Subgroups — #10618554

Order 640.

1150 conjugacy classes of subgroups.

The subgroup lattice has 706 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	#66168	C₂	1	1	yes	maximal, characteristic, complemented
3	#66166	C₂	1	1	yes	maximal, characteristic, complemented
4	#66139	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
6	#66008	C₂	1	1	yes	maximal, characteristic, complemented
7	#66005	C₂	1	1	yes	maximal, characteristic, complemented
8	#65995	C₂	1	2	yes	maximal, complemented
9	#65991	C₂	1	2	yes	maximal, complemented
10	#65977	C₂	1	1	yes	maximal, characteristic, complemented
11	#65965	C₂	1	1	yes	maximal, characteristic, complemented
12	#65954	C₂	1	2	yes	maximal, complemented
13	#65946	C₂	1	1	yes	maximal, characteristic, complemented
14	#65942	C₂	1	2	yes	maximal, complemented
15	#65930	C₂	1	1	yes	maximal, characteristic, complemented
16	#65929	C₂	1	2	yes	maximal, complemented
17	#65926	C₂	1	2	yes	maximal, complemented
18	#65895	C₂	1	1	yes	maximal, characteristic, complemented
19	#65887	C₂	1	1	yes	maximal, characteristic, complemented
20	#65887	C₂	1	1	yes	maximal, characteristic, complemented
21	#65872	C₂	1	1	yes	maximal, characteristic, complemented
22	#65828	C₂	1	2	yes	maximal, complemented
23	#65824	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×#713	C₂²	1	1	yes	characteristic, complemented
28	C₂×#711	C₂²	1	2	yes	complemented
29	C₂×D₄×D₅	C₂²	1	1	yes	characteristic
30	C₂×#709	C₂²	1	2	yes	complemented
31	C₂×#709	C₂²	1	1	yes	characteristic, complemented
32	C₂×#709	C₂²	1	1	yes	characteristic, complemented
33	C₅×#124	C₂²	1	1	yes	characteristic
34	C₅×#123	C₂²	1	2	yes	complemented
35	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₅×#121	C₂²	1	1	yes	characteristic
37	C₅×#121	C₂²	1	2	yes	complemented
38	C₅×#120	C₂²	1	2	yes	complemented
39	C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
40	C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
42	#4099	C₂²	1	2	yes	—
43	#4099	C₂²	1	2	yes	complemented
44	#4099	C₂²	1	2	yes	complemented
45	#4093	C₂²	1	1	yes	characteristic, complemented
46	Q₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
47	#4090	C₂²	1	1	yes	characteristic, complemented
48	#4086	C₂²	1	1	yes	characteristic
49	#4086	C₂²	1	1	yes	characteristic
50	#4086	C₂²	1	1	yes	characteristic, complemented
51	#4086	C₂²	1	2	yes	complemented
52	#4086	C₂²	1	2	yes	complemented
53	#4085	C₂²	1	1	yes	characteristic
54	#4085	C₂²	1	2	yes	—
55	#4085	C₂²	1	2	yes	complemented
56	#4085	C₂²	1	2	yes	complemented
57	#4085	C₂²	1	2	yes	complemented
58	#4084	C₂²	1	1	yes	characteristic
59	#4084	C₂²	1	2	yes	complemented
60	#4084	C₂²	1	2	yes	complemented
61	#4084	C₂²	1	2	yes	complemented
62	#4084	C₂²	1	2	yes	complemented
63	#4083	C₂²	1	2	yes	—
64	#4083	C₂²	1	2	yes	complemented
65	#4082	C₂²	1	1	yes	characteristic
66	#4082	C₂²	1	1	yes	characteristic, complemented
67	#4081	C₂²	1	1	yes	characteristic, complemented
68	D₄×Dic₅	C₂²	1	1	yes	characteristic
69	#4076	C₂²	1	1	yes	characteristic
70	#4076	C₂²	1	2	yes	complemented
71	#4076	C₂²	1	2	yes	complemented
72	#4076	C₂²	1	1	yes	characteristic, complemented
73	#4075	C₂²	1	2	yes	complemented
74	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
75	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
76	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
77	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
78	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
79	#4072	C₂²	1	1	yes	characteristic, complemented
80	#4070	C₂²	1	2	yes	complemented
81	C₂×C₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
82	#4044	C₂²	1	1	yes	characteristic, complemented
83	#4044	C₂²	1	2	yes	complemented
84	#4043	C₂²	1	1	yes	characteristic, complemented
85	#4043	C₂²	1	2	yes	complemented
86	#4040	C₂²	1	2	yes	complemented
87	#4039	C₂²	1	1	yes	characteristic, complemented
88	#4039	C₂²	1	1	yes	characteristic, complemented
89	#4039	C₂²	1	2	yes	complemented
90	D₅×C₄⋊C₄	C₂²	1	2	yes	complemented
91	#4035	C₂²	1	1	yes	characteristic, complemented
92	#4034	C₂²	1	1	yes	characteristic, complemented
93	#4032	C₂²	1	1	yes	characteristic, complemented
94	#4031	C₂²	1	1	yes	characteristic
95	#4031	C₂²	1	2	yes	complemented
96	#4031	C₂²	1	2	yes	complemented
97	#4031	C₂²	1	2	yes	complemented
98	#4030	C₂²	1	2	yes	—
99	#4030	C₂²	1	2	yes	complemented
100	#4030	C₂²	1	2	yes	complemented
101	#4030	C₂²	1	2	yes	complemented
102	#4030	C₂²	1	2	yes	complemented
103	#4030	C₂²	1	2	yes	complemented
104	#4030	C₂²	1	2	yes	complemented
105	#4029	C₂²	1	2	yes	complemented
106	#4029	C₂²	1	2	yes	complemented
107	#4029	C₂²	1	2	yes	complemented
108	#4028	C₂²	1	2	yes	complemented
109	#4028	C₂²	1	2	yes	complemented
110	#4027	C₂²	1	2	yes	complemented
111	D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
112	#4025	C₂²	1	1	yes	characteristic, complemented
113	#4025	C₂²	1	2	yes	complemented
114	#4025	C₂²	1	2	yes	complemented
115	#4025	C₂²	1	2	yes	complemented
116	#4024	C₂²	1	2	yes	complemented
117	#4024	C₂²	1	1	yes	characteristic, complemented
118	#4023	C₂²	1	2	yes	complemented
119	#4020	C₂²	1	1	yes	characteristic, complemented
120	#4018	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	#3546	—	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	—	4	4	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	2	yes	—
148	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
149	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
150	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
151	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
152	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
153	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
154	C₂²×Dic₅	C₂³	1	1	yes	characteristic
155	C₂²×Dic₅	C₂³	1	2	yes	—
156	C₂²×Dic₅	C₂³	1	1	yes	characteristic
157	#713	—	4	2	no	—
158	#711	—	4	4	no	—
159	D₄×D₅	—	4	2	no	—
160	#709	—	4	4	no	—
161	#709	—	4	2	no	—
162	#709	—	4	2	no	—
163	C₂×D₂₀	C₂³	1	1	yes	characteristic
164	C₂×D₂₀	C₂³	1	1	yes	characteristic
165	C₂×D₂₀	C₂³	1	2	yes	—
166	C₂×D₂₀	C₂³	1	2	yes	—
167	C₂×D₂₀	C₂³	1	2	yes	—
168	C₂×C₄×D₅	C₂³	1	2	yes	—
169	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
170	C₂×C₄×D₅	C₂³	1	2	yes	—
171	C₂×C₄×D₅	C₂³	1	2	yes	—
172	C₂×C₄×D₅	C₂³	1	2	yes	—
173	C₂×C₄×D₅	C₂³	1	2	yes	—
174	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
175	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
176	C₂×Dic₁₀	C₂³	1	2	yes	—
177	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
178	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
179	C₅×C₄⋊C₄	C₂³	1	2	yes	—
180	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
181	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
186	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₄²×C₅	C₂³	1	1	yes	characteristic
188	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
189	C₂²⋊Dic₅	C₂³	1	2	yes	—
190	C₂²⋊Dic₅	C₂³	1	2	yes	—
191	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
192	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
193	C₂²⋊Dic₅	C₂³	1	2	yes	—
194	C₂²⋊Dic₅	C₂³	1	2	yes	—
195	C₂²⋊Dic₅	C₂³	1	2	yes	—
196	C₂²⋊Dic₅	C₂³	1	2	yes	—
197	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
198	#685	C₂³	1	1	yes	characteristic
199	#685	C₂³	1	1	yes	characteristic
200	#685	C₂³	1	1	yes	characteristic
201	#685	C₂³	1	2	yes	—
202	#685	C₂³	1	2	yes	—
203	#685	C₂³	1	2	yes	—
204	#685	C₂³	1	2	yes	—
205	#685	C₂³	1	2	yes	—
206	#685	C₂³	1	2	yes	—
207	#685	C₂³	1	2	yes	—
208	#685	C₂³	1	1	yes	characteristic
209	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
210	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
211	C₄⋊Dic₅	C₂³	1	2	yes	—
212	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
213	C₄⋊Dic₅	C₂³	1	2	yes	—
214	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
215	#683	C₂³	1	1	yes	characteristic
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	#683	C₂³	1	2	yes	—
224	#683	C₂³	1	1	yes	characteristic
225	C₄×Dic₅	C₂³	1	2	yes	—
226	C₄×Dic₅	C₂³	1	1	yes	characteristic
227	C₄×Dic₅	C₂³	1	1	yes	characteristic
228	C₄×Dic₅	C₂³	1	1	yes	characteristic
229	C₄×Dic₅	C₂³	1	2	yes	—
230	C₄×Dic₅	C₂³	1	1	yes	characteristic
231	C₄×Dic₅	C₂³	1	1	yes	characteristic
232	#560	—	5	2	no	—
233	#560	—	5	2	no	—
234	#556	—	5	1	no	—
235	#553	—	5	2	no	—
236	#550	—	5	1	no	—
237	#550	—	5	1	no	—
238	#550	—	5	1	no	—
239	#547	—	5	1	no	—
240	#546	—	5	1	no	—
241	#546	—	5	2	no	—
242	#546	D₅	1	1	yes	characteristic, complemented
243	D₄²	—	5	1	no	—
244	#542	—	5	1	no	—
245	#542	—	5	1	no	—
246	#538	—	5	2	no	—
247	#538	—	5	2	no	—
248	#537	—	5	2	no	—
249	#535	—	5	1	no	—
250	#535	—	5	1	no	—
251	#535	—	5	2	no	—
252	#532	—	5	1	no	—
253	#532	—	5	1	no	—
254	#529	—	5	1	no	—
255	C₂³×C₅	—	4	2	no	—
256	C₂³×C₅	—	4	2	no	—
257	C₂³×C₅	—	4	2	no	—
258	C₂³×C₅	C₂⁴	1	2	yes	—
259	C₂³×C₅	C₂⁴	1	1	yes	characteristic
260	C₂³×C₅	C₂⁴	1	2	yes	—
261	C₂³×C₅	C₂⁴	1	1	yes	characteristic
262	C₂²×D₅	—	4	2	no	—
263	C₂²×D₅	—	4	2	no	—
264	C₂²×D₅	—	4	2	no	—
265	C₂²×D₅	C₂⁴	1	1	yes	characteristic
266	C₂²×D₅	C₂⁴	1	2	yes	—
267	C₂²×D₅	C₂⁴	1	2	yes	—
268	C₅×Q₈	—	2	2	no	—
269	C₅×D₄	—	2	2	no	—
270	C₅×D₄	—	2	2	no	—
271	C₅×D₄	—	4	2	no	—
272	C₅×D₄	—	4	2	no	—
273	C₅×D₄	—	4	1	no	—
274	C₅×D₄	—	4	2	no	—
275	C₂×C₄×C₅	—	2	2	no	—
276	C₂×C₄×C₅	—	2	2	no	—
277	C₂×C₄×C₅	—	4	2	no	—
278	C₂×C₄×C₅	—	4	2	no	—
279	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
280	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
281	C₂×C₄×C₅	C₂⁴	1	2	yes	—
282	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
283	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
284	C₂×C₄×C₅	C₂⁴	1	2	yes	—
285	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
286	C₂²⋊D₅	—	2	4	no	—
287	C₂²⋊D₅	—	2	2	no	—
288	C₂²⋊D₅	—	4	2	no	—
289	C₂²⋊D₅	—	4	2	no	—
290	C₂²⋊D₅	—	4	2	no	—
291	C₂²⋊D₅	—	4	2	no	—
292	C₂²⋊D₅	—	4	2	no	—
293	C₂²⋊D₅	—	4	2	no	—
294	C₂²⋊D₅	—	4	2	no	—
295	C₂²⋊D₅	—	4	2	no	—
296	C₂²⋊D₅	—	4	2	no	—
297	C₂²⋊D₅	—	4	2	no	—
298	C₂²⋊D₅	—	4	2	no	—
299	C₂²⋊D₅	—	4	1	no	—
300	C₂×Dic₅	—	2	2	no	—
301	C₂×Dic₅	—	2	4	no	—
302	C₂×Dic₅	—	4	1	no	—
303	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
304	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
305	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
306	C₂×Dic₅	C₂⁴	1	2	yes	—
307	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
308	C₂×Dic₅	C₂⁴	1	2	yes	—
309	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
310	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
311	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
312	D₂₀	—	2	2	no	—
313	D₂₀	—	2	2	no	—
314	D₂₀	—	4	2	no	—
315	D₂₀	—	4	2	no	—
316	D₂₀	—	4	2	no	—
317	C₄×D₅	—	2	2	no	—
318	C₄×D₅	—	2	4	no	—
319	C₄×D₅	—	4	2	no	—
320	C₄×D₅	—	4	2	no	—
321	C₄×D₅	—	4	2	no	—
322	C₄×D₅	—	4	2	no	—
323	Dic₁₀	—	2	2	no	—
324	Dic₁₀	—	2	2	no	—
325	Dic₁₀	—	4	2	no	—
326	C₂×#41	—	5	1	no	—
327	C₂×#41	—	5	2	no	—
328	C₂×#41	—	5	1	no	—
329	C₂×#41	—	5	1	no	—
330	C₂×#41	—	5	2	no	—
331	C₂×#41	C₂×D₅	1	1	yes	characteristic, complemented
332	C₂²×D₄	—	5	2	no	—
333	C₂²×D₄	—	5	1	no	—
334	C₂²×D₄	C₂×D₅	1	1	yes	characteristic
335	C₄⋊Q₈	—	5	1	no	—
336	C₄⋊Q₈	—	5	1	no	—
337	#127	—	5	1	no	—
338	#127	—	5	1	no	—
339	#127	—	5	1	no	—
340	#127	—	5	2	no	—
341	#127	—	5	2	no	—
342	#127	—	5	1	no	—
343	#126	—	5	1	no	—
344	#126	—	5	2	no	—
345	#126	—	5	1	no	—
346	#126	—	5	2	no	—
347	#126	—	5	2	no	—
348	#126	—	5	2	no	—
349	#125	—	5	1	no	—
350	#124	—	5	1	no	—
351	#124	—	5	1	no	—
352	#124	—	5	1	no	—
353	#124	—	5	1	no	—
354	#124	—	5	2	no	—
355	#124	—	5	2	no	—
356	#124	—	5	2	no	—
357	#124	C₂×D₅	1	1	yes	characteristic
358	#123	—	5	1	no	—
359	#123	—	5	2	no	—
360	#123	—	5	2	no	—
361	#123	—	5	1	no	—
362	#123	—	5	2	no	—
363	#123	—	5	2	no	—
364	#123	—	5	2	no	—
365	#123	C₂×D₅	1	2	yes	complemented
366	C₂²⋊Q₈	—	5	2	no	—
367	C₂²⋊Q₈	—	5	2	no	—
368	C₂²⋊Q₈	—	5	1	no	—
369	C₂²⋊Q₈	—	5	1	no	—
370	C₂²⋊Q₈	—	5	2	no	—
371	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
372	#121	—	5	1	no	—
373	#121	—	5	2	no	—
374	#121	—	5	2	no	—
375	#121	—	5	2	no	—
376	#121	—	5	2	no	—
377	#121	—	5	2	no	—
378	#121	—	5	2	no	—
379	#121	—	5	2	no	—
380	#121	—	5	2	no	—
381	#121	—	5	1	no	—
382	#121	—	5	1	no	—
383	#121	—	5	2	no	—
384	#121	—	5	2	no	—
385	#121	—	5	1	no	—
386	#121	—	5	2	no	—
387	#121	—	5	2	no	—
388	#121	—	5	2	no	—
389	#121	—	5	2	no	—
390	#121	—	5	2	no	—
391	#121	—	5	2	no	—
392	#121	—	5	2	no	—
393	#121	C₂×D₅	1	1	yes	characteristic
394	#121	C₂×D₅	1	2	yes	complemented
395	#120	—	5	2	no	—
396	#120	—	5	2	no	—
397	#120	—	5	2	no	—
398	#120	—	5	2	no	—
399	#120	—	5	2	no	—
400	#120	—	5	2	no	—
401	#120	—	5	2	no	—
402	#120	C₂×D₅	1	2	yes	complemented
403	C₄×Q₈	—	5	1	no	—
404	C₄×Q₈	—	5	1	no	—
405	C₄×Q₈	—	5	1	no	—
406	C₄×D₄	—	5	1	no	—
407	C₄×D₄	—	5	1	no	—
408	C₄×D₄	—	5	1	no	—
409	C₄×D₄	—	5	2	no	—
410	C₄×D₄	—	5	2	no	—
411	C₄×D₄	—	5	2	no	—
412	C₄×D₄	—	5	1	no	—
413	C₄×D₄	—	5	2	no	—
414	C₄×D₄	—	5	1	no	—
415	C₄×D₄	—	5	2	no	—
416	C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
417	C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
418	#117	—	5	1	no	—
419	#117	—	5	2	no	—
420	#117	—	5	1	no	—
421	C₂×C₄⋊C₄	—	5	2	no	—
422	C₂×C₂²⋊C₄	—	5	2	no	—
423	C₂×C₂²⋊C₄	C₂×D₅	1	2	yes	complemented
424	C₂×C₄²	—	5	1	no	—
425	C₂²×C₅	—	2	1	no	—
426	C₂²×C₅	—	2	2	no	—
427	C₂²×C₅	—	2	2	no	—
428	C₂²×C₅	—	2	1	no	—
429	C₂²×C₅	—	2	1	no	—
430	C₂²×C₅	—	2	1	no	—
431	C₂²×C₅	—	2	2	no	—
432	C₂²×C₅	—	2	2	no	—
433	C₂²×C₅	—	2	1	no	—
434	C₂²×C₅	—	2	2	no	—
435	C₂²×C₅	—	2	2	no	—
436	C₂²×C₅	—	2	1	no	—
437	C₂²×C₅	—	8	4	no	—
438	C₂²×C₅	C₂⁵	1	1	yes	characteristic
439	C₂×D₅	—	2	1	no	—
440	C₂×D₅	—	2	2	no	—
441	C₂×D₅	—	2	2	no	—
442	C₂×D₅	—	2	2	no	—
443	C₂×D₅	—	2	2	no	—
444	C₂×D₅	—	2	1	no	—
445	C₂×D₅	—	2	2	no	—
446	C₂×D₅	—	2	2	no	—
447	C₂×D₅	—	2	1	no	—
448	C₂×D₅	—	8	4	no	—
449	C₄×C₅	—	2	1	no	—
450	C₄×C₅	—	2	2	no	—
451	C₄×C₅	—	2	1	no	—
452	C₄×C₅	—	2	1	no	—
453	C₄×C₅	—	2	2	no	—
454	C₄×C₅	—	2	1	no	—
455	C₄×C₅	H(5,𝔽₂)	1	2	yes	—
456	Dic₅	—	2	2	no	—
457	Dic₅	—	2	1	no	—
458	Dic₅	—	2	1	no	—
459	Dic₅	—	2	2	no	—
460	Dic₅	—	2	1	no	—
461	Dic₅	—	2	1	no	—
462	Dic₅	—	2	1	no	—
463	Dic₅	—	2	1	no	—
464	Dic₅	H(5,𝔽₂)	1	2	yes	—
465	C₂⁴	—	5	2	no	—
466	C₂⁴	C₂²×D₅	1	2	yes	—
467	#41	—	4	2	no	—
468	#41	—	20	2	no	—
469	#41	—	20	2	no	—
470	#41	—	20	4	no	—
471	#41	—	20	4	no	—
472	#41	—	20	2	no	—
473	C₂×Q₈	—	5	1	no	—
474	C₂×Q₈	—	5	1	no	—
475	C₂×Q₈	—	5	2	no	—
476	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
477	C₂×D₄	—	4	2	no	—
478	C₂×D₄	—	5	1	no	—
479	C₂×D₄	—	5	2	no	—
480	C₂×D₄	—	5	2	no	—
481	C₂×D₄	—	5	2	no	—
482	C₂×D₄	—	5	1	no	—
483	C₂×D₄	—	5	2	no	—
484	C₂×D₄	—	5	2	no	—
485	C₂×D₄	—	5	2	no	—
486	C₂×D₄	—	5	2	no	—
487	C₂×D₄	—	5	2	no	—
488	C₂×D₄	—	5	2	no	—
489	C₂×D₄	—	5	2	no	—
490	C₂×D₄	—	5	2	no	—
491	C₂×D₄	—	5	2	no	—
492	C₂×D₄	—	5	1	no	—
493	C₂×D₄	—	5	1	no	—
494	C₂×D₄	—	5	2	no	—
495	C₂×D₄	—	5	2	no	—
496	C₂×D₄	—	5	2	no	—
497	C₂×D₄	—	20	2	no	—
498	C₂×D₄	—	20	4	no	—
499	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
500	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
501	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
502	C₂×D₄	C₂²×D₅	1	2	yes	—
503	C₂×D₄	C₂²×D₅	1	2	yes	—
504	C₂×D₄	C₂²×D₅	1	2	yes	—
505	C₂²×C₄	—	5	1	no	—
506	C₂²×C₄	—	5	2	no	—
507	C₂²×C₄	—	5	1	no	—
508	C₂²×C₄	—	5	2	no	—
509	C₂²×C₄	—	5	1	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	C₂²×D₅	1	1	yes	characteristic
515	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
516	C₂²×C₄	C₂²×D₅	1	2	yes	—
517	C₂²×C₄	C₂²×D₅	1	2	yes	—
518	C₄⋊C₄	—	5	1	no	—
519	C₄⋊C₄	—	5	2	no	—
520	C₄⋊C₄	—	5	2	no	—
521	C₄⋊C₄	—	5	1	no	—
522	C₄⋊C₄	—	5	1	no	—
523	C₄⋊C₄	—	5	1	no	—
524	C₄⋊C₄	—	5	1	no	—
525	C₄⋊C₄	—	5	1	no	—
526	C₄⋊C₄	—	5	1	no	—
527	C₄⋊C₄	—	5	1	no	—
528	C₄⋊C₄	—	5	2	no	—
529	C₄⋊C₄	—	5	2	no	—
530	C₄⋊C₄	—	5	2	no	—
531	C₄⋊C₄	—	5	2	no	—
532	C₄⋊C₄	—	5	1	no	—
533	C₄⋊C₄	—	5	1	no	—
534	C₄⋊C₄	C₂²×D₅	1	2	yes	—
535	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
536	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
537	C₂²⋊C₄	—	5	2	no	—
538	C₂²⋊C₄	—	5	2	no	—
539	C₂²⋊C₄	—	5	1	no	—
540	C₂²⋊C₄	—	5	1	no	—
541	C₂²⋊C₄	—	5	2	no	—
542	C₂²⋊C₄	—	5	1	no	—
543	C₂²⋊C₄	—	5	2	no	—
544	C₂²⋊C₄	—	5	2	no	—
545	C₂²⋊C₄	—	5	2	no	—
546	C₂²⋊C₄	—	5	1	no	—
547	C₂²⋊C₄	—	5	1	no	—
548	C₂²⋊C₄	—	5	2	no	—
549	C₂²⋊C₄	—	5	1	no	—
550	C₂²⋊C₄	—	5	1	no	—
551	C₂²⋊C₄	—	5	2	no	—
552	C₂²⋊C₄	—	5	1	no	—
553	C₂²⋊C₄	—	5	2	no	—
554	C₂²⋊C₄	—	5	2	no	—
555	C₂²⋊C₄	—	5	2	no	—
556	C₂²⋊C₄	—	5	2	no	—
557	C₂²⋊C₄	—	5	2	no	—
558	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
559	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
560	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
561	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
562	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
563	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
564	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
565	C₄²	—	5	1	no	—
566	C₄²	—	5	1	no	—
567	C₄²	—	5	1	no	—
568	C₄²	—	5	1	no	—
569	C₄²	—	5	1	no	—
570	C₄²	—	5	2	no	—
571	C₄²	—	5	2	no	—
572	C₄²	C₂²×D₅	1	1	yes	characteristic
573	C₂×C₅	—	4	2	no	—
574	C₂×C₅	—	4	1	no	—
575	C₂×C₅	—	4	2	no	—
576	C₂×C₅	—	4	1	no	—
577	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
578	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
579	C₂×C₅	#585	1	1	yes	characteristic
580	D₅	—	4	2	no	—
581	D₅	—	4	2	no	—
582	D₅	—	4	1	no	—
583	C₂³	—	4	2	no	—
584	C₂³	—	4	2	no	—
585	C₂³	—	4	2	no	—
586	C₂³	—	5	1	no	—
587	C₂³	—	5	2	no	—
588	C₂³	—	5	2	no	—
589	C₂³	—	20	2	no	—
590	C₂³	—	20	2	no	—
591	C₂³	—	20	2	no	—
592	C₂³	C₂³×D₅	1	2	yes	—
593	C₂³	C₂³×D₅	1	1	yes	characteristic
594	C₂³	C₂³×D₅	1	2	yes	—
595	C₂³	C₂³×D₅	1	1	yes	characteristic
596	Q₈	—	2	2	no	—
597	Q₈	—	10	2	no	—
598	Q₈	—	10	2	no	—
599	Q₈	—	20	2	no	—
600	D₄	—	2	2	no	—
601	D₄	—	2	2	no	—
602	D₄	—	4	2	no	—
603	D₄	—	4	2	no	—
604	D₄	—	4	2	no	—
605	D₄	—	4	1	no	—
606	D₄	—	10	2	no	—
607	D₄	—	10	4	no	—
608	D₄	—	10	2	no	—
609	D₄	—	10	2	no	—
610	D₄	—	20	2	no	—
611	D₄	—	20	2	no	—
612	D₄	—	20	2	no	—
613	D₄	—	20	2	no	—
614	D₄	—	20	2	no	—
615	D₄	—	20	2	no	—
616	D₄	—	20	2	no	—
617	D₄	—	20	2	no	—
618	D₄	—	20	2	no	—
619	D₄	—	20	2	no	—
620	D₄	—	20	2	no	—
621	D₄	—	20	2	no	—
622	D₄	—	20	2	no	—
623	D₄	—	20	1	no	—
624	D₄	—	20	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	4	2	no	—
628	C₂×C₄	—	4	2	no	—
629	C₂×C₄	—	5	1	no	—
630	C₂×C₄	—	5	1	no	—
631	C₂×C₄	—	5	1	no	—
632	C₂×C₄	—	5	1	no	—
633	C₂×C₄	—	5	1	no	—
634	C₂×C₄	—	5	2	no	—
635	C₂×C₄	—	5	2	no	—
636	C₂×C₄	—	5	1	no	—
637	C₂×C₄	—	5	1	no	—
638	C₂×C₄	—	10	4	no	—
639	C₂×C₄	—	10	4	no	—
640	C₂×C₄	—	10	2	no	—
641	C₂×C₄	—	10	2	no	—
642	C₂×C₄	—	20	2	no	—
643	C₂×C₄	—	20	2	no	—
644	C₂×C₄	—	20	2	no	—
645	C₂×C₄	—	20	2	no	—
646	C₂×C₄	—	20	1	no	—
647	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
648	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
649	C₂×C₄	C₂³×D₅	1	2	yes	—
650	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
651	C₂×C₄	C₂³×D₅	1	2	yes	—
652	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
653	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
654	C₅	#3546	1	1	yes	characteristic, complemented, Sylow
655	C₂²	—	2	1	no	—
656	C₂²	—	2	1	no	—
657	C₂²	—	2	2	no	—
658	C₂²	—	2	2	no	—
659	C₂²	—	2	1	no	—
660	C₂²	—	2	1	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	2	no	—
664	C₂²	—	2	1	no	—
665	C₂²	—	2	2	no	—
666	C₂²	—	2	1	no	—
667	C₂²	—	8	4	no	—
668	C₂²	—	10	1	no	—
669	C₂²	—	10	2	no	—
670	C₂²	—	10	2	no	—
671	C₂²	—	10	2	no	—
672	C₂²	—	10	2	no	—
673	C₂²	—	10	1	no	—
674	C₂²	—	10	2	no	—
675	C₂²	—	10	2	no	—
676	C₂²	—	10	1	no	—
677	C₂²	—	40	4	no	—
678	C₂²	C₂⁴×D₅	1	1	yes	characteristic
679	C₄	—	2	1	no	—
680	C₄	—	2	1	no	—
681	C₄	—	2	2	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	1	no	—
684	C₄	—	2	2	no	—
685	C₄	—	5	2	no	—
686	C₄	—	10	1	no	—
687	C₄	—	10	2	no	—
688	C₄	—	10	1	no	—
689	C₄	—	10	1	no	—
690	C₄	—	10	1	no	—
691	C₄	—	10	2	no	—
692	C₄	—	10	1	no	—
693	C₄	—	10	1	no	—
694	C₄	#4144	1	2	yes	—
695	C₂	—	4	1	no	—
696	C₂	—	4	2	no	—
697	C₂	—	4	2	no	—
698	C₂	—	4	1	no	—
699	C₂	—	20	1	no	—
700	C₂	—	20	2	no	—
701	C₂	—	20	2	no	—
702	C₂	C₂×#4144	1	1	yes	characteristic
703	C₂	#66283	1	1	yes	characteristic
704	C₂	D₅×H(5,𝔽₂)	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	#3546
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. #66168	C₂	semidirect
3. #66166	C₂	semidirect
4. #66139	C₂	semidirect
5. D₄×C₂²⋊D₅	C₂	semidirect
6. #66008	C₂	semidirect
7. #66005	C₂	semidirect
8. #65995	C₂	semidirect
9. #65991	C₂	semidirect
10. #65977	C₂	semidirect
11. #65965	C₂	semidirect
12. #65954	C₂	semidirect
13. #65946	C₂	semidirect
14. #65942	C₂	semidirect
15. #65930	C₂	semidirect
16. #65929	C₂	semidirect
17. #65926	C₂	semidirect
18. #65895	C₂	semidirect
19. #65887	C₂	semidirect
20. #65887	C₂	semidirect
21. #65872	C₂	semidirect
22. #65828	C₂	semidirect
23. #65824	C₂	semidirect
24. C₂×C₅×#41	C₂²	semidirect
27. C₂×#713	C₂²	semidirect
28. C₂×#711	C₂²	semidirect
30. C₂×#709	C₂²	semidirect
31. C₂×#709	C₂²	semidirect
32. C₂×#709	C₂²	semidirect
34. C₅×#123	C₂²	semidirect
35. C₅×C₂²⋊Q₈	C₂²	semidirect
37. C₅×#121	C₂²	semidirect
38. C₅×#120	C₂²	semidirect
39. C₄×C₅×D₄	C₂²	semidirect
40. C₄×C₅×D₄	C₂²	semidirect
41. C₂×C₅×C₂²⋊C₄	C₂²	semidirect
43. #4099	C₂²	semidirect
44. #4099	C₂²	semidirect
45. #4093	C₂²	semidirect
46. Q₈×Dic₅	C₂²	semidirect
47. #4090	C₂²	semidirect
50. #4086	C₂²	semidirect
51. #4086	C₂²	semidirect
52. #4086	C₂²	semidirect
55. #4085	C₂²	semidirect
56. #4085	C₂²	semidirect
57. #4085	C₂²	semidirect
59. #4084	C₂²	semidirect
60. #4084	C₂²	semidirect
61. #4084	C₂²	semidirect
62. #4084	C₂²	semidirect
64. #4083	C₂²	semidirect
66. #4082	C₂²	semidirect
67. #4081	C₂²	semidirect
70. #4076	C₂²	semidirect
71. #4076	C₂²	semidirect
72. #4076	C₂²	semidirect
73. #4075	C₂²	semidirect
75. C₄×C₂²⋊D₅	C₂²	semidirect
76. C₄×C₂²⋊D₅	C₂²	semidirect
77. C₄×C₂²⋊D₅	C₂²	semidirect
78. C₄×C₂²⋊D₅	C₂²	semidirect
79. #4072	C₂²	semidirect
80. #4070	C₂²	semidirect
81. C₂×C₄×Dic₅	C₂²	semidirect
82. #4044	C₂²	semidirect
83. #4044	C₂²	semidirect
84. #4043	C₂²	semidirect
85. #4043	C₂²	semidirect
86. #4040	C₂²	semidirect
87. #4039	C₂²	semidirect
88. #4039	C₂²	semidirect
89. #4039	C₂²	semidirect
90. D₅×C₄⋊C₄	C₂²	semidirect
91. #4035	C₂²	semidirect
92. #4034	C₂²	semidirect
93. #4032	C₂²	semidirect
95. #4031	C₂²	semidirect
96. #4031	C₂²	semidirect
97. #4031	C₂²	semidirect
99. #4030	C₂²	semidirect
100. #4030	C₂²	semidirect
101. #4030	C₂²	semidirect
102. #4030	C₂²	semidirect
103. #4030	C₂²	semidirect
104. #4030	C₂²	semidirect
105. #4029	C₂²	semidirect
106. #4029	C₂²	semidirect
107. #4029	C₂²	semidirect
108. #4028	C₂²	semidirect
109. #4028	C₂²	semidirect
110. #4027	C₂²	semidirect
111. D₅×C₂²⋊C₄	C₂²	semidirect
112. #4025	C₂²	semidirect
113. #4025	C₂²	semidirect
114. #4025	C₂²	semidirect
115. #4025	C₂²	semidirect
116. #4024	C₂²	semidirect
117. #4024	C₂²	semidirect
118. #4023	C₂²	semidirect
119. #4020	C₂²	semidirect
120. #4018	C₂²	semidirect
121. C₄×Dic₁₀	C₂²	semidirect
122. C₄×Dic₁₀	C₂²	semidirect
242. #546	D₅	semidirect
331. C₂×#41	C₂×D₅	semidirect
365. #123	C₂×D₅	semidirect
371. C₂²⋊Q₈	C₂×D₅	semidirect
394. #121	C₂×D₅	semidirect
402. #120	C₂×D₅	semidirect
416. C₄×D₄	C₂×D₅	semidirect
417. C₄×D₄	C₂×D₅	semidirect
423. C₂×C₂²⋊C₄	C₂×D₅	semidirect
654. C₅	#3546	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
#66168	2
#66166	2
#66139	2
D₄×C₂²⋊D₅	2
#66008	2
#66005	2
#65995	2
#65991	2
#65977	2
#65965	2
#65954	2
#65946	2
#65942	2
#65930	2
#65929	2
#65926	2
#65895	2
#65887	2
#65872	2
#65828	2
#65824	2
#3546	5