Subgroups — D₁₃×#3549 #16770717

Order 3328.

8802 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13129241	C₂	1	3	yes	maximal, complemented
2	#13129240	C₂	1	4	yes	maximal, complemented
3	#13129239	C₂	1	12	yes	maximal, complemented
4	#13129238	C₂	1	6	yes	maximal, complemented
5	#13129237	C₂	1	6	yes	maximal, complemented
6	D₁₃×H(3,𝔽₄)	C₂	1	4	yes	maximal, complemented
7	D₁₃×#555	C₂	1	6	yes	maximal, complemented
8	D₄²×D₁₃	C₂	1	6	yes	maximal, complemented
9	D₁₃×#535	C₂	1	12	yes	maximal, complemented
10	D₁₃×#532	C₂	1	3	yes	maximal, complemented
11	C₁₃×#3549	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#41×D₁₃	C₂²	1	6	yes	complemented
13	C₂²×D₄×D₁₃	C₂²	1	12	yes	complemented
14	C₁₃×H(3,𝔽₄)	C₂²	1	4	yes	complemented
15	C₁₃×#555	C₂²	1	6	yes	complemented
16	D₄²×C₁₃	C₂²	1	6	yes	complemented
17	C₁₃×#535	C₂²	1	12	yes	complemented
18	C₁₃×#532	C₂²	1	3	yes	complemented
19	#11719537	C₂²	1	6	yes	complemented
20	#11719535	C₂²	1	12	yes	complemented
21	#11719510	C₂²	1	12	yes	complemented
22	D₄×C₂²⋊D₁₃	C₂²	1	24	yes	complemented
23	#11719439	C₂²	1	6	yes	complemented
24	#11719430	C₂²	1	3	yes	complemented
25	D₁₃×C₄⋊Q₈	C₂²	1	3	yes	complemented
26	#11719422	C₂²	1	6	yes	complemented
27	#11719421	C₂²	1	3	yes	complemented
28	#11719420	C₂²	1	24	yes	complemented
29	D₁₃×#127	C₂²	1	3	yes	—
30	D₁₃×#127	C₂²	1	8	yes	complemented
31	#11719388	C₂²	1	24	yes	complemented
32	#11719388	C₂²	1	12	yes	complemented
33	#11719379	C₂²	1	24	yes	complemented
34	D₁₃×#124	C₂²	1	6	yes	complemented
35	D₁₃×#124	C₂²	1	24	yes	complemented
36	#11719375	C₂²	1	24	yes	complemented
37	#11719373	C₂²	1	6	yes	complemented
38	#11719321	C₂²	1	24	yes	complemented
39	#11719314	C₂²	1	24	yes	complemented
40	#11719312	C₂²	1	24	yes	complemented
41	#11719312	C₂²	1	24	yes	complemented
42	D₁₃×#121	C₂²	1	24	yes	complemented
43	D₁₃×#121	C₂²	1	12	yes	complemented
44	#11719301	C₂²	1	12	yes	complemented
45	#11719299	C₂²	1	24	yes	complemented
46	#11719297	C₂²	1	24	yes	complemented
47	#11719297	C₂²	1	24	yes	complemented
48	#11719295	C₂²	1	24	yes	complemented
49	D₁₃×#120	C₂²	1	24	yes	complemented
50	D₁₃×#120	C₂²	1	8	yes	complemented
51	#11719268	C₂²	1	12	yes	complemented
52	D₄×D₅₂	C₂²	1	12	yes	complemented
53	#11719253	C₂²	1	12	yes	complemented
54	C₄×D₄×D₁₃	C₂²	1	12	yes	complemented
55	#11719237	C₂²	1	24	yes	complemented
56	#11719230	C₂²	1	12	yes	complemented
57	D₁₃×#117	C₂²	1	12	yes	complemented
58	#11719182	C₂²	1	3	yes	complemented
59	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic, complemented
60	C₂⁴×D₁₃	C₂³	1	8	yes	—
61	C₂×C₁₃×#41	C₂³	1	6	yes	complemented
62	C₂²×D₄×C₁₃	C₂³	1	12	yes	complemented
63	C₂²×C₂²⋊D₁₃	C₂³	1	24	yes	complemented
64	#41×D₁₃	—	4	24	no	—
65	C₂×#6131	C₂³	1	6	yes	complemented
66	C₂×Q₈×D₁₃	C₂³	1	6	yes	—
67	C₂×#6129	C₂³	1	6	yes	complemented
68	C₂×#6129	C₂³	1	12	yes	complemented
69	C₂×D₄×D₁₃	—	4	48	no	—
70	C₂×D₄×D₁₃	C₂³	1	12	yes	—
71	C₂×D₄×D₁₃	C₂³	1	6	yes	—
72	C₂×D₄×D₁₃	C₂³	1	24	yes	—
73	C₂×D₄×D₁₃	C₂³	1	12	yes	—
74	C₂×D₄×D₁₃	C₂³	1	24	yes	complemented
75	C₂×D₄×D₁₃	C₂³	1	24	yes	complemented
76	C₂×#6127	C₂³	1	6	yes	complemented
77	C₂×#6127	C₂³	1	12	yes	complemented
78	C₂²×D₅₂	C₂³	1	12	yes	complemented
79	C₂²×C₄×D₁₃	C₂³	1	3	yes	—
80	C₂²×C₄×D₁₃	C₂³	1	12	yes	—
81	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	complemented
82	C₁₃×#127	C₂³	1	3	yes	—
83	C₁₃×#127	C₂³	1	8	yes	complemented
84	C₁₃×#124	C₂³	1	6	yes	complemented
85	C₁₃×#124	C₂³	1	24	yes	complemented
86	C₁₃×#121	C₂³	1	12	yes	complemented
87	C₁₃×#121	C₂³	1	24	yes	complemented
88	C₁₃×#120	C₂³	1	24	yes	complemented
89	C₁₃×#120	C₂³	1	8	yes	complemented
90	C₄×D₄×C₁₃	C₂³	1	12	yes	complemented
91	C₁₃×#117	C₂³	1	12	yes	complemented
92	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic, complemented
93	#88207	C₂³	1	24	yes	complemented
94	#88207	C₂³	1	8	yes	complemented
95	#88201	C₂³	1	6	yes	complemented
96	#88201	C₂³	1	24	yes	complemented
97	#88198	C₂³	1	6	yes	complemented
98	#88194	C₂³	1	12	yes	—
99	#88194	C₂³	1	6	yes	—
100	#88194	C₂³	1	24	yes	complemented
101	#88194	C₂³	1	24	yes	complemented
102	#88193	C₂³	1	48	yes	complemented
103	#88193	C₂³	1	24	yes	complemented
104	#88192	C₂³	1	24	yes	complemented
105	#88192	C₂³	1	12	yes	complemented
106	#88191	C₂³	1	48	yes	complemented
107	#88191	C₂³	1	24	yes	complemented
108	#88191	C₂³	1	24	yes	complemented
109	#88190	C₂³	1	24	yes	complemented
110	#88190	C₂³	1	6	yes	complemented
111	D₄×Dic₁₃	C₂³	1	12	yes	complemented
112	#88184	C₂³	1	12	yes	complemented
113	#88184	C₂³	1	24	yes	complemented
114	C₄×C₂²⋊D₁₃	C₂³	1	24	yes	complemented
115	#88180	C₂³	1	12	yes	complemented
116	C₂×C₄×Dic₁₃	C₂³	1	3	yes	complemented
117	#88149	C₂³	1	12	yes	complemented
118	#88149	C₂³	1	24	yes	complemented
119	#88147	C₂³	1	12	yes	complemented
120	#88146	C₂³	1	24	yes	complemented
121	C₄⋊C₄×D₁₃	C₂³	1	12	yes	—
122	#88142	C₂³	1	12	yes	complemented
123	#88139	C₂³	1	48	yes	complemented
124	#88139	C₂³	1	24	yes	complemented
125	#88139	C₂³	1	48	yes	complemented
126	#88138	C₂³	1	48	yes	complemented
127	#88138	C₂³	1	24	yes	complemented
128	#88136	C₂³	1	24	yes	complemented
129	#88136	C₂³	1	24	yes	complemented
130	#88136	C₂³	1	48	yes	complemented
131	#88135	C₂³	1	24	yes	complemented
132	C₂²⋊C₄×D₁₃	C₂³	1	24	yes	—
133	C₂²⋊C₄×D₁₃	C₂³	1	24	yes	—
134	#88131	C₂³	1	24	yes	complemented
135	#88129	C₂³	1	6	yes	complemented
136	#88129	C₂³	1	24	yes	complemented
137	#88128	C₂³	1	3	yes	—
138	#88128	C₂³	1	8	yes	complemented
139	C₄×D₅₂	C₂³	1	12	yes	complemented
140	#88126	C₂³	1	24	yes	complemented
141	C₄²×D₁₃	C₂³	1	3	yes	—
142	C₄²×D₁₃	C₂³	1	1	yes	characteristic
143	C₄²×D₁₃	C₂³	1	8	yes	—
144	C₄²×D₁₃	C₂³	1	3	yes	complemented
145	C₄²×D₁₃	C₂³	1	1	yes	characteristic, complemented
146	#88123	C₂³	1	3	yes	complemented
147	C₂×#3549	—	13	1	no	maximal, Sylow
148	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
149	C₂³×D₁₃	—	4	48	no	—
150	C₂³×D₁₃	C₂⁴	1	12	yes	—
151	C₂³×D₁₃	C₂⁴	1	1	yes	characteristic
152	C₂³×D₁₃	C₂⁴	1	24	yes	—
153	C₁₃×#41	—	4	12	no	—
154	C₂×Q₈×C₁₃	C₂⁴	1	6	yes	—
155	C₂×D₄×C₁₃	—	4	24	no	—
156	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
157	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
158	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
159	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
160	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
161	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
162	C₂×C₂²⋊D₁₃	—	4	48	no	—
163	C₂×C₂²⋊D₁₃	C₂⁴	1	24	yes	—
164	C₂×C₂²⋊D₁₃	C₂⁴	1	12	yes	—
165	C₂×C₂²⋊D₁₃	C₂⁴	1	12	yes	—
166	C₂×C₂²⋊D₁₃	C₂⁴	1	48	yes	—
167	C₂×C₂²⋊D₁₃	C₂⁴	1	12	yes	—
168	C₂²×Dic₁₃	C₂⁴	1	12	yes	—
169	C₂²×Dic₁₃	C₂⁴	1	3	yes	—
170	#6131	—	4	12	no	—
171	Q₈×D₁₃	—	4	12	no	—
172	#6129	—	4	24	no	—
173	#6129	—	4	12	no	—
174	D₄×D₁₃	—	2	48	no	—
175	D₄×D₁₃	—	4	48	no	—
176	D₄×D₁₃	—	4	48	no	—
177	D₄×D₁₃	—	4	48	no	—
178	D₄×D₁₃	—	4	24	no	—
179	D₄×D₁₃	—	4	12	no	—
180	#6127	—	4	24	no	—
181	#6127	—	4	12	no	—
182	C₂×D₅₂	—	4	24	no	—
183	C₂×D₅₂	C₂⁴	1	12	yes	—
184	C₂×D₅₂	C₂⁴	1	6	yes	—
185	C₂×D₅₂	C₂⁴	1	12	yes	—
186	C₂×D₅₂	C₂⁴	1	24	yes	—
187	C₂×C₄×D₁₃	—	2	48	no	—
188	C₂×C₄×D₁₃	—	2	12	no	—
189	C₂×C₄×D₁₃	C₂⁴	1	3	yes	—
190	C₂×C₄×D₁₃	C₂⁴	1	12	yes	—
191	C₂×C₄×D₁₃	C₂⁴	1	3	yes	—
192	C₂×C₄×D₁₃	C₂⁴	1	3	yes	—
193	C₂×C₄×D₁₃	C₂⁴	1	12	yes	—
194	C₂×C₄×D₁₃	C₂⁴	1	12	yes	—
195	C₂×C₄×D₁₃	C₂⁴	1	3	yes	—
196	C₂×Dic₂₆	C₂⁴	1	6	yes	—
197	C₂×Dic₂₆	C₂⁴	1	12	yes	—
198	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
199	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
200	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
201	C₄²×C₁₃	C₂⁴	1	3	yes	—
202	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
203	C₄²×C₁₃	C₂⁴	1	8	yes	—
204	C₂²⋊Dic₁₃	C₂⁴	1	24	yes	—
205	C₂²⋊Dic₁₃	C₂⁴	1	24	yes	—
206	#6103	C₂⁴	1	48	yes	—
207	#6103	C₂⁴	1	24	yes	—
208	#6103	C₂⁴	1	24	yes	—
209	C₄⋊Dic₁₃	C₂⁴	1	12	yes	—
210	#6101	C₂⁴	1	24	yes	—
211	C₄×Dic₁₃	C₂⁴	1	3	yes	—
212	C₄×Dic₁₃	C₂⁴	1	3	yes	—
213	C₄×Dic₁₃	C₂⁴	1	6	yes	—
214	C₄×Dic₁₃	C₂⁴	1	24	yes	—
215	#3549	—	13	4	no	—
216	#3549	—	13	6	no	—
217	#3549	—	13	6	no	—
218	#3549	—	13	12	no	—
219	#3549	—	13	3	no	—
220	#3549	D₁₃	1	1	yes	characteristic, direct product factor
221	C₂×H(3,𝔽₄)	—	13	4	no	—
222	C₂×#555	—	13	6	no	—
223	C₂×D₄²	—	13	6	no	—
224	C₂×#535	—	13	12	no	—
225	C₂×#532	—	13	3	no	—
226	C₂³×C₁₃	—	4	24	no	—
227	C₂³×C₁₃	C₂⁵	1	12	yes	—
228	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
229	C₂²×D₁₃	—	2	6	no	—
230	C₂²×D₁₃	—	2	24	no	—
231	C₂²×D₁₃	—	2	48	no	—
232	C₂²×D₁₃	—	4	24	no	—
233	C₂²×D₁₃	—	4	48	no	—
234	C₂²×D₁₃	—	8	64	no	—
235	C₂²×D₁₃	C₂⁵	1	12	yes	—
236	C₂²×D₁₃	C₂⁵	1	1	yes	characteristic
237	C₂²×D₁₃	C₂⁵	1	1	yes	characteristic
238	Q₈×C₁₃	—	4	6	no	—
239	D₄×C₁₃	—	2	24	no	—
240	D₄×C₁₃	—	4	24	no	—
241	D₄×C₁₃	—	4	6	no	—
242	D₄×C₁₃	—	4	12	no	—
243	C₂×C₄×C₁₃	—	2	24	no	—
244	C₂×C₄×C₁₃	—	2	6	no	—
245	C₂×C₄×C₁₃	C₂⁵	1	12	yes	—
246	C₂×C₄×C₁₃	C₂⁵	1	3	yes	—
247	C₂×C₄×C₁₃	C₂⁵	1	3	yes	—
248	C₂²⋊D₁₃	—	2	48	no	—
249	C₂²⋊D₁₃	—	4	12	no	—
250	C₂²⋊D₁₃	—	4	12	no	—
251	C₂²⋊D₁₃	—	4	12	no	—
252	C₂²⋊D₁₃	—	4	48	no	—
253	C₂×Dic₁₃	—	2	6	no	—
254	C₂×Dic₁₃	—	2	24	no	—
255	C₂×Dic₁₃	C₂⁵	1	12	yes	—
256	C₂×Dic₁₃	C₂⁵	1	3	yes	—
257	C₂×Dic₁₃	C₂⁵	1	3	yes	—
258	D₅₂	—	2	24	no	—
259	D₅₂	—	4	24	no	—
260	D₅₂	—	4	6	no	—
261	D₅₂	—	4	12	no	—
262	C₄×D₁₃	—	2	24	no	—
263	C₄×D₁₃	—	2	6	no	—
264	C₄×D₁₃	—	2	6	no	—
265	C₄×D₁₃	—	2	24	no	—
266	C₄×D₁₃	—	2	24	no	—
267	C₄×D₁₃	—	2	6	no	—
268	C₄×D₁₃	H(5,𝔽₂)	1	12	yes	—
269	Dic₂₆	—	4	12	no	—
270	Dic₂₆	—	4	6	no	—
271	C₂²×#41	—	13	6	no	—
272	C₂³×D₄	—	13	12	no	—
273	H(3,𝔽₄)	—	13	24	no	—
274	H(3,𝔽₄)	—	13	12	no	—
275	H(3,𝔽₄)	—	13	24	no	—
276	H(3,𝔽₄)	C₂×D₁₃	1	4	yes	complemented
277	#555	—	13	6	no	—
278	#555	—	13	24	no	—
279	#555	—	13	24	no	—
280	#555	—	13	12	no	—
281	#555	—	13	24	no	—
282	#555	C₂×D₁₃	1	6	yes	complemented
283	D₄²	—	13	24	no	—
284	D₄²	—	13	6	no	—
285	D₄²	—	13	24	no	—
286	D₄²	—	13	24	no	—
287	D₄²	—	13	12	no	—
288	D₄²	C₂×D₁₃	1	6	yes	complemented
289	#535	—	13	12	no	—
290	#535	—	13	12	no	—
291	#535	—	13	24	no	—
292	#535	—	13	24	no	—
293	#535	—	13	24	no	—
294	#535	—	13	24	no	—
295	#535	—	13	24	no	—
296	#535	—	13	24	no	—
297	#535	—	13	12	no	—
298	#535	C₂×D₁₃	1	12	yes	complemented
299	#532	—	13	6	no	—
300	#532	—	13	3	no	—
301	#532	—	13	3	no	—
302	#532	—	13	6	no	—
303	#532	—	13	12	no	—
304	#532	—	13	12	no	—
305	#532	—	13	3	no	—
306	#532	C₂×D₁₃	1	3	yes	complemented
307	C₂×C₄⋊Q₈	—	13	3	no	—
308	C₂×#127	—	13	3	no	—
309	C₂×#127	—	13	8	no	—
310	C₂×#124	—	13	6	no	—
311	C₂×#124	—	13	24	no	—
312	C₂×#121	—	13	12	no	—
313	C₂×#121	—	13	24	no	—
314	C₂×#120	—	13	8	no	—
315	C₂×#120	—	13	24	no	—
316	C₂×C₄×D₄	—	13	12	no	—
317	C₂×#117	—	13	12	no	—
318	C₂²×C₄²	—	13	1	no	—
319	C₂²×C₁₃	—	2	3	no	—
320	C₂²×C₁₃	—	2	12	no	—
321	C₂²×C₁₃	—	2	24	no	—
322	C₂²×C₁₃	—	8	16	no	—
323	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
324	C₂×D₁₃	—	2	3	no	—
325	C₂×D₁₃	—	2	12	no	—
326	C₂×D₁₃	—	2	24	no	—
327	C₂×D₁₃	—	4	4	no	—
328	C₂×D₁₃	—	4	48	no	—
329	C₂×D₁₃	—	8	48	no	—
330	C₂×D₁₃	C₂×H(5,𝔽₂)	1	6	yes	—
331	C₄×C₁₃	—	2	3	no	—
332	C₄×C₁₃	—	2	12	no	—
333	C₄×C₁₃	C₂×H(5,𝔽₂)	1	6	yes	—
334	Dic₁₃	—	2	3	no	—
335	Dic₁₃	—	2	12	no	—
336	Dic₁₃	C₂×H(5,𝔽₂)	1	6	yes	—
337	C₂⁵	—	13	8	no	—
338	C₂×#41	—	13	6	no	—
339	C₂×#41	—	13	12	no	—
340	C₂×#41	—	13	6	no	—
341	C₂×#41	—	13	12	no	—
342	C₂×#41	—	13	6	no	—
343	C₂×#41	—	52	24	no	—
344	C₂×#41	C₂²×D₁₃	1	6	yes	complemented
345	C₂²×Q₈	—	13	6	no	—
346	C₂²×D₄	—	13	24	no	—
347	C₂²×D₄	—	13	12	no	—
348	C₂²×D₄	—	13	6	no	—
349	C₂²×D₄	—	13	24	no	—
350	C₂²×D₄	—	13	12	no	—
351	C₂²×D₄	—	13	24	no	—
352	C₂²×D₄	—	13	24	no	—
353	C₂²×D₄	—	13	12	no	—
354	C₂²×D₄	—	52	48	no	—
355	C₂²×D₄	C₂²×D₁₃	1	12	yes	complemented
356	C₂³×C₄	—	13	12	no	—
357	C₂³×C₄	—	13	3	no	—
358	C₄⋊Q₈	—	13	6	no	—
359	C₄⋊Q₈	—	13	12	no	—
360	C₄⋊Q₈	—	13	3	no	—
361	C₄⋊Q₈	C₂²×D₁₃	1	3	yes	complemented
362	#127	—	13	6	no	—
363	#127	—	13	12	no	—
364	#127	—	13	24	no	—
365	#127	—	13	24	no	—
366	#127	—	13	3	no	—
367	#127	—	13	8	no	—
368	#127	C₂²×D₁₃	1	3	yes	—
369	#127	C₂²×D₁₃	1	8	yes	complemented
370	#124	—	13	6	no	—
371	#124	—	13	24	no	—
372	#124	—	13	6	no	—
373	#124	—	13	24	no	—
374	#124	—	13	24	no	—
375	#124	—	13	48	no	—
376	#124	—	13	48	no	—
377	#124	—	13	6	no	—
378	#124	—	13	24	no	—
379	#124	C₂²×D₁₃	1	6	yes	complemented
380	#124	C₂²×D₁₃	1	24	yes	complemented
381	#121	—	13	12	no	—
382	#121	—	13	24	no	—
383	#121	—	13	24	no	—
384	#121	—	13	48	no	—
385	#121	—	13	12	no	—
386	#121	—	13	24	no	—
387	#121	—	13	12	no	—
388	#121	—	13	24	no	—
389	#121	—	13	24	no	—
390	#121	—	13	48	no	—
391	#121	C₂²×D₁₃	1	12	yes	complemented
392	#121	C₂²×D₁₃	1	24	yes	complemented
393	#120	—	13	8	no	—
394	#120	—	13	24	no	—
395	#120	—	13	24	no	—
396	#120	—	13	24	no	—
397	#120	—	13	48	no	—
398	#120	—	13	24	no	—
399	#120	—	13	48	no	—
400	#120	—	13	24	no	—
401	#120	C₂²×D₁₃	1	8	yes	complemented
402	#120	C₂²×D₁₃	1	24	yes	complemented
403	C₄×D₄	—	13	12	no	—
404	C₄×D₄	—	13	24	no	—
405	C₄×D₄	—	13	12	no	—
406	C₄×D₄	—	13	24	no	—
407	C₄×D₄	—	13	12	no	—
408	C₄×D₄	C₂²×D₁₃	1	12	yes	complemented
409	#117	—	13	12	no	—
410	#117	—	13	24	no	—
411	#117	—	13	24	no	—
412	#117	—	13	24	no	—
413	#117	C₂²×D₁₃	1	12	yes	complemented
414	C₂×C₄⋊C₄	—	13	12	no	—
415	C₂×C₂²⋊C₄	—	13	24	no	—
416	C₂×C₂²⋊C₄	—	13	24	no	—
417	C₂×C₄²	—	13	3	no	—
418	C₂×C₄²	—	13	8	no	—
419	C₂×C₄²	—	13	3	no	—
420	C₂×C₄²	—	13	1	no	—
421	C₂×C₄²	—	13	1	no	—
422	C₂×C₄²	—	13	3	no	—
423	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic, complemented
424	C₂×C₁₃	—	4	12	no	—
425	C₂×C₁₃	—	4	1	no	—
426	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	3	yes	—
427	D₁₃	—	4	1	no	—
428	D₁₃	—	4	12	no	—
429	D₁₃	#3549	1	4	yes	direct product factor
430	C₂⁴	—	13	12	no	—
431	C₂⁴	—	13	1	no	—
432	C₂⁴	—	13	24	no	—
433	C₂⁴	—	52	48	no	—
434	C₂⁴	C₂³×D₁₃	1	8	yes	—
435	#41	—	4	12	no	—
436	#41	—	52	24	no	—
437	#41	—	52	12	no	—
438	#41	—	52	24	no	—
439	#41	—	52	12	no	—
440	#41	—	52	12	no	—
441	C₂×Q₈	—	13	12	no	—
442	C₂×Q₈	—	13	6	no	—
443	C₂×Q₈	—	52	12	no	—
444	C₂×Q₈	C₂³×D₁₃	1	6	yes	—
445	C₂×D₄	—	4	24	no	—
446	C₂×D₄	—	13	24	no	—
447	C₂×D₄	—	13	12	no	—
448	C₂×D₄	—	13	48	no	—
449	C₂×D₄	—	13	12	no	—
450	C₂×D₄	—	13	12	no	—
451	C₂×D₄	—	13	12	no	—
452	C₂×D₄	—	13	6	no	—
453	C₂×D₄	—	13	24	no	—
454	C₂×D₄	—	13	12	no	—
455	C₂×D₄	—	26	48	no	—
456	C₂×D₄	—	52	24	no	—
457	C₂×D₄	—	52	48	no	—
458	C₂×D₄	—	52	48	no	—
459	C₂×D₄	—	52	48	no	—
460	C₂×D₄	—	52	24	no	—
461	C₂×D₄	—	52	12	no	—
462	C₂×D₄	—	52	48	no	—
463	C₂×D₄	C₂³×D₁₃	1	12	yes	—
464	C₂×D₄	C₂³×D₁₃	1	6	yes	—
465	C₂×D₄	C₂³×D₁₃	1	24	yes	—
466	C₂×D₄	C₂³×D₁₃	1	12	yes	—
467	C₂²×C₄	—	13	3	no	—
468	C₂²×C₄	—	13	3	no	—
469	C₂²×C₄	—	13	12	no	—
470	C₂²×C₄	—	13	3	no	—
471	C₂²×C₄	—	13	12	no	—
472	C₂²×C₄	—	13	3	no	—
473	C₂²×C₄	—	13	3	no	—
474	C₂²×C₄	—	13	12	no	—
475	C₂²×C₄	—	13	12	no	—
476	C₂²×C₄	—	26	48	no	—
477	C₂²×C₄	—	26	12	no	—
478	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
479	C₂²×C₄	C₂³×D₁₃	1	12	yes	—
480	C₄⋊C₄	—	13	24	no	—
481	C₄⋊C₄	—	13	12	no	—
482	C₄⋊C₄	C₂³×D₁₃	1	12	yes	—
483	C₂²⋊C₄	—	13	24	no	—
484	C₂²⋊C₄	—	13	24	no	—
485	C₂²⋊C₄	—	13	48	no	—
486	C₂²⋊C₄	—	13	24	no	—
487	C₂²⋊C₄	—	13	24	no	—
488	C₂²⋊C₄	C₂³×D₁₃	1	24	yes	—
489	C₂²⋊C₄	C₂³×D₁₃	1	24	yes	—
490	C₄²	—	13	3	no	—
491	C₄²	—	13	6	no	—
492	C₄²	—	13	3	no	—
493	C₄²	—	13	24	no	—
494	C₄²	C₂³×D₁₃	1	3	yes	—
495	C₄²	C₂³×D₁₃	1	1	yes	characteristic
496	C₄²	C₂³×D₁₃	1	8	yes	—
497	C₁₃	C₂×#3549	1	1	yes	characteristic, complemented, Sylow
498	C₂³	—	4	24	no	—
499	C₂³	—	13	1	no	—
500	C₂³	—	13	12	no	—
501	C₂³	—	13	1	no	—
502	C₂³	—	26	6	no	—
503	C₂³	—	26	24	no	—
504	C₂³	—	26	48	no	—
505	C₂³	—	52	24	no	—
506	C₂³	—	52	48	no	—
507	C₂³	—	104	64	no	—
508	C₂³	C₂⁴×D₁₃	1	12	yes	—
509	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
510	Q₈	—	4	6	no	—
511	Q₈	—	52	12	no	—
512	Q₈	—	52	6	no	—
513	D₄	—	2	24	no	—
514	D₄	—	4	24	no	—
515	D₄	—	4	12	no	—
516	D₄	—	4	6	no	—
517	D₄	—	26	48	no	—
518	D₄	—	26	24	no	—
519	D₄	—	52	24	no	—
520	D₄	—	52	12	no	—
521	D₄	—	52	6	no	—
522	D₄	—	52	48	no	—
523	D₄	—	52	12	no	—
524	D₄	—	52	12	no	—
525	D₄	—	52	12	no	—
526	C₂×C₄	—	2	24	no	—
527	C₂×C₄	—	2	6	no	—
528	C₂×C₄	—	13	3	no	—
529	C₂×C₄	—	13	12	no	—
530	C₂×C₄	—	13	3	no	—
531	C₂×C₄	—	13	12	no	—
532	C₂×C₄	—	26	24	no	—
533	C₂×C₄	—	26	6	no	—
534	C₂×C₄	—	26	24	no	—
535	C₂×C₄	—	26	6	no	—
536	C₂×C₄	—	26	24	no	—
537	C₂×C₄	—	26	6	no	—
538	C₂×C₄	—	26	24	no	—
539	C₂×C₄	—	26	6	no	—
540	C₂×C₄	C₂⁴×D₁₃	1	3	yes	—
541	C₂×C₄	C₂⁴×D₁₃	1	12	yes	—
542	C₂×C₄	C₂⁴×D₁₃	1	3	yes	—
543	C₂²	—	2	3	no	—
544	C₂²	—	2	12	no	—
545	C₂²	—	2	24	no	—
546	C₂²	—	8	16	no	—
547	C₂²	—	13	6	no	—
548	C₂²	—	26	3	no	—
549	C₂²	—	26	12	no	—
550	C₂²	—	26	24	no	—
551	C₂²	—	52	4	no	—
552	C₂²	—	52	48	no	—
553	C₂²	—	104	48	no	—
554	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
555	C₄	—	2	12	no	—
556	C₄	—	2	3	no	—
557	C₄	—	13	6	no	—
558	C₄	—	26	12	no	—
559	C₄	—	26	3	no	—
560	C₄	D₁₃×H(5,𝔽₂)	1	6	yes	—
561	C₂	—	4	12	no	—
562	C₂	—	4	1	no	—
563	C₂	—	13	4	no	—
564	C₂	—	52	12	no	—
565	C₂	—	52	1	no	—
566	C₂	C₂×D₁₃×H(5,𝔽₂)	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁶
Fitting	C₁₃×#3549	C₂
hypercenter	#3549	D₁₃
hypocenter	C₁₃	C₂×#3549
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #3549

Complements

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

N	H ≅ G/N	type
1. #13129241	C₂	semidirect
2. #13129240	C₂	semidirect
3. #13129239	C₂	semidirect
4. #13129238	C₂	semidirect
5. #13129237	C₂	semidirect
6. D₁₃×H(3,𝔽₄)	C₂	semidirect
7. D₁₃×#555	C₂	semidirect
8. D₄²×D₁₃	C₂	semidirect
9. D₁₃×#535	C₂	semidirect
10. D₁₃×#532	C₂	semidirect
11. C₁₃×#3549	C₂	semidirect
12. C₂×#41×D₁₃	C₂²	semidirect
13. C₂²×D₄×D₁₃	C₂²	semidirect
14. C₁₃×H(3,𝔽₄)	C₂²	semidirect
15. C₁₃×#555	C₂²	semidirect
16. D₄²×C₁₃	C₂²	semidirect
17. C₁₃×#535	C₂²	semidirect
18. C₁₃×#532	C₂²	semidirect
19. #11719537	C₂²	semidirect
20. #11719535	C₂²	semidirect
21. #11719510	C₂²	semidirect
22. D₄×C₂²⋊D₁₃	C₂²	semidirect
23. #11719439	C₂²	semidirect
24. #11719430	C₂²	semidirect
25. D₁₃×C₄⋊Q₈	C₂²	semidirect
26. #11719422	C₂²	semidirect
27. #11719421	C₂²	semidirect
28. #11719420	C₂²	semidirect
30. D₁₃×#127	C₂²	semidirect
31. #11719388	C₂²	semidirect
32. #11719388	C₂²	semidirect
33. #11719379	C₂²	semidirect
34. D₁₃×#124	C₂²	semidirect
35. D₁₃×#124	C₂²	semidirect
36. #11719375	C₂²	semidirect
37. #11719373	C₂²	semidirect
38. #11719321	C₂²	semidirect
39. #11719314	C₂²	semidirect
40. #11719312	C₂²	semidirect
41. #11719312	C₂²	semidirect
42. D₁₃×#121	C₂²	semidirect
43. D₁₃×#121	C₂²	semidirect
44. #11719301	C₂²	semidirect
45. #11719299	C₂²	semidirect
46. #11719297	C₂²	semidirect
47. #11719297	C₂²	semidirect
48. #11719295	C₂²	semidirect
49. D₁₃×#120	C₂²	semidirect
50. D₁₃×#120	C₂²	semidirect
51. #11719268	C₂²	semidirect
52. D₄×D₅₂	C₂²	semidirect
53. #11719253	C₂²	semidirect
54. C₄×D₄×D₁₃	C₂²	semidirect
55. #11719237	C₂²	semidirect
56. #11719230	C₂²	semidirect
57. D₁₃×#117	C₂²	semidirect
58. #11719182	C₂²	semidirect
59. C₂×C₄²×D₁₃	C₂²	semidirect
61. C₂×C₁₃×#41	C₂³	semidirect
62. C₂²×D₄×C₁₃	C₂³	semidirect
63. C₂²×C₂²⋊D₁₃	C₂³	semidirect
65. C₂×#6131	C₂³	semidirect
67. C₂×#6129	C₂³	semidirect
68. C₂×#6129	C₂³	semidirect
74. C₂×D₄×D₁₃	C₂³	semidirect
75. C₂×D₄×D₁₃	C₂³	semidirect
76. C₂×#6127	C₂³	semidirect
77. C₂×#6127	C₂³	semidirect
78. C₂²×D₅₂	C₂³	semidirect
81. C₁₃×C₄⋊Q₈	C₂³	semidirect
83. C₁₃×#127	C₂³	semidirect
84. C₁₃×#124	C₂³	semidirect
85. C₁₃×#124	C₂³	semidirect
86. C₁₃×#121	C₂³	semidirect
87. C₁₃×#121	C₂³	semidirect
88. C₁₃×#120	C₂³	semidirect
89. C₁₃×#120	C₂³	semidirect
90. C₄×D₄×C₁₃	C₂³	semidirect
91. C₁₃×#117	C₂³	semidirect
92. C₂×C₄²×C₁₃	C₂³	semidirect
93. #88207	C₂³	semidirect
94. #88207	C₂³	semidirect
95. #88201	C₂³	semidirect
96. #88201	C₂³	semidirect
97. #88198	C₂³	semidirect
100. #88194	C₂³	semidirect
101. #88194	C₂³	semidirect
102. #88193	C₂³	semidirect
103. #88193	C₂³	semidirect
104. #88192	C₂³	semidirect
105. #88192	C₂³	semidirect
106. #88191	C₂³	semidirect
107. #88191	C₂³	semidirect
108. #88191	C₂³	semidirect
109. #88190	C₂³	semidirect
110. #88190	C₂³	semidirect
111. D₄×Dic₁₃	C₂³	semidirect
112. #88184	C₂³	semidirect
113. #88184	C₂³	semidirect
114. C₄×C₂²⋊D₁₃	C₂³	semidirect
115. #88180	C₂³	semidirect
116. C₂×C₄×Dic₁₃	C₂³	semidirect
117. #88149	C₂³	semidirect
118. #88149	C₂³	semidirect
119. #88147	C₂³	semidirect
120. #88146	C₂³	semidirect
122. #88142	C₂³	semidirect
123. #88139	C₂³	semidirect
124. #88139	C₂³	semidirect
125. #88139	C₂³	semidirect
126. #88138	C₂³	semidirect
127. #88138	C₂³	semidirect
128. #88136	C₂³	semidirect
129. #88136	C₂³	semidirect
130. #88136	C₂³	semidirect
131. #88135	C₂³	semidirect
134. #88131	C₂³	semidirect
135. #88129	C₂³	semidirect
136. #88129	C₂³	semidirect
138. #88128	C₂³	semidirect
139. C₄×D₅₂	C₂³	semidirect
140. #88126	C₂³	semidirect
144. C₄²×D₁₃	C₂³	semidirect
145. C₄²×D₁₃	C₂³	semidirect
146. #88123	C₂³	semidirect
220. #3549	D₁₃	direct (N × H)
276. H(3,𝔽₄)	C₂×D₁₃	semidirect
282. #555	C₂×D₁₃	semidirect
288. D₄²	C₂×D₁₃	semidirect
298. #535	C₂×D₁₃	semidirect
306. #532	C₂×D₁₃	semidirect
344. C₂×#41	C₂²×D₁₃	semidirect
355. C₂²×D₄	C₂²×D₁₃	semidirect
361. C₄⋊Q₈	C₂²×D₁₃	semidirect
369. #127	C₂²×D₁₃	semidirect
379. #124	C₂²×D₁₃	semidirect
380. #124	C₂²×D₁₃	semidirect
391. #121	C₂²×D₁₃	semidirect
392. #121	C₂²×D₁₃	semidirect
401. #120	C₂²×D₁₃	semidirect
402. #120	C₂²×D₁₃	semidirect
408. C₄×D₄	C₂²×D₁₃	semidirect
413. #117	C₂²×D₁₃	semidirect
423. C₂×C₄²	C₂²×D₁₃	semidirect
429. D₁₃	#3549	direct (N × H)
497. C₁₃	C₂×#3549	semidirect

Maximal subgroups

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

subgroup	index
#13129241	2
#13129240	2
#13129239	2
#13129238	2
#13129237	2
D₁₃×H(3,𝔽₄)	2
D₁₃×#555	2
D₄²×D₁₃	2
D₁₃×#535	2
D₁₃×#532	2
C₁₃×#3549	2
C₂×#3549	13

Subgroups — D13×#3549 #16770717

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×#3549 #16770717