Subgroups — C₂×#13128600 #16770813

Order 3328.

12378 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88251	C₂	1	2	yes	maximal, complemented
2	#13128600	C₂	1	32	yes	maximal, direct product factor
3	C₂×#11719260	C₂	1	4	yes	maximal, complemented
4	C₂×#11719259	C₂	1	8	yes	maximal, complemented
5	C₂×D₄×D₅₂	C₂	1	4	yes	maximal, complemented
6	C₂×#11719215	C₂	1	2	yes	maximal, complemented
7	C₂×#11719198	C₂	1	4	yes	maximal, complemented
8	C₂×#11719182	C₂	1	2	yes	maximal, complemented
9	C₂²×#88184	C₂	1	4	yes	maximal, complemented
10	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, 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	8	yes	complemented
14	C₂×#88251	—	2	32	no	—
15	C₂×#88251	C₂²	1	32	yes	complemented
16	C₂²×#6129	C₂²	1	8	yes	complemented
17	C₂²×D₄×D₁₃	C₂²	1	8	yes	complemented
18	C₂²×#6127	C₂²	1	4	yes	complemented
19	C₂³×D₅₂	C₂²	1	4	yes	complemented
20	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
21	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
22	C₂×C₄×D₄×C₁₃	C₂²	1	16	yes	complemented
23	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
24	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
25	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
26	C₂×#88184	C₂²	1	8	yes	complemented
27	C₂×#88184	C₂²	1	8	yes	complemented
28	C₂×#88184	C₂²	1	4	yes	complemented
29	C₂×#88184	C₂²	1	8	yes	complemented
30	C₂×#88184	C₂²	1	4	yes	complemented
31	C₂×#88184	C₂²	1	64	yes	complemented
32	C₂²×#6103	C₂²	1	8	yes	complemented
33	C₂²×C₄⋊Dic₁₃	C₂²	1	4	yes	complemented
34	#11719260	C₂²	1	64	yes	complemented
35	#11719259	C₂²	1	128	yes	complemented
36	D₄×D₅₂	C₂²	1	64	yes	complemented
37	#11719215	C₂²	1	32	yes	complemented
38	C₂×#88151	C₂²	1	8	yes	complemented
39	C₂×#88149	C₂²	1	8	yes	complemented
40	#11719198	C₂²	1	64	yes	complemented
41	C₂×#88140	C₂²	1	16	yes	complemented
42	C₂×#88136	C₂²	1	16	yes	complemented
43	#11719182	C₂²	1	32	yes	complemented
44	C₂×#88129	C₂²	1	4	yes	complemented
45	C₂×#88128	C₂²	1	2	yes	complemented
46	C₂×C₄×D₅₂	C₂²	1	4	yes	complemented
47	C₂×C₄×D₅₂	C₂²	1	4	yes	complemented
48	C₂×#88123	C₂²	1	2	yes	complemented
49	C₂⁵×C₁₃	C₂³	1	2	yes	—
50	C₂⁴×D₁₃	C₂³	1	8	yes	—
51	C₂²×D₄×C₁₃	D₄	1	16	yes	complemented
52	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
53	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
54	C₂³×C₄×C₁₃	—	4	8	no	—
55	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
56	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
58	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
60	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₃	C₂³	1	16	yes	complemented
62	C₂²×C₂²⋊D₁₃	—	2	64	no	—
63	C₂²×C₂²⋊D₁₃	C₂³	1	16	yes	—
64	C₂²×C₂²⋊D₁₃	C₂³	1	8	yes	—
65	C₂²×C₂²⋊D₁₃	C₂³	1	64	yes	complemented
66	C₂³×Dic₁₃	C₂³	1	8	yes	—
67	#88251	—	2	256	no	—
68	C₂×#6129	—	2	64	no	—
69	C₂×#6129	C₂³	1	64	yes	complemented
70	C₂×D₄×D₁₃	—	2	64	no	—
71	C₂×D₄×D₁₃	C₂³	1	64	yes	complemented
72	C₂×#6127	—	2	32	no	—
73	C₂×#6127	C₂³	1	32	yes	complemented
74	C₂²×D₅₂	—	4	16	no	—
75	C₂²×D₅₂	C₂³	1	4	yes	—
76	C₂²×D₅₂	C₂³	1	4	yes	—
77	C₂²×D₅₂	C₂³	1	4	yes	—
78	C₂²×D₅₂	C₂³	1	8	yes	—
79	C₂²×D₅₂	C₂³	1	32	yes	complemented
80	C₂²×C₄×D₁₃	C₂³	1	8	yes	—
81	C₂²×Dic₂₆	C₂³	1	4	yes	—
82	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
83	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	complemented
86	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
87	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	complemented
88	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
89	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
90	C₂×C₄²×C₁₃	C₂³	1	8	yes	complemented
91	#88184	C₂³	1	32	yes	complemented
92	#88184	C₂³	1	32	yes	complemented
93	#88184	C₂³	1	64	yes	complemented
94	#88184	C₂³	1	64	yes	complemented
95	#88184	C₂³	1	64	yes	complemented
96	C₂×#6103	C₂³	1	8	yes	—
97	C₂×#6103	C₂³	1	8	yes	—
98	C₂×#6103	C₂³	1	16	yes	—
99	C₂×#6103	C₂³	1	64	yes	complemented
100	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	—
101	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	—
102	C₂×C₄⋊Dic₁₃	C₂³	1	8	yes	—
103	C₂×C₄⋊Dic₁₃	C₂³	1	32	yes	complemented
104	#88151	C₂³	1	64	yes	complemented
105	#88149	C₂³	1	64	yes	complemented
106	#88140	C₂³	1	128	yes	complemented
107	#88136	C₂³	1	128	yes	complemented
108	#88129	C₂³	1	32	yes	complemented
109	#88128	C₂³	1	16	yes	complemented
110	C₄×D₅₂	C₂³	1	32	yes	complemented
111	C₄×D₅₂	C₂³	1	32	yes	complemented
112	#88123	C₂³	1	16	yes	complemented
113	C₂×#3496	—	13	1	no	maximal, Sylow
114	C₂⁴×C₁₃	—	4	4	no	—
115	C₂⁴×C₁₃	—	4	4	no	—
116	C₂⁴×C₁₃	C₂×D₄	1	16	yes	complemented
117	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
118	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
119	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
120	C₂³×D₁₃	—	2	32	no	—
121	C₂³×D₁₃	—	4	16	no	—
122	C₂³×D₁₃	—	4	16	no	—
123	C₂³×D₁₃	C₂⁴	1	8	yes	—
124	C₂³×D₁₃	C₂⁴	1	32	yes	—
125	C₂×D₄×C₁₃	C₂×D₄	1	32	yes	complemented
126	C₂×D₄×C₁₃	C₂×D₄	1	64	yes	complemented
127	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
128	C₂²×C₄×C₁₃	—	2	16	no	—
129	C₂²×C₄×C₁₃	—	2	4	no	—
130	C₂²×C₄×C₁₃	—	4	32	no	—
131	C₂²×C₄×C₁₃	—	4	4	no	—
132	C₂²×C₄×C₁₃	—	4	8	no	—
133	C₂²×C₄×C₁₃	—	4	2	no	—
134	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	complemented
135	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
136	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
137	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
138	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
140	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
141	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
142	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
143	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
144	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
145	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
146	C₂×C₂²⋊D₁₃	—	2	32	no	—
147	C₂×C₂²⋊D₁₃	—	2	64	no	—
148	C₂×C₂²⋊D₁₃	—	2	256	no	—
149	C₂×C₂²⋊D₁₃	C₂⁴	1	64	yes	—
150	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	—
151	C₂²×Dic₁₃	—	2	32	no	—
152	C₂²×Dic₁₃	C₂⁴	1	32	yes	—
153	C₂²×Dic₁₃	C₂⁴	1	8	yes	—
154	#6129	—	2	256	no	—
155	D₄×D₁₃	—	2	256	no	—
156	#6127	—	2	128	no	—
157	C₂×D₅₂	—	2	16	no	—
158	C₂×D₅₂	—	2	16	no	—
159	C₂×D₅₂	—	4	64	no	—
160	C₂×D₅₂	—	4	16	no	—
161	C₂×D₅₂	—	4	8	no	—
162	C₂×D₅₂	C₂⁴	1	16	yes	—
163	C₂×D₅₂	C₂⁴	1	16	yes	—
164	C₂×D₅₂	C₂⁴	1	16	yes	—
165	C₂×D₅₂	C₂⁴	1	32	yes	—
166	C₂×C₄×D₁₃	—	2	32	no	—
167	C₂×C₄×D₁₃	C₂⁴	1	32	yes	—
168	C₂×Dic₂₆	—	2	16	no	—
169	C₂×Dic₂₆	C₂⁴	1	16	yes	—
170	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
171	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
172	C₄²×C₁₃	C₂⁴	1	8	yes	—
173	C₄²×C₁₃	C₂⁴	1	8	yes	—
174	#6103	C₂⁴	1	32	yes	—
175	#6103	C₂⁴	1	32	yes	—
176	#6103	C₂⁴	1	64	yes	—
177	C₄⋊Dic₁₃	C₂⁴	1	16	yes	—
178	C₄⋊Dic₁₃	C₂⁴	1	16	yes	—
179	C₄⋊Dic₁₃	C₂⁴	1	32	yes	—
180	C₂²×H(5,𝔽₂)	—	13	2	no	—
181	#3496	—	13	32	no	—
182	C₂×#547	—	13	4	no	—
183	C₂×#546	—	13	8	no	—
184	C₂×D₄²	—	13	4	no	—
185	C₂×#537	—	13	2	no	—
186	C₂×#534	—	13	4	no	—
187	C₂×#532	—	13	2	no	—
188	C₂²×#121	—	13	4	no	—
189	C₂²×C₄×D₄	D₁₃	1	1	yes	characteristic, complemented
190	C₂³×C₁₃	—	2	2	no	—
191	C₂³×C₁₃	—	2	8	no	—
192	C₂³×C₁₃	—	2	2	no	—
193	C₂³×C₁₃	—	2	8	no	—
194	C₂³×C₁₃	—	4	8	no	—
195	C₂³×C₁₃	—	4	32	no	—
196	C₂³×C₁₃	—	4	8	no	—
197	C₂³×C₁₃	C₂²×D₄	1	16	yes	—
198	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
199	C₂³×C₁₃	C₂²×D₄	1	32	yes	complemented
200	C₂³×C₁₃	C₂⁵	1	8	yes	—
201	C₂³×C₁₃	C₂⁵	1	2	yes	—
202	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
203	C₂²×D₁₃	—	2	16	no	—
204	C₂²×D₁₃	—	2	16	no	—
205	C₂²×D₁₃	—	2	16	no	—
206	C₂²×D₁₃	—	2	64	no	—
207	C₂²×D₁₃	—	4	32	no	—
208	C₂²×D₁₃	—	4	32	no	—
209	C₂²×D₁₃	—	8	64	no	—
210	C₂²×D₁₃	C₂⁵	1	16	yes	—
211	D₄×C₁₃	C₂²×D₄	1	64	yes	complemented
212	C₂×C₄×C₁₃	—	2	8	no	—
213	C₂×C₄×C₁₃	—	2	2	no	—
214	C₂×C₄×C₁₃	—	2	4	no	—
215	C₂×C₄×C₁₃	—	2	32	no	—
216	C₂×C₄×C₁₃	—	2	8	no	—
217	C₂×C₄×C₁₃	—	4	8	no	—
218	C₂×C₄×C₁₃	—	4	16	no	—
219	C₂×C₄×C₁₃	—	4	4	no	—
220	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
221	C₂×C₄×C₁₃	C₂²×D₄	1	16	yes	complemented
222	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	complemented
223	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
224	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
225	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
226	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
227	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
228	C₂²⋊D₁₃	—	2	64	no	—
229	C₂²⋊D₁₃	—	2	128	no	—
230	C₂×Dic₁₃	—	2	16	no	—
231	C₂×Dic₁₃	—	2	64	no	—
232	C₂×Dic₁₃	C₂⁵	1	16	yes	—
233	D₅₂	—	2	32	no	—
234	D₅₂	—	2	32	no	—
235	D₅₂	—	4	32	no	—
236	D₅₂	—	4	16	no	—
237	C₄×D₁₃	—	2	64	no	—
238	Dic₂₆	—	2	32	no	—
239	C₂×H(5,𝔽₂)	—	13	32	no	—
240	C₂×H(5,𝔽₂)	—	26	32	no	—
241	C₂²×#41	—	13	8	no	—
242	C₂²×#41	—	13	4	no	—
243	C₂³×D₄	—	13	8	no	—
244	C₂³×D₄	—	13	8	no	—
245	C₂³×D₄	—	13	4	no	—
246	C₂³×D₄	C₂×D₁₃	1	1	yes	characteristic
247	C₂⁴×C₄	C₂×D₁₃	1	2	yes	complemented
248	#547	—	13	64	no	—
249	#546	—	13	128	no	—
250	D₄²	—	13	64	no	—
251	#537	—	13	32	no	—
252	#534	—	13	64	no	—
253	#532	—	13	32	no	—
254	C₂×C₄⋊Q₈	—	13	2	no	—
255	C₂×#127	—	13	2	no	—
256	C₂×#124	—	13	4	no	—
257	C₂×#123	—	13	16	no	—
258	C₂×C₂²⋊Q₈	—	13	8	no	—
259	C₂×#121	—	13	4	no	—
260	C₂×#121	—	13	8	no	—
261	C₂×#121	—	13	8	no	—
262	C₂×#121	—	13	8	no	—
263	C₂×#121	—	13	4	no	—
264	C₂×#121	—	13	64	no	—
265	C₂×#121	—	13	8	no	—
266	C₂×#120	—	13	16	no	—
267	C₂×C₄×D₄	—	13	4	no	—
268	C₂×C₄×D₄	—	13	4	no	—
269	C₂×C₄×D₄	C₂×D₁₃	1	4	yes	complemented
270	C₂×C₄×D₄	C₂×D₁₃	1	4	yes	complemented
271	C₂×C₄×D₄	C₂×D₁₃	1	16	yes	complemented
272	C₂²×C₄⋊C₄	—	13	4	no	—
273	C₂²×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
274	C₂²×C₂²⋊C₄	—	13	8	no	—
275	C₂²×C₂²⋊C₄	C₂×D₁₃	1	2	yes	complemented
276	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic, complemented
277	C₂²×C₁₃	—	2	2	no	—
278	C₂²×C₁₃	—	2	8	no	—
279	C₂²×C₁₃	—	2	2	no	—
280	C₂²×C₁₃	—	2	8	no	—
281	C₂²×C₁₃	—	2	32	no	—
282	C₂²×C₁₃	—	2	8	no	—
283	C₂²×C₁₃	—	4	32	no	—
284	C₂²×C₁₃	C₂³×D₄	1	16	yes	—
285	C₂²×C₁₃	C₂³×D₄	1	4	yes	—
286	C₂²×C₁₃	C₂³×D₄	1	2	yes	—
287	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
288	C₂²×C₁₃	#585	1	2	yes	—
289	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
290	C₂×D₁₃	—	2	16	no	—
291	C₂×D₁₃	—	2	16	no	—
292	C₂×D₁₃	—	2	16	no	—
293	C₂×D₁₃	—	4	32	no	—
294	C₂×D₁₃	—	8	64	no	—
295	C₄×C₁₃	—	2	8	no	—
296	C₄×C₁₃	—	2	2	no	—
297	C₄×C₁₃	—	2	4	no	—
298	C₄×C₁₃	C₂³×D₄	1	8	yes	—
299	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	complemented
300	Dic₁₃	—	2	16	no	—
301	C₂⁵	—	13	8	no	—
302	C₂⁵	C₂²×D₁₃	1	2	yes	—
303	H(5,𝔽₂)	—	26	256	no	—
304	C₂×#41	—	13	64	no	—
305	C₂×#41	—	13	32	no	—
306	C₂×#41	—	26	64	no	—
307	C₂×#41	—	26	32	no	—
308	C₂²×Q₈	—	13	4	no	—
309	C₂²×D₄	—	13	16	no	—
310	C₂²×D₄	—	13	8	no	—
311	C₂²×D₄	—	13	64	no	—
312	C₂²×D₄	—	13	64	no	—
313	C₂²×D₄	—	13	4	no	—
314	C₂²×D₄	—	13	4	no	—
315	C₂²×D₄	—	13	4	no	—
316	C₂²×D₄	—	13	8	no	—
317	C₂²×D₄	—	13	32	no	—
318	C₂²×D₄	—	26	64	no	—
319	C₂²×D₄	—	26	64	no	—
320	C₂²×D₄	—	52	16	no	—
321	C₂²×D₄	D₅₂	1	16	yes	complemented
322	C₂²×D₄	C₂²×D₁₃	1	4	yes	—
323	C₂²×D₄	C₂²×D₁₃	1	8	yes	—
324	C₂³×C₄	—	4	8	no	—
325	C₂³×C₄	—	13	8	no	—
326	C₂³×C₄	—	13	8	no	—
327	C₂³×C₄	C₂²×D₁₃	1	4	yes	—
328	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
329	C₂³×C₄	C₂²×D₁₃	1	4	yes	—
330	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
331	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
332	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
333	C₂³×C₄	C₂²×D₁₃	1	16	yes	complemented
334	C₄⋊Q₈	—	13	16	no	—
335	#127	—	13	16	no	—
336	#124	—	13	32	no	—
337	#123	—	13	128	no	—
338	C₂²⋊Q₈	—	13	64	no	—
339	#121	—	13	32	no	—
340	#121	—	13	64	no	—
341	#121	—	13	64	no	—
342	#121	—	13	64	no	—
343	#121	—	13	32	no	—
344	#121	—	13	64	no	—
345	#120	—	13	128	no	—
346	C₄×D₄	—	13	32	no	—
347	C₄×D₄	—	13	32	no	—
348	C₄×D₄	C₂²×D₁₃	1	32	yes	complemented
349	C₄×D₄	C₂²×D₁₃	1	32	yes	complemented
350	C₂×C₄⋊C₄	—	13	4	no	—
351	C₂×C₄⋊C₄	—	13	8	no	—
352	C₂×C₄⋊C₄	—	13	32	no	—
353	C₂×C₄⋊C₄	—	13	4	no	—
354	C₂×C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
355	C₂×C₄⋊C₄	C₂²×D₁₃	1	8	yes	complemented
356	C₂×C₂²⋊C₄	—	13	8	no	—
357	C₂×C₂²⋊C₄	—	13	16	no	—
358	C₂×C₂²⋊C₄	—	13	64	no	—
359	C₂×C₂²⋊C₄	—	13	8	no	—
360	C₂×C₂²⋊C₄	C₂²×D₁₃	1	8	yes	—
361	C₂×C₂²⋊C₄	C₂²×D₁₃	1	16	yes	complemented
362	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
363	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
364	C₂×C₄²	C₂²×D₁₃	1	8	yes	complemented
365	C₂×C₁₃	—	2	16	no	—
366	C₂×C₁₃	—	2	4	no	—
367	C₂×C₁₃	#3496	1	4	yes	complemented
368	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
369	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
370	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
371	D₁₃	—	4	16	no	—
372	C₂⁴	—	4	4	no	—
373	C₂⁴	—	4	4	no	—
374	C₂⁴	—	13	8	no	—
375	C₂⁴	—	13	32	no	—
376	C₂⁴	—	26	32	no	—
377	C₂⁴	—	52	16	no	—
378	C₂⁴	—	52	16	no	—
379	C₂⁴	C₂×D₅₂	1	16	yes	complemented
380	C₂⁴	C₂³×D₁₃	1	4	yes	—
381	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
382	C₂⁴	C₂³×D₁₃	1	8	yes	—
383	#41	—	26	256	no	—
384	#41	—	26	128	no	—
385	C₂×Q₈	—	13	16	no	—
386	C₂×Q₈	—	26	16	no	—
387	C₂×D₄	—	13	64	no	—
388	C₂×D₄	—	13	32	no	—
389	C₂×D₄	—	13	16	no	—
390	C₂×D₄	—	13	16	no	—
391	C₂×D₄	—	13	16	no	—
392	C₂×D₄	—	13	32	no	—
393	C₂×D₄	—	26	64	no	—
394	C₂×D₄	—	26	32	no	—
395	C₂×D₄	—	26	256	no	—
396	C₂×D₄	—	26	256	no	—
397	C₂×D₄	—	26	16	no	—
398	C₂×D₄	—	26	16	no	—
399	C₂×D₄	—	52	64	no	—
400	C₂×D₄	—	52	16	no	—
401	C₂×D₄	—	52	8	no	—
402	C₂×D₄	C₂×D₅₂	1	32	yes	complemented
403	C₂×D₄	C₂×D₅₂	1	64	yes	complemented
404	C₂×D₄	C₂³×D₁₃	1	16	yes	—
405	C₂²×C₄	—	2	4	no	—
406	C₂²×C₄	—	2	16	no	—
407	C₂²×C₄	—	4	32	no	—
408	C₂²×C₄	—	4	8	no	—
409	C₂²×C₄	—	4	4	no	—
410	C₂²×C₄	—	4	2	no	—
411	C₂²×C₄	—	13	32	no	—
412	C₂²×C₄	—	13	8	no	—
413	C₂²×C₄	—	13	32	no	—
414	C₂²×C₄	—	26	32	no	—
415	C₂²×C₄	—	26	32	no	—
416	C₂²×C₄	C₂×D₅₂	1	8	yes	complemented
417	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
418	C₂²×C₄	C₂³×D₁₃	1	16	yes	—
419	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
420	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
421	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
422	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
423	C₂²×C₄	C₂³×D₁₃	1	16	yes	—
424	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
425	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
426	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
427	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
428	C₄⋊C₄	—	13	16	no	—
429	C₄⋊C₄	—	13	32	no	—
430	C₄⋊C₄	—	13	16	no	—
431	C₄⋊C₄	C₂³×D₁₃	1	16	yes	—
432	C₂²⋊C₄	—	13	32	no	—
433	C₂²⋊C₄	—	13	64	no	—
434	C₂²⋊C₄	—	13	32	no	—
435	C₂²⋊C₄	C₂³×D₁₃	1	32	yes	—
436	C₄²	C₂³×D₁₃	1	8	yes	—
437	C₄²	C₂³×D₁₃	1	8	yes	—
438	C₁₃	C₂×#3496	1	1	yes	characteristic, complemented, Sylow
439	C₂³	—	2	2	no	—
440	C₂³	—	2	8	no	—
441	C₂³	—	2	2	no	—
442	C₂³	—	2	8	no	—
443	C₂³	—	4	8	no	—
444	C₂³	—	4	32	no	—
445	C₂³	—	4	8	no	—
446	C₂³	—	13	16	no	—
447	C₂³	—	26	16	no	—
448	C₂³	—	26	16	no	—
449	C₂³	—	26	16	no	—
450	C₂³	—	26	64	no	—
451	C₂³	—	52	32	no	—
452	C₂³	—	52	32	no	—
453	C₂³	—	104	64	no	—
454	C₂³	C₂²×D₅₂	1	16	yes	—
455	C₂³	C₂²×D₅₂	1	4	yes	—
456	C₂³	C₂²×D₅₂	1	32	yes	complemented
457	C₂³	C₂⁴×D₁₃	1	8	yes	—
458	C₂³	C₂⁴×D₁₃	1	2	yes	—
459	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
460	Q₈	—	26	32	no	—
461	D₄	—	26	128	no	—
462	D₄	—	26	64	no	—
463	D₄	—	26	32	no	—
464	D₄	—	26	32	no	—
465	D₄	—	52	16	no	—
466	D₄	—	52	32	no	—
467	D₄	C₂²×D₅₂	1	64	yes	complemented
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	8	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	2	8	no	—
472	C₂×C₄	—	2	32	no	—
473	C₂×C₄	—	4	16	no	—
474	C₂×C₄	—	4	8	no	—
475	C₂×C₄	—	4	4	no	—
476	C₂×C₄	—	13	16	no	—
477	C₂×C₄	—	26	16	no	—
478	C₂×C₄	—	26	64	no	—
479	C₂×C₄	—	26	64	no	—
480	C₂×C₄	C₂²×D₅₂	1	8	yes	—
481	C₂×C₄	C₂²×D₅₂	1	16	yes	complemented
482	C₂×C₄	#88251	1	4	yes	complemented
483	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
484	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
485	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
486	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
487	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
488	C₂²	—	2	8	no	—
489	C₂²	—	2	32	no	—
490	C₂²	—	2	2	no	—
491	C₂²	—	2	8	no	—
492	C₂²	—	2	2	no	—
493	C₂²	—	2	8	no	—
494	C₂²	—	4	32	no	—
495	C₂²	—	26	16	no	—
496	C₂²	—	26	16	no	—
497	C₂²	—	26	16	no	—
498	C₂²	—	52	32	no	—
499	C₂²	—	104	64	no	—
500	C₂²	C₂³×D₅₂	1	16	yes	—
501	C₂²	C₂³×D₅₂	1	4	yes	—
502	C₂²	C₂³×D₅₂	1	2	yes	—
503	C₂²	C₂×#88251	1	2	yes	—
504	C₂²	#11719648	1	2	yes	—
505	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
506	C₄	—	2	2	no	—
507	C₄	—	2	8	no	—
508	C₄	—	2	4	no	—
509	C₄	—	26	16	no	—
510	C₄	C₂³×D₅₂	1	8	yes	—
511	C₄	C₂×#88251	1	4	yes	complemented
512	C₂	—	2	4	no	—
513	C₂	—	2	16	no	—
514	C₂	—	52	16	no	—
515	C₂	#13128600	1	4	yes	direct product factor
516	C₂	C₂⁴×D₅₂	1	1	yes	characteristic
517	C₂	C₂²×#88251	1	1	yes	characteristic
518	C₂	C₂×#11719648	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂²×C₄×D₄×C₁₃	C₂
socle	C₂³×C₁₃	C₂⁵
hypercenter	C₂²×C₄×D₄	D₁₃
hypocenter	C₁₃	C₂×#3496
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×#88251	C₂	semidirect
2. #13128600	C₂	direct (N × H)
3. C₂×#11719260	C₂	semidirect
4. C₂×#11719259	C₂	semidirect
5. C₂×D₄×D₅₂	C₂	semidirect
6. C₂×#11719215	C₂	semidirect
7. C₂×#11719198	C₂	semidirect
8. C₂×#11719182	C₂	semidirect
9. C₂²×#88184	C₂	semidirect
10. C₂²×C₄×D₄×C₁₃	C₂	semidirect
12. C₂⁴×C₄×C₁₃	C₂²	semidirect
13. C₂³×C₂²⋊D₁₃	C₂²	semidirect
15. C₂×#88251	C₂²	semidirect
16. C₂²×#6129	C₂²	semidirect
17. C₂²×D₄×D₁₃	C₂²	semidirect
18. C₂²×#6127	C₂²	semidirect
19. C₂³×D₅₂	C₂²	semidirect
20. C₂×C₄×D₄×C₁₃	C₂²	semidirect
21. C₂×C₄×D₄×C₁₃	C₂²	semidirect
22. C₂×C₄×D₄×C₁₃	C₂²	semidirect
23. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
24. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
25. C₂²×C₄²×C₁₃	C₂²	semidirect
26. C₂×#88184	C₂²	semidirect
27. C₂×#88184	C₂²	semidirect
28. C₂×#88184	C₂²	semidirect
29. C₂×#88184	C₂²	semidirect
30. C₂×#88184	C₂²	semidirect
31. C₂×#88184	C₂²	semidirect
32. C₂²×#6103	C₂²	semidirect
33. C₂²×C₄⋊Dic₁₃	C₂²	semidirect
34. #11719260	C₂²	semidirect
35. #11719259	C₂²	semidirect
36. D₄×D₅₂	C₂²	semidirect
37. #11719215	C₂²	semidirect
38. C₂×#88151	C₂²	semidirect
39. C₂×#88149	C₂²	semidirect
40. #11719198	C₂²	semidirect
41. C₂×#88140	C₂²	semidirect
42. C₂×#88136	C₂²	semidirect
43. #11719182	C₂²	semidirect
44. C₂×#88129	C₂²	semidirect
45. C₂×#88128	C₂²	semidirect
46. C₂×C₄×D₅₂	C₂²	semidirect
47. C₂×C₄×D₅₂	C₂²	semidirect
48. C₂×#88123	C₂²	semidirect
51. C₂²×D₄×C₁₃	D₄	semidirect
61. C₂³×C₄×C₁₃	C₂³	semidirect
65. C₂²×C₂²⋊D₁₃	C₂³	semidirect
69. C₂×#6129	C₂³	semidirect
71. C₂×D₄×D₁₃	C₂³	semidirect
73. C₂×#6127	C₂³	semidirect
79. C₂²×D₅₂	C₂³	semidirect
82. C₄×D₄×C₁₃	C₂³	semidirect
83. C₄×D₄×C₁₃	C₂³	semidirect
85. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
87. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
90. C₂×C₄²×C₁₃	C₂³	semidirect
91. #88184	C₂³	semidirect
92. #88184	C₂³	semidirect
93. #88184	C₂³	semidirect
94. #88184	C₂³	semidirect
95. #88184	C₂³	semidirect
99. C₂×#6103	C₂³	semidirect
103. C₂×C₄⋊Dic₁₃	C₂³	semidirect
104. #88151	C₂³	semidirect
105. #88149	C₂³	semidirect
106. #88140	C₂³	semidirect
107. #88136	C₂³	semidirect
108. #88129	C₂³	semidirect
109. #88128	C₂³	semidirect
110. C₄×D₅₂	C₂³	semidirect
111. C₄×D₅₂	C₂³	semidirect
112. #88123	C₂³	semidirect
116. C₂⁴×C₁₃	C₂×D₄	semidirect
125. C₂×D₄×C₁₃	C₂×D₄	semidirect
126. C₂×D₄×C₁₃	C₂×D₄	semidirect
134. C₂²×C₄×C₁₃	C₂×D₄	semidirect
189. C₂²×C₄×D₄	D₁₃	semidirect
199. C₂³×C₁₃	C₂²×D₄	semidirect
211. D₄×C₁₃	C₂²×D₄	semidirect
221. C₂×C₄×C₁₃	C₂²×D₄	semidirect
222. C₂×C₄×C₁₃	H(5,𝔽₂)	semidirect
247. C₂⁴×C₄	C₂×D₁₃	semidirect
269. C₂×C₄×D₄	C₂×D₁₃	semidirect
270. C₂×C₄×D₄	C₂×D₁₃	semidirect
271. C₂×C₄×D₄	C₂×D₁₃	semidirect
273. C₂²×C₄⋊C₄	C₂×D₁₃	semidirect
275. C₂²×C₂²⋊C₄	C₂×D₁₃	semidirect
276. C₂²×C₄²	C₂×D₁₃	semidirect
299. C₄×C₁₃	C₂×H(5,𝔽₂)	semidirect
321. C₂²×D₄	D₅₂	semidirect
333. C₂³×C₄	C₂²×D₁₃	semidirect
348. C₄×D₄	C₂²×D₁₃	semidirect
349. C₄×D₄	C₂²×D₁₃	semidirect
355. C₂×C₄⋊C₄	C₂²×D₁₃	semidirect
361. C₂×C₂²⋊C₄	C₂²×D₁₃	semidirect
364. C₂×C₄²	C₂²×D₁₃	semidirect
367. C₂×C₁₃	#3496	semidirect
379. C₂⁴	C₂×D₅₂	semidirect
402. C₂×D₄	C₂×D₅₂	semidirect
403. C₂×D₄	C₂×D₅₂	semidirect
416. C₂²×C₄	C₂×D₅₂	semidirect
438. C₁₃	C₂×#3496	semidirect
456. C₂³	C₂²×D₅₂	semidirect
467. D₄	C₂²×D₅₂	semidirect
481. C₂×C₄	C₂²×D₅₂	semidirect
482. C₂×C₄	#88251	semidirect
511. C₄	C₂×#88251	semidirect
515. C₂	#13128600	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#88251	2
#13128600	2
C₂×#11719260	2
C₂×#11719259	2
C₂×D₄×D₅₂	2
C₂×#11719215	2
C₂×#11719198	2
C₂×#11719182	2
C₂²×#88184	2
C₂²×C₄×D₄×C₁₃	2
C₂×#3496	13

Subgroups — C2×#13128600 #16770813

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13128600 #16770813