Subgroups — #14300279

Order 1920.

540 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#91288	C₂	1	1	yes	maximal, characteristic
2	#11751100	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5002	C₂	1	1	yes	maximal, characteristic
4	C₂×#90993	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#90979	C₂	1	1	yes	maximal, characteristic
6	C₃×#64752	C₂	1	1	yes	maximal, characteristic, complemented
7	#11745966	C₂	1	1	yes	maximal, characteristic, complemented
8	#10601085	—	3	1	no	maximal, Hall
9	C₂×C₅×#235	C₂²	1	1	yes	characteristic
10	C₃×C₅×#117	C₂²	1	1	yes	characteristic
11	C₂×#6710	C₂²	1	1	yes	characteristic
12	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
13	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
15	C₂×C₃×#681	C₂²	1	1	yes	characteristic
16	C₂×#6650	—	2	1	no	—
17	#91288	—	2	2	no	—
18	#91288	—	2	2	no	—
19	C₂×D₃×#168	—	2	1	no	—
20	C₄⋊(C₃⋊#168)	—	2	1	no	—
21	C₄⋊(C₃⋊#168)	—	2	1	no	—
22	C₅×#810	C₄	1	1	yes	characteristic, complemented
23	C₅×#810	C₄	1	1	yes	characteristic, complemented
24	C₅×#809	C₄	1	1	yes	characteristic, complemented
25	C₅×#809	C₄	1	1	yes	characteristic, complemented
26	#90993	—	2	2	no	—
27	#90979	—	2	2	no	—
28	#68774	—	5	1	no	maximal, Hall
29	C₂×#4094	—	3	1	no	—
30	C₅×#416	—	3	1	no	—
31	C₂×#3969	—	3	1	no	—
32	C₂×#3951	—	3	1	no	—
33	#65288	—	3	1	no	—
34	#64770	—	3	1	no	—
35	#64752	D₃	1	1	yes	characteristic, complemented
36	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₂×C₅×#67	—	2	1	no	—
38	C₅×#235	—	2	1	no	—
39	C₅×#235	—	2	1	no	—
40	C₅×#235	D₄	1	2	yes	—
41	C₅×#235	Q₈	1	2	yes	—
42	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄×C₅×D₃	—	2	1	no	—
44	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₃×Dic₅	—	2	1	no	—
46	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
47	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
48	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
49	C₃×C₄²×C₅	—	2	1	no	—
50	#6710	—	2	1	no	—
51	#6710	—	2	1	no	—
52	C₂×C₃⋊#168	—	2	1	no	—
53	C₂×C₃⋊#168	—	2	1	no	—
54	C₂×C₃⋊#168	—	2	1	no	—
55	C₂×C₃⋊#168	D₄	1	1	yes	characteristic
56	C₂×C₃⋊#168	D₄	1	1	yes	characteristic
57	C₂×C₅×C₃⋊C₈	—	2	1	no	—
58	C₂×C₅×C₃⋊C₈	—	2	1	no	—
59	C₂×C₅×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
60	C₂×C₅×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
61	C₃×C₄×Dic₅	—	2	1	no	—
62	C₃×C₄×Dic₅	—	2	1	no	—
63	C₃×#681	—	2	1	no	—
64	C₃×#681	D₄	1	2	yes	—
65	C₂×C₃×#168	—	2	1	no	—
66	#6650	—	2	4	no	—
67	D₃×#168	—	2	4	no	—
68	C₂×#907	—	5	1	no	—
69	C₂×#822	—	5	1	no	—
70	#5002	D₅	1	1	yes	characteristic
71	#4999	—	5	1	no	—
72	C₂×#805	—	5	1	no	—
73	C₃×#339	—	5	1	no	—
74	#4524	—	5	1	no	—
75	C₂×C₅×#41	—	3	1	no	—
76	C₂²×C₅×C₈	—	3	1	no	—
77	C₅×#117	C₂×D₃	1	1	yes	characteristic
78	#4094	—	6	2	no	—
79	#4094	—	6	2	no	—
80	C₂×C₄×Dic₅	C₂×D₃	1	1	yes	characteristic
81	C₂×#681	—	3	1	no	—
82	C₂×#681	—	6	1	no	—
83	C₂×#681	C₂×D₃	1	1	yes	characteristic
84	C₂²×#168	—	3	1	no	—
85	C₂²×#168	—	6	1	no	—
86	C₅×#103	—	3	1	no	—
87	C₅×#103	—	3	1	no	—
88	C₅×#102	—	3	1	no	—
89	C₅×#102	—	3	1	no	—
90	#3969	—	6	2	no	—
91	#3951	—	6	2	no	—
92	C₄⋊#168	—	6	1	no	—
93	C₄⋊#168	—	6	1	no	—
94	#1866	—	15	1	no	Sylow
95	C₂³×C₃×C₅	#41	1	1	yes	characteristic
96	C₂²×C₅×D₃	—	2	1	no	—
97	C₂×C₃×C₄×C₅	—	2	1	no	—
98	C₂×C₃×C₄×C₅	—	2	1	no	—
99	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
101	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
105	C₅×#67	—	2	2	no	—
106	C₅×#67	—	2	2	no	—
107	C₂×C₅×Dic₃	—	2	1	no	—
108	C₅×D₁₂	—	2	1	no	—
109	C₅×D₁₂	C₄⋊C₄	1	2	yes	—
110	C₄×C₅×D₃	—	2	2	no	—
111	C₄×C₅×D₃	—	2	2	no	—
112	C₅×Dic₆	—	2	1	no	—
113	C₅×Dic₆	C₄⋊C₄	1	2	yes	—
114	C₂×C₃×Dic₅	—	2	2	no	—
115	C₂×C₃×Dic₅	—	4	1	no	—
116	C₂×C₃×Dic₅	—	4	1	no	—
117	C₃⋊#168	—	2	1	no	—
118	C₃⋊#168	—	2	1	no	—
119	C₃⋊#168	—	4	1	no	—
120	C₃×#168	—	2	2	no	—
121	C₅×C₃⋊C₈	—	2	1	no	—
122	C₅×C₃⋊C₈	—	2	1	no	—
123	C₂×#235	C₂×D₅	1	1	yes	characteristic
124	C₂×C₃×M₁₆	—	5	1	no	—
125	C₃×#117	C₂×D₅	1	1	yes	characteristic
126	C₂×C₃×C₄²	—	5	1	no	—
127	C₂×#208	—	5	1	no	—
128	C₂²×C₃⋊C₈	—	5	1	no	—
129	C₂²×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
130	#907	—	10	2	no	—
131	#907	—	10	2	no	—
132	C₂×ΓL(1,𝔽₂₅)	—	10	1	no	—
133	C₂×D₃×C₈	—	10	1	no	—
134	#822	—	10	2	no	—
135	#810	Dic₅	1	1	yes	characteristic, complemented
136	#810	Dic₅	1	1	yes	characteristic, complemented
137	#809	Dic₅	1	1	yes	characteristic, complemented
138	#809	Dic₅	1	1	yes	characteristic, complemented
139	#805	—	10	2	no	—
140	C₄⋊(C₃⋊C₈)	—	10	1	no	—
141	C₄⋊(C₃⋊C₈)	—	10	1	no	—
142	C₅×#41	—	3	2	no	—
143	C₅×#41	—	3	2	no	—
144	C₅×#41	—	6	1	no	—
145	C₅×#41	—	6	1	no	—
146	C₂×C₅×Q₈	—	3	1	no	—
147	C₂×C₅×D₄	—	3	1	no	—
148	C₂×C₅×D₄	—	6	1	no	—
149	C₂²×C₄×C₅	—	6	1	no	—
150	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
151	C₂²×Dic₅	—	2	1	no	—
152	C₂×C₅×C₈	—	3	1	no	—
153	C₂×C₅×C₈	—	3	1	no	—
154	C₂×C₅×C₈	—	6	1	no	—
155	C₂×C₅×C₈	—	6	1	no	—
156	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
157	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
158	C₅×C₂²⋊C₄	—	2	1	no	—
159	C₄²×C₅	—	2	1	no	—
160	C₄×Dic₅	—	2	1	no	—
161	C₄×Dic₅	—	2	1	no	—
162	#681	—	2	1	no	—
163	#681	—	6	4	no	—
164	#681	—	6	1	no	—
165	#681	—	6	1	no	—
166	#681	D₁₂	1	2	yes	—
167	C₂×#168	—	2	1	no	—
168	C₂×#168	—	3	1	no	—
169	C₂×#168	—	3	1	no	—
170	C₂×#168	—	6	4	no	—
171	C₂×#168	—	6	1	no	—
172	C₂×#168	—	6	1	no	—
173	C₂×#168	—	6	1	no	—
174	C₂×#131	—	15	1	no	—
175	C₂×#108	—	15	1	no	—
176	#424	—	15	1	no	—
177	C₂×#104	—	15	1	no	—
178	#416	—	3	1	no	—
179	#339	—	5	1	no	—
180	#336	—	15	1	no	—
181	C₂²×C₃×C₅	—	2	1	no	—
182	C₂²×C₃×C₅	—	2	1	no	—
183	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
184	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
185	C₂²×C₃×C₅	#123	1	1	yes	characteristic
186	C₂×C₅×D₃	—	2	2	no	—
187	C₂×C₅×D₃	—	4	1	no	—
188	C₂×C₅×D₃	—	4	1	no	—
189	C₃×C₄×C₅	—	4	1	no	—
190	C₃×C₄×C₅	—	4	1	no	—
191	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
192	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
193	C₃×C₄×C₅	#120	1	1	yes	characteristic
194	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
195	C₃×Dic₅	—	4	2	no	—
196	C₅×Dic₃	—	2	2	no	—
197	C₂²×C₃×C₄	—	10	1	no	—
198	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
199	C₂×#67	—	2	1	no	—
200	#235	—	2	1	no	—
201	#235	—	2	1	no	—
202	#235	Dic₁₀	1	2	yes	—
203	#235	D₂₀	1	2	yes	—
204	C₂×D₁₂	C₂×Dic₅	1	1	yes	characteristic
205	C₂×C₄×D₃	—	2	1	no	—
206	C₂×Dic₆	C₂×Dic₅	1	1	yes	characteristic
207	C₃×M₁₆	—	5	2	no	—
208	C₃×M₁₆	—	10	1	no	—
209	C₂×C₃×C₈	—	10	1	no	—
210	C₃×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
211	C₃×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
212	C₃×C₂²⋊C₄	—	2	1	no	—
213	C₃×C₄²	—	2	1	no	—
214	C₃×C₄²	—	10	1	no	—
215	C₃×C₄²	—	10	1	no	—
216	#208	—	10	1	no	—
217	#208	—	10	1	no	—
218	C₂×C₃⋊C₈	—	2	1	no	—
219	C₂×C₃⋊C₈	—	2	1	no	—
220	C₂×C₃⋊C₈	—	5	1	no	—
221	C₂×C₃⋊C₈	—	5	1	no	—
222	C₂×C₃⋊C₈	—	10	1	no	—
223	C₂×C₃⋊C₈	—	10	1	no	—
224	C₂×C₃⋊C₈	—	10	1	no	—
225	C₂×C₃⋊C₈	C₂×Dic₅	1	1	yes	characteristic
226	C₂×C₃⋊C₈	C₂×Dic₅	1	1	yes	characteristic
227	ΓL(1,𝔽₂₅)	—	10	4	no	—
228	D₃×C₈	—	10	4	no	—
229	C₂³×C₅	—	6	1	no	—
230	C₂³×C₅	#237	1	1	yes	characteristic
231	C₅×Q₈	—	3	2	no	—
232	C₅×Q₈	—	6	1	no	—
233	C₅×D₄	—	3	2	no	—
234	C₅×D₄	—	6	2	no	—
235	C₅×D₄	—	6	2	no	—
236	C₅×D₄	—	6	1	no	—
237	C₂×C₄×C₅	—	2	1	no	—
238	C₂×C₄×C₅	—	2	1	no	—
239	C₂×C₄×C₅	—	6	1	no	—
240	C₂×C₄×C₅	—	6	2	no	—
241	C₂×C₄×C₅	—	6	2	no	—
242	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
243	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
244	C₂×C₄×C₅	#235	1	1	yes	characteristic
245	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
246	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
247	C₂×C₄×C₅	D₃×Q₈	1	1	yes	characteristic
248	C₂×Dic₅	—	2	2	no	—
249	C₂×Dic₅	—	4	1	no	—
250	C₂×Dic₅	—	4	1	no	—
251	C₅×C₈	—	6	1	no	—
252	C₅×C₈	—	6	1	no	—
253	#168	—	2	2	no	—
254	#168	—	6	1	no	—
255	#168	—	6	1	no	—
256	#168	—	12	1	no	—
257	C₂×#41	—	3	1	no	—
258	#131	—	30	2	no	—
259	#131	—	30	2	no	—
260	C₂×M₁₆	—	5	1	no	—
261	C₂×M₁₆	—	15	1	no	—
262	C₂×M₁₆	—	30	1	no	—
263	C₂²×C₈	—	3	1	no	—
264	C₂²×C₈	—	15	1	no	—
265	C₂²×C₈	—	30	1	no	—
266	#117	D₃×D₅	1	1	yes	characteristic
267	C₂×C₄²	—	5	1	no	—
268	#108	—	30	2	no	—
269	C₄⋊C₈	—	30	1	no	—
270	C₄⋊C₈	—	30	1	no	—
271	#104	—	30	2	no	—
272	#103	—	3	1	no	—
273	#103	—	3	1	no	—
274	#102	—	3	1	no	—
275	#102	—	3	1	no	—
276	C₂×C₃×C₅	—	2	1	no	—
277	C₂×C₃×C₅	—	2	1	no	—
278	C₂×C₃×C₅	#385	1	1	yes	characteristic
279	C₂×C₃×C₅	#443	1	1	yes	characteristic
280	C₂×C₃×C₅	#444	1	1	yes	characteristic
281	C₅×D₃	—	4	2	no	—
282	C₂³×C₃	#711	1	1	yes	characteristic
283	C₂²×D₃	—	2	1	no	—
284	C₂×C₃×C₄	—	2	1	no	—
285	C₂×C₃×C₄	—	2	1	no	—
286	C₂×C₃×C₄	—	10	2	no	—
287	C₂×C₃×C₄	—	20	1	no	—
288	C₂×C₃×C₄	—	20	1	no	—
289	C₂×C₃×C₄	C₂×Dic₁₀	1	1	yes	characteristic
290	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
291	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
292	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
293	C₂×C₃×C₄	#711	1	1	yes	characteristic
294	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
295	#67	—	2	2	no	—
296	#67	—	2	2	no	—
297	C₂×Dic₃	—	2	1	no	—
298	D₁₂	—	2	1	no	—
299	D₁₂	C₄⋊Dic₅	1	2	yes	—
300	C₄×D₃	—	2	2	no	—
301	C₄×D₃	—	2	2	no	—
302	Dic₆	—	2	1	no	—
303	Dic₆	C₄⋊Dic₅	1	2	yes	—
304	C₃×C₈	—	10	2	no	—
305	C₃⋊C₈	—	2	1	no	—
306	C₃⋊C₈	—	2	1	no	—
307	C₃⋊C₈	—	10	1	no	—
308	C₃⋊C₈	—	10	1	no	—
309	C₃⋊C₈	—	20	1	no	—
310	C₂²×C₅	—	2	1	no	—
311	C₂²×C₅	—	2	1	no	—
312	C₂²×C₅	—	6	2	no	—
313	C₂²×C₅	—	12	1	no	—
314	C₂²×C₅	—	12	1	no	—
315	C₂²×C₅	#67⋊C₄	1	1	yes	characteristic
316	C₂²×C₅	#883	1	1	yes	characteristic
317	C₂²×C₅	#897	1	1	yes	characteristic
318	C₄×C₅	—	4	1	no	—
319	C₄×C₅	—	4	1	no	—
320	C₄×C₅	—	6	2	no	—
321	C₄×C₅	C₄×D₁₂	1	1	yes	characteristic
322	C₄×C₅	#882	1	1	yes	characteristic
323	C₄×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
324	C₄×C₅	#896	1	1	yes	characteristic
325	Dic₅	—	4	2	no	—
326	#41	—	3	2	no	—
327	#41	—	3	2	no	—
328	#41	—	6	1	no	—
329	#41	—	6	1	no	—
330	C₂×Q₈	—	3	1	no	—
331	C₂×D₄	—	3	1	no	—
332	C₂×D₄	—	6	1	no	—
333	C₂²×C₄	—	6	1	no	—
334	C₂²×C₄	—	10	1	no	—
335	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
336	M₁₆	—	5	2	no	—
337	M₁₆	—	10	1	no	—
338	M₁₆	—	30	4	no	—
339	M₁₆	—	30	1	no	—
340	M₁₆	—	30	1	no	—
341	C₂×C₈	—	3	1	no	—
342	C₂×C₈	—	3	1	no	—
343	C₂×C₈	—	6	1	no	—
344	C₂×C₈	—	6	1	no	—
345	C₂×C₈	—	10	1	no	—
346	C₂×C₈	—	15	1	no	—
347	C₂×C₈	—	15	1	no	—
348	C₂×C₈	—	30	4	no	—
349	C₂×C₈	—	30	1	no	—
350	C₂×C₈	—	30	1	no	—
351	C₂×C₈	—	30	1	no	—
352	C₄⋊C₄	D₃×Dic₅	1	1	yes	characteristic
353	C₄⋊C₄	D₃×Dic₅	1	1	yes	characteristic
354	C₂²⋊C₄	—	2	1	no	—
355	C₄²	—	2	1	no	—
356	C₄²	—	10	1	no	—
357	C₄²	—	10	1	no	—
358	C₃×C₅	#1866	1	1	yes	characteristic, complemented, Hall
359	C₂²×C₃	—	2	1	no	—
360	C₂²×C₃	—	2	1	no	—
361	C₂²×C₃	#4024	1	1	yes	characteristic
362	C₂²×C₃	#4032	1	1	yes	characteristic
363	C₂²×C₃	D₄×Dic₅	1	1	yes	characteristic
364	C₂×D₃	—	2	2	no	—
365	C₂×D₃	—	4	1	no	—
366	C₂×D₃	—	4	1	no	—
367	C₃×C₄	—	4	1	no	—
368	C₃×C₄	—	4	1	no	—
369	C₃×C₄	—	20	2	no	—
370	C₃×C₄	#4024	1	1	yes	characteristic
371	C₃×C₄	#4028	1	1	yes	characteristic
372	C₃×C₄	C₂×C₄⋊Dic₅	1	1	yes	characteristic
373	C₃×C₄	D₄×Dic₅	1	1	yes	characteristic
374	Dic₃	—	2	2	no	—
375	C₂×C₅	—	2	1	no	—
376	C₂×C₅	—	2	1	no	—
377	C₂×C₅	—	12	2	no	—
378	C₂×C₅	#4668	1	1	yes	characteristic
379	C₂×C₅	#4823	1	1	yes	characteristic
380	C₂×C₅	#4824	1	1	yes	characteristic
381	C₂³	—	6	1	no	—
382	C₂³	#6780	1	1	yes	characteristic
383	Q₈	—	3	2	no	—
384	Q₈	—	6	1	no	—
385	D₄	—	3	2	no	—
386	D₄	—	6	2	no	—
387	D₄	—	6	2	no	—
388	D₄	—	6	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	6	1	no	—
392	C₂×C₄	—	6	2	no	—
393	C₂×C₄	—	6	2	no	—
394	C₂×C₄	—	10	2	no	—
395	C₂×C₄	—	20	1	no	—
396	C₂×C₄	—	20	1	no	—
397	C₂×C₄	D₃×Dic₁₀	1	1	yes	characteristic
398	C₂×C₄	#6772	1	1	yes	characteristic
399	C₂×C₄	D₅×D₁₂	1	1	yes	characteristic
400	C₂×C₄	D₃×D₂₀	1	1	yes	characteristic
401	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
402	C₂×C₄	#6790	1	1	yes	characteristic
403	C₈	—	6	1	no	—
404	C₈	—	6	1	no	—
405	C₈	—	10	2	no	—
406	C₈	—	30	1	no	—
407	C₈	—	30	1	no	—
408	C₈	—	60	1	no	—
409	C₂×C₃	—	2	1	no	—
410	C₂×C₃	—	2	1	no	—
411	C₂×C₃	#65239	1	1	yes	characteristic
412	C₂×C₃	#65485	1	1	yes	characteristic
413	C₂×C₃	#65486	1	1	yes	characteristic
414	D₃	—	4	2	no	—
415	C₅	#68774	1	1	yes	characteristic, complemented, Sylow
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	6	2	no	—
419	C₂²	—	12	1	no	—
420	C₂²	—	12	1	no	—
421	C₂²	#91417	1	1	yes	characteristic
422	C₂²	#91457	1	1	yes	characteristic
423	C₂²	#67⋊Dic₅	1	1	yes	characteristic
424	C₄	—	4	1	no	—
425	C₄	—	4	1	no	—
426	C₄	—	6	2	no	—
427	C₄	—	20	2	no	—
428	C₄	Dic₅×D₁₂	1	1	yes	characteristic
429	C₄	D₃×C₄⋊Dic₅	1	1	yes	characteristic
430	C₄	#91432	1	1	yes	characteristic
431	C₄	#91476	1	1	yes	characteristic
432	C₃	#10601085	1	1	yes	characteristic, complemented, Sylow
433	C₂	—	2	1	no	—
434	C₂	—	2	1	no	—
435	C₂	—	12	2	no	—
436	C₂	#11748903	1	1	yes	characteristic
437	C₂	#11749442	1	1	yes	characteristic
438	C₂	#11749443	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#6790
commutator	C₂×C₃×C₄×C₅	C₂²×C₄
Frattini	C₂²×C₄	C₂×D₃×D₅
Fitting	C₃×C₅×#117	C₂²
socle	C₂²×C₃×C₅	C₄×D₄
prime radical	C₂×C₅×#235	C₂²
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	#117	D₃×D₅
hypocenter	C₃×C₅	#1866
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
2. #11751100	C₂	semidirect
4. C₂×#90993	C₂	semidirect
6. C₃×#64752	C₂	semidirect
7. #11745966	C₂	semidirect
22. C₅×#810	C₄	semidirect
23. C₅×#810	C₄	semidirect
24. C₅×#809	C₄	semidirect
25. C₅×#809	C₄	semidirect
35. #64752	D₃	semidirect
135. #810	Dic₅	semidirect
136. #810	Dic₅	semidirect
137. #809	Dic₅	semidirect
138. #809	Dic₅	semidirect
358. C₃×C₅	#1866	semidirect
415. C₅	#68774	semidirect
432. C₃	#10601085	semidirect

Maximal subgroups

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

subgroup	index
C₂×#91288	2
#11751100	2
C₅×#5002	2
C₂×#90993	2
C₂×#90979	2
C₃×#64752	2
#11745966	2
#10601085	3
#68774	5