Subgroups — #10618559

Order 640.

1032 conjugacy classes of subgroups.

The subgroup lattice has 658 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	#66165	C₂	1	1	yes	maximal, characteristic, complemented
3	#66159	C₂	1	1	yes	maximal, characteristic, complemented
4	#66140	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#4082	C₂	1	1	yes	maximal, characteristic, complemented
6	#66009	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	#65985	C₂	1	2	yes	maximal, complemented
10	#65966	C₂	1	1	yes	maximal, characteristic, complemented
11	#65956	C₂	1	1	yes	maximal, characteristic, complemented
12	#65955	C₂	1	2	yes	maximal, complemented
13	#65937	C₂	1	1	yes	maximal, characteristic, complemented
14	#65937	C₂	1	2	yes	maximal, complemented
15	#65932	C₂	1	1	yes	maximal, characteristic, complemented
16	#65927	C₂	1	2	yes	maximal, complemented
17	#65921	C₂	1	2	yes	maximal, complemented
18	#65895	C₂	1	1	yes	maximal, characteristic, complemented
19	#65876	C₂	1	1	yes	maximal, characteristic, complemented
20	#65872	C₂	1	1	yes	maximal, characteristic, complemented
21	D₄×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
22	#65829	C₂	1	2	yes	maximal, complemented
23	#65817	C₂	1	2	yes	maximal, complemented
24	C₂×C₅×#41	C₂²	1	1	yes	characteristic
25	C₂²×C₅×D₄	C₂²	1	1	yes	characteristic
26	C₂×Q₈×D₅	C₂²	1	1	yes	characteristic, complemented
27	C₂×#711	C₂²	1	1	yes	characteristic
28	C₂²×Dic₁₀	C₂²	1	1	yes	characteristic
29	C₂²×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
30	C₅×#124	C₂²	1	1	yes	characteristic
31	C₅×#123	C₂²	1	2	yes	—
32	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₅×#121	C₂²	1	1	yes	characteristic
34	C₅×#121	C₂²	1	2	yes	—
35	C₅×#120	C₂²	1	2	yes	—
36	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
37	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
38	C₂×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
39	#4099	C₂²	1	2	yes	—
40	C₂×C₂²⋊Dic₅	C₂²	1	2	yes	—
41	C₂×C₂²⋊Dic₅	C₂²	1	2	yes	—
42	C₂×C₂²⋊Dic₅	C₂²	1	2	yes	—
43	Q₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
44	#4090	C₂²	1	1	yes	characteristic, complemented
45	#4090	C₂²	1	1	yes	characteristic, complemented
46	#4085	C₂²	1	1	yes	characteristic
47	#4085	C₂²	1	2	yes	—
48	#4085	C₂²	1	2	yes	complemented
49	#4084	C₂²	1	1	yes	characteristic
50	#4084	C₂²	1	2	yes	complemented
51	#4082	C₂²	1	1	yes	characteristic
52	#4082	C₂²	1	1	yes	characteristic
53	#4082	C₂²	1	1	yes	characteristic
54	#4082	C₂²	1	2	yes	—
55	#4082	C₂²	1	1	yes	characteristic
56	#4082	C₂²	1	2	yes	—
57	#4082	C₂²	1	1	yes	characteristic
58	#4082	C₂²	1	2	yes	complemented
59	#4082	C₂²	1	2	yes	complemented
60	#4081	C₂²	1	1	yes	characteristic
61	#4081	C₂²	1	2	yes	—
62	#4081	C₂²	1	2	yes	complemented
63	#4081	C₂²	1	2	yes	complemented
64	#4081	C₂²	1	2	yes	complemented
65	D₄×Dic₅	C₂²	1	2	yes	—
66	D₄×Dic₅	C₂²	1	1	yes	characteristic
67	D₄×Dic₅	C₂²	1	2	yes	complemented
68	#4075	C₂²	1	2	yes	complemented
69	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
70	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
71	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
72	#4072	C₂²	1	2	yes	complemented
73	#4072	C₂²	1	1	yes	characteristic, complemented
74	#4070	C₂²	1	1	yes	characteristic
75	#4070	C₂²	1	2	yes	complemented
76	#4070	C₂²	1	2	yes	complemented
77	#4070	C₂²	1	2	yes	complemented
78	#4070	C₂²	1	2	yes	complemented
79	#4070	C₂²	1	2	yes	complemented
80	#4070	C₂²	1	1	yes	characteristic, complemented
81	C₂×C₄×Dic₅	C₂²	1	1	yes	characteristic
82	#4044	C₂²	1	1	yes	characteristic, complemented
83	#4043	C₂²	1	1	yes	characteristic, complemented
84	#4042	C₂²	1	2	yes	complemented
85	#4035	C₂²	1	1	yes	characteristic, complemented
86	#4035	C₂²	1	2	yes	complemented
87	#4034	C₂²	1	2	yes	complemented
88	#4034	C₂²	1	1	yes	characteristic, complemented
89	#4034	C₂²	1	2	yes	complemented
90	#4033	C₂²	1	1	yes	characteristic, complemented
91	#4033	C₂²	1	1	yes	characteristic, complemented
92	#4033	C₂²	1	2	yes	complemented
93	#4032	C₂²	1	1	yes	characteristic
94	#4031	C₂²	1	2	yes	complemented
95	#4031	C₂²	1	1	yes	characteristic, complemented
96	#4031	C₂²	1	2	yes	complemented
97	#4029	C₂²	1	2	yes	complemented
98	#4029	C₂²	1	2	yes	complemented
99	#4027	C₂²	1	2	yes	—
100	#4025	C₂²	1	2	yes	complemented
101	#4025	C₂²	1	2	yes	complemented
102	#4025	C₂²	1	1	yes	characteristic, complemented
103	#4025	C₂²	1	2	yes	complemented
104	#4025	C₂²	1	2	yes	complemented
105	#4025	C₂²	1	2	yes	complemented
106	#4025	C₂²	1	2	yes	complemented
107	#4024	C₂²	1	1	yes	characteristic
108	#4024	C₂²	1	2	yes	—
109	#4024	C₂²	1	2	yes	—
110	#4024	C₂²	1	2	yes	—
111	#4024	C₂²	1	2	yes	complemented
112	#4024	C₂²	1	2	yes	complemented
113	#4024	C₂²	1	2	yes	complemented
114	#4024	C₂²	1	2	yes	complemented
115	#4024	C₂²	1	2	yes	complemented
116	#4024	C₂²	1	2	yes	complemented
117	#4023	C₂²	1	2	yes	—
118	#4023	C₂²	1	2	yes	complemented
119	#4018	C₂²	1	1	yes	characteristic, complemented
120	#4015	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	#3561	—	5	1	no	maximal, Sylow
124	C₂⁴×C₅	C₂³	1	2	yes	—
125	C₅×#41	—	4	2	no	—
126	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
127	C₂×C₅×D₄	—	4	2	no	—
128	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
129	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
130	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
131	C₂×C₅×D₄	C₂³	1	2	yes	—
132	C₂×C₅×D₄	C₂³	1	2	yes	—
133	C₂×C₅×D₄	C₂³	1	2	yes	—
134	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
135	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₅	C₂³	1	2	yes	—
137	C₂²×C₄×C₅	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	1	yes	characteristic
142	C₂²×Dic₅	C₂³	1	1	yes	characteristic
143	C₂²×Dic₅	C₂³	1	2	yes	—
144	C₂²×Dic₅	C₂³	1	1	yes	characteristic
145	C₂²×Dic₅	C₂³	1	2	yes	—
146	C₂²×Dic₅	C₂³	1	2	yes	—
147	C₂²×Dic₅	C₂³	1	2	yes	—
148	Q₈×D₅	—	4	2	no	—
149	#711	—	4	2	no	—
150	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₅	C₂³	1	2	yes	—
152	C₂×Dic₁₀	—	4	2	no	—
153	C₂×Dic₁₀	—	4	2	no	—
154	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
155	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
156	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
157	C₂×Dic₁₀	C₂³	1	2	yes	—
158	C₂×Dic₁₀	C₂³	1	2	yes	—
159	C₂×Dic₁₀	C₂³	1	2	yes	—
160	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
161	C₂×Dic₁₀	C₂³	1	2	yes	—
162	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
164	C₅×C₄⋊C₄	C₂³	1	2	yes	—
165	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
166	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
171	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₄²×C₅	C₂³	1	1	yes	characteristic
173	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
174	C₂²⋊Dic₅	C₂³	1	2	yes	—
175	C₂²⋊Dic₅	C₂³	1	2	yes	—
176	C₂²⋊Dic₅	C₂³	1	2	yes	—
177	C₂²⋊Dic₅	C₂³	1	2	yes	—
178	C₂²⋊Dic₅	C₂³	1	2	yes	—
179	C₂²⋊Dic₅	C₂³	1	2	yes	—
180	C₂²⋊Dic₅	C₂³	1	2	yes	—
181	C₂²⋊Dic₅	C₂³	1	2	yes	—
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	1	yes	characteristic
189	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
190	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
191	#685	C₂³	1	1	yes	characteristic
192	#685	C₂³	1	1	yes	characteristic
193	#685	C₂³	1	2	yes	—
194	#685	C₂³	1	1	yes	characteristic
195	#685	C₂³	1	1	yes	characteristic
196	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
197	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
198	C₄⋊Dic₅	C₂³	1	2	yes	—
199	C₄⋊Dic₅	C₂³	1	2	yes	—
200	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
201	C₄⋊Dic₅	C₂³	1	2	yes	—
202	C₄⋊Dic₅	C₂³	1	2	yes	—
203	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
204	#683	C₂³	1	1	yes	characteristic
205	#683	C₂³	1	2	yes	—
206	#683	C₂³	1	1	yes	characteristic
207	#683	C₂³	1	1	yes	characteristic
208	#683	C₂³	1	1	yes	characteristic
209	#683	C₂³	1	2	yes	—
210	#683	C₂³	1	2	yes	—
211	#683	C₂³	1	2	yes	—
212	#683	C₂³	1	1	yes	characteristic
213	#683	C₂³	1	2	yes	—
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	#683	C₂³	1	2	yes	—
219	#683	C₂³	1	1	yes	characteristic
220	C₄×Dic₅	C₂³	1	2	yes	—
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	2	yes	—
225	C₄×Dic₅	C₂³	1	2	yes	—
226	C₄×Dic₅	C₂³	1	2	yes	—
227	C₄×Dic₅	C₂³	1	1	yes	characteristic
228	C₄×Dic₅	C₂³	1	1	yes	characteristic
229	#563	—	5	2	no	—
230	#562	—	5	2	no	—
231	#556	—	5	1	no	—
232	#556	—	5	1	no	—
233	#551	—	5	2	no	—
234	#551	—	5	2	no	—
235	D₄×Q₈	—	5	1	no	—
236	D₄×Q₈	—	5	1	no	—
237	#548	—	5	1	no	—
238	#548	—	5	1	no	—
239	#546	—	5	1	no	—
240	#546	D₅	1	1	yes	characteristic, complemented
241	#543	—	5	2	no	—
242	#542	—	5	2	no	—
243	#542	—	5	1	no	—
244	#542	—	5	2	no	—
245	#542	—	5	1	no	—
246	#538	—	5	2	no	—
247	#536	—	5	1	no	—
248	#536	—	5	1	no	—
249	#533	—	5	1	no	—
250	#529	—	5	1	no	—
251	C₂×#124	—	5	1	no	—
252	C₂³×C₅	—	2	4	no	—
253	C₂³×C₅	—	4	2	no	—
254	C₂³×C₅	—	4	2	no	—
255	C₂³×C₅	C₂⁴	1	2	yes	—
256	C₂³×C₅	C₂⁴	1	2	yes	—
257	C₂³×C₅	C₂⁴	1	1	yes	characteristic
258	C₂³×C₅	C₂⁴	1	1	yes	characteristic
259	C₂²×D₅	C₂⁴	1	1	yes	characteristic
260	C₅×Q₈	—	2	2	no	—
261	C₅×D₄	—	2	2	no	—
262	C₅×D₄	—	2	2	no	—
263	C₅×D₄	—	2	2	no	—
264	C₅×D₄	—	4	2	no	—
265	C₅×D₄	—	4	2	no	—
266	C₅×D₄	—	4	2	no	—
267	C₂×C₄×C₅	—	2	2	no	—
268	C₂×C₄×C₅	—	2	2	no	—
269	C₂×C₄×C₅	—	4	2	no	—
270	C₂×C₄×C₅	—	4	2	no	—
271	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
272	C₂×C₄×C₅	C₂⁴	1	2	yes	—
273	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
274	C₂×C₄×C₅	C₂⁴	1	2	yes	—
275	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
276	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
277	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
278	C₂²⋊D₅	—	2	2	no	—
279	C₂²⋊D₅	—	4	2	no	—
280	C₂²⋊D₅	—	4	2	no	—
281	C₂²⋊D₅	—	4	1	no	—
282	C₂×Dic₅	—	2	2	no	—
283	C₂×Dic₅	—	4	2	no	—
284	C₂×Dic₅	—	4	2	no	—
285	C₂×Dic₅	—	4	2	no	—
286	C₂×Dic₅	—	4	1	no	—
287	C₂×Dic₅	—	4	2	no	—
288	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
289	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
290	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
291	C₂×Dic₅	C₂⁴	1	2	yes	—
292	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
293	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
294	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
295	C₂×Dic₅	C₂⁴	1	2	yes	—
296	C₂×Dic₅	C₂⁴	1	2	yes	—
297	C₂×Dic₅	C₂⁴	1	2	yes	—
298	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
299	C₄×D₅	—	2	2	no	—
300	C₄×D₅	—	4	2	no	—
301	Dic₁₀	—	2	2	no	—
302	Dic₁₀	—	2	2	no	—
303	Dic₁₀	—	2	2	no	—
304	Dic₁₀	—	4	2	no	—
305	Dic₁₀	—	4	2	no	—
306	Dic₁₀	—	4	2	no	—
307	Dic₁₀	—	4	1	no	—
308	Dic₁₀	—	4	2	no	—
309	C₂×#41	—	5	1	no	—
310	C₂×#41	C₂×D₅	1	1	yes	characteristic
311	C₂²×Q₈	—	5	1	no	—
312	C₂²×Q₈	—	5	1	no	—
313	C₂²×Q₈	—	5	1	no	—
314	C₂²×D₄	C₂×D₅	1	1	yes	characteristic
315	C₄⋊Q₈	—	5	1	no	—
316	C₄⋊Q₈	—	5	1	no	—
317	C₄⋊Q₈	—	5	1	no	—
318	C₄⋊Q₈	—	5	2	no	—
319	C₄⋊Q₈	—	5	2	no	—
320	C₄⋊Q₈	—	5	1	no	—
321	#126	—	5	1	no	—
322	#126	—	5	1	no	—
323	#126	—	5	2	no	—
324	#126	—	5	2	no	—
325	#126	—	5	2	no	—
326	#126	—	5	2	no	—
327	#126	—	5	2	no	—
328	#126	—	5	2	no	—
329	#125	—	5	1	no	—
330	#125	—	5	2	no	—
331	#124	—	5	1	no	—
332	#124	—	5	1	no	—
333	#124	—	5	2	no	—
334	#124	—	5	1	no	—
335	#124	—	5	1	no	—
336	#124	—	5	2	no	—
337	#124	—	5	1	no	—
338	#124	—	5	2	no	—
339	#124	—	5	2	no	—
340	#124	—	5	1	no	—
341	#124	—	5	2	no	—
342	#124	—	5	2	no	—
343	#124	C₂×D₅	1	1	yes	characteristic
344	#123	—	5	1	no	—
345	#123	—	5	2	no	—
346	#123	—	5	2	no	—
347	#123	—	5	2	no	—
348	#123	—	5	2	no	—
349	#123	—	5	2	no	—
350	#123	—	5	1	no	—
351	#123	—	5	2	no	—
352	#123	—	5	2	no	—
353	#123	C₂×D₅	1	2	yes	—
354	C₂²⋊Q₈	—	5	1	no	—
355	C₂²⋊Q₈	—	5	2	no	—
356	C₂²⋊Q₈	—	5	2	no	—
357	C₂²⋊Q₈	—	5	2	no	—
358	C₂²⋊Q₈	—	5	1	no	—
359	C₂²⋊Q₈	—	5	2	no	—
360	C₂²⋊Q₈	—	5	2	no	—
361	C₂²⋊Q₈	—	5	1	no	—
362	C₂²⋊Q₈	—	5	2	no	—
363	C₂²⋊Q₈	—	5	1	no	—
364	C₂²⋊Q₈	—	5	2	no	—
365	C₂²⋊Q₈	—	5	2	no	—
366	C₂²⋊Q₈	—	5	2	no	—
367	C₂²⋊Q₈	—	5	2	no	—
368	C₂²⋊Q₈	—	5	2	no	—
369	C₂²⋊Q₈	—	5	2	no	—
370	C₂²⋊Q₈	—	5	2	no	—
371	C₂²⋊Q₈	—	5	2	no	—
372	C₂²⋊Q₈	—	5	2	no	—
373	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic
374	#121	—	5	1	no	—
375	#121	—	5	2	no	—
376	#121	—	5	2	no	—
377	#121	—	5	1	no	—
378	#121	—	5	2	no	—
379	#121	C₂×D₅	1	1	yes	characteristic
380	#121	C₂×D₅	1	2	yes	—
381	#120	—	5	2	no	—
382	#120	C₂×D₅	1	2	yes	—
383	C₄×Q₈	—	5	1	no	—
384	C₄×Q₈	—	5	2	no	—
385	C₄×Q₈	—	5	1	no	—
386	C₄×Q₈	—	5	1	no	—
387	C₄×Q₈	—	5	1	no	—
388	C₄×Q₈	—	5	1	no	—
389	C₄×D₄	—	5	2	no	—
390	C₄×D₄	—	5	1	no	—
391	C₄×D₄	—	5	2	no	—
392	C₄×D₄	—	5	1	no	—
393	C₄×D₄	—	5	1	no	—
394	C₄×D₄	—	5	2	no	—
395	C₄×D₄	—	5	2	no	—
396	C₄×D₄	C₂×D₅	1	1	yes	characteristic
397	C₄×D₄	C₂×D₅	1	1	yes	characteristic
398	#117	—	5	1	no	—
399	#117	—	5	2	no	—
400	#117	—	5	2	no	—
401	#117	—	5	2	no	—
402	#117	—	5	1	no	—
403	C₂×C₂²⋊C₄	—	5	2	no	—
404	C₂×C₂²⋊C₄	—	5	2	no	—
405	C₂×C₂²⋊C₄	—	5	2	no	—
406	C₂×C₂²⋊C₄	C₂×D₅	1	2	yes	—
407	C₂×C₄²	—	5	1	no	—
408	C₂²×C₅	—	2	1	no	—
409	C₂²×C₅	—	2	1	no	—
410	C₂²×C₅	—	2	1	no	—
411	C₂²×C₅	—	2	2	no	—
412	C₂²×C₅	—	2	2	no	—
413	C₂²×C₅	—	2	1	no	—
414	C₂²×C₅	—	2	2	no	—
415	C₂²×C₅	—	2	2	no	—
416	C₂²×C₅	—	2	2	no	—
417	C₂²×C₅	—	2	2	no	—
418	C₂²×C₅	—	2	1	no	—
419	C₂²×C₅	—	8	4	no	—
420	C₂²×C₅	2₋¹⁺⁴	1	2	yes	—
421	C₂²×C₅	C₂⁵	1	1	yes	characteristic
422	C₂×D₅	—	2	1	no	—
423	C₂×D₅	—	2	1	no	—
424	C₂×D₅	—	2	1	no	—
425	C₄×C₅	—	2	1	no	—
426	C₄×C₅	—	2	1	no	—
427	C₄×C₅	—	2	2	no	—
428	C₄×C₅	—	2	1	no	—
429	C₄×C₅	—	2	1	no	—
430	C₄×C₅	—	2	2	no	—
431	C₄×C₅	H(5,𝔽₂)	1	2	yes	—
432	Dic₅	—	2	2	no	—
433	Dic₅	—	2	2	no	—
434	Dic₅	—	2	2	no	—
435	Dic₅	—	2	1	no	—
436	Dic₅	—	2	1	no	—
437	Dic₅	—	2	1	no	—
438	Dic₅	—	2	1	no	—
439	Dic₅	—	2	1	no	—
440	Dic₅	—	2	1	no	—
441	Dic₅	—	2	2	no	—
442	Dic₅	—	2	1	no	—
443	C₂⁴	C₂²×D₅	1	2	yes	—
444	#41	—	4	2	no	—
445	#41	—	20	2	no	—
446	C₂×Q₈	—	5	1	no	—
447	C₂×Q₈	—	5	1	no	—
448	C₂×Q₈	—	5	1	no	—
449	C₂×Q₈	—	5	1	no	—
450	C₂×Q₈	—	5	2	no	—
451	C₂×Q₈	—	5	2	no	—
452	C₂×Q₈	—	5	2	no	—
453	C₂×Q₈	—	5	2	no	—
454	C₂×Q₈	—	20	2	no	—
455	C₂×Q₈	—	20	2	no	—
456	C₂×Q₈	—	20	2	no	—
457	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
458	C₂×D₄	—	4	2	no	—
459	C₂×D₄	—	5	1	no	—
460	C₂×D₄	—	5	2	no	—
461	C₂×D₄	—	5	1	no	—
462	C₂×D₄	—	5	2	no	—
463	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
464	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
465	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
466	C₂×D₄	C₂²×D₅	1	2	yes	—
467	C₂×D₄	C₂²×D₅	1	2	yes	—
468	C₂×D₄	C₂²×D₅	1	2	yes	—
469	C₂²×C₄	—	5	1	no	—
470	C₂²×C₄	—	5	1	no	—
471	C₂²×C₄	—	5	2	no	—
472	C₂²×C₄	—	5	2	no	—
473	C₂²×C₄	—	5	2	no	—
474	C₂²×C₄	—	5	2	no	—
475	C₂²×C₄	—	5	1	no	—
476	C₂²×C₄	—	5	2	no	—
477	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
478	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
479	C₂²×C₄	C₂²×D₅	1	2	yes	—
480	C₂²×C₄	C₂²×D₅	1	2	yes	—
481	C₄⋊C₄	—	5	1	no	—
482	C₄⋊C₄	—	5	1	no	—
483	C₄⋊C₄	—	5	1	no	—
484	C₄⋊C₄	—	5	1	no	—
485	C₄⋊C₄	—	5	2	no	—
486	C₄⋊C₄	—	5	2	no	—
487	C₄⋊C₄	—	5	2	no	—
488	C₄⋊C₄	—	5	1	no	—
489	C₄⋊C₄	—	5	1	no	—
490	C₄⋊C₄	—	5	2	no	—
491	C₄⋊C₄	—	5	1	no	—
492	C₄⋊C₄	—	5	1	no	—
493	C₄⋊C₄	—	5	2	no	—
494	C₄⋊C₄	—	5	2	no	—
495	C₄⋊C₄	—	5	2	no	—
496	C₄⋊C₄	—	5	2	no	—
497	C₄⋊C₄	—	5	1	no	—
498	C₄⋊C₄	—	5	2	no	—
499	C₄⋊C₄	—	5	2	no	—
500	C₄⋊C₄	—	5	2	no	—
501	C₄⋊C₄	—	5	1	no	—
502	C₄⋊C₄	—	5	2	no	—
503	C₄⋊C₄	—	5	2	no	—
504	C₄⋊C₄	—	5	2	no	—
505	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
506	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
507	C₄⋊C₄	C₂²×D₅	1	2	yes	—
508	C₂²⋊C₄	—	5	1	no	—
509	C₂²⋊C₄	—	5	2	no	—
510	C₂²⋊C₄	—	5	2	no	—
511	C₂²⋊C₄	—	5	2	no	—
512	C₂²⋊C₄	—	5	2	no	—
513	C₂²⋊C₄	—	5	2	no	—
514	C₂²⋊C₄	—	5	2	no	—
515	C₂²⋊C₄	—	5	2	no	—
516	C₂²⋊C₄	—	5	2	no	—
517	C₂²⋊C₄	—	5	2	no	—
518	C₂²⋊C₄	—	5	2	no	—
519	C₂²⋊C₄	—	5	2	no	—
520	C₂²⋊C₄	—	5	2	no	—
521	C₂²⋊C₄	—	5	1	no	—
522	C₂²⋊C₄	—	5	1	no	—
523	C₂²⋊C₄	—	5	1	no	—
524	C₂²⋊C₄	—	5	2	no	—
525	C₂²⋊C₄	—	5	2	no	—
526	C₂²⋊C₄	—	5	1	no	—
527	C₂²⋊C₄	—	5	1	no	—
528	C₂²⋊C₄	—	5	1	no	—
529	C₂²⋊C₄	—	5	1	no	—
530	C₂²⋊C₄	—	5	2	no	—
531	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
532	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
533	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
534	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
535	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
536	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
537	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
538	C₄²	—	5	1	no	—
539	C₄²	—	5	1	no	—
540	C₄²	—	5	1	no	—
541	C₄²	—	5	1	no	—
542	C₄²	—	5	2	no	—
543	C₄²	—	5	2	no	—
544	C₄²	—	5	1	no	—
545	C₄²	—	5	2	no	—
546	C₄²	—	5	2	no	—
547	C₄²	C₂²×D₅	1	1	yes	characteristic
548	C₂×C₅	—	2	2	no	—
549	C₂×C₅	—	4	1	no	—
550	C₂×C₅	—	4	2	no	—
551	C₂×C₅	—	4	2	no	—
552	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
553	C₂×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
554	C₂×C₅	#585	1	1	yes	characteristic
555	D₅	—	4	1	no	—
556	C₂³	—	2	4	no	—
557	C₂³	—	4	2	no	—
558	C₂³	—	4	2	no	—
559	C₂³	—	5	1	no	—
560	C₂³	C₂³×D₅	1	2	yes	—
561	C₂³	C₂³×D₅	1	2	yes	—
562	C₂³	C₂³×D₅	1	1	yes	characteristic
563	C₂³	C₂³×D₅	1	1	yes	characteristic
564	Q₈	—	2	2	no	—
565	Q₈	—	10	2	no	—
566	Q₈	—	10	2	no	—
567	Q₈	—	10	2	no	—
568	Q₈	—	20	2	no	—
569	Q₈	—	20	2	no	—
570	Q₈	—	20	2	no	—
571	Q₈	—	20	1	no	—
572	Q₈	—	20	2	no	—
573	D₄	—	2	2	no	—
574	D₄	—	2	2	no	—
575	D₄	—	2	2	no	—
576	D₄	—	4	2	no	—
577	D₄	—	4	2	no	—
578	D₄	—	4	2	no	—
579	D₄	—	10	2	no	—
580	D₄	—	20	2	no	—
581	D₄	—	20	2	no	—
582	D₄	—	20	1	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	4	2	no	—
586	C₂×C₄	—	4	2	no	—
587	C₂×C₄	—	5	1	no	—
588	C₂×C₄	—	5	1	no	—
589	C₂×C₄	—	5	1	no	—
590	C₂×C₄	—	5	1	no	—
591	C₂×C₄	—	5	1	no	—
592	C₂×C₄	—	5	2	no	—
593	C₂×C₄	—	5	1	no	—
594	C₂×C₄	—	5	2	no	—
595	C₂×C₄	—	5	2	no	—
596	C₂×C₄	—	5	2	no	—
597	C₂×C₄	—	5	1	no	—
598	C₂×C₄	—	10	2	no	—
599	C₂×C₄	—	10	2	no	—
600	C₂×C₄	—	20	2	no	—
601	C₂×C₄	—	20	2	no	—
602	C₂×C₄	—	20	2	no	—
603	C₂×C₄	—	20	2	no	—
604	C₂×C₄	—	20	2	no	—
605	C₂×C₄	—	20	1	no	—
606	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
607	C₂×C₄	C₂³×D₅	1	2	yes	—
608	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
609	C₂×C₄	C₂³×D₅	1	2	yes	—
610	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
611	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
612	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
613	C₅	#3561	1	1	yes	characteristic, complemented, Sylow
614	C₂²	—	2	1	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	2	no	—
619	C₂²	—	2	1	no	—
620	C₂²	—	2	2	no	—
621	C₂²	—	2	2	no	—
622	C₂²	—	2	2	no	—
623	C₂²	—	2	2	no	—
624	C₂²	—	2	1	no	—
625	C₂²	—	8	4	no	—
626	C₂²	—	10	1	no	—
627	C₂²	—	10	1	no	—
628	C₂²	—	10	1	no	—
629	C₂²	#4150	1	2	yes	—
630	C₂²	C₂⁴×D₅	1	1	yes	characteristic
631	C₄	—	2	1	no	—
632	C₄	—	2	1	no	—
633	C₄	—	2	2	no	—
634	C₄	—	2	1	no	—
635	C₄	—	2	1	no	—
636	C₄	—	2	2	no	—
637	C₄	—	10	1	no	—
638	C₄	—	10	2	no	—
639	C₄	—	10	2	no	—
640	C₄	—	10	2	no	—
641	C₄	—	10	1	no	—
642	C₄	—	10	1	no	—
643	C₄	—	10	1	no	—
644	C₄	—	10	1	no	—
645	C₄	—	10	1	no	—
646	C₄	—	10	2	no	—
647	C₄	—	10	1	no	—
648	C₄	#4144	1	2	yes	—
649	C₂	—	2	2	no	—
650	C₂	—	4	2	no	—
651	C₂	—	4	2	no	—
652	C₂	—	4	1	no	—
653	C₂	—	20	1	no	—
654	C₂	C₂×#4144	1	1	yes	characteristic
655	C₂	C₂×#4150	1	1	yes	characteristic
656	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	#3561
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. #66165	C₂	semidirect
3. #66159	C₂	semidirect
4. #66140	C₂	semidirect
5. C₂×#4082	C₂	semidirect
6. #66009	C₂	semidirect
7. #66005	C₂	semidirect
8. #65996	C₂	semidirect
9. #65985	C₂	semidirect
10. #65966	C₂	semidirect
11. #65956	C₂	semidirect
12. #65955	C₂	semidirect
13. #65937	C₂	semidirect
14. #65937	C₂	semidirect
15. #65932	C₂	semidirect
16. #65927	C₂	semidirect
17. #65921	C₂	semidirect
18. #65895	C₂	semidirect
19. #65876	C₂	semidirect
20. #65872	C₂	semidirect
21. D₄×Dic₁₀	C₂	semidirect
22. #65829	C₂	semidirect
23. #65817	C₂	semidirect
26. C₂×Q₈×D₅	C₂²	semidirect
29. C₂²×Dic₁₀	C₂²	semidirect
43. Q₈×Dic₅	C₂²	semidirect
44. #4090	C₂²	semidirect
45. #4090	C₂²	semidirect
48. #4085	C₂²	semidirect
50. #4084	C₂²	semidirect
58. #4082	C₂²	semidirect
59. #4082	C₂²	semidirect
62. #4081	C₂²	semidirect
63. #4081	C₂²	semidirect
64. #4081	C₂²	semidirect
67. D₄×Dic₅	C₂²	semidirect
68. #4075	C₂²	semidirect
70. C₄×C₂²⋊D₅	C₂²	semidirect
71. C₄×C₂²⋊D₅	C₂²	semidirect
72. #4072	C₂²	semidirect
73. #4072	C₂²	semidirect
75. #4070	C₂²	semidirect
76. #4070	C₂²	semidirect
77. #4070	C₂²	semidirect
78. #4070	C₂²	semidirect
79. #4070	C₂²	semidirect
80. #4070	C₂²	semidirect
82. #4044	C₂²	semidirect
83. #4043	C₂²	semidirect
84. #4042	C₂²	semidirect
85. #4035	C₂²	semidirect
86. #4035	C₂²	semidirect
87. #4034	C₂²	semidirect
88. #4034	C₂²	semidirect
89. #4034	C₂²	semidirect
90. #4033	C₂²	semidirect
91. #4033	C₂²	semidirect
92. #4033	C₂²	semidirect
94. #4031	C₂²	semidirect
95. #4031	C₂²	semidirect
96. #4031	C₂²	semidirect
97. #4029	C₂²	semidirect
98. #4029	C₂²	semidirect
100. #4025	C₂²	semidirect
101. #4025	C₂²	semidirect
102. #4025	C₂²	semidirect
103. #4025	C₂²	semidirect
104. #4025	C₂²	semidirect
105. #4025	C₂²	semidirect
106. #4025	C₂²	semidirect
111. #4024	C₂²	semidirect
112. #4024	C₂²	semidirect
113. #4024	C₂²	semidirect
114. #4024	C₂²	semidirect
115. #4024	C₂²	semidirect
116. #4024	C₂²	semidirect
118. #4023	C₂²	semidirect
119. #4018	C₂²	semidirect
120. #4015	C₂²	semidirect
121. C₄×Dic₁₀	C₂²	semidirect
122. C₄×Dic₁₀	C₂²	semidirect
240. #546	D₅	semidirect
613. C₅	#3561	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
#66165	2
#66159	2
#66140	2
C₂×#4082	2
#66009	2
#66005	2
#65996	2
#65985	2
#65966	2
#65956	2
#65955	2
#65937	2
#65932	2
#65927	2
#65921	2
#65895	2
#65876	2
#65872	2
D₄×Dic₁₀	2
#65829	2
#65817	2
#3561	5