Subgroups — #10618883

Order 640.

1022 conjugacy classes of subgroups.

The subgroup lattice has 644 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	#66064	C₂	1	1	yes	maximal, characteristic, complemented
3	#66063	C₂	1	1	yes	maximal, characteristic, complemented
4	#66042	C₂	1	2	yes	maximal, complemented
5	#66040	C₂	1	2	yes	maximal, complemented
6	#66039	C₂	1	2	yes	maximal, complemented
7	#66035	C₂	1	2	yes	maximal, complemented
8	#66013	C₂	1	2	yes	maximal, complemented
9	#66003	C₂	1	2	yes	maximal, complemented
10	#65973	C₂	1	1	yes	maximal, characteristic, complemented
11	#65969	C₂	1	1	yes	maximal, characteristic, complemented
12	#65962	C₂	1	1	yes	maximal, characteristic, complemented
13	D₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
14	#65915	C₂	1	1	yes	maximal, characteristic, complemented
15	#65915	C₂	1	2	yes	maximal, complemented
16	#65912	C₂	1	2	yes	maximal, complemented
17	#65906	C₂	1	1	yes	maximal, characteristic, complemented
18	#65881	C₂	1	1	yes	maximal, characteristic
19	#65875	C₂	1	1	yes	maximal, characteristic, complemented
20	#65867	C₂	1	1	yes	maximal, characteristic, complemented
21	#65863	C₂	1	1	yes	maximal, characteristic, complemented
22	#65857	C₂	1	1	yes	maximal, characteristic, complemented
23	D₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₈×D₅	C₂²	1	1	yes	characteristic
25	C₂×#709	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₅	C₂²	1	1	yes	characteristic
27	C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₅×#126	C₂²	1	2	yes	—
29	C₅×#126	C₂²	1	2	yes	complemented
30	C₅×#124	C₂²	1	2	yes	—
31	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₄×C₅×Q₈	C₂²	1	2	yes	complemented
35	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
36	C₅×#117	C₂²	1	1	yes	characteristic
37	C₅×#117	C₂²	1	1	yes	characteristic, complemented
38	#4092	C₂²	1	2	yes	—
39	#4092	C₂²	1	2	yes	—
40	#4092	C₂²	1	1	yes	characteristic
41	#4092	C₂²	1	2	yes	complemented
42	#4092	C₂²	1	1	yes	characteristic, complemented
43	Q₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
44	#4090	C₂²	1	2	yes	complemented
45	#4085	C₂²	1	1	yes	characteristic
46	#4083	C₂²	1	1	yes	characteristic
47	#4081	C₂²	1	2	yes	—
48	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
49	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
50	#4072	C₂²	1	1	yes	characteristic
51	C₂×C₄⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
52	#4070	C₂²	1	1	yes	characteristic
53	#4070	C₂²	1	1	yes	characteristic, complemented
54	#4043	C₂²	1	1	yes	characteristic
55	#4043	C₂²	1	2	yes	—
56	#4043	C₂²	1	1	yes	characteristic, complemented
57	#4042	C₂²	1	2	yes	—
58	#4042	C₂²	1	1	yes	characteristic
59	#4042	C₂²	1	2	yes	—
60	#4040	C₂²	1	1	yes	characteristic
61	#4040	C₂²	1	2	yes	—
62	#4040	C₂²	1	2	yes	—
63	#4039	C₂²	1	2	yes	—
64	#4038	C₂²	1	1	yes	characteristic
65	#4038	C₂²	1	1	yes	characteristic
66	#4038	C₂²	1	2	yes	—
67	#4038	C₂²	1	1	yes	characteristic, complemented
68	#4038	C₂²	1	2	yes	complemented
69	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
70	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
71	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
72	D₅×C₄⋊C₄	C₂²	1	2	yes	—
73	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
74	#4036	C₂²	1	1	yes	characteristic, complemented
75	#4036	C₂²	1	2	yes	complemented
76	#4035	C₂²	1	2	yes	complemented
77	#4035	C₂²	1	2	yes	complemented
78	#4035	C₂²	1	2	yes	complemented
79	#4035	C₂²	1	2	yes	complemented
80	#4035	C₂²	1	2	yes	complemented
81	#4034	C₂²	1	1	yes	characteristic, complemented
82	#4034	C₂²	1	2	yes	complemented
83	#4033	C₂²	1	1	yes	characteristic, complemented
84	#4033	C₂²	1	2	yes	complemented
85	#4031	C₂²	1	2	yes	—
86	#4031	C₂²	1	2	yes	complemented
87	#4030	C₂²	1	1	yes	characteristic
88	#4029	C₂²	1	2	yes	—
89	#4029	C₂²	1	1	yes	characteristic
90	#4029	C₂²	1	2	yes	—
91	#4029	C₂²	1	2	yes	—
92	#4028	C₂²	1	1	yes	characteristic
93	#4027	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	#4025	C₂²	1	2	yes	—
99	#4025	C₂²	1	2	yes	—
100	#4025	C₂²	1	2	yes	—
101	#4025	C₂²	1	2	yes	complemented
102	#4024	C₂²	1	1	yes	characteristic
103	#4024	C₂²	1	2	yes	—
104	#4024	C₂²	1	2	yes	complemented
105	#4023	C₂²	1	2	yes	—
106	#4023	C₂²	1	2	yes	complemented
107	#4022	C₂²	1	2	yes	complemented
108	#4022	C₂²	1	2	yes	complemented
109	C₄×D₂₀	C₂²	1	1	yes	characteristic
110	C₄×D₂₀	C₂²	1	2	yes	—
111	#4018	C₂²	1	1	yes	characteristic
112	#4018	C₂²	1	2	yes	—
113	#4018	C₂²	1	2	yes	—
114	#4018	C₂²	1	2	yes	—
115	#4018	C₂²	1	2	yes	—
116	C₄²×D₅	C₂²	1	2	yes	—
117	#4016	C₂²	1	1	yes	characteristic, complemented
118	#4016	C₂²	1	2	yes	complemented
119	C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
120	C₄×Dic₁₀	C₂²	1	2	yes	complemented
121	C₄×Dic₁₀	C₂²	1	2	yes	complemented
122	C₄×Dic₁₀	C₂²	1	2	yes	complemented
123	#3495	—	5	1	no	maximal, Sylow
124	C₂³×D₅	C₂³	1	1	yes	characteristic
125	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
126	C₂×C₅×Q₈	C₂³	1	2	yes	—
127	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
130	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
131	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
132	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
134	C₂²×Dic₅	C₂³	1	1	yes	characteristic
135	C₂²×Dic₅	C₂³	1	2	yes	—
136	Q₈×D₅	—	2	4	no	—
137	#709	—	2	4	no	—
138	C₂×D₂₀	C₂³	1	1	yes	characteristic
139	C₂×D₂₀	C₂³	1	1	yes	characteristic
140	C₂×C₄×D₅	—	2	4	no	—
141	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
142	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₅	C₂³	1	2	yes	—
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	2	yes	—
155	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
162	C₅×C₄⋊C₄	C₂³	1	2	yes	—
163	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
166	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
173	C₂²⋊Dic₅	C₂³	1	2	yes	—
174	C₂²⋊Dic₅	C₂³	1	2	yes	—
175	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₅	C₂³	1	2	yes	—
177	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
178	#685	C₂³	1	1	yes	characteristic
179	#685	C₂³	1	2	yes	—
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	1	yes	characteristic
186	#685	C₂³	1	2	yes	—
187	#685	C₂³	1	1	yes	characteristic
188	#685	C₂³	1	1	yes	characteristic
189	#685	C₂³	1	2	yes	—
190	#685	C₂³	1	2	yes	—
191	C₄⋊Dic₅	C₂³	1	2	yes	—
192	C₄⋊Dic₅	C₂³	1	2	yes	—
193	C₄⋊Dic₅	C₂³	1	2	yes	—
194	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
195	C₄⋊Dic₅	C₂³	1	2	yes	—
196	C₄⋊Dic₅	C₂³	1	2	yes	—
197	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
198	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
199	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
200	#683	C₂³	1	2	yes	—
201	#683	C₂³	1	1	yes	characteristic
202	#683	C₂³	1	1	yes	characteristic
203	#683	C₂³	1	2	yes	—
204	#683	C₂³	1	2	yes	—
205	#683	C₂³	1	2	yes	—
206	#683	C₂³	1	1	yes	characteristic
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	#683	C₂³	1	2	yes	—
213	#683	C₂³	1	1	yes	characteristic
214	#683	C₂³	1	2	yes	—
215	#683	C₂³	1	2	yes	—
216	#683	C₂³	1	2	yes	—
217	#683	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	2	yes	—
223	C₄×Dic₅	C₂³	1	2	yes	—
224	C₄×Dic₅	C₂³	1	2	yes	—
225	C₄×Dic₅	C₂³	1	1	yes	characteristic
226	#556	—	5	1	no	—
227	#556	D₅	1	1	yes	characteristic, complemented
228	#554	—	5	1	no	—
229	#554	—	5	1	no	—
230	#552	—	5	2	no	—
231	#552	—	5	1	no	—
232	#552	—	5	1	no	—
233	#552	—	5	2	no	—
234	#552	—	5	1	no	—
235	#552	—	5	1	no	—
236	#551	—	5	2	no	—
237	#551	—	5	2	no	—
238	#544	—	5	1	no	—
239	#542	—	5	2	no	—
240	#541	—	5	2	no	—
241	#536	—	5	1	no	—
242	#533	—	5	2	no	—
243	#529	—	5	2	no	—
244	#525	—	5	1	no	—
245	C₂×C₂²⋊Q₈	—	5	1	no	—
246	#520	—	5	1	no	—
247	#519	—	5	1	no	—
248	C₂×#117	—	5	1	no	—
249	C₂³×C₅	C₂⁴	1	1	yes	characteristic
250	C₂³×C₅	C₂⁴	1	1	yes	characteristic
251	C₂²×D₅	—	2	2	no	—
252	C₂²×D₅	—	2	2	no	—
253	C₂²×D₅	—	4	1	no	—
254	C₂²×D₅	C₂⁴	1	1	yes	characteristic
255	C₂²×D₅	C₂⁴	1	1	yes	characteristic
256	C₂²×D₅	C₂⁴	1	1	yes	characteristic
257	C₅×Q₈	—	2	2	no	—
258	C₅×Q₈	—	4	2	no	—
259	C₅×D₄	—	4	1	no	—
260	C₂×C₄×C₅	—	2	2	no	—
261	C₂×C₄×C₅	—	2	2	no	—
262	C₂×C₄×C₅	C₂⁴	1	2	yes	—
263	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
264	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
265	C₂×C₄×C₅	C₂⁴	1	2	yes	—
266	C₂×C₄×C₅	C₂⁴	1	2	yes	—
267	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
268	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
269	C₂×C₄×C₅	C₂⁴	1	2	yes	—
270	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
271	C₂²⋊D₅	—	2	2	no	—
272	C₂²⋊D₅	—	2	2	no	—
273	C₂²⋊D₅	—	2	2	no	—
274	C₂²⋊D₅	—	4	1	no	—
275	C₂×Dic₅	—	2	2	no	—
276	C₂×Dic₅	—	4	2	no	—
277	C₂×Dic₅	C₂⁴	1	2	yes	—
278	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
279	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
280	C₂×Dic₅	C₂⁴	1	2	yes	—
281	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
282	C₂×Dic₅	C₂⁴	1	2	yes	—
283	C₂×Dic₅	C₂⁴	1	2	yes	—
284	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
285	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
286	D₂₀	—	2	2	no	—
287	D₂₀	—	2	2	no	—
288	C₄×D₅	—	2	2	no	—
289	C₄×D₅	—	2	4	no	—
290	C₄×D₅	—	2	4	no	—
291	C₄×D₅	—	2	2	no	—
292	C₄×D₅	—	2	2	no	—
293	C₄×D₅	—	2	2	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	2	no	—
300	Dic₁₀	—	2	4	no	—
301	Dic₁₀	—	4	2	no	—
302	C₂×#41	—	5	1	no	—
303	C₂²×Q₈	—	5	1	no	—
304	C₂³×C₄	—	5	1	no	—
305	C₄⋊Q₈	—	5	2	no	—
306	C₄⋊Q₈	—	5	2	no	—
307	C₄⋊Q₈	—	5	1	no	—
308	C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
309	#126	—	5	2	no	—
310	#126	—	5	2	no	—
311	#126	—	5	2	no	—
312	#126	—	5	2	no	—
313	#126	—	5	2	no	—
314	#126	—	5	2	no	—
315	#126	C₂×D₅	1	2	yes	—
316	#126	C₂×D₅	1	2	yes	complemented
317	#125	—	5	2	no	—
318	#125	—	5	2	no	—
319	#125	—	5	2	no	—
320	#125	—	5	2	no	—
321	#125	—	5	2	no	—
322	#125	—	5	2	no	—
323	#125	—	5	1	no	—
324	#125	—	5	2	no	—
325	#125	—	5	1	no	—
326	#124	—	5	2	no	—
327	#124	—	5	2	no	—
328	#124	C₂×D₅	1	2	yes	—
329	#123	—	5	2	no	—
330	#123	—	5	1	no	—
331	#123	—	5	2	no	—
332	#123	—	5	2	no	—
333	#123	—	5	1	no	—
334	#123	—	5	2	no	—
335	#123	—	5	2	no	—
336	#123	—	5	2	no	—
337	C₂²⋊Q₈	—	5	1	no	—
338	C₂²⋊Q₈	—	5	2	no	—
339	C₂²⋊Q₈	—	5	1	no	—
340	C₂²⋊Q₈	—	5	2	no	—
341	C₂²⋊Q₈	—	5	2	no	—
342	C₂²⋊Q₈	—	5	1	no	—
343	C₂²⋊Q₈	—	5	1	no	—
344	C₂²⋊Q₈	—	5	2	no	—
345	C₂²⋊Q₈	—	5	1	no	—
346	C₂²⋊Q₈	—	5	1	no	—
347	C₂²⋊Q₈	—	5	2	no	—
348	C₂²⋊Q₈	—	5	1	no	—
349	C₂²⋊Q₈	—	5	2	no	—
350	C₂²⋊Q₈	—	5	2	no	—
351	C₂²⋊Q₈	—	5	1	no	—
352	C₂²⋊Q₈	—	5	2	no	—
353	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic
354	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
355	#121	—	5	1	no	—
356	#121	—	5	1	no	—
357	#120	—	5	1	no	—
358	#120	—	5	1	no	—
359	C₄×Q₈	—	5	1	no	—
360	C₄×Q₈	—	5	2	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	2	no	—
366	C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
367	C₄×Q₈	C₂×D₅	1	2	yes	complemented
368	C₄×D₄	—	5	1	no	—
369	C₄×D₄	—	5	1	no	—
370	C₄×D₄	—	5	2	no	—
371	C₄×D₄	—	5	2	no	—
372	C₄×D₄	—	5	2	no	—
373	C₄×D₄	—	5	2	no	—
374	C₄×D₄	—	5	2	no	—
375	C₄×D₄	—	5	1	no	—
376	C₄×D₄	C₂×D₅	1	1	yes	characteristic
377	#117	—	5	1	no	—
378	#117	—	5	1	no	—
379	#117	—	5	1	no	—
380	#117	—	5	2	no	—
381	#117	—	5	1	no	—
382	#117	—	5	2	no	—
383	#117	—	5	2	no	—
384	#117	—	5	2	no	—
385	#117	—	5	2	no	—
386	#117	—	5	1	no	—
387	#117	—	5	2	no	—
388	#117	—	5	2	no	—
389	#117	—	5	2	no	—
390	#117	C₂×D₅	1	1	yes	characteristic
391	#117	C₂×D₅	1	1	yes	characteristic, complemented
392	C₂×C₄⋊C₄	—	5	1	no	—
393	C₂×C₄⋊C₄	—	5	1	no	—
394	C₂×C₄⋊C₄	—	5	1	no	—
395	C₂×C₄⋊C₄	—	5	1	no	—
396	C₂×C₄⋊C₄	—	5	1	no	—
397	C₂×C₄⋊C₄	—	5	2	no	—
398	C₂×C₂²⋊C₄	—	5	2	no	—
399	C₂×C₂²⋊C₄	—	5	2	no	—
400	C₂×C₄²	—	5	2	no	—
401	C₂²×C₅	—	2	1	no	—
402	C₂²×C₅	—	2	1	no	—
403	C₂²×C₅	—	2	1	no	—
404	C₂²×C₅	—	2	1	no	—
405	C₂²×C₅	—	2	1	no	—
406	C₂²×C₅	—	2	1	no	—
407	C₂²×C₅	C₂⁵	1	1	yes	characteristic
408	C₂×D₅	—	2	1	no	—
409	C₂×D₅	—	2	1	no	—
410	C₂×D₅	—	2	1	no	—
411	C₂×D₅	—	2	1	no	—
412	C₂×D₅	—	2	1	no	—
413	C₂×D₅	—	2	1	no	—
414	C₂×D₅	—	2	1	no	—
415	C₂×D₅	—	4	4	no	—
416	C₂×D₅	C₂×#41	1	2	yes	—
417	C₂×D₅	2₋¹⁺⁴	1	2	yes	—
418	C₄×C₅	—	2	2	no	—
419	C₄×C₅	—	2	1	no	—
420	C₄×C₅	—	2	1	no	—
421	C₄×C₅	—	2	2	no	—
422	C₄×C₅	—	2	1	no	—
423	C₄×C₅	—	2	2	no	—
424	C₄×C₅	—	2	2	no	—
425	C₄×C₅	—	2	1	no	—
426	C₄×C₅	C₂×#41	1	2	yes	—
427	Dic₅	—	2	2	no	—
428	Dic₅	—	2	1	no	—
429	Dic₅	—	2	1	no	—
430	Dic₅	—	2	2	no	—
431	Dic₅	—	2	1	no	—
432	Dic₅	—	2	1	no	—
433	Dic₅	—	2	2	no	—
434	Dic₅	—	2	2	no	—
435	Dic₅	C₂×#41	1	2	yes	—
436	C₂⁴	—	5	1	no	—
437	#41	—	10	4	no	—
438	C₂×Q₈	—	5	1	no	—
439	C₂×Q₈	—	5	2	no	—
440	C₂×Q₈	—	5	1	no	—
441	C₂×Q₈	—	5	2	no	—
442	C₂×Q₈	—	10	4	no	—
443	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
444	C₂×Q₈	C₂²×D₅	1	2	yes	—
445	C₂×D₄	—	5	1	no	—
446	C₂×D₄	—	5	1	no	—
447	C₂×D₄	—	5	1	no	—
448	C₂×D₄	—	5	1	no	—
449	C₂×D₄	—	5	1	no	—
450	C₂×D₄	—	5	1	no	—
451	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
452	C₂²×C₄	—	5	1	no	—
453	C₂²×C₄	—	5	1	no	—
454	C₂²×C₄	—	5	2	no	—
455	C₂²×C₄	—	5	1	no	—
456	C₂²×C₄	—	5	2	no	—
457	C₂²×C₄	—	5	2	no	—
458	C₂²×C₄	—	5	1	no	—
459	C₂²×C₄	—	5	1	no	—
460	C₂²×C₄	—	5	1	no	—
461	C₂²×C₄	—	5	2	no	—
462	C₂²×C₄	—	5	2	no	—
463	C₂²×C₄	—	5	2	no	—
464	C₂²×C₄	—	10	4	no	—
465	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
466	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
467	C₄⋊C₄	—	5	1	no	—
468	C₄⋊C₄	—	5	1	no	—
469	C₄⋊C₄	—	5	2	no	—
470	C₄⋊C₄	—	5	1	no	—
471	C₄⋊C₄	—	5	2	no	—
472	C₄⋊C₄	—	5	2	no	—
473	C₄⋊C₄	—	5	2	no	—
474	C₄⋊C₄	—	5	2	no	—
475	C₄⋊C₄	—	5	2	no	—
476	C₄⋊C₄	—	5	2	no	—
477	C₄⋊C₄	—	5	2	no	—
478	C₄⋊C₄	—	5	1	no	—
479	C₄⋊C₄	—	5	1	no	—
480	C₄⋊C₄	—	5	2	no	—
481	C₄⋊C₄	—	5	2	no	—
482	C₄⋊C₄	—	5	2	no	—
483	C₄⋊C₄	—	5	2	no	—
484	C₄⋊C₄	—	5	2	no	—
485	C₄⋊C₄	—	5	2	no	—
486	C₄⋊C₄	—	5	2	no	—
487	C₄⋊C₄	—	5	2	no	—
488	C₄⋊C₄	—	5	2	no	—
489	C₄⋊C₄	—	5	1	no	—
490	C₄⋊C₄	—	5	1	no	—
491	C₄⋊C₄	—	5	1	no	—
492	C₄⋊C₄	—	5	2	no	—
493	C₄⋊C₄	—	5	2	no	—
494	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
495	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
496	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
497	C₄⋊C₄	C₂²×D₅	1	2	yes	—
498	C₄⋊C₄	C₂²×D₅	1	2	yes	—
499	C₄⋊C₄	C₂²×D₅	1	2	yes	—
500	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
501	C₄⋊C₄	C₂²×D₅	1	2	yes	—
502	C₂²⋊C₄	—	5	2	no	—
503	C₂²⋊C₄	—	5	2	no	—
504	C₂²⋊C₄	—	5	2	no	—
505	C₂²⋊C₄	—	5	1	no	—
506	C₂²⋊C₄	—	5	1	no	—
507	C₂²⋊C₄	—	5	2	no	—
508	C₂²⋊C₄	—	5	2	no	—
509	C₂²⋊C₄	—	5	2	no	—
510	C₂²⋊C₄	—	5	2	no	—
511	C₂²⋊C₄	—	5	1	no	—
512	C₂²⋊C₄	—	5	1	no	—
513	C₂²⋊C₄	—	5	1	no	—
514	C₂²⋊C₄	—	5	1	no	—
515	C₂²⋊C₄	—	5	1	no	—
516	C₂²⋊C₄	—	5	2	no	—
517	C₂²⋊C₄	—	5	2	no	—
518	C₂²⋊C₄	—	5	1	no	—
519	C₂²⋊C₄	—	5	2	no	—
520	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
521	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
522	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
523	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
524	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
525	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
526	C₄²	—	5	2	no	—
527	C₄²	—	5	2	no	—
528	C₄²	—	5	2	no	—
529	C₄²	—	5	2	no	—
530	C₄²	—	5	2	no	—
531	C₄²	—	5	2	no	—
532	C₄²	—	5	2	no	—
533	C₄²	—	5	1	no	—
534	C₄²	C₂²×D₅	1	2	yes	—
535	C₄²	C₂²×D₅	1	2	yes	—
536	C₄²	C₂²×D₅	1	2	yes	—
537	C₄²	C₂²×D₅	1	1	yes	characteristic
538	C₂×C₅	—	4	1	no	—
539	C₂×C₅	—	4	1	no	—
540	C₂×C₅	C₂²×#41	1	1	yes	characteristic
541	C₂×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
542	C₂×C₅	#585	1	1	yes	characteristic
543	D₅	—	2	2	no	—
544	D₅	—	2	2	no	—
545	D₅	—	4	1	no	—
546	C₂³	—	5	1	no	—
547	C₂³	—	5	1	no	—
548	C₂³	—	5	1	no	—
549	C₂³	—	10	2	no	—
550	C₂³	—	10	2	no	—
551	C₂³	—	20	1	no	—
552	C₂³	C₂³×D₅	1	1	yes	characteristic
553	C₂³	C₂³×D₅	1	1	yes	characteristic
554	Q₈	—	2	2	no	—
555	Q₈	—	4	2	no	—
556	Q₈	—	10	4	no	—
557	Q₈	—	10	2	no	—
558	Q₈	—	10	2	no	—
559	Q₈	—	20	2	no	—
560	D₄	—	4	1	no	—
561	D₄	—	10	2	no	—
562	D₄	—	10	2	no	—
563	D₄	—	10	2	no	—
564	D₄	—	10	2	no	—
565	D₄	—	10	2	no	—
566	D₄	—	20	1	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	5	1	no	—
570	C₂×C₄	—	5	4	no	—
571	C₂×C₄	—	5	2	no	—
572	C₂×C₄	—	5	1	no	—
573	C₂×C₄	—	5	1	no	—
574	C₂×C₄	—	5	2	no	—
575	C₂×C₄	—	5	2	no	—
576	C₂×C₄	—	5	1	no	—
577	C₂×C₄	—	5	2	no	—
578	C₂×C₄	—	5	1	no	—
579	C₂×C₄	—	10	2	no	—
580	C₂×C₄	—	10	2	no	—
581	C₂×C₄	—	10	4	no	—
582	C₂×C₄	—	10	4	no	—
583	C₂×C₄	—	10	2	no	—
584	C₂×C₄	—	10	2	no	—
585	C₂×C₄	—	10	2	no	—
586	C₂×C₄	—	20	2	no	—
587	C₂×C₄	—	20	2	no	—
588	C₂×C₄	—	20	2	no	—
589	C₂×C₄	—	20	2	no	—
590	C₂×C₄	C₂³×D₅	1	2	yes	—
591	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
592	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
593	C₂×C₄	C₂³×D₅	1	2	yes	—
594	C₂×C₄	C₂³×D₅	1	2	yes	—
595	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
596	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
597	C₂×C₄	C₂³×D₅	1	2	yes	—
598	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
599	C₅	#3495	1	1	yes	characteristic, complemented, Sylow
600	C₂²	—	2	1	no	—
601	C₂²	—	2	1	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	5	2	no	—
607	C₂²	—	5	2	no	—
608	C₂²	—	10	1	no	—
609	C₂²	—	10	1	no	—
610	C₂²	—	10	1	no	—
611	C₂²	—	10	1	no	—
612	C₂²	—	10	1	no	—
613	C₂²	—	10	1	no	—
614	C₂²	—	10	1	no	—
615	C₂²	—	20	4	no	—
616	C₂²	C₂⁴×D₅	1	1	yes	characteristic
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	2	no	—
620	C₄	—	2	2	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	1	no	—
623	C₄	—	2	2	no	—
624	C₄	—	2	1	no	—
625	C₄	—	5	2	no	—
626	C₄	—	10	1	no	—
627	C₄	—	10	1	no	—
628	C₄	—	10	2	no	—
629	C₄	—	10	2	no	—
630	C₄	—	10	2	no	—
631	C₄	—	10	1	no	—
632	C₄	—	10	2	no	—
633	C₄	—	10	1	no	—
634	C₄	D₅×#41	1	2	yes	—
635	C₂	—	4	1	no	—
636	C₂	—	4	1	no	—
637	C₂	—	10	2	no	—
638	C₂	—	10	2	no	—
639	C₂	—	20	1	no	—
640	C₂	C₂×D₅×#41	1	1	yes	characteristic
641	C₂	#66283	1	1	yes	characteristic
642	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	#65881	C₂
hypercenter	#556	D₅
hypocenter	C₅	#3495
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. #66064	C₂	semidirect
3. #66063	C₂	semidirect
4. #66042	C₂	semidirect
5. #66040	C₂	semidirect
6. #66039	C₂	semidirect
7. #66035	C₂	semidirect
8. #66013	C₂	semidirect
9. #66003	C₂	semidirect
10. #65973	C₂	semidirect
11. #65969	C₂	semidirect
12. #65962	C₂	semidirect
13. D₅×C₂²⋊Q₈	C₂	semidirect
14. #65915	C₂	semidirect
15. #65915	C₂	semidirect
16. #65912	C₂	semidirect
17. #65906	C₂	semidirect
19. #65875	C₂	semidirect
20. #65867	C₂	semidirect
21. #65863	C₂	semidirect
22. #65857	C₂	semidirect
23. D₅×#117	C₂	semidirect
27. C₅×C₄⋊Q₈	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
37. C₅×#117	C₂²	semidirect
41. #4092	C₂²	semidirect
42. #4092	C₂²	semidirect
43. Q₈×Dic₅	C₂²	semidirect
44. #4090	C₂²	semidirect
51. C₂×C₄⋊Dic₅	C₂²	semidirect
53. #4070	C₂²	semidirect
56. #4043	C₂²	semidirect
67. #4038	C₂²	semidirect
68. #4038	C₂²	semidirect
73. D₅×C₄⋊C₄	C₂²	semidirect
74. #4036	C₂²	semidirect
75. #4036	C₂²	semidirect
76. #4035	C₂²	semidirect
77. #4035	C₂²	semidirect
78. #4035	C₂²	semidirect
79. #4035	C₂²	semidirect
80. #4035	C₂²	semidirect
81. #4034	C₂²	semidirect
82. #4034	C₂²	semidirect
83. #4033	C₂²	semidirect
84. #4033	C₂²	semidirect
86. #4031	C₂²	semidirect
95. #4027	C₂²	semidirect
101. #4025	C₂²	semidirect
104. #4024	C₂²	semidirect
106. #4023	C₂²	semidirect
107. #4022	C₂²	semidirect
108. #4022	C₂²	semidirect
117. #4016	C₂²	semidirect
118. #4016	C₂²	semidirect
119. C₄×Dic₁₀	C₂²	semidirect
120. C₄×Dic₁₀	C₂²	semidirect
121. C₄×Dic₁₀	C₂²	semidirect
122. C₄×Dic₁₀	C₂²	semidirect
227. #556	D₅	semidirect
308. C₄⋊Q₈	C₂×D₅	semidirect
316. #126	C₂×D₅	semidirect
354. C₂²⋊Q₈	C₂×D₅	semidirect
366. C₄×Q₈	C₂×D₅	semidirect
367. C₄×Q₈	C₂×D₅	semidirect
391. #117	C₂×D₅	semidirect
599. C₅	#3495	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
#66064	2
#66063	2
#66042	2
#66040	2
#66039	2
#66035	2
#66013	2
#66003	2
#65973	2
#65969	2
#65962	2
D₅×C₂²⋊Q₈	2
#65915	2
#65912	2
#65906	2
#65881	2
#65875	2
#65867	2
#65863	2
#65857	2
D₅×#117	2
#3495	5