Subgroups — #10618539

Order 640.

1142 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#546	C₂	1	1	yes	maximal, characteristic, complemented
2	#66166	C₂	1	1	yes	maximal, characteristic, complemented
3	#66165	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#4082	C₂	1	1	yes	maximal, characteristic, complemented
6	D₅×#124	C₂	1	1	yes	maximal, characteristic, complemented
7	#66005	C₂	1	1	yes	maximal, characteristic, complemented
8	#65996	C₂	1	2	yes	maximal, complemented
9	#65993	C₂	1	2	yes	maximal, complemented
10	#65966	C₂	1	1	yes	maximal, characteristic, complemented
11	#65958	C₂	1	1	yes	maximal, characteristic, complemented
12	#65950	C₂	1	2	yes	maximal, complemented
13	#65947	C₂	1	2	yes	maximal, complemented
14	#65946	C₂	1	1	yes	maximal, characteristic, complemented
15	#65934	C₂	1	1	yes	maximal, characteristic, complemented
16	#65927	C₂	1	2	yes	maximal, complemented
17	#65925	C₂	1	2	yes	maximal, complemented
18	#65893	C₂	1	1	yes	maximal, characteristic, complemented
19	#65891	C₂	1	1	yes	maximal, characteristic, complemented
20	#65886	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#711	C₂	1	1	yes	maximal, characteristic, complemented
22	#65829	C₂	1	2	yes	maximal, complemented
23	#65820	C₂	1	2	yes	maximal, complemented
24	C₂×C₅×#41	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₅×D₄	C₂²	1	1	yes	characteristic
26	C₂²×C₂²⋊D₅	C₂²	1	2	yes	—
27	C₂×Q₈×D₅	C₂²	1	1	yes	characteristic, complemented
28	C₂×#711	C₂²	1	1	yes	characteristic
29	C₂×D₄×D₅	C₂²	1	1	yes	characteristic
30	C₂×#709	C₂²	1	1	yes	characteristic, complemented
31	C₂²×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
32	C₅×#124	C₂²	1	1	yes	characteristic
33	C₅×#123	C₂²	1	2	yes	complemented
34	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₅×#121	C₂²	1	1	yes	characteristic
36	C₅×#121	C₂²	1	2	yes	complemented
37	C₅×#120	C₂²	1	2	yes	complemented
38	C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
39	C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
41	#4099	C₂²	1	2	yes	—
42	C₂×C₂²⋊Dic₅	C₂²	1	2	yes	complemented
43	C₂×C₂²⋊Dic₅	C₂²	1	2	yes	complemented
44	#4093	C₂²	1	1	yes	characteristic, complemented
45	Q₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
46	#4090	C₂²	1	1	yes	characteristic, complemented
47	#4086	C₂²	1	1	yes	characteristic
48	#4085	C₂²	1	2	yes	—
49	#4085	C₂²	1	2	yes	complemented
50	#4085	C₂²	1	2	yes	complemented
51	#4085	C₂²	1	2	yes	complemented
52	#4084	C₂²	1	1	yes	characteristic
53	#4084	C₂²	1	2	yes	complemented
54	#4084	C₂²	1	2	yes	complemented
55	#4083	C₂²	1	2	yes	—
56	#4083	C₂²	1	2	yes	complemented
57	#4082	C₂²	1	1	yes	characteristic
58	#4082	C₂²	1	1	yes	characteristic
59	#4082	C₂²	1	1	yes	characteristic, complemented
60	#4082	C₂²	1	1	yes	characteristic, complemented
61	#4082	C₂²	1	2	yes	complemented
62	#4082	C₂²	1	2	yes	complemented
63	#4082	C₂²	1	2	yes	complemented
64	#4081	C₂²	1	2	yes	complemented
65	D₄×Dic₅	C₂²	1	1	yes	characteristic
66	D₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
67	D₄×Dic₅	C₂²	1	2	yes	complemented
68	#4076	C₂²	1	1	yes	characteristic
69	#4075	C₂²	1	2	yes	complemented
70	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
71	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
72	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
73	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
74	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
75	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
76	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
77	#4072	C₂²	1	2	yes	complemented
78	#4070	C₂²	1	2	yes	complemented
79	#4070	C₂²	1	1	yes	characteristic, complemented
80	C₂×C₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
81	C₂×C₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
82	#4044	C₂²	1	2	yes	complemented
83	#4043	C₂²	1	1	yes	characteristic, complemented
84	#4042	C₂²	1	2	yes	complemented
85	#4042	C₂²	1	2	yes	complemented
86	#4039	C₂²	1	1	yes	characteristic, complemented
87	#4038	C₂²	1	1	yes	characteristic, complemented
88	#4038	C₂²	1	2	yes	complemented
89	#4036	C₂²	1	1	yes	characteristic, complemented
90	#4034	C₂²	1	2	yes	complemented
91	#4033	C₂²	1	1	yes	characteristic, complemented
92	#4033	C₂²	1	1	yes	characteristic, complemented
93	#4032	C₂²	1	2	yes	complemented
94	#4031	C₂²	1	2	yes	complemented
95	#4031	C₂²	1	2	yes	complemented
96	#4031	C₂²	1	2	yes	complemented
97	#4031	C₂²	1	2	yes	complemented
98	#4029	C₂²	1	2	yes	complemented
99	#4029	C₂²	1	2	yes	complemented
100	#4029	C₂²	1	2	yes	complemented
101	#4027	C₂²	1	1	yes	characteristic
102	#4027	C₂²	1	2	yes	—
103	#4027	C₂²	1	2	yes	complemented
104	#4027	C₂²	1	2	yes	complemented
105	#4027	C₂²	1	1	yes	characteristic, complemented
106	D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
107	D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
108	D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
109	#4025	C₂²	1	2	yes	complemented
110	#4025	C₂²	1	2	yes	complemented
111	#4025	C₂²	1	2	yes	complemented
112	#4025	C₂²	1	2	yes	complemented
113	#4024	C₂²	1	2	yes	complemented
114	#4024	C₂²	1	2	yes	complemented
115	#4023	C₂²	1	2	yes	complemented
116	#4023	C₂²	1	2	yes	complemented
117	#4023	C₂²	1	1	yes	characteristic, complemented
118	#4023	C₂²	1	1	yes	characteristic, complemented
119	#4021	C₂²	1	1	yes	characteristic, complemented
120	C₄²×D₅	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	#3514	—	5	1	no	maximal, Sylow
124	C₂⁴×C₅	C₂³	1	2	yes	—
125	C₂³×D₅	C₂³	1	2	yes	—
126	C₅×#41	—	4	2	no	—
127	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
128	C₂×C₅×D₄	—	4	2	no	—
129	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
130	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
131	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
132	C₂×C₅×D₄	C₂³	1	2	yes	—
133	C₂×C₅×D₄	C₂³	1	2	yes	—
134	C₂×C₅×D₄	C₂³	1	2	yes	—
135	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
137	C₂²×C₄×C₅	C₂³	1	2	yes	—
138	C₂²×C₄×C₅	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₅	—	2	8	no	—
140	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
147	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
148	C₂²×Dic₅	C₂³	1	1	yes	characteristic
149	C₂²×Dic₅	C₂³	1	1	yes	characteristic
150	C₂²×Dic₅	C₂³	1	2	yes	—
151	C₂²×Dic₅	C₂³	1	2	yes	—
152	C₂²×Dic₅	C₂³	1	1	yes	characteristic
153	C₂²×Dic₅	C₂³	1	1	yes	characteristic
154	Q₈×D₅	—	4	2	no	—
155	#711	—	2	4	no	—
156	D₄×D₅	—	4	2	no	—
157	#709	—	4	2	no	—
158	C₂×D₂₀	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	2	yes	—
162	C₂×C₄×D₅	C₂³	1	2	yes	—
163	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
164	C₂×C₄×D₅	C₂³	1	2	yes	—
165	C₂×Dic₁₀	—	4	2	no	—
166	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
167	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
168	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
169	C₂×Dic₁₀	C₂³	1	2	yes	—
170	C₂×Dic₁₀	C₂³	1	2	yes	—
171	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₅×C₄⋊C₄	C₂³	1	2	yes	—
174	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
175	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
180	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₄²×C₅	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₅	C₂³	1	2	yes	—
183	C₂²⋊Dic₅	C₂³	1	2	yes	—
184	C₂²⋊Dic₅	C₂³	1	2	yes	—
185	C₂²⋊Dic₅	C₂³	1	2	yes	—
186	C₂²⋊Dic₅	C₂³	1	2	yes	—
187	C₂²⋊Dic₅	C₂³	1	2	yes	—
188	C₂²⋊Dic₅	C₂³	1	2	yes	—
189	C₂²⋊Dic₅	C₂³	1	2	yes	—
190	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
191	C₂²⋊Dic₅	C₂³	1	2	yes	—
192	C₂²⋊Dic₅	C₂³	1	2	yes	—
193	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
194	C₂²⋊Dic₅	C₂³	1	2	yes	—
195	#685	C₂³	1	2	yes	—
196	#685	C₂³	1	2	yes	—
197	#685	C₂³	1	1	yes	characteristic
198	#685	C₂³	1	2	yes	—
199	#685	C₂³	1	2	yes	—
200	#685	C₂³	1	2	yes	—
201	#685	C₂³	1	1	yes	characteristic
202	#685	C₂³	1	2	yes	—
203	#685	C₂³	1	2	yes	—
204	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
205	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
206	C₄⋊Dic₅	C₂³	1	2	yes	—
207	C₄⋊Dic₅	C₂³	1	2	yes	—
208	C₄⋊Dic₅	C₂³	1	2	yes	—
209	#683	C₂³	1	1	yes	characteristic
210	#683	C₂³	1	1	yes	characteristic
211	#683	C₂³	1	2	yes	—
212	#683	C₂³	1	2	yes	—
213	#683	C₂³	1	2	yes	—
214	#683	C₂³	1	2	yes	—
215	#683	C₂³	1	1	yes	characteristic
216	#683	C₂³	1	1	yes	characteristic
217	#683	C₂³	1	2	yes	—
218	#683	C₂³	1	2	yes	—
219	C₄×Dic₅	C₂³	1	2	yes	—
220	C₄×Dic₅	C₂³	1	1	yes	characteristic
221	C₄×Dic₅	C₂³	1	1	yes	characteristic
222	C₄×Dic₅	C₂³	1	1	yes	characteristic
223	C₄×Dic₅	C₂³	1	1	yes	characteristic
224	C₄×Dic₅	C₂³	1	1	yes	characteristic
225	C₄×Dic₅	C₂³	1	1	yes	characteristic
226	C₄×Dic₅	C₂³	1	1	yes	characteristic
227	C₄×Dic₅	C₂³	1	2	yes	—
228	C₄×Dic₅	C₂³	1	2	yes	—
229	C₄×Dic₅	C₂³	1	1	yes	characteristic
230	C₄×Dic₅	C₂³	1	1	yes	characteristic
231	#559	—	5	1	no	—
232	#556	—	5	1	no	—
233	#555	—	5	2	no	—
234	#551	—	5	2	no	—
235	#551	—	5	2	no	—
236	D₄×Q₈	—	5	1	no	—
237	#548	—	5	1	no	—
238	#548	—	5	1	no	—
239	#546	—	5	1	no	—
240	#546	—	5	2	no	—
241	#546	D₅	1	1	yes	characteristic, complemented
242	D₄²	—	5	1	no	—
243	#542	—	5	2	no	—
244	#538	—	5	2	no	—
245	#538	—	5	2	no	—
246	#532	—	5	1	no	—
247	#529	—	5	1	no	—
248	#529	—	5	1	no	—
249	#529	—	5	1	no	—
250	C₂×#124	—	5	1	no	—
251	C₂×#124	—	5	1	no	—
252	#518	—	5	2	no	—
253	C₄×#41	—	5	1	no	—
254	C₂³×C₅	—	2	4	no	—
255	C₂³×C₅	—	4	2	no	—
256	C₂³×C₅	—	4	2	no	—
257	C₂³×C₅	C₂⁴	1	2	yes	—
258	C₂³×C₅	C₂⁴	1	2	yes	—
259	C₂³×C₅	C₂⁴	1	1	yes	characteristic
260	C₂³×C₅	C₂⁴	1	1	yes	characteristic
261	C₂²×D₅	—	2	4	no	—
262	C₂²×D₅	—	4	2	no	—
263	C₂²×D₅	—	4	2	no	—
264	C₂²×D₅	C₂⁴	1	2	yes	—
265	C₂²×D₅	C₂⁴	1	1	yes	characteristic
266	C₅×Q₈	—	2	2	no	—
267	C₅×D₄	—	2	2	no	—
268	C₅×D₄	—	2	2	no	—
269	C₅×D₄	—	2	2	no	—
270	C₅×D₄	—	4	2	no	—
271	C₅×D₄	—	4	2	no	—
272	C₅×D₄	—	4	2	no	—
273	C₂×C₄×C₅	—	2	2	no	—
274	C₂×C₄×C₅	—	2	2	no	—
275	C₂×C₄×C₅	—	4	2	no	—
276	C₂×C₄×C₅	—	4	2	no	—
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	2	yes	—
281	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
282	C₂×C₄×C₅	C₂⁴	1	2	yes	—
283	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
284	C₂²⋊D₅	—	2	4	no	—
285	C₂²⋊D₅	—	2	2	no	—
286	C₂²⋊D₅	—	2	4	no	—
287	C₂²⋊D₅	—	2	4	no	—
288	C₂²⋊D₅	—	4	2	no	—
289	C₂²⋊D₅	—	4	2	no	—
290	C₂²⋊D₅	—	4	2	no	—
291	C₂²⋊D₅	#41	1	4	yes	complemented
292	C₂×Dic₅	—	2	2	no	—
293	C₂×Dic₅	—	2	2	no	—
294	C₂×Dic₅	—	2	4	no	—
295	C₂×Dic₅	—	4	2	no	—
296	C₂×Dic₅	—	4	1	no	—
297	C₂×Dic₅	—	4	1	no	—
298	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
299	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
300	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
301	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
302	C₂×Dic₅	C₂⁴	1	2	yes	—
303	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
304	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
305	C₂×Dic₅	C₂⁴	1	2	yes	—
306	C₂×Dic₅	C₂⁴	1	2	yes	—
307	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
308	D₂₀	—	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	1	no	—
313	C₄×D₅	—	4	2	no	—
314	C₄×D₅	—	4	2	no	—
315	Dic₁₀	—	2	2	no	—
316	Dic₁₀	—	2	2	no	—
317	Dic₁₀	—	2	2	no	—
318	Dic₁₀	—	4	2	no	—
319	Dic₁₀	—	4	2	no	—
320	C₂×#41	—	5	1	no	—
321	C₂×#41	—	5	1	no	—
322	C₂×#41	C₂×D₅	1	1	yes	characteristic, complemented
323	C₂²×Q₈	—	5	1	no	—
324	C₂²×Q₈	—	5	1	no	—
325	C₂²×D₄	—	5	2	no	—
326	C₂²×D₄	—	5	1	no	—
327	C₂²×D₄	C₂×D₅	1	1	yes	characteristic
328	C₄⋊Q₈	—	5	1	no	—
329	C₄⋊Q₈	—	5	2	no	—
330	#127	—	5	1	no	—
331	#126	—	5	2	no	—
332	#126	—	5	2	no	—
333	#126	—	5	2	no	—
334	#126	—	5	2	no	—
335	#126	—	5	2	no	—
336	#125	—	5	1	no	—
337	#124	—	5	1	no	—
338	#124	—	5	1	no	—
339	#124	—	5	1	no	—
340	#124	—	5	2	no	—
341	#124	—	5	1	no	—
342	#124	—	5	1	no	—
343	#124	—	5	2	no	—
344	#124	—	5	2	no	—
345	#124	—	5	2	no	—
346	#124	—	5	2	no	—
347	#124	—	5	2	no	—
348	#124	—	5	2	no	—
349	#124	—	5	1	no	—
350	#124	C₂×D₅	1	1	yes	characteristic
351	#123	—	5	2	no	—
352	#123	—	5	2	no	—
353	#123	—	5	2	no	—
354	#123	—	5	2	no	—
355	#123	—	5	2	no	—
356	#123	—	5	2	no	—
357	#123	C₂×D₅	1	2	yes	complemented
358	C₂²⋊Q₈	—	5	1	no	—
359	C₂²⋊Q₈	—	5	2	no	—
360	C₂²⋊Q₈	—	5	1	no	—
361	C₂²⋊Q₈	—	5	2	no	—
362	C₂²⋊Q₈	—	5	2	no	—
363	C₂²⋊Q₈	—	5	2	no	—
364	C₂²⋊Q₈	—	5	2	no	—
365	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
366	#121	—	5	1	no	—
367	#121	—	5	2	no	—
368	#121	—	5	2	no	—
369	#121	—	5	2	no	—
370	#121	—	5	2	no	—
371	#121	—	5	2	no	—
372	#121	—	5	2	no	—
373	#121	—	5	1	no	—
374	#121	C₂×D₅	1	1	yes	characteristic
375	#121	C₂×D₅	1	2	yes	complemented
376	#120	—	5	2	no	—
377	#120	—	5	2	no	—
378	#120	—	5	2	no	—
379	#120	C₂×D₅	1	2	yes	complemented
380	C₄×Q₈	—	5	1	no	—
381	C₄×Q₈	—	5	1	no	—
382	C₄×Q₈	—	5	1	no	—
383	C₄×Q₈	—	5	1	no	—
384	C₄×Q₈	—	5	1	no	—
385	C₄×D₄	—	5	1	no	—
386	C₄×D₄	—	5	1	no	—
387	C₄×D₄	—	5	2	no	—
388	C₄×D₄	—	5	1	no	—
389	C₄×D₄	—	5	1	no	—
390	C₄×D₄	—	5	2	no	—
391	C₄×D₄	—	5	2	no	—
392	C₄×D₄	—	5	2	no	—
393	C₄×D₄	—	5	2	no	—
394	C₄×D₄	—	5	2	no	—
395	C₄×D₄	—	5	1	no	—
396	C₄×D₄	—	5	1	no	—
397	C₄×D₄	—	5	1	no	—
398	C₄×D₄	—	5	2	no	—
399	C₄×D₄	—	5	2	no	—
400	C₄×D₄	—	5	2	no	—
401	C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
402	C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
403	#117	—	5	2	no	—
404	#117	—	5	1	no	—
405	#117	—	5	2	no	—
406	#117	—	5	1	no	—
407	#117	—	5	1	no	—
408	#117	—	5	2	no	—
409	#117	—	5	2	no	—
410	C₂×C₂²⋊C₄	—	5	2	no	—
411	C₂×C₂²⋊C₄	—	5	2	no	—
412	C₂×C₂²⋊C₄	—	5	2	no	—
413	C₂×C₂²⋊C₄	—	5	2	no	—
414	C₂×C₂²⋊C₄	—	5	2	no	—
415	C₂×C₂²⋊C₄	C₂×D₅	1	2	yes	complemented
416	C₂×C₄²	—	5	1	no	—
417	C₂×C₄²	—	5	1	no	—
418	C₂×C₄²	—	5	1	no	—
419	C₂²×C₅	—	2	1	no	—
420	C₂²×C₅	—	2	1	no	—
421	C₂²×C₅	—	2	1	no	—
422	C₂²×C₅	—	2	2	no	—
423	C₂²×C₅	—	2	2	no	—
424	C₂²×C₅	—	2	1	no	—
425	C₂²×C₅	—	2	2	no	—
426	C₂²×C₅	—	2	2	no	—
427	C₂²×C₅	—	2	1	no	—
428	C₂²×C₅	—	2	2	no	—
429	C₂²×C₅	—	2	2	no	—
430	C₂²×C₅	—	8	4	no	—
431	C₂²×C₅	C₂×#41	1	2	yes	—
432	C₂²×C₅	C₂⁵	1	1	yes	characteristic
433	C₂×D₅	—	2	1	no	—
434	C₂×D₅	—	2	1	no	—
435	C₂×D₅	—	2	2	no	—
436	C₂×D₅	—	2	2	no	—
437	C₂×D₅	—	2	2	no	—
438	C₂×D₅	—	8	4	no	—
439	C₂×D₅	C₂×#41	1	2	yes	—
440	C₄×C₅	—	2	1	no	—
441	C₄×C₅	—	2	1	no	—
442	C₄×C₅	—	2	2	no	—
443	C₄×C₅	—	2	1	no	—
444	C₄×C₅	—	2	1	no	—
445	C₄×C₅	—	2	2	no	—
446	C₄×C₅	H(5,𝔽₂)	1	2	yes	—
447	Dic₅	—	2	1	no	—
448	Dic₅	—	2	1	no	—
449	Dic₅	—	2	2	no	—
450	Dic₅	—	2	2	no	—
451	Dic₅	—	2	2	no	—
452	Dic₅	—	2	1	no	—
453	Dic₅	—	2	1	no	—
454	Dic₅	—	2	1	no	—
455	Dic₅	—	2	1	no	—
456	Dic₅	C₂×#41	1	2	yes	—
457	C₂⁴	—	5	2	no	—
458	C₂⁴	C₂²×D₅	1	2	yes	—
459	#41	—	4	2	no	—
460	#41	—	10	4	no	—
461	#41	—	20	2	no	—
462	C₂×Q₈	—	5	1	no	—
463	C₂×Q₈	—	5	1	no	—
464	C₂×Q₈	—	5	1	no	—
465	C₂×Q₈	—	5	2	no	—
466	C₂×Q₈	—	5	2	no	—
467	C₂×Q₈	—	20	2	no	—
468	C₂×Q₈	—	20	2	no	—
469	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
470	C₂×D₄	—	4	2	no	—
471	C₂×D₄	—	5	1	no	—
472	C₂×D₄	—	5	1	no	—
473	C₂×D₄	—	5	2	no	—
474	C₂×D₄	—	5	2	no	—
475	C₂×D₄	—	5	2	no	—
476	C₂×D₄	—	5	2	no	—
477	C₂×D₄	—	5	2	no	—
478	C₂×D₄	—	5	2	no	—
479	C₂×D₄	—	5	1	no	—
480	C₂×D₄	—	10	8	no	—
481	C₂×D₄	—	20	2	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	1	yes	characteristic
485	C₂×D₄	C₂²×D₅	1	2	yes	—
486	C₂×D₄	C₂²×D₅	1	2	yes	—
487	C₂×D₄	C₂²×D₅	1	2	yes	—
488	C₂²×C₄	—	5	1	no	—
489	C₂²×C₄	—	5	1	no	—
490	C₂²×C₄	—	5	2	no	—
491	C₂²×C₄	—	5	1	no	—
492	C₂²×C₄	—	5	1	no	—
493	C₂²×C₄	—	5	2	no	—
494	C₂²×C₄	—	5	1	no	—
495	C₂²×C₄	—	5	1	no	—
496	C₂²×C₄	—	5	1	no	—
497	C₂²×C₄	—	5	2	no	—
498	C₂²×C₄	—	5	2	no	—
499	C₂²×C₄	—	5	2	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	2	no	—
506	C₄⋊C₄	—	5	2	no	—
507	C₄⋊C₄	—	5	2	no	—
508	C₄⋊C₄	—	5	2	no	—
509	C₄⋊C₄	—	5	1	no	—
510	C₄⋊C₄	—	5	1	no	—
511	C₄⋊C₄	—	5	1	no	—
512	C₄⋊C₄	—	5	1	no	—
513	C₄⋊C₄	—	5	2	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	C₂²×D₅	1	1	yes	characteristic
520	C₄⋊C₄	C₂²×D₅	1	2	yes	—
521	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
522	C₂²⋊C₄	—	5	2	no	—
523	C₂²⋊C₄	—	5	2	no	—
524	C₂²⋊C₄	—	5	2	no	—
525	C₂²⋊C₄	—	5	2	no	—
526	C₂²⋊C₄	—	5	2	no	—
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	2	no	—
534	C₂²⋊C₄	—	5	2	no	—
535	C₂²⋊C₄	—	5	1	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	1	no	—
542	C₂²⋊C₄	—	5	2	no	—
543	C₂²⋊C₄	—	5	2	no	—
544	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
545	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
546	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
547	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
548	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
549	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
550	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
551	C₄²	—	5	1	no	—
552	C₄²	—	5	1	no	—
553	C₄²	—	5	1	no	—
554	C₄²	—	5	1	no	—
555	C₄²	—	5	1	no	—
556	C₄²	—	5	1	no	—
557	C₄²	—	5	1	no	—
558	C₄²	—	5	1	no	—
559	C₄²	—	5	1	no	—
560	C₄²	—	5	2	no	—
561	C₄²	—	5	2	no	—
562	C₄²	—	5	2	no	—
563	C₄²	C₂²×D₅	1	1	yes	characteristic
564	C₂×C₅	—	2	2	no	—
565	C₂×C₅	—	4	2	no	—
566	C₂×C₅	—	4	1	no	—
567	C₂×C₅	—	4	2	no	—
568	C₂×C₅	C₂²×#41	1	1	yes	characteristic
569	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
570	C₂×C₅	#585	1	1	yes	characteristic
571	D₅	—	2	2	no	—
572	D₅	—	4	2	no	—
573	C₂³	—	2	4	no	—
574	C₂³	—	4	2	no	—
575	C₂³	—	4	2	no	—
576	C₂³	—	5	1	no	—
577	C₂³	—	5	2	no	—
578	C₂³	—	10	4	no	—
579	C₂³	—	20	2	no	—
580	C₂³	—	20	2	no	—
581	C₂³	C₂³×D₅	1	2	yes	—
582	C₂³	C₂³×D₅	1	2	yes	—
583	C₂³	C₂³×D₅	1	1	yes	characteristic
584	C₂³	C₂³×D₅	1	1	yes	characteristic
585	Q₈	—	2	2	no	—
586	Q₈	—	10	2	no	—
587	Q₈	—	10	2	no	—
588	Q₈	—	10	2	no	—
589	Q₈	—	20	2	no	—
590	Q₈	—	20	2	no	—
591	D₄	—	2	2	no	—
592	D₄	—	2	2	no	—
593	D₄	—	2	2	no	—
594	D₄	—	4	2	no	—
595	D₄	—	4	2	no	—
596	D₄	—	4	2	no	—
597	D₄	—	5	4	no	—
598	D₄	—	10	4	no	—
599	D₄	—	10	4	no	—
600	D₄	—	10	2	no	—
601	D₄	—	10	4	no	—
602	D₄	—	10	2	no	—
603	D₄	—	20	2	no	—
604	D₄	—	20	2	no	—
605	D₄	—	20	2	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	4	2	no	—
609	C₂×C₄	—	4	2	no	—
610	C₂×C₄	—	5	1	no	—
611	C₂×C₄	—	5	1	no	—
612	C₂×C₄	—	5	1	no	—
613	C₂×C₄	—	5	1	no	—
614	C₂×C₄	—	5	1	no	—
615	C₂×C₄	—	5	2	no	—
616	C₂×C₄	—	5	1	no	—
617	C₂×C₄	—	5	1	no	—
618	C₂×C₄	—	5	2	no	—
619	C₂×C₄	—	5	2	no	—
620	C₂×C₄	—	10	2	no	—
621	C₂×C₄	—	10	4	no	—
622	C₂×C₄	—	10	2	no	—
623	C₂×C₄	—	10	2	no	—
624	C₂×C₄	—	10	2	no	—
625	C₂×C₄	—	20	2	no	—
626	C₂×C₄	—	20	2	no	—
627	C₂×C₄	—	20	1	no	—
628	C₂×C₄	—	20	2	no	—
629	C₂×C₄	—	20	2	no	—
630	C₂×C₄	—	20	1	no	—
631	C₂×C₄	—	20	1	no	—
632	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
633	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
634	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
635	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
636	C₂×C₄	C₂³×D₅	1	2	yes	—
637	C₂×C₄	C₂³×D₅	1	2	yes	—
638	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
639	C₅	#3514	1	1	yes	characteristic, complemented, Sylow
640	C₂²	—	2	1	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	2	2	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	2	no	—
649	C₂²	—	2	1	no	—
650	C₂²	—	2	2	no	—
651	C₂²	—	5	2	no	—
652	C₂²	—	8	4	no	—
653	C₂²	—	10	1	no	—
654	C₂²	—	10	1	no	—
655	C₂²	—	10	2	no	—
656	C₂²	—	10	2	no	—
657	C₂²	—	10	2	no	—
658	C₂²	—	40	4	no	—
659	C₂²	D₅×#41	1	2	yes	—
660	C₂²	C₂⁴×D₅	1	1	yes	characteristic
661	C₄	—	2	1	no	—
662	C₄	—	2	1	no	—
663	C₄	—	2	2	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	1	no	—
666	C₄	—	2	2	no	—
667	C₄	—	5	2	no	—
668	C₄	—	10	1	no	—
669	C₄	—	10	2	no	—
670	C₄	—	10	2	no	—
671	C₄	—	10	1	no	—
672	C₄	—	10	2	no	—
673	C₄	—	10	1	no	—
674	C₄	—	10	1	no	—
675	C₄	—	10	1	no	—
676	C₄	—	10	1	no	—
677	C₄	#4144	1	2	yes	—
678	C₂	—	2	2	no	—
679	C₂	—	4	2	no	—
680	C₂	—	4	2	no	—
681	C₂	—	4	1	no	—
682	C₂	—	10	2	no	—
683	C₂	—	20	2	no	—
684	C₂	C₂×#4144	1	1	yes	characteristic
685	C₂	C₂×D₅×#41	1	1	yes	characteristic
686	C₂	#66285	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁵
Fitting	C₅×#546	C₂
hypercenter	#546	D₅
hypocenter	C₅	#3514
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #546

Complements

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

N	H ≅ G/N	type
1. C₅×#546	C₂	semidirect
2. #66166	C₂	semidirect
3. #66165	C₂	semidirect
4. D₄×C₂²⋊D₅	C₂	semidirect
5. C₂×#4082	C₂	semidirect
6. D₅×#124	C₂	semidirect
7. #66005	C₂	semidirect
8. #65996	C₂	semidirect
9. #65993	C₂	semidirect
10. #65966	C₂	semidirect
11. #65958	C₂	semidirect
12. #65950	C₂	semidirect
13. #65947	C₂	semidirect
14. #65946	C₂	semidirect
15. #65934	C₂	semidirect
16. #65927	C₂	semidirect
17. #65925	C₂	semidirect
18. #65893	C₂	semidirect
19. #65891	C₂	semidirect
20. #65886	C₂	semidirect
21. C₄×#711	C₂	semidirect
22. #65829	C₂	semidirect
23. #65820	C₂	semidirect
24. C₂×C₅×#41	C₂²	semidirect
27. C₂×Q₈×D₅	C₂²	semidirect
30. C₂×#709	C₂²	semidirect
31. C₂²×Dic₁₀	C₂²	semidirect
33. C₅×#123	C₂²	semidirect
34. C₅×C₂²⋊Q₈	C₂²	semidirect
36. C₅×#121	C₂²	semidirect
37. C₅×#120	C₂²	semidirect
38. C₄×C₅×D₄	C₂²	semidirect
39. C₄×C₅×D₄	C₂²	semidirect
40. C₂×C₅×C₂²⋊C₄	C₂²	semidirect
42. C₂×C₂²⋊Dic₅	C₂²	semidirect
43. C₂×C₂²⋊Dic₅	C₂²	semidirect
44. #4093	C₂²	semidirect
45. Q₈×Dic₅	C₂²	semidirect
46. #4090	C₂²	semidirect
49. #4085	C₂²	semidirect
50. #4085	C₂²	semidirect
51. #4085	C₂²	semidirect
53. #4084	C₂²	semidirect
54. #4084	C₂²	semidirect
56. #4083	C₂²	semidirect
59. #4082	C₂²	semidirect
60. #4082	C₂²	semidirect
61. #4082	C₂²	semidirect
62. #4082	C₂²	semidirect
63. #4082	C₂²	semidirect
64. #4081	C₂²	semidirect
66. D₄×Dic₅	C₂²	semidirect
67. D₄×Dic₅	C₂²	semidirect
69. #4075	C₂²	semidirect
71. C₄×C₂²⋊D₅	C₂²	semidirect
72. C₄×C₂²⋊D₅	C₂²	semidirect
73. C₄×C₂²⋊D₅	C₂²	semidirect
74. C₄×C₂²⋊D₅	C₂²	semidirect
75. C₄×C₂²⋊D₅	C₂²	semidirect
76. C₄×C₂²⋊D₅	C₂²	semidirect
77. #4072	C₂²	semidirect
78. #4070	C₂²	semidirect
79. #4070	C₂²	semidirect
80. C₂×C₄×Dic₅	C₂²	semidirect
81. C₂×C₄×Dic₅	C₂²	semidirect
82. #4044	C₂²	semidirect
83. #4043	C₂²	semidirect
84. #4042	C₂²	semidirect
85. #4042	C₂²	semidirect
86. #4039	C₂²	semidirect
87. #4038	C₂²	semidirect
88. #4038	C₂²	semidirect
89. #4036	C₂²	semidirect
90. #4034	C₂²	semidirect
91. #4033	C₂²	semidirect
92. #4033	C₂²	semidirect
93. #4032	C₂²	semidirect
94. #4031	C₂²	semidirect
95. #4031	C₂²	semidirect
96. #4031	C₂²	semidirect
97. #4031	C₂²	semidirect
98. #4029	C₂²	semidirect
99. #4029	C₂²	semidirect
100. #4029	C₂²	semidirect
103. #4027	C₂²	semidirect
104. #4027	C₂²	semidirect
105. #4027	C₂²	semidirect
106. D₅×C₂²⋊C₄	C₂²	semidirect
107. D₅×C₂²⋊C₄	C₂²	semidirect
108. D₅×C₂²⋊C₄	C₂²	semidirect
109. #4025	C₂²	semidirect
110. #4025	C₂²	semidirect
111. #4025	C₂²	semidirect
112. #4025	C₂²	semidirect
113. #4024	C₂²	semidirect
114. #4024	C₂²	semidirect
115. #4023	C₂²	semidirect
116. #4023	C₂²	semidirect
117. #4023	C₂²	semidirect
118. #4023	C₂²	semidirect
119. #4021	C₂²	semidirect
120. C₄²×D₅	C₂²	semidirect
121. C₄×Dic₁₀	C₂²	semidirect
122. C₄×Dic₁₀	C₂²	semidirect
241. #546	D₅	semidirect
291. C₂²⋊D₅	#41	semidirect
322. C₂×#41	C₂×D₅	semidirect
357. #123	C₂×D₅	semidirect
365. C₂²⋊Q₈	C₂×D₅	semidirect
375. #121	C₂×D₅	semidirect
379. #120	C₂×D₅	semidirect
401. C₄×D₄	C₂×D₅	semidirect
402. C₄×D₄	C₂×D₅	semidirect
415. C₂×C₂²⋊C₄	C₂×D₅	semidirect
639. C₅	#3514	semidirect

Maximal subgroups

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

subgroup	index
C₅×#546	2
#66166	2
#66165	2
D₄×C₂²⋊D₅	2
C₂×#4082	2
D₅×#124	2
#66005	2
#65996	2
#65993	2
#65966	2
#65958	2
#65950	2
#65947	2
#65946	2
#65934	2
#65927	2
#65925	2
#65893	2
#65891	2
#65886	2
C₄×#711	2
#65829	2
#65820	2
#3514	5