Subgroups — #10618778

Order 640.

1142 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#553	C₂	1	1	yes	maximal, characteristic, complemented
2	#66044	C₂	1	2	yes	maximal, complemented
3	#66039	C₂	1	2	yes	maximal, complemented
4	#66029	C₂	1	1	yes	maximal, characteristic, complemented
5	#66023	C₂	1	1	yes	maximal, characteristic, complemented
6	#65997	C₂	1	2	yes	maximal, complemented
7	#65992	C₂	1	2	yes	maximal, complemented
8	#65952	C₂	1	1	yes	maximal, characteristic, complemented
9	#65945	C₂	1	1	yes	maximal, characteristic, complemented
10	#65944	C₂	1	2	yes	maximal, complemented
11	#65941	C₂	1	1	yes	maximal, characteristic, complemented
12	D₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
13	#65930	C₂	1	2	yes	maximal, complemented
14	#65897	C₂	1	1	yes	maximal, characteristic, complemented
15	#65889	C₂	1	1	yes	maximal, characteristic, complemented
16	#65888	C₂	1	2	yes	maximal, complemented
17	#65881	C₂	1	1	yes	maximal, characteristic, complemented
18	#65879	C₂	1	1	yes	maximal, characteristic, complemented
19	#65872	C₂	1	2	yes	maximal, complemented
20	#65866	C₂	1	1	yes	maximal, characteristic, complemented
21	#65857	C₂	1	1	yes	maximal, characteristic, complemented
22	#65848	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#4038	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#711	C₂²	1	2	yes	complemented
25	C₂×#711	C₂²	1	2	yes	complemented
26	C₂×D₄×D₅	C₂²	1	1	yes	characteristic
27	C₂×D₄×D₅	C₂²	1	2	yes	—
28	C₂×#709	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₅	C₂²	1	1	yes	characteristic
30	C₅×#126	C₂²	1	2	yes	complemented
31	C₅×#125	C₂²	1	1	yes	characteristic, complemented
32	C₅×#123	C₂²	1	2	yes	complemented
33	C₅×#121	C₂²	1	1	yes	characteristic
34	C₅×#121	C₂²	1	2	yes	complemented
35	C₅×#121	C₂²	1	1	yes	characteristic, complemented
36	C₄×C₅×D₄	C₂²	1	2	yes	complemented
37	C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
38	C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
39	C₅×#117	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
41	#4086	C₂²	1	2	yes	complemented
42	#4085	C₂²	1	2	yes	—
43	#4085	C₂²	1	1	yes	characteristic, complemented
44	#4085	C₂²	1	2	yes	complemented
45	#4084	C₂²	1	1	yes	characteristic
46	#4084	C₂²	1	1	yes	characteristic, complemented
47	#4083	C₂²	1	1	yes	characteristic
48	#4083	C₂²	1	2	yes	—
49	#4081	C₂²	1	2	yes	complemented
50	D₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
51	D₄×Dic₅	C₂²	1	2	yes	complemented
52	#4076	C₂²	1	1	yes	characteristic
53	#4076	C₂²	1	2	yes	complemented
54	#4076	C₂²	1	1	yes	characteristic, complemented
55	#4076	C₂²	1	2	yes	complemented
56	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
57	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
58	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
59	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
60	C₂×#685	C₂²	1	2	yes	—
61	C₂×#685	C₂²	1	2	yes	—
62	#4072	C₂²	1	2	yes	complemented
63	C₂×C₄⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₄⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₄×Dic₅	C₂²	1	2	yes	complemented
66	#4044	C₂²	1	2	yes	complemented
67	#4044	C₂²	1	2	yes	complemented
68	#4043	C₂²	1	2	yes	—
69	#4043	C₂²	1	2	yes	complemented
70	#4042	C₂²	1	2	yes	—
71	#4042	C₂²	1	1	yes	characteristic, complemented
72	#4041	C₂²	1	1	yes	characteristic
73	#4041	C₂²	1	1	yes	characteristic, complemented
74	#4041	C₂²	1	2	yes	complemented
75	#4040	C₂²	1	1	yes	characteristic
76	#4040	C₂²	1	2	yes	complemented
77	#4040	C₂²	1	2	yes	complemented
78	#4039	C₂²	1	1	yes	characteristic, complemented
79	#4039	C₂²	1	2	yes	complemented
80	#4038	C₂²	1	1	yes	characteristic
81	#4038	C₂²	1	1	yes	characteristic
82	#4038	C₂²	1	2	yes	—
83	#4038	C₂²	1	1	yes	characteristic, complemented
84	#4038	C₂²	1	1	yes	characteristic, complemented
85	#4038	C₂²	1	2	yes	complemented
86	#4038	C₂²	1	1	yes	characteristic, complemented
87	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
88	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
89	#4036	C₂²	1	1	yes	characteristic, complemented
90	#4035	C₂²	1	2	yes	complemented
91	#4034	C₂²	1	1	yes	characteristic, complemented
92	#4034	C₂²	1	2	yes	complemented
93	#4032	C₂²	1	2	yes	complemented
94	#4032	C₂²	1	2	yes	complemented
95	#4032	C₂²	1	2	yes	complemented
96	#4031	C₂²	1	2	yes	complemented
97	#4031	C₂²	1	2	yes	complemented
98	#4031	C₂²	1	2	yes	complemented
99	#4031	C₂²	1	2	yes	complemented
100	#4030	C₂²	1	2	yes	—
101	#4030	C₂²	1	2	yes	complemented
102	#4030	C₂²	1	1	yes	characteristic, complemented
103	#4029	C₂²	1	1	yes	characteristic
104	#4029	C₂²	1	2	yes	complemented
105	#4028	C₂²	1	1	yes	characteristic
106	#4028	C₂²	1	2	yes	—
107	#4027	C₂²	1	2	yes	—
108	#4027	C₂²	1	2	yes	complemented
109	#4027	C₂²	1	2	yes	complemented
110	D₅×C₂²⋊C₄	C₂²	1	2	yes	—
111	D₅×C₂²⋊C₄	C₂²	1	2	yes	—
112	#4025	C₂²	1	2	yes	complemented
113	#4024	C₂²	1	1	yes	characteristic, complemented
114	#4024	C₂²	1	2	yes	complemented
115	#4021	C₂²	1	2	yes	complemented
116	C₄×D₂₀	C₂²	1	2	yes	—
117	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
119	#4018	C₂²	1	1	yes	characteristic
120	#4018	C₂²	1	2	yes	complemented
121	#4015	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₁₀	C₂²	1	2	yes	complemented
123	#3494	—	5	1	no	maximal, Sylow
124	C₂³×D₅	C₂³	1	1	yes	characteristic
125	C₂³×D₅	C₂³	1	2	yes	—
126	C₂×C₅×D₄	C₂³	1	2	yes	—
127	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
128	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
129	C₂×C₅×D₄	C₂³	1	2	yes	—
130	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
132	C₂²×C₄×C₅	C₂³	1	2	yes	—
133	C₂²×C₄×C₅	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
143	C₂²×Dic₅	C₂³	1	1	yes	characteristic
144	C₂²×Dic₅	C₂³	1	2	yes	—
145	C₂²×Dic₅	C₂³	1	2	yes	—
146	C₂²×Dic₅	C₂³	1	2	yes	—
147	#711	—	4	4	no	—
148	#711	—	4	4	no	—
149	D₄×D₅	—	2	4	no	—
150	D₄×D₅	—	4	4	no	—
151	#709	—	2	4	no	—
152	C₂×D₂₀	C₂³	1	1	yes	characteristic
153	C₂×D₂₀	C₂³	1	1	yes	characteristic
154	C₂×D₂₀	C₂³	1	2	yes	—
155	C₂×D₂₀	C₂³	1	1	yes	characteristic
156	C₂×D₂₀	C₂³	1	2	yes	—
157	C₂×C₄×D₅	—	2	4	no	—
158	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₅	C₂³	1	2	yes	—
163	C₂×C₄×D₅	C₂³	1	2	yes	—
164	C₂×C₄×D₅	C₂³	1	2	yes	—
165	C₂×C₄×D₅	C₂³	1	2	yes	—
166	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
167	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
168	C₂×Dic₁₀	C₂³	1	2	yes	—
169	C₂×Dic₁₀	C₂³	1	2	yes	—
170	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₅×C₄⋊C₄	C₂³	1	2	yes	—
173	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
174	C₅×C₄⋊C₄	C₂³	1	2	yes	—
175	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₅×C₄⋊C₄	C₂³	1	2	yes	—
177	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
179	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
182	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₄²×C₅	C₂³	1	2	yes	—
184	C₄²×C₅	C₂³	1	1	yes	characteristic
185	C₂²⋊Dic₅	C₂³	1	2	yes	—
186	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
187	C₂²⋊Dic₅	C₂³	1	2	yes	—
188	C₂²⋊Dic₅	C₂³	1	2	yes	—
189	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
190	#685	C₂³	1	1	yes	characteristic
191	#685	C₂³	1	1	yes	characteristic
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	#685	C₂³	1	1	yes	characteristic
197	#685	C₂³	1	1	yes	characteristic
198	#685	C₂³	1	2	yes	—
199	#685	C₂³	1	1	yes	characteristic
200	#685	C₂³	1	2	yes	—
201	#685	C₂³	1	2	yes	—
202	#685	C₂³	1	2	yes	—
203	#685	C₂³	1	2	yes	—
204	#685	C₂³	1	1	yes	characteristic
205	#685	C₂³	1	2	yes	—
206	#685	C₂³	1	2	yes	—
207	C₄⋊Dic₅	C₂³	1	2	yes	—
208	C₄⋊Dic₅	C₂³	1	2	yes	—
209	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
210	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
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	2	yes	—
215	#683	C₂³	1	2	yes	—
216	#683	C₂³	1	2	yes	—
217	#683	C₂³	1	1	yes	characteristic
218	#683	C₂³	1	1	yes	characteristic
219	#683	C₂³	1	1	yes	characteristic
220	#683	C₂³	1	2	yes	—
221	#683	C₂³	1	1	yes	characteristic
222	#683	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	C₄×Dic₅	C₂³	1	2	yes	—
227	C₄×Dic₅	C₂³	1	2	yes	—
228	C₄×Dic₅	C₂³	1	2	yes	—
229	#555	—	5	1	no	—
230	#555	—	5	1	no	—
231	#553	—	5	1	no	—
232	#553	—	5	1	no	—
233	#553	—	5	1	no	—
234	#553	D₅	1	1	yes	characteristic, complemented
235	#551	—	5	2	no	—
236	#551	—	5	2	no	—
237	#547	—	5	1	no	—
238	#547	—	5	1	no	—
239	#546	—	5	2	no	—
240	#546	—	5	2	no	—
241	#544	—	5	1	no	—
242	#542	—	5	2	no	—
243	#540	—	5	2	no	—
244	#535	—	5	1	no	—
245	#532	—	5	2	no	—
246	#529	—	5	2	no	—
247	#525	—	5	1	no	—
248	C₂×#121	—	5	1	no	—
249	#520	—	5	1	no	—
250	#518	—	5	1	no	—
251	C₂×#117	—	5	1	no	—
252	C₂³×C₅	C₂⁴	1	2	yes	—
253	C₂³×C₅	C₂⁴	1	1	yes	characteristic
254	C₂³×C₅	C₂⁴	1	1	yes	characteristic
255	C₂²×D₅	—	2	2	no	—
256	C₂²×D₅	—	2	2	no	—
257	C₂²×D₅	—	2	4	no	—
258	C₂²×D₅	—	4	1	no	—
259	C₂²×D₅	—	4	2	no	—
260	C₂²×D₅	—	4	2	no	—
261	C₂²×D₅	C₂⁴	1	1	yes	characteristic
262	C₂²×D₅	C₂⁴	1	2	yes	—
263	C₂²×D₅	C₂⁴	1	1	yes	characteristic
264	C₂²×D₅	C₂⁴	1	1	yes	characteristic
265	C₅×D₄	—	2	4	no	—
266	C₅×D₄	—	2	2	no	—
267	C₅×D₄	—	2	2	no	—
268	C₅×D₄	—	4	2	no	—
269	C₂×C₄×C₅	—	2	2	no	—
270	C₂×C₄×C₅	—	2	2	no	—
271	C₂×C₄×C₅	—	4	2	no	—
272	C₂×C₄×C₅	—	4	2	no	—
273	C₂×C₄×C₅	C₂⁴	1	2	yes	—
274	C₂×C₄×C₅	C₂⁴	1	2	yes	—
275	C₂×C₄×C₅	C₂⁴	1	2	yes	—
276	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
277	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
278	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
279	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
280	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
281	C₂²⋊D₅	—	2	4	no	—
282	C₂²⋊D₅	—	2	2	no	—
283	C₂²⋊D₅	—	2	2	no	—
284	C₂²⋊D₅	—	2	2	no	—
285	C₂²⋊D₅	—	2	4	no	—
286	C₂²⋊D₅	—	4	2	no	—
287	C₂²⋊D₅	—	4	2	no	—
288	C₂²⋊D₅	—	4	2	no	—
289	C₂²⋊D₅	—	4	1	no	—
290	C₂×Dic₅	—	2	4	no	—
291	C₂×Dic₅	—	2	2	no	—
292	C₂×Dic₅	—	4	2	no	—
293	C₂×Dic₅	—	4	2	no	—
294	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
295	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
296	C₂×Dic₅	C₂⁴	1	2	yes	—
297	C₂×Dic₅	C₂⁴	1	2	yes	—
298	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
299	C₂×Dic₅	C₂⁴	1	2	yes	—
300	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
301	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
302	D₂₀	—	2	2	no	—
303	D₂₀	—	2	2	no	—
304	D₂₀	—	4	1	no	—
305	D₂₀	—	4	2	no	—
306	D₂₀	—	4	2	no	—
307	C₄×D₅	—	2	2	no	—
308	C₄×D₅	—	2	2	no	—
309	C₄×D₅	—	2	2	no	—
310	C₄×D₅	—	2	2	no	—
311	C₄×D₅	—	4	2	no	—
312	C₄×D₅	—	4	2	no	—
313	C₄×D₅	—	4	2	no	—
314	C₄×D₅	—	4	2	no	—
315	C₄×D₅	#41	1	4	yes	complemented
316	Dic₁₀	—	2	2	no	—
317	Dic₁₀	—	4	2	no	—
318	Dic₁₀	—	4	2	no	—
319	C₂×#41	—	5	2	no	—
320	C₂×#41	—	5	2	no	—
321	C₂×#41	—	5	1	no	—
322	C₂²×D₄	—	5	1	no	—
323	C₂²×D₄	—	5	2	no	—
324	C₂³×C₄	—	5	1	no	—
325	C₄⋊Q₈	—	5	2	no	—
326	C₄⋊Q₈	—	5	1	no	—
327	C₄⋊Q₈	—	5	1	no	—
328	#127	—	5	2	no	—
329	#126	—	5	2	no	—
330	#126	—	5	2	no	—
331	#126	—	5	2	no	—
332	#126	C₂×D₅	1	2	yes	complemented
333	#125	—	5	2	no	—
334	#125	—	5	1	no	—
335	#125	C₂×D₅	1	1	yes	characteristic, complemented
336	#124	—	5	2	no	—
337	#124	—	5	2	no	—
338	#124	—	5	2	no	—
339	#124	—	5	2	no	—
340	#124	—	5	2	no	—
341	#123	—	5	2	no	—
342	#123	—	5	1	no	—
343	#123	—	5	2	no	—
344	#123	—	5	2	no	—
345	#123	—	5	1	no	—
346	#123	—	5	2	no	—
347	#123	—	5	2	no	—
348	#123	—	5	2	no	—
349	#123	—	5	2	no	—
350	#123	C₂×D₅	1	2	yes	complemented
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	—	5	1	no	—
356	C₂²⋊Q₈	—	5	2	no	—
357	#121	—	5	2	no	—
358	#121	—	5	1	no	—
359	#121	—	5	1	no	—
360	#121	—	5	1	no	—
361	#121	—	5	2	no	—
362	#121	—	5	1	no	—
363	#121	—	5	2	no	—
364	#121	—	5	1	no	—
365	#121	—	5	2	no	—
366	#121	—	5	1	no	—
367	#121	—	5	1	no	—
368	#121	—	5	2	no	—
369	#121	—	5	2	no	—
370	#121	—	5	1	no	—
371	#121	—	5	2	no	—
372	#121	C₂×D₅	1	1	yes	characteristic
373	#121	C₂×D₅	1	2	yes	complemented
374	#121	C₂×D₅	1	1	yes	characteristic, complemented
375	#120	—	5	1	no	—
376	#120	—	5	2	no	—
377	#120	—	5	1	no	—
378	#120	—	5	2	no	—
379	C₄×Q₈	—	5	2	no	—
380	C₄×D₄	—	5	1	no	—
381	C₄×D₄	—	5	2	no	—
382	C₄×D₄	—	5	2	no	—
383	C₄×D₄	—	5	1	no	—
384	C₄×D₄	—	5	1	no	—
385	C₄×D₄	—	5	2	no	—
386	C₄×D₄	—	5	1	no	—
387	C₄×D₄	—	5	2	no	—
388	C₄×D₄	—	5	2	no	—
389	C₄×D₄	—	5	2	no	—
390	C₄×D₄	—	5	2	no	—
391	C₄×D₄	—	5	1	no	—
392	C₄×D₄	—	5	2	no	—
393	C₄×D₄	—	5	1	no	—
394	C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
395	C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
396	C₄×D₄	C₂×D₅	1	2	yes	complemented
397	#117	—	5	2	no	—
398	#117	—	5	1	no	—
399	#117	—	5	1	no	—
400	#117	—	5	2	no	—
401	#117	—	5	2	no	—
402	#117	—	5	1	no	—
403	#117	—	5	1	no	—
404	#117	—	5	1	no	—
405	#117	—	5	1	no	—
406	#117	—	5	2	no	—
407	#117	C₂×D₅	1	1	yes	characteristic, complemented
408	C₂×C₄⋊C₄	—	5	1	no	—
409	C₂×C₄⋊C₄	—	5	1	no	—
410	C₂×C₄⋊C₄	—	5	1	no	—
411	C₂×C₄⋊C₄	—	5	1	no	—
412	C₂×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
413	C₂×C₂²⋊C₄	—	5	2	no	—
414	C₂×C₂²⋊C₄	—	5	2	no	—
415	C₂×C₂²⋊C₄	—	5	2	no	—
416	C₂×C₂²⋊C₄	—	5	2	no	—
417	C₂×C₄²	—	5	2	no	—
418	C₂²×C₅	—	2	1	no	—
419	C₂²×C₅	—	2	1	no	—
420	C₂²×C₅	—	2	1	no	—
421	C₂²×C₅	—	2	2	no	—
422	C₂²×C₅	—	2	1	no	—
423	C₂²×C₅	—	2	2	no	—
424	C₂²×C₅	—	2	1	no	—
425	C₂²×C₅	—	2	2	no	—
426	C₂²×C₅	H(5,𝔽₂)	1	2	yes	—
427	C₂²×C₅	C₂⁵	1	1	yes	characteristic
428	C₂×D₅	—	2	1	no	—
429	C₂×D₅	—	2	1	no	—
430	C₂×D₅	—	2	1	no	—
431	C₂×D₅	—	2	1	no	—
432	C₂×D₅	—	2	2	no	—
433	C₂×D₅	—	2	1	no	—
434	C₂×D₅	—	2	2	no	—
435	C₂×D₅	—	2	1	no	—
436	C₂×D₅	—	2	2	no	—
437	C₂×D₅	—	2	1	no	—
438	C₂×D₅	—	2	1	no	—
439	C₂×D₅	—	4	4	no	—
440	C₂×D₅	—	8	4	no	—
441	C₂×D₅	C₂×#41	1	2	yes	—
442	C₄×C₅	—	2	1	no	—
443	C₄×C₅	—	2	1	no	—
444	C₄×C₅	—	2	1	no	—
445	C₄×C₅	—	2	2	no	—
446	C₄×C₅	—	2	2	no	—
447	C₄×C₅	—	2	1	no	—
448	C₄×C₅	—	2	2	no	—
449	C₄×C₅	C₂×#41	1	2	yes	—
450	Dic₅	—	2	1	no	—
451	Dic₅	—	2	1	no	—
452	Dic₅	—	2	2	no	—
453	Dic₅	—	2	1	no	—
454	Dic₅	—	2	2	no	—
455	Dic₅	—	2	2	no	—
456	Dic₅	—	2	1	no	—
457	Dic₅	C₂×#41	1	2	yes	—
458	C₂⁴	—	5	1	no	—
459	C₂⁴	—	5	2	no	—
460	#41	—	10	4	no	—
461	#41	—	20	4	no	—
462	#41	—	20	4	no	—
463	C₂×Q₈	—	5	1	no	—
464	C₂×Q₈	—	5	2	no	—
465	C₂×Q₈	—	5	2	no	—
466	C₂×D₄	—	5	1	no	—
467	C₂×D₄	—	5	2	no	—
468	C₂×D₄	—	5	1	no	—
469	C₂×D₄	—	5	1	no	—
470	C₂×D₄	—	5	2	no	—
471	C₂×D₄	—	5	1	no	—
472	C₂×D₄	—	5	2	no	—
473	C₂×D₄	—	5	2	no	—
474	C₂×D₄	—	5	2	no	—
475	C₂×D₄	—	5	1	no	—
476	C₂×D₄	—	5	1	no	—
477	C₂×D₄	—	5	1	no	—
478	C₂×D₄	—	5	2	no	—
479	C₂×D₄	—	5	2	no	—
480	C₂×D₄	—	10	4	no	—
481	C₂×D₄	—	20	4	no	—
482	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
483	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
484	C₂×D₄	C₂²×D₅	1	2	yes	—
485	C₂×D₄	C₂²×D₅	1	2	yes	—
486	C₂²×C₄	—	5	1	no	—
487	C₂²×C₄	—	5	1	no	—
488	C₂²×C₄	—	5	2	no	—
489	C₂²×C₄	—	5	2	no	—
490	C₂²×C₄	—	5	2	no	—
491	C₂²×C₄	—	5	1	no	—
492	C₂²×C₄	—	5	1	no	—
493	C₂²×C₄	—	5	1	no	—
494	C₂²×C₄	—	5	1	no	—
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	—	10	4	no	—
500	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
501	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
502	C₂²×C₄	C₂²×D₅	1	2	yes	—
503	C₂²×C₄	C₂²×D₅	1	2	yes	—
504	C₄⋊C₄	—	5	1	no	—
505	C₄⋊C₄	—	5	1	no	—
506	C₄⋊C₄	—	5	1	no	—
507	C₄⋊C₄	—	5	2	no	—
508	C₄⋊C₄	—	5	2	no	—
509	C₄⋊C₄	—	5	2	no	—
510	C₄⋊C₄	—	5	2	no	—
511	C₄⋊C₄	—	5	1	no	—
512	C₄⋊C₄	—	5	1	no	—
513	C₄⋊C₄	—	5	1	no	—
514	C₄⋊C₄	—	5	1	no	—
515	C₄⋊C₄	—	5	2	no	—
516	C₄⋊C₄	—	5	2	no	—
517	C₄⋊C₄	—	5	2	no	—
518	C₄⋊C₄	—	5	2	no	—
519	C₄⋊C₄	—	5	1	no	—
520	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
521	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
522	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
523	C₄⋊C₄	C₂²×D₅	1	2	yes	—
524	C₄⋊C₄	C₂²×D₅	1	2	yes	—
525	C₄⋊C₄	C₂²×D₅	1	2	yes	—
526	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
527	C₂²⋊C₄	—	5	2	no	—
528	C₂²⋊C₄	—	5	2	no	—
529	C₂²⋊C₄	—	5	2	no	—
530	C₂²⋊C₄	—	5	1	no	—
531	C₂²⋊C₄	—	5	1	no	—
532	C₂²⋊C₄	—	5	2	no	—
533	C₂²⋊C₄	—	5	1	no	—
534	C₂²⋊C₄	—	5	1	no	—
535	C₂²⋊C₄	—	5	2	no	—
536	C₂²⋊C₄	—	5	2	no	—
537	C₂²⋊C₄	—	5	2	no	—
538	C₂²⋊C₄	—	5	2	no	—
539	C₂²⋊C₄	—	5	2	no	—
540	C₂²⋊C₄	—	5	2	no	—
541	C₂²⋊C₄	—	5	2	no	—
542	C₂²⋊C₄	—	5	2	no	—
543	C₂²⋊C₄	—	5	2	no	—
544	C₂²⋊C₄	—	5	1	no	—
545	C₂²⋊C₄	—	5	2	no	—
546	C₂²⋊C₄	—	5	1	no	—
547	C₂²⋊C₄	—	5	1	no	—
548	C₂²⋊C₄	—	5	1	no	—
549	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
550	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
551	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
552	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
553	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
554	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
555	C₄²	—	5	2	no	—
556	C₄²	—	5	2	no	—
557	C₄²	—	5	2	no	—
558	C₄²	—	5	2	no	—
559	C₄²	—	5	2	no	—
560	C₄²	—	5	1	no	—
561	C₄²	C₂²×D₅	1	2	yes	—
562	C₄²	C₂²×D₅	1	1	yes	characteristic
563	C₂×C₅	—	2	2	no	—
564	C₂×C₅	—	4	2	no	—
565	C₂×C₅	—	4	1	no	—
566	C₂×C₅	C₂²×#41	1	1	yes	characteristic
567	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
568	C₂×C₅	#585	1	1	yes	characteristic
569	D₅	—	2	2	no	—
570	D₅	—	4	1	no	—
571	D₅	—	4	1	no	—
572	D₅	—	4	2	no	—
573	C₂³	—	5	1	no	—
574	C₂³	—	5	1	no	—
575	C₂³	—	5	2	no	—
576	C₂³	—	5	1	no	—
577	C₂³	—	10	2	no	—
578	C₂³	—	10	4	no	—
579	C₂³	—	10	2	no	—
580	C₂³	—	20	1	no	—
581	C₂³	—	20	2	no	—
582	C₂³	—	20	2	no	—
583	C₂³	C₂³×D₅	1	2	yes	—
584	C₂³	C₂³×D₅	1	1	yes	characteristic
585	C₂³	C₂³×D₅	1	1	yes	characteristic
586	Q₈	—	10	2	no	—
587	Q₈	—	20	2	no	—
588	Q₈	—	20	2	no	—
589	D₄	—	2	4	no	—
590	D₄	—	2	2	no	—
591	D₄	—	2	2	no	—
592	D₄	—	4	2	no	—
593	D₄	—	10	2	no	—
594	D₄	—	10	4	no	—
595	D₄	—	10	2	no	—
596	D₄	—	10	2	no	—
597	D₄	—	10	4	no	—
598	D₄	—	10	2	no	—
599	D₄	—	10	2	no	—
600	D₄	—	20	2	no	—
601	D₄	—	20	1	no	—
602	D₄	—	20	2	no	—
603	D₄	—	20	2	no	—
604	D₄	—	20	2	no	—
605	D₄	—	20	2	no	—
606	D₄	—	20	1	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	4	2	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	5	1	no	—
612	C₂×C₄	—	5	4	no	—
613	C₂×C₄	—	5	1	no	—
614	C₂×C₄	—	5	1	no	—
615	C₂×C₄	—	5	2	no	—
616	C₂×C₄	—	5	2	no	—
617	C₂×C₄	—	5	1	no	—
618	C₂×C₄	—	5	1	no	—
619	C₂×C₄	—	5	2	no	—
620	C₂×C₄	—	10	2	no	—
621	C₂×C₄	—	10	2	no	—
622	C₂×C₄	—	10	2	no	—
623	C₂×C₄	—	10	4	no	—
624	C₂×C₄	—	10	2	no	—
625	C₂×C₄	—	10	2	no	—
626	C₂×C₄	—	20	2	no	—
627	C₂×C₄	—	20	2	no	—
628	C₂×C₄	—	20	2	no	—
629	C₂×C₄	—	20	2	no	—
630	C₂×C₄	—	20	2	no	—
631	C₂×C₄	—	20	2	no	—
632	C₂×C₄	C₂³×D₅	1	2	yes	—
633	C₂×C₄	C₂³×D₅	1	2	yes	—
634	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
635	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
636	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
637	C₂×C₄	C₂³×D₅	1	2	yes	—
638	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
639	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
640	C₅	#3494	1	1	yes	characteristic, complemented, Sylow
641	C₂²	—	2	1	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	2	2	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	1	no	—
649	C₂²	—	5	2	no	—
650	C₂²	—	10	1	no	—
651	C₂²	—	10	1	no	—
652	C₂²	—	10	1	no	—
653	C₂²	—	10	1	no	—
654	C₂²	—	10	2	no	—
655	C₂²	—	10	1	no	—
656	C₂²	—	10	2	no	—
657	C₂²	—	10	1	no	—
658	C₂²	—	10	2	no	—
659	C₂²	—	10	1	no	—
660	C₂²	—	10	1	no	—
661	C₂²	—	20	4	no	—
662	C₂²	—	40	4	no	—
663	C₂²	#4149	1	2	yes	—
664	C₂²	C₂⁴×D₅	1	1	yes	characteristic
665	C₄	—	2	1	no	—
666	C₄	—	2	1	no	—
667	C₄	—	2	2	no	—
668	C₄	—	2	1	no	—
669	C₄	—	2	2	no	—
670	C₄	—	2	1	no	—
671	C₄	—	2	2	no	—
672	C₄	—	5	2	no	—
673	C₄	—	10	1	no	—
674	C₄	—	10	1	no	—
675	C₄	—	10	2	no	—
676	C₄	—	10	2	no	—
677	C₄	—	10	2	no	—
678	C₄	—	10	1	no	—
679	C₄	—	10	1	no	—
680	C₄	D₅×#41	1	2	yes	—
681	C₂	—	2	2	no	—
682	C₂	—	4	2	no	—
683	C₂	—	4	1	no	—
684	C₂	—	10	2	no	—
685	C₂	—	20	1	no	—
686	C₂	—	20	2	no	—
687	C₂	—	20	1	no	—
688	C₂	C₂×D₅×#41	1	1	yes	characteristic
689	C₂	C₂×#4149	1	1	yes	characteristic
690	C₂	#66285	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁵
Fitting	C₅×#553	C₂
hypercenter	#553	D₅
hypocenter	C₅	#3494
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #553

Complements

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

N	H ≅ G/N	type
1. C₅×#553	C₂	semidirect
2. #66044	C₂	semidirect
3. #66039	C₂	semidirect
4. #66029	C₂	semidirect
5. #66023	C₂	semidirect
6. #65997	C₂	semidirect
7. #65992	C₂	semidirect
8. #65952	C₂	semidirect
9. #65945	C₂	semidirect
10. #65944	C₂	semidirect
11. #65941	C₂	semidirect
12. D₅×#121	C₂	semidirect
13. #65930	C₂	semidirect
14. #65897	C₂	semidirect
15. #65889	C₂	semidirect
16. #65888	C₂	semidirect
17. #65881	C₂	semidirect
18. #65879	C₂	semidirect
19. #65872	C₂	semidirect
20. #65866	C₂	semidirect
21. #65857	C₂	semidirect
22. #65848	C₂	semidirect
23. C₂×#4038	C₂	semidirect
24. C₂×#711	C₂²	semidirect
25. C₂×#711	C₂²	semidirect
30. C₅×#126	C₂²	semidirect
31. C₅×#125	C₂²	semidirect
32. C₅×#123	C₂²	semidirect
34. C₅×#121	C₂²	semidirect
35. C₅×#121	C₂²	semidirect
36. C₄×C₅×D₄	C₂²	semidirect
37. C₄×C₅×D₄	C₂²	semidirect
38. C₄×C₅×D₄	C₂²	semidirect
39. C₅×#117	C₂²	semidirect
40. C₂×C₅×C₄⋊C₄	C₂²	semidirect
41. #4086	C₂²	semidirect
43. #4085	C₂²	semidirect
44. #4085	C₂²	semidirect
46. #4084	C₂²	semidirect
49. #4081	C₂²	semidirect
50. D₄×Dic₅	C₂²	semidirect
51. D₄×Dic₅	C₂²	semidirect
53. #4076	C₂²	semidirect
54. #4076	C₂²	semidirect
55. #4076	C₂²	semidirect
56. C₄×C₂²⋊D₅	C₂²	semidirect
57. C₄×C₂²⋊D₅	C₂²	semidirect
58. C₄×C₂²⋊D₅	C₂²	semidirect
59. C₄×C₂²⋊D₅	C₂²	semidirect
62. #4072	C₂²	semidirect
63. C₂×C₄⋊Dic₅	C₂²	semidirect
64. C₂×C₄⋊Dic₅	C₂²	semidirect
65. C₂×C₄×Dic₅	C₂²	semidirect
66. #4044	C₂²	semidirect
67. #4044	C₂²	semidirect
69. #4043	C₂²	semidirect
71. #4042	C₂²	semidirect
73. #4041	C₂²	semidirect
74. #4041	C₂²	semidirect
76. #4040	C₂²	semidirect
77. #4040	C₂²	semidirect
78. #4039	C₂²	semidirect
79. #4039	C₂²	semidirect
83. #4038	C₂²	semidirect
84. #4038	C₂²	semidirect
85. #4038	C₂²	semidirect
86. #4038	C₂²	semidirect
88. D₅×C₄⋊C₄	C₂²	semidirect
89. #4036	C₂²	semidirect
90. #4035	C₂²	semidirect
91. #4034	C₂²	semidirect
92. #4034	C₂²	semidirect
93. #4032	C₂²	semidirect
94. #4032	C₂²	semidirect
95. #4032	C₂²	semidirect
96. #4031	C₂²	semidirect
97. #4031	C₂²	semidirect
98. #4031	C₂²	semidirect
99. #4031	C₂²	semidirect
101. #4030	C₂²	semidirect
102. #4030	C₂²	semidirect
104. #4029	C₂²	semidirect
108. #4027	C₂²	semidirect
109. #4027	C₂²	semidirect
112. #4025	C₂²	semidirect
113. #4024	C₂²	semidirect
114. #4024	C₂²	semidirect
115. #4021	C₂²	semidirect
117. C₄×D₂₀	C₂²	semidirect
118. C₄×D₂₀	C₂²	semidirect
120. #4018	C₂²	semidirect
121. #4015	C₂²	semidirect
122. C₄×Dic₁₀	C₂²	semidirect
234. #553	D₅	semidirect
315. C₄×D₅	#41	semidirect
332. #126	C₂×D₅	semidirect
335. #125	C₂×D₅	semidirect
350. #123	C₂×D₅	semidirect
373. #121	C₂×D₅	semidirect
374. #121	C₂×D₅	semidirect
394. C₄×D₄	C₂×D₅	semidirect
395. C₄×D₄	C₂×D₅	semidirect
396. C₄×D₄	C₂×D₅	semidirect
407. #117	C₂×D₅	semidirect
412. C₂×C₄⋊C₄	C₂×D₅	semidirect
640. C₅	#3494	semidirect

Maximal subgroups

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

subgroup	index
C₅×#553	2
#66044	2
#66039	2
#66029	2
#66023	2
#65997	2
#65992	2
#65952	2
#65945	2
#65944	2
#65941	2
D₅×#121	2
#65930	2
#65897	2
#65889	2
#65888	2
#65881	2
#65879	2
#65872	2
#65866	2
#65857	2
#65848	2
C₂×#4038	2
#3494	5