Subgroups — C₂×#13128480 #16770963

Order 3328.

11686 conjugacy classes of subgroups.

The subgroup lattice has 532 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	1	yes	maximal, characteristic, complemented
2	#13128480	C₂	1	32	yes	maximal, direct product factor
3	C₂×#11719529	C₂	1	8	yes	maximal, complemented
4	C₂×#11719534	C₂	1	8	yes	maximal, complemented
5	C₂×#11719521	C₂	1	2	yes	maximal, complemented
6	C₂×#11719509	C₂	1	4	yes	maximal, complemented
7	C₂×#11719496	C₂	1	2	yes	maximal, complemented
8	C₂²×#88183	C₂	1	4	yes	maximal, complemented
9	C₂×#11719503	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₁₃×#41	—	2	16	no	—
12	C₂²×C₁₃×#41	C₂²	1	8	yes	complemented
13	C₂²×C₁₃×#41	C₂²	1	16	yes	complemented
14	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
15	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₂³×D₄×C₁₃	C₂²	1	2	yes	complemented
17	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	complemented
18	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
19	C₂³×C₂²⋊D₁₃	C₂²	1	4	yes	—
20	C₂×#88251	—	2	16	no	—
21	C₂×#88251	C₂²	1	16	yes	complemented
22	C₂²×#6129	C₂²	1	4	yes	complemented
23	C₂²×D₄×D₁₃	C₂²	1	4	yes	complemented
24	C₂²×#6127	C₂²	1	2	yes	—
25	C₂×#88207	C₂²	1	4	yes	complemented
26	C₂²×C₂²⋊Dic₁₃	C₂²	1	4	yes	complemented
27	#11719534	C₂²	1	128	yes	complemented
28	#11719529	C₂²	1	128	yes	complemented
29	#11719521	C₂²	1	32	yes	complemented
30	C₂×#88201	C₂²	1	4	yes	complemented
31	C₂×#88200	C₂²	1	8	yes	complemented
32	C₂×#88198	C₂²	1	4	yes	complemented
33	#11719509	C₂²	1	64	yes	complemented
34	C₂×#88193	C₂²	1	16	yes	complemented
35	C₂×#88191	C₂²	1	8	yes	complemented
36	#11719503	C₂²	1	16	yes	complemented
37	C₂×#88189	C₂²	1	8	yes	complemented
38	C₂×D₄×Dic₁₃	C₂²	1	8	yes	complemented
39	#11719496	C₂²	1	32	yes	complemented
40	C₂×#88184	C₂²	1	4	yes	complemented
41	C₂×#88183	C₂²	1	16	yes	complemented
42	C₂×#88183	C₂²	1	4	yes	complemented
43	C₂×#88183	C₂²	1	8	yes	complemented
44	C₂×#88183	C₂²	1	64	yes	complemented
45	C₂×C₄×C₂²⋊D₁₃	C₂²	1	8	yes	complemented
46	C₂²×#6103	C₂²	1	8	yes	complemented
47	C₂×#88180	C₂²	1	2	yes	complemented
48	C₂×#88178	C₂²	1	4	yes	complemented
49	C₂²×#6101	C₂²	1	8	yes	complemented
50	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
51	C₂⁵×C₁₃	C₂³	1	2	yes	—
52	C₂⁴×D₁₃	C₂³	1	4	yes	—
53	C₂×C₁₃×#41	—	2	64	no	—
54	C₂×C₁₃×#41	—	2	128	no	—
55	C₂×C₁₃×#41	C₂³	1	64	yes	complemented
56	C₂²×Q₈×C₁₃	—	2	8	no	—
57	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
58	C₂²×Q₈×C₁₃	C₂³	1	8	yes	complemented
59	C₂²×D₄×C₁₃	—	2	16	no	—
60	C₂²×D₄×C₁₃	D₄	1	16	yes	complemented
61	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
62	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
63	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
64	C₂²×D₄×C₁₃	C₂³	1	16	yes	complemented
65	C₂³×C₄×C₁₃	—	2	16	no	—
66	C₂³×C₄×C₁₃	—	2	8	no	—
67	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
68	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
69	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
71	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₁₃	C₂³	1	16	yes	complemented
73	C₂³×C₄×C₁₃	C₂³	1	8	yes	complemented
74	C₂²×C₂²⋊D₁₃	—	2	32	no	—
75	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
76	C₂²×C₂²⋊D₁₃	C₂³	1	8	yes	—
77	C₂²×C₂²⋊D₁₃	C₂³	1	32	yes	—
78	C₂²×C₂²⋊D₁₃	C₂³	1	8	yes	—
79	C₂³×Dic₁₃	C₂³	1	4	yes	—
80	C₂³×Dic₁₃	C₂³	1	8	yes	—
81	#88251	—	2	128	no	—
82	C₂×#6129	—	2	32	no	—
83	C₂×#6129	C₂³	1	32	yes	complemented
84	C₂×D₄×D₁₃	—	2	32	no	—
85	C₂×D₄×D₁₃	C₂³	1	32	yes	complemented
86	C₂×#6127	—	2	16	no	—
87	C₂×#6127	C₂³	1	16	yes	—
88	C₂²×D₅₂	C₂³	1	2	yes	—
89	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
90	C₂²×Dic₂₆	C₂³	1	2	yes	—
91	#88207	C₂³	1	32	yes	complemented
92	C₂×C₂²⋊Dic₁₃	C₂³	1	8	yes	—
93	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
94	C₂×C₂²⋊Dic₁₃	C₂³	1	8	yes	—
95	C₂×C₂²⋊Dic₁₃	C₂³	1	32	yes	complemented
96	#88201	C₂³	1	32	yes	complemented
97	#88200	C₂³	1	64	yes	complemented
98	#88198	C₂³	1	32	yes	complemented
99	#88193	C₂³	1	128	yes	complemented
100	#88191	C₂³	1	64	yes	complemented
101	#88189	C₂³	1	64	yes	complemented
102	D₄×Dic₁₃	C₂³	1	64	yes	complemented
103	#88184	C₂³	1	32	yes	complemented
104	#88183	C₂³	1	32	yes	complemented
105	#88183	C₂³	1	64	yes	complemented
106	#88183	C₂³	1	128	yes	complemented
107	C₄×C₂²⋊D₁₃	C₂³	1	64	yes	complemented
108	C₂×#6103	C₂³	1	8	yes	—
109	C₂×#6103	C₂³	1	16	yes	—
110	C₂×#6103	C₂³	1	64	yes	complemented
111	#88180	C₂³	1	16	yes	complemented
112	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	—
113	#88178	C₂³	1	32	yes	complemented
114	C₂×#6101	C₂³	1	8	yes	—
115	C₂×#6101	C₂³	1	16	yes	—
116	C₂×#6101	C₂³	1	64	yes	complemented
117	C₂×C₄×Dic₁₃	C₂³	1	4	yes	—
118	C₂×#3485	—	13	1	no	maximal, Sylow
119	C₂⁴×C₁₃	—	2	4	no	—
120	C₂⁴×C₁₃	—	4	8	no	—
121	C₂⁴×C₁₃	—	4	4	no	—
122	C₂⁴×C₁₃	C₂×D₄	1	16	yes	—
123	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
124	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
125	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
126	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
127	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
128	C₂³×D₁₃	—	2	16	no	—
129	C₂³×D₁₃	—	4	16	no	—
130	C₂³×D₁₃	C₂⁴	1	4	yes	—
131	C₂³×D₁₃	C₂⁴	1	16	yes	—
132	C₁₃×#41	—	2	256	no	—
133	C₂×Q₈×C₁₃	—	2	16	no	—
134	C₂×Q₈×C₁₃	—	2	32	no	—
135	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	—
136	C₂×D₄×C₁₃	—	2	32	no	—
137	C₂×D₄×C₁₃	—	2	64	no	—
138	C₂×D₄×C₁₃	C₂×D₄	1	32	yes	—
139	C₂×D₄×C₁₃	C₂×D₄	1	64	yes	complemented
140	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
141	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
142	C₂²×C₄×C₁₃	—	2	4	no	—
143	C₂²×C₄×C₁₃	—	2	8	no	—
144	C₂²×C₄×C₁₃	—	2	32	no	—
145	C₂²×C₄×C₁₃	—	2	64	no	—
146	C₂²×C₄×C₁₃	—	2	16	no	—
147	C₂²×C₄×C₁₃	—	2	32	no	—
148	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
149	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
150	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
151	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	—
152	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
153	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
154	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
155	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
156	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
157	C₂×C₂²⋊D₁₃	—	2	16	no	—
158	C₂×C₂²⋊D₁₃	—	2	32	no	—
159	C₂×C₂²⋊D₁₃	—	2	128	no	—
160	C₂×C₂²⋊D₁₃	—	4	16	no	—
161	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
162	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	—
163	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	—
164	C₂²×Dic₁₃	—	2	16	no	—
165	C₂²×Dic₁₃	—	4	16	no	—
166	C₂²×Dic₁₃	C₂⁴	1	8	yes	—
167	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
168	C₂²×Dic₁₃	C₂⁴	1	16	yes	—
169	C₂²×Dic₁₃	C₂⁴	1	32	yes	—
170	#6129	—	2	128	no	—
171	D₄×D₁₃	—	2	128	no	—
172	#6127	—	2	64	no	—
173	C₂×D₅₂	—	2	8	no	—
174	C₂×D₅₂	C₂⁴	1	8	yes	—
175	C₂×C₄×D₁₃	—	2	16	no	—
176	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
177	C₂×Dic₂₆	—	2	8	no	—
178	C₂×Dic₂₆	C₂⁴	1	8	yes	—
179	C₂²⋊Dic₁₃	C₂⁴	1	32	yes	—
180	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
181	C₂²⋊Dic₁₃	C₂⁴	1	32	yes	—
182	#6103	C₂⁴	1	32	yes	—
183	#6103	C₂⁴	1	64	yes	—
184	C₄⋊Dic₁₃	C₂⁴	1	16	yes	—
185	#6101	C₂⁴	1	32	yes	—
186	#6101	C₂⁴	1	64	yes	—
187	C₄×Dic₁₃	C₂⁴	1	16	yes	—
188	C₂²×H(5,𝔽₂)	—	13	1	no	—
189	C₂³×#41	D₁₃	1	1	yes	characteristic, complemented
190	#3485	—	13	32	no	—
191	C₂×#547	—	13	8	no	—
192	C₂×#546	—	13	8	no	—
193	C₂×#536	—	13	2	no	—
194	C₂×#534	—	13	4	no	—
195	C₂×#525	—	13	2	no	—
196	C₂²×#123	—	13	4	no	—
197	C₂×#518	—	13	1	no	—
198	C₂³×C₁₃	—	2	16	no	—
199	C₂³×C₁₃	—	2	4	no	—
200	C₂³×C₁₃	—	2	8	no	—
201	C₂³×C₁₃	—	2	4	no	—
202	C₂³×C₁₃	—	2	8	no	—
203	C₂³×C₁₃	—	4	32	no	—
204	C₂³×C₁₃	—	4	16	no	—
205	C₂³×C₁₃	—	4	8	no	—
206	C₂³×C₁₃	—	4	16	no	—
207	C₂³×C₁₃	C₂²×D₄	1	16	yes	—
208	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
209	C₂³×C₁₃	C₂²×D₄	1	32	yes	—
210	C₂³×C₁₃	C₂⁵	1	4	yes	—
211	C₂³×C₁₃	C₂⁵	1	2	yes	—
212	C₂³×C₁₃	C₂⁵	1	8	yes	—
213	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
214	C₂²×D₁₃	—	2	8	no	—
215	C₂²×D₁₃	—	2	16	no	—
216	C₂²×D₁₃	—	2	32	no	—
217	C₂²×D₁₃	—	4	32	no	—
218	C₂²×D₁₃	—	8	32	no	—
219	C₂²×D₁₃	C₂⁵	1	8	yes	—
220	Q₈×C₁₃	—	2	32	no	—
221	D₄×C₁₃	—	2	64	no	—
222	D₄×C₁₃	C₂²×D₄	1	64	yes	—
223	C₂×C₄×C₁₃	—	2	8	no	—
224	C₂×C₄×C₁₃	—	2	4	no	—
225	C₂×C₄×C₁₃	—	2	16	no	—
226	C₂×C₄×C₁₃	—	2	8	no	—
227	C₂×C₄×C₁₃	—	2	64	no	—
228	C₂×C₄×C₁₃	—	2	32	no	—
229	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
230	C₂×C₄×C₁₃	C₂²×D₄	1	16	yes	—
231	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
232	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
233	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
234	C₂²⋊D₁₃	—	2	32	no	—
235	C₂²⋊D₁₃	—	2	64	no	—
236	C₂²⋊D₁₃	—	4	32	no	—
237	C₂×Dic₁₃	—	2	8	no	—
238	C₂×Dic₁₃	—	2	32	no	—
239	C₂×Dic₁₃	—	2	16	no	—
240	C₂×Dic₁₃	—	4	32	no	—
241	C₂×Dic₁₃	C₂⁵	1	16	yes	—
242	C₂×Dic₁₃	C₂⁵	1	8	yes	—
243	D₅₂	—	2	16	no	—
244	C₄×D₁₃	—	2	32	no	—
245	Dic₂₆	—	2	16	no	—
246	C₂×H(5,𝔽₂)	—	13	16	no	—
247	C₂×H(5,𝔽₂)	—	26	16	no	—
248	C₂²×#41	—	2	16	no	—
249	C₂²×#41	—	13	4	no	—
250	C₂²×#41	—	13	2	no	—
251	C₂²×#41	C₂×D₁₃	1	8	yes	complemented
252	C₂²×#41	C₂×D₁₃	1	16	yes	complemented
253	C₂³×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
254	C₂³×D₄	—	13	4	no	—
255	C₂³×D₄	—	13	4	no	—
256	C₂³×D₄	C₂×D₁₃	1	1	yes	characteristic
257	C₂³×D₄	C₂×D₁₃	1	2	yes	complemented
258	C₂⁴×C₄	C₂×D₁₃	1	2	yes	complemented
259	C₂⁴×C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
260	#547	—	13	128	no	—
261	#546	—	13	128	no	—
262	#536	—	13	32	no	—
263	#534	—	13	64	no	—
264	C₂×C₄⋊Q₈	—	13	4	no	—
265	C₂×#124	—	13	4	no	—
266	#525	—	13	32	no	—
267	C₂×#123	—	13	8	no	—
268	C₂×#123	—	13	4	no	—
269	C₂×#123	—	13	8	no	—
270	C₂×#123	—	13	16	no	—
271	C₂×#123	—	13	64	no	—
272	C₂×C₂²⋊Q₈	—	13	8	no	—
273	C₂×C₂²⋊Q₈	—	13	4	no	—
274	C₂×#121	—	13	16	no	—
275	C₂×#121	—	13	4	no	—
276	C₂×#120	—	13	4	no	—
277	C₂×#120	—	13	8	no	—
278	#518	—	13	16	no	—
279	C₂×C₄×D₄	—	13	8	no	—
280	C₂×C₄×D₄	—	13	8	no	—
281	C₂×#117	—	13	2	no	—
282	C₂²×C₄⋊C₄	—	13	8	no	—
283	C₂²×C₂²⋊C₄	—	13	4	no	—
284	C₂²×C₂²⋊C₄	—	13	8	no	—
285	C₂²×C₁₃	—	2	16	no	—
286	C₂²×C₁₃	—	2	4	no	—
287	C₂²×C₁₃	—	2	32	no	—
288	C₂²×C₁₃	—	2	8	no	—
289	C₂²×C₁₃	—	2	4	no	—
290	C₂²×C₁₃	—	2	8	no	—
291	C₂²×C₁₃	—	4	32	no	—
292	C₂²×C₁₃	—	4	16	no	—
293	C₂²×C₁₃	—	4	8	no	—
294	C₂²×C₁₃	C₂³×D₄	1	16	yes	—
295	C₂²×C₁₃	C₂³×D₄	1	4	yes	—
296	C₂²×C₁₃	C₂³×D₄	1	2	yes	—
297	C₂²×C₁₃	#585	1	4	yes	—
298	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
299	C₂×D₁₃	—	2	8	no	—
300	C₂×D₁₃	—	2	16	no	—
301	C₂×D₁₃	—	4	16	no	—
302	C₂×D₁₃	—	8	32	no	—
303	C₄×C₁₃	—	2	4	no	—
304	C₄×C₁₃	—	2	8	no	—
305	C₄×C₁₃	C₂³×D₄	1	8	yes	—
306	Dic₁₃	—	2	8	no	—
307	Dic₁₃	—	2	16	no	—
308	C₂⁵	—	13	4	no	—
309	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
310	C₂⁵	C₂²×D₁₃	1	2	yes	—
311	H(5,𝔽₂)	—	26	128	no	—
312	C₂×#41	—	2	64	no	—
313	C₂×#41	—	2	128	no	—
314	C₂×#41	—	13	32	no	—
315	C₂×#41	—	13	16	no	—
316	C₂×#41	—	26	32	no	—
317	C₂×#41	—	26	16	no	—
318	C₂×#41	C₂²×D₁₃	1	64	yes	complemented
319	C₂²×Q₈	—	2	8	no	—
320	C₂²×Q₈	—	13	2	no	—
321	C₂²×Q₈	C₂²×D₁₃	1	4	yes	—
322	C₂²×Q₈	C₂²×D₁₃	1	8	yes	complemented
323	C₂²×D₄	—	2	16	no	—
324	C₂²×D₄	—	13	4	no	—
325	C₂²×D₄	—	13	8	no	—
326	C₂²×D₄	—	13	32	no	—
327	C₂²×D₄	—	13	8	no	—
328	C₂²×D₄	—	13	32	no	—
329	C₂²×D₄	—	13	2	no	—
330	C₂²×D₄	—	26	32	no	—
331	C₂²×D₄	—	26	32	no	—
332	C₂²×D₄	C₂²⋊D₁₃	1	16	yes	complemented
333	C₂²×D₄	C₂²×D₁₃	1	8	yes	—
334	C₂²×D₄	C₂²×D₁₃	1	4	yes	—
335	C₂²×D₄	C₂²×D₁₃	1	8	yes	—
336	C₂²×D₄	C₂²×D₁₃	1	16	yes	complemented
337	C₂³×C₄	—	2	16	no	—
338	C₂³×C₄	—	2	8	no	—
339	C₂³×C₄	—	13	4	no	—
340	C₂³×C₄	—	13	8	no	—
341	C₂³×C₄	—	13	4	no	—
342	C₂³×C₄	C₂²×D₁₃	1	8	yes	—
343	C₂³×C₄	C₂²×D₁₃	1	4	yes	—
344	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
345	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
346	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
347	C₂³×C₄	C₂²×D₁₃	1	16	yes	complemented
348	C₂³×C₄	C₂²×D₁₃	1	8	yes	complemented
349	C₄⋊Q₈	—	13	32	no	—
350	#124	—	13	32	no	—
351	#123	—	13	64	no	—
352	#123	—	13	32	no	—
353	#123	—	13	64	no	—
354	#123	—	13	128	no	—
355	C₂²⋊Q₈	—	13	64	no	—
356	C₂²⋊Q₈	—	13	32	no	—
357	#121	—	13	128	no	—
358	#121	—	13	32	no	—
359	#120	—	13	32	no	—
360	#120	—	13	64	no	—
361	C₄×D₄	—	13	64	no	—
362	C₄×D₄	—	13	64	no	—
363	#117	—	13	16	no	—
364	C₂×C₄⋊C₄	—	13	8	no	—
365	C₂×C₄⋊C₄	—	13	16	no	—
366	C₂×C₄⋊C₄	—	13	64	no	—
367	C₂×C₄⋊C₄	—	13	4	no	—
368	C₂×C₂²⋊C₄	—	13	4	no	—
369	C₂×C₂²⋊C₄	—	13	8	no	—
370	C₂×C₂²⋊C₄	—	13	32	no	—
371	C₂×C₂²⋊C₄	—	13	8	no	—
372	C₂×C₂²⋊C₄	—	13	8	no	—
373	C₂×C₂²⋊C₄	—	13	16	no	—
374	C₂×C₂²⋊C₄	—	13	64	no	—
375	C₂×C₄²	—	13	4	no	—
376	C₂×C₁₃	—	2	16	no	—
377	C₂×C₁₃	—	2	4	no	—
378	C₂×C₁₃	—	4	4	no	—
379	C₂×C₁₃	#3485	1	4	yes	complemented
380	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
381	C₂×C₁₃	C₂×#585	1	2	yes	—
382	D₁₃	—	4	8	no	—
383	C₂⁴	—	2	4	no	—
384	C₂⁴	—	4	8	no	—
385	C₂⁴	—	4	4	no	—
386	C₂⁴	—	13	4	no	—
387	C₂⁴	—	13	16	no	—
388	C₂⁴	—	26	16	no	—
389	C₂⁴	—	52	16	no	—
390	C₂⁴	C₂×C₂²⋊D₁₃	1	16	yes	—
391	C₂⁴	C₂³×D₁₃	1	2	yes	—
392	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
393	C₂⁴	C₂³×D₁₃	1	4	yes	—
394	C₂⁴	C₂³×D₁₃	1	4	yes	—
395	C₂⁴	C₂³×D₁₃	1	8	yes	—
396	#41	—	2	256	no	—
397	#41	—	26	128	no	—
398	#41	—	26	64	no	—
399	C₂×Q₈	—	2	16	no	—
400	C₂×Q₈	—	2	32	no	—
401	C₂×Q₈	—	13	8	no	—
402	C₂×Q₈	—	26	8	no	—
403	C₂×Q₈	C₂³×D₁₃	1	16	yes	—
404	C₂×D₄	—	2	32	no	—
405	C₂×D₄	—	2	64	no	—
406	C₂×D₄	—	13	16	no	—
407	C₂×D₄	—	13	32	no	—
408	C₂×D₄	—	13	32	no	—
409	C₂×D₄	—	13	8	no	—
410	C₂×D₄	—	26	16	no	—
411	C₂×D₄	—	26	32	no	—
412	C₂×D₄	—	26	128	no	—
413	C₂×D₄	—	26	128	no	—
414	C₂×D₄	—	26	8	no	—
415	C₂×D₄	—	52	16	no	—
416	C₂×D₄	C₂×C₂²⋊D₁₃	1	32	yes	—
417	C₂×D₄	C₂×C₂²⋊D₁₃	1	64	yes	complemented
418	C₂×D₄	C₂³×D₁₃	1	32	yes	—
419	C₂×D₄	C₂³×D₁₃	1	16	yes	—
420	C₂²×C₄	—	2	4	no	—
421	C₂²×C₄	—	2	8	no	—
422	C₂²×C₄	—	2	32	no	—
423	C₂²×C₄	—	2	64	no	—
424	C₂²×C₄	—	2	16	no	—
425	C₂²×C₄	—	2	32	no	—
426	C₂²×C₄	—	13	16	no	—
427	C₂²×C₄	—	13	8	no	—
428	C₂²×C₄	—	13	4	no	—
429	C₂²×C₄	—	13	32	no	—
430	C₂²×C₄	—	13	16	no	—
431	C₂²×C₄	—	26	16	no	—
432	C₂²×C₄	—	26	16	no	—
433	C₂²×C₄	—	52	16	no	—
434	C₂²×C₄	C₂×C₂²⋊D₁₃	1	8	yes	—
435	C₂²×C₄	C₂³×D₁₃	1	32	yes	—
436	C₂²×C₄	C₂³×D₁₃	1	16	yes	—
437	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
438	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
439	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
440	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
441	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
442	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
443	C₄⋊C₄	—	13	32	no	—
444	C₄⋊C₄	—	13	64	no	—
445	C₄⋊C₄	—	13	16	no	—
446	C₂²⋊C₄	—	13	16	no	—
447	C₂²⋊C₄	—	13	32	no	—
448	C₂²⋊C₄	—	13	32	no	—
449	C₂²⋊C₄	—	13	32	no	—
450	C₂²⋊C₄	—	13	64	no	—
451	C₄²	—	13	16	no	—
452	C₁₃	C₂×#3485	1	1	yes	characteristic, complemented, Sylow
453	C₂³	—	2	16	no	—
454	C₂³	—	2	4	no	—
455	C₂³	—	2	8	no	—
456	C₂³	—	2	8	no	—
457	C₂³	—	2	4	no	—
458	C₂³	—	4	32	no	—
459	C₂³	—	4	16	no	—
460	C₂³	—	4	8	no	—
461	C₂³	—	4	16	no	—
462	C₂³	—	13	8	no	—
463	C₂³	—	26	16	no	—
464	C₂³	—	26	8	no	—
465	C₂³	—	26	32	no	—
466	C₂³	—	52	32	no	—
467	C₂³	—	104	32	no	—
468	C₂³	C₂²×C₂²⋊D₁₃	1	4	yes	—
469	C₂³	C₂²×C₂²⋊D₁₃	1	16	yes	—
470	C₂³	C₂²×C₂²⋊D₁₃	1	32	yes	—
471	C₂³	C₂⁴×D₁₃	1	4	yes	—
472	C₂³	C₂⁴×D₁₃	1	2	yes	—
473	C₂³	C₂⁴×D₁₃	1	8	yes	—
474	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
475	Q₈	—	2	32	no	—
476	Q₈	—	26	16	no	—
477	D₄	—	2	64	no	—
478	D₄	—	26	32	no	—
479	D₄	—	26	64	no	—
480	D₄	—	26	16	no	—
481	D₄	—	52	32	no	—
482	D₄	C₂²×C₂²⋊D₁₃	1	64	yes	—
483	C₂×C₄	—	2	8	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	16	no	—
486	C₂×C₄	—	2	8	no	—
487	C₂×C₄	—	2	64	no	—
488	C₂×C₄	—	2	32	no	—
489	C₂×C₄	—	13	16	no	—
490	C₂×C₄	—	13	8	no	—
491	C₂×C₄	—	26	16	no	—
492	C₂×C₄	—	26	8	no	—
493	C₂×C₄	—	26	32	no	—
494	C₂×C₄	—	26	32	no	—
495	C₂×C₄	—	52	32	no	—
496	C₂×C₄	C₂²×C₂²⋊D₁₃	1	8	yes	—
497	C₂×C₄	C₂²×C₂²⋊D₁₃	1	16	yes	—
498	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
499	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
500	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
501	C₂²	—	2	8	no	—
502	C₂²	—	2	32	no	—
503	C₂²	—	2	16	no	—
504	C₂²	—	2	4	no	—
505	C₂²	—	2	4	no	—
506	C₂²	—	2	8	no	—
507	C₂²	—	4	32	no	—
508	C₂²	—	4	16	no	—
509	C₂²	—	4	8	no	—
510	C₂²	—	26	8	no	—
511	C₂²	—	26	16	no	—
512	C₂²	—	52	16	no	—
513	C₂²	—	104	32	no	—
514	C₂²	#11719648	1	4	yes	—
515	C₂²	C₂³×C₂²⋊D₁₃	1	4	yes	—
516	C₂²	C₂³×C₂²⋊D₁₃	1	16	yes	—
517	C₂²	C₂³×C₂²⋊D₁₃	1	2	yes	—
518	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
519	C₄	—	2	4	no	—
520	C₄	—	2	8	no	—
521	C₄	—	26	8	no	—
522	C₄	—	26	16	no	—
523	C₄	C₂³×C₂²⋊D₁₃	1	8	yes	—
524	C₂	—	2	4	no	—
525	C₂	—	2	16	no	—
526	C₂	—	4	4	no	—
527	C₂	—	52	8	no	—
528	C₂	#13128480	1	4	yes	direct product factor
529	C₂	C₂⁴×C₂²⋊D₁₃	1	1	yes	characteristic
530	C₂	C₂×#11719648	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂³×C₁₃×#41	C₂
socle	C₂³×C₁₃	C₂⁵
hypercenter	C₂³×#41	D₁₃
hypocenter	C₁₃	C₂×#3485
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂³×#41

Complements

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

N	H ≅ G/N	type
1. C₂²×#88251	C₂	semidirect
2. #13128480	C₂	direct (N × H)
3. C₂×#11719529	C₂	semidirect
4. C₂×#11719534	C₂	semidirect
5. C₂×#11719521	C₂	semidirect
6. C₂×#11719509	C₂	semidirect
7. C₂×#11719496	C₂	semidirect
8. C₂²×#88183	C₂	semidirect
9. C₂×#11719503	C₂	semidirect
10. C₂³×C₁₃×#41	C₂	semidirect
12. C₂²×C₁₃×#41	C₂²	semidirect
13. C₂²×C₁₃×#41	C₂²	semidirect
14. C₂³×Q₈×C₁₃	C₂²	semidirect
16. C₂³×D₄×C₁₃	C₂²	semidirect
17. C₂⁴×C₄×C₁₃	C₂²	semidirect
18. C₂⁴×C₄×C₁₃	C₂²	semidirect
21. C₂×#88251	C₂²	semidirect
22. C₂²×#6129	C₂²	semidirect
23. C₂²×D₄×D₁₃	C₂²	semidirect
25. C₂×#88207	C₂²	semidirect
26. C₂²×C₂²⋊Dic₁₃	C₂²	semidirect
27. #11719534	C₂²	semidirect
28. #11719529	C₂²	semidirect
29. #11719521	C₂²	semidirect
30. C₂×#88201	C₂²	semidirect
31. C₂×#88200	C₂²	semidirect
32. C₂×#88198	C₂²	semidirect
33. #11719509	C₂²	semidirect
34. C₂×#88193	C₂²	semidirect
35. C₂×#88191	C₂²	semidirect
36. #11719503	C₂²	semidirect
37. C₂×#88189	C₂²	semidirect
38. C₂×D₄×Dic₁₃	C₂²	semidirect
39. #11719496	C₂²	semidirect
40. C₂×#88184	C₂²	semidirect
41. C₂×#88183	C₂²	semidirect
42. C₂×#88183	C₂²	semidirect
43. C₂×#88183	C₂²	semidirect
44. C₂×#88183	C₂²	semidirect
45. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
46. C₂²×#6103	C₂²	semidirect
47. C₂×#88180	C₂²	semidirect
48. C₂×#88178	C₂²	semidirect
49. C₂²×#6101	C₂²	semidirect
55. C₂×C₁₃×#41	C₂³	semidirect
58. C₂²×Q₈×C₁₃	C₂³	semidirect
60. C₂²×D₄×C₁₃	D₄	semidirect
64. C₂²×D₄×C₁₃	C₂³	semidirect
72. C₂³×C₄×C₁₃	C₂³	semidirect
73. C₂³×C₄×C₁₃	C₂³	semidirect
83. C₂×#6129	C₂³	semidirect
85. C₂×D₄×D₁₃	C₂³	semidirect
91. #88207	C₂³	semidirect
95. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
96. #88201	C₂³	semidirect
97. #88200	C₂³	semidirect
98. #88198	C₂³	semidirect
99. #88193	C₂³	semidirect
100. #88191	C₂³	semidirect
101. #88189	C₂³	semidirect
102. D₄×Dic₁₃	C₂³	semidirect
103. #88184	C₂³	semidirect
104. #88183	C₂³	semidirect
105. #88183	C₂³	semidirect
106. #88183	C₂³	semidirect
107. C₄×C₂²⋊D₁₃	C₂³	semidirect
110. C₂×#6103	C₂³	semidirect
111. #88180	C₂³	semidirect
113. #88178	C₂³	semidirect
116. C₂×#6101	C₂³	semidirect
139. C₂×D₄×C₁₃	C₂×D₄	semidirect
189. C₂³×#41	D₁₃	semidirect
251. C₂²×#41	C₂×D₁₃	semidirect
252. C₂²×#41	C₂×D₁₃	semidirect
253. C₂³×Q₈	C₂×D₁₃	semidirect
257. C₂³×D₄	C₂×D₁₃	semidirect
258. C₂⁴×C₄	C₂×D₁₃	semidirect
259. C₂⁴×C₄	C₂×D₁₃	semidirect
318. C₂×#41	C₂²×D₁₃	semidirect
322. C₂²×Q₈	C₂²×D₁₃	semidirect
332. C₂²×D₄	C₂²⋊D₁₃	semidirect
336. C₂²×D₄	C₂²×D₁₃	semidirect
347. C₂³×C₄	C₂²×D₁₃	semidirect
348. C₂³×C₄	C₂²×D₁₃	semidirect
379. C₂×C₁₃	#3485	semidirect
417. C₂×D₄	C₂×C₂²⋊D₁₃	semidirect
452. C₁₃	C₂×#3485	semidirect
528. C₂	#13128480	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
#13128480	2
C₂×#11719529	2
C₂×#11719534	2
C₂×#11719521	2
C₂×#11719509	2
C₂×#11719496	2
C₂²×#88183	2
C₂×#11719503	2
C₂³×C₁₃×#41	2
C₂×#3485	13

Subgroups — C2×#13128480 #16770963

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13128480 #16770963