Subgroups — C₂²×D₄×D₅₂ #16769830

Order 3328.

20038 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₅₂	C₂	1	2	yes	maximal, complemented
2	C₂³×D₄×D₁₃	C₂	1	2	yes	maximal, complemented
3	C₂×D₄×D₅₂	C₂	1	48	yes	maximal, direct product factor
4	C₂²×#88128	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#88149	C₂	1	2	yes	maximal, complemented
6	C₂²×#88184	C₂	1	2	yes	maximal, complemented
7	C₂²×#88136	C₂	1	4	yes	maximal, complemented
8	C₂²×C₄×D₅₂	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂⁵×D₁₃	C₂²	1	4	yes	complemented
11	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	complemented
13	C₂³×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
14	C₂²×D₄×D₁₃	—	2	32	no	—
15	C₂²×D₄×D₁₃	C₂²	1	48	yes	complemented
16	C₂³×D₅₂	—	2	32	no	—
17	C₂³×D₅₂	C₂²	1	1	yes	characteristic
18	C₂³×D₅₂	C₂²	1	48	yes	complemented
19	C₂³×D₅₂	C₂²	1	4	yes	complemented
20	C₂³×D₅₂	C₂²	1	2	yes	complemented
21	C₂³×D₅₂	C₂²	1	2	yes	complemented
22	C₂³×D₅₂	C₂²	1	2	yes	complemented
23	C₂³×C₄×D₁₃	C₂²	1	2	yes	complemented
24	C₂×C₄×D₄×C₁₃	C₂²	1	24	yes	complemented
25	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
27	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
28	C₂×#88184	C₂²	1	48	yes	complemented
29	C₂²×#6103	C₂²	1	2	yes	complemented
30	C₂²×#6103	C₂²	1	4	yes	complemented
31	C₂²×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic, complemented
32	D₄×D₅₂	C₂²	1	256	yes	direct product factor
33	C₂×#88149	C₂²	1	48	yes	complemented
34	C₂×#88136	C₂²	1	96	yes	complemented
35	C₂×#88128	C₂²	1	24	yes	complemented
36	C₂×C₄×D₅₂	C₂²	1	24	yes	complemented
37	C₂⁵×C₁₃	C₂³	1	2	yes	—
38	C₂⁴×D₁₃	—	2	32	no	—
39	C₂⁴×D₁₃	—	2	32	no	—
40	C₂⁴×D₁₃	—	4	16	no	—
41	C₂⁴×D₁₃	C₂³	1	4	yes	—
42	C₂⁴×D₁₃	C₂³	1	2	yes	—
43	C₂⁴×D₁₃	C₂³	1	48	yes	complemented
44	C₂²×D₄×C₁₃	D₄	1	16	yes	complemented
45	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
46	C₂³×C₄×C₁₃	—	2	16	no	—
47	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
49	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₃	C₂³	1	24	yes	complemented
52	C₂²×C₂²⋊D₁₃	—	2	32	no	—
53	C₂²×C₂²⋊D₁₃	C₂³	1	48	yes	complemented
54	C₂³×Dic₁₃	C₂³	1	2	yes	—
55	C₂×D₄×D₁₃	—	2	384	no	—
56	C₂×D₄×D₁₃	C₂³	1	128	yes	complemented
57	C₂²×D₅₂	—	2	32	no	—
58	C₂²×D₅₂	—	2	16	no	—
59	C₂²×D₅₂	—	2	16	no	—
60	C₂²×D₅₂	—	2	384	no	—
61	C₂²×D₅₂	—	4	8	no	—
62	C₂²×D₅₂	D₄	1	16	yes	direct product factor
63	C₂²×D₅₂	C₂³	1	12	yes	—
64	C₂²×D₅₂	C₂³	1	128	yes	complemented
65	C₂²×D₅₂	C₂³	1	24	yes	complemented
66	C₂²×D₅₂	C₂³	1	24	yes	complemented
67	C₂²×D₅₂	C₂³	1	48	yes	complemented
68	C₂²×D₅₂	C₂³	1	24	yes	complemented
69	C₂²×C₄×D₁₃	—	2	16	no	—
70	C₂²×C₄×D₁₃	C₂³	1	24	yes	complemented
71	C₄×D₄×C₁₃	C₂³	1	64	yes	complemented
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	complemented
73	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	complemented
74	C₂×C₄²×C₁₃	C₂³	1	12	yes	complemented
75	#88184	C₂³	1	128	yes	complemented
76	C₂×#6103	C₂³	1	24	yes	complemented
77	C₂×#6103	C₂³	1	48	yes	complemented
78	C₂×C₄⋊Dic₁₃	C₂³	1	12	yes	complemented
79	#88149	C₂³	1	128	yes	complemented
80	#88136	C₂³	1	256	yes	complemented
81	#88128	C₂³	1	64	yes	complemented
82	C₄×D₅₂	C₂³	1	64	yes	complemented
83	C₂²×D₄²	—	13	1	no	maximal, Sylow
84	C₂⁴×C₁₃	—	2	8	no	—
85	C₂⁴×C₁₃	—	2	8	no	—
86	C₂⁴×C₁₃	C₂×D₄	1	16	yes	complemented
87	C₂⁴×C₁₃	C₂⁴	1	12	yes	—
88	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
89	C₂³×D₁₃	—	2	8	no	—
90	C₂³×D₁₃	—	2	8	no	—
91	C₂³×D₁₃	—	2	16	no	—
92	C₂³×D₁₃	—	2	16	no	—
93	C₂³×D₁₃	—	2	192	no	—
94	C₂³×D₁₃	—	2	16	no	—
95	C₂³×D₁₃	—	2	192	no	—
96	C₂³×D₁₃	—	4	96	no	—
97	C₂³×D₁₃	—	4	256	no	—
98	C₂³×D₁₃	C₂×D₄	1	16	yes	complemented
99	C₂³×D₁₃	C₂⁴	1	24	yes	—
100	C₂³×D₁₃	C₂⁴	1	12	yes	—
101	C₂³×D₁₃	C₂⁴	1	64	yes	complemented
102	C₂×D₄×C₁₃	C₂×D₄	1	96	yes	complemented
103	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
104	C₂²×C₄×C₁₃	—	2	8	no	—
105	C₂²×C₄×C₁₃	—	2	4	no	—
106	C₂²×C₄×C₁₃	—	2	96	no	—
107	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	complemented
108	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	complemented
109	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
110	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
111	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
112	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
113	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	complemented
114	C₂×C₂²⋊D₁₃	—	2	192	no	—
115	C₂×C₂²⋊D₁₃	C₂⁴	1	64	yes	complemented
116	C₂²×Dic₁₃	—	2	8	no	—
117	C₂²×Dic₁₃	C₂⁴	1	12	yes	—
118	D₄×D₁₃	—	2	512	no	—
119	C₂×D₅₂	—	2	192	no	—
120	C₂×D₅₂	—	2	96	no	—
121	C₂×D₅₂	—	2	96	no	—
122	C₂×D₅₂	—	2	512	no	—
123	C₂×D₅₂	—	4	48	no	—
124	C₂×D₅₂	C₂×D₄	1	96	yes	direct product factor
125	C₂×D₅₂	C₂⁴	1	16	yes	—
126	C₂×D₅₂	C₂⁴	1	32	yes	complemented
127	C₂×D₅₂	C₂⁴	1	32	yes	complemented
128	C₂×D₅₂	C₂⁴	1	64	yes	complemented
129	C₂×D₅₂	C₂⁴	1	32	yes	complemented
130	C₂×C₄×D₁₃	—	2	96	no	—
131	C₂×C₄×D₁₃	C₂⁴	1	32	yes	complemented
132	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	complemented
133	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	complemented
134	C₄²×C₁₃	C₂⁴	1	16	yes	complemented
135	#6103	C₂⁴	1	32	yes	complemented
136	#6103	C₂⁴	1	64	yes	complemented
137	C₄⋊Dic₁₃	C₂⁴	1	16	yes	complemented
138	C₂⁴×D₄	—	13	2	no	—
139	C₂⁴×D₄	—	13	2	no	—
140	C₂×D₄²	—	13	48	no	—
141	C₂²×#127	—	13	1	no	—
142	C₂²×#121	—	13	2	no	—
143	C₂²×#121	—	13	2	no	—
144	C₂²×#120	—	13	4	no	—
145	C₂²×C₄×D₄	—	13	1	no	—
146	C₂²×C₄×D₄	D₁₃	1	1	yes	characteristic, complemented
147	C₂³×C₁₃	—	2	64	no	—
148	C₂³×C₁₃	—	2	24	no	—
149	C₂³×C₁₃	—	2	24	no	—
150	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
151	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
152	C₂³×C₁₃	C₂²×D₄	1	48	yes	complemented
153	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
154	C₂³×C₁₃	C₂⁵	1	8	yes	—
155	C₂³×C₁₃	C₂⁵	1	3	yes	—
156	C₂²×D₁₃	—	2	64	no	—
157	C₂²×D₁₃	—	2	24	no	—
158	C₂²×D₁₃	—	2	24	no	—
159	C₂²×D₁₃	—	2	48	no	—
160	C₂²×D₁₃	—	2	48	no	—
161	C₂²×D₁₃	—	2	128	no	—
162	C₂²×D₁₃	—	2	48	no	—
163	C₂²×D₁₃	—	2	128	no	—
164	C₂²×D₁₃	—	4	64	no	—
165	C₂²×D₁₃	—	4	768	no	—
166	C₂²×D₁₃	—	4	64	no	—
167	C₂²×D₁₃	C₂²×D₄	1	48	yes	complemented
168	C₂²×D₁₃	C₂⁵	1	16	yes	—
169	C₂²×D₁₃	C₂⁵	1	8	yes	—
170	D₄×C₁₃	C₂²×D₄	1	64	yes	complemented
171	C₂×C₄×C₁₃	—	2	24	no	—
172	C₂×C₄×C₁₃	—	2	12	no	—
173	C₂×C₄×C₁₃	—	2	64	no	—
174	C₂×C₄×C₁₃	C₂²×D₄	1	24	yes	complemented
175	C₂×C₄×C₁₃	C₂²×D₄	1	24	yes	complemented
176	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
177	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
178	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
179	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
180	C₂²⋊D₁₃	—	2	128	no	—
181	C₂×Dic₁₃	—	2	24	no	—
182	C₂×Dic₁₃	C₂⁵	1	8	yes	—
183	D₅₂	—	2	128	no	—
184	D₅₂	—	2	64	no	—
185	D₅₂	—	2	64	no	—
186	D₅₂	—	4	32	no	—
187	D₅₂	C₂²×D₄	1	64	yes	direct product factor
188	C₄×D₁₃	—	2	64	no	—
189	C₂⁶	—	13	4	no	—
190	C₂³×D₄	—	13	4	no	—
191	C₂³×D₄	—	13	48	no	—
192	C₂³×D₄	—	13	1	no	—
193	C₂³×D₄	—	13	4	no	—
194	C₂³×D₄	—	13	2	no	—
195	C₂³×D₄	—	13	2	no	—
196	C₂³×D₄	—	13	2	no	—
197	C₂³×D₄	—	13	48	no	—
198	C₂³×D₄	—	26	32	no	—
199	C₂³×D₄	—	26	32	no	—
200	C₂³×D₄	C₂×D₁₃	1	1	yes	characteristic
201	C₂⁴×C₄	—	13	2	no	—
202	C₂⁴×C₄	C₂×D₁₃	1	2	yes	complemented
203	D₄²	—	13	256	no	—
204	C₂×#127	—	13	24	no	—
205	C₂×#121	—	13	48	no	—
206	C₂×#121	—	13	48	no	—
207	C₂×#120	—	13	96	no	—
208	C₂×C₄×D₄	—	13	24	no	—
209	C₂×C₄×D₄	C₂×D₁₃	1	24	yes	complemented
210	C₂²×C₄⋊C₄	—	13	1	no	—
211	C₂²×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
212	C₂²×C₂²⋊C₄	—	13	2	no	—
213	C₂²×C₂²⋊C₄	—	13	4	no	—
214	C₂²×C₂²⋊C₄	C₂×D₁₃	1	2	yes	complemented
215	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic, complemented
216	C₂²×C₁₃	—	2	8	no	—
217	C₂²×C₁₃	—	2	8	no	—
218	C₂²×C₁₃	—	2	96	no	—
219	C₂²×C₁₃	D₄²	1	16	yes	complemented
220	C₂²×C₁₃	C₂³×D₄	1	6	yes	—
221	C₂²×C₁₃	C₂³×D₄	1	6	yes	—
222	C₂²×C₁₃	C₂³×D₄	1	16	yes	complemented
223	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	6	yes	—
224	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
225	C₂×D₁₃	—	2	8	no	—
226	C₂×D₁₃	—	2	8	no	—
227	C₂×D₁₃	—	2	96	no	—
228	C₂×D₁₃	—	2	16	no	—
229	C₂×D₁₃	—	2	16	no	—
230	C₂×D₁₃	—	2	16	no	—
231	C₂×D₁₃	—	4	256	no	—
232	C₂×D₁₃	—	4	96	no	—
233	C₂×D₁₃	C₂³×D₄	1	16	yes	complemented
234	C₄×C₁₃	—	2	8	no	—
235	C₄×C₁₃	—	2	4	no	—
236	C₄×C₁₃	C₂³×D₄	1	8	yes	complemented
237	C₄×C₁₃	C₂³×D₄	1	8	yes	complemented
238	Dic₁₃	—	2	8	no	—
239	C₂⁵	—	13	2	no	—
240	C₂⁵	—	13	4	no	—
241	C₂⁵	—	13	48	no	—
242	C₂⁵	—	26	32	no	—
243	C₂⁵	—	26	32	no	—
244	C₂⁵	—	52	16	no	—
245	C₂⁵	C₂²×D₁₃	1	2	yes	—
246	C₂²×D₄	—	13	48	no	—
247	C₂²×D₄	—	13	128	no	—
248	C₂²×D₄	—	13	16	no	—
249	C₂²×D₄	—	13	12	no	—
250	C₂²×D₄	—	13	48	no	—
251	C₂²×D₄	—	13	24	no	—
252	C₂²×D₄	—	13	24	no	—
253	C₂²×D₄	—	13	24	no	—
254	C₂²×D₄	—	13	128	no	—
255	C₂²×D₄	—	26	384	no	—
256	C₂²×D₄	—	26	32	no	—
257	C₂²×D₄	—	26	32	no	—
258	C₂²×D₄	—	26	384	no	—
259	C₂²×D₄	—	26	16	no	—
260	C₂²×D₄	—	26	16	no	—
261	C₂²×D₄	—	52	8	no	—
262	C₂²×D₄	D₅₂	1	16	yes	direct product factor
263	C₂²×D₄	C₂²×D₁₃	1	12	yes	—
264	C₂³×C₄	—	2	16	no	—
265	C₂³×C₄	—	13	2	no	—
266	C₂³×C₄	—	13	24	no	—
267	C₂³×C₄	—	26	16	no	—
268	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
269	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
270	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
271	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
272	C₂³×C₄	C₂²×D₁₃	1	24	yes	complemented
273	#127	—	13	64	no	—
274	#121	—	13	128	no	—
275	#121	—	13	128	no	—
276	#120	—	13	256	no	—
277	C₄×D₄	—	13	64	no	—
278	C₄×D₄	C₂²×D₁₃	1	64	yes	complemented
279	C₂×C₄⋊C₄	—	13	12	no	—
280	C₂×C₄⋊C₄	C₂²×D₁₃	1	12	yes	complemented
281	C₂×C₂²⋊C₄	—	13	24	no	—
282	C₂×C₂²⋊C₄	—	13	48	no	—
283	C₂×C₂²⋊C₄	C₂²×D₁₃	1	24	yes	complemented
284	C₂×C₄²	C₂²×D₁₃	1	12	yes	complemented
285	C₂×C₁₃	—	2	16	no	—
286	C₂×C₁₃	C₂×D₄²	1	12	yes	complemented
287	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
288	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
289	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
290	D₁₃	—	2	16	no	—
291	D₁₃	—	4	16	no	—
292	C₂⁴	—	2	8	no	—
293	C₂⁴	—	2	8	no	—
294	C₂⁴	—	13	16	no	—
295	C₂⁴	—	13	12	no	—
296	C₂⁴	—	13	24	no	—
297	C₂⁴	—	13	64	no	—
298	C₂⁴	—	26	192	no	—
299	C₂⁴	—	26	8	no	—
300	C₂⁴	—	26	8	no	—
301	C₂⁴	—	26	16	no	—
302	C₂⁴	—	26	192	no	—
303	C₂⁴	—	26	16	no	—
304	C₂⁴	—	26	16	no	—
305	C₂⁴	—	52	96	no	—
306	C₂⁴	—	52	256	no	—
307	C₂⁴	C₂×D₅₂	1	16	yes	complemented
308	C₂⁴	C₂³×D₁₃	1	12	yes	—
309	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
310	C₂×D₄	—	13	64	no	—
311	C₂×D₄	—	13	96	no	—
312	C₂×D₄	—	13	16	no	—
313	C₂×D₄	—	13	64	no	—
314	C₂×D₄	—	13	32	no	—
315	C₂×D₄	—	13	32	no	—
316	C₂×D₄	—	13	32	no	—
317	C₂×D₄	—	26	512	no	—
318	C₂×D₄	—	26	192	no	—
319	C₂×D₄	—	26	192	no	—
320	C₂×D₄	—	26	512	no	—
321	C₂×D₄	—	26	96	no	—
322	C₂×D₄	—	26	96	no	—
323	C₂×D₄	—	52	48	no	—
324	C₂×D₄	C₂×D₅₂	1	96	yes	direct product factor
325	C₂×D₄	C₂³×D₁₃	1	16	yes	—
326	C₂²×C₄	—	2	8	no	—
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	2	96	no	—
329	C₂²×C₄	—	13	12	no	—
330	C₂²×C₄	—	13	32	no	—
331	C₂²×C₄	—	26	8	no	—
332	C₂²×C₄	—	26	96	no	—
333	C₂²×C₄	C₂×D₅₂	1	8	yes	complemented
334	C₂²×C₄	D₄×D₁₃	1	8	yes	complemented
335	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
336	C₂²×C₄	C₂³×D₁₃	1	12	yes	—
337	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
338	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
339	C₂²×C₄	C₂³×D₁₃	1	32	yes	complemented
340	C₄⋊C₄	—	13	16	no	—
341	C₄⋊C₄	C₂³×D₁₃	1	16	yes	complemented
342	C₂²⋊C₄	—	13	32	no	—
343	C₂²⋊C₄	—	13	64	no	—
344	C₂²⋊C₄	C₂³×D₁₃	1	32	yes	complemented
345	C₄²	C₂³×D₁₃	1	16	yes	complemented
346	C₁₃	C₂²×D₄²	1	1	yes	characteristic, complemented, Sylow
347	C₂³	—	2	64	no	—
348	C₂³	—	2	24	no	—
349	C₂³	—	2	24	no	—
350	C₂³	—	13	48	no	—
351	C₂³	—	13	8	no	—
352	C₂³	—	13	16	no	—
353	C₂³	—	26	128	no	—
354	C₂³	—	26	64	no	—
355	C₂³	—	26	24	no	—
356	C₂³	—	26	24	no	—
357	C₂³	—	26	48	no	—
358	C₂³	—	26	128	no	—
359	C₂³	—	26	48	no	—
360	C₂³	—	26	48	no	—
361	C₂³	—	52	64	no	—
362	C₂³	—	52	768	no	—
363	C₂³	—	52	64	no	—
364	C₂³	C₂²×D₅₂	1	4	yes	—
365	C₂³	C₂²×D₅₂	1	48	yes	complemented
366	C₂³	C₂×D₄×D₁₃	1	4	yes	—
367	C₂³	#88256	1	4	yes	—
368	C₂³	C₂⁴×D₁₃	1	8	yes	—
369	C₂³	C₂⁴×D₁₃	1	3	yes	—
370	D₄	—	13	64	no	—
371	D₄	—	26	128	no	—
372	D₄	—	26	128	no	—
373	D₄	—	26	64	no	—
374	D₄	—	26	64	no	—
375	D₄	—	52	32	no	—
376	D₄	C₂²×D₅₂	1	64	yes	direct product factor
377	C₂×C₄	—	2	24	no	—
378	C₂×C₄	—	2	12	no	—
379	C₂×C₄	—	2	64	no	—
380	C₂×C₄	—	13	8	no	—
381	C₂×C₄	—	26	24	no	—
382	C₂×C₄	—	26	64	no	—
383	C₂×C₄	C₂²×D₅₂	1	24	yes	complemented
384	C₂×C₄	C₂×D₄×D₁₃	1	24	yes	complemented
385	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
386	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
387	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
388	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
389	C₂²	—	2	96	no	—
390	C₂²	—	2	8	no	—
391	C₂²	—	2	8	no	—
392	C₂²	—	13	16	no	—
393	C₂²	—	26	96	no	—
394	C₂²	—	26	8	no	—
395	C₂²	—	26	8	no	—
396	C₂²	—	26	16	no	—
397	C₂²	—	26	16	no	—
398	C₂²	—	26	16	no	—
399	C₂²	—	52	256	no	—
400	C₂²	—	52	96	no	—
401	C₂²	D₄×D₅₂	1	16	yes	direct product factor
402	C₂²	C₂³×D₅₂	1	6	yes	—
403	C₂²	C₂³×D₅₂	1	16	yes	complemented
404	C₂²	C₂²×D₄×D₁₃	1	6	yes	—
405	C₂²	C₂×#88256	1	6	yes	—
406	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
407	C₄	—	2	8	no	—
408	C₄	—	2	4	no	—
409	C₄	—	26	8	no	—
410	C₄	C₂³×D₅₂	1	8	yes	complemented
411	C₄	C₂²×D₄×D₁₃	1	8	yes	complemented
412	C₂	—	2	16	no	—
413	C₂	—	26	16	no	—
414	C₂	—	52	16	no	—
415	C₂	C₂×D₄×D₅₂	1	12	yes	direct product factor
416	C₂	C₂³×D₄×D₁₃	1	1	yes	characteristic
417	C₂	C₂⁴×D₅₂	1	1	yes	characteristic
418	C₂	C₂²×#88256	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂³×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂²×C₄×D₄×C₁₃	C₂
socle	C₂⁴×C₁₃	C₂⁴
hypercenter	C₂²×C₄×D₄	D₁₃
hypocenter	C₁₃	C₂²×D₄²
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂⁴×D₅₂	C₂	semidirect
2. C₂³×D₄×D₁₃	C₂	semidirect
3. C₂×D₄×D₅₂	C₂	direct (N × H)
4. C₂²×#88128	C₂	semidirect
5. C₂²×#88149	C₂	semidirect
6. C₂²×#88184	C₂	semidirect
7. C₂²×#88136	C₂	semidirect
8. C₂²×C₄×D₅₂	C₂	semidirect
9. C₂²×C₄×D₄×C₁₃	C₂	semidirect
10. C₂⁵×D₁₃	C₂²	semidirect
12. C₂⁴×C₄×C₁₃	C₂²	semidirect
13. C₂³×C₂²⋊D₁₃	C₂²	semidirect
15. C₂²×D₄×D₁₃	C₂²	semidirect
18. C₂³×D₅₂	C₂²	semidirect
19. C₂³×D₅₂	C₂²	semidirect
20. C₂³×D₅₂	C₂²	semidirect
21. C₂³×D₅₂	C₂²	semidirect
22. C₂³×D₅₂	C₂²	semidirect
23. C₂³×C₄×D₁₃	C₂²	semidirect
24. C₂×C₄×D₄×C₁₃	C₂²	semidirect
25. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
26. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
27. C₂²×C₄²×C₁₃	C₂²	semidirect
28. C₂×#88184	C₂²	semidirect
29. C₂²×#6103	C₂²	semidirect
30. C₂²×#6103	C₂²	semidirect
31. C₂²×C₄⋊Dic₁₃	C₂²	semidirect
32. D₄×D₅₂	C₂²	direct (N × H)
33. C₂×#88149	C₂²	semidirect
34. C₂×#88136	C₂²	semidirect
35. C₂×#88128	C₂²	semidirect
36. C₂×C₄×D₅₂	C₂²	semidirect
43. C₂⁴×D₁₃	C₂³	semidirect
44. C₂²×D₄×C₁₃	D₄	semidirect
51. C₂³×C₄×C₁₃	C₂³	semidirect
53. C₂²×C₂²⋊D₁₃	C₂³	semidirect
56. C₂×D₄×D₁₃	C₂³	semidirect
62. C₂²×D₅₂	D₄	direct (N × H)
64. C₂²×D₅₂	C₂³	semidirect
65. C₂²×D₅₂	C₂³	semidirect
66. C₂²×D₅₂	C₂³	semidirect
67. C₂²×D₅₂	C₂³	semidirect
68. C₂²×D₅₂	C₂³	semidirect
70. C₂²×C₄×D₁₃	C₂³	semidirect
71. C₄×D₄×C₁₃	C₂³	semidirect
72. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
73. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
74. C₂×C₄²×C₁₃	C₂³	semidirect
75. #88184	C₂³	semidirect
76. C₂×#6103	C₂³	semidirect
77. C₂×#6103	C₂³	semidirect
78. C₂×C₄⋊Dic₁₃	C₂³	semidirect
79. #88149	C₂³	semidirect
80. #88136	C₂³	semidirect
81. #88128	C₂³	semidirect
82. C₄×D₅₂	C₂³	semidirect
86. C₂⁴×C₁₃	C₂×D₄	semidirect
98. C₂³×D₁₃	C₂×D₄	semidirect
101. C₂³×D₁₃	C₂⁴	semidirect
102. C₂×D₄×C₁₃	C₂×D₄	semidirect
107. C₂²×C₄×C₁₃	C₂×D₄	semidirect
108. C₂²×C₄×C₁₃	C₂×D₄	semidirect
113. C₂²×C₄×C₁₃	C₂⁴	semidirect
115. C₂×C₂²⋊D₁₃	C₂⁴	semidirect
124. C₂×D₅₂	C₂×D₄	direct (N × H)
126. C₂×D₅₂	C₂⁴	semidirect
127. C₂×D₅₂	C₂⁴	semidirect
128. C₂×D₅₂	C₂⁴	semidirect
129. C₂×D₅₂	C₂⁴	semidirect
131. C₂×C₄×D₁₃	C₂⁴	semidirect
132. C₁₃×C₄⋊C₄	C₂⁴	semidirect
133. C₁₃×C₂²⋊C₄	C₂⁴	semidirect
134. C₄²×C₁₃	C₂⁴	semidirect
135. #6103	C₂⁴	semidirect
136. #6103	C₂⁴	semidirect
137. C₄⋊Dic₁₃	C₂⁴	semidirect
146. C₂²×C₄×D₄	D₁₃	semidirect
152. C₂³×C₁₃	C₂²×D₄	semidirect
167. C₂²×D₁₃	C₂²×D₄	semidirect
170. D₄×C₁₃	C₂²×D₄	semidirect
174. C₂×C₄×C₁₃	C₂²×D₄	semidirect
175. C₂×C₄×C₁₃	C₂²×D₄	semidirect
187. D₅₂	C₂²×D₄	direct (N × H)
202. C₂⁴×C₄	C₂×D₁₃	semidirect
209. C₂×C₄×D₄	C₂×D₁₃	semidirect
211. C₂²×C₄⋊C₄	C₂×D₁₃	semidirect
214. C₂²×C₂²⋊C₄	C₂×D₁₃	semidirect
215. C₂²×C₄²	C₂×D₁₃	semidirect
219. C₂²×C₁₃	D₄²	semidirect
222. C₂²×C₁₃	C₂³×D₄	semidirect
233. C₂×D₁₃	C₂³×D₄	semidirect
236. C₄×C₁₃	C₂³×D₄	semidirect
237. C₄×C₁₃	C₂³×D₄	semidirect
262. C₂²×D₄	D₅₂	direct (N × H)
272. C₂³×C₄	C₂²×D₁₃	semidirect
278. C₄×D₄	C₂²×D₁₃	semidirect
280. C₂×C₄⋊C₄	C₂²×D₁₃	semidirect
283. C₂×C₂²⋊C₄	C₂²×D₁₃	semidirect
284. C₂×C₄²	C₂²×D₁₃	semidirect
286. C₂×C₁₃	C₂×D₄²	semidirect
307. C₂⁴	C₂×D₅₂	semidirect
324. C₂×D₄	C₂×D₅₂	direct (N × H)
333. C₂²×C₄	C₂×D₅₂	semidirect
334. C₂²×C₄	D₄×D₁₃	semidirect
339. C₂²×C₄	C₂³×D₁₃	semidirect
341. C₄⋊C₄	C₂³×D₁₃	semidirect
344. C₂²⋊C₄	C₂³×D₁₃	semidirect
345. C₄²	C₂³×D₁₃	semidirect
346. C₁₃	C₂²×D₄²	semidirect
365. C₂³	C₂²×D₅₂	semidirect
376. D₄	C₂²×D₅₂	direct (N × H)
383. C₂×C₄	C₂²×D₅₂	semidirect
384. C₂×C₄	C₂×D₄×D₁₃	semidirect
401. C₂²	D₄×D₅₂	direct (N × H)
403. C₂²	C₂³×D₅₂	semidirect
410. C₄	C₂³×D₅₂	semidirect
411. C₄	C₂²×D₄×D₁₃	semidirect
415. C₂	C₂×D₄×D₅₂	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×D₅₂	2
C₂³×D₄×D₁₃	2
C₂×D₄×D₅₂	2
C₂²×#88128	2
C₂²×#88149	2
C₂²×#88184	2
C₂²×#88136	2
C₂²×C₄×D₅₂	2
C₂²×C₄×D₄×C₁₃	2
C₂²×D₄²	13

Subgroups — C22×D4×D52 #16769830

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×D₄×D₅₂ #16769830