Subgroups — C₂²×C₅×#452 #11983072

Order 1280.

5110 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₅×#41	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#452	C₂	1	24	yes	maximal, direct product factor
6	C₂²×C₅×#103	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₅×#102	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₅×#41	—	2	8	no	—
10	C₂²×C₅×#41	—	2	8	no	—
11	C₂²×C₅×#41	—	2	6	no	—
12	C₂²×C₅×#41	C₂²	1	12	yes	—
13	C₂³×C₅×Q₈	C₂²	1	1	yes	characteristic
14	C₂³×C₅×Q₈	C₂²	1	1	yes	characteristic
15	C₂³×C₅×D₄	—	2	1	no	—
16	C₂³×C₅×D₄	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₅	—	2	1	no	—
18	C₂⁴×C₄×C₅	C₂²	1	1	yes	characteristic
19	C₂²×C₅×Q₁₆	—	2	8	no	—
20	C₂²×C₅×Q₁₆	C₂²	1	12	yes	complemented
21	C₂²×C₅×SD₁₆	—	2	8	no	—
22	C₂²×C₅×SD₁₆	C₂²	1	12	yes	complemented
23	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
24	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
25	C₂×C₅×C₂²⋊Q₈	—	2	6	no	—
26	C₂×C₅×C₂²⋊Q₈	C₂²	1	12	yes	complemented
27	C₂²×C₅×C₄⋊C₄	—	2	1	no	—
28	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂²×C₅×C₂²⋊C₄	—	2	1	no	—
30	C₅×#452	C₂²	1	64	yes	direct product factor
31	C₂×C₅×#103	C₂²	1	12	yes	complemented
32	C₂×C₅×#102	C₂²	1	12	yes	complemented
33	C₂×C₅×C₂²⋊C₈	C₂²	1	12	yes	complemented
34	C₂²×#452	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
35	C₂⁵×C₅	—	2	1	no	—
36	C₂⁵×C₅	D₄	1	1	yes	characteristic
37	C₂×C₅×#41	—	2	96	no	—
38	C₂×C₅×#41	—	2	48	no	—
39	C₂×C₅×#41	—	2	48	no	—
40	C₂×C₅×#41	—	2	24	no	—
41	C₂×C₅×#41	C₂³	1	16	yes	—
42	C₂²×C₅×Q₈	—	2	4	no	—
43	C₂²×C₅×Q₈	—	2	3	no	—
44	C₂²×C₅×Q₈	—	2	3	no	—
45	C₂²×C₅×Q₈	—	2	4	no	—
46	C₂²×C₅×Q₈	—	2	4	no	—
47	C₂²×C₅×Q₈	D₄	1	8	yes	—
48	C₂²×C₅×Q₈	C₂³	1	6	yes	—
49	C₂²×C₅×Q₈	C₂³	1	6	yes	—
50	C₂²×C₅×D₄	—	2	16	no	—
51	C₂²×C₅×D₄	—	2	12	no	—
52	C₂²×C₅×D₄	—	2	3	no	—
53	C₂²×C₅×D₄	—	2	4	no	—
54	C₂²×C₅×D₄	D₄	1	8	yes	—
55	C₂²×C₅×D₄	C₂³	1	6	yes	—
56	C₂³×C₄×C₅	—	2	16	no	—
57	C₂³×C₄×C₅	—	2	1	no	—
58	C₂³×C₄×C₅	—	2	12	no	—
59	C₂³×C₄×C₅	—	2	4	no	—
60	C₂³×C₄×C₅	—	2	4	no	—
61	C₂³×C₄×C₅	—	2	1	no	—
62	C₂³×C₄×C₅	—	2	1	no	—
63	C₂³×C₄×C₅	D₄	1	6	yes	—
64	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
65	C₂³×C₄×C₅	C₂³	1	6	yes	—
66	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
67	C₂×C₅×Q₁₆	—	2	48	no	—
68	C₂×C₅×Q₁₆	C₂³	1	16	yes	complemented
69	C₂×C₅×SD₁₆	—	2	48	no	—
70	C₂×C₅×SD₁₆	C₂³	1	16	yes	complemented
71	C₂²×C₅×C₈	—	2	4	no	—
72	C₂²×C₅×C₈	—	2	4	no	—
73	C₂²×C₅×C₈	C₂³	1	6	yes	—
74	C₂²×C₅×C₈	C₂³	1	6	yes	—
75	C₅×C₂²⋊Q₈	—	2	24	no	—
76	C₅×C₂²⋊Q₈	C₂³	1	16	yes	complemented
77	C₂×C₅×C₄⋊C₄	—	2	12	no	—
78	C₂×C₅×C₄⋊C₄	—	2	3	no	—
79	C₂×C₅×C₄⋊C₄	C₂³	1	6	yes	—
80	C₂×C₅×C₂²⋊C₄	—	2	12	no	—
81	C₅×#103	C₂³	1	16	yes	complemented
82	C₅×#102	C₂³	1	16	yes	complemented
83	C₅×C₂²⋊C₈	C₂³	1	16	yes	complemented
84	C₂³×#41	C₂×C₅	1	1	yes	characteristic
85	C₂³×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
86	C₂³×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
87	C₂²×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
88	C₂×#452	C₂×C₅	1	24	yes	direct product factor
89	C₂²×#103	C₂×C₅	1	1	yes	characteristic, complemented
90	C₂²×#102	C₂×C₅	1	1	yes	characteristic, complemented
91	C₂²×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
92	C₂⁴×C₅	—	2	4	no	—
93	C₂⁴×C₅	—	2	8	no	—
94	C₂⁴×C₅	—	2	4	no	—
95	C₂⁴×C₅	—	2	4	no	—
96	C₂⁴×C₅	—	2	6	no	—
97	C₂⁴×C₅	—	4	4	no	—
98	C₂⁴×C₅	—	4	4	no	—
99	C₂⁴×C₅	C₂×D₄	1	6	yes	—
100	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
101	C₅×#41	—	2	192	no	—
102	C₅×#41	—	2	32	no	—
103	C₅×#41	—	2	32	no	—
104	C₂×C₅×Q₈	—	2	24	no	—
105	C₂×C₅×Q₈	—	2	12	no	—
106	C₂×C₅×Q₈	—	2	6	no	—
107	C₂×C₅×Q₈	—	2	6	no	—
108	C₂×C₅×Q₈	—	2	12	no	—
109	C₂×C₅×Q₈	—	2	12	no	—
110	C₂×C₅×Q₈	—	4	12	no	—
111	C₂×C₅×Q₈	C₂×D₄	1	24	yes	—
112	C₂×C₅×Q₈	C₂⁴	1	4	yes	—
113	C₂×C₅×Q₈	C₂⁴	1	4	yes	—
114	C₂×C₅×D₄	—	2	96	no	—
115	C₂×C₅×D₄	—	2	16	no	—
116	C₂×C₅×D₄	—	2	24	no	—
117	C₂×C₅×D₄	—	2	6	no	—
118	C₂×C₅×D₄	—	2	12	no	—
119	C₂×C₅×D₄	C₂×D₄	1	24	yes	—
120	C₂×C₅×D₄	C₂⁴	1	4	yes	—
121	C₂²×C₄×C₅	—	2	96	no	—
122	C₂²×C₄×C₅	—	2	4	no	—
123	C₂²×C₄×C₅	—	2	8	no	—
124	C₂²×C₄×C₅	—	2	6	no	—
125	C₂²×C₄×C₅	—	2	24	no	—
126	C₂²×C₄×C₅	—	2	16	no	—
127	C₂²×C₄×C₅	—	2	12	no	—
128	C₂²×C₄×C₅	—	2	12	no	—
129	C₂²×C₄×C₅	—	2	6	no	—
130	C₂²×C₄×C₅	—	2	6	no	—
131	C₂²×C₄×C₅	—	4	4	no	—
132	C₂²×C₄×C₅	—	4	4	no	—
133	C₂²×C₄×C₅	C₂×D₄	1	6	yes	—
134	C₂²×C₄×C₅	C₂×D₄	1	12	yes	—
135	C₂²×C₄×C₅	C₂×D₄	1	3	yes	—
136	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
137	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
138	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
139	C₂²×C₄×C₅	C₂⁴	1	3	yes	—
140	C₅×Q₁₆	—	2	32	no	—
141	C₅×SD₁₆	—	2	32	no	—
142	C₂×C₅×C₈	—	2	12	no	—
143	C₂×C₅×C₈	—	2	12	no	—
144	C₂×C₅×C₈	C₂⁴	1	4	yes	—
145	C₂×C₅×C₈	C₂⁴	1	4	yes	—
146	C₅×C₄⋊C₄	—	2	16	no	—
147	C₅×C₄⋊C₄	—	2	6	no	—
148	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
149	C₅×C₂²⋊C₄	—	2	16	no	—
150	C₂²×#41	—	2	8	no	—
151	C₂²×#41	—	2	8	no	—
152	C₂²×#41	—	2	6	no	—
153	C₂²×#41	C₂²×C₅	1	12	yes	—
154	C₂³×Q₈	C₂²×C₅	1	1	yes	characteristic
155	C₂³×Q₈	C₂²×C₅	1	1	yes	characteristic
156	C₂³×D₄	—	2	1	no	—
157	C₂³×D₄	C₂²×C₅	1	1	yes	characteristic
158	C₂⁴×C₄	—	2	1	no	—
159	C₂⁴×C₄	C₂²×C₅	1	1	yes	characteristic
160	C₂²×Q₁₆	—	2	8	no	—
161	C₂²×Q₁₆	C₂²×C₅	1	12	yes	complemented
162	C₂²×SD₁₆	—	2	8	no	—
163	C₂²×SD₁₆	C₂²×C₅	1	12	yes	complemented
164	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
165	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
166	C₂×C₂²⋊Q₈	—	2	6	no	—
167	C₂×C₂²⋊Q₈	C₂²×C₅	1	12	yes	complemented
168	C₂²×C₄⋊C₄	—	2	1	no	—
169	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
170	C₂²×C₂²⋊C₄	—	2	1	no	—
171	#452	C₂²×C₅	1	64	yes	direct product factor
172	C₂×#103	C₂²×C₅	1	12	yes	complemented
173	C₂×#102	C₂²×C₅	1	12	yes	complemented
174	C₂×C₂²⋊C₈	C₂²×C₅	1	12	yes	complemented
175	C₂³×C₅	—	2	12	no	—
176	C₂³×C₅	—	2	24	no	—
177	C₂³×C₅	—	2	12	no	—
178	C₂³×C₅	—	2	12	no	—
179	C₂³×C₅	—	2	4	no	—
180	C₂³×C₅	—	4	12	no	—
181	C₂³×C₅	—	4	12	no	—
182	C₂³×C₅	—	4	16	no	—
183	C₂³×C₅	—	4	32	no	—
184	C₂³×C₅	#120	1	4	yes	—
185	C₂³×C₅	#135	1	4	yes	—
186	C₂³×C₅	#137	1	4	yes	—
187	C₂³×C₅	C₂²×D₄	1	4	yes	—
188	C₂³×C₅	C₂²×D₄	1	3	yes	—
189	C₅×Q₈	—	2	24	no	—
190	C₅×Q₈	—	2	4	no	—
191	C₅×Q₈	—	2	4	no	—
192	C₅×Q₈	—	2	4	no	—
193	C₅×Q₈	—	4	12	no	—
194	C₅×Q₈	C₂²×D₄	1	8	yes	—
195	C₅×D₄	—	2	64	no	—
196	C₅×D₄	—	2	24	no	—
197	C₅×D₄	—	2	4	no	—
198	C₅×D₄	C₂²×D₄	1	8	yes	—
199	C₂×C₄×C₅	—	2	64	no	—
200	C₂×C₄×C₅	—	2	12	no	—
201	C₂×C₄×C₅	—	2	24	no	—
202	C₂×C₄×C₅	—	2	4	no	—
203	C₂×C₄×C₅	—	2	24	no	—
204	C₂×C₄×C₅	—	2	4	no	—
205	C₂×C₄×C₅	—	2	4	no	—
206	C₂×C₄×C₅	—	2	4	no	—
207	C₂×C₄×C₅	—	2	4	no	—
208	C₂×C₄×C₅	—	4	12	no	—
209	C₂×C₄×C₅	—	4	12	no	—
210	C₂×C₄×C₅	#120	1	12	yes	—
211	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
212	C₂×C₄×C₅	C₂²×D₄	1	3	yes	—
213	C₂×C₄×C₅	C₂²×D₄	1	6	yes	—
214	C₂×C₄×C₅	C₂²×D₄	1	6	yes	—
215	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
216	C₅×C₈	—	2	4	no	—
217	C₅×C₈	—	2	4	no	—
218	C₂⁵	—	2	1	no	—
219	C₂⁵	C₅×D₄	1	1	yes	characteristic
220	C₂×#41	—	2	96	no	—
221	C₂×#41	—	2	48	no	—
222	C₂×#41	—	2	48	no	—
223	C₂×#41	—	2	24	no	—
224	C₂×#41	C₂³×C₅	1	16	yes	—
225	C₂²×Q₈	—	2	4	no	—
226	C₂²×Q₈	—	2	3	no	—
227	C₂²×Q₈	—	2	3	no	—
228	C₂²×Q₈	—	2	4	no	—
229	C₂²×Q₈	—	2	4	no	—
230	C₂²×Q₈	C₅×D₄	1	8	yes	—
231	C₂²×Q₈	C₂³×C₅	1	6	yes	—
232	C₂²×Q₈	C₂³×C₅	1	6	yes	—
233	C₂²×D₄	—	2	16	no	—
234	C₂²×D₄	—	2	12	no	—
235	C₂²×D₄	—	2	3	no	—
236	C₂²×D₄	—	2	4	no	—
237	C₂²×D₄	C₅×D₄	1	8	yes	—
238	C₂²×D₄	C₂³×C₅	1	6	yes	—
239	C₂³×C₄	—	2	16	no	—
240	C₂³×C₄	—	2	1	no	—
241	C₂³×C₄	—	2	12	no	—
242	C₂³×C₄	—	2	4	no	—
243	C₂³×C₄	—	2	4	no	—
244	C₂³×C₄	—	2	1	no	—
245	C₂³×C₄	—	2	1	no	—
246	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
247	C₂³×C₄	C₅×D₄	1	6	yes	—
248	C₂³×C₄	C₂³×C₅	1	6	yes	—
249	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
250	C₂×Q₁₆	—	2	48	no	—
251	C₂×Q₁₆	C₂³×C₅	1	16	yes	complemented
252	C₂×SD₁₆	—	2	48	no	—
253	C₂×SD₁₆	C₂³×C₅	1	16	yes	complemented
254	C₂²×C₈	—	2	4	no	—
255	C₂²×C₈	—	2	4	no	—
256	C₂²×C₈	C₂³×C₅	1	6	yes	—
257	C₂²×C₈	C₂³×C₅	1	6	yes	—
258	C₂²⋊Q₈	—	2	24	no	—
259	C₂²⋊Q₈	C₂³×C₅	1	16	yes	complemented
260	C₂×C₄⋊C₄	—	2	12	no	—
261	C₂×C₄⋊C₄	—	2	3	no	—
262	C₂×C₄⋊C₄	C₂³×C₅	1	6	yes	—
263	C₂×C₂²⋊C₄	—	2	12	no	—
264	#103	C₂³×C₅	1	16	yes	complemented
265	#102	C₂³×C₅	1	16	yes	complemented
266	C₂²⋊C₈	C₂³×C₅	1	16	yes	complemented
267	C₂²×C₅	—	2	4	no	—
268	C₂²×C₅	—	2	8	no	—
269	C₂²×C₅	—	2	4	no	—
270	C₂²×C₅	—	2	4	no	—
271	C₂²×C₅	—	4	24	no	—
272	C₂²×C₅	—	4	48	no	—
273	C₂²×C₅	—	4	4	no	—
274	C₂²×C₅	—	4	4	no	—
275	C₂²×C₅	#452	1	16	yes	direct product factor
276	C₂²×C₅	C₂×#120	1	6	yes	—
277	C₂²×C₅	C₂×#135	1	6	yes	—
278	C₂²×C₅	C₂×#137	1	6	yes	—
279	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
280	C₄×C₅	—	2	4	no	—
281	C₄×C₅	—	2	8	no	—
282	C₄×C₅	—	4	4	no	—
283	C₄×C₅	—	4	4	no	—
284	C₄×C₅	C₂×#120	1	6	yes	—
285	C₄×C₅	C₂³×D₄	1	1	yes	characteristic
286	C₄×C₅	C₂³×D₄	1	1	yes	characteristic
287	C₂⁴	—	2	4	no	—
288	C₂⁴	—	2	8	no	—
289	C₂⁴	—	2	4	no	—
290	C₂⁴	—	2	4	no	—
291	C₂⁴	—	2	6	no	—
292	C₂⁴	—	4	4	no	—
293	C₂⁴	—	4	4	no	—
294	C₂⁴	C₂×C₅×D₄	1	6	yes	—
295	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
296	#41	—	2	192	no	—
297	#41	—	2	32	no	—
298	#41	—	2	32	no	—
299	C₂×Q₈	—	2	24	no	—
300	C₂×Q₈	—	2	12	no	—
301	C₂×Q₈	—	2	6	no	—
302	C₂×Q₈	—	2	6	no	—
303	C₂×Q₈	—	2	12	no	—
304	C₂×Q₈	—	2	12	no	—
305	C₂×Q₈	—	4	12	no	—
306	C₂×Q₈	C₂×C₅×D₄	1	24	yes	—
307	C₂×Q₈	C₂⁴×C₅	1	4	yes	—
308	C₂×Q₈	C₂⁴×C₅	1	4	yes	—
309	C₂×D₄	—	2	96	no	—
310	C₂×D₄	—	2	16	no	—
311	C₂×D₄	—	2	24	no	—
312	C₂×D₄	—	2	6	no	—
313	C₂×D₄	—	2	12	no	—
314	C₂×D₄	C₂×C₅×D₄	1	24	yes	—
315	C₂×D₄	C₂⁴×C₅	1	4	yes	—
316	C₂²×C₄	—	2	96	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	8	no	—
319	C₂²×C₄	—	2	6	no	—
320	C₂²×C₄	—	2	24	no	—
321	C₂²×C₄	—	2	16	no	—
322	C₂²×C₄	—	2	12	no	—
323	C₂²×C₄	—	2	12	no	—
324	C₂²×C₄	—	2	6	no	—
325	C₂²×C₄	—	2	6	no	—
326	C₂²×C₄	—	4	4	no	—
327	C₂²×C₄	—	4	4	no	—
328	C₂²×C₄	C₂×C₅×D₄	1	6	yes	—
329	C₂²×C₄	C₂×C₅×D₄	1	12	yes	—
330	C₂²×C₄	C₂×C₅×D₄	1	3	yes	—
331	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
332	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
333	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
334	C₂²×C₄	C₂⁴×C₅	1	3	yes	—
335	Q₁₆	—	2	32	no	—
336	SD₁₆	—	2	32	no	—
337	C₂×C₈	—	2	12	no	—
338	C₂×C₈	—	2	12	no	—
339	C₂×C₈	C₂⁴×C₅	1	4	yes	—
340	C₂×C₈	C₂⁴×C₅	1	4	yes	—
341	C₄⋊C₄	—	2	16	no	—
342	C₄⋊C₄	—	2	6	no	—
343	C₄⋊C₄	C₂⁴×C₅	1	4	yes	—
344	C₂²⋊C₄	—	2	16	no	—
345	C₂×C₅	—	4	4	no	—
346	C₂×C₅	—	4	8	no	—
347	C₂×C₅	C₂×#452	1	12	yes	direct product factor
348	C₂×C₅	C₂²×#120	1	1	yes	characteristic
349	C₂×C₅	C₂²×#135	1	1	yes	characteristic
350	C₂×C₅	C₂²×#137	1	1	yes	characteristic
351	C₂³	—	2	12	no	—
352	C₂³	—	2	24	no	—
353	C₂³	—	2	12	no	—
354	C₂³	—	2	12	no	—
355	C₂³	—	2	4	no	—
356	C₂³	—	4	16	no	—
357	C₂³	—	4	32	no	—
358	C₂³	—	4	12	no	—
359	C₂³	—	4	12	no	—
360	C₂³	C₅×#120	1	4	yes	—
361	C₂³	C₅×#135	1	4	yes	—
362	C₂³	C₅×#137	1	4	yes	—
363	C₂³	C₂²×C₅×D₄	1	4	yes	—
364	C₂³	C₂²×C₅×D₄	1	3	yes	—
365	Q₈	—	2	24	no	—
366	Q₈	—	2	4	no	—
367	Q₈	—	2	4	no	—
368	Q₈	—	2	4	no	—
369	Q₈	—	4	12	no	—
370	Q₈	C₂²×C₅×D₄	1	8	yes	—
371	D₄	—	2	64	no	—
372	D₄	—	2	24	no	—
373	D₄	—	2	4	no	—
374	D₄	C₂²×C₅×D₄	1	8	yes	—
375	C₂×C₄	—	2	64	no	—
376	C₂×C₄	—	2	12	no	—
377	C₂×C₄	—	2	24	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	24	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	4	12	no	—
385	C₂×C₄	—	4	12	no	—
386	C₂×C₄	C₅×#120	1	12	yes	—
387	C₂×C₄	C₂²×C₅×D₄	1	4	yes	—
388	C₂×C₄	C₂²×C₅×D₄	1	3	yes	—
389	C₂×C₄	C₂²×C₅×D₄	1	6	yes	—
390	C₂×C₄	C₂²×C₅×D₄	1	6	yes	—
391	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
392	C₈	—	2	4	no	—
393	C₈	—	2	4	no	—
394	C₅	C₂²×#452	1	1	yes	characteristic, direct product factor, Sylow
395	C₂²	—	2	4	no	—
396	C₂²	—	2	8	no	—
397	C₂²	—	2	4	no	—
398	C₂²	—	2	4	no	—
399	C₂²	—	4	24	no	—
400	C₂²	—	4	48	no	—
401	C₂²	—	4	4	no	—
402	C₂²	—	4	4	no	—
403	C₂²	C₅×#452	1	16	yes	direct product factor
404	C₂²	C₂×C₅×#120	1	6	yes	—
405	C₂²	C₂×C₅×#135	1	6	yes	—
406	C₂²	C₂×C₅×#137	1	6	yes	—
407	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
408	C₄	—	2	4	no	—
409	C₄	—	2	8	no	—
410	C₄	—	4	4	no	—
411	C₄	—	4	4	no	—
412	C₄	C₂×C₅×#120	1	6	yes	—
413	C₄	C₂³×C₅×D₄	1	1	yes	characteristic
414	C₄	C₂³×C₅×D₄	1	1	yes	characteristic
415	C₂	—	4	4	no	—
416	C₂	—	4	8	no	—
417	C₂	C₂×C₅×#452	1	12	yes	direct product factor
418	C₂	C₂²×C₅×#120	1	1	yes	characteristic
419	C₂	C₂²×C₅×#135	1	1	yes	characteristic
420	C₂	C₂²×C₅×#137	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅
prime radical	C₂³×C₅×#41	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₅ ◁ C₂⁴×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂³×C₅×Q₁₆	C₂	semidirect
3. C₂³×C₅×SD₁₆	C₂	semidirect
4. C₂²×C₅×C₂²⋊Q₈	C₂	semidirect
5. C₂×C₅×#452	C₂	direct (N × H)
6. C₂²×C₅×#103	C₂	semidirect
7. C₂²×C₅×#102	C₂	semidirect
8. C₂²×C₅×C₂²⋊C₈	C₂	semidirect
20. C₂²×C₅×Q₁₆	C₂²	semidirect
22. C₂²×C₅×SD₁₆	C₂²	semidirect
26. C₂×C₅×C₂²⋊Q₈	C₂²	semidirect
30. C₅×#452	C₂²	direct (N × H)
31. C₂×C₅×#103	C₂²	semidirect
32. C₂×C₅×#102	C₂²	semidirect
33. C₂×C₅×C₂²⋊C₈	C₂²	semidirect
34. C₂²×#452	C₅	direct (N × H)
68. C₂×C₅×Q₁₆	C₂³	semidirect
70. C₂×C₅×SD₁₆	C₂³	semidirect
76. C₅×C₂²⋊Q₈	C₂³	semidirect
81. C₅×#103	C₂³	semidirect
82. C₅×#102	C₂³	semidirect
83. C₅×C₂²⋊C₈	C₂³	semidirect
85. C₂³×Q₁₆	C₂×C₅	semidirect
86. C₂³×SD₁₆	C₂×C₅	semidirect
87. C₂²×C₂²⋊Q₈	C₂×C₅	semidirect
88. C₂×#452	C₂×C₅	direct (N × H)
89. C₂²×#103	C₂×C₅	semidirect
90. C₂²×#102	C₂×C₅	semidirect
91. C₂²×C₂²⋊C₈	C₂×C₅	semidirect
161. C₂²×Q₁₆	C₂²×C₅	semidirect
163. C₂²×SD₁₆	C₂²×C₅	semidirect
167. C₂×C₂²⋊Q₈	C₂²×C₅	semidirect
171. #452	C₂²×C₅	direct (N × H)
172. C₂×#103	C₂²×C₅	semidirect
173. C₂×#102	C₂²×C₅	semidirect
174. C₂×C₂²⋊C₈	C₂²×C₅	semidirect
251. C₂×Q₁₆	C₂³×C₅	semidirect
253. C₂×SD₁₆	C₂³×C₅	semidirect
259. C₂²⋊Q₈	C₂³×C₅	semidirect
264. #103	C₂³×C₅	semidirect
265. #102	C₂³×C₅	semidirect
266. C₂²⋊C₈	C₂³×C₅	semidirect
275. C₂²×C₅	#452	direct (N × H)
347. C₂×C₅	C₂×#452	direct (N × H)
394. C₅	C₂²×#452	direct (N × H)
403. C₂²	C₅×#452	direct (N × H)
417. C₂	C₂×C₅×#452	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₅×#41	2
C₂³×C₅×Q₁₆	2
C₂³×C₅×SD₁₆	2
C₂²×C₅×C₂²⋊Q₈	2
C₂×C₅×#452	2
C₂²×C₅×#103	2
C₂²×C₅×#102	2
C₂²×C₅×C₂²⋊C₈	2
C₂²×#452	5

Subgroups — C22×C5×#452 #11983072

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₅×#452 #11983072