄	—	2	1	no	—
112	C₂×C₅×C₄⋊C₄	—	2	1	no	—
113	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
114	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
115	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
117	C₅×#107	—	2	1	no	—
118	C₅×#107	—	2	1	no	—
119	C₅×#107	—	2	1	no	—
120	C₅×#107	—	2	1	no	—
121	C₅×#107	—	2	1	no	—
122	C₅×#107	D₄	1	1	yes	characteristic
123	C₅×#107	D₄	1	1	yes	characteristic
124	C₅×#106	—	2	1	no	—
125	C₅×#106	—	2	1	no	—
126	C₅×#106	—	2	1	no	—
127	C₅×#106	—	2	1	no	—
128	C₅×#106	—	2	1	no	—
129	C₅×#106	D₄	1	1	yes	characteristic
130	C₅×#106	D₄	1	1	yes	characteristic
131	C₅×C₄⋊C₈	—	2	1	no	—
132	C₅×C₄⋊C₈	—	2	1	no	—
133	C₅×#104	—	2	2	no	—
134	C₅×#104	—	2	2	no	—
135	C₅×#103	—	2	1	no	—
136	C₅×#103	—	2	1	no	—
137	C₅×#103	—	2	1	no	—
138	C₅×#103	—	2	1	no	—
139	C₅×#103	—	2	1	no	—
140	C₅×#103	—	2	1	no	—
141	C₅×#103	—	2	1	no	—
142	C₅×#103	—	2	1	no	—
143	C₅×#103	—	2	1	no	—
144	C₅×#102	—	2	1	no	—
145	C₅×#102	—	2	1	no	—
146	C₅×#102	—	2	1	no	—
147	C₅×#101	—	2	2	no	—
148	C₅×C₂²⋊C₈	—	2	1	no	—
149	C₅×C₂²⋊C₈	—	2	1	no	—
150	C₅×#97	—	2	1	no	—
151	C₄×C₅×C₈	—	2	1	no	—
152	C₅×#95	—	4	1	no	—
153	C₅×#95	—	4	1	no	—
154	#3097	C₂×C₅	1	1	yes	characteristic, complemented
155	#3046	C₂×C₅	1	1	yes	characteristic
156	#2952	C₂×C₅	1	1	yes	characteristic
157	#2913	C₂×C₅	1	1	yes	characteristic, complemented
158	#2097	C₂×C₅	1	1	yes	characteristic, complemented
159	#2090	C₂×C₅	1	1	yes	characteristic, complemented
160	#2078	C₂×C₅	1	1	yes	characteristic, complemented
161	#2038	C₂×C₅	1	1	yes	characteristic, complemented
162	#1930	C₂×C₅	1	1	yes	characteristic, complemented
163	#1922	C₂×C₅	1	1	yes	characteristic, complemented
164	#1908	C₂×C₅	1	1	yes	characteristic, complemented
165	#1882	C₂×C₅	1	1	yes	characteristic, complemented
166	#1876	C₂×C₅	1	1	yes	characteristic
167	#1860	C₂×C₅	1	1	yes	characteristic, complemented
168	#1860	C₂×C₅	1	1	yes	characteristic, complemented
169	C₅×#41	—	2	1	no	—
170	C₅×#41	—	2	1	no	—
171	C₅×#41	—	2	1	no	—
172	C₅×#41	—	2	1	no	—
173	C₅×#41	—	2	1	no	—
174	C₅×#41	—	2	1	no	—
175	C₅×#41	#41	1	2	yes	—
176	C₅×#41	#41	1	2	yes	—
177	C₂×C₅×Q₈	—	2	1	no	—
178	C₂×C₅×Q₈	—	2	1	no	—
179	C₂×C₅×Q₈	—	2	1	no	—
180	C₂×C₅×Q₈	—	2	1	no	—
181	C₂×C₅×Q₈	—	2	1	no	—
182	C₂×C₅×Q₈	—	2	1	no	—
183	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
184	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
185	C₂×C₅×D₄	—	2	1	no	—
186	C₂×C₅×D₄	—	2	1	no	—
187	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
188	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₅	—	2	1	no	—
190	C₂²×C₄×C₅	—	2	1	no	—
191	C₂²×C₄×C₅	—	2	1	no	—
192	C₂²×C₄×C₅	—	2	1	no	—
193	C₂²×C₄×C₅	—	2	1	no	—
194	C₂²×C₄×C₅	—	2	1	no	—
195	C₂²×C₄×C₅	—	2	1	no	—
196	C₂²×C₄×C₅	—	4	1	no	—
197	C₂²×C₄×C₅	—	4	1	no	—
198	C₂²×C₄×C₅	—	4	1	no	—
199	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
200	C₅×Q₁₆	—	2	2	no	—
201	C₅×Q₁₆	—	4	2	no	—
202	C₅×SD₁₆	—	2	2	no	—
203	C₅×SD₁₆	—	2	2	no	—
204	C₅×SD₁₆	—	4	2	no	—
205	C₅×D₈	—	2	2	no	—
206	C₅×M₁₆	—	2	4	no	—
207	C₅×M₁₆	—	2	1	no	—
208	C₅×M₁₆	—	2	1	no	—
209	C₅×M₁₆	—	2	1	no	—
210	C₅×M₁₆	—	2	1	no	—
211	C₅×M₁₆	—	2	1	no	—
212	C₅×M₁₆	—	2	1	no	—
213	C₅×M₁₆	—	2	1	no	—
214	C₅×M₁₆	#41	1	2	yes	—
215	C₂×C₅×C₈	—	2	4	no	—
216	C₂×C₅×C₈	—	2	1	no	—
217	C₂×C₅×C₈	—	2	1	no	—
218	C₂×C₅×C₈	—	2	1	no	—
219	C₂×C₅×C₈	—	2	1	no	—
220	C₂×C₅×C₈	—	2	1	no	—
221	C₂×C₅×C₈	—	2	1	no	—
222	C₂×C₅×C₈	—	2	1	no	—
223	C₂×C₅×C₈	—	2	1	no	—
224	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
225	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
226	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
227	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
228	C₅×C₄⋊C₄	—	2	1	no	—
229	C₅×C₄⋊C₄	—	2	1	no	—
230	C₅×C₄⋊C₄	—	2	1	no	—
231	C₅×C₄⋊C₄	—	2	1	no	—
232	C₅×C₄⋊C₄	—	2	1	no	—
233	C₅×C₄⋊C₄	—	2	1	no	—
234	C₅×C₄⋊C₄	—	4	1	no	—
235	C₅×C₄⋊C₄	—	4	1	no	—
236	C₅×C₄⋊C₄	—	4	1	no	—
237	C₅×C₄⋊C₄	—	4	1	no	—
238	C₅×C₄⋊C₄	—	4	1	no	—
239	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
240	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
241	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
242	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
243	C₅×C₂²⋊C₄	—	2	1	no	—
244	C₅×C₂²⋊C₄	—	2	1	no	—
245	C₅×C₂²⋊C₄	—	4	1	no	—
246	C₅×C₂²⋊C₄	—	4	1	no	—
247	C₅×C₂²⋊C₄	—	4	1	no	—
248	C₅×C₂²⋊C₄	—	4	1	no	—
249	C₅×C₂²⋊C₄	—	4	1	no	—
250	C₄²×C₅	—	2	1	no	—
251	C₄²×C₅	—	2	1	no	—
252	C₄²×C₅	—	2	1	no	—
253	C₄²×C₅	—	2	1	no	—
254	C₄²×C₅	—	4	1	no	—
255	C₄²×C₅	—	4	1	no	—
256	C₄²×C₅	—	4	1	no	—
257	C₂×#137	C₂²×C₅	1	1	yes	characteristic
258	C₂×#135	C₂²×C₅	1	1	yes	characteristic
259	C₂×#131	C₂²×C₅	1	1	yes	characteristic
260	#536	C₂²×C₅	1	1	yes	characteristic
261	#520	C₂²×C₅	1	1	yes	characteristic
262	#520	C₂²×C₅	1	1	yes	characteristic
263	#520	C₂²×C₅	1	1	yes	characteristic
264	#485	—	2	1	no	—
265	#485	—	2	1	no	—
266	#484	—	2	1	no	—
267	#483	—	2	1	no	—
268	#464	—	2	1	no	—
269	#463	—	2	1	no	—
270	#462	—	2	1	no	—
271	#461	—	2	1	no	—
272	#442	—	2	1	no	—
273	#441	—	2	1	no	—
274	C₄×SD₁₆	—	2	1	no	—
275	C₄×SD₁₆	—	2	1	no	—
276	#428	—	2	1	no	—
277	#428	—	2	1	no	—
278	#428	C₂²×C₅	1	1	yes	characteristic
279	#428	C₂²×C₅	1	1	yes	characteristic
280	#428	C₂²×C₅	1	1	yes	characteristic
281	#427	—	2	1	no	—
282	#427	C₂²×C₅	1	1	yes	characteristic
283	C₂×#107	—	2	1	no	—
284	C₂×#107	C₂²×C₅	1	1	yes	characteristic
285	C₂×#106	C₂²×C₅	1	1	yes	characteristic
286	#424	C₂²×C₅	1	1	yes	characteristic
287	C₂×#104	C₂²×C₅	1	1	yes	characteristic
288	C₂×#104	C₂²×C₅	1	1	yes	characteristic
289	#419	C₂²×C₅	1	1	yes	characteristic
290	#417	C₂²×C₅	1	1	yes	characteristic
291	#417	C₂²×C₅	1	1	yes	characteristic
292	#417	C₂²×C₅	1	1	yes	characteristic
293	C₂×#103	C₂²×C₅	1	1	yes	characteristic
294	C₂×#103	C₂²×C₅	1	1	yes	characteristic
295	C₂×#101	C₂²×C₅	1	1	yes	characteristic
296	#408	C₂²×C₅	1	1	yes	characteristic
297	#405	C₂²×C₅	1	1	yes	characteristic
298	#391	C₂²×C₅	1	1	yes	characteristic
299	#382	C₂²×C₅	1	1	yes	characteristic
300	#343	C₂²×C₅	1	1	yes	characteristic
301	#343	C₂²×C₅	1	1	yes	characteristic
302	#343	C₂²×C₅	1	1	yes	characteristic
303	#341	C₂²×C₅	1	1	yes	characteristic
304	#341	C₂²×C₅	1	1	yes	characteristic
305	#339	C₂²×C₅	1	1	yes	characteristic
306	#339	C₂²×C₅	1	1	yes	characteristic
307	#336	C₂²×C₅	1	1	yes	characteristic
308	C₂³×C₅	—	2	1	no	—
309	C₂³×C₅	—	2	1	no	—
310	C₂³×C₅	H(5,𝔽₂)	1	1	yes	characteristic
311	C₅×Q₈	—	2	1	no	—
312	C₅×Q₈	—	2	1	no	—
313	C₅×Q₈	—	2	1	no	—
314	C₅×Q₈	—	4	1	no	—
315	C₅×Q₈	—	4	1	no	—
316	C₅×Q₈	—	4	1	no	—
317	C₅×Q₈	—	4	1	no	—
318	C₅×Q₈	#123	1	2	yes	—
319	C₅×D₄	—	2	2	no	—
320	C₅×D₄	—	2	2	no	—
321	C₅×D₄	—	2	1	no	—
322	C₅×D₄	—	2	1	no	—
323	C₅×D₄	—	2	1	no	—
324	C₅×D₄	—	4	1	no	—
325	C₅×D₄	—	4	1	no	—
326	C₅×D₄	#123	1	2	yes	—
327	C₂×C₄×C₅	—	2	1	no	—
328	C₂×C₄×C₅	—	2	2	no	—
329	C₂×C₄×C₅	—	2	2	no	—
330	C₂×C₄×C₅	—	2	1	no	—
331	C₂×C₄×C₅	—	2	1	no	—
332	C₂×C₄×C₅	—	2	1	no	—
333	C₂×C₄×C₅	—	2	1	no	—
334	C₂×C₄×C₅	—	2	1	no	—
335	C₂×C₄×C₅	—	4	1	no	—
336	C₂×C₄×C₅	—	4	1	no	—
337	C₂×C₄×C₅	—	4	1	no	—
338	C₂×C₄×C₅	—	4	1	no	—
339	C₂×C₄×C₅	—	4	1	no	—
340	C₂×C₄×C₅	—	4	1	no	—
341	C₂×C₄×C₅	—	4	1	no	—
342	C₂×C₄×C₅	—	4	1	no	—
343	C₂×C₄×C₅	—	4	1	no	—
344	C₂×C₄×C₅	—	4	1	no	—
345	C₂×C₄×C₅	—	4	1	no	—
346	C₂×C₄×C₅	—	8	1	no	—
347	C₂×C₄×C₅	—	8	1	no	—
348	C₂×C₄×C₅	—	8	1	no	—
349	C₂×C₄×C₅	—	16	1	no	—
350	C₂×C₄×C₅	—	16	1	no	—
351	C₂×C₄×C₅	—	16	1	no	—
352	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
353	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
354	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
355	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
356	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
357	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
358	C₅×C₈	—	2	1	no	—
359	C₅×C₈	—	2	1	no	—
360	C₅×C₈	—	2	1	no	—
361	C₅×C₈	—	2	2	no	—
362	C₅×C₈	—	2	1	no	—
363	C₅×C₈	—	4	1	no	—
364	C₅×C₈	—	4	1	no	—
365	C₅×C₈	—	4	1	no	—
366	C₂×#41	C₂³×C₅	1	1	yes	characteristic
367	C₂×#41	C₂³×C₅	1	1	yes	characteristic
368	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
369	#137	—	2	2	no	—
370	#137	—	2	2	no	—
371	#135	—	2	2	no	—
372	#135	—	2	2	no	—
373	C₂×Q₁₆	—	2	1	no	—
374	C₂×Q₁₆	C₅×D₄	1	1	yes	characteristic
375	C₂×SD₁₆	—	2	1	no	—
376	C₂×SD₁₆	C₅×D₄	1	1	yes	characteristic
377	C₂×SD₁₆	C₅×D₄	1	1	yes	characteristic
378	C₂×D₈	C₅×D₄	1	1	yes	characteristic
379	#131	—	2	2	no	—
380	#131	—	2	2	no	—
381	C₂×M₁₆	—	2	1	no	—
382	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
383	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
384	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
385	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
386	C₂²×C₈	—	2	1	no	—
387	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
388	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
389	C₄⋊Q₈	—	2	1	no	—
390	#124	—	2	1	no	—
391	#123	—	4	1	no	—
392	C₂²⋊Q₈	—	2	1	no	—
393	C₂²⋊Q₈	—	2	1	no	—
394	C₄×Q₈	—	2	1	no	—
395	C₄×Q₈	—	2	1	no	—
396	C₄×Q₈	—	2	1	no	—
397	C₄×D₄	—	2	1	no	—
398	C₄×D₄	—	2	1	no	—
399	C₄×D₄	—	2	1	no	—
400	C₄×D₄	—	4	1	no	—
401	C₄×D₄	—	4	1	no	—
402	C₄×D₄	—	4	1	no	—
403	#117	—	2	1	no	—
404	#117	—	2	1	no	—
405	#117	—	2	1	no	—
406	#117	C₂³×C₅	1	1	yes	characteristic
407	#117	C₂³×C₅	1	1	yes	characteristic
408	C₂×C₄⋊C₄	—	2	1	no	—
409	C₂×C₄⋊C₄	—	2	1	no	—
410	C₂×C₄⋊C₄	—	2	1	no	—
411	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
412	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
413	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
414	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
415	#107	—	2	1	no	—
416	#107	—	2	1	no	—
417	#107	—	2	1	no	—
418	#107	—	2	1	no	—
419	#107	—	2	1	no	—
420	#107	C₅×D₄	1	1	yes	characteristic
421	#107	C₅×D₄	1	1	yes	characteristic
422	#106	—	2	1	no	—
423	#106	—	2	1	no	—
424	#106	—	2	1	no	—
425	#106	—	2	1	no	—
426	#106	—	2	1	no	—
427	#106	C₅×D₄	1	1	yes	characteristic
428	#106	C₅×D₄	1	1	yes	characteristic
429	C₄⋊C₈	—	2	1	no	—
430	C₄⋊C₈	—	2	1	no	—
431	#104	—	2	2	no	—
432	#104	—	2	2	no	—
433	#103	—	2	1	no	—
434	#103	—	2	1	no	—
435	#103	—	2	1	no	—
436	#103	—	2	1	no	—
437	#103	—	2	1	no	—
438	#103	—	2	1	no	—
439	#103	—	2	1	no	—
440	#103	—	2	1	no	—
441	#103	—	2	1	no	—
442	#102	—	2	1	no	—
443	#102	—	2	1	no	—
444	#102	—	2	1	no	—
445	#101	—	2	2	no	—
446	C₂²⋊C₈	—	2	1	no	—
447	C₂²⋊C₈	—	2	1	no	—
448	#97	—	2	1	no	—
449	C₄×C₈	—	2	1	no	—
450	#95	—	4	1	no	—
451	#95	—	4	1	no	—
452	C₂²×C₅	—	2	1	no	—
453	C₂²×C₅	—	2	1	no	—
454	C₂²×C₅	—	2	2	no	—
455	C₂²×C₅	—	4	1	no	—
456	C₂²×C₅	—	4	1	no	—
457	C₂²×C₅	—	4	1	no	—
458	C₂²×C₅	—	4	1	no	—
459	C₂²×C₅	—	4	1	no	—
460	C₂²×C₅	#539	1	1	yes	characteristic
461	C₂²×C₅	D₄²	1	1	yes	characteristic
462	C₂²×C₅	#553	1	1	yes	characteristic
463	C₄×C₅	—	2	2	no	—
464	C₄×C₅	—	4	1	no	—
465	C₄×C₅	—	4	1	no	—
466	C₄×C₅	—	4	1	no	—
467	C₄×C₅	—	4	1	no	—
468	C₄×C₅	—	4	1	no	—
469	C₄×C₅	—	8	1	no	—
470	C₄×C₅	—	8	1	no	—
471	C₄×C₅	—	8	1	no	—
472	C₄×C₅	—	8	1	no	—
473	C₄×C₅	—	8	1	no	—
474	C₄×C₅	C₂×#123	1	1	yes	characteristic
475	C₄×C₅	#525	1	1	yes	characteristic
476	C₄×C₅	#547	1	1	yes	characteristic
477	C₄×C₅	#548	1	1	yes	characteristic
478	#41	—	2	1	no	—
479	#41	—	2	1	no	—
480	#41	—	2	1	no	—
481	#41	—	2	1	no	—
482	#41	—	2	1	no	—
483	#41	—	2	1	no	—
484	#41	C₅×#41	1	2	yes	—
485	#41	C₅×#41	1	2	yes	—
486	C₂×Q₈	—	2	1	no	—
487	C₂×Q₈	—	2	1	no	—
488	C₂×Q₈	—	2	1	no	—
489	C₂×Q₈	—	2	1	no	—
490	C₂×Q₈	—	2	1	no	—
491	C₂×Q₈	—	2	1	no	—
492	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
493	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
494	C₂×D₄	—	2	1	no	—
495	C₂×D₄	—	2	1	no	—
496	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
497	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	4	1	no	—
506	C₂²×C₄	—	4	1	no	—
507	C₂²×C₄	—	4	1	no	—
508	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
509	Q₁₆	—	2	2	no	—
510	Q₁₆	—	4	2	no	—
511	SD₁₆	—	2	2	no	—
512	SD₁₆	—	2	2	no	—
513	SD₁₆	—	4	2	no	—
514	D₈	—	2	2	no	—
515	M₁₆	—	2	4	no	—
516	M₁₆	—	2	1	no	—
517	M₁₆	—	2	1	no	—
518	M₁₆	—	2	1	no	—
519	M₁₆	—	2	1	no	—
520	M₁₆	—	2	1	no	—
521	M₁₆	—	2	1	no	—
522	M₁₆	—	2	1	no	—
523	M₁₆	C₅×#41	1	2	yes	—
524	C₂×C₈	—	2	4	no	—
525	C₂×C₈	—	2	1	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	—	2	1	no	—
528	C₂×C₈	—	2	1	no	—
529	C₂×C₈	—	2	1	no	—
530	C₂×C₈	—	2	1	no	—
531	C₂×C₈	—	2	1	no	—
532	C₂×C₈	—	2	1	no	—
533	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
534	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
535	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
536	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
537	C₄⋊C₄	—	2	1	no	—
538	C₄⋊C₄	—	2	1	no	—
539	C₄⋊C₄	—	2	1	no	—
540	C₄⋊C₄	—	2	1	no	—
541	C₄⋊C₄	—	2	1	no	—
542	C₄⋊C₄	—	2	1	no	—
543	C₄⋊C₄	—	4	1	no	—
544	C₄⋊C₄	—	4	1	no	—
545	C₄⋊C₄	—	4	1	no	—
546	C₄⋊C₄	—	4	1	no	—
547	C₄⋊C₄	—	4	1	no	—
548	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
549	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
550	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
551	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
552	C₂²⋊C₄	—	2	1	no	—
553	C₂²⋊C₄	—	2	1	no	—
554	C₂²⋊C₄	—	4	1	no	—
555	C₂²⋊C₄	—	4	1	no	—
556	C₂²⋊C₄	—	4	1	no	—
557	C₂²⋊C₄	—	4	1	no	—
558	C₂²⋊C₄	—	4	1	no	—
559	C₄²	—	2	1	no	—
560	C₄²	—	2	1	no	—
561	C₄²	—	2	1	no	—
562	C₄²	—	2	1	no	—
563	C₄²	—	4	1	no	—
564	C₄²	—	4	1	no	—
565	C₄²	—	4	1	no	—
566	C₂×C₅	—	2	1	no	—
567	C₂×C₅	—	2	1	no	—
568	C₂×C₅	—	4	2	no	—
569	C₂×C₅	—	8	1	no	—
570	C₂×C₅	#2443	1	1	yes	characteristic
571	C₂×C₅	#3289	1	1	yes	characteristic
572	C₂×C₅	#3290	1	1	yes	characteristic
573	C₂³	—	2	1	no	—
574	C₂³	—	2	1	no	—
575	C₂³	C₅×H(5,𝔽₂)	1	1	yes	characteristic
576	Q₈	—	2	1	no	—
577	Q₈	—	2	1	no	—
578	Q₈	—	2	1	no	—
579	Q₈	—	4	1	no	—
580	Q₈	—	4	1	no	—
581	Q₈	—	4	1	no	—
582	Q₈	—	4	1	no	—
583	Q₈	C₅×#123	1	2	yes	—
584	D₄	—	2	2	no	—
585	D₄	—	2	2	no	—
586	D₄	—	2	1	no	—
587	D₄	—	2	1	no	—
588	D₄	—	2	1	no	—
589	D₄	—	4	1	no	—
590	D₄	—	4	1	no	—
591	D₄	C₅×#123	1	2	yes	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	8	1	no	—
612	C₂×C₄	—	8	1	no	—
613	C₂×C₄	—	8	1	no	—
614	C₂×C₄	—	16	1	no	—
615	C₂×C₄	—	16	1	no	—
616	C₂×C₄	—	16	1	no	—
617	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
618	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
619	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
620	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
621	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
622	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
623	C₈	—	2	1	no	—
624	C₈	—	2	1	no	—
625	C₈	—	2	1	no	—
626	C₈	—	2	2	no	—
627	C₈	—	2	1	no	—
628	C₈	—	4	1	no	—
629	C₈	—	4	1	no	—
630	C₈	—	4	1	no	—
631	C₅	#26193	1	1	yes	characteristic, direct product factor, Sylow
632	C₂²	—	2	1	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	4	1	no	—
636	C₂²	—	4	1	no	—
637	C₂²	—	4	1	no	—
638	C₂²	—	4	1	no	—
639	C₂²	—	4	1	no	—
640	C₂²	C₅×#539	1	1	yes	characteristic
641	C₂²	C₅×D₄²	1	1	yes	characteristic
642	C₂²	C₅×#553	1	1	yes	characteristic
643	C₄	—	2	2	no	—
644	C₄	—	4	1	no	—
645	C₄	—	4	1	no	—
646	C₄	—	4	1	no	—
647	C₄	—	4	1	no	—
648	C₄	—	4	1	no	—
649	C₄	—	8	1	no	—
650	C₄	—	8	1	no	—
651	C₄	—	8	1	no	—
652	C₄	—	8	1	no	—
653	C₄	—	8	1	no	—
654	C₄	C₂×C₅×#123	1	1	yes	characteristic
655	C₄	C₅×#525	1	1	yes	characteristic
656	C₄	C₅×#547	1	1	yes	characteristic
657	C₄	C₅×#548	1	1	yes	characteristic
658	C₂	—	2	1	no	—
659	C₂	—	2	1	no	—
660	C₂	—	4	2	no	—
661	C₂	—	8	1	no	—
662	C₂	C₅×#2443	1	1	yes	characteristic
663	C₂	C₅×#3289	1	1	yes	characteristic
664	C₂	C₅×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂×C₅×#135	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3097	C₂	semidirect
4. C₅×#2913	C₂	semidirect
5. C₅×#2097	C₂	semidirect
6. C₅×#2090	C₂	semidirect
7. C₅×#2078	C₂	semidirect
8. C₅×#2038	C₂	semidirect
9. C₅×#1930	C₂	semidirect
10. C₅×#1922	C₂	semidirect
11. C₅×#1908	C₂	semidirect
12. C₅×#1882	C₂	semidirect
14. C₅×#1860	C₂	semidirect
15. C₅×#1860	C₂	semidirect
67. #26193	C₅	direct (N × H)
154. #3097	C₂×C₅	semidirect
157. #2913	C₂×C₅	semidirect
158. #2097	C₂×C₅	semidirect
159. #2090	C₂×C₅	semidirect
160. #2078	C₂×C₅	semidirect
161. #2038	C₂×C₅	semidirect
162. #1930	C₂×C₅	semidirect
163. #1922	C₂×C₅	semidirect
164. #1908	C₂×C₅	semidirect
165. #1882	C₂×C₅	semidirect
167. #1860	C₂×C₅	semidirect
168. #1860	C₂×C₅	semidirect
631. C₅	#26193	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×#3097	2
C₅×#3046	2
C₅×#2952	2
C₅×#2913	2
C₅×#2097	2
C₅×#2090	2
C₅×#2078	2
C₅×#2038	2
C₅×#1930	2
C₅×#1922	2
C₅×#1908	2
C₅×#1882	2
C₅×#1876	2
C₅×#1860	2
#26193	5

Subgroups — C5×#26193 #11948913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#26193 #11948913