Subgroups — #12068615

Order 1280.

594 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2990	C₂	1	1	yes	maximal, characteristic
2	#10614253	C₂	1	1	yes	maximal, characteristic
3	#10614248	C₂	1	1	yes	maximal, characteristic
4	#10601590	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601589	C₂	1	1	yes	maximal, characteristic, complemented
6	#10601588	C₂	1	1	yes	maximal, characteristic, complemented
7	#10601587	C₂	1	1	yes	maximal, characteristic, complemented
8	#10601540	C₂	1	1	yes	maximal, characteristic, complemented
9	#10601539	C₂	1	1	yes	maximal, characteristic, complemented
10	#10601286	C₂	1	1	yes	maximal, characteristic, complemented
11	#10601285	C₂	1	1	yes	maximal, characteristic, complemented
12	#10601216	C₂	1	1	yes	maximal, characteristic, complemented
13	#10601214	C₂	1	1	yes	maximal, characteristic, complemented
14	#10601213	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#64700	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₅×#41	C₂²	1	1	yes	characteristic
17	C₅×#446	—	2	1	no	—
18	C₅×#435	—	2	1	no	—
19	C₅×#435	—	2	1	no	—
20	C₅×C₈×D₄	—	2	1	no	—
21	C₅×#432	C₂²	1	1	yes	characteristic
22	C₅×#432	C₂²	1	1	yes	characteristic
23	C₅×#431	C₂²	1	1	yes	characteristic
24	C₅×#423	C₂²	1	1	yes	characteristic
25	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	#65313	—	2	1	no	—
28	#65313	C₄	1	1	yes	characteristic
29	#65313	C₄	1	1	yes	characteristic
30	#65301	C₄	1	1	yes	characteristic
31	#65301	C₄	1	1	yes	characteristic
32	#65300	—	2	1	no	—
33	#65300	—	2	1	no	—
34	#65300	C₄	1	1	yes	characteristic
35	#65300	C₄	1	1	yes	characteristic
36	#65300	C₄	1	1	yes	characteristic
37	#65300	C₄	1	1	yes	characteristic
38	D₄×#168	—	2	1	no	—
39	#65215	C₂²	1	1	yes	characteristic
40	#65215	C₂²	1	1	yes	characteristic
41	#65214	C₂²	1	1	yes	characteristic
42	#65214	C₂²	1	1	yes	characteristic
43	#65214	C₂²	1	1	yes	characteristic
44	#65214	C₂²	1	1	yes	characteristic
45	#65213	C₂²	1	1	yes	characteristic
46	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
47	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
48	C₄×#681	C₂²	1	1	yes	characteristic
49	C₄×#681	C₂²	1	1	yes	characteristic
50	C₂×C₄×#168	C₂²	1	1	yes	characteristic
51	#64700	C₂²	1	1	yes	characteristic
52	#64700	C₂²	1	1	yes	characteristic
53	#64700	C₂²	1	1	yes	characteristic
54	#64700	C₂²	1	1	yes	characteristic
55	#64700	C₂²	1	1	yes	characteristic
56	#64700	C₂²	1	1	yes	characteristic
57	#64700	C₂²	1	1	yes	characteristic
58	#64700	C₂²	1	1	yes	characteristic
59	#64700	C₂²	1	1	yes	characteristic
60	#64700	C₂²	1	1	yes	characteristic
61	#64699	C₂²	1	1	yes	characteristic
62	#64699	C₂²	1	1	yes	characteristic
63	#64699	C₂²	1	1	yes	characteristic
64	#64699	C₂²	1	1	yes	characteristic
65	#64699	C₂²	1	1	yes	characteristic
66	#64699	C₂²	1	1	yes	characteristic
67	#17838	—	5	1	no	maximal, Sylow
68	C₂×C₅×#41	Q₈	1	1	yes	characteristic
69	C₂×C₅×M₁₆	—	2	1	no	—
70	C₂²×C₅×C₈	—	2	1	no	—
71	C₂²×C₅×C₈	—	2	1	no	—
72	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
73	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
74	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
75	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
76	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
77	C₄×C₅×D₄	D₄	1	1	yes	characteristic
78	C₄×C₅×D₄	D₄	1	1	yes	characteristic
79	C₄×C₅×D₄	D₄	1	1	yes	characteristic
80	C₅×#117	Q₈	1	1	yes	characteristic
81	C₅×#117	Q₈	1	1	yes	characteristic
82	C₅×#117	Q₈	1	1	yes	characteristic
83	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
86	C₂×#681	—	2	1	no	—
87	C₂×#681	C₂×C₄	1	1	yes	characteristic
88	C₂×#681	C₂×C₄	1	1	yes	characteristic
89	C₂×#681	C₂×C₄	1	1	yes	characteristic
90	C₂×#681	C₂×C₄	1	1	yes	characteristic
91	C₂²×#168	—	2	1	no	—
92	C₂²×#168	—	2	1	no	—
93	C₂²×#168	C₂×C₄	1	1	yes	characteristic
94	C₂²×#168	C₂×C₄	1	1	yes	characteristic
95	C₅×C₄⋊C₈	—	2	1	no	—
96	C₅×C₄⋊C₈	—	2	1	no	—
97	C₅×C₄⋊C₈	—	2	1	no	—
98	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
99	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
100	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
101	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
102	C₅×C₂²⋊C₈	—	2	1	no	—
103	C₅×C₂²⋊C₈	—	2	1	no	—
104	C₅×C₂²⋊C₈	—	2	1	no	—
105	C₅×#97	—	2	1	no	—
106	C₅×#97	—	2	1	no	—
107	C₄×C₅×C₈	—	2	1	no	—
108	C₂²⋊#168	—	2	1	no	—
109	C₂²⋊#168	—	2	1	no	—
110	C₂²⋊#168	—	2	1	no	—
111	C₂²⋊#168	C₂×C₄	1	1	yes	characteristic
112	C₂²⋊#168	C₂×C₄	1	1	yes	characteristic
113	C₂²⋊#168	C₂×C₄	1	1	yes	characteristic
114	C₂²⋊#168	C₂×C₄	1	1	yes	characteristic
115	C₂²⋊#168	C₂×C₄	1	1	yes	characteristic
116	C₂²⋊#168	C₂×C₄	1	1	yes	characteristic
117	C₄⋊#168	—	2	1	no	—
118	C₄⋊#168	—	2	1	no	—
119	C₄⋊#168	—	2	1	no	—
120	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
121	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
122	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
123	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
124	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
125	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
126	C₄⋊#168	C₂³	1	1	yes	characteristic
127	C₄⋊#168	C₂³	1	1	yes	characteristic
128	C₄⋊#168	C₂³	1	1	yes	characteristic
129	C₄⋊#168	C₂³	1	1	yes	characteristic
130	#3935	—	2	1	no	—
131	#3935	—	2	1	no	—
132	#3935	C₂×C₄	1	1	yes	characteristic
133	#3935	C₂×C₄	1	1	yes	characteristic
134	#3935	C₂×C₄	1	1	yes	characteristic
135	#3935	C₂×C₄	1	1	yes	characteristic
136	C₄×#168	—	2	1	no	—
137	C₄×#168	C₂×C₄	1	1	yes	characteristic
138	C₄×#168	C₂×C₄	1	1	yes	characteristic
139	C₄×#168	C₂³	1	1	yes	characteristic
140	C₄×#168	C₂³	1	1	yes	characteristic
141	C₄×#168	C₂³	1	1	yes	characteristic
142	C₄×#168	C₂³	1	1	yes	characteristic
143	#2990	—	5	1	no	—
144	#2990	D₅	1	1	yes	characteristic
145	#2965	—	5	1	no	—
146	#1573	—	5	1	no	—
147	#1573	—	5	1	no	—
148	#1572	—	5	1	no	—
149	#1572	—	5	1	no	—
150	#1570	—	5	1	no	—
151	#1570	—	5	1	no	—
152	#1569	—	5	1	no	—
153	#1569	—	5	1	no	—
154	#1568	—	5	1	no	—
155	#1565	—	5	1	no	—
156	#1565	—	5	1	no	—
157	C₂×#334	—	5	1	no	—
158	C₅×#41	—	4	2	no	—
159	C₂×C₅×Q₈	C₄⋊C₄	1	1	yes	characteristic
160	C₂×C₅×D₄	C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₅×D₄	C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₅×D₄	C₄⋊C₄	1	1	yes	characteristic
163	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
166	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
170	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
171	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
172	C₅×M₁₆	—	8	1	no	—
173	C₂×C₅×C₈	—	2	1	no	—
174	C₂×C₅×C₈	—	2	1	no	—
175	C₂×C₅×C₈	—	2	1	no	—
176	C₂×C₅×C₈	—	2	1	no	—
177	C₂×C₅×C₈	—	8	1	no	—
178	C₂×C₅×C₈	—	8	1	no	—
179	C₅×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
180	C₅×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
181	C₅×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
182	C₅×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
183	C₅×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
184	C₅×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
185	C₅×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
186	C₅×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
187	C₅×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
188	C₅×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
189	C₅×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
190	C₅×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
191	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
192	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
193	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
194	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
195	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
196	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
197	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
198	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
199	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
200	C₄²×C₅	C₂⁴	1	1	yes	characteristic
201	#681	—	2	2	no	—
202	#681	—	2	2	no	—
203	#681	—	4	1	no	—
204	#681	—	4	1	no	—
205	#681	—	8	1	no	—
206	C₂×#168	—	2	2	no	—
207	C₂×#168	—	2	1	no	—
208	C₂×#168	—	2	1	no	—
209	C₂×#168	—	2	1	no	—
210	C₂×#168	—	2	1	no	—
211	C₂×#168	—	4	1	no	—
212	C₂×#168	—	8	1	no	—
213	C₂×#168	—	8	1	no	—
214	C₂×#168	C₂²×C₄	1	1	yes	characteristic
215	C₂×#168	C₂²×C₄	1	1	yes	characteristic
216	C₂×#168	C₂²×C₄	1	1	yes	characteristic
217	C₂×#168	C₂²×C₄	1	1	yes	characteristic
218	C₂×#168	C₂²×C₄	1	1	yes	characteristic
219	C₂×#168	C₂²×C₄	1	1	yes	characteristic
220	C₂×#168	C₂²×C₄	1	1	yes	characteristic
221	C₂×#168	C₂²×C₄	1	1	yes	characteristic
222	C₄×#41	C₂×D₅	1	1	yes	characteristic
223	#446	—	2	1	no	—
224	#446	—	5	1	no	—
225	#446	—	5	1	no	—
226	#446	—	10	1	no	—
227	#436	—	5	1	no	—
228	#436	—	5	1	no	—
229	#435	—	2	1	no	—
230	#435	—	2	1	no	—
231	#435	—	5	1	no	—
232	#435	—	5	1	no	—
233	#435	—	5	1	no	—
234	#435	—	5	1	no	—
235	#435	—	10	1	no	—
236	#435	—	10	1	no	—
237	C₈×D₄	—	2	1	no	—
238	C₈×D₄	—	10	1	no	—
239	#432	—	5	1	no	—
240	#432	—	5	1	no	—
241	#432	C₂×D₅	1	1	yes	characteristic
242	#432	C₂×D₅	1	1	yes	characteristic
243	#431	—	5	1	no	—
244	#431	—	5	1	no	—
245	#431	—	5	1	no	—
246	#431	—	5	1	no	—
247	#431	C₂×D₅	1	1	yes	characteristic
248	#423	—	5	1	no	—
249	#423	C₂×D₅	1	1	yes	characteristic
250	C₂×C₄⋊C₈	—	5	1	no	—
251	C₂×C₄⋊C₈	—	5	1	no	—
252	C₂×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
253	C₂×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
254	C₄×M₁₆	—	5	1	no	—
255	C₄×M₁₆	—	5	1	no	—
256	C₂×C₄×C₈	—	5	1	no	—
257	#335	—	5	1	no	—
258	#335	—	5	1	no	—
259	#335	—	5	1	no	—
260	#335	—	5	1	no	—
261	#335	—	5	1	no	—
262	#335	—	5	1	no	—
263	#334	—	5	1	no	—
264	#334	—	5	1	no	—
265	#334	—	5	1	no	—
266	#334	—	5	1	no	—
267	#334	—	5	1	no	—
268	#334	—	5	1	no	—
269	#334	—	5	1	no	—
270	#334	—	5	1	no	—
271	#334	—	5	1	no	—
272	#334	—	5	1	no	—
273	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
274	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
275	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
276	C₅×Q₈	—	4	1	no	—
277	C₅×D₄	—	2	2	no	—
278	C₅×D₄	—	2	2	no	—
279	C₅×D₄	—	4	1	no	—
280	C₂×C₄×C₅	—	2	2	no	—
281	C₂×C₄×C₅	—	2	1	no	—
282	C₂×C₄×C₅	—	2	1	no	—
283	C₂×C₄×C₅	—	2	1	no	—
284	C₂×C₄×C₅	—	2	1	no	—
285	C₂×C₄×C₅	—	2	1	no	—
286	C₂×C₄×C₅	—	2	1	no	—
287	C₂×C₄×C₅	—	2	1	no	—
288	C₂×C₄×C₅	—	2	1	no	—
289	C₂×C₄×C₅	—	2	1	no	—
290	C₂×C₄×C₅	—	2	1	no	—
291	C₂×C₄×C₅	—	2	1	no	—
292	C₂×C₄×C₅	—	2	1	no	—
293	C₂×C₄×C₅	—	4	1	no	—
294	C₂×C₄×C₅	—	4	1	no	—
295	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
296	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
297	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
298	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
299	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
300	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
301	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
302	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
303	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
304	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
305	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
306	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
307	C₅×C₈	—	4	1	no	—
308	C₅×C₈	—	4	1	no	—
309	C₅×C₈	—	4	1	no	—
310	C₅×C₈	—	4	1	no	—
311	#168	—	2	1	no	—
312	#168	—	2	1	no	—
313	#168	—	2	1	no	—
314	#168	—	2	1	no	—
315	#168	—	2	1	no	—
316	#168	—	2	1	no	—
317	#168	—	2	1	no	—
318	#168	—	4	1	no	—
319	#168	—	4	1	no	—
320	#168	—	4	1	no	—
321	#168	—	4	1	no	—
322	#168	#131	1	2	yes	—
323	C₂×#41	Dic₁₀	1	1	yes	characteristic
324	C₂×M₁₆	—	2	1	no	—
325	C₂×M₁₆	—	5	1	no	—
326	C₂×M₁₆	—	5	1	no	—
327	C₂×M₁₆	—	5	1	no	—
328	C₂×M₁₆	—	5	1	no	—
329	C₂×M₁₆	—	10	1	no	—
330	C₂²×C₈	—	2	1	no	—
331	C₂²×C₈	—	2	1	no	—
332	C₂²×C₈	—	5	1	no	—
333	C₂²×C₈	—	5	1	no	—
334	C₂²×C₈	—	10	1	no	—
335	C₂²×C₈	—	10	1	no	—
336	C₄×Q₈	C₄×D₅	1	1	yes	characteristic
337	C₄×Q₈	C₂²⋊D₅	1	1	yes	characteristic
338	C₄×D₄	C₄×D₅	1	1	yes	characteristic
339	C₄×D₄	C₄×D₅	1	1	yes	characteristic
340	C₄×D₄	C₄×D₅	1	1	yes	characteristic
341	C₄×D₄	C₂²⋊D₅	1	1	yes	characteristic
342	C₄×D₄	C₂²⋊D₅	1	1	yes	characteristic
343	C₄×D₄	C₂²⋊D₅	1	1	yes	characteristic
344	#117	Dic₁₀	1	1	yes	characteristic
345	#117	Dic₁₀	1	1	yes	characteristic
346	#117	Dic₁₀	1	1	yes	characteristic
347	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
348	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
349	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
350	C₄⋊C₈	—	2	1	no	—
351	C₄⋊C₈	—	2	1	no	—
352	C₄⋊C₈	—	2	1	no	—
353	C₄⋊C₈	—	5	1	no	—
354	C₄⋊C₈	—	5	1	no	—
355	C₄⋊C₈	—	5	1	no	—
356	C₄⋊C₈	—	5	1	no	—
357	C₄⋊C₈	—	5	1	no	—
358	C₄⋊C₈	—	5	1	no	—
359	C₄⋊C₈	—	5	1	no	—
360	C₄⋊C₈	—	5	1	no	—
361	C₄⋊C₈	—	5	1	no	—
362	C₄⋊C₈	—	5	1	no	—
363	C₄⋊C₈	—	10	1	no	—
364	C₄⋊C₈	—	10	1	no	—
365	C₄⋊C₈	—	10	1	no	—
366	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
367	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
368	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
369	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
370	C₂²⋊C₈	—	2	1	no	—
371	C₂²⋊C₈	—	2	1	no	—
372	C₂²⋊C₈	—	2	1	no	—
373	C₂²⋊C₈	—	5	1	no	—
374	C₂²⋊C₈	—	5	1	no	—
375	C₂²⋊C₈	—	5	1	no	—
376	C₂²⋊C₈	—	5	1	no	—
377	C₂²⋊C₈	—	5	1	no	—
378	C₂²⋊C₈	—	5	1	no	—
379	C₂²⋊C₈	—	10	1	no	—
380	C₂²⋊C₈	—	10	1	no	—
381	C₂²⋊C₈	—	10	1	no	—
382	#97	—	2	1	no	—
383	#97	—	2	1	no	—
384	#97	—	5	1	no	—
385	#97	—	5	1	no	—
386	#97	—	5	1	no	—
387	#97	—	5	1	no	—
388	#97	—	10	1	no	—
389	#97	—	10	1	no	—
390	C₄×C₈	—	2	1	no	—
391	C₄×C₈	—	5	1	no	—
392	C₄×C₈	—	5	1	no	—
393	C₄×C₈	—	5	1	no	—
394	C₄×C₈	—	5	1	no	—
395	C₄×C₈	—	5	1	no	—
396	C₄×C₈	—	5	1	no	—
397	C₄×C₈	—	10	1	no	—
398	C₂²×C₅	—	2	1	no	—
399	C₂²×C₅	—	2	1	no	—
400	C₂²×C₅	—	2	1	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	#430	1	2	yes	—
407	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
408	C₄×C₅	—	2	1	no	—
409	C₄×C₅	—	2	1	no	—
410	C₄×C₅	—	2	1	no	—
411	C₄×C₅	—	2	1	no	—
412	C₄×C₅	—	2	1	no	—
413	C₄×C₅	—	2	1	no	—
414	C₄×C₅	—	2	1	no	—
415	C₄×C₅	—	2	1	no	—
416	C₄×C₅	—	2	1	no	—
417	C₄×C₅	—	2	1	no	—
418	C₄×C₅	C₂×#131	1	1	yes	characteristic
419	C₄×C₅	#568	1	1	yes	characteristic
420	C₄×C₅	#577	1	1	yes	characteristic
421	C₄×C₅	#577	1	1	yes	characteristic
422	#41	—	4	2	no	—
423	C₂×Q₈	#683	1	1	yes	characteristic
424	C₂×D₄	#683	1	1	yes	characteristic
425	C₂×D₄	#683	1	1	yes	characteristic
426	C₂×D₄	#683	1	1	yes	characteristic
427	C₂²×C₄	C₂×Dic₁₀	1	1	yes	characteristic
428	C₂²×C₄	C₂×Dic₁₀	1	1	yes	characteristic
429	C₂²×C₄	C₂×Dic₁₀	1	1	yes	characteristic
430	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
431	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
432	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
433	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
434	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
435	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
436	M₁₆	—	8	1	no	—
437	M₁₆	—	10	2	no	—
438	M₁₆	—	10	2	no	—
439	M₁₆	—	20	1	no	—
440	M₁₆	—	20	1	no	—
441	M₁₆	—	40	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	5	1	no	—
447	C₂×C₈	—	5	1	no	—
448	C₂×C₈	—	5	1	no	—
449	C₂×C₈	—	5	1	no	—
450	C₂×C₈	—	5	1	no	—
451	C₂×C₈	—	5	1	no	—
452	C₂×C₈	—	5	1	no	—
453	C₂×C₈	—	5	1	no	—
454	C₂×C₈	—	8	1	no	—
455	C₂×C₈	—	8	1	no	—
456	C₂×C₈	—	10	2	no	—
457	C₂×C₈	—	10	1	no	—
458	C₂×C₈	—	10	1	no	—
459	C₂×C₈	—	10	1	no	—
460	C₂×C₈	—	10	1	no	—
461	C₂×C₈	—	20	1	no	—
462	C₂×C₈	—	40	1	no	—
463	C₂×C₈	—	40	1	no	—
464	C₄⋊C₄	#683	1	1	yes	characteristic
465	C₄⋊C₄	#683	1	1	yes	characteristic
466	C₄⋊C₄	#683	1	1	yes	characteristic
467	C₄⋊C₄	#683	1	1	yes	characteristic
468	C₄⋊C₄	#683	1	1	yes	characteristic
469	C₄⋊C₄	#683	1	1	yes	characteristic
470	C₂²⋊C₄	#683	1	1	yes	characteristic
471	C₂²⋊C₄	#683	1	1	yes	characteristic
472	C₂²⋊C₄	#683	1	1	yes	characteristic
473	C₂²⋊C₄	#683	1	1	yes	characteristic
474	C₂²⋊C₄	#683	1	1	yes	characteristic
475	C₂²⋊C₄	#683	1	1	yes	characteristic
476	C₄²	C₂×Dic₁₀	1	1	yes	characteristic
477	C₄²	C₂×Dic₁₀	1	1	yes	characteristic
478	C₄²	C₂×Dic₁₀	1	1	yes	characteristic
479	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
480	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
481	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
482	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
483	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
484	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
485	C₄²	C₂³×D₅	1	1	yes	characteristic
486	C₂×C₅	—	2	2	no	—
487	C₂×C₅	—	4	1	no	—
488	C₂×C₅	—	4	1	no	—
489	C₂×C₅	#2906	1	1	yes	characteristic
490	C₂×C₅	#2912	1	1	yes	characteristic
491	C₂×C₅	C₂×#430	1	1	yes	characteristic
492	C₂³	C₂×#683	1	1	yes	characteristic
493	C₂³	C₂×#683	1	1	yes	characteristic
494	C₂³	C₂×#683	1	1	yes	characteristic
495	Q₈	—	4	1	no	—
496	D₄	—	2	2	no	—
497	D₄	—	2	2	no	—
498	D₄	—	4	1	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	C₂×#683	1	1	yes	characteristic
515	C₂×C₄	C₂×#683	1	1	yes	characteristic
516	C₂×C₄	C₂×#683	1	1	yes	characteristic
517	C₂×C₄	C₂×#683	1	1	yes	characteristic
518	C₂×C₄	C₂×#683	1	1	yes	characteristic
519	C₂×C₄	C₂×#683	1	1	yes	characteristic
520	C₂×C₄	C₂×#683	1	1	yes	characteristic
521	C₂×C₄	C₂×#683	1	1	yes	characteristic
522	C₂×C₄	C₂×#683	1	1	yes	characteristic
523	C₂×C₄	C₂²×Dic₁₀	1	1	yes	characteristic
524	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
525	C₂×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
526	C₈	—	4	1	no	—
527	C₈	—	4	1	no	—
528	C₈	—	4	1	no	—
529	C₈	—	4	1	no	—
530	C₈	—	5	2	no	—
531	C₈	—	10	1	no	—
532	C₈	—	10	1	no	—
533	C₈	—	10	1	no	—
534	C₈	—	10	1	no	—
535	C₈	—	10	1	no	—
536	C₈	—	10	1	no	—
537	C₈	—	10	1	no	—
538	C₈	—	20	1	no	—
539	C₈	—	20	1	no	—
540	C₈	—	20	1	no	—
541	C₈	—	20	1	no	—
542	C₅	#17838	1	1	yes	characteristic, complemented, Sylow
543	C₂²	—	2	1	no	—
544	C₂²	—	2	1	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	2	1	no	—
548	C₂²	—	2	1	no	—
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	#65413	1	2	yes	—
552	C₂²	C₂²×#683	1	1	yes	characteristic
553	C₄	—	2	1	no	—
554	C₄	—	2	1	no	—
555	C₄	—	2	1	no	—
556	C₄	—	2	1	no	—
557	C₄	—	2	1	no	—
558	C₄	—	2	1	no	—
559	C₄	—	2	1	no	—
560	C₄	—	2	1	no	—
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	D₅×#131	1	1	yes	characteristic
564	C₄	#66084	1	1	yes	characteristic
565	C₄	#66170	1	1	yes	characteristic
566	C₄	#66171	1	1	yes	characteristic
567	C₂	—	2	2	no	—
568	C₂	—	4	1	no	—
569	C₂	—	4	1	no	—
570	C₂	#10614292	1	1	yes	characteristic
571	C₂	C₂×#65413	1	1	yes	characteristic
572	C₂	#10615514	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₅
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₄²	C₂³×D₅
Fitting	C₅×#2990	C₂
socle	C₂²×C₅	C₂²×C₄⋊C₄
prime radical	C₂×C₅×#41	Q₈
cosocle	C₄²×C₅	C₂⁴
hypercenter	#2990	D₅
hypocenter	C₅	#17838
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ #2990

Complements

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

N	H ≅ G/N	type
4. #10601590	C₂	semidirect
5. #10601589	C₂	semidirect
6. #10601588	C₂	semidirect
7. #10601587	C₂	semidirect
8. #10601540	C₂	semidirect
9. #10601539	C₂	semidirect
10. #10601286	C₂	semidirect
11. #10601285	C₂	semidirect
12. #10601216	C₂	semidirect
13. #10601214	C₂	semidirect
14. #10601213	C₂	semidirect
15. C₂×#64700	C₂	semidirect
542. C₅	#17838	semidirect

Maximal subgroups

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

subgroup	index
C₅×#2990	2
#10614253	2
#10614248	2
#10601590	2
#10601589	2
#10601588	2
#10601587	2
#10601540	2
#10601539	2
#10601286	2
#10601285	2
#10601216	2
#10601214	2
#10601213	2
C₂×#64700	2
#17838	5