Subgroups — #12068486

Order 1280.

618 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10611062	C₂	1	1	yes	maximal, characteristic
2	#10611013	C₂	1	1	yes	maximal, characteristic
3	C₂×#65124	C₂	1	1	yes	maximal, characteristic
4	C₅×#1573	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601590	C₂	1	1	yes	maximal, characteristic, complemented
6	#10601545	C₂	1	1	yes	maximal, characteristic, complemented
7	#10601216	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599366	C₂	1	2	yes	maximal, complemented
9	#10599364	C₂	1	2	yes	maximal, complemented
10	#10599326	C₂	1	2	yes	maximal, complemented
11	#10599324	C₂	1	2	yes	maximal, complemented
12	C₂×C₄²×D₅	C₂²	1	1	yes	characteristic
13	C₅×#432	C₂²	1	1	yes	characteristic
14	C₅×#431	C₂²	1	1	yes	characteristic
15	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×#3952	—	2	1	no	—
17	C₂×#3947	—	2	1	no	—
18	#65215	C₂²	1	1	yes	characteristic
19	#65214	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
21	#65126	C₄	1	2	yes	—
22	#65126	C₂²	1	1	yes	characteristic
23	#65126	C₂²	1	1	yes	characteristic
24	#65124	—	2	1	no	—
25	#65124	—	2	1	no	—
26	#65124	C₄	1	2	yes	—
27	#65124	C₂²	1	2	yes	—
28	#65124	C₂²	1	2	yes	—
29	#65122	C₂²	1	1	yes	characteristic
30	#65122	C₂²	1	1	yes	characteristic
31	#65015	—	2	1	no	—
32	#65015	C₄	1	2	yes	—
33	#65008	C₄	1	2	yes	—
34	#65007	—	2	1	no	—
35	#64996	—	2	1	no	—
36	#64994	—	2	1	no	—
37	C₄×#676	C₂²	1	2	yes	—
38	#64974	C₂²	1	2	yes	—
39	C₅×#335	C₂²	1	2	yes	complemented
40	C₅×#334	C₂²	1	2	yes	complemented
41	#64700	C₂²	1	2	yes	complemented
42	#64700	C₂²	1	2	yes	complemented
43	#64699	C₂²	1	2	yes	complemented
44	#64699	C₂²	1	2	yes	complemented
45	#64678	C₂²	1	2	yes	complemented
46	#64677	C₂²	1	2	yes	complemented
47	#17821	—	5	1	no	maximal, Sylow
48	C₂²×C₄×D₅	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₄×D₅	D₄	1	1	yes	characteristic
50	C₂²×C₄×D₅	Q₈	1	1	yes	characteristic
51	C₂²×C₅×C₈	—	2	1	no	—
52	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
53	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄×Dic₅	D₄	1	1	yes	characteristic
55	C₂×C₄×Dic₅	Q₈	1	1	yes	characteristic
56	C₂²×#168	—	2	1	no	—
57	C₂×#676	—	2	1	no	—
58	C₂×#676	—	2	1	no	—
59	C₂×#676	C₂×C₄	1	4	yes	—
60	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
61	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
62	C₄²×D₅	D₄	1	1	yes	characteristic
63	C₄²×D₅	D₄	1	1	yes	characteristic
64	C₄²×D₅	Q₈	1	1	yes	characteristic
65	C₄²×D₅	Q₈	1	1	yes	characteristic
66	C₄²×D₅	C₂³	1	1	yes	characteristic
67	C₄²×D₅	C₂³	1	1	yes	characteristic
68	C₅×C₄⋊C₈	—	2	1	no	—
69	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
70	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
71	C₅×C₄⋊C₈	C₂³	1	2	yes	—
72	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
73	C₅×C₂²⋊C₈	—	2	1	no	—
74	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
75	C₅×#97	—	2	1	no	—
76	C₄×C₅×C₈	C₂³	1	2	yes	—
77	C₂²⋊#168	—	2	1	no	—
78	C₂²⋊#168	C₂×C₄	1	2	yes	—
79	#3952	—	2	1	no	—
80	#3952	—	2	1	no	—
81	#3952	—	2	2	no	—
82	#3952	—	2	2	no	—
83	#3952	C₂×C₄	1	4	yes	—
84	#3947	—	2	2	no	—
85	#3947	—	2	2	no	—
86	#3947	C₂×C₄	1	4	yes	—
87	#3946	—	2	1	no	—
88	#3946	—	2	1	no	—
89	#3946	C₂×C₄	1	4	yes	—
90	C₈×Dic₅	—	2	1	no	—
91	C₈×Dic₅	—	2	1	no	—
92	C₄⋊#168	—	2	1	no	—
93	C₄⋊#168	C₂×C₄	1	2	yes	—
94	C₄⋊#168	C₂³	1	1	yes	characteristic
95	C₄⋊#168	C₂³	1	1	yes	characteristic
96	C₄⋊#168	C₂³	1	2	yes	—
97	#3935	—	2	1	no	—
98	C₄×#168	C₂³	1	2	yes	—
99	#2920	—	5	1	no	—
100	#2920	—	5	1	no	—
101	C₂×#432	—	5	1	no	—
102	#1573	—	5	1	no	—
103	#1573	—	5	1	no	—
104	#1573	—	5	1	no	—
105	#1573	D₅	1	1	yes	characteristic, complemented
106	#1572	—	5	2	no	—
107	#1572	—	5	2	no	—
108	#1569	—	5	2	no	—
109	#1569	—	5	2	no	—
110	C₂³×D₅	C₄⋊C₄	1	1	yes	characteristic
111	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
114	C₂²×Dic₅	C₄⋊C₄	1	1	yes	characteristic
115	C₂²×Dic₅	C₄⋊C₄	1	1	yes	characteristic
116	C₂²×Dic₅	C₄⋊C₄	1	1	yes	characteristic
117	C₂×C₄×D₅	—	4	2	no	—
118	C₂×C₄×D₅	—	4	1	no	—
119	C₂×C₄×D₅	—	4	1	no	—
120	C₂×C₄×D₅	—	4	2	no	—
121	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
122	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
123	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
124	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
125	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
126	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
127	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
130	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
131	C₂×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
132	C₂×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
133	C₂×C₅×C₈	—	2	2	no	—
134	C₂×C₅×C₈	—	2	1	no	—
135	C₂×C₅×C₈	—	2	1	no	—
136	C₂×C₅×C₈	—	4	2	no	—
137	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
138	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
139	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
141	C₄²×C₅	C₂⁴	1	1	yes	characteristic
142	C₄×Dic₅	C₄⋊C₄	1	1	yes	characteristic
143	C₄×Dic₅	C₄⋊C₄	1	1	yes	characteristic
144	C₄×Dic₅	C₄⋊C₄	1	1	yes	characteristic
145	C₄×Dic₅	C₄⋊C₄	1	1	yes	characteristic
146	C₄×Dic₅	C₄⋊C₄	1	1	yes	characteristic
147	C₄×Dic₅	C₄⋊C₄	1	1	yes	characteristic
148	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
149	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
150	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
151	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
152	C₄×Dic₅	C₂×Q₈	1	1	yes	characteristic
153	C₄×Dic₅	C₂×Q₈	1	1	yes	characteristic
154	C₂×#168	—	2	1	no	—
155	C₂×#168	—	2	1	no	—
156	C₂×#168	—	2	2	no	—
157	C₂×#168	—	4	2	no	—
158	C₂×#168	C₂²×C₄	1	4	yes	—
159	#676	—	4	4	no	—
160	#676	—	4	2	no	—
161	#676	—	4	2	no	—
162	C₂²×C₄²	—	5	1	no	—
163	#432	—	5	2	no	—
164	#432	—	5	2	no	—
165	#432	—	5	1	no	—
166	#432	—	5	2	no	—
167	#432	—	5	2	no	—
168	#432	—	10	1	no	—
169	#432	—	10	1	no	—
170	#432	—	10	1	no	—
171	#432	C₂×D₅	1	1	yes	characteristic
172	#431	—	5	1	no	—
173	#431	—	5	2	no	—
174	#431	—	5	1	no	—
175	#431	—	5	1	no	—
176	#431	—	10	1	no	—
177	#431	C₂×D₅	1	1	yes	characteristic
178	#423	—	5	2	no	—
179	#423	—	5	1	no	—
180	#423	—	5	1	no	—
181	C₂×C₄⋊C₈	—	5	1	no	—
182	C₂×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
183	#407	—	5	2	no	—
184	#407	—	10	1	no	—
185	C₂×C₂²⋊C₈	—	10	1	no	—
186	C₄×M₁₆	—	5	2	no	—
187	C₄×M₁₆	—	10	1	no	—
188	C₂×#97	—	10	1	no	—
189	#335	—	5	2	no	—
190	#335	—	5	2	no	—
191	#335	—	5	2	no	—
192	#335	C₂×D₅	1	2	yes	complemented
193	#334	—	5	2	no	—
194	#334	—	5	2	no	—
195	#334	—	5	2	no	—
196	#334	C₂×D₅	1	2	yes	complemented
197	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
198	C₂²×D₅	—	2	2	no	—
199	C₂²×D₅	—	4	1	no	—
200	C₂²×D₅	—	4	1	no	—
201	C₂²×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
202	C₂²×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
203	C₂×C₄×C₅	—	2	2	no	—
204	C₂×C₄×C₅	—	2	2	no	—
205	C₂×C₄×C₅	—	2	1	no	—
206	C₂×C₄×C₅	—	2	1	no	—
207	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
208	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
209	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
210	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
211	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
213	C₂×Dic₅	—	2	2	no	—
214	C₂×Dic₅	—	4	1	no	—
215	C₂×Dic₅	—	4	1	no	—
216	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
217	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
218	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
219	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
220	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
221	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
222	C₄×D₅	—	2	2	no	—
223	C₄×D₅	—	2	2	no	—
224	C₄×D₅	—	2	1	no	—
225	C₄×D₅	—	2	1	no	—
226	C₄×D₅	—	2	1	no	—
227	C₄×D₅	—	2	1	no	—
228	C₄×D₅	—	4	1	no	—
229	C₄×D₅	—	4	1	no	—
230	C₄×D₅	—	4	1	no	—
231	C₄×D₅	—	4	1	no	—
232	C₄×D₅	—	4	1	no	—
233	C₄×D₅	—	4	1	no	—
234	C₄×D₅	—	4	1	no	—
235	C₄×D₅	—	4	1	no	—
236	C₅×C₈	—	2	4	no	—
237	C₅×C₈	—	4	1	no	—
238	C₅×C₈	—	4	1	no	—
239	C₅×C₈	—	4	2	no	—
240	#168	—	2	4	no	—
241	#168	—	4	1	no	—
242	#168	—	4	1	no	—
243	#168	—	4	2	no	—
244	C₂³×C₄	—	5	1	no	—
245	C₂³×C₄	—	5	1	no	—
246	C₂³×C₄	—	5	1	no	—
247	C₂×M₁₆	—	5	4	no	—
248	C₂×M₁₆	—	10	1	no	—
249	C₂×M₁₆	—	10	1	no	—
250	C₂²×C₈	—	2	1	no	—
251	C₂²×C₈	—	10	1	no	—
252	C₂×C₄²	—	5	1	no	—
253	C₂×C₄²	—	5	1	no	—
254	C₂×C₄²	—	5	1	no	—
255	C₂×C₄²	—	5	1	no	—
256	C₂×C₄²	—	5	1	no	—
257	C₂×C₄²	—	5	1	no	—
258	C₂×C₄²	—	5	1	no	—
259	C₂×C₄²	—	5	1	no	—
260	C₂×C₄²	—	5	1	no	—
261	C₂×C₄²	—	5	1	no	—
262	C₂×C₄²	—	5	1	no	—
263	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
264	C₄⋊C₈	—	2	1	no	—
265	C₄⋊C₈	—	5	4	no	—
266	C₄⋊C₈	—	5	2	no	—
267	C₄⋊C₈	—	5	2	no	—
268	C₄⋊C₈	—	5	1	no	—
269	C₄⋊C₈	—	5	1	no	—
270	C₄⋊C₈	—	10	1	no	—
271	C₄⋊C₈	—	10	1	no	—
272	C₄⋊C₈	—	10	1	no	—
273	C₄⋊C₈	C₄×D₅	1	2	yes	—
274	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
275	C₄⋊C₈	C₂²×D₅	1	2	yes	—
276	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
277	C₂²⋊C₈	—	2	1	no	—
278	C₂²⋊C₈	—	5	2	no	—
279	C₂²⋊C₈	—	5	4	no	—
280	C₂²⋊C₈	—	10	2	no	—
281	C₂²⋊C₈	—	10	2	no	—
282	C₂²⋊C₈	—	10	1	no	—
283	C₂²⋊C₈	—	10	1	no	—
284	C₂²⋊C₈	—	10	1	no	—
285	C₂²⋊C₈	C₄×D₅	1	2	yes	—
286	#97	—	2	1	no	—
287	#97	—	5	4	no	—
288	#97	—	10	2	no	—
289	#97	—	10	2	no	—
290	#97	—	10	1	no	—
291	C₄×C₈	—	5	2	no	—
292	C₄×C₈	—	10	1	no	—
293	C₄×C₈	—	10	1	no	—
294	C₄×C₈	C₂²×D₅	1	2	yes	—
295	C₂²×C₅	—	2	1	no	—
296	C₂²×C₅	—	2	1	no	—
297	C₂²×C₅	#430	1	2	yes	—
298	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
299	C₂×D₅	—	2	1	no	—
300	C₂×D₅	—	2	1	no	—
301	C₂×D₅	—	2	1	no	—
302	C₂×D₅	—	2	1	no	—
303	C₂×D₅	—	2	1	no	—
304	C₂×D₅	—	2	1	no	—
305	C₂×D₅	—	4	4	no	—
306	C₄×C₅	—	2	1	no	—
307	C₄×C₅	—	2	1	no	—
308	C₄×C₅	—	2	1	no	—
309	C₄×C₅	—	2	1	no	—
310	C₄×C₅	#568	1	2	yes	—
311	C₄×C₅	#575	1	1	yes	characteristic
312	C₄×C₅	#575	1	1	yes	characteristic
313	Dic₅	—	2	1	no	—
314	Dic₅	—	2	1	no	—
315	Dic₅	—	2	1	no	—
316	Dic₅	—	2	1	no	—
317	Dic₅	—	2	1	no	—
318	Dic₅	—	2	1	no	—
319	C₂⁴	—	5	1	no	—
320	C₂²×C₄	—	5	1	no	—
321	C₂²×C₄	—	5	1	no	—
322	C₂²×C₄	—	5	1	no	—
323	C₂²×C₄	—	5	1	no	—
324	C₂²×C₄	—	5	1	no	—
325	C₂²×C₄	—	5	1	no	—
326	C₂²×C₄	—	5	1	no	—
327	C₂²×C₄	—	5	1	no	—
328	C₂²×C₄	—	5	1	no	—
329	C₂²×C₄	—	5	1	no	—
330	C₂²×C₄	—	5	1	no	—
331	C₂²×C₄	—	5	1	no	—
332	C₂²×C₄	—	5	1	no	—
333	C₂²×C₄	—	5	1	no	—
334	C₂²×C₄	—	5	1	no	—
335	C₂²×C₄	—	20	2	no	—
336	C₂²×C₄	—	20	1	no	—
337	C₂²×C₄	—	20	1	no	—
338	C₂²×C₄	—	20	2	no	—
339	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
340	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
341	C₂²×C₄	Q₈×D₅	1	1	yes	characteristic
342	M₁₆	—	20	4	no	—
343	M₁₆	—	20	2	no	—
344	M₁₆	—	20	2	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	4	2	no	—
349	C₂×C₈	—	5	4	no	—
350	C₂×C₈	—	10	1	no	—
351	C₂×C₈	—	10	1	no	—
352	C₂×C₈	—	10	2	no	—
353	C₂×C₈	—	20	2	no	—
354	C₂×C₈	C₂×C₄×D₅	1	4	yes	—
355	C₄²	—	5	1	no	—
356	C₄²	—	5	1	no	—
357	C₄²	—	5	1	no	—
358	C₄²	—	5	1	no	—
359	C₄²	—	5	1	no	—
360	C₄²	—	5	1	no	—
361	C₄²	—	5	1	no	—
362	C₄²	—	5	1	no	—
363	C₄²	—	5	1	no	—
364	C₄²	—	5	1	no	—
365	C₄²	—	5	1	no	—
366	C₄²	—	5	1	no	—
367	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
368	C₄²	D₄×D₅	1	1	yes	characteristic
369	C₄²	Q₈×D₅	1	1	yes	characteristic
370	C₄²	C₂³×D₅	1	1	yes	characteristic
371	C₂×C₅	—	2	2	no	—
372	C₂×C₅	#2905	1	1	yes	characteristic
373	C₂×C₅	#2911	1	1	yes	characteristic
374	C₂×C₅	C₂×#430	1	1	yes	characteristic
375	D₅	—	4	1	no	—
376	D₅	—	4	1	no	—
377	C₂³	—	5	1	no	—
378	C₂³	—	5	1	no	—
379	C₂³	—	10	2	no	—
380	C₂³	—	20	1	no	—
381	C₂³	—	20	1	no	—
382	C₂³	D₅×C₄⋊C₄	1	1	yes	characteristic
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	5	1	no	—
388	C₂×C₄	—	5	1	no	—
389	C₂×C₄	—	5	1	no	—
390	C₂×C₄	—	5	1	no	—
391	C₂×C₄	—	5	1	no	—
392	C₂×C₄	—	5	1	no	—
393	C₂×C₄	—	10	2	no	—
394	C₂×C₄	—	10	2	no	—
395	C₂×C₄	—	10	2	no	—
396	C₂×C₄	—	10	1	no	—
397	C₂×C₄	—	10	1	no	—
398	C₂×C₄	—	10	1	no	—
399	C₂×C₄	—	10	1	no	—
400	C₂×C₄	—	20	1	no	—
401	C₂×C₄	—	20	1	no	—
402	C₂×C₄	—	20	1	no	—
403	C₂×C₄	—	20	1	no	—
404	C₂×C₄	—	20	1	no	—
405	C₂×C₄	—	20	1	no	—
406	C₂×C₄	—	20	1	no	—
407	C₂×C₄	—	20	1	no	—
408	C₂×C₄	—	20	1	no	—
409	C₂×C₄	—	20	1	no	—
410	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
411	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
412	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
413	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
414	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
415	C₂×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
416	C₈	—	2	4	no	—
417	C₈	—	4	2	no	—
418	C₈	—	4	1	no	—
419	C₈	—	4	1	no	—
420	C₈	—	10	4	no	—
421	C₈	—	20	1	no	—
422	C₈	—	20	2	no	—
423	C₈	—	20	1	no	—
424	C₅	#17821	1	1	yes	characteristic, complemented, Sylow
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	10	1	no	—
428	C₂²	—	10	1	no	—
429	C₂²	—	10	1	no	—
430	C₂²	—	10	1	no	—
431	C₂²	—	10	1	no	—
432	C₂²	—	10	1	no	—
433	C₂²	—	20	4	no	—
434	C₂²	#65182	1	2	yes	—
435	C₂²	C₂×D₅×C₄⋊C₄	1	1	yes	characteristic
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	2	1	no	—
440	C₄	—	10	1	no	—
441	C₄	—	10	1	no	—
442	C₄	—	10	1	no	—
443	C₄	—	10	1	no	—
444	C₄	—	10	1	no	—
445	C₄	—	10	1	no	—
446	C₄	#66084	1	2	yes	—
447	C₄	#66107	1	1	yes	characteristic
448	C₄	#66111	1	1	yes	characteristic
449	C₂	—	2	2	no	—
450	C₂	—	20	1	no	—
451	C₂	—	20	1	no	—
452	C₂	#10610811	1	1	yes	characteristic
453	C₂	#10610939	1	1	yes	characteristic
454	C₂	C₂×#65182	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₄²	C₂³×D₅
Fitting	C₅×#1573	C₂
socle	C₂²×C₅	C₂²×C₄⋊C₄
prime radical	C₂³×D₅	C₄⋊C₄
cosocle	C₄²×C₅	C₂⁴
hypercenter	#1573	D₅
hypocenter	C₅	#17821
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1573

Complements

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

N	H ≅ G/N	type
4. C₅×#1573	C₂	semidirect
5. #10601590	C₂	semidirect
6. #10601545	C₂	semidirect
7. #10601216	C₂	semidirect
8. #10599366	C₂	semidirect
9. #10599364	C₂	semidirect
10. #10599326	C₂	semidirect
11. #10599324	C₂	semidirect
39. C₅×#335	C₂²	semidirect
40. C₅×#334	C₂²	semidirect
41. #64700	C₂²	semidirect
42. #64700	C₂²	semidirect
43. #64699	C₂²	semidirect
44. #64699	C₂²	semidirect
45. #64678	C₂²	semidirect
46. #64677	C₂²	semidirect
105. #1573	D₅	semidirect
192. #335	C₂×D₅	semidirect
196. #334	C₂×D₅	semidirect
424. C₅	#17821	semidirect

Maximal subgroups

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

subgroup	index
#10611062	2
#10611013	2
C₂×#65124	2
C₅×#1573	2
#10601590	2
#10601545	2
#10601216	2
#10599366	2
#10599364	2
#10599326	2
#10599324	2
#17821	5