Subgroups — #12005246

Order 1280.

730 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#427	C₂	1	1	yes	maximal, characteristic
2	C₂²×#3951	C₂	1	1	yes	maximal, characteristic
3	C₂×#65390	C₂	1	1	yes	maximal, characteristic
4	C₂×#64753	C₂	1	2	yes	maximal
5	#10602371	C₂	1	2	yes	maximal
6	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
7	C₂×C₅×#117	C₂²	1	2	yes	—
8	C₂×#4072	C₂²	1	1	yes	characteristic
9	C₂²×#681	C₂²	1	2	yes	—
10	C₂²×#681	C₂²	1	1	yes	characteristic
11	C₅×#427	—	2	2	no	—
12	C₅×#427	C₄	1	4	yes	complemented
13	C₂×C₅×#107	—	2	1	no	—
14	C₂×C₅×#106	—	2	1	no	—
15	C₂×#3951	—	2	1	no	—
16	C₂×#3951	—	2	1	no	—
17	C₂×#3951	—	2	2	no	—
18	C₂×#3951	C₄	1	4	yes	complemented
19	#65390	—	2	1	no	—
20	#65390	—	2	1	no	—
21	#65390	C₄	1	2	yes	complemented
22	#65390	C₄	1	2	yes	complemented
23	C₂×#3947	—	2	1	no	—
24	C₂×C₈×Dic₅	—	2	1	no	—
25	#64753	—	2	4	no	—
26	#64743	—	2	4	no	—
27	#10872	—	5	1	no	maximal, Sylow
28	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
29	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
32	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
33	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
34	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
35	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
36	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
37	C₂²×C₅×C₈	D₄	1	2	yes	—
38	C₂²×C₅×C₈	Q₈	1	2	yes	—
39	C₅×#117	—	2	2	no	—
40	C₅×#117	—	2	2	no	—
41	C₅×#117	—	2	2	no	—
42	C₅×#117	C₂×C₄	1	4	yes	—
43	C₂×C₅×C₄⋊C₄	—	2	2	no	—
44	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
45	C₂×C₄²×C₅	—	2	2	no	—
46	C₂×C₂²⋊Dic₅	—	2	1	no	—
47	#4072	—	2	1	no	—
48	#4072	—	2	1	no	—
49	#4072	C₂×C₄	1	2	yes	—
50	#4072	D₄	1	2	yes	—
51	C₂×C₄⋊Dic₅	Q₈	1	2	yes	—
52	C₂×C₄×Dic₅	—	2	1	no	—
53	C₂×#681	—	2	1	no	—
54	C₂×#681	—	2	1	no	—
55	C₂×#681	—	2	1	no	—
56	C₂×#681	—	2	2	no	—
57	C₂×#681	—	2	2	no	—
58	C₂×#681	—	2	2	no	—
59	C₂×#681	—	2	2	no	—
60	C₂×#681	—	2	2	no	—
61	C₂×#681	C₂×C₄	1	4	yes	—
62	C₂×#681	C₂×C₄	1	2	yes	—
63	C₂×#681	D₄	1	2	yes	—
64	C₂×#681	Q₈	1	2	yes	—
65	C₂²×#168	—	2	1	no	—
66	C₂²×#168	—	2	2	no	—
67	C₅×#107	—	2	4	no	—
68	C₅×#106	—	2	4	no	—
69	#3951	—	2	4	no	—
70	#3951	—	2	4	no	—
71	#3947	—	2	2	no	—
72	#3947	—	2	2	no	—
73	C₈×Dic₅	—	2	2	no	—
74	C₈×Dic₅	—	2	2	no	—
75	C₂²×#108	—	5	1	no	—
76	C₂×#427	D₅	1	1	yes	characteristic
77	C₂×#405	—	5	1	no	—
78	C₂×#344	—	5	2	no	—
79	#1733	—	5	2	no	—
80	C₂⁴×C₅	#41	1	1	yes	characteristic
81	C₂²×C₄×C₅	—	4	2	no	—
82	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
91	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
92	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
93	C₂²×C₄×C₅	#41	1	1	yes	characteristic
94	C₂²×C₄×C₅	#41	1	1	yes	characteristic
95	C₂²×C₄×C₅	#41	1	1	yes	characteristic
96	C₂²×Dic₅	—	2	2	no	—
97	C₂×C₅×C₈	C₄²	1	2	yes	—
98	C₂×C₅×C₈	C₄²	1	2	yes	—
99	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
100	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
101	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
102	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
103	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
104	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
105	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
106	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
107	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
108	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
109	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
110	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
111	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
112	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
113	C₅×C₄⋊C₄	—	2	4	no	—
114	C₅×C₄⋊C₄	—	4	2	no	—
115	C₅×C₂²⋊C₄	—	2	4	no	—
116	C₅×C₂²⋊C₄	—	4	2	no	—
117	C₄²×C₅	—	2	4	no	—
118	C₄²×C₅	—	4	2	no	—
119	C₂²⋊Dic₅	—	2	2	no	—
120	C₂²⋊Dic₅	—	2	2	no	—
121	C₄⋊Dic₅	—	2	2	no	—
122	C₄⋊Dic₅	C₄⋊C₄	1	4	yes	—
123	C₄×Dic₅	—	2	2	no	—
124	C₄×Dic₅	—	2	2	no	—
125	#681	—	2	2	no	—
126	#681	—	2	2	no	—
127	#681	—	2	2	no	—
128	#681	—	2	4	no	—
129	#681	—	2	4	no	—
130	#681	—	4	2	no	—
131	#681	—	4	2	no	—
132	#681	C₄⋊C₄	1	4	yes	—
133	C₂×#168	—	2	2	no	—
134	C₂×#168	—	2	2	no	—
135	C₂×#168	—	2	2	no	—
136	C₂×#168	—	2	4	no	—
137	C₂×#168	—	4	2	no	—
138	C₂×#168	—	4	2	no	—
139	C₂²×M₁₆	—	5	1	no	—
140	C₂²×M₁₆	—	5	2	no	—
141	C₂³×C₈	C₂×D₅	1	1	yes	characteristic
142	C₂×#117	—	5	1	no	—
143	C₂×#117	C₂×D₅	1	2	yes	—
144	C₂×#108	—	5	4	no	—
145	C₂×#108	—	10	1	no	—
146	C₂×#108	—	10	1	no	—
147	C₂×#108	—	10	2	no	—
148	#427	—	2	2	no	—
149	#427	Dic₅	1	4	yes	complemented
150	C₂×#107	—	2	1	no	—
151	C₂×#106	—	2	1	no	—
152	#405	—	5	2	no	—
153	#405	—	5	2	no	—
154	#405	—	10	1	no	—
155	#405	—	10	1	no	—
156	C₂×#97	—	10	1	no	—
157	C₂×C₄×C₈	—	10	1	no	—
158	#344	—	10	4	no	—
159	#339	—	10	4	no	—
160	C₂³×C₅	—	4	2	no	—
161	C₂³×C₅	#117	1	1	yes	characteristic
162	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
163	C₂³×C₅	C₄×Q₈	1	1	yes	characteristic
164	C₂³×C₅	#121	1	1	yes	characteristic
165	C₂³×C₅	C₂²⋊Q₈	1	1	yes	characteristic
166	C₂³×C₅	#124	1	1	yes	characteristic
167	C₂³×C₅	#125	1	1	yes	characteristic
168	C₂×C₄×C₅	—	4	4	no	—
169	C₂×C₄×C₅	—	8	4	no	—
170	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
171	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
173	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
178	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₅	#117	1	1	yes	characteristic
180	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
181	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
182	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
183	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
184	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
185	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
186	C₂×C₄×C₅	#121	1	1	yes	characteristic
187	C₂×C₄×C₅	#121	1	1	yes	characteristic
188	C₂×C₄×C₅	#121	1	1	yes	characteristic
189	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
190	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
191	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
192	C₂×C₄×C₅	#124	1	1	yes	characteristic
193	C₂×C₄×C₅	#125	1	1	yes	characteristic
194	C₂×C₄×C₅	#127	1	1	yes	characteristic
195	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
196	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
197	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
198	C₂×Dic₅	—	2	4	no	—
199	C₂×Dic₅	—	4	4	no	—
200	C₅×C₈	#95	1	2	yes	—
201	C₅×C₈	#95	1	2	yes	—
202	C₅×C₈	#95	1	2	yes	—
203	C₅×C₈	#95	1	2	yes	—
204	#168	—	2	4	no	—
205	#168	—	4	4	no	—
206	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
207	C₂×M₁₆	—	5	2	no	—
208	C₂×M₁₆	—	5	2	no	—
209	C₂×M₁₆	—	5	2	no	—
210	C₂×M₁₆	—	5	4	no	—
211	C₂×M₁₆	—	10	1	no	—
212	C₂×M₁₆	—	10	1	no	—
213	C₂×M₁₆	—	10	1	no	—
214	C₂×M₁₆	—	10	2	no	—
215	C₂×M₁₆	—	10	2	no	—
216	C₂×M₁₆	—	10	2	no	—
217	C₂×M₁₆	—	10	2	no	—
218	C₂×M₁₆	—	10	2	no	—
219	C₂²×C₈	—	10	1	no	—
220	C₂²×C₈	—	10	2	no	—
221	C₂²×C₈	Dic₁₀	1	2	yes	—
222	C₂²×C₈	C₄×D₅	1	1	yes	characteristic
223	C₂²×C₈	C₄×D₅	1	1	yes	characteristic
224	C₂²×C₈	C₄×D₅	1	2	yes	—
225	C₂²×C₈	D₂₀	1	1	yes	characteristic
226	C₂²×C₈	D₂₀	1	1	yes	characteristic
227	C₂²×C₈	C₂×Dic₅	1	2	yes	—
228	C₂²×C₈	C₂²⋊D₅	1	1	yes	characteristic
229	C₂²×C₈	C₂²⋊D₅	1	1	yes	characteristic
230	C₂²×C₈	C₂²⋊D₅	1	2	yes	—
231	#117	—	2	2	no	—
232	#117	—	2	2	no	—
233	#117	—	2	2	no	—
234	#117	—	5	2	no	—
235	#117	—	5	2	no	—
236	#117	—	10	1	no	—
237	#117	—	10	1	no	—
238	#117	C₂×Dic₅	1	4	yes	—
239	C₂×C₄⋊C₄	—	2	2	no	—
240	C₂×C₄⋊C₄	—	5	2	no	—
241	C₂×C₂²⋊C₄	—	2	2	no	—
242	C₂×C₂²⋊C₄	—	10	1	no	—
243	C₂×C₄²	—	2	2	no	—
244	C₂×C₄²	—	10	1	no	—
245	#108	—	10	4	no	—
246	#108	—	10	4	no	—
247	#107	—	2	4	no	—
248	#106	—	2	4	no	—
249	#97	—	10	2	no	—
250	#97	—	10	2	no	—
251	C₄×C₈	—	10	2	no	—
252	C₄×C₈	—	10	2	no	—
253	C₂²×C₅	—	2	2	no	—
254	C₂²×C₅	—	2	2	no	—
255	C₂²×C₅	—	2	2	no	—
256	C₂²×C₅	—	4	1	no	—
257	C₂²×C₅	—	4	1	no	—
258	C₂²×C₅	—	4	1	no	—
259	C₂²×C₅	—	4	1	no	—
260	C₂²×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
261	C₂²×C₅	#380	1	1	yes	characteristic
262	C₂²×C₅	#382	1	1	yes	characteristic
263	C₂²×C₅	#389	1	1	yes	characteristic
264	C₂²×C₅	#389	1	1	yes	characteristic
265	C₂²×C₅	#390	1	1	yes	characteristic
266	C₂²×C₅	#391	1	1	yes	characteristic
267	C₄×C₅	—	8	4	no	—
268	C₄×C₅	C₂×#95	1	1	yes	characteristic
269	C₄×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
270	C₄×C₅	#380	1	1	yes	characteristic
271	C₄×C₅	#384	1	1	yes	characteristic
272	C₄×C₅	#389	1	1	yes	characteristic
273	C₄×C₅	#389	1	1	yes	characteristic
274	C₄×C₅	#390	1	1	yes	characteristic
275	C₄×C₅	#391	1	1	yes	characteristic
276	Dic₅	—	4	4	no	—
277	C₂⁴	#711	1	1	yes	characteristic
278	C₂²×C₄	—	4	2	no	—
279	C₂²×C₄	—	10	2	no	—
280	C₂²×C₄	C₂×Dic₁₀	1	1	yes	characteristic
281	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
282	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₂₀	1	1	yes	characteristic
284	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
285	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
286	C₂²×C₄	#711	1	1	yes	characteristic
287	C₂²×C₄	Q₈×D₅	1	1	yes	characteristic
288	C₂²×C₄	Q₈×D₅	1	1	yes	characteristic
289	C₂²×C₄	#713	1	1	yes	characteristic
290	C₂²×C₄	#713	1	1	yes	characteristic
291	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
292	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
293	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
294	M₁₆	—	5	4	no	—
295	M₁₆	—	10	2	no	—
296	M₁₆	—	10	2	no	—
297	M₁₆	—	10	2	no	—
298	M₁₆	—	10	4	no	—
299	M₁₆	—	10	4	no	—
300	M₁₆	—	20	2	no	—
301	M₁₆	—	20	2	no	—
302	C₂×C₈	—	10	2	no	—
303	C₂×C₈	—	10	2	no	—
304	C₂×C₈	—	10	2	no	—
305	C₂×C₈	—	10	4	no	—
306	C₂×C₈	—	20	2	no	—
307	C₂×C₈	—	20	2	no	—
308	C₂×C₈	C₄×Dic₅	1	2	yes	—
309	C₂×C₈	C₄×Dic₅	1	2	yes	—
310	C₂×C₈	#683	1	2	yes	—
311	C₂×C₈	#683	1	2	yes	—
312	C₂×C₈	#683	1	2	yes	—
313	C₂×C₈	#683	1	2	yes	—
314	C₂×C₈	C₄⋊Dic₅	1	2	yes	—
315	C₂×C₈	C₄⋊Dic₅	1	2	yes	—
316	C₂×C₈	#685	1	1	yes	characteristic
317	C₂×C₈	#685	1	1	yes	characteristic
318	C₂×C₈	#685	1	1	yes	characteristic
319	C₂×C₈	#685	1	1	yes	characteristic
320	C₂×C₈	#685	1	2	yes	—
321	C₂×C₈	#685	1	2	yes	—
322	C₂×C₈	C₂²⋊Dic₅	1	2	yes	—
323	C₂×C₈	C₂²⋊Dic₅	1	2	yes	—
324	C₄⋊C₄	—	2	4	no	—
325	C₄⋊C₄	—	4	2	no	—
326	C₄⋊C₄	—	5	4	no	—
327	C₄⋊C₄	—	10	2	no	—
328	C₂²⋊C₄	—	2	4	no	—
329	C₂²⋊C₄	—	4	2	no	—
330	C₂²⋊C₄	—	10	2	no	—
331	C₂²⋊C₄	—	10	2	no	—
332	C₄²	—	2	4	no	—
333	C₄²	—	4	2	no	—
334	C₄²	—	10	2	no	—
335	C₄²	—	10	2	no	—
336	C₂×C₅	—	2	1	no	—
337	C₂×C₅	—	2	1	no	—
338	C₂×C₅	—	2	1	no	—
339	C₂×C₅	—	2	1	no	—
340	C₂×C₅	—	2	1	no	—
341	C₂×C₅	—	2	1	no	—
342	C₂×C₅	C₄⋊#95	1	1	yes	characteristic
343	C₂×C₅	#1814	1	2	yes	—
344	C₂³	—	4	2	no	—
345	C₂³	#4033	1	1	yes	characteristic
346	C₂³	#4036	1	1	yes	characteristic
347	C₂³	#4038	1	1	yes	characteristic
348	C₂³	#4043	1	1	yes	characteristic
349	C₂³	D₄×Dic₅	1	1	yes	characteristic
350	C₂³	#4082	1	1	yes	characteristic
351	C₂³	#4084	1	1	yes	characteristic
352	C₂×C₄	—	4	4	no	—
353	C₂×C₄	—	8	4	no	—
354	C₂×C₄	—	10	4	no	—
355	C₂×C₄	—	20	4	no	—
356	C₂×C₄	#4033	1	1	yes	characteristic
357	C₂×C₄	#4034	1	1	yes	characteristic
358	C₂×C₄	#4034	1	1	yes	characteristic
359	C₂×C₄	#4036	1	1	yes	characteristic
360	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
361	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
362	C₂×C₄	#4038	1	1	yes	characteristic
363	C₂×C₄	#4039	1	1	yes	characteristic
364	C₂×C₄	#4039	1	1	yes	characteristic
365	C₂×C₄	#4041	1	1	yes	characteristic
366	C₂×C₄	#4041	1	1	yes	characteristic
367	C₂×C₄	#4043	1	1	yes	characteristic
368	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
369	C₂×C₄	C₂×#683	1	1	yes	characteristic
370	C₂×C₄	C₂×#683	1	1	yes	characteristic
371	C₂×C₄	C₂×C₄⋊Dic₅	1	1	yes	characteristic
372	C₂×C₄	C₂×#685	1	1	yes	characteristic
373	C₂×C₄	C₂×#685	1	1	yes	characteristic
374	C₂×C₄	D₄×Dic₅	1	1	yes	characteristic
375	C₂×C₄	#4084	1	1	yes	characteristic
376	C₂×C₄	#4086	1	1	yes	characteristic
377	C₂×C₄	#4090	1	1	yes	characteristic
378	C₂×C₄	Q₈×Dic₅	1	1	yes	characteristic
379	C₂×C₄	Q₈×Dic₅	1	1	yes	characteristic
380	C₂×C₄	#4092	1	1	yes	characteristic
381	C₂×C₄	#4092	1	1	yes	characteristic
382	C₂×C₄	#4093	1	1	yes	characteristic
383	C₂×C₄	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
384	C₈	—	10	4	no	—
385	C₈	—	20	4	no	—
386	C₈	#3963	1	2	yes	—
387	C₈	#3963	1	2	yes	—
388	C₈	#3963	1	2	yes	—
389	C₈	#3963	1	2	yes	—
390	C₅	#10872	1	1	yes	characteristic, complemented, Sylow
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	2	2	no	—
394	C₂²	—	4	1	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	4	1	no	—
397	C₂²	—	4	1	no	—
398	C₂²	#65262	1	1	yes	characteristic
399	C₂²	#65263	1	1	yes	characteristic
400	C₂²	C₄⋊C₄×Dic₅	1	1	yes	characteristic
401	C₂²	#65266	1	1	yes	characteristic
402	C₂²	#65274	1	1	yes	characteristic
403	C₂²	#65276	1	1	yes	characteristic
404	C₂²	#65510	1	1	yes	characteristic
405	C₄	—	8	4	no	—
406	C₄	—	20	4	no	—
407	C₄	#65262	1	1	yes	characteristic
408	C₄	C₄⋊C₄×Dic₅	1	1	yes	characteristic
409	C₄	#65265	1	1	yes	characteristic
410	C₄	#65274	1	1	yes	characteristic
411	C₄	#65276	1	1	yes	characteristic
412	C₄	#65277	1	1	yes	characteristic
413	C₄	C₂×#3963	1	1	yes	characteristic
414	C₄	#65519	1	1	yes	characteristic
415	C₂	—	2	1	no	—
416	C₂	—	2	1	no	—
417	C₂	—	2	1	no	—
418	C₂	—	2	1	no	—
419	C₂	—	2	1	no	—
420	C₂	—	2	1	no	—
421	C₂	#10601458	1	2	yes	—
422	C₂	#10602356	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#4041
commutator	C₂×C₄×C₅	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₅
Fitting	C₂×C₅×#427	C₂
socle	C₂²×C₅	#380
prime radical	C₂⁴×C₅	#41
cosocle	C₂³×C₄×C₅	C₂³
hypercenter	C₂×#427	D₅
hypocenter	C₅	#10872
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#427

Complements

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

N	H ≅ G/N	type
12. C₅×#427	C₄	semidirect
18. C₂×#3951	C₄	semidirect
21. #65390	C₄	semidirect
22. #65390	C₄	semidirect
149. #427	Dic₅	semidirect
390. C₅	#10872	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#427	2
C₂²×#3951	2
C₂×#65390	2
C₂×#64753	2
#10602371	2
#10872	5