Subgroups — #12068484

Order 1280.

618 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×#432	C₂	1	1	yes	maximal, characteristic
2	#10611013	C₂	1	1	yes	maximal, characteristic
3	#10611013	C₂	1	1	yes	maximal, characteristic
4	C₅×#1572	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601589	C₂	1	1	yes	maximal, characteristic, complemented
6	#10601544	C₂	1	1	yes	maximal, characteristic, complemented
7	#10601540	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599367	C₂	1	2	yes	maximal, complemented
9	#10599364	C₂	1	2	yes	maximal, complemented
10	#10599327	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	C₅×#431	C₂²	1	1	yes	characteristic
16	#65215	C₂²	1	1	yes	characteristic
17	#65214	C₂²	1	1	yes	characteristic
18	#65214	C₂²	1	1	yes	characteristic
19	#65126	C₄	1	2	yes	—
20	#65126	C₂²	1	2	yes	—
21	#65124	C₄	1	2	yes	—
22	#65124	C₂²	1	2	yes	—
23	#65124	C₂²	1	2	yes	—
24	D₅×C₄⋊C₈	C₂²	1	2	yes	—
25	#65015	—	2	1	no	—
26	#65015	C₄	1	2	yes	—
27	D₅×C₂²⋊C₈	—	2	1	no	—
28	#65008	—	2	1	no	—
29	#65008	—	2	1	no	—
30	#65008	C₄	1	2	yes	—
31	#64994	—	2	1	no	—
32	D₅×#97	—	2	1	no	—
33	C₄×#676	—	2	1	no	—
34	C₄×#676	C₂²	1	1	yes	characteristic
35	C₄×#676	C₂²	1	1	yes	characteristic
36	#64974	—	2	1	no	—
37	#64974	C₂²	1	1	yes	characteristic
38	#64974	C₂²	1	1	yes	characteristic
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	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
52	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄×Dic₅	D₄	1	1	yes	characteristic
54	C₂×C₄×Dic₅	Q₈	1	1	yes	characteristic
55	C₂×#676	—	2	2	no	—
56	C₂×#676	C₂×C₄	1	2	yes	—
57	C₂×#676	C₂×C₄	1	2	yes	—
58	C₂×C₈×D₅	—	2	2	no	—
59	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
60	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
61	C₄²×D₅	D₄	1	1	yes	characteristic
62	C₄²×D₅	D₄	1	1	yes	characteristic
63	C₄²×D₅	Q₈	1	1	yes	characteristic
64	C₄²×D₅	Q₈	1	1	yes	characteristic
65	C₄²×D₅	C₂³	1	1	yes	characteristic
66	C₄²×D₅	C₂³	1	1	yes	characteristic
67	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
68	C₅×C₄⋊C₈	C₂³	1	2	yes	—
69	C₅×C₄⋊C₈	C₂³	1	2	yes	—
70	C₅×C₂²⋊C₈	—	2	1	no	—
71	C₅×C₂²⋊C₈	—	2	1	no	—
72	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
73	C₅×#97	—	2	1	no	—
74	C₄×C₅×C₈	—	2	1	no	—
75	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
76	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
77	C₂²⋊#168	—	2	1	no	—
78	C₂²⋊#168	—	2	1	no	—
79	C₂²⋊#168	C₂×C₄	1	2	yes	—
80	#3952	—	2	2	no	—
81	#3952	—	2	2	no	—
82	#3952	C₂×C₄	1	2	yes	—
83	#3952	C₂×C₄	1	2	yes	—
84	#3947	—	2	2	no	—
85	#3947	—	2	2	no	—
86	#3947	C₂×C₄	1	2	yes	—
87	#3947	C₂×C₄	1	2	yes	—
88	#3946	—	2	2	no	—
89	#3946	—	2	2	no	—
90	#3946	C₂×C₄	1	2	yes	—
91	#3946	C₂×C₄	1	2	yes	—
92	C₄⋊#168	C₂×C₄	1	2	yes	—
93	C₄⋊#168	C₂³	1	2	yes	—
94	C₄⋊#168	C₂³	1	2	yes	—
95	#3935	—	2	1	no	—
96	C₄×#168	—	2	1	no	—
97	C₄×#168	C₂³	1	1	yes	characteristic
98	C₄×#168	C₂³	1	1	yes	characteristic
99	#2920	—	5	1	no	—
100	#2920	—	5	1	no	—
101	C₂×#432	—	5	1	no	—
102	#1573	—	5	2	no	—
103	#1573	—	5	2	no	—
104	#1572	—	5	1	no	—
105	#1572	—	5	1	no	—
106	#1572	—	5	1	no	—
107	#1572	D₅	1	1	yes	characteristic, complemented
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	2	no	—
119	C₂×C₄×D₅	—	4	2	no	—
120	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
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	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
129	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
130	C₂×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
131	C₂×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
132	C₂×C₅×C₈	—	2	2	no	—
133	C₂×C₅×C₈	—	2	2	no	—
134	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
135	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
136	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
137	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
139	C₄²×C₅	C₂⁴	1	1	yes	characteristic
140	C₄×Dic₅	C₄⋊C₄	1	1	yes	characteristic
141	C₄×Dic₅	C₄⋊C₄	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	C₂²×C₄	1	1	yes	characteristic
147	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
148	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
149	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
150	C₄×Dic₅	C₂×Q₈	1	1	yes	characteristic
151	C₄×Dic₅	C₂×Q₈	1	1	yes	characteristic
152	C₂×#168	—	2	2	no	—
153	C₂×#168	—	2	2	no	—
154	C₂×#168	C₂²×C₄	1	2	yes	—
155	C₂×#168	C₂²×C₄	1	2	yes	—
156	#676	—	4	2	no	—
157	#676	—	4	2	no	—
158	#676	—	4	4	no	—
159	C₈×D₅	—	4	4	no	—
160	C₂²×C₄²	—	5	1	no	—
161	#432	—	5	2	no	—
162	#432	—	5	2	no	—
163	#432	—	5	1	no	—
164	#432	—	5	2	no	—
165	#432	—	5	2	no	—
166	#432	—	10	1	no	—
167	#432	—	10	1	no	—
168	#432	—	10	1	no	—
169	#432	C₂×D₅	1	1	yes	characteristic
170	#431	—	5	1	no	—
171	#431	—	5	1	no	—
172	#431	—	5	1	no	—
173	#431	—	5	1	no	—
174	#431	—	10	1	no	—
175	#431	C₂×D₅	1	1	yes	characteristic
176	#431	C₂×D₅	1	1	yes	characteristic
177	#423	—	5	2	no	—
178	#423	—	5	2	no	—
179	C₂×C₄⋊C₈	—	5	2	no	—
180	#407	—	5	2	no	—
181	#407	—	10	1	no	—
182	C₂×C₂²⋊C₈	—	10	1	no	—
183	C₄×M₁₆	—	5	1	no	—
184	C₄×M₁₆	—	5	1	no	—
185	C₄×M₁₆	—	10	1	no	—
186	C₂×#97	—	10	1	no	—
187	#335	—	5	2	no	—
188	#335	—	5	2	no	—
189	#335	—	5	2	no	—
190	#335	C₂×D₅	1	2	yes	complemented
191	#334	—	5	2	no	—
192	#334	—	5	2	no	—
193	#334	—	5	2	no	—
194	#334	C₂×D₅	1	2	yes	complemented
195	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
196	C₂²×D₅	—	2	2	no	—
197	C₂²×D₅	—	4	1	no	—
198	C₂²×D₅	—	4	1	no	—
199	C₂²×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
200	C₂²×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
201	C₂×C₄×C₅	—	2	2	no	—
202	C₂×C₄×C₅	—	2	2	no	—
203	C₂×C₄×C₅	—	4	1	no	—
204	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
205	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
206	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
207	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
208	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
210	C₂×Dic₅	—	4	1	no	—
211	C₂×Dic₅	—	4	1	no	—
212	C₂×Dic₅	—	4	1	no	—
213	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
214	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
215	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
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	C₄×D₅	—	2	2	no	—
220	C₄×D₅	—	2	2	no	—
221	C₄×D₅	—	2	2	no	—
222	C₄×D₅	—	2	2	no	—
223	C₄×D₅	—	2	2	no	—
224	C₄×D₅	—	2	2	no	—
225	C₄×D₅	—	4	1	no	—
226	C₄×D₅	—	4	1	no	—
227	C₄×D₅	—	4	1	no	—
228	C₄×D₅	—	4	1	no	—
229	C₄×D₅	—	4	1	no	—
230	C₄×D₅	—	4	1	no	—
231	C₅×C₈	—	2	2	no	—
232	C₅×C₈	—	2	2	no	—
233	C₅×C₈	—	4	2	no	—
234	C₅×C₈	—	4	2	no	—
235	#168	—	2	2	no	—
236	#168	—	2	2	no	—
237	#168	—	4	2	no	—
238	#168	—	4	2	no	—
239	C₂³×C₄	—	5	1	no	—
240	C₂³×C₄	—	5	1	no	—
241	C₂³×C₄	—	5	1	no	—
242	C₂×M₁₆	—	5	2	no	—
243	C₂×M₁₆	—	5	2	no	—
244	C₂×M₁₆	—	10	2	no	—
245	C₂²×C₈	—	10	2	no	—
246	C₂×C₄²	—	5	1	no	—
247	C₂×C₄²	—	5	1	no	—
248	C₂×C₄²	—	5	1	no	—
249	C₂×C₄²	—	5	1	no	—
250	C₂×C₄²	—	5	1	no	—
251	C₂×C₄²	—	5	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	C₂²×D₅	1	1	yes	characteristic
258	C₄⋊C₈	—	5	2	no	—
259	C₄⋊C₈	—	5	2	no	—
260	C₄⋊C₈	—	5	2	no	—
261	C₄⋊C₈	—	5	2	no	—
262	C₄⋊C₈	—	5	2	no	—
263	C₄⋊C₈	—	10	2	no	—
264	C₄⋊C₈	—	10	2	no	—
265	C₄⋊C₈	C₄×D₅	1	2	yes	—
266	C₄⋊C₈	C₂²×D₅	1	2	yes	—
267	C₄⋊C₈	C₂²×D₅	1	2	yes	—
268	C₂²⋊C₈	—	2	1	no	—
269	C₂²⋊C₈	—	2	1	no	—
270	C₂²⋊C₈	—	5	2	no	—
271	C₂²⋊C₈	—	5	2	no	—
272	C₂²⋊C₈	—	5	2	no	—
273	C₂²⋊C₈	—	10	2	no	—
274	C₂²⋊C₈	—	10	2	no	—
275	C₂²⋊C₈	—	10	1	no	—
276	C₂²⋊C₈	—	10	1	no	—
277	C₂²⋊C₈	C₄×D₅	1	2	yes	—
278	#97	—	2	1	no	—
279	#97	—	5	2	no	—
280	#97	—	5	2	no	—
281	#97	—	10	2	no	—
282	#97	—	10	2	no	—
283	#97	—	10	1	no	—
284	C₄×C₈	—	2	1	no	—
285	C₄×C₈	—	5	1	no	—
286	C₄×C₈	—	5	1	no	—
287	C₄×C₈	—	10	1	no	—
288	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
289	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
290	C₂²×C₅	—	2	1	no	—
291	C₂²×C₅	—	2	1	no	—
292	C₂²×C₅	—	2	1	no	—
293	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
294	C₂×D₅	—	2	1	no	—
295	C₂×D₅	—	2	1	no	—
296	C₂×D₅	—	2	1	no	—
297	C₂×D₅	—	2	1	no	—
298	C₂×D₅	—	2	1	no	—
299	C₂×D₅	—	4	4	no	—
300	C₂×D₅	#430	1	2	yes	—
301	C₄×C₅	—	2	1	no	—
302	C₄×C₅	—	2	1	no	—
303	C₄×C₅	—	2	1	no	—
304	C₄×C₅	—	2	1	no	—
305	C₄×C₅	#568	1	2	yes	—
306	C₄×C₅	#575	1	2	yes	—
307	Dic₅	—	2	1	no	—
308	Dic₅	—	2	1	no	—
309	Dic₅	—	2	1	no	—
310	Dic₅	—	2	1	no	—
311	Dic₅	—	2	1	no	—
312	Dic₅	—	2	1	no	—
313	C₂⁴	—	5	1	no	—
314	C₂²×C₄	—	5	1	no	—
315	C₂²×C₄	—	5	1	no	—
316	C₂²×C₄	—	5	1	no	—
317	C₂²×C₄	—	5	1	no	—
318	C₂²×C₄	—	5	1	no	—
319	C₂²×C₄	—	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	—	20	2	no	—
330	C₂²×C₄	—	20	2	no	—
331	C₂²×C₄	—	20	2	no	—
332	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
333	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
334	C₂²×C₄	Q₈×D₅	1	1	yes	characteristic
335	M₁₆	—	20	2	no	—
336	M₁₆	—	20	2	no	—
337	M₁₆	—	20	4	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	5	2	no	—
341	C₂×C₈	—	5	2	no	—
342	C₂×C₈	—	10	2	no	—
343	C₂×C₈	—	10	2	no	—
344	C₂×C₈	—	20	4	no	—
345	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
346	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
347	C₄²	—	5	1	no	—
348	C₄²	—	5	1	no	—
349	C₄²	—	5	1	no	—
350	C₄²	—	5	1	no	—
351	C₄²	—	5	1	no	—
352	C₄²	—	5	1	no	—
353	C₄²	—	5	1	no	—
354	C₄²	—	5	1	no	—
355	C₄²	—	5	1	no	—
356	C₄²	—	5	1	no	—
357	C₄²	—	5	1	no	—
358	C₄²	—	5	1	no	—
359	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
360	C₄²	D₄×D₅	1	1	yes	characteristic
361	C₄²	Q₈×D₅	1	1	yes	characteristic
362	C₄²	C₂³×D₅	1	1	yes	characteristic
363	C₂×C₅	—	4	1	no	—
364	C₂×C₅	#2905	1	1	yes	characteristic
365	C₂×C₅	#2911	1	1	yes	characteristic
366	C₂×C₅	C₂×#430	1	1	yes	characteristic
367	D₅	—	2	2	no	—
368	D₅	—	4	1	no	—
369	C₂³	—	5	1	no	—
370	C₂³	—	5	1	no	—
371	C₂³	—	10	2	no	—
372	C₂³	—	20	1	no	—
373	C₂³	—	20	1	no	—
374	C₂³	D₅×C₄⋊C₄	1	1	yes	characteristic
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	5	1	no	—
379	C₂×C₄	—	5	1	no	—
380	C₂×C₄	—	5	1	no	—
381	C₂×C₄	—	5	1	no	—
382	C₂×C₄	—	5	1	no	—
383	C₂×C₄	—	5	1	no	—
384	C₂×C₄	—	10	2	no	—
385	C₂×C₄	—	10	2	no	—
386	C₂×C₄	—	10	2	no	—
387	C₂×C₄	—	10	2	no	—
388	C₂×C₄	—	10	2	no	—
389	C₂×C₄	—	10	2	no	—
390	C₂×C₄	—	20	1	no	—
391	C₂×C₄	—	20	1	no	—
392	C₂×C₄	—	20	1	no	—
393	C₂×C₄	—	20	1	no	—
394	C₂×C₄	—	20	1	no	—
395	C₂×C₄	—	20	1	no	—
396	C₂×C₄	—	20	1	no	—
397	C₂×C₄	—	20	1	no	—
398	C₂×C₄	—	20	1	no	—
399	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
400	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
401	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
402	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
403	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
404	C₂×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
405	C₈	—	2	2	no	—
406	C₈	—	2	2	no	—
407	C₈	—	4	2	no	—
408	C₈	—	4	2	no	—
409	C₈	—	10	2	no	—
410	C₈	—	10	2	no	—
411	C₈	—	20	2	no	—
412	C₈	—	20	2	no	—
413	C₅	#17821	1	1	yes	characteristic, complemented, Sylow
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	5	2	no	—
418	C₂²	—	10	1	no	—
419	C₂²	—	10	1	no	—
420	C₂²	—	10	1	no	—
421	C₂²	—	10	1	no	—
422	C₂²	—	10	1	no	—
423	C₂²	—	20	4	no	—
424	C₂²	C₂×D₅×C₄⋊C₄	1	1	yes	characteristic
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	10	1	no	—
430	C₄	—	10	1	no	—
431	C₄	—	10	1	no	—
432	C₄	—	10	1	no	—
433	C₄	—	10	1	no	—
434	C₄	—	10	1	no	—
435	C₄	#66084	1	2	yes	—
436	C₄	#66102	1	2	yes	—
437	C₂	—	4	1	no	—
438	C₂	—	10	2	no	—
439	C₂	—	20	1	no	—
440	C₂	#10610811	1	1	yes	characteristic
441	C₂	#10610908	1	1	yes	characteristic
442	C₂	D₅×#430	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×#1572	C₂
socle	C₂²×C₅	C₂²×C₄⋊C₄
prime radical	C₂³×D₅	C₄⋊C₄
cosocle	C₄²×C₅	C₂⁴
hypercenter	#1572	D₅
hypocenter	C₅	#17821
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1572

Complements

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

N	H ≅ G/N	type
4. C₅×#1572	C₂	semidirect
5. #10601589	C₂	semidirect
6. #10601544	C₂	semidirect
7. #10601540	C₂	semidirect
8. #10599367	C₂	semidirect
9. #10599364	C₂	semidirect
10. #10599327	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
107. #1572	D₅	semidirect
190. #335	C₂×D₅	semidirect
194. #334	C₂×D₅	semidirect
413. C₅	#17821	semidirect

Maximal subgroups

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

subgroup	index
D₅×#432	2
#10611013	2
C₅×#1572	2
#10601589	2
#10601544	2
#10601540	2
#10599367	2
#10599364	2
#10599327	2
#10599324	2
#17821	5