Subgroups — C₁₃×#61430 #15747769

Order 3328.

1870 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3480	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3396	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3383	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3365	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3342	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3339	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3304	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3301	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3287	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3285	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3169	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3168	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3103	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3102	C₂	1	4	yes	maximal, complemented
15	C₈×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₁₃×#135	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×#135	C₂²	1	2	yes	—
19	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
20	C₁₃×#559	—	2	2	no	—
21	C₁₃×#559	C₂²	1	2	yes	—
22	C₁₃×#557	C₂²	1	2	yes	—
23	C₁₃×#556	—	2	2	no	—
24	C₁₃×#556	C₂²	1	2	yes	—
25	C₁₃×#553	—	2	4	no	—
26	C₁₃×#553	C₂²	1	4	yes	—
27	C₁₃×#550	C₂²	1	2	yes	—
28	C₁₃×#548	C₂²	1	4	yes	—
29	C₁₃×#532	—	2	2	no	—
30	C₁₃×#532	C₂²	1	2	yes	—
31	C₁₃×#529	—	2	4	no	—
32	C₁₃×#529	C₂²	1	4	yes	—
33	C₄×C₁₃×#41	—	2	2	no	—
34	C₄×C₁₃×#41	C₂²	1	4	yes	—
35	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
37	C₁₃×#500	C₂²	1	1	yes	characteristic
38	C₁₃×#499	C₂²	1	2	yes	—
39	C₁₃×#495	C₂²	1	2	yes	—
40	C₁₃×#493	C₂²	1	1	yes	characteristic
41	C₁₃×#488	C₂²	1	4	yes	—
42	C₁₃×#486	C₂²	1	2	yes	—
43	C₁₃×#485	C₂²	1	4	yes	—
44	C₁₃×#482	C₂²	1	4	yes	—
45	C₁₃×#481	C₂²	1	4	yes	—
46	C₁₃×#479	C₂²	1	4	yes	—
47	C₁₃×#478	C₂²	1	4	yes	—
48	C₁₃×#475	C₂²	1	2	yes	—
49	C₁₃×#475	C₂²	1	2	yes	—
50	C₁₃×#467	C₂²	1	2	yes	—
51	C₁₃×#466	C₂²	1	2	yes	—
52	C₁₃×#466	C₂²	1	2	yes	—
53	C₁₃×#466	C₂²	1	2	yes	—
54	C₁₃×#465	C₂²	1	4	yes	—
55	C₁₃×#464	C₂²	1	4	yes	—
56	C₁₃×#463	C₂²	1	4	yes	—
57	C₁₃×#460	C₂²	1	2	yes	—
58	C₁₃×#460	C₂²	1	2	yes	—
59	C₁₃×#452	C₂²	1	4	yes	—
60	C₁₃×#449	C₂²	1	4	yes	—
61	C₁₃×#448	C₂²	1	4	yes	—
62	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
63	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
64	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
65	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
66	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
67	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
68	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
69	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
70	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
71	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
72	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
73	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
74	C₄×C₁₃×D₈	C₂²	1	2	yes	—
75	C₄×C₁₃×D₈	C₂²	1	2	yes	—
76	C₄×C₁₃×D₈	C₂²	1	2	yes	—
77	C₈×D₄×C₁₃	C₂²	1	2	yes	—
78	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
79	C₈×D₄×C₁₃	C₂²	1	2	yes	—
80	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
81	C₁₃×#431	C₂²	1	2	yes	—
82	C₁₃×#431	C₂²	1	1	yes	characteristic
83	C₁₃×#427	C₂²	1	2	yes	—
84	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
85	C₁₃×#416	C₂²	1	4	yes	—
86	C₂×C₁₃×#103	C₂²	1	2	yes	—
87	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
88	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
89	C₂×C₁₃×#41	—	2	2	no	—
90	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
91	C₂×C₁₃×#41	C₂³	1	4	yes	—
92	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
93	C₁₃×#135	—	2	8	no	—
94	C₂×C₁₃×Q₁₆	—	2	4	no	—
95	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
96	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
97	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
98	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
99	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
100	C₂×C₁₃×D₈	C₂³	1	2	yes	—
101	C₂×C₁₃×D₈	C₂³	1	2	yes	—
102	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
104	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
106	C₁₃×C₄⋊Q₈	—	2	2	no	—
107	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
108	C₁₃×#127	—	2	2	no	—
109	C₁₃×#127	C₂³	1	2	yes	—
110	C₁₃×#126	—	2	4	no	—
111	C₁₃×#126	—	2	4	no	—
112	C₁₃×#126	—	2	4	no	—
113	C₁₃×#125	—	2	4	no	—
114	C₁₃×#125	C₂³	1	4	yes	—
115	C₁₃×#124	—	2	2	no	—
116	C₁₃×#124	—	2	2	no	—
117	C₁₃×#124	—	2	4	no	—
118	C₁₃×#124	—	2	2	no	—
119	C₁₃×#124	C₂³	1	4	yes	—
120	C₁₃×#123	—	2	4	no	—
121	C₁₃×#123	—	2	4	no	—
122	C₁₃×#123	—	2	4	no	—
123	C₁₃×C₂²⋊Q₈	—	2	4	no	—
124	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
125	C₁₃×#121	—	2	4	no	—
126	C₁₃×#121	—	2	4	no	—
127	C₁₃×#121	—	2	2	no	—
128	C₁₃×#121	—	2	4	no	—
129	C₁₃×#121	C₂³	1	4	yes	—
130	C₁₃×#121	C₂³	1	4	yes	—
131	C₄×Q₈×C₁₃	—	2	2	no	—
132	C₄×Q₈×C₁₃	—	2	2	no	—
133	C₄×Q₈×C₁₃	—	2	2	no	—
134	C₄×Q₈×C₁₃	—	2	2	no	—
135	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
136	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
137	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
138	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
139	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
140	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
141	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
142	C₄×D₄×C₁₃	—	2	4	no	—
143	C₄×D₄×C₁₃	—	2	4	no	—
144	C₄×D₄×C₁₃	—	2	4	no	—
145	C₄×D₄×C₁₃	—	2	2	no	—
146	C₄×D₄×C₁₃	—	2	2	no	—
147	C₄×D₄×C₁₃	—	2	4	no	—
148	C₄×D₄×C₁₃	—	2	4	no	—
149	C₄×D₄×C₁₃	—	2	2	no	—
150	C₄×D₄×C₁₃	D₄	1	2	yes	—
151	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
152	C₄×D₄×C₁₃	C₂³	1	4	yes	—
153	C₄×D₄×C₁₃	C₂³	1	4	yes	—
154	C₄×D₄×C₁₃	C₂³	1	2	yes	—
155	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
156	C₁₃×#117	—	2	4	no	—
157	C₁₃×#117	—	2	4	no	—
158	C₁₃×#117	D₄	1	1	yes	characteristic
159	C₁₃×#117	D₄	1	2	yes	—
160	C₁₃×#117	C₂³	1	4	yes	—
161	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
162	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
163	C₂×C₄²×C₁₃	—	2	2	no	—
164	C₂×C₄²×C₁₃	—	2	4	no	—
165	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
167	C₁₃×#107	C₂³	1	1	yes	characteristic
168	C₁₃×#107	C₂³	1	1	yes	characteristic
169	C₁₃×#107	C₂³	1	2	yes	—
170	C₁₃×#107	C₂³	1	2	yes	—
171	C₁₃×#107	C₂³	1	2	yes	—
172	C₁₃×#106	C₂³	1	4	yes	—
173	C₁₃×#106	C₂³	1	4	yes	—
174	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
175	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
176	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
177	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
178	C₁₃×#103	C₂³	1	2	yes	—
179	C₁₃×#103	C₂³	1	2	yes	—
180	C₁₃×#103	C₂³	1	2	yes	—
181	C₁₃×#103	C₂³	1	2	yes	—
182	C₁₃×#103	C₂³	1	4	yes	—
183	C₁₃×#103	C₂³	1	4	yes	—
184	C₁₃×#102	C₂³	1	4	yes	—
185	C₁₃×#102	C₂³	1	4	yes	—
186	C₁₃×#102	C₂³	1	4	yes	—
187	C₁₃×#102	C₂³	1	4	yes	—
188	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
189	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
190	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
191	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
192	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
193	C₄×C₈×C₁₃	C₂³	1	2	yes	—
194	C₄×C₈×C₁₃	C₂³	1	2	yes	—
195	C₄×C₈×C₁₃	C₂³	1	2	yes	—
196	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
197	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
198	#61430	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₁₃×#41	—	2	4	no	—
200	C₁₃×#41	—	2	8	no	—
201	C₁₃×#41	—	4	4	no	—
202	C₁₃×#41	—	4	8	no	—
203	C₂×Q₈×C₁₃	—	2	2	no	—
204	C₂×Q₈×C₁₃	—	2	2	no	—
205	C₂×Q₈×C₁₃	—	2	4	no	—
206	C₂×Q₈×C₁₃	—	4	2	no	—
207	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
208	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
209	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
210	C₂×D₄×C₁₃	—	2	4	no	—
211	C₂×D₄×C₁₃	—	2	4	no	—
212	C₂×D₄×C₁₃	—	2	4	no	—
213	C₂×D₄×C₁₃	—	2	2	no	—
214	C₂×D₄×C₁₃	—	2	2	no	—
215	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
216	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
217	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
218	C₂²×C₄×C₁₃	—	2	2	no	—
219	C₂²×C₄×C₁₃	—	2	2	no	—
220	C₂²×C₄×C₁₃	—	2	4	no	—
221	C₂²×C₄×C₁₃	—	2	4	no	—
222	C₂²×C₄×C₁₃	—	2	4	no	—
223	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
224	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
226	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
227	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
229	C₁₃×Q₁₆	—	2	4	no	—
230	C₁₃×Q₁₆	—	2	2	no	—
231	C₁₃×Q₁₆	#41	1	4	yes	complemented
232	C₁₃×SD₁₆	—	2	8	no	—
233	C₁₃×SD₁₆	—	4	4	no	—
234	C₁₃×D₈	—	2	4	no	—
235	C₁₃×D₈	—	4	2	no	—
236	C₂×C₈×C₁₃	—	2	2	no	—
237	C₂×C₈×C₁₃	—	2	4	no	—
238	C₂×C₈×C₁₃	—	4	1	no	—
239	C₂×C₈×C₁₃	—	4	2	no	—
240	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
241	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
242	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
243	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
244	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
245	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
246	C₁₃×C₄⋊C₄	—	2	2	no	—
247	C₁₃×C₄⋊C₄	—	2	2	no	—
248	C₁₃×C₄⋊C₄	—	2	2	no	—
249	C₁₃×C₄⋊C₄	—	2	2	no	—
250	C₁₃×C₄⋊C₄	—	2	2	no	—
251	C₁₃×C₄⋊C₄	—	2	4	no	—
252	C₁₃×C₄⋊C₄	—	2	4	no	—
253	C₁₃×C₄⋊C₄	—	2	4	no	—
254	C₁₃×C₄⋊C₄	—	2	2	no	—
255	C₁₃×C₄⋊C₄	—	2	4	no	—
256	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
257	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
258	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
259	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
260	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
261	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
262	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
263	C₁₃×C₂²⋊C₄	—	2	4	no	—
264	C₁₃×C₂²⋊C₄	—	2	4	no	—
265	C₁₃×C₂²⋊C₄	—	2	4	no	—
266	C₁₃×C₂²⋊C₄	—	2	4	no	—
267	C₁₃×C₂²⋊C₄	—	2	4	no	—
268	C₁₃×C₂²⋊C₄	—	2	4	no	—
269	C₁₃×C₂²⋊C₄	—	2	4	no	—
270	C₁₃×C₂²⋊C₄	—	2	4	no	—
271	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
272	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
273	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
274	C₄²×C₁₃	—	2	4	no	—
275	C₄²×C₁₃	—	2	4	no	—
276	C₄²×C₁₃	—	2	2	no	—
277	C₄²×C₁₃	—	2	2	no	—
278	C₄²×C₁₃	—	2	2	no	—
279	C₄²×C₁₃	—	2	2	no	—
280	C₄²×C₁₃	C₂×D₄	1	2	yes	—
281	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
282	C₄²×C₁₃	C₂×D₄	1	2	yes	—
283	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
284	C₄²×C₁₃	C₂⁴	1	2	yes	—
285	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
286	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
287	#3480	C₂×C₁₃	1	2	yes	complemented
288	#3396	C₂×C₁₃	1	1	yes	characteristic, complemented
289	#3383	C₂×C₁₃	1	1	yes	characteristic, complemented
290	#3365	C₂×C₁₃	1	2	yes	complemented
291	#3342	C₂×C₁₃	1	1	yes	characteristic, complemented
292	#3339	C₂×C₁₃	1	2	yes	complemented
293	#3304	C₂×C₁₃	1	2	yes	complemented
294	#3301	C₂×C₁₃	1	4	yes	complemented
295	#3287	C₂×C₁₃	1	1	yes	characteristic, complemented
296	#3285	C₂×C₁₃	1	2	yes	complemented
297	#3169	C₂×C₁₃	1	1	yes	characteristic, complemented
298	#3168	C₂×C₁₃	1	2	yes	complemented
299	#3103	C₂×C₁₃	1	2	yes	complemented
300	#3102	C₂×C₁₃	1	4	yes	complemented
301	C₈×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
302	C₄×#135	C₂×C₁₃	1	2	yes	complemented
303	C₂×C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
304	C₂³×C₁₃	—	2	4	no	—
305	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
306	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
307	Q₈×C₁₃	—	2	2	no	—
308	Q₈×C₁₃	—	2	2	no	—
309	Q₈×C₁₃	—	2	2	no	—
310	Q₈×C₁₃	—	2	2	no	—
311	Q₈×C₁₃	—	4	4	no	—
312	Q₈×C₁₃	—	4	4	no	—
313	Q₈×C₁₃	C₂×#41	1	4	yes	—
314	D₄×C₁₃	—	2	4	no	—
315	D₄×C₁₃	—	2	2	no	—
316	D₄×C₁₃	—	2	4	no	—
317	D₄×C₁₃	—	2	4	no	—
318	D₄×C₁₃	—	4	8	no	—
319	D₄×C₁₃	—	4	8	no	—
320	D₄×C₁₃	—	4	4	no	—
321	D₄×C₁₃	—	8	2	no	—
322	D₄×C₁₃	—	8	4	no	—
323	C₂×C₄×C₁₃	—	2	2	no	—
324	C₂×C₄×C₁₃	—	2	4	no	—
325	C₂×C₄×C₁₃	—	2	1	no	—
326	C₂×C₄×C₁₃	—	2	2	no	—
327	C₂×C₄×C₁₃	—	2	1	no	—
328	C₂×C₄×C₁₃	—	2	2	no	—
329	C₂×C₄×C₁₃	—	2	2	no	—
330	C₂×C₄×C₁₃	—	2	2	no	—
331	C₂×C₄×C₁₃	—	2	4	no	—
332	C₂×C₄×C₁₃	—	2	2	no	—
333	C₂×C₄×C₁₃	—	4	2	no	—
334	C₂×C₄×C₁₃	—	4	1	no	—
335	C₂×C₄×C₁₃	—	4	8	no	—
336	C₂×C₄×C₁₃	—	4	4	no	—
337	C₂×C₄×C₁₃	—	4	8	no	—
338	C₂×C₄×C₁₃	—	8	4	no	—
339	C₂×C₄×C₁₃	—	8	2	no	—
340	C₂×C₄×C₁₃	#135	1	4	yes	complemented
341	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
342	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
343	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
344	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
345	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
346	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
347	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
350	C₈×C₁₃	—	2	2	no	—
351	C₈×C₁₃	—	2	1	no	—
352	C₈×C₁₃	—	2	1	no	—
353	C₈×C₁₃	—	2	1	no	—
354	C₈×C₁₃	—	2	2	no	—
355	C₈×C₁₃	C₂×#41	1	2	yes	—
356	C₂×#135	C₂²×C₁₃	1	2	yes	—
357	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
358	#559	—	2	2	no	—
359	#559	C₂²×C₁₃	1	2	yes	—
360	#557	C₂²×C₁₃	1	2	yes	—
361	#556	—	2	2	no	—
362	#556	C₂²×C₁₃	1	2	yes	—
363	#553	—	2	4	no	—
364	#553	C₂²×C₁₃	1	4	yes	—
365	#550	C₂²×C₁₃	1	2	yes	—
366	#548	C₂²×C₁₃	1	4	yes	—
367	#532	—	2	2	no	—
368	#532	C₂²×C₁₃	1	2	yes	—
369	#529	—	2	4	no	—
370	#529	C₂²×C₁₃	1	4	yes	—
371	C₄×#41	—	2	2	no	—
372	C₄×#41	C₂²×C₁₃	1	4	yes	—
373	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
374	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
375	#500	C₂²×C₁₃	1	1	yes	characteristic
376	#499	C₂²×C₁₃	1	2	yes	—
377	#495	C₂²×C₁₃	1	2	yes	—
378	#493	C₂²×C₁₃	1	1	yes	characteristic
379	#488	C₂²×C₁₃	1	4	yes	—
380	#486	C₂²×C₁₃	1	2	yes	—
381	#485	C₂²×C₁₃	1	4	yes	—
382	#482	C₂²×C₁₃	1	4	yes	—
383	#481	C₂²×C₁₃	1	4	yes	—
384	#479	C₂²×C₁₃	1	4	yes	—
385	#478	C₂²×C₁₃	1	4	yes	—
386	#475	C₂²×C₁₃	1	2	yes	—
387	#475	C₂²×C₁₃	1	2	yes	—
388	#467	C₂²×C₁₃	1	2	yes	—
389	#466	C₂²×C₁₃	1	2	yes	—
390	#466	C₂²×C₁₃	1	2	yes	—
391	#466	C₂²×C₁₃	1	2	yes	—
392	#465	C₂²×C₁₃	1	4	yes	—
393	#464	C₂²×C₁₃	1	4	yes	—
394	#463	C₂²×C₁₃	1	4	yes	—
395	#460	C₂²×C₁₃	1	2	yes	—
396	#460	C₂²×C₁₃	1	2	yes	—
397	#452	C₂²×C₁₃	1	4	yes	—
398	#449	C₂²×C₁₃	1	4	yes	—
399	#448	C₂²×C₁₃	1	4	yes	—
400	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
401	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
402	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
403	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
404	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
405	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
406	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
407	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
408	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
409	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
410	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
411	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
412	C₄×D₈	C₂²×C₁₃	1	2	yes	—
413	C₄×D₈	C₂²×C₁₃	1	2	yes	—
414	C₄×D₈	C₂²×C₁₃	1	2	yes	—
415	C₈×D₄	C₂²×C₁₃	1	2	yes	—
416	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
417	C₈×D₄	C₂²×C₁₃	1	2	yes	—
418	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
419	#431	C₂²×C₁₃	1	2	yes	—
420	#431	C₂²×C₁₃	1	1	yes	characteristic
421	#427	C₂²×C₁₃	1	2	yes	—
422	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
423	#416	C₂²×C₁₃	1	4	yes	—
424	C₂×#103	C₂²×C₁₃	1	2	yes	—
425	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
426	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
427	C₂²×C₁₃	—	2	1	no	—
428	C₂²×C₁₃	—	2	1	no	—
429	C₂²×C₁₃	—	2	2	no	—
430	C₂²×C₁₃	—	2	2	no	—
431	C₂²×C₁₃	—	2	2	no	—
432	C₂²×C₁₃	—	4	4	no	—
433	C₂²×C₁₃	—	4	4	no	—
434	C₂²×C₁₃	—	4	4	no	—
435	C₂²×C₁₃	C₂×#135	1	2	yes	—
436	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
437	C₄×C₁₃	—	2	1	no	—
438	C₄×C₁₃	—	2	2	no	—
439	C₄×C₁₃	—	2	1	no	—
440	C₄×C₁₃	—	2	2	no	—
441	C₄×C₁₃	—	2	1	no	—
442	C₄×C₁₃	—	2	4	no	—
443	C₄×C₁₃	—	2	2	no	—
444	C₄×C₁₃	—	4	2	no	—
445	C₄×C₁₃	—	4	2	no	—
446	C₄×C₁₃	—	4	2	no	—
447	C₄×C₁₃	—	4	4	no	—
448	C₄×C₁₃	C₂×#135	1	2	yes	—
449	C₄×C₁₃	C₂×#135	1	2	yes	—
450	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
451	C₄×C₁₃	#585	1	1	yes	characteristic
452	C₂×#41	—	2	2	no	—
453	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
454	C₂×#41	C₂³×C₁₃	1	4	yes	—
455	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
456	#135	—	2	8	no	—
457	C₂×Q₁₆	—	2	4	no	—
458	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
459	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
460	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
461	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
462	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
463	C₂×D₈	C₂³×C₁₃	1	2	yes	—
464	C₂×D₈	C₂³×C₁₃	1	2	yes	—
465	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
466	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
467	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
468	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
469	C₄⋊Q₈	—	2	2	no	—
470	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
471	#127	—	2	2	no	—
472	#127	C₂³×C₁₃	1	2	yes	—
473	#126	—	2	4	no	—
474	#126	—	2	4	no	—
475	#126	—	2	4	no	—
476	#125	—	2	4	no	—
477	#125	C₂³×C₁₃	1	4	yes	—
478	#124	—	2	2	no	—
479	#124	—	2	2	no	—
480	#124	—	2	4	no	—
481	#124	—	2	2	no	—
482	#124	C₂³×C₁₃	1	4	yes	—
483	#123	—	2	4	no	—
484	#123	—	2	4	no	—
485	#123	—	2	4	no	—
486	C₂²⋊Q₈	—	2	4	no	—
487	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
488	#121	—	2	4	no	—
489	#121	—	2	4	no	—
490	#121	—	2	2	no	—
491	#121	—	2	4	no	—
492	#121	C₂³×C₁₃	1	4	yes	—
493	#121	C₂³×C₁₃	1	4	yes	—
494	C₄×Q₈	—	2	2	no	—
495	C₄×Q₈	—	2	2	no	—
496	C₄×Q₈	—	2	2	no	—
497	C₄×Q₈	—	2	2	no	—
498	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
499	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
500	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
501	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
502	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
503	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
504	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
505	C₄×D₄	—	2	4	no	—
506	C₄×D₄	—	2	4	no	—
507	C₄×D₄	—	2	4	no	—
508	C₄×D₄	—	2	2	no	—
509	C₄×D₄	—	2	2	no	—
510	C₄×D₄	—	2	4	no	—
511	C₄×D₄	—	2	4	no	—
512	C₄×D₄	—	2	2	no	—
513	C₄×D₄	D₄×C₁₃	1	2	yes	—
514	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
515	C₄×D₄	C₂³×C₁₃	1	4	yes	—
516	C₄×D₄	C₂³×C₁₃	1	4	yes	—
517	C₄×D₄	C₂³×C₁₃	1	2	yes	—
518	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
519	#117	—	2	4	no	—
520	#117	—	2	4	no	—
521	#117	D₄×C₁₃	1	1	yes	characteristic
522	#117	D₄×C₁₃	1	2	yes	—
523	#117	C₂³×C₁₃	1	4	yes	—
524	C₂×C₄⋊C₄	—	2	2	no	—
525	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
526	C₂×C₄²	—	2	2	no	—
527	C₂×C₄²	—	2	4	no	—
528	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
529	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
530	#107	C₂³×C₁₃	1	1	yes	characteristic
531	#107	C₂³×C₁₃	1	1	yes	characteristic
532	#107	C₂³×C₁₃	1	2	yes	—
533	#107	C₂³×C₁₃	1	2	yes	—
534	#107	C₂³×C₁₃	1	2	yes	—
535	#106	C₂³×C₁₃	1	4	yes	—
536	#106	C₂³×C₁₃	1	4	yes	—
537	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
538	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
539	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
540	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
541	#103	C₂³×C₁₃	1	2	yes	—
542	#103	C₂³×C₁₃	1	2	yes	—
543	#103	C₂³×C₁₃	1	2	yes	—
544	#103	C₂³×C₁₃	1	2	yes	—
545	#103	C₂³×C₁₃	1	4	yes	—
546	#103	C₂³×C₁₃	1	4	yes	—
547	#102	C₂³×C₁₃	1	4	yes	—
548	#102	C₂³×C₁₃	1	4	yes	—
549	#102	C₂³×C₁₃	1	4	yes	—
550	#102	C₂³×C₁₃	1	4	yes	—
551	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
552	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
553	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
554	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
555	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
556	C₄×C₈	C₂³×C₁₃	1	2	yes	—
557	C₄×C₈	C₂³×C₁₃	1	2	yes	—
558	C₄×C₈	C₂³×C₁₃	1	2	yes	—
559	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
560	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
561	C₂×C₁₃	—	2	2	no	—
562	C₂×C₁₃	—	4	2	no	—
563	C₂×C₁₃	—	8	4	no	—
564	C₂×C₁₃	D₄×#41	1	1	yes	characteristic
565	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
566	C₂×C₁₃	#3584	1	1	yes	characteristic
567	#41	—	2	4	no	—
568	#41	—	2	8	no	—
569	#41	—	4	4	no	—
570	#41	—	4	8	no	—
571	C₂×Q₈	—	2	2	no	—
572	C₂×Q₈	—	2	2	no	—
573	C₂×Q₈	—	2	4	no	—
574	C₂×Q₈	—	4	2	no	—
575	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
576	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
577	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
578	C₂×D₄	—	2	4	no	—
579	C₂×D₄	—	2	4	no	—
580	C₂×D₄	—	2	4	no	—
581	C₂×D₄	—	2	2	no	—
582	C₂×D₄	—	2	2	no	—
583	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
584	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
585	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
586	C₂²×C₄	—	2	2	no	—
587	C₂²×C₄	—	2	2	no	—
588	C₂²×C₄	—	2	4	no	—
589	C₂²×C₄	—	2	4	no	—
590	C₂²×C₄	—	2	4	no	—
591	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
592	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
593	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
594	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
595	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
596	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
597	Q₁₆	—	2	4	no	—
598	Q₁₆	—	2	2	no	—
599	Q₁₆	C₁₃×#41	1	4	yes	complemented
600	SD₁₆	—	2	8	no	—
601	SD₁₆	—	4	4	no	—
602	D₈	—	2	4	no	—
603	D₈	—	4	2	no	—
604	C₂×C₈	—	2	2	no	—
605	C₂×C₈	—	2	4	no	—
606	C₂×C₈	—	4	1	no	—
607	C₂×C₈	—	4	2	no	—
608	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
609	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
610	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
611	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
612	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
613	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
614	C₄⋊C₄	—	2	2	no	—
615	C₄⋊C₄	—	2	2	no	—
616	C₄⋊C₄	—	2	2	no	—
617	C₄⋊C₄	—	2	2	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	2	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
625	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
626	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
627	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
628	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
629	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
630	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	—	2	4	no	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
640	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
641	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
642	C₄²	—	2	2	no	—
643	C₄²	—	2	2	no	—
644	C₄²	—	2	4	no	—
645	C₄²	—	2	4	no	—
646	C₄²	—	2	2	no	—
647	C₄²	—	2	2	no	—
648	C₄²	C₂×D₄×C₁₃	1	2	yes	—
649	C₄²	C₂×D₄×C₁₃	1	2	yes	—
650	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
651	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
652	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
653	C₄²	C₂⁴×C₁₃	1	2	yes	—
654	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
655	C₁₃	#61430	1	1	yes	characteristic, direct product factor, Sylow
656	C₂³	—	2	4	no	—
657	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
658	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
659	Q₈	—	2	2	no	—
660	Q₈	—	2	2	no	—
661	Q₈	—	2	2	no	—
662	Q₈	—	2	2	no	—
663	Q₈	—	4	4	no	—
664	Q₈	—	4	4	no	—
665	Q₈	C₂×C₁₃×#41	1	4	yes	—
666	D₄	—	2	4	no	—
667	D₄	—	2	2	no	—
668	D₄	—	2	4	no	—
669	D₄	—	2	4	no	—
670	D₄	—	4	8	no	—
671	D₄	—	4	8	no	—
672	D₄	—	4	4	no	—
673	D₄	—	8	2	no	—
674	D₄	—	8	4	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	4	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	4	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	4	2	no	—
686	C₂×C₄	—	4	1	no	—
687	C₂×C₄	—	4	8	no	—
688	C₂×C₄	—	4	4	no	—
689	C₂×C₄	—	4	8	no	—
690	C₂×C₄	—	8	4	no	—
691	C₂×C₄	—	8	2	no	—
692	C₂×C₄	C₁₃×#135	1	4	yes	complemented
693	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
694	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
695	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
696	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
697	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
698	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
699	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
700	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
701	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
702	C₈	—	2	2	no	—
703	C₈	—	2	1	no	—
704	C₈	—	2	1	no	—
705	C₈	—	2	1	no	—
706	C₈	—	2	2	no	—
707	C₈	C₂×C₁₃×#41	1	2	yes	—
708	C₂²	—	2	1	no	—
709	C₂²	—	2	1	no	—
710	C₂²	—	2	2	no	—
711	C₂²	—	2	2	no	—
712	C₂²	—	2	2	no	—
713	C₂²	—	4	4	no	—
714	C₂²	—	4	4	no	—
715	C₂²	—	4	4	no	—
716	C₂²	C₂×C₁₃×#135	1	2	yes	—
717	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
718	C₄	—	2	2	no	—
719	C₄	—	2	1	no	—
720	C₄	—	2	2	no	—
721	C₄	—	2	1	no	—
722	C₄	—	2	2	no	—
723	C₄	—	2	1	no	—
724	C₄	—	2	4	no	—
725	C₄	—	4	4	no	—
726	C₄	—	4	2	no	—
727	C₄	—	4	2	no	—
728	C₄	—	4	2	no	—
729	C₄	C₂×C₁₃×#135	1	2	yes	—
730	C₄	C₂×C₁₃×#135	1	2	yes	—
731	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
732	C₄	C₁₃×#585	1	1	yes	characteristic
733	C₂	—	2	2	no	—
734	C₂	—	4	2	no	—
735	C₂	—	8	4	no	—
736	C₂	D₄×C₁₃×#41	1	1	yes	characteristic
737	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
738	C₂	C₁₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
socle	C₂²×C₁₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3480	C₂	semidirect
2. C₁₃×#3396	C₂	semidirect
3. C₁₃×#3383	C₂	semidirect
4. C₁₃×#3365	C₂	semidirect
5. C₁₃×#3342	C₂	semidirect
6. C₁₃×#3339	C₂	semidirect
7. C₁₃×#3304	C₂	semidirect
8. C₁₃×#3301	C₂	semidirect
9. C₁₃×#3287	C₂	semidirect
10. C₁₃×#3285	C₂	semidirect
11. C₁₃×#3169	C₂	semidirect
12. C₁₃×#3168	C₂	semidirect
13. C₁₃×#3103	C₂	semidirect
14. C₁₃×#3102	C₂	semidirect
15. C₈×C₁₃×#41	C₂	semidirect
16. C₄×C₁₃×#135	C₂	semidirect
17. C₂×C₄×C₁₃×Q₁₆	C₂	semidirect
198. #61430	C₁₃	direct (N × H)
231. C₁₃×Q₁₆	#41	semidirect
287. #3480	C₂×C₁₃	semidirect
288. #3396	C₂×C₁₃	semidirect
289. #3383	C₂×C₁₃	semidirect
290. #3365	C₂×C₁₃	semidirect
291. #3342	C₂×C₁₃	semidirect
292. #3339	C₂×C₁₃	semidirect
293. #3304	C₂×C₁₃	semidirect
294. #3301	C₂×C₁₃	semidirect
295. #3287	C₂×C₁₃	semidirect
296. #3285	C₂×C₁₃	semidirect
297. #3169	C₂×C₁₃	semidirect
298. #3168	C₂×C₁₃	semidirect
299. #3103	C₂×C₁₃	semidirect
300. #3102	C₂×C₁₃	semidirect
301. C₈×#41	C₂×C₁₃	semidirect
302. C₄×#135	C₂×C₁₃	semidirect
303. C₂×C₄×Q₁₆	C₂×C₁₃	semidirect
340. C₂×C₄×C₁₃	#135	semidirect
599. Q₁₆	C₁₃×#41	semidirect
655. C₁₃	#61430	direct (N × H)
692. C₂×C₄	C₁₃×#135	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3480	2
C₁₃×#3396	2
C₁₃×#3383	2
C₁₃×#3365	2
C₁₃×#3342	2
C₁₃×#3339	2
C₁₃×#3304	2
C₁₃×#3301	2
C₁₃×#3287	2
C₁₃×#3285	2
C₁₃×#3169	2
C₁₃×#3168	2
C₁₃×#3103	2
C₁₃×#3102	2
C₈×C₁₃×#41	2
C₄×C₁₃×#135	2
C₂×C₄×C₁₃×Q₁₆	2
#61430	13

Subgroups — C13×#61430 #15747769

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61430 #15747769