Subgroups — #12068330

Order 1280.

756 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2920	C₂	1	1	yes	maximal, characteristic
2	C₂×#65213	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×#681	C₂	1	1	yes	maximal, characteristic
4	#10601588	C₂	1	4	yes	maximal, complemented
5	#10601539	C₂	1	4	yes	maximal, complemented
6	#10601284	C₂	1	2	yes	maximal, complemented
7	#10601283	C₂	1	2	yes	maximal, complemented
8	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
9	C₂²×#681	—	2	1	no	—
10	C₂²×#681	C₄	1	2	yes	—
11	C₅×#432	—	2	1	no	—
12	C₅×#432	C₂²	1	2	yes	—
13	C₅×#431	—	2	1	no	—
14	C₅×#431	C₂²	1	2	yes	—
15	C₅×#423	C₂²	1	1	yes	characteristic
16	C₅×#423	C₂²	1	1	yes	characteristic
17	C₅×#407	—	2	1	no	—
18	C₄×C₅×M₁₆	—	2	1	no	—
19	#65213	—	2	1	no	—
20	#65213	—	2	1	no	—
21	#65213	C₂²	1	2	yes	—
22	#65213	C₂²	1	2	yes	—
23	C₂×C₄⋊#168	—	2	1	no	—
24	C₂×C₄⋊#168	C₂²	1	2	yes	—
25	C₄×#681	C₄	1	2	yes	—
26	C₄×#681	C₄	1	1	yes	characteristic
27	C₄×#681	C₄	1	1	yes	characteristic
28	C₄×#681	C₂²	1	2	yes	—
29	C₄×#681	C₂²	1	2	yes	—
30	C₂×#3935	C₄	1	2	yes	—
31	C₂×C₄×#168	C₂²	1	2	yes	—
32	#64700	C₂²	1	8	yes	complemented
33	#64699	C₂²	1	8	yes	complemented
34	#17796	—	5	1	no	maximal, Sylow
35	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₅	Q₈	1	1	yes	characteristic
38	C₂×C₅×M₁₆	—	2	1	no	—
39	C₂×C₅×M₁₆	—	2	1	no	—
40	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
45	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
46	C₂×C₄²×C₅	Q₈	1	1	yes	characteristic
47	C₂×C₄²×C₅	Q₈	1	1	yes	characteristic
48	C₂×C₄²×C₅	Q₈	1	1	yes	characteristic
49	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
50	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
51	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
52	C₂×#681	—	2	8	no	—
53	C₂×#681	—	2	2	no	—
54	C₂×#681	—	2	2	no	—
55	C₂×#681	—	4	4	no	—
56	C₂×#681	C₂×C₄	1	2	yes	—
57	C₂×#681	C₂×C₄	1	4	yes	—
58	C₂×#681	C₂×C₄	1	2	yes	—
59	C₂²×#168	—	2	2	no	—
60	C₂²×#168	C₂×C₄	1	4	yes	—
61	C₅×C₄⋊C₈	—	2	1	no	—
62	C₅×C₄⋊C₈	—	2	1	no	—
63	C₅×C₄⋊C₈	C₂³	1	2	yes	—
64	C₅×C₄⋊C₈	C₂³	1	2	yes	—
65	C₅×C₂²⋊C₈	—	2	2	no	—
66	C₅×C₂²⋊C₈	—	2	2	no	—
67	C₅×#97	—	2	2	no	—
68	C₄×C₅×C₈	—	2	2	no	—
69	C₄⋊#168	—	2	2	no	—
70	C₄⋊#168	—	2	2	no	—
71	C₄⋊#168	—	2	2	no	—
72	C₄⋊#168	C₂³	1	4	yes	—
73	#3935	C₂×C₄	1	2	yes	—
74	#3935	C₂×C₄	1	4	yes	—
75	#3935	C₂×C₄	1	2	yes	—
76	C₄×#168	C₂×C₄	1	2	yes	—
77	C₄×#168	C₂×C₄	1	2	yes	—
78	C₄×#168	C₂³	1	4	yes	—
79	#2920	D₅	1	1	yes	characteristic
80	C₂×#423	—	5	1	no	—
81	C₂×C₄×M₁₆	—	5	1	no	—
82	#1569	—	5	4	no	—
83	#1567	—	5	2	no	—
84	#1566	—	5	2	no	—
85	#1565	—	5	4	no	—
86	C₂⁴×C₅	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₅	—	2	4	no	—
88	C₂²×C₄×C₅	—	2	2	no	—
89	C₂²×C₄×C₅	—	2	2	no	—
90	C₂²×C₄×C₅	—	4	2	no	—
91	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
93	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
94	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
95	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
96	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
97	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
98	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
99	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
100	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
107	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
108	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
109	C₅×M₁₆	—	4	2	no	—
110	C₅×M₁₆	—	4	2	no	—
111	C₂×C₅×C₈	—	2	2	no	—
112	C₂×C₅×C₈	—	2	2	no	—
113	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
114	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
115	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
116	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
117	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
118	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
119	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
120	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
122	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
124	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
126	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
127	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
128	C₄²×C₅	C₂⁴	1	1	yes	characteristic
129	#681	—	2	4	no	—
130	#681	—	2	8	no	—
131	#681	—	4	4	no	—
132	#681	—	4	4	no	—
133	#681	M₁₆	1	8	yes	complemented
134	C₂×#168	—	2	8	no	—
135	C₂×#168	—	2	4	no	—
136	C₂×#168	—	4	4	no	—
137	C₂×#168	C₂²×C₄	1	4	yes	—
138	C₂×#168	C₂²×C₄	1	4	yes	—
139	C₂²×M₁₆	—	5	2	no	—
140	C₂²×M₁₆	—	10	1	no	—
141	C₂²×C₄²	C₂×D₅	1	1	yes	characteristic
142	#432	—	2	1	no	—
143	#432	C₂×D₅	1	2	yes	—
144	#431	—	2	1	no	—
145	#431	C₂×D₅	1	2	yes	—
146	#423	—	5	2	no	—
147	#423	—	5	2	no	—
148	#423	—	10	1	no	—
149	#423	—	10	1	no	—
150	#423	C₂×D₅	1	1	yes	characteristic
151	#423	C₂×D₅	1	1	yes	characteristic
152	C₂×C₄⋊C₈	—	5	2	no	—
153	C₂×C₄⋊C₈	—	10	1	no	—
154	#407	—	2	1	no	—
155	C₄×M₁₆	—	2	1	no	—
156	C₄×M₁₆	—	5	1	no	—
157	C₄×M₁₆	—	5	2	no	—
158	C₄×M₁₆	—	5	1	no	—
159	C₄×M₁₆	—	5	2	no	—
160	C₄×M₁₆	—	5	2	no	—
161	C₂×#97	—	5	2	no	—
162	C₂×C₄×C₈	—	5	2	no	—
163	#335	—	5	8	no	—
164	#334	—	5	8	no	—
165	C₂³×C₅	—	2	2	no	—
166	C₂³×C₅	—	2	2	no	—
167	C₂³×C₅	—	4	1	no	—
168	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₅	—	2	2	no	—
172	C₂×C₄×C₅	—	2	2	no	—
173	C₂×C₄×C₅	—	2	2	no	—
174	C₂×C₄×C₅	—	2	2	no	—
175	C₂×C₄×C₅	—	2	1	no	—
176	C₂×C₄×C₅	—	2	1	no	—
177	C₂×C₄×C₅	—	2	1	no	—
178	C₂×C₄×C₅	—	2	1	no	—
179	C₂×C₄×C₅	—	2	2	no	—
180	C₂×C₄×C₅	—	2	2	no	—
181	C₂×C₄×C₅	—	2	2	no	—
182	C₂×C₄×C₅	—	2	2	no	—
183	C₂×C₄×C₅	—	2	2	no	—
184	C₂×C₄×C₅	—	2	2	no	—
185	C₂×C₄×C₅	—	2	2	no	—
186	C₂×C₄×C₅	—	4	1	no	—
187	C₂×C₄×C₅	—	4	1	no	—
188	C₂×C₄×C₅	—	4	1	no	—
189	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
191	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
192	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
193	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
194	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
195	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
196	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
197	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
198	C₂×C₄×C₅	C₂×M₁₆	1	4	yes	—
199	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
200	C₂×C₄×C₅	#137	1	2	yes	—
201	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
202	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
204	C₅×C₈	—	4	2	no	—
205	C₅×C₈	—	4	2	no	—
206	#168	—	2	4	no	—
207	#168	—	4	4	no	—
208	#168	C₂×M₁₆	1	8	yes	complemented
209	C₂³×C₄	Dic₁₀	1	1	yes	characteristic
210	C₂³×C₄	C₄×D₅	1	1	yes	characteristic
211	C₂³×C₄	C₂²⋊D₅	1	1	yes	characteristic
212	C₂×M₁₆	—	2	1	no	—
213	C₂×M₁₆	—	2	1	no	—
214	C₂×M₁₆	—	5	2	no	—
215	C₂×M₁₆	—	5	4	no	—
216	C₂×M₁₆	—	5	2	no	—
217	C₂×M₁₆	—	10	8	no	—
218	C₂×M₁₆	—	10	2	no	—
219	C₂×M₁₆	—	10	2	no	—
220	C₂×M₁₆	—	20	4	no	—
221	C₂²×C₈	—	5	4	no	—
222	C₂²×C₈	—	10	2	no	—
223	C₂×C₄²	Dic₁₀	1	1	yes	characteristic
224	C₂×C₄²	Dic₁₀	1	1	yes	characteristic
225	C₂×C₄²	Dic₁₀	1	1	yes	characteristic
226	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
227	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
228	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
229	C₂×C₄²	C₂²⋊D₅	1	1	yes	characteristic
230	C₂×C₄²	C₂²⋊D₅	1	1	yes	characteristic
231	C₂×C₄²	C₂²⋊D₅	1	1	yes	characteristic
232	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
233	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
234	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
235	C₄⋊C₈	—	2	1	no	—
236	C₄⋊C₈	—	2	1	no	—
237	C₄⋊C₈	—	5	4	no	—
238	C₄⋊C₈	—	10	2	no	—
239	C₄⋊C₈	—	10	2	no	—
240	C₄⋊C₈	—	10	2	no	—
241	C₄⋊C₈	C₂²×D₅	1	2	yes	—
242	C₄⋊C₈	C₂²×D₅	1	2	yes	—
243	C₂²⋊C₈	—	2	2	no	—
244	C₂²⋊C₈	—	2	2	no	—
245	#97	—	2	2	no	—
246	#97	—	5	2	no	—
247	#97	—	5	4	no	—
248	#97	—	5	2	no	—
249	C₄×C₈	—	2	2	no	—
250	C₄×C₈	—	5	2	no	—
251	C₄×C₈	—	5	2	no	—
252	C₄×C₈	—	5	4	no	—
253	C₂²×C₅	—	2	1	no	—
254	C₂²×C₅	—	2	1	no	—
255	C₂²×C₅	—	2	1	no	—
256	C₂²×C₅	—	2	1	no	—
257	C₂²×C₅	—	2	1	no	—
258	C₂²×C₅	—	2	1	no	—
259	C₂²×C₅	—	2	1	no	—
260	C₂²×C₅	—	4	4	no	—
261	C₂²×C₅	#423	1	2	yes	—
262	C₂²×C₅	#428	1	2	yes	—
263	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
264	C₄×C₅	—	2	1	no	—
265	C₄×C₅	—	2	1	no	—
266	C₄×C₅	—	2	1	no	—
267	C₄×C₅	—	2	1	no	—
268	C₄×C₅	—	2	1	no	—
269	C₄×C₅	—	2	1	no	—
270	C₄×C₅	—	2	1	no	—
271	C₄×C₅	#423	1	2	yes	—
272	C₄×C₅	#428	1	2	yes	—
273	C₄×C₅	#430	1	2	yes	—
274	C₄×C₅	C₂²×M₁₆	1	2	yes	—
275	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
276	C₄×C₅	C₂×#137	1	1	yes	characteristic
277	C₂⁴	#683	1	1	yes	characteristic
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	4	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	4	2	no	—
282	C₂²×C₄	#683	1	1	yes	characteristic
283	C₂²×C₄	#683	1	1	yes	characteristic
284	C₂²×C₄	#683	1	1	yes	characteristic
285	C₂²×C₄	#683	1	1	yes	characteristic
286	C₂²×C₄	#683	1	1	yes	characteristic
287	C₂²×C₄	#683	1	1	yes	characteristic
288	C₂²×C₄	#683	1	1	yes	characteristic
289	C₂²×C₄	#683	1	1	yes	characteristic
290	C₂²×C₄	#683	1	1	yes	characteristic
291	C₂²×C₄	C₂×Dic₁₀	1	1	yes	characteristic
292	C₂²×C₄	C₂×Dic₁₀	1	1	yes	characteristic
293	C₂²×C₄	C₂×Dic₁₀	1	1	yes	characteristic
294	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
295	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
296	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
297	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
298	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
299	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
300	M₁₆	—	4	2	no	—
301	M₁₆	—	4	2	no	—
302	M₁₆	—	5	8	no	—
303	M₁₆	—	10	8	no	—
304	M₁₆	—	10	4	no	—
305	M₁₆	—	20	4	no	—
306	M₁₆	—	20	4	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	5	4	no	—
310	C₂×C₈	—	5	4	no	—
311	C₂×C₈	—	10	8	no	—
312	C₂×C₈	—	10	4	no	—
313	C₂×C₈	—	20	4	no	—
314	C₄²	#683	1	1	yes	characteristic
315	C₄²	#683	1	1	yes	characteristic
316	C₄²	#683	1	1	yes	characteristic
317	C₄²	#683	1	1	yes	characteristic
318	C₄²	#683	1	1	yes	characteristic
319	C₄²	#683	1	1	yes	characteristic
320	C₄²	C₂×Dic₁₀	1	1	yes	characteristic
321	C₄²	C₂×Dic₁₀	1	1	yes	characteristic
322	C₄²	C₂×Dic₁₀	1	1	yes	characteristic
323	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
324	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
325	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
326	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
327	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
328	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
329	C₄²	C₂³×D₅	1	1	yes	characteristic
330	C₂×C₅	—	2	2	no	—
331	C₂×C₅	—	2	2	no	—
332	C₂×C₅	—	4	1	no	—
333	C₂×C₅	C₂×#423	1	1	yes	characteristic
334	C₂×C₅	C₂×#428	1	1	yes	characteristic
335	C₂×C₅	C₂×#430	1	1	yes	characteristic
336	C₂³	—	2	2	no	—
337	C₂³	—	2	2	no	—
338	C₂³	—	4	1	no	—
339	C₂³	C₂×#683	1	1	yes	characteristic
340	C₂³	C₂×#683	1	1	yes	characteristic
341	C₂³	C₂×#683	1	1	yes	characteristic
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	D₅×M₁₆	1	4	yes	—
361	C₂×C₄	C₂×#683	1	1	yes	characteristic
362	C₂×C₄	C₂×#683	1	1	yes	characteristic
363	C₂×C₄	C₂×#683	1	1	yes	characteristic
364	C₂×C₄	C₂×#683	1	1	yes	characteristic
365	C₂×C₄	C₂×#683	1	1	yes	characteristic
366	C₂×C₄	C₂×#683	1	1	yes	characteristic
367	C₂×C₄	C₂×#683	1	1	yes	characteristic
368	C₂×C₄	C₂×#683	1	1	yes	characteristic
369	C₂×C₄	C₂×#683	1	1	yes	characteristic
370	C₂×C₄	#4095	1	2	yes	—
371	C₂×C₄	#4097	1	2	yes	—
372	C₂×C₄	C₂²×Dic₁₀	1	1	yes	characteristic
373	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
374	C₂×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
375	C₈	—	4	2	no	—
376	C₈	—	4	2	no	—
377	C₈	—	5	8	no	—
378	C₈	—	10	4	no	—
379	C₈	—	20	4	no	—
380	C₅	#17796	1	1	yes	characteristic, complemented, Sylow
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	4	4	no	—
389	C₂²	#65284	1	2	yes	—
390	C₂²	#65407	1	2	yes	—
391	C₂²	C₂²×#683	1	1	yes	characteristic
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	2	1	no	—
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	1	no	—
399	C₄	#65284	1	2	yes	—
400	C₄	#65407	1	2	yes	—
401	C₄	#65413	1	2	yes	—
402	C₄	C₂×D₅×M₁₆	1	2	yes	—
403	C₄	C₂×#4095	1	1	yes	characteristic
404	C₄	C₂×#4097	1	1	yes	characteristic
405	C₂	—	2	2	no	—
406	C₂	—	2	2	no	—
407	C₂	—	4	1	no	—
408	C₂	C₂×#65284	1	1	yes	characteristic
409	C₂	C₂×#65407	1	1	yes	characteristic
410	C₂	C₂×#65413	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₅
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₄²	C₂³×D₅
Fitting	C₅×#2920	C₂
socle	C₂²×C₅	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₅	C₄⋊C₄
cosocle	C₄²×C₅	C₂⁴
hypercenter	#2920	D₅
hypocenter	C₅	#17796
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ #2920

Complements

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

N	H ≅ G/N	type
4. #10601588	C₂	semidirect
5. #10601539	C₂	semidirect
6. #10601284	C₂	semidirect
7. #10601283	C₂	semidirect
32. #64700	C₂²	semidirect
33. #64699	C₂²	semidirect
133. #681	M₁₆	semidirect
208. #168	C₂×M₁₆	semidirect
380. C₅	#17796	semidirect

Maximal subgroups

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

subgroup	index
C₅×#2920	2
C₂×#65213	2
C₂×C₄×#681	2
#10601588	2
#10601539	2
#10601284	2
#10601283	2
#17796	5