Subgroups — #10618885

Order 640.

1040 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	#66066	C₂	1	1	yes	maximal, characteristic, complemented
3	#66058	C₂	1	1	yes	maximal, characteristic, complemented
4	#66044	C₂	1	2	yes	maximal, complemented
5	#66040	C₂	1	2	yes	maximal, complemented
6	#66039	C₂	1	2	yes	maximal, complemented
7	#66039	C₂	1	2	yes	maximal, complemented
8	#66015	C₂	1	1	yes	maximal, characteristic, complemented
9	#66008	C₂	1	1	yes	maximal, characteristic
10	D₅×#124	C₂	1	1	yes	maximal, characteristic, complemented
11	#66005	C₂	1	1	yes	maximal, characteristic, complemented
12	#65974	C₂	1	2	yes	maximal, complemented
13	#65971	C₂	1	2	yes	maximal, complemented
14	#65919	C₂	1	1	yes	maximal, characteristic, complemented
15	#65919	C₂	1	1	yes	maximal, characteristic, complemented
16	#65912	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#713	C₂	1	1	yes	maximal, characteristic, complemented
18	#65906	C₂	1	1	yes	maximal, characteristic, complemented
19	#65902	C₂	1	1	yes	maximal, characteristic, complemented
20	#65893	C₂	1	1	yes	maximal, characteristic, complemented
21	#65879	C₂	1	1	yes	maximal, characteristic, complemented
22	#65862	C₂	1	2	yes	maximal, complemented
23	#65861	C₂	1	2	yes	maximal, complemented
24	C₂×#713	C₂²	1	1	yes	characteristic
25	C₂×Q₈×D₅	C₂²	1	1	yes	characteristic
26	C₂×D₄×D₅	C₂²	1	1	yes	characteristic
27	C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₅×#126	C₂²	1	2	yes	complemented
29	C₅×#126	C₂²	1	2	yes	complemented
30	C₅×#124	C₂²	1	1	yes	characteristic
31	C₅×#124	C₂²	1	1	yes	characteristic
32	C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
33	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
37	C₅×#117	C₂²	1	2	yes	complemented
38	#4093	C₂²	1	1	yes	characteristic
39	#4093	C₂²	1	1	yes	characteristic
40	#4093	C₂²	1	1	yes	characteristic, complemented
41	#4093	C₂²	1	2	yes	complemented
42	#4092	C₂²	1	1	yes	characteristic
43	Q₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
44	Q₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
45	#4090	C₂²	1	1	yes	characteristic, complemented
46	#4090	C₂²	1	1	yes	characteristic, complemented
47	#4086	C₂²	1	1	yes	characteristic
48	#4082	C₂²	1	1	yes	characteristic
49	D₄×Dic₅	C₂²	1	1	yes	characteristic
50	#4075	C₂²	1	2	yes	complemented
51	C₄×C₂²⋊D₅	C₂²	1	2	yes	—
52	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
53	C₂×#685	C₂²	1	2	yes	—
54	#4044	C₂²	1	2	yes	complemented
55	#4044	C₂²	1	2	yes	complemented
56	#4044	C₂²	1	2	yes	complemented
57	#4043	C₂²	1	1	yes	characteristic
58	#4043	C₂²	1	2	yes	complemented
59	#4042	C₂²	1	1	yes	characteristic
60	#4042	C₂²	1	1	yes	characteristic
61	#4042	C₂²	1	2	yes	complemented
62	#4042	C₂²	1	2	yes	complemented
63	#4042	C₂²	1	2	yes	complemented
64	#4040	C₂²	1	2	yes	—
65	#4040	C₂²	1	2	yes	—
66	#4040	C₂²	1	2	yes	complemented
67	#4040	C₂²	1	2	yes	complemented
68	#4040	C₂²	1	2	yes	complemented
69	#4040	C₂²	1	2	yes	complemented
70	#4039	C₂²	1	1	yes	characteristic
71	#4039	C₂²	1	2	yes	—
72	#4039	C₂²	1	1	yes	characteristic, complemented
73	#4039	C₂²	1	2	yes	complemented
74	#4038	C₂²	1	1	yes	characteristic
75	#4038	C₂²	1	2	yes	—
76	#4038	C₂²	1	2	yes	complemented
77	#4038	C₂²	1	2	yes	complemented
78	#4035	C₂²	1	1	yes	characteristic, complemented
79	#4035	C₂²	1	1	yes	characteristic, complemented
80	#4034	C₂²	1	1	yes	characteristic, complemented
81	#4033	C₂²	1	1	yes	characteristic, complemented
82	#4033	C₂²	1	2	yes	complemented
83	#4032	C₂²	1	2	yes	complemented
84	#4031	C₂²	1	2	yes	—
85	#4031	C₂²	1	2	yes	—
86	#4031	C₂²	1	2	yes	complemented
87	#4031	C₂²	1	2	yes	complemented
88	#4030	C₂²	1	2	yes	—
89	#4030	C₂²	1	2	yes	—
90	#4029	C₂²	1	2	yes	complemented
91	#4029	C₂²	1	2	yes	complemented
92	#4028	C₂²	1	2	yes	—
93	#4028	C₂²	1	2	yes	—
94	#4027	C₂²	1	2	yes	—
95	#4027	C₂²	1	2	yes	complemented
96	D₅×C₂²⋊C₄	C₂²	1	2	yes	—
97	D₅×C₂²⋊C₄	C₂²	1	2	yes	—
98	D₅×C₂²⋊C₄	C₂²	1	2	yes	—
99	#4025	C₂²	1	2	yes	complemented
100	#4025	C₂²	1	2	yes	complemented
101	#4024	C₂²	1	2	yes	complemented
102	#4023	C₂²	1	2	yes	complemented
103	#4022	C₂²	1	2	yes	complemented
104	#4021	C₂²	1	1	yes	characteristic
105	#4021	C₂²	1	1	yes	characteristic, complemented
106	#4021	C₂²	1	2	yes	complemented
107	#4020	C₂²	1	1	yes	characteristic
108	C₄×D₂₀	C₂²	1	1	yes	characteristic
109	C₄×D₂₀	C₂²	1	2	yes	—
110	C₄×D₂₀	C₂²	1	2	yes	complemented
111	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
112	#4018	C₂²	1	1	yes	characteristic
113	#4018	C₂²	1	2	yes	—
114	#4018	C₂²	1	1	yes	characteristic
115	#4018	C₂²	1	2	yes	complemented
116	C₄²×D₅	C₂²	1	1	yes	characteristic
117	C₄²×D₅	C₂²	1	2	yes	complemented
118	C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
119	C₄×Dic₁₀	C₂²	1	2	yes	complemented
120	C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
123	#3510	—	5	1	no	maximal, Sylow
124	C₂³×D₅	C₂³	1	2	yes	—
125	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
126	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
127	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
128	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₅	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
133	C₂²×Dic₅	C₂³	1	2	yes	—
134	#713	—	2	4	no	—
135	Q₈×D₅	—	2	4	no	—
136	D₄×D₅	—	2	4	no	—
137	C₂×D₂₀	C₂³	1	1	yes	characteristic
138	C₂×D₂₀	C₂³	1	2	yes	—
139	C₂×D₂₀	C₂³	1	1	yes	characteristic
140	C₂×D₂₀	C₂³	1	2	yes	—
141	C₂×D₂₀	C₂³	1	2	yes	—
142	C₂×C₄×D₅	C₂³	1	2	yes	—
143	C₂×C₄×D₅	C₂³	1	2	yes	—
144	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₅	C₂³	1	2	yes	—
147	C₂×C₄×D₅	C₂³	1	2	yes	—
148	C₂×C₄×D₅	C₂³	1	2	yes	—
149	C₂×C₄×D₅	C₂³	1	2	yes	—
150	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
151	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
152	C₂×Dic₁₀	C₂³	1	2	yes	—
153	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
154	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
155	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
156	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₅×C₄⋊C₄	C₂³	1	2	yes	—
158	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₅×C₄⋊C₄	C₂³	1	2	yes	—
160	C₅×C₄⋊C₄	C₂³	1	2	yes	—
161	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
162	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₅×C₄⋊C₄	C₂³	1	2	yes	—
164	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₄²×C₅	C₂³	1	2	yes	—
170	C₄²×C₅	C₂³	1	2	yes	—
171	C₄²×C₅	C₂³	1	1	yes	characteristic
172	C₄²×C₅	C₂³	1	1	yes	characteristic
173	C₄²×C₅	C₂³	1	1	yes	characteristic
174	C₂²⋊Dic₅	C₂³	1	2	yes	—
175	C₂²⋊Dic₅	C₂³	1	2	yes	—
176	C₂²⋊Dic₅	C₂³	1	2	yes	—
177	#685	C₂³	1	1	yes	characteristic
178	#685	C₂³	1	2	yes	—
179	#685	C₂³	1	1	yes	characteristic
180	#685	C₂³	1	1	yes	characteristic
181	#685	C₂³	1	1	yes	characteristic
182	#685	C₂³	1	2	yes	—
183	#685	C₂³	1	2	yes	—
184	#685	C₂³	1	2	yes	—
185	#685	C₂³	1	2	yes	—
186	#685	C₂³	1	2	yes	—
187	#685	C₂³	1	2	yes	—
188	#685	C₂³	1	2	yes	—
189	#685	C₂³	1	2	yes	—
190	#685	C₂³	1	2	yes	—
191	#685	C₂³	1	2	yes	—
192	#685	C₂³	1	2	yes	—
193	#685	C₂³	1	2	yes	—
194	#685	C₂³	1	2	yes	—
195	#685	C₂³	1	2	yes	—
196	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
197	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
198	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
199	C₄⋊Dic₅	C₂³	1	2	yes	—
200	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
201	C₄⋊Dic₅	C₂³	1	2	yes	—
202	#683	C₂³	1	2	yes	—
203	#683	C₂³	1	1	yes	characteristic
204	#683	C₂³	1	1	yes	characteristic
205	#683	C₂³	1	1	yes	characteristic
206	#683	C₂³	1	1	yes	characteristic
207	#683	C₂³	1	1	yes	characteristic
208	#683	C₂³	1	1	yes	characteristic
209	#683	C₂³	1	1	yes	characteristic
210	#683	C₂³	1	2	yes	—
211	#683	C₂³	1	1	yes	characteristic
212	#683	C₂³	1	1	yes	characteristic
213	#683	C₂³	1	1	yes	characteristic
214	#683	C₂³	1	2	yes	—
215	#683	C₂³	1	2	yes	—
216	C₄×Dic₅	C₂³	1	1	yes	characteristic
217	C₄×Dic₅	C₂³	1	1	yes	characteristic
218	C₄×Dic₅	C₂³	1	1	yes	characteristic
219	C₄×Dic₅	C₂³	1	2	yes	—
220	C₄×Dic₅	C₂³	1	2	yes	—
221	C₄×Dic₅	C₂³	1	2	yes	—
222	C₄×Dic₅	C₂³	1	1	yes	characteristic
223	C₄×Dic₅	C₂³	1	1	yes	characteristic
224	C₄×Dic₅	C₂³	1	2	yes	—
225	C₄×Dic₅	C₂³	1	2	yes	—
226	#559	—	5	1	no	—
227	#559	—	5	1	no	—
228	#559	—	5	1	no	—
229	#559	—	5	1	no	—
230	#556	—	5	1	no	—
231	#556	—	5	1	no	—
232	#556	—	5	1	no	—
233	#556	D₅	1	1	yes	characteristic, complemented
234	#551	—	5	2	no	—
235	#551	—	5	2	no	—
236	#551	—	5	2	no	—
237	#551	—	5	2	no	—
238	#542	—	5	2	no	—
239	#542	—	5	2	no	—
240	#536	—	5	1	no	—
241	#535	—	5	1	no	—
242	#533	—	5	1	no	—
243	#529	—	5	2	no	—
244	#529	—	5	2	no	—
245	C₂×#124	—	5	1	no	—
246	#519	—	5	1	no	—
247	#518	—	5	1	no	—
248	C₄×#41	—	5	1	no	—
249	C₂³×C₅	C₂⁴	1	2	yes	—
250	C₂²×D₅	—	2	4	no	—
251	C₂²×D₅	—	4	2	no	—
252	C₂²×D₅	—	4	2	no	—
253	C₂²×D₅	C₂⁴	1	2	yes	—
254	C₂²×D₅	C₂⁴	1	2	yes	—
255	C₂²×D₅	C₂⁴	1	1	yes	characteristic
256	C₅×Q₈	—	2	2	no	—
257	C₅×Q₈	—	2	2	no	—
258	C₅×Q₈	—	4	1	no	—
259	C₅×D₄	—	2	2	no	—
260	C₂×C₄×C₅	—	4	2	no	—
261	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
262	C₂×C₄×C₅	C₂⁴	1	2	yes	—
263	C₂×C₄×C₅	C₂⁴	1	2	yes	—
264	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
265	C₂×C₄×C₅	C₂⁴	1	2	yes	—
266	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
267	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
268	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
269	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
270	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
271	C₂²⋊D₅	—	2	4	no	—
272	C₂²⋊D₅	—	4	2	no	—
273	C₂²⋊D₅	—	4	2	no	—
274	C₂×Dic₅	—	4	2	no	—
275	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
276	C₂×Dic₅	C₂⁴	1	2	yes	—
277	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
278	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
279	C₂×Dic₅	C₂⁴	1	2	yes	—
280	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
281	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
282	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
283	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
284	D₂₀	—	2	4	no	—
285	D₂₀	—	2	2	no	—
286	D₂₀	—	2	2	no	—
287	D₂₀	—	4	2	no	—
288	D₂₀	—	4	2	no	—
289	C₄×D₅	—	2	4	no	—
290	C₄×D₅	—	2	4	no	—
291	C₄×D₅	—	4	1	no	—
292	C₄×D₅	—	4	2	no	—
293	C₄×D₅	—	4	1	no	—
294	C₄×D₅	—	4	2	no	—
295	C₄×D₅	—	4	2	no	—
296	C₄×D₅	—	4	2	no	—
297	C₄×D₅	#41	1	4	yes	—
298	Dic₁₀	—	2	2	no	—
299	Dic₁₀	—	2	4	no	—
300	Dic₁₀	—	4	1	no	—
301	Dic₁₀	—	4	1	no	—
302	Dic₁₀	—	4	1	no	—
303	C₂×#41	—	5	1	no	—
304	C₂²×Q₈	—	5	1	no	—
305	C₂²×D₄	—	5	1	no	—
306	C₄⋊Q₈	—	5	1	no	—
307	C₄⋊Q₈	—	5	1	no	—
308	C₄⋊Q₈	—	5	1	no	—
309	C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
310	#127	—	5	1	no	—
311	#127	—	5	1	no	—
312	#126	—	5	2	no	—
313	#126	—	5	2	no	—
314	#126	—	5	2	no	—
315	#126	—	5	2	no	—
316	#126	—	5	2	no	—
317	#126	—	5	2	no	—
318	#126	C₂×D₅	1	2	yes	complemented
319	#126	C₂×D₅	1	2	yes	complemented
320	#125	—	5	1	no	—
321	#125	—	5	1	no	—
322	#124	—	5	1	no	—
323	#124	—	5	1	no	—
324	#124	—	5	1	no	—
325	#124	—	5	2	no	—
326	#124	—	5	1	no	—
327	#124	—	5	2	no	—
328	#124	—	5	2	no	—
329	#124	—	5	2	no	—
330	#124	—	5	2	no	—
331	#124	—	5	1	no	—
332	#124	—	5	1	no	—
333	#124	—	5	2	no	—
334	#124	C₂×D₅	1	1	yes	characteristic
335	#124	C₂×D₅	1	1	yes	characteristic
336	#123	—	5	2	no	—
337	#123	—	5	2	no	—
338	#123	—	5	2	no	—
339	#123	—	5	2	no	—
340	#123	—	5	2	no	—
341	#123	—	5	2	no	—
342	#123	—	5	2	no	—
343	#123	—	5	2	no	—
344	#123	—	5	2	no	—
345	#123	—	5	2	no	—
346	C₂²⋊Q₈	—	5	1	no	—
347	C₂²⋊Q₈	—	5	2	no	—
348	C₂²⋊Q₈	—	5	2	no	—
349	C₂²⋊Q₈	—	5	1	no	—
350	C₂²⋊Q₈	—	5	1	no	—
351	C₂²⋊Q₈	—	5	1	no	—
352	C₂²⋊Q₈	—	5	2	no	—
353	C₂²⋊Q₈	—	5	2	no	—
354	C₂²⋊Q₈	—	5	2	no	—
355	C₂²⋊Q₈	C₂×D₅	1	2	yes	complemented
356	#121	—	5	2	no	—
357	#121	—	5	2	no	—
358	#120	—	5	2	no	—
359	#120	—	5	2	no	—
360	C₄×Q₈	—	5	1	no	—
361	C₄×Q₈	—	5	1	no	—
362	C₄×Q₈	—	5	2	no	—
363	C₄×Q₈	—	5	1	no	—
364	C₄×Q₈	—	5	2	no	—
365	C₄×Q₈	—	5	1	no	—
366	C₄×Q₈	—	5	1	no	—
367	C₄×Q₈	—	5	1	no	—
368	C₄×Q₈	—	5	1	no	—
369	C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
370	C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
371	C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
372	C₄×D₄	—	5	1	no	—
373	C₄×D₄	—	5	2	no	—
374	C₄×D₄	—	5	2	no	—
375	C₄×D₄	—	5	2	no	—
376	C₄×D₄	—	5	1	no	—
377	C₄×D₄	—	5	1	no	—
378	C₄×D₄	—	5	2	no	—
379	C₄×D₄	—	5	2	no	—
380	C₄×D₄	—	5	2	no	—
381	C₄×D₄	—	5	2	no	—
382	C₄×D₄	—	5	1	no	—
383	C₄×D₄	—	5	1	no	—
384	C₄×D₄	—	5	2	no	—
385	C₄×D₄	C₂×D₅	1	1	yes	characteristic
386	#117	—	5	1	no	—
387	#117	—	5	2	no	—
388	#117	—	5	2	no	—
389	#117	—	5	2	no	—
390	#117	—	5	2	no	—
391	#117	—	5	1	no	—
392	#117	—	5	1	no	—
393	#117	—	5	2	no	—
394	#117	—	5	2	no	—
395	#117	C₂×D₅	1	2	yes	complemented
396	C₂×C₂²⋊C₄	—	5	2	no	—
397	C₂×C₂²⋊C₄	—	5	2	no	—
398	C₂×C₂²⋊C₄	—	5	2	no	—
399	C₂×C₂²⋊C₄	—	5	2	no	—
400	C₂×C₄²	—	5	1	no	—
401	C₂×C₄²	—	5	2	no	—
402	C₂²×C₅	—	2	2	no	—
403	C₂²×C₅	—	2	2	no	—
404	C₂²×C₅	—	2	2	no	—
405	C₂²×C₅	C₂⁵	1	1	yes	characteristic
406	C₂×D₅	—	2	1	no	—
407	C₂×D₅	—	2	1	no	—
408	C₂×D₅	—	2	2	no	—
409	C₂×D₅	—	2	2	no	—
410	C₂×D₅	—	2	2	no	—
411	C₂×D₅	—	2	2	no	—
412	C₂×D₅	—	2	2	no	—
413	C₂×D₅	—	2	2	no	—
414	C₂×D₅	—	8	4	no	—
415	C₂×D₅	C₂×#41	1	2	yes	—
416	C₄×C₅	—	2	2	no	—
417	C₄×C₅	—	2	2	no	—
418	C₄×C₅	—	2	1	no	—
419	C₄×C₅	—	2	1	no	—
420	C₄×C₅	—	2	1	no	—
421	C₄×C₅	—	2	1	no	—
422	C₄×C₅	—	2	2	no	—
423	C₄×C₅	—	2	1	no	—
424	C₄×C₅	—	2	1	no	—
425	C₄×C₅	C₂×#41	1	2	yes	—
426	Dic₅	—	2	2	no	—
427	Dic₅	—	2	1	no	—
428	Dic₅	—	2	1	no	—
429	Dic₅	—	2	1	no	—
430	Dic₅	—	2	1	no	—
431	Dic₅	—	2	1	no	—
432	Dic₅	—	2	1	no	—
433	Dic₅	—	2	2	no	—
434	Dic₅	C₂×#41	1	2	yes	—
435	C₂⁴	—	5	2	no	—
436	#41	—	10	4	no	—
437	C₂×Q₈	—	5	2	no	—
438	C₂×Q₈	—	5	1	no	—
439	C₂×Q₈	—	5	1	no	—
440	C₂×Q₈	—	5	1	no	—
441	C₂×Q₈	—	5	1	no	—
442	C₂×Q₈	—	10	4	no	—
443	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
444	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
445	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
446	C₂×D₄	—	5	2	no	—
447	C₂×D₄	—	5	2	no	—
448	C₂×D₄	—	5	2	no	—
449	C₂×D₄	—	5	2	no	—
450	C₂×D₄	—	5	1	no	—
451	C₂×D₄	—	5	1	no	—
452	C₂×D₄	—	5	2	no	—
453	C₂×D₄	—	5	2	no	—
454	C₂×D₄	—	10	4	no	—
455	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
456	C₂²×C₄	—	5	1	no	—
457	C₂²×C₄	—	5	2	no	—
458	C₂²×C₄	—	5	2	no	—
459	C₂²×C₄	—	5	2	no	—
460	C₂²×C₄	—	5	1	no	—
461	C₂²×C₄	—	5	1	no	—
462	C₂²×C₄	—	5	2	no	—
463	C₂²×C₄	—	5	2	no	—
464	C₂²×C₄	—	5	2	no	—
465	C₂²×C₄	—	5	2	no	—
466	C₂²×C₄	C₂²×D₅	1	2	yes	—
467	C₄⋊C₄	—	5	1	no	—
468	C₄⋊C₄	—	5	1	no	—
469	C₄⋊C₄	—	5	1	no	—
470	C₄⋊C₄	—	5	1	no	—
471	C₄⋊C₄	—	5	1	no	—
472	C₄⋊C₄	—	5	1	no	—
473	C₄⋊C₄	—	5	2	no	—
474	C₄⋊C₄	—	5	1	no	—
475	C₄⋊C₄	—	5	1	no	—
476	C₄⋊C₄	—	5	2	no	—
477	C₄⋊C₄	—	5	2	no	—
478	C₄⋊C₄	—	5	2	no	—
479	C₄⋊C₄	—	5	2	no	—
480	C₄⋊C₄	—	5	2	no	—
481	C₄⋊C₄	—	5	1	no	—
482	C₄⋊C₄	—	5	1	no	—
483	C₄⋊C₄	—	5	1	no	—
484	C₄⋊C₄	—	5	1	no	—
485	C₄⋊C₄	—	5	1	no	—
486	C₄⋊C₄	—	5	1	no	—
487	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
488	C₄⋊C₄	C₂²×D₅	1	2	yes	—
489	C₄⋊C₄	C₂²×D₅	1	2	yes	—
490	C₄⋊C₄	C₂²×D₅	1	2	yes	—
491	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
492	C₄⋊C₄	C₂²×D₅	1	2	yes	—
493	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
494	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
495	C₂²⋊C₄	—	5	2	no	—
496	C₂²⋊C₄	—	5	2	no	—
497	C₂²⋊C₄	—	5	2	no	—
498	C₂²⋊C₄	—	5	2	no	—
499	C₂²⋊C₄	—	5	1	no	—
500	C₂²⋊C₄	—	5	1	no	—
501	C₂²⋊C₄	—	5	2	no	—
502	C₂²⋊C₄	—	5	2	no	—
503	C₂²⋊C₄	—	5	2	no	—
504	C₂²⋊C₄	—	5	2	no	—
505	C₂²⋊C₄	—	5	2	no	—
506	C₂²⋊C₄	—	5	2	no	—
507	C₂²⋊C₄	—	5	1	no	—
508	C₂²⋊C₄	—	5	1	no	—
509	C₂²⋊C₄	—	5	2	no	—
510	C₂²⋊C₄	—	5	2	no	—
511	C₂²⋊C₄	—	5	2	no	—
512	C₂²⋊C₄	—	5	2	no	—
513	C₂²⋊C₄	—	5	2	no	—
514	C₂²⋊C₄	—	5	2	no	—
515	C₂²⋊C₄	—	5	2	no	—
516	C₂²⋊C₄	—	5	2	no	—
517	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
518	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
519	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
520	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
521	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
522	C₄²	—	5	1	no	—
523	C₄²	—	5	2	no	—
524	C₄²	—	5	2	no	—
525	C₄²	—	5	1	no	—
526	C₄²	—	5	1	no	—
527	C₄²	—	5	2	no	—
528	C₄²	—	5	2	no	—
529	C₄²	—	5	2	no	—
530	C₄²	—	5	1	no	—
531	C₄²	—	5	1	no	—
532	C₄²	C₂²×D₅	1	2	yes	—
533	C₄²	C₂²×D₅	1	1	yes	characteristic
534	C₄²	C₂²×D₅	1	2	yes	—
535	C₄²	C₂²×D₅	1	1	yes	characteristic
536	C₄²	C₂²×D₅	1	1	yes	characteristic
537	C₂×C₅	—	4	2	no	—
538	C₂×C₅	C₂²×#41	1	1	yes	characteristic
539	C₂×C₅	#585	1	1	yes	characteristic
540	C₂×C₅	#585	1	1	yes	characteristic
541	D₅	—	2	2	no	—
542	D₅	—	4	2	no	—
543	D₅	—	4	2	no	—
544	C₂³	—	5	1	no	—
545	C₂³	—	5	2	no	—
546	C₂³	—	5	2	no	—
547	C₂³	—	10	4	no	—
548	C₂³	—	20	2	no	—
549	C₂³	—	20	2	no	—
550	C₂³	C₂³×D₅	1	2	yes	—
551	Q₈	—	2	2	no	—
552	Q₈	—	2	2	no	—
553	Q₈	—	4	1	no	—
554	Q₈	—	10	4	no	—
555	Q₈	—	10	2	no	—
556	Q₈	—	20	1	no	—
557	Q₈	—	20	1	no	—
558	Q₈	—	20	1	no	—
559	D₄	—	2	2	no	—
560	D₄	—	10	4	no	—
561	D₄	—	10	4	no	—
562	D₄	—	10	2	no	—
563	D₄	—	10	2	no	—
564	D₄	—	20	2	no	—
565	D₄	—	20	2	no	—
566	D₄	—	20	2	no	—
567	D₄	—	20	2	no	—
568	C₂×C₄	—	4	2	no	—
569	C₂×C₄	—	5	1	no	—
570	C₂×C₄	—	5	4	no	—
571	C₂×C₄	—	5	1	no	—
572	C₂×C₄	—	5	2	no	—
573	C₂×C₄	—	5	1	no	—
574	C₂×C₄	—	5	1	no	—
575	C₂×C₄	—	5	2	no	—
576	C₂×C₄	—	5	1	no	—
577	C₂×C₄	—	5	1	no	—
578	C₂×C₄	—	5	1	no	—
579	C₂×C₄	—	10	4	no	—
580	C₂×C₄	—	10	4	no	—
581	C₂×C₄	—	20	2	no	—
582	C₂×C₄	—	20	2	no	—
583	C₂×C₄	—	20	1	no	—
584	C₂×C₄	—	20	2	no	—
585	C₂×C₄	—	20	1	no	—
586	C₂×C₄	—	20	2	no	—
587	C₂×C₄	—	20	2	no	—
588	C₂×C₄	C₂³×D₅	1	2	yes	—
589	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
590	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
591	C₂×C₄	C₂³×D₅	1	2	yes	—
592	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
593	C₂×C₄	C₂³×D₅	1	2	yes	—
594	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
595	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
596	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
597	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
598	C₅	#3510	1	1	yes	characteristic, complemented, Sylow
599	C₂²	—	2	2	no	—
600	C₂²	—	2	2	no	—
601	C₂²	—	2	2	no	—
602	C₂²	—	5	2	no	—
603	C₂²	—	10	1	no	—
604	C₂²	—	10	1	no	—
605	C₂²	—	10	2	no	—
606	C₂²	—	10	2	no	—
607	C₂²	—	10	2	no	—
608	C₂²	—	10	2	no	—
609	C₂²	—	10	2	no	—
610	C₂²	—	10	2	no	—
611	C₂²	—	40	4	no	—
612	C₂²	C₂⁴×D₅	1	1	yes	characteristic
613	C₄	—	2	2	no	—
614	C₄	—	2	2	no	—
615	C₄	—	2	1	no	—
616	C₄	—	2	2	no	—
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	1	no	—
622	C₄	—	5	2	no	—
623	C₄	—	10	2	no	—
624	C₄	—	10	1	no	—
625	C₄	—	10	1	no	—
626	C₄	—	10	1	no	—
627	C₄	—	10	2	no	—
628	C₄	—	10	1	no	—
629	C₄	—	10	1	no	—
630	C₄	—	10	1	no	—
631	C₄	D₅×#41	1	2	yes	—
632	C₂	—	4	2	no	—
633	C₂	—	10	2	no	—
634	C₂	—	20	2	no	—
635	C₂	—	20	2	no	—
636	C₂	C₂×D₅×#41	1	1	yes	characteristic
637	C₂	#66283	1	1	yes	characteristic
638	C₂	#66287	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁵
Fitting	C₅×#556	C₂
prime radical	#66008	C₂
hypercenter	#556	D₅
hypocenter	C₅	#3510
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #556

Complements

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

N	H ≅ G/N	type
1. C₅×#556	C₂	semidirect
2. #66066	C₂	semidirect
3. #66058	C₂	semidirect
4. #66044	C₂	semidirect
5. #66040	C₂	semidirect
6. #66039	C₂	semidirect
7. #66039	C₂	semidirect
8. #66015	C₂	semidirect
10. D₅×#124	C₂	semidirect
11. #66005	C₂	semidirect
12. #65974	C₂	semidirect
13. #65971	C₂	semidirect
14. #65919	C₂	semidirect
15. #65919	C₂	semidirect
16. #65912	C₂	semidirect
17. C₄×#713	C₂	semidirect
18. #65906	C₂	semidirect
19. #65902	C₂	semidirect
20. #65893	C₂	semidirect
21. #65879	C₂	semidirect
22. #65862	C₂	semidirect
23. #65861	C₂	semidirect
27. C₅×C₄⋊Q₈	C₂²	semidirect
28. C₅×#126	C₂²	semidirect
29. C₅×#126	C₂²	semidirect
32. C₅×C₂²⋊Q₈	C₂²	semidirect
33. C₄×C₅×Q₈	C₂²	semidirect
34. C₄×C₅×Q₈	C₂²	semidirect
35. C₄×C₅×Q₈	C₂²	semidirect
37. C₅×#117	C₂²	semidirect
40. #4093	C₂²	semidirect
41. #4093	C₂²	semidirect
43. Q₈×Dic₅	C₂²	semidirect
44. Q₈×Dic₅	C₂²	semidirect
45. #4090	C₂²	semidirect
46. #4090	C₂²	semidirect
50. #4075	C₂²	semidirect
52. C₄×C₂²⋊D₅	C₂²	semidirect
54. #4044	C₂²	semidirect
55. #4044	C₂²	semidirect
56. #4044	C₂²	semidirect
58. #4043	C₂²	semidirect
61. #4042	C₂²	semidirect
62. #4042	C₂²	semidirect
63. #4042	C₂²	semidirect
66. #4040	C₂²	semidirect
67. #4040	C₂²	semidirect
68. #4040	C₂²	semidirect
69. #4040	C₂²	semidirect
72. #4039	C₂²	semidirect
73. #4039	C₂²	semidirect
76. #4038	C₂²	semidirect
77. #4038	C₂²	semidirect
78. #4035	C₂²	semidirect
79. #4035	C₂²	semidirect
80. #4034	C₂²	semidirect
81. #4033	C₂²	semidirect
82. #4033	C₂²	semidirect
83. #4032	C₂²	semidirect
86. #4031	C₂²	semidirect
87. #4031	C₂²	semidirect
90. #4029	C₂²	semidirect
91. #4029	C₂²	semidirect
95. #4027	C₂²	semidirect
99. #4025	C₂²	semidirect
100. #4025	C₂²	semidirect
101. #4024	C₂²	semidirect
102. #4023	C₂²	semidirect
103. #4022	C₂²	semidirect
105. #4021	C₂²	semidirect
106. #4021	C₂²	semidirect
110. C₄×D₂₀	C₂²	semidirect
111. C₄×D₂₀	C₂²	semidirect
115. #4018	C₂²	semidirect
117. C₄²×D₅	C₂²	semidirect
118. C₄×Dic₁₀	C₂²	semidirect
119. C₄×Dic₁₀	C₂²	semidirect
120. C₄×Dic₁₀	C₂²	semidirect
121. C₄×Dic₁₀	C₂²	semidirect
122. C₄×Dic₁₀	C₂²	semidirect
233. #556	D₅	semidirect
309. C₄⋊Q₈	C₂×D₅	semidirect
318. #126	C₂×D₅	semidirect
319. #126	C₂×D₅	semidirect
355. C₂²⋊Q₈	C₂×D₅	semidirect
369. C₄×Q₈	C₂×D₅	semidirect
370. C₄×Q₈	C₂×D₅	semidirect
371. C₄×Q₈	C₂×D₅	semidirect
395. #117	C₂×D₅	semidirect
598. C₅	#3510	semidirect

Maximal subgroups

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

subgroup	index
C₅×#556	2
#66066	2
#66058	2
#66044	2
#66040	2
#66039	2
#66015	2
#66008	2
D₅×#124	2
#66005	2
#65974	2
#65971	2
#65919	2
#65912	2
C₄×#713	2
#65906	2
#65902	2
#65893	2
#65879	2
#65862	2
#65861	2
#3510	5