Subgroups — #10618828

Order 640.

988 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	#66063	C₂	1	1	yes	maximal, characteristic, complemented
3	#66055	C₂	1	1	yes	maximal, characteristic, complemented
4	#66023	C₂	1	1	yes	maximal, characteristic, complemented
5	D₅×#125	C₂	1	1	yes	maximal, characteristic, complemented
6	#66019	C₂	1	1	yes	maximal, characteristic, complemented
7	#66019	C₂	1	1	yes	maximal, characteristic, complemented
8	#65970	C₂	1	2	yes	maximal, complemented
9	#65970	C₂	1	2	yes	maximal, complemented
10	#65969	C₂	1	2	yes	maximal, complemented
11	#65957	C₂	1	2	yes	maximal, complemented
12	#65957	C₂	1	2	yes	maximal, complemented
13	#65956	C₂	1	2	yes	maximal, complemented
14	#65912	C₂	1	1	yes	maximal, characteristic, complemented
15	#65901	C₂	1	1	yes	maximal, characteristic, complemented
16	#65880	C₂	1	1	yes	maximal, characteristic
17	#65880	C₂	1	1	yes	maximal, characteristic
18	#65877	C₂	1	1	yes	maximal, characteristic, complemented
19	#65873	C₂	1	1	yes	maximal, characteristic, complemented
20	#65873	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#711	C₂	1	1	yes	maximal, characteristic
22	#65845	C₂	1	2	yes	maximal, complemented
23	C₂×#4035	C₂	1	2	yes	maximal, complemented
24	C₂×#711	C₂²	1	1	yes	characteristic
25	C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₅×#125	C₂²	1	1	yes	characteristic
27	C₅×#125	C₂²	1	1	yes	characteristic
28	C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
31	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
32	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
33	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
34	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
35	C₂×C₅×C₄⋊C₄	C₂²	1	2	yes	—
36	#4092	C₂²	1	2	yes	—
37	#4092	C₂²	1	1	yes	characteristic
38	Q₈×Dic₅	C₂²	1	2	yes	—
39	#4090	C₂²	1	2	yes	—
40	#4090	C₂²	1	2	yes	—
41	#4090	C₂²	1	2	yes	—
42	#4090	C₂²	1	1	yes	characteristic
43	D₄×Dic₅	C₂²	1	1	yes	characteristic
44	D₄×Dic₅	C₂²	1	1	yes	characteristic
45	D₄×Dic₅	C₂²	1	1	yes	characteristic
46	C₄×C₂²⋊D₅	C₂²	1	2	yes	—
47	C₄×C₂²⋊D₅	C₂²	1	2	yes	—
48	C₄×C₂²⋊D₅	C₂²	1	2	yes	—
49	C₂×C₄⋊Dic₅	C₂²	1	2	yes	—
50	#4070	C₂²	1	2	yes	—
51	#4070	C₂²	1	2	yes	—
52	#4070	C₂²	1	2	yes	—
53	C₂×#683	C₂²	1	2	yes	—
54	C₂×#683	C₂²	1	2	yes	—
55	C₂×#683	C₂²	1	2	yes	—
56	C₂×#683	C₂²	1	2	yes	—
57	C₂×C₄×Dic₅	C₂²	1	2	yes	—
58	#4043	C₂²	1	2	yes	—
59	#4043	C₂²	1	1	yes	characteristic
60	#4042	C₂²	1	2	yes	—
61	#4042	C₂²	1	1	yes	characteristic
62	#4042	C₂²	1	1	yes	characteristic
63	#4042	C₂²	1	2	yes	—
64	#4038	C₂²	1	1	yes	characteristic
65	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
66	D₅×C₄⋊C₄	C₂²	1	2	yes	—
67	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
68	D₅×C₄⋊C₄	C₂²	1	2	yes	—
69	#4036	C₂²	1	1	yes	characteristic
70	#4036	C₂²	1	1	yes	characteristic
71	#4036	C₂²	1	1	yes	characteristic
72	#4036	C₂²	1	1	yes	characteristic
73	#4035	C₂²	1	2	yes	—
74	#4035	C₂²	1	2	yes	—
75	#4035	C₂²	1	2	yes	—
76	#4035	C₂²	1	1	yes	characteristic
77	#4035	C₂²	1	2	yes	—
78	#4035	C₂²	1	2	yes	—
79	#4035	C₂²	1	2	yes	—
80	#4035	C₂²	1	2	yes	—
81	#4035	C₂²	1	2	yes	—
82	#4035	C₂²	1	2	yes	—
83	#4035	C₂²	1	1	yes	characteristic
84	#4035	C₂²	1	2	yes	—
85	#4035	C₂²	1	2	yes	—
86	#4035	C₂²	1	2	yes	—
87	#4034	C₂²	1	1	yes	characteristic
88	#4034	C₂²	1	2	yes	—
89	#4034	C₂²	1	1	yes	characteristic
90	#4034	C₂²	1	1	yes	characteristic
91	#4034	C₂²	1	2	yes	—
92	#4034	C₂²	1	2	yes	—
93	#4033	C₂²	1	1	yes	characteristic
94	#4033	C₂²	1	1	yes	characteristic
95	#4033	C₂²	1	2	yes	—
96	#4033	C₂²	1	1	yes	characteristic
97	#4033	C₂²	1	2	yes	—
98	#4033	C₂²	1	2	yes	—
99	#4027	C₂²	1	2	yes	—
100	#4027	C₂²	1	2	yes	—
101	#4027	C₂²	1	2	yes	—
102	#4024	C₂²	1	2	yes	—
103	#4024	C₂²	1	2	yes	—
104	#4024	C₂²	1	2	yes	—
105	#4024	C₂²	1	2	yes	—
106	#4024	C₂²	1	2	yes	—
107	#4024	C₂²	1	2	yes	—
108	#4023	C₂²	1	2	yes	—
109	#4023	C₂²	1	2	yes	—
110	#4023	C₂²	1	2	yes	—
111	#4018	C₂²	1	1	yes	characteristic
112	#4018	C₂²	1	1	yes	characteristic
113	C₄²×D₅	C₂²	1	1	yes	characteristic
114	#4016	C₂²	1	1	yes	characteristic
115	#4016	C₂²	1	1	yes	characteristic
116	#4015	C₂²	1	1	yes	characteristic
117	C₄×Dic₁₀	C₂²	1	1	yes	characteristic
118	C₄×Dic₁₀	C₂²	1	1	yes	characteristic
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	#3504	—	5	1	no	maximal, Sylow
124	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
125	C₂×C₅×Q₈	C₂³	1	2	yes	—
126	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₅	C₂³	1	2	yes	—
128	C₂²×C₄×C₅	C₂³	1	2	yes	—
129	C₂²×C₄×C₅	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
131	C₂²×Dic₅	C₂³	1	2	yes	—
132	C₂²×Dic₅	C₂³	1	2	yes	—
133	C₂²×Dic₅	C₂³	1	2	yes	—
134	C₂²×Dic₅	C₂³	1	2	yes	—
135	#711	Q₈	1	8	yes	complemented
136	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
137	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
138	C₂×C₄×D₅	C₂³	1	2	yes	—
139	C₂×C₄×D₅	C₂³	1	2	yes	—
140	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
141	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
142	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
143	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
144	C₂×Dic₁₀	C₂³	1	2	yes	—
145	C₂×Dic₁₀	C₂³	1	2	yes	—
146	C₂×Dic₁₀	C₂³	1	2	yes	—
147	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
148	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₅×C₄⋊C₄	C₂³	1	2	yes	—
150	C₅×C₄⋊C₄	C₂³	1	2	yes	—
151	C₅×C₄⋊C₄	C₂³	1	2	yes	—
152	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
154	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₅×C₄⋊C₄	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	2	yes	—
159	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
160	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₄²×C₅	C₂³	1	1	yes	characteristic
163	C₄²×C₅	C₂³	1	1	yes	characteristic
164	C₄²×C₅	C₂³	1	1	yes	characteristic
165	C₂²⋊Dic₅	C₂³	1	2	yes	—
166	C₂²⋊Dic₅	C₂³	1	2	yes	—
167	C₂²⋊Dic₅	C₂³	1	2	yes	—
168	#685	C₂³	1	1	yes	characteristic
169	#685	C₂³	1	1	yes	characteristic
170	#685	C₂³	1	1	yes	characteristic
171	#685	C₂³	1	1	yes	characteristic
172	#685	C₂³	1	2	yes	—
173	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
178	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
179	C₄⋊Dic₅	C₂³	1	2	yes	—
180	C₄⋊Dic₅	C₂³	1	2	yes	—
181	C₄⋊Dic₅	C₂³	1	2	yes	—
182	C₄⋊Dic₅	C₂³	1	2	yes	—
183	C₄⋊Dic₅	C₂³	1	2	yes	—
184	#683	C₂³	1	2	yes	—
185	#683	C₂³	1	1	yes	characteristic
186	#683	C₂³	1	1	yes	characteristic
187	#683	C₂³	1	1	yes	characteristic
188	#683	C₂³	1	2	yes	—
189	#683	C₂³	1	1	yes	characteristic
190	#683	C₂³	1	1	yes	characteristic
191	#683	C₂³	1	2	yes	—
192	#683	C₂³	1	1	yes	characteristic
193	#683	C₂³	1	2	yes	—
194	#683	C₂³	1	2	yes	—
195	#683	C₂³	1	2	yes	—
196	#683	C₂³	1	2	yes	—
197	#683	C₂³	1	1	yes	characteristic
198	#683	C₂³	1	1	yes	characteristic
199	#683	C₂³	1	1	yes	characteristic
200	#683	C₂³	1	1	yes	characteristic
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	2	yes	—
208	#683	C₂³	1	2	yes	—
209	#683	C₂³	1	2	yes	—
210	#683	C₂³	1	2	yes	—
211	#683	C₂³	1	2	yes	—
212	C₄×Dic₅	C₂³	1	1	yes	characteristic
213	C₄×Dic₅	C₂³	1	1	yes	characteristic
214	C₄×Dic₅	C₂³	1	1	yes	characteristic
215	C₄×Dic₅	C₂³	1	2	yes	—
216	C₄×Dic₅	C₂³	1	2	yes	—
217	C₄×Dic₅	C₂³	1	2	yes	—
218	C₄×Dic₅	C₂³	1	1	yes	characteristic
219	C₄×Dic₅	C₂³	1	1	yes	characteristic
220	C₄×Dic₅	C₂³	1	2	yes	—
221	C₄×Dic₅	C₂³	1	2	yes	—
222	C₄×Dic₅	C₂³	1	2	yes	—
223	C₄×Dic₅	C₂³	1	2	yes	—
224	#557	—	5	1	no	—
225	#557	—	5	1	no	—
226	#557	—	5	1	no	—
227	#557	—	5	1	no	—
228	#554	—	5	2	no	—
229	#554	—	5	2	no	—
230	#554	—	5	2	no	—
231	#554	—	5	1	no	—
232	#554	—	5	1	no	—
233	#554	—	5	1	no	—
234	#554	—	5	2	no	—
235	#554	D₅	1	1	yes	characteristic, complemented
236	#544	—	5	1	no	—
237	#544	—	5	1	no	—
238	#544	—	5	2	no	—
239	#544	—	5	2	no	—
240	#533	—	5	2	no	—
241	#533	—	5	1	no	—
242	C₂×#125	—	5	1	no	—
243	C₂×#125	—	5	2	no	—
244	#520	—	5	1	no	—
245	#520	—	5	1	no	—
246	C₄×#41	—	5	1	no	—
247	C₂³×C₅	C₂⁴	1	2	yes	—
248	C₂²×D₅	C₂⁴	1	1	yes	characteristic
249	C₅×Q₈	—	4	1	no	—
250	C₅×Q₈	—	4	2	no	—
251	C₅×D₄	C₂×Q₈	1	4	yes	—
252	C₂×C₄×C₅	—	4	2	no	—
253	C₂×C₄×C₅	—	4	2	no	—
254	C₂×C₄×C₅	—	4	2	no	—
255	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
256	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₅	C₂⁴	1	2	yes	—
258	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
259	C₂×C₄×C₅	C₂⁴	1	2	yes	—
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	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
264	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
265	C₂²⋊D₅	C₂×Q₈	1	8	yes	—
266	C₂×Dic₅	—	4	2	no	—
267	C₂×Dic₅	—	4	2	no	—
268	C₂×Dic₅	—	4	2	no	—
269	C₂×Dic₅	C₂×Q₈	1	8	yes	—
270	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
273	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₅	C₂⁴	1	2	yes	—
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	2	yes	—
279	C₂×Dic₅	C₂⁴	1	2	yes	—
280	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
281	C₄×D₅	—	4	1	no	—
282	C₄×D₅	—	4	2	no	—
283	C₄×D₅	—	4	2	no	—
284	C₄×D₅	—	4	1	no	—
285	C₄×D₅	C₂×Q₈	1	4	yes	—
286	Dic₁₀	—	4	1	no	—
287	Dic₁₀	—	4	2	no	—
288	Dic₁₀	—	4	2	no	—
289	Dic₁₀	—	4	1	no	—
290	Dic₁₀	—	4	1	no	—
291	Dic₁₀	—	4	2	no	—
292	Dic₁₀	C₂×Q₈	1	4	yes	—
293	C₂×#41	—	5	1	no	—
294	C₄⋊Q₈	—	5	2	no	—
295	C₄⋊Q₈	—	5	1	no	—
296	C₄⋊Q₈	—	5	2	no	—
297	C₄⋊Q₈	—	5	2	no	—
298	C₄⋊Q₈	—	5	2	no	—
299	C₄⋊Q₈	—	5	1	no	—
300	C₄⋊Q₈	—	5	2	no	—
301	C₄⋊Q₈	—	5	2	no	—
302	C₄⋊Q₈	—	5	1	no	—
303	C₄⋊Q₈	—	5	1	no	—
304	C₄⋊Q₈	—	5	1	no	—
305	C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic
306	#125	—	5	2	no	—
307	#125	—	5	1	no	—
308	#125	—	5	2	no	—
309	#125	—	5	2	no	—
310	#125	—	5	2	no	—
311	#125	—	5	2	no	—
312	#125	—	5	2	no	—
313	#125	—	5	2	no	—
314	#125	—	5	2	no	—
315	#125	—	5	1	no	—
316	#125	—	5	1	no	—
317	#125	—	5	1	no	—
318	#125	—	5	2	no	—
319	#125	—	5	2	no	—
320	#125	—	5	2	no	—
321	#125	—	5	2	no	—
322	#125	—	5	1	no	—
323	#125	—	5	1	no	—
324	#125	—	5	1	no	—
325	#125	—	5	1	no	—
326	#125	C₂×D₅	1	1	yes	characteristic
327	#125	C₂×D₅	1	1	yes	characteristic
328	C₂²⋊Q₈	—	5	1	no	—
329	C₂²⋊Q₈	—	5	2	no	—
330	C₂²⋊Q₈	—	5	2	no	—
331	C₂²⋊Q₈	—	5	2	no	—
332	C₂²⋊Q₈	—	5	2	no	—
333	C₂²⋊Q₈	—	5	1	no	—
334	C₂²⋊Q₈	—	5	1	no	—
335	C₂²⋊Q₈	—	5	1	no	—
336	C₂²⋊Q₈	—	5	2	no	—
337	C₂²⋊Q₈	—	5	2	no	—
338	C₂²⋊Q₈	—	5	2	no	—
339	C₂²⋊Q₈	—	5	2	no	—
340	C₂²⋊Q₈	—	5	2	no	—
341	C₂²⋊Q₈	—	5	2	no	—
342	C₂²⋊Q₈	—	5	2	no	—
343	C₂²⋊Q₈	—	5	2	no	—
344	C₂²⋊Q₈	—	5	2	no	—
345	C₂²⋊Q₈	C₂×D₅	1	2	yes	—
346	C₂²⋊Q₈	C₂×D₅	1	2	yes	—
347	C₂²⋊Q₈	C₂×D₅	1	2	yes	—
348	C₄×Q₈	—	5	2	no	—
349	C₄×Q₈	—	5	1	no	—
350	C₄×Q₈	—	5	1	no	—
351	C₄×Q₈	—	5	1	no	—
352	C₄×Q₈	—	5	2	no	—
353	C₄×Q₈	—	5	2	no	—
354	C₄×Q₈	—	5	2	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	1	no	—
360	C₄×Q₈	—	5	1	no	—
361	C₄×Q₈	C₂×D₅	1	1	yes	characteristic
362	C₄×D₄	—	5	1	no	—
363	C₄×D₄	—	5	1	no	—
364	C₄×D₄	—	5	1	no	—
365	C₄×D₄	—	5	2	no	—
366	C₄×D₄	—	5	2	no	—
367	C₄×D₄	—	5	2	no	—
368	C₄×D₄	—	5	2	no	—
369	C₄×D₄	—	5	2	no	—
370	C₄×D₄	—	5	2	no	—
371	C₄×D₄	C₂×D₅	1	1	yes	characteristic
372	C₄×D₄	C₂×D₅	1	1	yes	characteristic
373	C₄×D₄	C₂×D₅	1	1	yes	characteristic
374	#117	—	5	1	no	—
375	#117	—	5	2	no	—
376	#117	—	5	2	no	—
377	#117	—	5	2	no	—
378	#117	—	5	1	no	—
379	#117	—	5	1	no	—
380	C₂×C₄⋊C₄	—	5	2	no	—
381	C₂×C₄⋊C₄	—	5	2	no	—
382	C₂×C₄⋊C₄	—	5	2	no	—
383	C₂×C₄⋊C₄	—	5	2	no	—
384	C₂×C₄⋊C₄	—	5	2	no	—
385	C₂×C₄⋊C₄	—	5	1	no	—
386	C₂×C₄⋊C₄	—	5	1	no	—
387	C₂×C₄⋊C₄	—	5	2	no	—
388	C₂×C₄⋊C₄	—	5	2	no	—
389	C₂×C₄⋊C₄	C₂×D₅	1	2	yes	—
390	C₂×C₄²	—	5	2	no	—
391	C₂×C₄²	—	5	1	no	—
392	C₂²×C₅	—	2	2	no	—
393	C₂²×C₅	—	2	2	no	—
394	C₂²×C₅	C₂²×Q₈	1	4	yes	—
395	C₂²×C₅	C₂⁵	1	1	yes	characteristic
396	C₂×D₅	—	2	1	no	—
397	C₂×D₅	—	2	1	no	—
398	C₂×D₅	C₂²×Q₈	1	2	yes	—
399	C₄×C₅	—	2	1	no	—
400	C₄×C₅	—	2	2	no	—
401	C₄×C₅	—	2	1	no	—
402	C₄×C₅	—	2	1	no	—
403	C₄×C₅	—	2	2	no	—
404	C₄×C₅	—	2	1	no	—
405	C₄×C₅	—	2	1	no	—
406	C₄×C₅	—	2	2	no	—
407	C₄×C₅	—	2	1	no	—
408	C₄×C₅	C₂²×Q₈	1	2	yes	—
409	Dic₅	—	2	1	no	—
410	Dic₅	—	2	1	no	—
411	Dic₅	—	2	1	no	—
412	Dic₅	—	2	2	no	—
413	Dic₅	—	2	2	no	—
414	Dic₅	—	2	2	no	—
415	Dic₅	—	2	1	no	—
416	Dic₅	—	2	1	no	—
417	Dic₅	—	2	1	no	—
418	Dic₅	C₂²×Q₈	1	4	yes	—
419	Dic₅	C₂²×Q₈	1	2	yes	—
420	#41	—	5	8	no	—
421	C₂×Q₈	—	5	1	no	—
422	C₂×Q₈	—	5	2	no	—
423	C₂×Q₈	—	5	1	no	—
424	C₂×Q₈	—	5	2	no	—
425	C₂×Q₈	—	5	1	no	—
426	C₂×Q₈	—	5	1	no	—
427	C₂×Q₈	—	5	2	no	—
428	C₂×Q₈	C₂²×D₅	1	2	yes	—
429	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
430	C₂×D₄	—	5	2	no	—
431	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
432	C₂²×C₄	—	5	2	no	—
433	C₂²×C₄	—	5	1	no	—
434	C₂²×C₄	—	5	2	no	—
435	C₂²×C₄	—	5	2	no	—
436	C₂²×C₄	—	5	2	no	—
437	C₂²×C₄	—	5	1	no	—
438	C₂²×C₄	—	5	1	no	—
439	C₂²×C₄	—	5	2	no	—
440	C₂²×C₄	—	5	2	no	—
441	C₂²×C₄	C₂²×D₅	1	2	yes	—
442	C₂²×C₄	C₂²×D₅	1	2	yes	—
443	C₂²×C₄	C₂²×D₅	1	2	yes	—
444	C₄⋊C₄	—	5	2	no	—
445	C₄⋊C₄	—	5	2	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	2	no	—
452	C₄⋊C₄	—	5	2	no	—
453	C₄⋊C₄	—	5	1	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	1	no	—
459	C₄⋊C₄	—	5	1	no	—
460	C₄⋊C₄	—	5	2	no	—
461	C₄⋊C₄	—	5	2	no	—
462	C₄⋊C₄	—	5	2	no	—
463	C₄⋊C₄	—	5	2	no	—
464	C₄⋊C₄	—	5	2	no	—
465	C₄⋊C₄	—	5	2	no	—
466	C₄⋊C₄	—	5	2	no	—
467	C₄⋊C₄	—	5	2	no	—
468	C₄⋊C₄	—	5	2	no	—
469	C₄⋊C₄	—	5	1	no	—
470	C₄⋊C₄	—	5	1	no	—
471	C₄⋊C₄	—	5	2	no	—
472	C₄⋊C₄	—	5	2	no	—
473	C₄⋊C₄	—	5	1	no	—
474	C₄⋊C₄	—	5	1	no	—
475	C₄⋊C₄	—	5	1	no	—
476	C₄⋊C₄	—	5	1	no	—
477	C₄⋊C₄	—	5	2	no	—
478	C₄⋊C₄	—	5	1	no	—
479	C₄⋊C₄	—	5	2	no	—
480	C₄⋊C₄	—	5	1	no	—
481	C₄⋊C₄	—	5	2	no	—
482	C₄⋊C₄	—	5	1	no	—
483	C₄⋊C₄	C₂²×D₅	1	2	yes	—
484	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
485	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
486	C₄⋊C₄	C₂²×D₅	1	2	yes	—
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	1	yes	characteristic
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	C₂²⋊C₄	—	5	2	no	—
495	C₂²⋊C₄	—	5	2	no	—
496	C₂²⋊C₄	—	5	2	no	—
497	C₂²⋊C₄	—	5	1	no	—
498	C₂²⋊C₄	—	5	1	no	—
499	C₂²⋊C₄	—	5	2	no	—
500	C₂²⋊C₄	—	5	1	no	—
501	C₂²⋊C₄	—	5	1	no	—
502	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
503	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
504	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
505	C₄²	—	5	1	no	—
506	C₄²	—	5	2	no	—
507	C₄²	—	5	1	no	—
508	C₄²	—	5	2	no	—
509	C₄²	—	5	2	no	—
510	C₄²	—	5	1	no	—
511	C₄²	—	5	2	no	—
512	C₄²	—	5	2	no	—
513	C₄²	—	5	2	no	—
514	C₄²	—	5	2	no	—
515	C₄²	—	5	1	no	—
516	C₄²	—	5	1	no	—
517	C₄²	C₂²×D₅	1	1	yes	characteristic
518	C₄²	C₂²×D₅	1	1	yes	characteristic
519	C₄²	C₂²×D₅	1	1	yes	characteristic
520	C₂×C₅	—	2	4	no	—
521	C₂×C₅	C₂³×Q₈	1	1	yes	characteristic
522	C₂×C₅	#585	1	1	yes	characteristic
523	C₂×C₅	#585	1	1	yes	characteristic
524	D₅	—	2	2	no	—
525	C₂³	—	5	1	no	—
526	C₂³	C₂³×D₅	1	2	yes	—
527	Q₈	—	4	1	no	—
528	Q₈	—	4	2	no	—
529	Q₈	—	5	4	no	—
530	Q₈	—	20	2	no	—
531	Q₈	—	20	1	no	—
532	Q₈	—	20	2	no	—
533	Q₈	—	20	1	no	—
534	Q₈	—	20	2	no	—
535	Q₈	—	20	1	no	—
536	D₄	—	5	8	no	—
537	D₄	Q₈×D₅	1	4	yes	—
538	C₂×C₄	—	4	2	no	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	5	8	no	—
542	C₂×C₄	—	5	2	no	—
543	C₂×C₄	—	5	1	no	—
544	C₂×C₄	—	5	4	no	—
545	C₂×C₄	—	5	1	no	—
546	C₂×C₄	—	5	1	no	—
547	C₂×C₄	—	5	1	no	—
548	C₂×C₄	—	5	2	no	—
549	C₂×C₄	—	5	1	no	—
550	C₂×C₄	—	5	2	no	—
551	C₂×C₄	—	5	1	no	—
552	C₂×C₄	—	5	2	no	—
553	C₂×C₄	—	5	1	no	—
554	C₂×C₄	—	20	2	no	—
555	C₂×C₄	—	20	1	no	—
556	C₂×C₄	—	20	1	no	—
557	C₂×C₄	—	20	2	no	—
558	C₂×C₄	—	20	2	no	—
559	C₂×C₄	—	20	2	no	—
560	C₂×C₄	—	20	2	no	—
561	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
562	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
563	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
564	C₂×C₄	C₂³×D₅	1	2	yes	—
565	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
566	C₂×C₄	C₂³×D₅	1	2	yes	—
567	C₂×C₄	C₂³×D₅	1	2	yes	—
568	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
569	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
570	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
571	C₅	#3504	1	1	yes	characteristic, complemented, Sylow
572	C₂²	—	2	2	no	—
573	C₂²	—	2	2	no	—
574	C₂²	—	5	2	no	—
575	C₂²	—	10	1	no	—
576	C₂²	—	10	1	no	—
577	C₂²	C₂×Q₈×D₅	1	4	yes	—
578	C₂²	C₂⁴×D₅	1	1	yes	characteristic
579	C₄	—	2	1	no	—
580	C₄	—	2	2	no	—
581	C₄	—	2	1	no	—
582	C₄	—	2	1	no	—
583	C₄	—	2	1	no	—
584	C₄	—	2	1	no	—
585	C₄	—	2	2	no	—
586	C₄	—	2	2	no	—
587	C₄	—	2	1	no	—
588	C₄	—	5	2	no	—
589	C₄	—	5	4	no	—
590	C₄	—	10	1	no	—
591	C₄	—	10	2	no	—
592	C₄	—	10	1	no	—
593	C₄	—	10	2	no	—
594	C₄	—	10	1	no	—
595	C₄	—	10	2	no	—
596	C₄	—	10	1	no	—
597	C₄	—	10	1	no	—
598	C₄	—	10	1	no	—
599	C₄	C₂×Q₈×D₅	1	2	yes	—
600	C₂	—	2	4	no	—
601	C₂	—	10	2	no	—
602	C₂	C₂²×Q₈×D₅	1	1	yes	characteristic
603	C₂	#66283	1	1	yes	characteristic
604	C₂	#66285	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁵
Fitting	C₅×#554	C₂
prime radical	C₂×#711	C₂²
hypercenter	#554	D₅
hypocenter	C₅	#3504
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. C₅×#554	C₂	semidirect
2. #66063	C₂	semidirect
3. #66055	C₂	semidirect
4. #66023	C₂	semidirect
5. D₅×#125	C₂	semidirect
6. #66019	C₂	semidirect
7. #66019	C₂	semidirect
8. #65970	C₂	semidirect
9. #65970	C₂	semidirect
10. #65969	C₂	semidirect
11. #65957	C₂	semidirect
12. #65957	C₂	semidirect
13. #65956	C₂	semidirect
14. #65912	C₂	semidirect
15. #65901	C₂	semidirect
18. #65877	C₂	semidirect
19. #65873	C₂	semidirect
20. #65873	C₂	semidirect
22. #65845	C₂	semidirect
23. C₂×#4035	C₂	semidirect
135. #711	Q₈	semidirect
235. #554	D₅	semidirect
571. C₅	#3504	semidirect

Maximal subgroups

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

subgroup	index
C₅×#554	2
#66063	2
#66055	2
#66023	2
D₅×#125	2
#66019	2
#65970	2
#65969	2
#65957	2
#65956	2
#65912	2
#65901	2
#65880	2
#65877	2
#65873	2
C₄×#711	2
#65845	2
C₂×#4035	2
#3504	5