Subgroups — D₁₃×#3444 #16769626

Order 3328.

8518 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13128133	C₂	1	3	yes	maximal, complemented
2	#13128132	C₂	1	1	yes	maximal, characteristic, complemented
3	#13128131	C₂	1	3	yes	maximal, complemented
4	#13128130	C₂	1	12	yes	maximal, complemented
5	#13128129	C₂	1	6	yes	maximal, complemented
6	#13128128	C₂	1	6	yes	maximal, complemented
7	D₁₃×#533	C₂	1	3	yes	maximal, complemented
8	D₁₃×#532	C₂	1	3	yes	maximal, complemented
9	D₁₃×#529	C₂	1	12	yes	maximal, complemented
10	D₁₃×#525	C₂	1	6	yes	maximal, complemented
11	C₄×#41×D₁₃	C₂	1	6	yes	maximal, complemented
12	C₂²×C₄²×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3444	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#41×D₁₃	C₂²	1	6	yes	—
15	C₂³×C₄×D₁₃	C₂²	1	3	yes	—
16	C₁₃×#533	C₂²	1	3	yes	complemented
17	C₁₃×#532	C₂²	1	3	yes	complemented
18	C₁₃×#529	C₂²	1	12	yes	complemented
19	C₁₃×#525	C₂²	1	6	yes	complemented
20	C₄×C₁₃×#41	C₂²	1	6	yes	complemented
21	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
22	#11719537	C₂²	1	6	yes	complemented
23	#11719533	C₂²	1	6	yes	complemented
24	#41×Dic₁₃	C₂²	1	6	yes	complemented
25	#11719496	C₂²	1	6	yes	complemented
26	C₂²×C₄×Dic₁₃	C₂²	1	3	yes	complemented
27	#11719433	C₂²	1	6	yes	complemented
28	#11719430	C₂²	1	3	yes	complemented
29	D₁₃×C₄⋊Q₈	C₂²	1	3	yes	complemented
30	#11719421	C₂²	1	3	yes	complemented
31	D₁₃×#127	C₂²	1	1	yes	characteristic, complemented
32	#11719411	C₂²	1	24	yes	complemented
33	D₁₃×#126	C₂²	1	8	yes	complemented
34	#11719396	C₂²	1	12	yes	complemented
35	#11719393	C₂²	1	6	yes	complemented
36	D₁₃×#125	C₂²	1	6	yes	complemented
37	#11719385	C₂²	1	12	yes	complemented
38	D₁₃×#124	C₂²	1	6	yes	complemented
39	#11719373	C₂²	1	6	yes	complemented
40	#11719361	C₂²	1	12	yes	complemented
41	D₁₃×#123	C₂²	1	12	yes	—
42	#11719354	C₂²	1	24	yes	complemented
43	#11719332	C₂²	1	12	yes	complemented
44	D₁₃×C₂²⋊Q₈	C₂²	1	12	yes	—
45	#11719329	C₂²	1	12	yes	complemented
46	#11719327	C₂²	1	12	yes	complemented
47	#11719311	C₂²	1	12	yes	complemented
48	D₁₃×#121	C₂²	1	12	yes	—
49	#11719305	C₂²	1	12	yes	complemented
50	#11719301	C₂²	1	12	yes	complemented
51	D₁₃×#120	C₂²	1	4	yes	—
52	#11719291	C₂²	1	12	yes	complemented
53	#11719285	C₂²	1	12	yes	complemented
54	#11719283	C₂²	1	12	yes	complemented
55	C₄×#6131	C₂²	1	12	yes	complemented
56	C₄×Q₈×D₁₃	C₂²	1	12	yes	complemented
57	#11719262	C₂²	1	12	yes	complemented
58	#11719253	C₂²	1	12	yes	complemented
59	#11719252	C₂²	1	24	yes	complemented
60	C₄×D₄×D₁₃	C₂²	1	24	yes	—
61	C₄×D₄×D₁₃	C₂²	1	12	yes	complemented
62	#11719243	C₂²	1	24	yes	complemented
63	C₄×#6129	C₂²	1	12	yes	complemented
64	C₄×#6129	C₂²	1	24	yes	complemented
65	#11719233	C₂²	1	24	yes	complemented
66	#11719229	C₂²	1	6	yes	complemented
67	#11719227	C₂²	1	12	yes	complemented
68	#11719227	C₂²	1	6	yes	complemented
69	D₁₃×#117	C₂²	1	6	yes	—
70	D₁₃×#117	C₂²	1	12	yes	complemented
71	#11719222	C₂²	1	6	yes	complemented
72	#11719184	C₂²	1	12	yes	complemented
73	#11719182	C₂²	1	3	yes	complemented
74	C₄×#6127	C₂²	1	12	yes	complemented
75	C₄×#6127	C₂²	1	6	yes	complemented
76	C₂×C₄²×D₁₃	C₂²	1	3	yes	—
77	C₂×C₄²×D₁₃	C₂²	1	6	yes	—
78	C₂×C₄²×D₁₃	C₂²	1	3	yes	—
79	C₂×C₄²×D₁₃	C₂²	1	3	yes	complemented
80	C₂×C₄²×D₁₃	C₂²	1	6	yes	complemented
81	C₂×C₄²×D₁₃	C₂²	1	3	yes	complemented
82	C₂×C₄²×D₁₃	C₂²	1	4	yes	complemented
83	#11719175	C₂²	1	3	yes	complemented
84	C₂⁴×D₁₃	C₂³	1	1	yes	characteristic
85	C₂×C₁₃×#41	C₂³	1	6	yes	—
86	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
87	C₂³×Dic₁₃	C₂³	1	3	yes	—
88	#41×D₁₃	—	2	48	no	—
89	C₂×#6131	C₂³	1	6	yes	—
90	C₂×Q₈×D₁₃	C₂³	1	6	yes	—
91	C₂×#6129	C₂³	1	12	yes	—
92	C₂×#6129	C₂³	1	6	yes	—
93	C₂×D₄×D₁₃	C₂³	1	12	yes	—
94	C₂×D₄×D₁₃	C₂³	1	6	yes	—
95	C₂×#6127	C₂³	1	6	yes	—
96	C₂×#6127	C₂³	1	12	yes	—
97	C₂²×C₄×D₁₃	—	2	24	no	—
98	C₂²×C₄×D₁₃	C₂³	1	6	yes	—
99	C₂²×C₄×D₁₃	C₂³	1	6	yes	—
100	C₂²×C₄×D₁₃	C₂³	1	3	yes	—
101	C₂²×C₄×D₁₃	C₂³	1	3	yes	—
102	C₂²×C₄×D₁₃	C₂³	1	6	yes	—
103	C₂²×C₄×D₁₃	C₂³	1	6	yes	—
104	C₂²×C₄×D₁₃	C₂³	1	3	yes	—
105	C₂²×C₄×D₁₃	C₂³	1	12	yes	—
106	C₂²×C₄×D₁₃	C₂³	1	3	yes	—
107	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	complemented
108	C₁₃×#127	C₂³	1	1	yes	characteristic, complemented
109	C₁₃×#126	C₂³	1	8	yes	complemented
110	C₁₃×#125	C₂³	1	6	yes	complemented
111	C₁₃×#124	C₂³	1	6	yes	complemented
112	C₁₃×#123	C₂³	1	12	yes	—
113	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
114	C₁₃×#121	C₂³	1	12	yes	—
115	C₁₃×#120	C₂³	1	4	yes	—
116	C₄×Q₈×C₁₃	C₂³	1	12	yes	complemented
117	C₄×D₄×C₁₃	C₂³	1	24	yes	—
118	C₄×D₄×C₁₃	C₂³	1	12	yes	complemented
119	C₁₃×#117	C₂³	1	6	yes	—
120	C₁₃×#117	C₂³	1	12	yes	complemented
121	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
122	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
123	C₂×C₄²×C₁₃	C₂³	1	6	yes	—
124	C₂×C₄²×C₁₃	C₂³	1	4	yes	complemented
125	#88207	C₂³	1	4	yes	—
126	#88201	C₂³	1	6	yes	complemented
127	#88200	C₂³	1	12	yes	—
128	Q₈×Dic₁₃	C₂³	1	12	yes	complemented
129	#88198	C₂³	1	6	yes	complemented
130	#88194	C₂³	1	6	yes	complemented
131	#88193	C₂³	1	24	yes	—
132	#88192	C₂³	1	12	yes	—
133	#88191	C₂³	1	12	yes	—
134	#88190	C₂³	1	6	yes	complemented
135	#88189	C₂³	1	12	yes	—
136	D₄×Dic₁₃	C₂³	1	24	yes	—
137	D₄×Dic₁₃	C₂³	1	12	yes	complemented
138	#88184	C₂³	1	12	yes	—
139	#88183	C₂³	1	12	yes	—
140	C₄×C₂²⋊D₁₃	C₂³	1	24	yes	—
141	C₄×C₂²⋊D₁₃	C₂³	1	24	yes	—
142	C₄×C₂²⋊D₁₃	C₂³	1	24	yes	complemented
143	#88180	C₂³	1	6	yes	—
144	#88180	C₂³	1	12	yes	complemented
145	#88178	C₂³	1	12	yes	—
146	C₂×C₄×Dic₁₃	C₂³	1	3	yes	—
147	C₂×C₄×Dic₁₃	C₂³	1	3	yes	—
148	C₂×C₄×Dic₁₃	C₂³	1	6	yes	—
149	C₂×C₄×Dic₁₃	C₂³	1	6	yes	—
150	C₂×C₄×Dic₁₃	C₂³	1	6	yes	—
151	C₂×C₄×Dic₁₃	C₂³	1	6	yes	—
152	C₂×C₄×Dic₁₃	C₂³	1	6	yes	—
153	C₂×C₄×Dic₁₃	C₂³	1	12	yes	complemented
154	#88152	C₂³	1	24	yes	complemented
155	#88151	C₂³	1	12	yes	—
156	#88150	C₂³	1	24	yes	—
157	#88149	C₂³	1	12	yes	—
158	#88148	C₂³	1	24	yes	—
159	#88147	C₂³	1	24	yes	—
160	#88147	C₂³	1	12	yes	complemented
161	#88146	C₂³	1	12	yes	—
162	#88146	C₂³	1	24	yes	complemented
163	C₄⋊C₄×D₁₃	C₂³	1	12	yes	—
164	C₄⋊C₄×D₁₃	C₂³	1	24	yes	—
165	#88144	C₂³	1	12	yes	complemented
166	#88143	C₂³	1	24	yes	complemented
167	#88142	C₂³	1	12	yes	complemented
168	#88141	C₂³	1	12	yes	complemented
169	#88141	C₂³	1	24	yes	complemented
170	#88140	C₂³	1	12	yes	—
171	#88139	C₂³	1	24	yes	complemented
172	#88138	C₂³	1	24	yes	—
173	#88137	C₂³	1	24	yes	—
174	#88136	C₂³	1	12	yes	—
175	#88135	C₂³	1	24	yes	—
176	#88135	C₂³	1	24	yes	—
177	#88135	C₂³	1	24	yes	complemented
178	C₂²⋊C₄×D₁₃	C₂³	1	12	yes	—
179	C₂²⋊C₄×D₁₃	C₂³	1	24	yes	—
180	#88133	C₂³	1	24	yes	complemented
181	#88132	C₂³	1	24	yes	—
182	#88131	C₂³	1	12	yes	—
183	#88131	C₂³	1	24	yes	complemented
184	#88130	C₂³	1	8	yes	complemented
185	#88129	C₂³	1	6	yes	complemented
186	#88128	C₂³	1	1	yes	characteristic, complemented
187	C₄×D₅₂	C₂³	1	24	yes	—
188	C₄×D₅₂	C₂³	1	12	yes	complemented
189	#88126	C₂³	1	12	yes	—
190	#88126	C₂³	1	12	yes	complemented
191	#88126	C₂³	1	12	yes	complemented
192	C₄²×D₁₃	C₂³	1	1	yes	characteristic
193	C₄²×D₁₃	C₂³	1	3	yes	—
194	C₄²×D₁₃	C₂³	1	1	yes	characteristic
195	C₄²×D₁₃	C₂³	1	3	yes	—
196	C₄²×D₁₃	C₂³	1	6	yes	—
197	C₄²×D₁₃	C₂³	1	3	yes	—
198	C₄²×D₁₃	C₂³	1	2	yes	—
199	C₄²×D₁₃	C₂³	1	3	yes	—
200	C₄²×D₁₃	C₂³	1	3	yes	—
201	C₄²×D₁₃	C₂³	1	6	yes	—
202	C₄²×D₁₃	C₂³	1	6	yes	—
203	C₄²×D₁₃	C₂³	1	6	yes	—
204	C₄²×D₁₃	C₂³	1	6	yes	—
205	C₄²×D₁₃	C₂³	1	3	yes	—
206	C₄²×D₁₃	C₂³	1	6	yes	—
207	C₄²×D₁₃	C₂³	1	6	yes	—
208	C₄²×D₁₃	C₂³	1	12	yes	—
209	C₄²×D₁₃	C₂³	1	4	yes	complemented
210	C₄²×D₁₃	C₂³	1	12	yes	complemented
211	#88124	C₂³	1	6	yes	complemented
212	#88123	C₂³	1	3	yes	complemented
213	C₄×Dic₂₆	C₂³	1	12	yes	complemented
214	C₄×Dic₂₆	C₂³	1	24	yes	complemented
215	C₂×#3444	—	13	1	no	maximal, Sylow
216	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
217	C₂³×D₁₃	—	2	12	no	—
218	C₂³×D₁₃	C₂⁴	1	4	yes	—
219	C₂³×D₁₃	C₂⁴	1	3	yes	—
220	C₂³×D₁₃	C₂⁴	1	3	yes	—
221	C₁₃×#41	—	2	24	no	—
222	C₂×Q₈×C₁₃	C₂⁴	1	6	yes	—
223	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
224	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
225	C₂²×C₄×C₁₃	—	2	12	no	—
226	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
227	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
228	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
229	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
230	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
231	C₂×C₂²⋊D₁₃	C₂⁴	1	12	yes	—
232	C₂×C₂²⋊D₁₃	C₂⁴	1	12	yes	—
233	C₂×C₂²⋊D₁₃	C₂⁴	1	12	yes	—
234	C₂²×Dic₁₃	—	2	12	no	—
235	C₂²×Dic₁₃	C₂⁴	1	12	yes	—
236	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
237	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
238	C₂²×Dic₁₃	C₂⁴	1	3	yes	—
239	C₂²×Dic₁₃	C₂⁴	1	3	yes	—
240	#6131	—	2	24	no	—
241	Q₈×D₁₃	—	2	24	no	—
242	#6129	—	2	48	no	—
243	#6129	—	2	24	no	—
244	D₄×D₁₃	—	2	48	no	—
245	D₄×D₁₃	—	2	24	no	—
246	#6127	—	2	24	no	—
247	#6127	—	2	48	no	—
248	C₂×D₅₂	C₂⁴	1	12	yes	—
249	C₂×D₅₂	C₂⁴	1	6	yes	—
250	C₂×C₄×D₁₃	—	2	12	no	—
251	C₂×C₄×D₁₃	—	2	12	no	—
252	C₂×C₄×D₁₃	—	2	12	no	—
253	C₂×C₄×D₁₃	—	2	24	no	—
254	C₂×C₄×D₁₃	—	2	24	no	—
255	C₂×C₄×D₁₃	—	2	48	no	—
256	C₂×C₄×D₁₃	—	2	24	no	—
257	C₂×C₄×D₁₃	—	2	24	no	—
258	C₂×C₄×D₁₃	#41	1	24	yes	complemented
259	C₂×C₄×D₁₃	C₂⁴	1	6	yes	—
260	C₂×C₄×D₁₃	C₂⁴	1	6	yes	—
261	C₂×C₄×D₁₃	C₂⁴	1	6	yes	—
262	C₂×C₄×D₁₃	C₂⁴	1	6	yes	—
263	C₂×C₄×D₁₃	C₂⁴	1	6	yes	—
264	C₂×C₄×D₁₃	C₂⁴	1	6	yes	—
265	C₂×C₄×D₁₃	C₂⁴	1	12	yes	—
266	C₂×C₄×D₁₃	C₂⁴	1	12	yes	—
267	C₂×C₄×D₁₃	C₂⁴	1	12	yes	—
268	C₂×C₄×D₁₃	C₂⁴	1	3	yes	—
269	C₂×C₄×D₁₃	C₂⁴	1	3	yes	—
270	C₂×C₄×D₁₃	C₂⁴	1	3	yes	—
271	C₂×C₄×D₁₃	C₂⁴	1	3	yes	—
272	C₂×Dic₂₆	C₂⁴	1	6	yes	—
273	C₂×Dic₂₆	C₂⁴	1	12	yes	—
274	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
275	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
276	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
277	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
278	C₄²×C₁₃	C₂⁴	1	6	yes	—
279	C₄²×C₁₃	C₂⁴	1	12	yes	—
280	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
281	C₄²×C₁₃	C₂⁴	1	3	yes	—
282	C₄²×C₁₃	C₂⁴	1	3	yes	—
283	C₄²×C₁₃	C₂⁴	1	2	yes	—
284	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
285	C₂²⋊Dic₁₃	C₂⁴	1	12	yes	—
286	C₂²⋊Dic₁₃	C₂⁴	1	24	yes	—
287	#6103	C₂⁴	1	24	yes	—
288	#6103	C₂⁴	1	24	yes	—
289	#6103	C₂⁴	1	24	yes	—
290	C₄⋊Dic₁₃	C₂⁴	1	12	yes	—
291	C₄⋊Dic₁₃	C₂⁴	1	24	yes	—
292	#6101	C₂⁴	1	24	yes	—
293	#6101	C₂⁴	1	24	yes	—
294	#6101	C₂⁴	1	24	yes	—
295	C₄×Dic₁₃	C₂⁴	1	6	yes	—
296	C₄×Dic₁₃	C₂⁴	1	12	yes	—
297	C₄×Dic₁₃	C₂⁴	1	3	yes	—
298	C₄×Dic₁₃	C₂⁴	1	3	yes	—
299	C₄×Dic₁₃	C₂⁴	1	6	yes	—
300	C₄×Dic₁₃	C₂⁴	1	6	yes	—
301	C₄×Dic₁₃	C₂⁴	1	6	yes	—
302	C₄×Dic₁₃	C₂⁴	1	6	yes	—
303	C₄×Dic₁₃	C₂⁴	1	6	yes	—
304	C₄×Dic₁₃	C₂⁴	1	3	yes	—
305	C₄×Dic₁₃	C₂⁴	1	3	yes	—
306	C₄×Dic₁₃	C₂⁴	1	24	yes	—
307	#3444	—	13	1	no	—
308	#3444	—	13	3	no	—
309	#3444	—	13	3	no	—
310	#3444	—	13	12	no	—
311	#3444	—	13	6	no	—
312	#3444	—	13	6	no	—
313	#3444	D₁₃	1	1	yes	characteristic, direct product factor
314	C₂×#533	—	13	3	no	—
315	C₂×#532	—	13	3	no	—
316	C₂×#529	—	13	12	no	—
317	C₂×#525	—	13	6	no	—
318	C₂×C₄×#41	—	13	6	no	—
319	C₂³×C₄²	—	13	1	no	—
320	C₂³×C₁₃	—	2	6	no	—
321	C₂³×C₁₃	C₂⁵	1	4	yes	—
322	C₂³×C₁₃	C₂⁵	1	3	yes	—
323	C₂²×D₁₃	—	2	32	no	—
324	C₂²×D₁₃	—	2	6	no	—
325	C₂²×D₁₃	—	2	12	no	—
326	C₂²×D₁₃	—	2	12	no	—
327	C₂²×D₁₃	—	2	24	no	—
328	C₂²×D₁₃	C₂×#41	1	12	yes	—
329	C₂²×D₁₃	C₂⁵	1	4	yes	—
330	C₂²×D₁₃	C₂⁵	1	3	yes	—
331	C₂²×D₁₃	C₂⁵	1	1	yes	characteristic
332	Q₈×C₁₃	—	2	12	no	—
333	D₄×C₁₃	—	2	24	no	—
334	D₄×C₁₃	—	2	12	no	—
335	C₂×C₄×C₁₃	—	2	6	no	—
336	C₂×C₄×C₁₃	—	2	12	no	—
337	C₂×C₄×C₁₃	—	2	12	no	—
338	C₂×C₄×C₁₃	—	2	24	no	—
339	C₂×C₄×C₁₃	C₂×#41	1	12	yes	complemented
340	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
341	C₂×C₄×C₁₃	C₂⁵	1	12	yes	—
342	C₂×C₄×C₁₃	C₂⁵	1	3	yes	—
343	C₂×C₄×C₁₃	C₂⁵	1	3	yes	—
344	C₂²⋊D₁₃	—	2	24	no	—
345	C₂²⋊D₁₃	—	2	24	no	—
346	C₂²⋊D₁₃	—	2	24	no	—
347	C₂×Dic₁₃	—	2	6	no	—
348	C₂×Dic₁₃	—	2	12	no	—
349	C₂×Dic₁₃	—	2	12	no	—
350	C₂×Dic₁₃	—	2	24	no	—
351	C₂×Dic₁₃	C₂×#41	1	12	yes	complemented
352	C₂×Dic₁₃	C₂⁵	1	6	yes	—
353	C₂×Dic₁₃	C₂⁵	1	12	yes	—
354	C₂×Dic₁₃	C₂⁵	1	3	yes	—
355	C₂×Dic₁₃	C₂⁵	1	3	yes	—
356	D₅₂	—	2	24	no	—
357	D₅₂	—	2	12	no	—
358	C₄×D₁₃	—	2	12	no	—
359	C₄×D₁₃	—	2	12	no	—
360	C₄×D₁₃	—	2	24	no	—
361	C₄×D₁₃	—	2	12	no	—
362	C₄×D₁₃	—	2	12	no	—
363	C₄×D₁₃	—	2	24	no	—
364	C₄×D₁₃	—	2	12	no	—
365	C₄×D₁₃	—	2	12	no	—
366	C₄×D₁₃	—	2	24	no	—
367	C₄×D₁₃	C₂×#41	1	12	yes	—
368	C₄×D₁₃	C₂×#41	1	12	yes	—
369	C₄×D₁₃	C₂×#41	1	12	yes	complemented
370	C₄×D₁₃	C₂×#41	1	12	yes	complemented
371	Dic₂₆	—	2	12	no	—
372	Dic₂₆	—	2	24	no	—
373	C₂²×#41	—	13	6	no	—
374	C₂⁴×C₄	—	13	3	no	—
375	#533	—	13	6	no	—
376	#533	—	13	6	no	—
377	#533	—	13	12	no	—
378	#533	—	13	12	no	—
379	#533	—	13	6	no	—
380	#533	—	13	3	no	—
381	#533	C₂×D₁₃	1	3	yes	complemented
382	#532	—	13	6	no	—
383	#532	—	13	3	no	—
384	#532	—	13	3	no	—
385	#532	—	13	6	no	—
386	#532	—	13	12	no	—
387	#532	—	13	12	no	—
388	#532	—	13	3	no	—
389	#532	C₂×D₁₃	1	3	yes	complemented
390	C₂×C₄⋊Q₈	—	13	3	no	—
391	C₂×#127	—	13	1	no	—
392	#529	—	13	24	no	—
393	#529	—	13	12	no	—
394	#529	—	13	12	no	—
395	#529	—	13	24	no	—
396	#529	—	13	12	no	—
397	#529	—	13	12	no	—
398	#529	—	13	12	no	—
399	#529	—	13	24	no	—
400	#529	—	13	12	no	—
401	#529	—	13	24	no	—
402	#529	—	13	12	no	—
403	#529	C₂×D₁₃	1	12	yes	complemented
404	C₂×#126	—	13	8	no	—
405	C₂×#125	—	13	6	no	—
406	C₂×#124	—	13	6	no	—
407	#525	—	13	6	no	—
408	#525	—	13	6	no	—
409	#525	—	13	12	no	—
410	#525	—	13	12	no	—
411	#525	—	13	12	no	—
412	#525	—	13	12	no	—
413	#525	—	13	24	no	—
414	#525	—	13	6	no	—
415	#525	C₂×D₁₃	1	6	yes	complemented
416	C₂×#123	—	13	12	no	—
417	C₂×C₂²⋊Q₈	—	13	12	no	—
418	C₂×#121	—	13	12	no	—
419	C₂×#120	—	13	4	no	—
420	C₄×#41	—	13	6	no	—
421	C₄×#41	—	13	12	no	—
422	C₄×#41	—	13	24	no	—
423	C₄×#41	—	13	12	no	—
424	C₄×#41	—	13	6	no	—
425	C₄×#41	—	13	12	no	—
426	C₄×#41	—	13	6	no	—
427	C₄×#41	—	13	12	no	—
428	C₄×#41	C₂×D₁₃	1	6	yes	complemented
429	C₂×C₄×Q₈	—	13	12	no	—
430	C₂×C₄×D₄	—	13	24	no	—
431	C₂×C₄×D₄	—	13	12	no	—
432	C₂×#117	—	13	6	no	—
433	C₂×#117	—	13	12	no	—
434	C₂²×C₄²	—	13	3	no	—
435	C₂²×C₄²	—	13	3	no	—
436	C₂²×C₄²	—	13	6	no	—
437	C₂²×C₄²	—	13	3	no	—
438	C₂²×C₄²	—	13	3	no	—
439	C₂²×C₄²	—	13	6	no	—
440	C₂²×C₄²	—	13	3	no	—
441	C₂²×C₄²	—	13	4	no	—
442	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic, complemented
443	C₂²×C₁₃	—	2	8	no	—
444	C₂²×C₁₃	—	2	6	no	—
445	C₂²×C₁₃	—	2	12	no	—
446	C₂²×C₁₃	C₂²×#41	1	6	yes	—
447	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
448	C₂×D₁₃	—	2	24	no	—
449	C₂×D₁₃	—	2	6	no	—
450	C₂×D₁₃	—	2	24	no	—
451	C₂×D₁₃	—	2	12	no	—
452	C₂×D₁₃	—	4	16	no	—
453	C₂×D₁₃	C₂²×#41	1	6	yes	—
454	C₂×D₁₃	C₂²×#41	1	6	yes	—
455	C₄×C₁₃	—	2	12	no	—
456	C₄×C₁₃	—	2	6	no	—
457	C₄×C₁₃	C₂²×#41	1	6	yes	—
458	C₄×C₁₃	C₂²×#41	1	6	yes	—
459	Dic₁₃	—	2	12	no	—
460	Dic₁₃	—	2	6	no	—
461	Dic₁₃	C₂²×#41	1	6	yes	—
462	Dic₁₃	C₂²×#41	1	6	yes	—
463	C₂⁵	—	13	1	no	—
464	C₂×#41	—	13	6	no	—
465	C₂×#41	—	13	12	no	—
466	C₂×#41	—	13	6	no	—
467	C₂×#41	—	13	12	no	—
468	C₂×#41	—	13	6	no	—
469	C₂×#41	—	26	48	no	—
470	C₂×#41	C₂²×D₁₃	1	6	yes	—
471	C₂²×Q₈	—	13	6	no	—
472	C₂²×D₄	—	13	12	no	—
473	C₂²×D₄	—	13	6	no	—
474	C₂³×C₄	—	13	3	no	—
475	C₂³×C₄	—	13	3	no	—
476	C₂³×C₄	—	13	12	no	—
477	C₂³×C₄	—	13	6	no	—
478	C₂³×C₄	—	13	6	no	—
479	C₂³×C₄	—	13	3	no	—
480	C₂³×C₄	—	13	3	no	—
481	C₂³×C₄	—	13	6	no	—
482	C₂³×C₄	—	13	6	no	—
483	C₂³×C₄	—	13	3	no	—
484	C₂³×C₄	—	26	24	no	—
485	C₂³×C₄	C₂²×D₁₃	1	3	yes	—
486	C₄⋊Q₈	—	13	6	no	—
487	C₄⋊Q₈	—	13	12	no	—
488	C₄⋊Q₈	—	13	3	no	—
489	C₄⋊Q₈	C₂²×D₁₃	1	3	yes	complemented
490	#127	—	13	6	no	—
491	#127	—	13	1	no	—
492	#127	C₂²×D₁₃	1	1	yes	characteristic, complemented
493	#126	—	13	24	no	—
494	#126	—	13	24	no	—
495	#126	—	13	8	no	—
496	#126	C₂²×D₁₃	1	8	yes	complemented
497	#125	—	13	24	no	—
498	#125	—	13	12	no	—
499	#125	—	13	6	no	—
500	#125	C₂²×D₁₃	1	6	yes	complemented
501	#124	—	13	6	no	—
502	#124	—	13	6	no	—
503	#124	—	13	24	no	—
504	#124	—	13	6	no	—
505	#124	C₂²×D₁₃	1	6	yes	complemented
506	#123	—	13	12	no	—
507	#123	—	13	12	no	—
508	#123	—	13	24	no	—
509	#123	—	13	24	no	—
510	#123	—	13	12	no	—
511	#123	C₂²×D₁₃	1	12	yes	—
512	C₂²⋊Q₈	—	13	12	no	—
513	C₂²⋊Q₈	—	13	12	no	—
514	C₂²⋊Q₈	—	13	24	no	—
515	C₂²⋊Q₈	—	13	12	no	—
516	C₂²⋊Q₈	—	13	24	no	—
517	C₂²⋊Q₈	C₂²×D₁₃	1	12	yes	—
518	#121	—	13	12	no	—
519	#121	—	13	24	no	—
520	#121	—	13	12	no	—
521	#121	—	13	12	no	—
522	#121	—	13	24	no	—
523	#121	C₂²×D₁₃	1	12	yes	—
524	#120	—	13	4	no	—
525	#120	—	13	12	no	—
526	#120	—	13	12	no	—
527	#120	C₂²×D₁₃	1	4	yes	—
528	C₄×Q₈	—	13	12	no	—
529	C₄×Q₈	—	13	24	no	—
530	C₄×Q₈	—	13	12	no	—
531	C₄×Q₈	—	13	24	no	—
532	C₄×Q₈	—	13	12	no	—
533	C₄×Q₈	C₂²×D₁₃	1	12	yes	complemented
534	C₄×D₄	—	13	24	no	—
535	C₄×D₄	—	13	12	no	—
536	C₄×D₄	—	13	24	no	—
537	C₄×D₄	—	13	24	no	—
538	C₄×D₄	—	13	24	no	—
539	C₄×D₄	—	13	24	no	—
540	C₄×D₄	—	13	12	no	—
541	C₄×D₄	—	13	24	no	—
542	C₄×D₄	—	13	24	no	—
543	C₄×D₄	—	13	24	no	—
544	C₄×D₄	—	13	24	no	—
545	C₄×D₄	—	13	12	no	—
546	C₄×D₄	C₂²×D₁₃	1	24	yes	—
547	C₄×D₄	C₂²×D₁₃	1	12	yes	complemented
548	#117	—	13	6	no	—
549	#117	—	13	12	no	—
550	#117	—	13	12	no	—
551	#117	—	13	24	no	—
552	#117	—	13	12	no	—
553	#117	—	13	24	no	—
554	#117	—	13	12	no	—
555	#117	—	13	12	no	—
556	#117	—	13	12	no	—
557	#117	C₂²×D₁₃	1	6	yes	—
558	#117	C₂²×D₁₃	1	12	yes	complemented
559	C₂×C₄⋊C₄	—	13	12	no	—
560	C₂×C₄⋊C₄	—	13	24	no	—
561	C₂×C₂²⋊C₄	—	13	12	no	—
562	C₂×C₂²⋊C₄	—	13	24	no	—
563	C₂×C₄²	—	13	12	no	—
564	C₂×C₄²	—	13	6	no	—
565	C₂×C₄²	—	13	3	no	—
566	C₂×C₄²	—	13	6	no	—
567	C₂×C₄²	—	13	6	no	—
568	C₂×C₄²	—	13	6	no	—
569	C₂×C₄²	—	13	6	no	—
570	C₂×C₄²	—	13	3	no	—
571	C₂×C₄²	—	13	3	no	—
572	C₂×C₄²	—	13	12	no	—
573	C₂×C₄²	—	13	6	no	—
574	C₂×C₄²	—	13	12	no	—
575	C₂×C₄²	—	13	6	no	—
576	C₂×C₄²	—	13	3	no	—
577	C₂×C₄²	—	13	3	no	—
578	C₂×C₄²	—	13	2	no	—
579	C₂×C₄²	—	13	6	no	—
580	C₂×C₄²	—	13	6	no	—
581	C₂×C₄²	—	13	6	no	—
582	C₂×C₄²	—	13	6	no	—
583	C₂×C₄²	—	13	1	no	—
584	C₂×C₄²	—	13	3	no	—
585	C₂×C₄²	—	13	3	no	—
586	C₂×C₄²	—	13	6	no	—
587	C₂×C₄²	—	13	4	no	—
588	C₂×C₄²	—	13	3	no	—
589	C₂×C₄²	—	13	1	no	—
590	C₂×C₄²	C₂²×D₁₃	1	6	yes	—
591	C₂×C₄²	C₂²×D₁₃	1	3	yes	—
592	C₂×C₄²	C₂²×D₁₃	1	3	yes	—
593	C₂×C₄²	C₂²×D₁₃	1	4	yes	complemented
594	C₂×C₁₃	—	2	6	no	—
595	C₂×C₁₃	—	4	4	no	—
596	C₂×C₁₃	C₂³×#41	1	3	yes	—
597	D₁₃	—	2	6	no	—
598	D₁₃	—	4	4	no	—
599	D₁₃	#3444	1	4	yes	direct product factor
600	C₂⁴	—	13	3	no	—
601	C₂⁴	—	13	4	no	—
602	C₂⁴	—	13	3	no	—
603	C₂⁴	—	26	12	no	—
604	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
605	#41	—	2	24	no	—
606	#41	—	26	48	no	—
607	#41	—	26	48	no	—
608	#41	—	26	24	no	—
609	#41	—	26	24	no	—
610	#41	—	26	24	no	—
611	C₂×Q₈	—	13	12	no	—
612	C₂×Q₈	—	13	6	no	—
613	C₂×Q₈	—	26	24	no	—
614	C₂×Q₈	C₂³×D₁₃	1	6	yes	—
615	C₂×D₄	—	13	12	no	—
616	C₂×D₄	—	13	12	no	—
617	C₂×D₄	—	13	12	no	—
618	C₂×D₄	—	13	12	no	—
619	C₂×D₄	—	13	6	no	—
620	C₂×D₄	—	26	24	no	—
621	C₂×D₄	—	26	48	no	—
622	C₂×D₄	C₂³×D₁₃	1	12	yes	—
623	C₂×D₄	C₂³×D₁₃	1	6	yes	—
624	C₂²×C₄	—	2	12	no	—
625	C₂²×C₄	—	13	3	no	—
626	C₂²×C₄	—	13	24	no	—
627	C₂²×C₄	—	13	3	no	—
628	C₂²×C₄	—	13	3	no	—
629	C₂²×C₄	—	13	3	no	—
630	C₂²×C₄	—	13	3	no	—
631	C₂²×C₄	—	13	6	no	—
632	C₂²×C₄	—	13	6	no	—
633	C₂²×C₄	—	13	3	no	—
634	C₂²×C₄	—	13	12	no	—
635	C₂²×C₄	—	13	6	no	—
636	C₂²×C₄	—	13	6	no	—
637	C₂²×C₄	—	13	6	no	—
638	C₂²×C₄	—	13	6	no	—
639	C₂²×C₄	—	13	6	no	—
640	C₂²×C₄	—	13	6	no	—
641	C₂²×C₄	—	13	12	no	—
642	C₂²×C₄	—	13	12	no	—
643	C₂²×C₄	—	13	12	no	—
644	C₂²×C₄	—	26	12	no	—
645	C₂²×C₄	—	26	24	no	—
646	C₂²×C₄	—	26	24	no	—
647	C₂²×C₄	—	26	24	no	—
648	C₂²×C₄	—	26	24	no	—
649	C₂²×C₄	—	26	48	no	—
650	C₂²×C₄	—	26	12	no	—
651	C₂²×C₄	—	26	12	no	—
652	C₂²×C₄	—	26	12	no	—
653	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
654	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
655	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
656	C₂²×C₄	C₂³×D₁₃	1	12	yes	—
657	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
658	C₄⋊C₄	—	13	24	no	—
659	C₄⋊C₄	—	13	12	no	—
660	C₄⋊C₄	—	13	24	no	—
661	C₄⋊C₄	—	13	24	no	—
662	C₄⋊C₄	—	13	24	no	—
663	C₄⋊C₄	C₂³×D₁₃	1	12	yes	—
664	C₄⋊C₄	C₂³×D₁₃	1	24	yes	—
665	C₂²⋊C₄	—	13	12	no	—
666	C₂²⋊C₄	—	13	24	no	—
667	C₂²⋊C₄	—	13	24	no	—
668	C₂²⋊C₄	—	13	24	no	—
669	C₂²⋊C₄	—	13	24	no	—
670	C₂²⋊C₄	C₂³×D₁₃	1	12	yes	—
671	C₂²⋊C₄	C₂³×D₁₃	1	24	yes	—
672	C₄²	—	13	3	no	—
673	C₄²	—	13	6	no	—
674	C₄²	—	13	3	no	—
675	C₄²	—	13	6	no	—
676	C₄²	—	13	6	no	—
677	C₄²	—	13	6	no	—
678	C₄²	—	13	6	no	—
679	C₄²	—	13	3	no	—
680	C₄²	—	13	6	no	—
681	C₄²	—	13	3	no	—
682	C₄²	—	13	24	no	—
683	C₄²	—	13	12	no	—
684	C₄²	C₂³×D₁₃	1	3	yes	—
685	C₄²	C₂³×D₁₃	1	6	yes	—
686	C₄²	C₂³×D₁₃	1	3	yes	—
687	C₄²	C₂³×D₁₃	1	2	yes	—
688	C₄²	C₂³×D₁₃	1	1	yes	characteristic
689	C₄²	C₂³×D₁₃	1	12	yes	—
690	C₄²	C₂³×D₁₃	1	1	yes	characteristic
691	C₁₃	C₂×#3444	1	1	yes	characteristic, complemented, Sylow
692	C₂³	—	2	6	no	—
693	C₂³	—	13	1	no	—
694	C₂³	—	13	12	no	—
695	C₂³	—	13	3	no	—
696	C₂³	—	13	4	no	—
697	C₂³	—	26	12	no	—
698	C₂³	—	26	12	no	—
699	C₂³	—	26	24	no	—
700	C₂³	—	26	32	no	—
701	C₂³	—	26	6	no	—
702	C₂³	C₂⁴×D₁₃	1	4	yes	—
703	C₂³	C₂⁴×D₁₃	1	3	yes	—
704	Q₈	—	2	12	no	—
705	Q₈	—	26	24	no	—
706	Q₈	—	26	12	no	—
707	D₄	—	2	24	no	—
708	D₄	—	2	12	no	—
709	D₄	—	26	24	no	—
710	D₄	—	26	24	no	—
711	D₄	—	26	24	no	—
712	D₄	—	26	24	no	—
713	D₄	—	26	12	no	—
714	C₂×C₄	—	2	6	no	—
715	C₂×C₄	—	2	12	no	—
716	C₂×C₄	—	2	12	no	—
717	C₂×C₄	—	2	24	no	—
718	C₂×C₄	—	13	12	no	—
719	C₂×C₄	—	13	3	no	—
720	C₂×C₄	—	13	3	no	—
721	C₂×C₄	—	13	12	no	—
722	C₂×C₄	—	13	12	no	—
723	C₂×C₄	—	13	12	no	—
724	C₂×C₄	—	13	12	no	—
725	C₂×C₄	—	13	6	no	—
726	C₂×C₄	—	13	12	no	—
727	C₂×C₄	—	26	12	no	—
728	C₂×C₄	—	26	12	no	—
729	C₂×C₄	—	26	24	no	—
730	C₂×C₄	—	26	12	no	—
731	C₂×C₄	—	26	12	no	—
732	C₂×C₄	—	26	24	no	—
733	C₂×C₄	—	26	12	no	—
734	C₂×C₄	—	26	12	no	—
735	C₂×C₄	—	26	24	no	—
736	C₂×C₄	—	26	6	no	—
737	C₂×C₄	—	26	12	no	—
738	C₂×C₄	—	26	12	no	—
739	C₂×C₄	—	26	24	no	—
740	C₂×C₄	#41×D₁₃	1	12	yes	complemented
741	C₂×C₄	C₂⁴×D₁₃	1	6	yes	—
742	C₂×C₄	C₂⁴×D₁₃	1	12	yes	—
743	C₂×C₄	C₂⁴×D₁₃	1	3	yes	—
744	C₂×C₄	C₂⁴×D₁₃	1	3	yes	—
745	C₂²	—	2	8	no	—
746	C₂²	—	2	6	no	—
747	C₂²	—	2	12	no	—
748	C₂²	—	13	6	no	—
749	C₂²	—	13	6	no	—
750	C₂²	—	26	24	no	—
751	C₂²	—	26	24	no	—
752	C₂²	—	26	6	no	—
753	C₂²	—	26	12	no	—
754	C₂²	—	52	16	no	—
755	C₂²	C₂×#41×D₁₃	1	6	yes	—
756	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
757	C₄	—	2	6	no	—
758	C₄	—	2	12	no	—
759	C₄	—	13	6	no	—
760	C₄	—	13	6	no	—
761	C₄	—	26	6	no	—
762	C₄	—	26	12	no	—
763	C₄	C₂×#41×D₁₃	1	6	yes	—
764	C₄	C₂×#41×D₁₃	1	6	yes	—
765	C₂	—	2	6	no	—
766	C₂	—	4	4	no	—
767	C₂	—	13	4	no	—
768	C₂	—	26	6	no	—
769	C₂	—	52	4	no	—
770	C₂	C₂²×#41×D₁₃	1	3	yes	—

	subgroup	G/H
center	C₄²	C₂³×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₁₃×#3444	C₂
hypercenter	#3444	D₁₃
hypocenter	C₁₃	C₂×#3444
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ #3444

Complements

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

N	H ≅ G/N	type
1. #13128133	C₂	semidirect
2. #13128132	C₂	semidirect
3. #13128131	C₂	semidirect
4. #13128130	C₂	semidirect
5. #13128129	C₂	semidirect
6. #13128128	C₂	semidirect
7. D₁₃×#533	C₂	semidirect
8. D₁₃×#532	C₂	semidirect
9. D₁₃×#529	C₂	semidirect
10. D₁₃×#525	C₂	semidirect
11. C₄×#41×D₁₃	C₂	semidirect
12. C₂²×C₄²×D₁₃	C₂	semidirect
13. C₁₃×#3444	C₂	semidirect
16. C₁₃×#533	C₂²	semidirect
17. C₁₃×#532	C₂²	semidirect
18. C₁₃×#529	C₂²	semidirect
19. C₁₃×#525	C₂²	semidirect
20. C₄×C₁₃×#41	C₂²	semidirect
21. C₂²×C₄²×C₁₃	C₂²	semidirect
22. #11719537	C₂²	semidirect
23. #11719533	C₂²	semidirect
24. #41×Dic₁₃	C₂²	semidirect
25. #11719496	C₂²	semidirect
26. C₂²×C₄×Dic₁₃	C₂²	semidirect
27. #11719433	C₂²	semidirect
28. #11719430	C₂²	semidirect
29. D₁₃×C₄⋊Q₈	C₂²	semidirect
30. #11719421	C₂²	semidirect
31. D₁₃×#127	C₂²	semidirect
32. #11719411	C₂²	semidirect
33. D₁₃×#126	C₂²	semidirect
34. #11719396	C₂²	semidirect
35. #11719393	C₂²	semidirect
36. D₁₃×#125	C₂²	semidirect
37. #11719385	C₂²	semidirect
38. D₁₃×#124	C₂²	semidirect
39. #11719373	C₂²	semidirect
40. #11719361	C₂²	semidirect
42. #11719354	C₂²	semidirect
43. #11719332	C₂²	semidirect
45. #11719329	C₂²	semidirect
46. #11719327	C₂²	semidirect
47. #11719311	C₂²	semidirect
49. #11719305	C₂²	semidirect
50. #11719301	C₂²	semidirect
52. #11719291	C₂²	semidirect
53. #11719285	C₂²	semidirect
54. #11719283	C₂²	semidirect
55. C₄×#6131	C₂²	semidirect
56. C₄×Q₈×D₁₃	C₂²	semidirect
57. #11719262	C₂²	semidirect
58. #11719253	C₂²	semidirect
59. #11719252	C₂²	semidirect
61. C₄×D₄×D₁₃	C₂²	semidirect
62. #11719243	C₂²	semidirect
63. C₄×#6129	C₂²	semidirect
64. C₄×#6129	C₂²	semidirect
65. #11719233	C₂²	semidirect
66. #11719229	C₂²	semidirect
67. #11719227	C₂²	semidirect
68. #11719227	C₂²	semidirect
70. D₁₃×#117	C₂²	semidirect
71. #11719222	C₂²	semidirect
72. #11719184	C₂²	semidirect
73. #11719182	C₂²	semidirect
74. C₄×#6127	C₂²	semidirect
75. C₄×#6127	C₂²	semidirect
79. C₂×C₄²×D₁₃	C₂²	semidirect
80. C₂×C₄²×D₁₃	C₂²	semidirect
81. C₂×C₄²×D₁₃	C₂²	semidirect
82. C₂×C₄²×D₁₃	C₂²	semidirect
83. #11719175	C₂²	semidirect
107. C₁₃×C₄⋊Q₈	C₂³	semidirect
108. C₁₃×#127	C₂³	semidirect
109. C₁₃×#126	C₂³	semidirect
110. C₁₃×#125	C₂³	semidirect
111. C₁₃×#124	C₂³	semidirect
116. C₄×Q₈×C₁₃	C₂³	semidirect
118. C₄×D₄×C₁₃	C₂³	semidirect
120. C₁₃×#117	C₂³	semidirect
124. C₂×C₄²×C₁₃	C₂³	semidirect
126. #88201	C₂³	semidirect
128. Q₈×Dic₁₃	C₂³	semidirect
129. #88198	C₂³	semidirect
130. #88194	C₂³	semidirect
134. #88190	C₂³	semidirect
137. D₄×Dic₁₃	C₂³	semidirect
142. C₄×C₂²⋊D₁₃	C₂³	semidirect
144. #88180	C₂³	semidirect
153. C₂×C₄×Dic₁₃	C₂³	semidirect
154. #88152	C₂³	semidirect
160. #88147	C₂³	semidirect
162. #88146	C₂³	semidirect
165. #88144	C₂³	semidirect
166. #88143	C₂³	semidirect
167. #88142	C₂³	semidirect
168. #88141	C₂³	semidirect
169. #88141	C₂³	semidirect
171. #88139	C₂³	semidirect
177. #88135	C₂³	semidirect
180. #88133	C₂³	semidirect
183. #88131	C₂³	semidirect
184. #88130	C₂³	semidirect
185. #88129	C₂³	semidirect
186. #88128	C₂³	semidirect
188. C₄×D₅₂	C₂³	semidirect
190. #88126	C₂³	semidirect
191. #88126	C₂³	semidirect
209. C₄²×D₁₃	C₂³	semidirect
210. C₄²×D₁₃	C₂³	semidirect
211. #88124	C₂³	semidirect
212. #88123	C₂³	semidirect
213. C₄×Dic₂₆	C₂³	semidirect
214. C₄×Dic₂₆	C₂³	semidirect
258. C₂×C₄×D₁₃	#41	semidirect
313. #3444	D₁₃	direct (N × H)
339. C₂×C₄×C₁₃	C₂×#41	semidirect
351. C₂×Dic₁₃	C₂×#41	semidirect
369. C₄×D₁₃	C₂×#41	semidirect
370. C₄×D₁₃	C₂×#41	semidirect
381. #533	C₂×D₁₃	semidirect
389. #532	C₂×D₁₃	semidirect
403. #529	C₂×D₁₃	semidirect
415. #525	C₂×D₁₃	semidirect
428. C₄×#41	C₂×D₁₃	semidirect
442. C₂²×C₄²	C₂×D₁₃	semidirect
489. C₄⋊Q₈	C₂²×D₁₃	semidirect
492. #127	C₂²×D₁₃	semidirect
496. #126	C₂²×D₁₃	semidirect
500. #125	C₂²×D₁₃	semidirect
505. #124	C₂²×D₁₃	semidirect
533. C₄×Q₈	C₂²×D₁₃	semidirect
547. C₄×D₄	C₂²×D₁₃	semidirect
558. #117	C₂²×D₁₃	semidirect
593. C₂×C₄²	C₂²×D₁₃	semidirect
599. D₁₃	#3444	direct (N × H)
691. C₁₃	C₂×#3444	semidirect
740. C₂×C₄	#41×D₁₃	semidirect

Maximal subgroups

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

subgroup	index
#13128133	2
#13128132	2
#13128131	2
#13128130	2
#13128129	2
#13128128	2
D₁₃×#533	2
D₁₃×#532	2
D₁₃×#529	2
D₁₃×#525	2
C₄×#41×D₁₃	2
C₂²×C₄²×D₁₃	2
C₁₃×#3444	2
C₂×#3444	13

Subgroups — D13×#3444 #16769626

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×#3444 #16769626