Subgroups — #10618913

Order 640.

910 conjugacy classes of subgroups.

The subgroup lattice has 594 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	#66065	C₂	1	1	yes	maximal, characteristic, complemented
3	#66055	C₂	1	1	yes	maximal, characteristic, complemented
4	#66046	C₂	1	2	yes	maximal, complemented
5	#66036	C₂	1	2	yes	maximal, complemented
6	#66035	C₂	1	2	yes	maximal, complemented
7	#66035	C₂	1	2	yes	maximal, complemented
8	#66016	C₂	1	1	yes	maximal, characteristic
9	#66014	C₂	1	1	yes	maximal, characteristic
10	#66005	C₂	1	1	yes	maximal, characteristic, complemented
11	#66005	C₂	1	1	yes	maximal, characteristic, complemented
12	#65980	C₂	1	2	yes	maximal, complemented
13	#65957	C₂	1	2	yes	maximal, complemented
14	#65917	C₂	1	1	yes	maximal, characteristic, complemented
15	#65912	C₂	1	1	yes	maximal, characteristic, complemented
16	#65912	C₂	1	1	yes	maximal, characteristic, complemented
17	#65903	C₂	1	1	yes	maximal, characteristic, complemented
18	#65901	C₂	1	1	yes	maximal, characteristic, complemented
19	Q₈×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
20	#65895	C₂	1	1	yes	maximal, characteristic
21	#65873	C₂	1	1	yes	maximal, characteristic, complemented
22	#65865	C₂	1	2	yes	maximal, complemented
23	#65852	C₂	1	2	yes	maximal, complemented
24	C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₅×#126	C₂²	1	2	yes	—
26	C₅×#126	C₂²	1	2	yes	—
27	C₅×#124	C₂²	1	1	yes	characteristic
28	C₅×#124	C₂²	1	1	yes	characteristic
29	C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
31	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
32	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
33	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
34	C₅×#117	C₂²	1	2	yes	—
35	#4092	C₂²	1	1	yes	characteristic
36	#4092	C₂²	1	1	yes	characteristic
37	#4092	C₂²	1	1	yes	characteristic
38	Q₈×Dic₅	C₂²	1	1	yes	characteristic
39	Q₈×Dic₅	C₂²	1	1	yes	characteristic
40	Q₈×Dic₅	C₂²	1	1	yes	characteristic
41	Q₈×Dic₅	C₂²	1	1	yes	characteristic
42	#4090	C₂²	1	1	yes	characteristic
43	#4090	C₂²	1	1	yes	characteristic
44	#4090	C₂²	1	2	yes	—
45	#4090	C₂²	1	1	yes	characteristic
46	#4084	C₂²	1	1	yes	characteristic
47	#4082	C₂²	1	1	yes	characteristic
48	D₄×Dic₅	C₂²	1	1	yes	characteristic
49	D₄×Dic₅	C₂²	1	1	yes	characteristic
50	#4075	C₂²	1	2	yes	—
51	#4070	C₂²	1	2	yes	—
52	#4070	C₂²	1	2	yes	—
53	C₂×#683	C₂²	1	2	yes	—
54	#4044	C₂²	1	2	yes	—
55	#4044	C₂²	1	2	yes	—
56	#4044	C₂²	1	2	yes	—
57	#4043	C₂²	1	1	yes	characteristic
58	#4043	C₂²	1	1	yes	characteristic
59	#4042	C₂²	1	1	yes	characteristic
60	#4042	C₂²	1	2	yes	—
61	#4042	C₂²	1	1	yes	characteristic
62	#4036	C₂²	1	2	yes	—
63	#4036	C₂²	1	1	yes	characteristic
64	#4036	C₂²	1	2	yes	—
65	#4035	C₂²	1	2	yes	—
66	#4035	C₂²	1	2	yes	—
67	#4035	C₂²	1	2	yes	—
68	#4035	C₂²	1	2	yes	—
69	#4035	C₂²	1	1	yes	characteristic
70	#4035	C₂²	1	2	yes	—
71	#4035	C₂²	1	2	yes	—
72	#4035	C₂²	1	2	yes	—
73	#4035	C₂²	1	1	yes	characteristic
74	#4035	C₂²	1	2	yes	—
75	#4034	C₂²	1	1	yes	characteristic
76	#4034	C₂²	1	1	yes	characteristic
77	#4034	C₂²	1	2	yes	—
78	#4034	C₂²	1	2	yes	—
79	#4034	C₂²	1	2	yes	—
80	#4034	C₂²	1	1	yes	characteristic
81	#4033	C₂²	1	2	yes	—
82	#4033	C₂²	1	2	yes	—
83	#4032	C₂²	1	2	yes	—
84	#4031	C₂²	1	2	yes	—
85	#4031	C₂²	1	2	yes	—
86	#4029	C₂²	1	2	yes	—
87	#4027	C₂²	1	2	yes	—
88	#4025	C₂²	1	2	yes	—
89	#4025	C₂²	1	2	yes	—
90	#4025	C₂²	1	2	yes	—
91	#4025	C₂²	1	2	yes	—
92	#4025	C₂²	1	2	yes	—
93	#4025	C₂²	1	2	yes	—
94	#4025	C₂²	1	2	yes	—
95	#4024	C₂²	1	2	yes	—
96	#4024	C₂²	1	2	yes	—
97	#4024	C₂²	1	2	yes	—
98	#4024	C₂²	1	2	yes	—
99	#4024	C₂²	1	2	yes	—
100	#4023	C₂²	1	2	yes	—
101	#4023	C₂²	1	2	yes	—
102	#4023	C₂²	1	2	yes	—
103	#4022	C₂²	1	2	yes	—
104	#4018	C₂²	1	1	yes	characteristic
105	#4018	C₂²	1	2	yes	—
106	#4018	C₂²	1	1	yes	characteristic
107	C₄²×D₅	C₂²	1	1	yes	characteristic
108	#4016	C₂²	1	1	yes	characteristic
109	#4016	C₂²	1	2	yes	—
110	#4016	C₂²	1	2	yes	—
111	#4016	C₂²	1	1	yes	characteristic
112	#4015	C₂²	1	2	yes	—
113	#4015	C₂²	1	1	yes	characteristic
114	C₄×Dic₁₀	C₂²	1	1	yes	characteristic
115	C₄×Dic₁₀	C₂²	1	1	yes	characteristic
116	C₄×Dic₁₀	C₂²	1	2	yes	—
117	C₄×Dic₁₀	C₂²	1	2	yes	—
118	C₄×Dic₁₀	C₂²	1	2	yes	—
119	C₄×Dic₁₀	C₂²	1	1	yes	characteristic
120	C₄×Dic₁₀	C₂²	1	1	yes	characteristic
121	C₄×Dic₁₀	C₂²	1	1	yes	characteristic
122	C₄×Dic₁₀	C₂²	1	1	yes	characteristic
123	#3555	—	5	1	no	maximal, Sylow
124	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
125	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
126	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
127	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₅	C₂³	1	2	yes	—
129	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
130	C₂²×Dic₅	C₂³	1	2	yes	—
131	C₂²×Dic₅	C₂³	1	2	yes	—
132	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
133	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
134	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
135	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
136	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
137	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
138	C₂×Dic₁₀	C₂³	1	2	yes	—
139	C₂×Dic₁₀	C₂³	1	2	yes	—
140	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
141	C₂×Dic₁₀	C₂³	1	2	yes	—
142	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
143	C₅×C₄⋊C₄	C₂³	1	2	yes	—
144	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
145	C₅×C₄⋊C₄	C₂³	1	2	yes	—
146	C₅×C₄⋊C₄	C₂³	1	2	yes	—
147	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
148	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₅×C₄⋊C₄	C₂³	1	2	yes	—
150	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
151	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
152	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
153	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
154	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
155	C₄²×C₅	C₂³	1	2	yes	—
156	C₄²×C₅	C₂³	1	2	yes	—
157	C₄²×C₅	C₂³	1	1	yes	characteristic
158	C₄²×C₅	C₂³	1	1	yes	characteristic
159	C₄²×C₅	C₂³	1	1	yes	characteristic
160	C₂²⋊Dic₅	C₂³	1	2	yes	—
161	C₂²⋊Dic₅	C₂³	1	2	yes	—
162	C₂²⋊Dic₅	C₂³	1	2	yes	—
163	C₂²⋊Dic₅	C₂³	1	2	yes	—
164	C₂²⋊Dic₅	C₂³	1	2	yes	—
165	#685	C₂³	1	1	yes	characteristic
166	#685	C₂³	1	2	yes	—
167	#685	C₂³	1	1	yes	characteristic
168	#685	C₂³	1	1	yes	characteristic
169	#685	C₂³	1	2	yes	—
170	#685	C₂³	1	1	yes	characteristic
171	#685	C₂³	1	2	yes	—
172	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
173	C₄⋊Dic₅	C₂³	1	2	yes	—
174	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
175	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
176	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
177	C₄⋊Dic₅	C₂³	1	2	yes	—
178	C₄⋊Dic₅	C₂³	1	2	yes	—
179	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
180	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
181	C₄⋊Dic₅	C₂³	1	2	yes	—
182	C₄⋊Dic₅	C₂³	1	2	yes	—
183	C₄⋊Dic₅	C₂³	1	2	yes	—
184	C₄⋊Dic₅	C₂³	1	2	yes	—
185	#683	C₂³	1	1	yes	characteristic
186	#683	C₂³	1	1	yes	characteristic
187	#683	C₂³	1	2	yes	—
188	#683	C₂³	1	2	yes	—
189	#683	C₂³	1	2	yes	—
190	#683	C₂³	1	2	yes	—
191	#683	C₂³	1	1	yes	characteristic
192	#683	C₂³	1	2	yes	—
193	#683	C₂³	1	2	yes	—
194	#683	C₂³	1	1	yes	characteristic
195	#683	C₂³	1	2	yes	—
196	#683	C₂³	1	1	yes	characteristic
197	#683	C₂³	1	2	yes	—
198	#683	C₂³	1	1	yes	characteristic
199	#683	C₂³	1	1	yes	characteristic
200	#683	C₂³	1	2	yes	—
201	#683	C₂³	1	2	yes	—
202	#683	C₂³	1	2	yes	—
203	#683	C₂³	1	2	yes	—
204	#683	C₂³	1	2	yes	—
205	#683	C₂³	1	2	yes	—
206	#683	C₂³	1	2	yes	—
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	C₄×Dic₅	C₂³	1	1	yes	characteristic
212	C₄×Dic₅	C₂³	1	1	yes	characteristic
213	C₄×Dic₅	C₂³	1	2	yes	—
214	C₄×Dic₅	C₂³	1	1	yes	characteristic
215	C₄×Dic₅	C₂³	1	1	yes	characteristic
216	C₄×Dic₅	C₂³	1	2	yes	—
217	C₄×Dic₅	C₂³	1	2	yes	—
218	C₄×Dic₅	C₂³	1	2	yes	—
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	#563	—	5	2	no	—
224	#563	—	5	2	no	—
225	Q₈²	—	5	1	no	—
226	#557	—	5	1	no	—
227	#557	—	5	1	no	—
228	#557	—	5	1	no	—
229	#556	—	5	2	no	—
230	#556	—	5	1	no	—
231	#556	—	5	1	no	—
232	#556	D₅	1	1	yes	characteristic, complemented
233	#554	—	5	1	no	—
234	#552	—	5	2	no	—
235	#544	—	5	2	no	—
236	#542	—	5	1	no	—
237	#542	—	5	1	no	—
238	#541	—	5	1	no	—
239	#541	—	5	2	no	—
240	#541	—	5	2	no	—
241	#541	—	5	1	no	—
242	#541	—	5	2	no	—
243	#533	—	5	1	no	—
244	#533	—	5	1	no	—
245	#529	—	5	1	no	—
246	C₂³×C₅	C₂⁴	1	2	yes	—
247	C₂²×D₅	C₂⁴	1	1	yes	characteristic
248	C₅×Q₈	—	2	2	no	—
249	C₅×Q₈	—	2	2	no	—
250	C₅×Q₈	—	4	1	no	—
251	C₅×D₄	—	2	2	no	—
252	C₂×C₄×C₅	—	4	2	no	—
253	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₅	C₂⁴	1	2	yes	—
255	C₂×C₄×C₅	C₂⁴	1	2	yes	—
256	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
258	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
259	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
260	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
261	C₂×C₄×C₅	C₂⁴	1	2	yes	—
262	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
263	C₂²⋊D₅	—	4	2	no	—
264	C₂×Dic₅	—	2	4	no	—
265	C₂×Dic₅	—	4	2	no	—
266	C₂×Dic₅	C₂⁴	1	2	yes	—
267	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
268	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₅	C₂⁴	1	2	yes	—
270	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₅	C₂⁴	1	2	yes	—
273	C₂×Dic₅	C₂⁴	1	2	yes	—
274	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
275	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
276	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
277	C₄×D₅	—	2	2	no	—
278	C₄×D₅	—	2	2	no	—
279	C₄×D₅	—	4	1	no	—
280	Dic₁₀	—	2	2	no	—
281	Dic₁₀	—	2	2	no	—
282	Dic₁₀	—	2	2	no	—
283	Dic₁₀	—	4	2	no	—
284	Dic₁₀	—	4	1	no	—
285	Dic₁₀	—	4	2	no	—
286	Dic₁₀	—	4	2	no	—
287	C₄⋊Q₈	—	5	1	no	—
288	C₄⋊Q₈	—	5	1	no	—
289	C₄⋊Q₈	—	5	1	no	—
290	C₄⋊Q₈	—	5	2	no	—
291	C₄⋊Q₈	—	5	1	no	—
292	C₄⋊Q₈	—	5	1	no	—
293	C₄⋊Q₈	—	5	2	no	—
294	C₄⋊Q₈	—	5	1	no	—
295	C₄⋊Q₈	—	5	2	no	—
296	C₄⋊Q₈	—	5	2	no	—
297	C₄⋊Q₈	—	5	2	no	—
298	C₄⋊Q₈	—	5	1	no	—
299	C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic
300	#126	—	5	2	no	—
301	#126	—	5	2	no	—
302	#126	—	5	2	no	—
303	#126	—	5	2	no	—
304	#126	—	5	2	no	—
305	#126	—	5	2	no	—
306	#126	—	5	2	no	—
307	#126	—	5	2	no	—
308	#126	—	5	2	no	—
309	#126	—	5	2	no	—
310	#126	—	5	2	no	—
311	#126	C₂×D₅	1	2	yes	—
312	#126	C₂×D₅	1	2	yes	—
313	#125	—	5	1	no	—
314	#125	—	5	1	no	—
315	#125	—	5	2	no	—
316	#125	—	5	2	no	—
317	#125	—	5	2	no	—
318	#125	—	5	2	no	—
319	#125	—	5	2	no	—
320	#125	—	5	1	no	—
321	#125	—	5	2	no	—
322	#125	—	5	2	no	—
323	#125	—	5	2	no	—
324	#125	—	5	2	no	—
325	#125	—	5	2	no	—
326	#125	—	5	1	no	—
327	#125	—	5	2	no	—
328	#125	—	5	2	no	—
329	#125	—	5	1	no	—
330	#124	—	5	1	no	—
331	#124	—	5	2	no	—
332	#124	—	5	2	no	—
333	#124	C₂×D₅	1	1	yes	characteristic
334	#124	C₂×D₅	1	1	yes	characteristic
335	#123	—	5	2	no	—
336	#123	—	5	2	no	—
337	#123	—	5	2	no	—
338	C₂²⋊Q₈	—	5	1	no	—
339	C₂²⋊Q₈	—	5	1	no	—
340	C₂²⋊Q₈	—	5	1	no	—
341	C₂²⋊Q₈	—	5	2	no	—
342	C₂²⋊Q₈	—	5	2	no	—
343	C₂²⋊Q₈	—	5	1	no	—
344	C₂²⋊Q₈	—	5	1	no	—
345	C₂²⋊Q₈	—	5	1	no	—
346	C₂²⋊Q₈	—	5	2	no	—
347	C₂²⋊Q₈	—	5	1	no	—
348	C₂²⋊Q₈	—	5	2	no	—
349	C₂²⋊Q₈	—	5	2	no	—
350	C₂²⋊Q₈	—	5	2	no	—
351	C₂²⋊Q₈	—	5	2	no	—
352	C₂²⋊Q₈	—	5	2	no	—
353	C₂²⋊Q₈	C₂×D₅	1	2	yes	—
354	#121	—	5	1	no	—
355	C₄×Q₈	—	5	1	no	—
356	C₄×Q₈	—	5	1	no	—
357	C₄×Q₈	—	5	1	no	—
358	C₄×Q₈	—	5	1	no	—
359	C₄×Q₈	—	5	2	no	—
360	C₄×Q₈	—	5	2	no	—
361	C₄×Q₈	—	5	2	no	—
362	C₄×Q₈	—	5	1	no	—
363	C₄×Q₈	—	5	1	no	—
364	C₄×Q₈	—	5	1	no	—
365	C₄×Q₈	—	5	1	no	—
366	C₄×Q₈	—	5	2	no	—
367	C₄×Q₈	—	5	1	no	—
368	C₄×Q₈	—	5	2	no	—
369	C₄×Q₈	—	5	1	no	—
370	C₄×Q₈	C₂×D₅	1	1	yes	characteristic
371	C₄×Q₈	C₂×D₅	1	1	yes	characteristic
372	C₄×Q₈	C₂×D₅	1	1	yes	characteristic
373	C₄×D₄	—	5	1	no	—
374	C₄×D₄	—	5	1	no	—
375	C₄×D₄	—	5	2	no	—
376	C₄×D₄	C₂×D₅	1	1	yes	characteristic
377	#117	—	5	2	no	—
378	#117	—	5	2	no	—
379	#117	—	5	2	no	—
380	#117	—	5	1	no	—
381	#117	—	5	1	no	—
382	#117	—	5	2	no	—
383	#117	C₂×D₅	1	2	yes	—
384	C₂×C₄⋊C₄	—	5	2	no	—
385	C₂×C₄²	—	5	1	no	—
386	C₂²×C₅	—	2	2	no	—
387	C₂²×C₅	—	2	2	no	—
388	C₂²×C₅	—	2	2	no	—
389	C₂²×C₅	C₂⁵	1	1	yes	characteristic
390	C₂×D₅	—	2	1	no	—
391	C₂×D₅	—	2	1	no	—
392	C₂×D₅	—	2	1	no	—
393	C₄×C₅	—	2	1	no	—
394	C₄×C₅	—	2	1	no	—
395	C₄×C₅	—	2	1	no	—
396	C₄×C₅	—	2	2	no	—
397	C₄×C₅	—	2	2	no	—
398	C₄×C₅	—	2	2	no	—
399	C₄×C₅	—	2	1	no	—
400	C₄×C₅	—	2	1	no	—
401	C₄×C₅	—	2	1	no	—
402	C₄×C₅	2₋¹⁺⁴	1	2	yes	—
403	Dic₅	—	2	2	no	—
404	Dic₅	—	2	1	no	—
405	Dic₅	—	2	1	no	—
406	Dic₅	—	2	1	no	—
407	Dic₅	—	2	2	no	—
408	Dic₅	—	2	1	no	—
409	Dic₅	—	2	1	no	—
410	Dic₅	—	2	2	no	—
411	Dic₅	—	2	2	no	—
412	Dic₅	—	2	1	no	—
413	Dic₅	2₋¹⁺⁴	1	2	yes	—
414	C₂×Q₈	—	5	1	no	—
415	C₂×Q₈	—	5	1	no	—
416	C₂×Q₈	—	5	1	no	—
417	C₂×Q₈	—	5	1	no	—
418	C₂×Q₈	—	5	2	no	—
419	C₂×Q₈	—	5	2	no	—
420	C₂×Q₈	—	5	2	no	—
421	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
422	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
423	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
424	C₂×D₄	—	5	2	no	—
425	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
426	C₂²×C₄	—	5	2	no	—
427	C₂²×C₄	—	5	2	no	—
428	C₂²×C₄	—	5	1	no	—
429	C₂²×C₄	—	5	1	no	—
430	C₂²×C₄	—	5	1	no	—
431	C₂²×C₄	C₂²×D₅	1	2	yes	—
432	C₄⋊C₄	—	5	1	no	—
433	C₄⋊C₄	—	5	2	no	—
434	C₄⋊C₄	—	5	2	no	—
435	C₄⋊C₄	—	5	2	no	—
436	C₄⋊C₄	—	5	1	no	—
437	C₄⋊C₄	—	5	2	no	—
438	C₄⋊C₄	—	5	1	no	—
439	C₄⋊C₄	—	5	1	no	—
440	C₄⋊C₄	—	5	1	no	—
441	C₄⋊C₄	—	5	2	no	—
442	C₄⋊C₄	—	5	2	no	—
443	C₄⋊C₄	—	5	2	no	—
444	C₄⋊C₄	—	5	1	no	—
445	C₄⋊C₄	—	5	1	no	—
446	C₄⋊C₄	—	5	1	no	—
447	C₄⋊C₄	—	5	1	no	—
448	C₄⋊C₄	—	5	2	no	—
449	C₄⋊C₄	—	5	1	no	—
450	C₄⋊C₄	—	5	1	no	—
451	C₄⋊C₄	—	5	1	no	—
452	C₄⋊C₄	—	5	1	no	—
453	C₄⋊C₄	—	5	2	no	—
454	C₄⋊C₄	—	5	2	no	—
455	C₄⋊C₄	—	5	2	no	—
456	C₄⋊C₄	—	5	2	no	—
457	C₄⋊C₄	—	5	2	no	—
458	C₄⋊C₄	—	5	2	no	—
459	C₄⋊C₄	—	5	2	no	—
460	C₄⋊C₄	—	5	2	no	—
461	C₄⋊C₄	—	5	2	no	—
462	C₄⋊C₄	—	5	2	no	—
463	C₄⋊C₄	—	5	1	no	—
464	C₄⋊C₄	—	5	1	no	—
465	C₄⋊C₄	—	5	2	no	—
466	C₄⋊C₄	—	5	1	no	—
467	C₄⋊C₄	—	5	2	no	—
468	C₄⋊C₄	—	5	2	no	—
469	C₄⋊C₄	—	5	2	no	—
470	C₄⋊C₄	—	5	2	no	—
471	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
472	C₄⋊C₄	C₂²×D₅	1	2	yes	—
473	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
474	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
475	C₄⋊C₄	C₂²×D₅	1	2	yes	—
476	C₄⋊C₄	C₂²×D₅	1	2	yes	—
477	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
478	C₄⋊C₄	C₂²×D₅	1	2	yes	—
479	C₂²⋊C₄	—	5	2	no	—
480	C₂²⋊C₄	—	5	2	no	—
481	C₂²⋊C₄	—	5	2	no	—
482	C₂²⋊C₄	—	5	2	no	—
483	C₂²⋊C₄	—	5	2	no	—
484	C₂²⋊C₄	—	5	1	no	—
485	C₂²⋊C₄	—	5	1	no	—
486	C₂²⋊C₄	—	5	2	no	—
487	C₂²⋊C₄	—	5	2	no	—
488	C₂²⋊C₄	—	5	1	no	—
489	C₂²⋊C₄	—	5	1	no	—
490	C₂²⋊C₄	—	5	2	no	—
491	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
492	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
493	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
494	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
495	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
496	C₄²	—	5	1	no	—
497	C₄²	—	5	1	no	—
498	C₄²	—	5	1	no	—
499	C₄²	—	5	2	no	—
500	C₄²	—	5	2	no	—
501	C₄²	—	5	1	no	—
502	C₄²	—	5	1	no	—
503	C₄²	—	5	2	no	—
504	C₄²	—	5	2	no	—
505	C₄²	—	5	2	no	—
506	C₄²	—	5	2	no	—
507	C₄²	—	5	2	no	—
508	C₄²	C₂²×D₅	1	1	yes	characteristic
509	C₄²	C₂²×D₅	1	2	yes	—
510	C₄²	C₂²×D₅	1	1	yes	characteristic
511	C₄²	C₂²×D₅	1	1	yes	characteristic
512	C₄²	C₂²×D₅	1	2	yes	—
513	C₂×C₅	—	4	2	no	—
514	C₂×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
515	C₂×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
516	C₂×C₅	#585	1	1	yes	characteristic
517	D₅	—	4	1	no	—
518	C₂³	—	5	1	no	—
519	C₂³	C₂³×D₅	1	2	yes	—
520	Q₈	—	2	2	no	—
521	Q₈	—	2	2	no	—
522	Q₈	—	4	1	no	—
523	Q₈	—	10	2	no	—
524	Q₈	—	10	2	no	—
525	Q₈	—	10	2	no	—
526	Q₈	—	20	2	no	—
527	Q₈	—	20	2	no	—
528	Q₈	—	20	1	no	—
529	Q₈	—	20	2	no	—
530	D₄	—	2	2	no	—
531	D₄	—	20	2	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	5	1	no	—
534	C₂×C₄	—	5	2	no	—
535	C₂×C₄	—	5	1	no	—
536	C₂×C₄	—	5	1	no	—
537	C₂×C₄	—	5	1	no	—
538	C₂×C₄	—	5	2	no	—
539	C₂×C₄	—	5	1	no	—
540	C₂×C₄	—	5	2	no	—
541	C₂×C₄	—	5	1	no	—
542	C₂×C₄	—	5	2	no	—
543	C₂×C₄	—	5	1	no	—
544	C₂×C₄	—	10	2	no	—
545	C₂×C₄	—	10	4	no	—
546	C₂×C₄	—	10	2	no	—
547	C₂×C₄	—	20	1	no	—
548	C₂×C₄	—	20	2	no	—
549	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
550	C₂×C₄	C₂³×D₅	1	2	yes	—
551	C₂×C₄	C₂³×D₅	1	2	yes	—
552	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
553	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
554	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
555	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
556	C₂×C₄	C₂³×D₅	1	2	yes	—
557	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
558	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
559	C₅	#3555	1	1	yes	characteristic, complemented, Sylow
560	C₂²	—	2	2	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	2	2	no	—
563	C₂²	—	10	1	no	—
564	C₂²	—	10	1	no	—
565	C₂²	—	10	1	no	—
566	C₂²	C₂⁴×D₅	1	1	yes	characteristic
567	C₄	—	2	2	no	—
568	C₄	—	2	2	no	—
569	C₄	—	2	1	no	—
570	C₄	—	2	2	no	—
571	C₄	—	2	1	no	—
572	C₄	—	2	1	no	—
573	C₄	—	2	1	no	—
574	C₄	—	2	1	no	—
575	C₄	—	2	1	no	—
576	C₄	—	5	2	no	—
577	C₄	—	10	1	no	—
578	C₄	—	10	2	no	—
579	C₄	—	10	1	no	—
580	C₄	—	10	1	no	—
581	C₄	—	10	2	no	—
582	C₄	—	10	2	no	—
583	C₄	—	10	1	no	—
584	C₄	—	10	2	no	—
585	C₄	—	10	1	no	—
586	C₄	—	10	1	no	—
587	C₄	#4150	1	2	yes	—
588	C₂	—	4	2	no	—
589	C₂	—	20	1	no	—
590	C₂	C₂×#4150	1	1	yes	characteristic
591	C₂	#66283	1	1	yes	characteristic
592	C₂	D₅×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁵
Fitting	C₅×#556	C₂
prime radical	#4084	C₂²
hypercenter	#556	D₅
hypocenter	C₅	#3555
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. #66065	C₂	semidirect
3. #66055	C₂	semidirect
4. #66046	C₂	semidirect
5. #66036	C₂	semidirect
6. #66035	C₂	semidirect
7. #66035	C₂	semidirect
10. #66005	C₂	semidirect
11. #66005	C₂	semidirect
12. #65980	C₂	semidirect
13. #65957	C₂	semidirect
14. #65917	C₂	semidirect
15. #65912	C₂	semidirect
16. #65912	C₂	semidirect
17. #65903	C₂	semidirect
18. #65901	C₂	semidirect
19. Q₈×Dic₁₀	C₂	semidirect
21. #65873	C₂	semidirect
22. #65865	C₂	semidirect
23. #65852	C₂	semidirect
232. #556	D₅	semidirect
559. C₅	#3555	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
#66065	2
#66055	2
#66046	2
#66036	2
#66035	2
#66016	2
#66014	2
#66005	2
#65980	2
#65957	2
#65917	2
#65912	2
#65903	2
#65901	2
Q₈×Dic₁₀	2
#65895	2
#65873	2
#65865	2
#65852	2
#3555	5