Subgroups — #12121387

Order 1280.

692 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10614243	C₂	1	1	yes	maximal, characteristic
2	#10614238	C₂	1	1	yes	maximal, characteristic
3	#10610239	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1759	C₂	1	1	yes	maximal, characteristic
5	#10601169	C₂	1	1	yes	maximal, characteristic
6	#10601169	C₂	1	1	yes	maximal, characteristic
7	#10601163	C₂	1	1	yes	maximal, characteristic
8	#10601162	C₂	1	1	yes	maximal, characteristic
9	#10600668	C₂	1	1	yes	maximal, characteristic, complemented
10	#10600234	C₂	1	1	yes	maximal, characteristic, complemented
11	#10600229	C₂	1	1	yes	maximal, characteristic, complemented
12	#10599541	C₂	1	1	yes	maximal, characteristic, complemented
13	#10599540	C₂	1	1	yes	maximal, characteristic, complemented
14	#10599531	C₂	1	1	yes	maximal, characteristic, complemented
15	#10599531	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₅×#41	C₂²	1	1	yes	characteristic
17	C₂×#4094	C₂²	1	1	yes	characteristic
18	C₂×#4094	C₂²	1	1	yes	characteristic
19	#65804	C₂²	1	1	yes	characteristic
20	C₂×C₅×#104	C₂²	1	1	yes	characteristic
21	C₂×C₅×#104	C₂²	1	1	yes	characteristic
22	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
23	C₅×#376	C₂²	1	1	yes	characteristic
24	#65522	C₂²	1	1	yes	characteristic
25	#65522	C₂²	1	1	yes	characteristic
26	C₂×#3954	C₂²	1	1	yes	characteristic
27	C₂×#3954	C₂²	1	1	yes	characteristic
28	#65411	C₂²	1	1	yes	characteristic
29	#65411	C₂²	1	1	yes	characteristic
30	#65408	C₂²	1	1	yes	characteristic
31	#65408	C₂²	1	1	yes	characteristic
32	#65311	C₄	1	1	yes	characteristic, complemented
33	#65311	C₄	1	1	yes	characteristic, complemented
34	#65310	C₄	1	1	yes	characteristic, complemented
35	#65309	C₄	1	1	yes	characteristic, complemented
36	#65298	C₄	1	1	yes	characteristic, complemented
37	#65298	C₄	1	1	yes	characteristic, complemented
38	#65297	C₄	1	1	yes	characteristic, complemented
39	#65296	C₄	1	1	yes	characteristic, complemented
40	#65288	—	2	1	no	—
41	#65288	—	2	1	no	—
42	#65288	C₂²	1	1	yes	characteristic
43	#65288	C₂²	1	1	yes	characteristic
44	#65287	C₂²	1	1	yes	characteristic
45	#65287	C₂²	1	1	yes	characteristic
46	#65213	—	2	1	no	—
47	#65213	C₂²	1	1	yes	characteristic
48	C₂×C₄⋊#168	—	2	1	no	—
49	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
50	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
51	C₂×#3935	C₂²	1	1	yes	characteristic
52	C₂×C₄×#168	C₂²	1	1	yes	characteristic
53	#64990	—	2	1	no	—
54	#64990	—	2	1	no	—
55	#64968	—	2	1	no	—
56	C₈×Dic₁₀	—	2	1	no	—
57	C₅×#339	C₂²	1	1	yes	characteristic
58	C₅×#339	C₂²	1	1	yes	characteristic
59	#64778	C₂²	1	1	yes	characteristic
60	#64778	C₂²	1	1	yes	characteristic
61	#64744	C₂²	1	1	yes	characteristic
62	#64744	C₂²	1	1	yes	characteristic
63	#64743	C₂²	1	1	yes	characteristic
64	#64743	C₂²	1	1	yes	characteristic
65	#64743	C₂²	1	1	yes	characteristic
66	#64743	C₂²	1	1	yes	characteristic
67	#22984	—	5	1	no	maximal, Sylow
68	C₂×C₅×#41	C₂³	1	1	yes	characteristic
69	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
70	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
71	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
72	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
73	C₄×C₅×D₄	—	2	1	no	—
74	C₄×C₅×D₄	—	2	1	no	—
75	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
76	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
77	C₅×#117	—	2	1	no	—
78	C₅×#117	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₅	—	2	1	no	—
80	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
83	#4094	—	2	2	no	—
84	#4094	—	2	2	no	—
85	#4094	—	4	1	no	—
86	#4094	—	4	1	no	—
87	#4072	C₂³	1	1	yes	characteristic
88	#4072	C₂³	1	1	yes	characteristic
89	#4070	—	2	1	no	—
90	#4070	—	2	1	no	—
91	C₂×#681	—	2	1	no	—
92	C₂×#681	—	2	1	no	—
93	C₂×#681	C₂³	1	1	yes	characteristic
94	C₂×#681	C₂³	1	1	yes	characteristic
95	C₂²×#168	—	2	1	no	—
96	C₂²×#168	—	2	1	no	—
97	C₂²×#168	C₂³	1	1	yes	characteristic
98	C₂²×#168	C₂³	1	1	yes	characteristic
99	C₂²×#168	C₂³	1	1	yes	characteristic
100	C₂²×#168	C₂³	1	1	yes	characteristic
101	#4016	C₂×C₄	1	1	yes	characteristic
102	#4016	C₂×C₄	1	1	yes	characteristic
103	#4015	C₂×C₄	1	1	yes	characteristic
104	#4015	C₂×C₄	1	1	yes	characteristic
105	C₄×Dic₁₀	—	2	1	no	—
106	C₄×Dic₁₀	—	2	1	no	—
107	C₅×#104	—	2	2	no	—
108	C₅×#104	Q₈	1	4	yes	complemented
109	C₅×#97	—	2	1	no	—
110	C₄×C₅×C₈	—	2	1	no	—
111	C₅×#95	—	2	1	no	—
112	C₅×#95	—	2	1	no	—
113	#3967	C₂×C₄	1	1	yes	characteristic
114	#3967	C₂×C₄	1	1	yes	characteristic
115	#3967	C₂×C₄	1	1	yes	characteristic
116	#3967	C₂×C₄	1	1	yes	characteristic
117	#3964	C₂×C₄	1	1	yes	characteristic
118	#3964	C₂×C₄	1	1	yes	characteristic
119	#3964	C₂×C₄	1	1	yes	characteristic
120	#3964	C₂×C₄	1	1	yes	characteristic
121	#3954	—	4	1	no	—
122	#3954	—	4	1	no	—
123	#3947	—	2	1	no	—
124	#3947	—	2	1	no	—
125	#3946	—	2	1	no	—
126	#3946	—	2	1	no	—
127	#3946	—	2	1	no	—
128	#3946	—	2	1	no	—
129	C₈×Dic₅	—	2	1	no	—
130	C₈×Dic₅	—	2	1	no	—
131	#3940	C₂×C₄	1	1	yes	characteristic
132	#3940	C₂×C₄	1	1	yes	characteristic
133	#3940	C₂×C₄	1	1	yes	characteristic
134	#3940	C₂×C₄	1	1	yes	characteristic
135	#3939	C₂×C₄	1	1	yes	characteristic
136	#3939	C₂×C₄	1	1	yes	characteristic
137	#3939	C₂×C₄	1	1	yes	characteristic
138	#3939	C₂×C₄	1	1	yes	characteristic
139	C₄⋊#168	—	2	1	no	—
140	C₄⋊#168	—	2	1	no	—
141	C₄⋊#168	—	2	1	no	—
142	C₄⋊#168	—	2	1	no	—
143	C₄⋊#168	—	2	1	no	—
144	C₄⋊#168	—	2	1	no	—
145	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
146	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
147	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
148	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
149	C₄⋊#168	D₄	1	1	yes	characteristic
150	C₄⋊#168	D₄	1	1	yes	characteristic
151	C₄⋊#168	D₄	1	1	yes	characteristic
152	C₄⋊#168	D₄	1	1	yes	characteristic
153	#3935	—	4	1	no	—
154	C₄×#168	—	4	1	no	—
155	#3076	—	5	1	no	—
156	#2962	—	5	1	no	—
157	#2906	—	5	1	no	—
158	#1995	—	5	1	no	—
159	#1950	—	5	1	no	—
160	#1946	—	5	1	no	—
161	#1945	—	5	1	no	—
162	#1922	—	5	1	no	—
163	#1922	—	5	1	no	—
164	#1866	—	5	1	no	—
165	#1866	—	5	1	no	—
166	#1768	—	5	1	no	—
167	#1765	—	5	1	no	—
168	#1764	—	5	1	no	—
169	#1759	D₅	1	1	yes	characteristic
170	C₅×#41	—	2	1	no	—
171	C₅×#41	—	2	1	no	—
172	C₅×#41	C₂×Q₈	1	2	yes	—
173	C₅×#41	#41	1	2	yes	—
174	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
175	C₂×C₅×D₄	—	2	1	no	—
176	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
177	C₂²×C₄×C₅	—	2	1	no	—
178	C₂²×C₄×C₅	—	2	1	no	—
179	C₂²×C₄×C₅	—	2	1	no	—
180	C₂²×C₄×C₅	—	2	1	no	—
181	C₂²×C₄×C₅	—	2	1	no	—
182	C₂²×C₄×C₅	#41	1	1	yes	characteristic
183	C₂²×C₄×C₅	#41	1	1	yes	characteristic
184	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
185	C₂×Dic₁₀	—	2	1	no	—
186	C₂×Dic₁₀	—	2	1	no	—
187	C₅×M₁₆	—	2	1	no	—
188	C₅×M₁₆	—	2	1	no	—
189	C₅×M₁₆	—	2	1	no	—
190	C₅×M₁₆	C₂×Q₈	1	2	yes	—
191	C₂×C₅×C₈	—	2	1	no	—
192	C₂×C₅×C₈	—	2	1	no	—
193	C₅×C₄⋊C₄	—	2	1	no	—
194	C₅×C₄⋊C₄	—	2	1	no	—
195	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
196	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
197	C₅×C₂²⋊C₄	—	2	1	no	—
198	C₅×C₂²⋊C₄	—	2	1	no	—
199	C₅×C₂²⋊C₄	—	2	1	no	—
200	C₄²×C₅	—	2	1	no	—
201	C₄²×C₅	—	2	1	no	—
202	C₄²×C₅	—	2	1	no	—
203	C₄²×C₅	—	2	1	no	—
204	C₄²×C₅	—	2	1	no	—
205	C₄²×C₅	—	2	1	no	—
206	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
207	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
208	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
209	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
210	C₄²×C₅	C₂×Q₈	1	2	yes	—
211	C₂²⋊Dic₅	—	2	1	no	—
212	C₂²⋊Dic₅	—	2	1	no	—
213	C₄⋊Dic₅	—	2	1	no	—
214	C₄⋊Dic₅	—	2	1	no	—
215	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
216	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
217	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
218	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
219	#683	—	2	1	no	—
220	#683	—	2	1	no	—
221	#683	—	2	1	no	—
222	#683	—	2	1	no	—
223	C₄×Dic₅	—	2	1	no	—
224	C₄×Dic₅	—	2	1	no	—
225	#681	—	2	1	no	—
226	#681	—	2	1	no	—
227	#681	—	2	1	no	—
228	#681	—	2	1	no	—
229	#681	—	4	2	no	—
230	#681	—	4	2	no	—
231	C₂×#168	—	2	1	no	—
232	C₂×#168	—	2	1	no	—
233	C₂×#168	—	2	1	no	—
234	C₂×#168	—	2	1	no	—
235	C₂×#168	—	2	1	no	—
236	C₂×#168	—	2	1	no	—
237	C₂×#168	—	2	1	no	—
238	C₂×#168	—	2	1	no	—
239	C₂×#168	—	2	1	no	—
240	C₂×#168	—	2	1	no	—
241	C₂×#168	—	4	2	no	—
242	C₂×#168	—	4	2	no	—
243	C₂×#168	C₂²×C₄	1	1	yes	characteristic
244	C₂×#168	C₂²×C₄	1	1	yes	characteristic
245	C₂×#168	C₂²×C₄	1	1	yes	characteristic
246	C₂×#168	C₂²×C₄	1	1	yes	characteristic
247	C₂×#168	C₂×D₄	1	1	yes	characteristic
248	C₂×#168	C₂×D₄	1	1	yes	characteristic
249	C₂×#168	C₂×D₄	1	1	yes	characteristic
250	C₂×#168	C₂×D₄	1	1	yes	characteristic
251	C₂×#131	—	5	1	no	—
252	C₂×#131	—	5	1	no	—
253	#533	—	5	1	no	—
254	C₄×#41	C₂×D₅	1	1	yes	characteristic
255	#479	—	5	1	no	—
256	#479	—	5	1	no	—
257	#478	—	5	1	no	—
258	#478	—	5	1	no	—
259	#477	—	5	1	no	—
260	#476	—	5	1	no	—
261	#475	—	5	1	no	—
262	#474	—	5	1	no	—
263	#446	—	10	1	no	—
264	#446	—	10	1	no	—
265	#446	—	10	1	no	—
266	C₈×Q₈	—	10	1	no	—
267	C₂×#108	—	5	1	no	—
268	C₂×#108	—	5	1	no	—
269	#427	—	5	1	no	—
270	#427	—	5	1	no	—
271	#424	—	5	1	no	—
272	#424	—	5	1	no	—
273	#424	—	5	1	no	—
274	#424	—	5	1	no	—
275	#424	—	10	1	no	—
276	#424	—	10	1	no	—
277	#423	—	5	1	no	—
278	#423	—	10	1	no	—
279	C₂×C₄⋊C₈	—	5	1	no	—
280	C₂×C₄⋊C₈	—	5	1	no	—
281	C₂×C₄⋊C₈	—	10	1	no	—
282	C₂×#104	C₂×D₅	1	1	yes	characteristic
283	C₂×#104	C₂×D₅	1	1	yes	characteristic
284	#416	—	5	1	no	—
285	#416	—	5	1	no	—
286	#405	—	5	1	no	—
287	#405	—	5	1	no	—
288	C₄×M₁₆	C₂×D₅	1	1	yes	characteristic
289	C₂×#97	—	5	1	no	—
290	C₂×C₄×C₈	—	5	1	no	—
291	#376	C₂×D₅	1	1	yes	characteristic
292	#341	—	5	1	no	—
293	#341	—	5	1	no	—
294	#339	—	5	1	no	—
295	#339	—	5	1	no	—
296	#339	—	5	1	no	—
297	#339	—	5	1	no	—
298	#339	C₂×D₅	1	1	yes	characteristic
299	#339	C₂×D₅	1	1	yes	characteristic
300	#336	—	5	1	no	—
301	#336	—	5	1	no	—
302	C₂³×C₅	—	2	1	no	—
303	C₂³×C₅	C₂×#41	1	1	yes	characteristic
304	C₅×Q₈	—	2	1	no	—
305	C₅×Q₈	C₄×Q₈	1	2	yes	—
306	C₅×D₄	—	2	2	no	—
307	C₅×D₄	—	2	2	no	—
308	C₅×D₄	—	2	1	no	—
309	C₅×D₄	C₄×Q₈	1	2	yes	—
310	C₂×C₄×C₅	—	2	1	no	—
311	C₂×C₄×C₅	—	2	2	no	—
312	C₂×C₄×C₅	—	2	2	no	—
313	C₂×C₄×C₅	—	2	1	no	—
314	C₂×C₄×C₅	—	2	1	no	—
315	C₂×C₄×C₅	—	2	2	no	—
316	C₂×C₄×C₅	—	4	1	no	—
317	C₂×C₄×C₅	—	4	1	no	—
318	C₂×C₄×C₅	—	4	2	no	—
319	C₂×C₄×C₅	—	4	1	no	—
320	C₂×C₄×C₅	—	4	1	no	—
321	C₂×C₄×C₅	—	4	1	no	—
322	C₂×C₄×C₅	—	4	1	no	—
323	C₂×C₄×C₅	—	4	1	no	—
324	C₂×C₄×C₅	—	8	1	no	—
325	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
326	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
327	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
328	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
329	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
330	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
332	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
333	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
334	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
335	C₂×Dic₅	—	2	1	no	—
336	C₂×Dic₅	—	2	1	no	—
337	C₂×Dic₅	—	2	1	no	—
338	C₂×Dic₅	—	2	1	no	—
339	Dic₁₀	—	4	2	no	—
340	Dic₁₀	—	8	1	no	—
341	C₅×C₈	—	2	2	no	—
342	C₅×C₈	—	4	1	no	—
343	#168	—	2	1	no	—
344	#168	—	2	1	no	—
345	#168	—	2	1	no	—
346	#168	—	2	1	no	—
347	#168	—	2	1	no	—
348	#168	—	2	1	no	—
349	#168	—	2	1	no	—
350	#168	—	2	1	no	—
351	#168	—	4	1	no	—
352	#168	—	4	1	no	—
353	C₂×#41	C₂²×D₅	1	1	yes	characteristic
354	#131	—	10	2	no	—
355	#131	—	10	2	no	—
356	#131	—	20	1	no	—
357	#131	—	20	1	no	—
358	C₂×M₁₆	—	5	1	no	—
359	C₂×M₁₆	—	5	1	no	—
360	C₂×M₁₆	—	10	1	no	—
361	C₂×M₁₆	—	10	1	no	—
362	C₂×M₁₆	C₂²×D₅	1	1	yes	characteristic
363	C₂×M₁₆	C₂²×D₅	1	1	yes	characteristic
364	C₂²×C₈	—	5	1	no	—
365	C₂²×C₈	—	5	1	no	—
366	C₂²×C₈	—	5	1	no	—
367	C₂²×C₈	—	5	1	no	—
368	C₂²×C₈	—	10	1	no	—
369	C₂²×C₈	—	10	1	no	—
370	C₄⋊Q₈	—	5	1	no	—
371	C₄⋊Q₈	—	5	1	no	—
372	#125	—	5	1	no	—
373	#125	—	5	1	no	—
374	C₂²⋊Q₈	—	10	1	no	—
375	C₂²⋊Q₈	—	10	1	no	—
376	C₄×Q₈	—	10	1	no	—
377	C₄×Q₈	—	10	1	no	—
378	C₄×Q₈	C₄×D₅	1	1	yes	characteristic
379	C₄×Q₈	C₄×D₅	1	1	yes	characteristic
380	C₄×D₄	—	2	1	no	—
381	C₄×D₄	—	2	1	no	—
382	C₄×D₄	C₄×D₅	1	1	yes	characteristic
383	C₄×D₄	C₄×D₅	1	1	yes	characteristic
384	#117	—	2	1	no	—
385	#117	—	5	1	no	—
386	#117	—	5	1	no	—
387	#117	C₂²×D₅	1	1	yes	characteristic
388	C₂×C₄²	—	2	1	no	—
389	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
390	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
391	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
392	#108	—	20	1	no	—
393	#108	—	20	1	no	—
394	#107	—	5	1	no	—
395	#107	—	5	1	no	—
396	#107	—	5	1	no	—
397	#107	—	5	1	no	—
398	#106	—	5	1	no	—
399	#106	—	5	1	no	—
400	#106	—	5	1	no	—
401	#106	—	5	1	no	—
402	C₄⋊C₈	—	5	1	no	—
403	C₄⋊C₈	—	5	1	no	—
404	C₄⋊C₈	—	5	1	no	—
405	C₄⋊C₈	—	5	1	no	—
406	C₄⋊C₈	—	5	1	no	—
407	C₄⋊C₈	—	5	1	no	—
408	C₄⋊C₈	—	5	1	no	—
409	C₄⋊C₈	—	5	1	no	—
410	C₄⋊C₈	—	10	1	no	—
411	C₄⋊C₈	—	10	1	no	—
412	C₄⋊C₈	—	10	1	no	—
413	C₄⋊C₈	—	10	1	no	—
414	C₄⋊C₈	—	10	1	no	—
415	C₄⋊C₈	—	10	1	no	—
416	C₄⋊C₈	—	10	1	no	—
417	C₄⋊C₈	—	10	1	no	—
418	C₄⋊C₈	—	10	1	no	—
419	C₄⋊C₈	—	10	1	no	—
420	#104	—	2	2	no	—
421	#104	Dic₁₀	1	4	yes	complemented
422	#103	—	5	1	no	—
423	#103	—	5	1	no	—
424	#103	—	5	1	no	—
425	#103	—	5	1	no	—
426	#102	—	5	1	no	—
427	#102	—	5	1	no	—
428	#102	—	5	1	no	—
429	#102	—	5	1	no	—
430	#97	—	2	1	no	—
431	#97	—	10	1	no	—
432	#97	—	10	1	no	—
433	#97	—	20	1	no	—
434	C₄×C₈	—	2	1	no	—
435	C₄×C₈	—	10	1	no	—
436	C₄×C₈	—	10	1	no	—
437	C₄×C₈	—	20	1	no	—
438	#95	—	2	1	no	—
439	#95	—	2	1	no	—
440	C₂²×C₅	—	2	1	no	—
441	C₂²×C₅	—	2	1	no	—
442	C₂²×C₅	—	2	2	no	—
443	C₂²×C₅	—	4	1	no	—
444	C₂²×C₅	—	4	1	no	—
445	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
446	C₂²×C₅	#552	1	1	yes	characteristic
447	C₂²×C₅	#554	1	1	yes	characteristic
448	C₄×C₅	—	2	2	no	—
449	C₄×C₅	—	2	1	no	—
450	C₄×C₅	—	2	1	no	—
451	C₄×C₅	—	2	1	no	—
452	C₄×C₅	—	2	1	no	—
453	C₄×C₅	—	4	2	no	—
454	C₄×C₅	—	4	1	no	—
455	C₄×C₅	—	4	1	no	—
456	C₄×C₅	—	8	1	no	—
457	C₄×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
458	C₄×C₅	#520	1	1	yes	characteristic
459	C₄×C₅	#546	1	1	yes	characteristic
460	C₄×C₅	D₄×Q₈	1	1	yes	characteristic
461	Dic₅	—	4	1	no	—
462	Dic₅	—	4	1	no	—
463	Dic₅	—	4	1	no	—
464	Dic₅	—	4	1	no	—
465	#41	—	2	1	no	—
466	#41	—	2	1	no	—
467	#41	C₂×Dic₁₀	1	2	yes	—
468	#41	#709	1	2	yes	—
469	C₂×Q₈	—	10	1	no	—
470	C₂×Q₈	—	10	1	no	—
471	C₂×Q₈	C₂×C₄×D₅	1	1	yes	characteristic
472	C₂×D₄	—	2	1	no	—
473	C₂×D₄	C₂×C₄×D₅	1	1	yes	characteristic
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	#711	1	1	yes	characteristic
480	C₂²×C₄	#711	1	1	yes	characteristic
481	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
482	M₁₆	—	2	1	no	—
483	M₁₆	—	2	1	no	—
484	M₁₆	—	2	1	no	—
485	M₁₆	—	10	1	no	—
486	M₁₆	—	10	1	no	—
487	M₁₆	—	10	1	no	—
488	M₁₆	—	10	1	no	—
489	M₁₆	—	20	2	no	—
490	M₁₆	—	20	2	no	—
491	M₁₆	C₂×Dic₁₀	1	2	yes	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	5	1	no	—
495	C₂×C₈	—	5	1	no	—
496	C₂×C₈	—	5	1	no	—
497	C₂×C₈	—	5	1	no	—
498	C₂×C₈	—	5	1	no	—
499	C₂×C₈	—	5	1	no	—
500	C₂×C₈	—	5	1	no	—
501	C₂×C₈	—	5	1	no	—
502	C₂×C₈	—	10	1	no	—
503	C₂×C₈	—	10	1	no	—
504	C₂×C₈	—	10	1	no	—
505	C₂×C₈	—	10	1	no	—
506	C₂×C₈	—	10	1	no	—
507	C₂×C₈	—	10	1	no	—
508	C₂×C₈	—	10	1	no	—
509	C₂×C₈	—	10	1	no	—
510	C₂×C₈	—	10	1	no	—
511	C₂×C₈	—	10	1	no	—
512	C₂×C₈	—	20	2	no	—
513	C₂×C₈	—	20	2	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	5	1	no	—
517	C₄⋊C₄	—	5	1	no	—
518	C₄⋊C₄	—	5	1	no	—
519	C₄⋊C₄	—	5	1	no	—
520	C₄⋊C₄	—	10	1	no	—
521	C₄⋊C₄	—	10	1	no	—
522	C₄⋊C₄	—	10	1	no	—
523	C₄⋊C₄	—	10	1	no	—
524	C₄⋊C₄	—	10	1	no	—
525	C₄⋊C₄	—	10	1	no	—
526	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
527	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
528	C₂²⋊C₄	—	2	1	no	—
529	C₂²⋊C₄	—	2	1	no	—
530	C₂²⋊C₄	—	2	1	no	—
531	C₂²⋊C₄	—	10	1	no	—
532	C₂²⋊C₄	—	10	1	no	—
533	C₄²	—	2	1	no	—
534	C₄²	—	2	1	no	—
535	C₄²	—	2	1	no	—
536	C₄²	—	2	1	no	—
537	C₄²	—	2	1	no	—
538	C₄²	—	2	1	no	—
539	C₄²	—	10	1	no	—
540	C₄²	—	10	1	no	—
541	C₄²	C₂×Dic₁₀	1	2	yes	—
542	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
543	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
544	C₄²	D₄×D₅	1	1	yes	characteristic
545	C₄²	D₄×D₅	1	1	yes	characteristic
546	C₂×C₅	—	2	1	no	—
547	C₂×C₅	—	2	1	no	—
548	C₂×C₅	—	4	2	no	—
549	C₂×C₅	#2360	1	1	yes	characteristic
550	C₂×C₅	#2955	1	1	yes	characteristic
551	C₂×C₅	#2957	1	1	yes	characteristic
552	C₂³	—	2	1	no	—
553	C₂³	C₂×#711	1	1	yes	characteristic
554	Q₈	—	2	1	no	—
555	Q₈	—	20	2	no	—
556	Q₈	—	40	1	no	—
557	Q₈	C₄×Dic₁₀	1	2	yes	—
558	D₄	—	2	2	no	—
559	D₄	—	2	2	no	—
560	D₄	—	2	1	no	—
561	D₄	C₄×Dic₁₀	1	2	yes	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	8	1	no	—
577	C₂×C₄	—	10	1	no	—
578	C₂×C₄	—	10	1	no	—
579	C₂×C₄	—	10	1	no	—
580	C₂×C₄	—	10	1	no	—
581	C₂×C₄	#4027	1	1	yes	characteristic
582	C₂×C₄	#4027	1	1	yes	characteristic
583	C₂×C₄	#4027	1	1	yes	characteristic
584	C₂×C₄	#4027	1	1	yes	characteristic
585	C₂×C₄	C₂²×Dic₁₀	1	1	yes	characteristic
586	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
587	C₂×C₄	C₂×#709	1	1	yes	characteristic
588	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
589	C₂×C₄	#4149	1	1	yes	characteristic
590	C₂×C₄	#4150	1	1	yes	characteristic
591	C₈	—	2	2	no	—
592	C₈	—	4	1	no	—
593	C₈	—	10	1	no	—
594	C₈	—	10	1	no	—
595	C₈	—	10	1	no	—
596	C₈	—	10	1	no	—
597	C₈	—	10	1	no	—
598	C₈	—	10	1	no	—
599	C₈	—	10	1	no	—
600	C₈	—	10	1	no	—
601	C₈	—	20	1	no	—
602	C₈	—	20	1	no	—
603	C₅	#22984	1	1	yes	characteristic, complemented, Sylow
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	4	1	no	—
608	C₂²	—	4	1	no	—
609	C₂²	C₂×#4027	1	1	yes	characteristic
610	C₂²	#65875	1	1	yes	characteristic
611	C₂²	#65877	1	1	yes	characteristic
612	C₄	—	2	1	no	—
613	C₄	—	2	1	no	—
614	C₄	—	2	1	no	—
615	C₄	—	2	1	no	—
616	C₄	—	2	2	no	—
617	C₄	—	4	2	no	—
618	C₄	—	4	1	no	—
619	C₄	—	4	1	no	—
620	C₄	—	8	1	no	—
621	C₄	—	20	1	no	—
622	C₄	—	20	1	no	—
623	C₄	—	20	1	no	—
624	C₄	—	20	1	no	—
625	C₄	C₂×C₄×Dic₁₀	1	1	yes	characteristic
626	C₄	#65857	1	1	yes	characteristic
627	C₄	D₄×Dic₁₀	1	1	yes	characteristic
628	C₄	#65884	1	1	yes	characteristic
629	C₂	—	2	1	no	—
630	C₂	—	2	1	no	—
631	C₂	—	4	2	no	—
632	C₂	#10605196	1	1	yes	characteristic
633	C₂	#10610720	1	1	yes	characteristic
634	C₂	#10610721	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅
Fitting	C₅×#1759	C₂
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₂×C₅×#41	C₂³
cosocle	C₂²×C₄×C₅	C₂⁴
hypercenter	#1759	D₅
hypocenter	C₅	#22984
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1759

Complements

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

N	H ≅ G/N	type
3. #10610239	C₂	semidirect
9. #10600668	C₂	semidirect
10. #10600234	C₂	semidirect
11. #10600229	C₂	semidirect
12. #10599541	C₂	semidirect
13. #10599540	C₂	semidirect
14. #10599531	C₂	semidirect
15. #10599531	C₂	semidirect
32. #65311	C₄	semidirect
33. #65311	C₄	semidirect
34. #65310	C₄	semidirect
35. #65309	C₄	semidirect
36. #65298	C₄	semidirect
37. #65298	C₄	semidirect
38. #65297	C₄	semidirect
39. #65296	C₄	semidirect
108. C₅×#104	Q₈	semidirect
421. #104	Dic₁₀	semidirect
603. C₅	#22984	semidirect

Maximal subgroups

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

subgroup	index
#10614243	2
#10614238	2
#10610239	2
C₅×#1759	2
#10601169	2
#10601163	2
#10601162	2
#10600668	2
#10600234	2
#10600229	2
#10599541	2
#10599540	2
#10599531	2
#22984	5