Subgroups — C₁₃×#61869 #15748208

Order 3328.

1644 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3503	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3387	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3386	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3383	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3381	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3374	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3372	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3363	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3359	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3242	C₂	1	4	yes	maximal, complemented
12	C₁₃×#3230	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3229	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3120	C₂	1	4	yes	maximal
15	C₁₃×#3107	C₂	1	1	yes	maximal, characteristic
16	C₁₃×#3107	C₂	1	1	yes	maximal, characteristic
17	C₁₃×#2986	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#564	—	2	2	no	—
19	Q₈²×C₁₃	C₂²	1	2	yes	—
20	C₁₃×#557	—	2	1	no	—
21	C₁₃×#557	—	2	1	no	—
22	C₁₃×#557	C₂²	1	2	yes	—
23	C₁₃×#557	C₂²	1	2	yes	—
24	C₁₃×#557	C₂²	1	2	yes	—
25	C₁₃×#557	C₂²	1	2	yes	—
26	C₁₃×#557	C₂²	1	2	yes	—
27	C₁₃×#554	—	2	2	no	—
28	C₁₃×#554	C₂²	1	2	yes	—
29	D₄×Q₈×C₁₃	—	2	2	no	—
30	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
31	C₁₃×#544	—	2	2	no	—
32	C₁₃×#544	C₂²	1	2	yes	—
33	C₁₃×#541	—	2	2	no	—
34	C₁₃×#541	—	2	2	no	—
35	C₁₃×#541	C₂²	1	4	yes	—
36	C₁₃×#533	—	2	1	no	—
37	C₁₃×#533	C₂²	1	1	yes	characteristic
38	C₁₃×#533	C₂²	1	1	yes	characteristic
39	C₁₃×#533	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
41	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
42	C₁₃×#520	C₂²	1	2	yes	—
43	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
44	C₁₃×#501	C₂²	1	4	yes	—
45	C₁₃×#500	C₂²	1	2	yes	—
46	C₁₃×#499	C₂²	1	4	yes	—
47	C₁₃×#498	C₂²	1	2	yes	—
48	C₁₃×#491	C₂²	1	4	yes	—
49	C₁₃×#487	C₂²	1	4	yes	—
50	C₁₃×#487	C₂²	1	2	yes	—
51	C₁₃×#487	C₂²	1	2	yes	—
52	C₁₃×#485	C₂²	1	2	yes	—
53	C₁₃×#485	C₂²	1	2	yes	—
54	C₁₃×#484	C₂²	1	4	yes	—
55	C₁₃×#483	C₂²	1	4	yes	—
56	C₁₃×#479	C₂²	1	4	yes	—
57	C₁₃×#479	C₂²	1	4	yes	—
58	C₁₃×#479	C₂²	1	4	yes	—
59	C₁₃×#478	C₂²	1	4	yes	—
60	C₁₃×#477	C₂²	1	2	yes	—
61	C₁₃×#477	C₂²	1	4	yes	—
62	C₁₃×#477	C₂²	1	2	yes	—
63	C₁₃×#475	C₂²	1	2	yes	—
64	C₁₃×#475	C₂²	1	4	yes	—
65	C₁₃×#475	C₂²	1	1	yes	characteristic
66	C₁₃×#475	C₂²	1	1	yes	characteristic
67	C₁₃×#475	C₂²	1	2	yes	—
68	C₁₃×#474	C₂²	1	1	yes	characteristic
69	C₁₃×#474	C₂²	1	1	yes	characteristic
70	C₁₃×#462	C₂²	1	1	yes	characteristic
71	C₁₃×#462	C₂²	1	1	yes	characteristic
72	C₁₃×#462	C₂²	1	4	yes	—
73	C₁₃×#461	C₂²	1	1	yes	characteristic
74	C₁₃×#461	C₂²	1	4	yes	—
75	C₁₃×#461	C₂²	1	1	yes	characteristic
76	C₁₃×#452	C₂²	1	2	yes	—
77	C₁₃×#452	C₂²	1	2	yes	—
78	C₁₃×#446	C₂²	1	2	yes	—
79	C₁₃×#446	C₂²	1	2	yes	—
80	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
81	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
82	C₁₃×#441	C₂²	1	4	yes	—
83	C₁₃×#440	C₂²	1	4	yes	—
84	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
85	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
86	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	—
87	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
88	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
89	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
90	C₁₃×#433	C₂²	1	4	yes	—
91	C₁₃×#431	C₂²	1	1	yes	characteristic
92	C₁₃×#431	C₂²	1	1	yes	characteristic
93	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
94	C₂²×Q₈×C₁₃	—	2	2	no	—
95	C₂²×Q₈×C₁₃	—	2	1	no	—
96	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
97	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
98	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
99	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
100	C₁₃×C₄⋊Q₈	—	2	2	no	—
101	C₁₃×C₄⋊Q₈	—	2	2	no	—
102	C₁₃×C₄⋊Q₈	—	2	2	no	—
103	C₁₃×C₄⋊Q₈	—	2	2	no	—
104	C₁₃×C₄⋊Q₈	—	2	2	no	—
105	C₁₃×C₄⋊Q₈	—	2	4	no	—
106	C₁₃×C₄⋊Q₈	—	2	1	no	—
107	C₁₃×C₄⋊Q₈	—	2	1	no	—
108	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
109	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
110	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
111	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
112	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
113	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
116	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
117	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₁₃×#126	—	2	4	no	—
119	C₁₃×#126	—	2	4	no	—
120	C₁₃×#125	—	2	2	no	—
121	C₁₃×#125	—	2	2	no	—
122	C₁₃×#125	—	2	2	no	—
123	C₁₃×#125	—	2	4	no	—
124	C₁₃×#125	—	2	4	no	—
125	C₁₃×#125	—	2	4	no	—
126	C₁₃×#125	—	2	4	no	—
127	C₁₃×#125	—	2	4	no	—
128	C₁₃×#125	—	2	4	no	—
129	C₁₃×#125	—	2	4	no	—
130	C₁₃×#125	—	2	1	no	—
131	C₁₃×#125	—	2	1	no	—
132	C₁₃×#125	D₄	1	2	yes	—
133	C₁₃×#125	C₂³	1	4	yes	—
134	C₁₃×#125	C₂³	1	4	yes	—
135	C₁₃×C₂²⋊Q₈	—	2	2	no	—
136	C₁₃×C₂²⋊Q₈	—	2	1	no	—
137	C₁₃×C₂²⋊Q₈	—	2	1	no	—
138	C₁₃×C₂²⋊Q₈	—	2	2	no	—
139	C₁₃×C₂²⋊Q₈	—	2	4	no	—
140	C₁₃×C₂²⋊Q₈	—	2	4	no	—
141	C₁₃×C₂²⋊Q₈	—	2	4	no	—
142	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
143	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
144	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
145	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
146	C₄×Q₈×C₁₃	—	2	2	no	—
147	C₄×Q₈×C₁₃	—	2	2	no	—
148	C₄×Q₈×C₁₃	—	2	2	no	—
149	C₄×Q₈×C₁₃	—	2	2	no	—
150	C₄×Q₈×C₁₃	—	2	2	no	—
151	C₄×Q₈×C₁₃	—	2	2	no	—
152	C₄×Q₈×C₁₃	—	2	1	no	—
153	C₄×Q₈×C₁₃	—	2	1	no	—
154	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
155	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
156	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
157	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
158	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
159	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
160	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
161	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
162	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
163	C₄×D₄×C₁₃	—	2	1	no	—
164	C₄×D₄×C₁₃	—	2	1	no	—
165	C₄×D₄×C₁₃	—	2	4	no	—
166	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
167	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
168	C₄×D₄×C₁₃	C₂³	1	4	yes	—
169	C₁₃×#117	—	2	1	no	—
170	C₁₃×#117	—	2	1	no	—
171	C₁₃×#117	—	2	2	no	—
172	C₁₃×#117	—	2	1	no	—
173	C₁₃×#117	C₂³	1	1	yes	characteristic
174	C₁₃×#117	C₂³	1	2	yes	—
175	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
176	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
177	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
178	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
179	C₂×C₄²×C₁₃	—	2	1	no	—
180	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
181	C₁₃×#107	C₂³	1	2	yes	—
182	C₁₃×#107	C₂³	1	2	yes	—
183	C₁₃×#107	C₂³	1	4	yes	—
184	C₁₃×#107	C₂³	1	4	yes	—
185	C₁₃×#106	C₂³	1	2	yes	—
186	C₁₃×#106	C₂³	1	4	yes	—
187	C₁₃×#106	C₂³	1	2	yes	—
188	C₁₃×#106	C₂³	1	4	yes	—
189	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
190	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
191	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
192	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
193	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
194	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
195	C₁₃×#103	C₂³	1	2	yes	—
196	C₁₃×#103	C₂³	1	4	yes	—
197	C₁₃×#103	C₂³	1	2	yes	—
198	C₁₃×#103	C₂³	1	2	yes	—
199	C₁₃×#103	C₂³	1	2	yes	—
200	C₁₃×#103	C₂³	1	2	yes	—
201	C₁₃×#103	C₂³	1	4	yes	—
202	C₁₃×#103	C₂³	1	2	yes	—
203	C₁₃×#103	C₂³	1	4	yes	—
204	C₁₃×#103	C₂³	1	4	yes	—
205	C₁₃×#102	C₂³	1	2	yes	—
206	C₁₃×#102	C₂³	1	2	yes	—
207	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
208	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
209	C₁₃×#97	C₂³	1	4	yes	—
210	C₄×C₈×C₁₃	C₂³	1	2	yes	—
211	C₄×C₈×C₁₃	C₂³	1	2	yes	—
212	C₄×C₈×C₁₃	C₂³	1	4	yes	—
213	#61869	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₁₃×#41	—	2	2	no	—
215	C₁₃×#41	—	2	2	no	—
216	C₂×Q₈×C₁₃	—	2	1	no	—
217	C₂×Q₈×C₁₃	—	2	1	no	—
218	C₂×Q₈×C₁₃	—	2	2	no	—
219	C₂×Q₈×C₁₃	—	2	4	no	—
220	C₂×Q₈×C₁₃	—	2	2	no	—
221	C₂×Q₈×C₁₃	—	8	2	no	—
222	C₂×Q₈×C₁₃	—	8	4	no	—
223	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
224	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
225	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
226	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
227	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
228	C₂×D₄×C₁₃	—	2	1	no	—
229	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₁₃	—	2	1	no	—
231	C₂²×C₄×C₁₃	—	2	2	no	—
232	C₂²×C₄×C₁₃	—	2	1	no	—
233	C₂²×C₄×C₁₃	—	2	1	no	—
234	C₂²×C₄×C₁₃	—	2	4	no	—
235	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
238	C₁₃×Q₁₆	—	2	4	no	—
239	C₁₃×Q₁₆	—	2	4	no	—
240	C₁₃×SD₁₆	—	2	4	no	—
241	C₁₃×SD₁₆	—	2	4	no	—
242	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
243	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
244	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
245	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
246	C₁₃×C₄⋊C₄	—	2	2	no	—
247	C₁₃×C₄⋊C₄	—	2	2	no	—
248	C₁₃×C₄⋊C₄	—	2	4	no	—
249	C₁₃×C₄⋊C₄	—	2	2	no	—
250	C₁₃×C₄⋊C₄	—	2	4	no	—
251	C₁₃×C₄⋊C₄	—	2	1	no	—
252	C₁₃×C₄⋊C₄	—	2	1	no	—
253	C₁₃×C₄⋊C₄	—	2	1	no	—
254	C₁₃×C₄⋊C₄	—	2	1	no	—
255	C₁₃×C₄⋊C₄	—	2	1	no	—
256	C₁₃×C₄⋊C₄	—	2	1	no	—
257	C₁₃×C₄⋊C₄	—	2	1	no	—
258	C₁₃×C₄⋊C₄	—	2	1	no	—
259	C₁₃×C₄⋊C₄	—	2	4	no	—
260	C₁₃×C₄⋊C₄	—	2	4	no	—
261	C₁₃×C₄⋊C₄	—	2	2	no	—
262	C₁₃×C₄⋊C₄	—	2	2	no	—
263	C₁₃×C₄⋊C₄	—	2	4	no	—
264	C₁₃×C₄⋊C₄	—	2	4	no	—
265	C₁₃×C₄⋊C₄	—	2	4	no	—
266	C₁₃×C₄⋊C₄	—	2	4	no	—
267	C₁₃×C₄⋊C₄	—	2	2	no	—
268	C₁₃×C₄⋊C₄	—	2	2	no	—
269	C₁₃×C₄⋊C₄	—	2	4	no	—
270	C₁₃×C₄⋊C₄	—	2	4	no	—
271	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
272	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
273	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
274	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
275	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
276	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
277	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
278	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
279	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
280	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
281	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
282	C₁₃×C₂²⋊C₄	—	2	2	no	—
283	C₁₃×C₂²⋊C₄	—	2	2	no	—
284	C₁₃×C₂²⋊C₄	—	2	1	no	—
285	C₁₃×C₂²⋊C₄	—	2	1	no	—
286	C₁₃×C₂²⋊C₄	—	2	1	no	—
287	C₁₃×C₂²⋊C₄	—	2	4	no	—
288	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
289	C₄²×C₁₃	—	2	1	no	—
290	C₄²×C₁₃	—	2	1	no	—
291	C₄²×C₁₃	—	2	1	no	—
292	C₄²×C₁₃	—	2	4	no	—
293	C₄²×C₁₃	—	2	2	no	—
294	C₄²×C₁₃	—	2	2	no	—
295	C₄²×C₁₃	—	2	4	no	—
296	C₄²×C₁₃	—	2	4	no	—
297	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
298	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
299	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
300	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
301	C₄²×C₁₃	C₂⁴	1	4	yes	—
302	#3556	C₂×C₁₃	1	1	yes	characteristic, complemented
303	#3503	C₂×C₁₃	1	1	yes	characteristic
304	#3387	C₂×C₁₃	1	2	yes	complemented
305	#3386	C₂×C₁₃	1	2	yes	complemented
306	#3383	C₂×C₁₃	1	2	yes	complemented
307	#3381	C₂×C₁₃	1	2	yes	complemented
308	#3374	C₂×C₁₃	1	2	yes	complemented
309	#3372	C₂×C₁₃	1	2	yes	complemented
310	#3363	C₂×C₁₃	1	2	yes	complemented
311	#3359	C₂×C₁₃	1	2	yes	complemented
312	#3242	C₂×C₁₃	1	4	yes	complemented
313	#3230	C₂×C₁₃	1	1	yes	characteristic, complemented
314	#3229	C₂×C₁₃	1	1	yes	characteristic, complemented
315	#3120	C₂×C₁₃	1	4	yes	—
316	#3107	C₂×C₁₃	1	1	yes	characteristic
317	#3107	C₂×C₁₃	1	1	yes	characteristic
318	#2986	C₂×C₁₃	1	1	yes	characteristic, complemented
319	C₂³×C₁₃	—	2	1	no	—
320	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
321	Q₈×C₁₃	—	2	4	no	—
322	Q₈×C₁₃	—	2	4	no	—
323	Q₈×C₁₃	—	2	1	no	—
324	Q₈×C₁₃	—	2	2	no	—
325	Q₈×C₁₃	—	2	2	no	—
326	Q₈×C₁₃	—	2	2	no	—
327	Q₈×C₁₃	—	2	2	no	—
328	Q₈×C₁₃	—	4	2	no	—
329	Q₈×C₁₃	—	4	4	no	—
330	Q₈×C₁₃	—	4	2	no	—
331	Q₈×C₁₃	—	8	2	no	—
332	Q₈×C₁₃	—	8	4	no	—
333	Q₈×C₁₃	2₋¹⁺⁴	1	2	yes	—
334	D₄×C₁₃	—	2	4	no	—
335	D₄×C₁₃	—	2	1	no	—
336	D₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
337	C₂×C₄×C₁₃	—	2	4	no	—
338	C₂×C₄×C₁₃	—	2	1	no	—
339	C₂×C₄×C₁₃	—	2	2	no	—
340	C₂×C₄×C₁₃	—	2	2	no	—
341	C₂×C₄×C₁₃	—	2	1	no	—
342	C₂×C₄×C₁₃	—	2	1	no	—
343	C₂×C₄×C₁₃	—	2	2	no	—
344	C₂×C₄×C₁₃	—	2	2	no	—
345	C₂×C₄×C₁₃	—	2	2	no	—
346	C₂×C₄×C₁₃	—	2	2	no	—
347	C₂×C₄×C₁₃	—	2	1	no	—
348	C₂×C₄×C₁₃	—	2	1	no	—
349	C₂×C₄×C₁₃	—	2	4	no	—
350	C₂×C₄×C₁₃	—	4	2	no	—
351	C₂×C₄×C₁₃	—	4	2	no	—
352	C₂×C₄×C₁₃	—	8	4	no	—
353	C₂×C₄×C₁₃	—	8	2	no	—
354	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
355	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
356	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
357	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
361	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
362	C₈×C₁₃	—	2	2	no	—
363	C₈×C₁₃	—	2	2	no	—
364	C₈×C₁₃	—	2	2	no	—
365	C₈×C₁₃	—	2	2	no	—
366	#564	—	2	2	no	—
367	Q₈²	C₂²×C₁₃	1	2	yes	—
368	#557	—	2	1	no	—
369	#557	—	2	1	no	—
370	#557	C₂²×C₁₃	1	2	yes	—
371	#557	C₂²×C₁₃	1	2	yes	—
372	#557	C₂²×C₁₃	1	2	yes	—
373	#557	C₂²×C₁₃	1	2	yes	—
374	#557	C₂²×C₁₃	1	2	yes	—
375	#554	—	2	2	no	—
376	#554	C₂²×C₁₃	1	2	yes	—
377	D₄×Q₈	—	2	2	no	—
378	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
379	#544	—	2	2	no	—
380	#544	C₂²×C₁₃	1	2	yes	—
381	#541	—	2	2	no	—
382	#541	—	2	2	no	—
383	#541	C₂²×C₁₃	1	4	yes	—
384	#533	—	2	1	no	—
385	#533	C₂²×C₁₃	1	1	yes	characteristic
386	#533	C₂²×C₁₃	1	1	yes	characteristic
387	#533	C₂²×C₁₃	1	1	yes	characteristic
388	C₂×C₄⋊Q₈	—	2	1	no	—
389	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
390	#520	C₂²×C₁₃	1	2	yes	—
391	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
392	#501	C₂²×C₁₃	1	4	yes	—
393	#500	C₂²×C₁₃	1	2	yes	—
394	#499	C₂²×C₁₃	1	4	yes	—
395	#498	C₂²×C₁₃	1	2	yes	—
396	#491	C₂²×C₁₃	1	4	yes	—
397	#487	C₂²×C₁₃	1	4	yes	—
398	#487	C₂²×C₁₃	1	2	yes	—
399	#487	C₂²×C₁₃	1	2	yes	—
400	#485	C₂²×C₁₃	1	2	yes	—
401	#485	C₂²×C₁₃	1	2	yes	—
402	#484	C₂²×C₁₃	1	4	yes	—
403	#483	C₂²×C₁₃	1	4	yes	—
404	#479	C₂²×C₁₃	1	4	yes	—
405	#479	C₂²×C₁₃	1	4	yes	—
406	#479	C₂²×C₁₃	1	4	yes	—
407	#478	C₂²×C₁₃	1	4	yes	—
408	#477	C₂²×C₁₃	1	2	yes	—
409	#477	C₂²×C₁₃	1	4	yes	—
410	#477	C₂²×C₁₃	1	2	yes	—
411	#475	C₂²×C₁₃	1	2	yes	—
412	#475	C₂²×C₁₃	1	4	yes	—
413	#475	C₂²×C₁₃	1	1	yes	characteristic
414	#475	C₂²×C₁₃	1	1	yes	characteristic
415	#475	C₂²×C₁₃	1	2	yes	—
416	#474	C₂²×C₁₃	1	1	yes	characteristic
417	#474	C₂²×C₁₃	1	1	yes	characteristic
418	#462	C₂²×C₁₃	1	1	yes	characteristic
419	#462	C₂²×C₁₃	1	1	yes	characteristic
420	#462	C₂²×C₁₃	1	4	yes	—
421	#461	C₂²×C₁₃	1	1	yes	characteristic
422	#461	C₂²×C₁₃	1	4	yes	—
423	#461	C₂²×C₁₃	1	1	yes	characteristic
424	#452	C₂²×C₁₃	1	2	yes	—
425	#452	C₂²×C₁₃	1	2	yes	—
426	#446	C₂²×C₁₃	1	2	yes	—
427	#446	C₂²×C₁₃	1	2	yes	—
428	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
429	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
430	#441	C₂²×C₁₃	1	4	yes	—
431	#440	C₂²×C₁₃	1	4	yes	—
432	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
433	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
434	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	—
435	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
436	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
437	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
438	#433	C₂²×C₁₃	1	4	yes	—
439	#431	C₂²×C₁₃	1	1	yes	characteristic
440	#431	C₂²×C₁₃	1	1	yes	characteristic
441	C₂²×C₁₃	—	2	1	no	—
442	C₂²×C₁₃	—	2	2	no	—
443	C₂²×C₁₃	—	2	1	no	—
444	C₂²×C₁₃	—	2	1	no	—
445	C₂²×C₁₃	—	4	1	no	—
446	C₂²×C₁₃	—	4	1	no	—
447	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
448	C₄×C₁₃	—	2	1	no	—
449	C₄×C₁₃	—	2	2	no	—
450	C₄×C₁₃	—	2	1	no	—
451	C₄×C₁₃	—	2	4	no	—
452	C₄×C₁₃	—	2	1	no	—
453	C₄×C₁₃	—	2	4	no	—
454	C₄×C₁₃	—	4	2	no	—
455	C₄×C₁₃	—	4	2	no	—
456	C₄×C₁₃	—	4	1	no	—
457	C₄×C₁₃	—	4	4	no	—
458	C₄×C₁₃	—	4	2	no	—
459	C₄×C₁₃	—	4	1	no	—
460	C₄×C₁₃	—	4	2	no	—
461	C₄×C₁₃	#577	1	2	yes	—
462	C₄×C₁₃	#578	1	2	yes	—
463	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
464	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
465	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
466	C₂²×Q₈	—	2	2	no	—
467	C₂²×Q₈	—	2	1	no	—
468	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
469	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
470	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
471	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
472	C₄⋊Q₈	—	2	2	no	—
473	C₄⋊Q₈	—	2	2	no	—
474	C₄⋊Q₈	—	2	2	no	—
475	C₄⋊Q₈	—	2	2	no	—
476	C₄⋊Q₈	—	2	2	no	—
477	C₄⋊Q₈	—	2	4	no	—
478	C₄⋊Q₈	—	2	1	no	—
479	C₄⋊Q₈	—	2	1	no	—
480	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
481	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
482	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
483	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
484	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
485	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
486	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
487	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
488	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
489	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
490	#126	—	2	4	no	—
491	#126	—	2	4	no	—
492	#125	—	2	2	no	—
493	#125	—	2	2	no	—
494	#125	—	2	2	no	—
495	#125	—	2	4	no	—
496	#125	—	2	4	no	—
497	#125	—	2	4	no	—
498	#125	—	2	4	no	—
499	#125	—	2	4	no	—
500	#125	—	2	4	no	—
501	#125	—	2	4	no	—
502	#125	—	2	1	no	—
503	#125	—	2	1	no	—
504	#125	D₄×C₁₃	1	2	yes	—
505	#125	C₂³×C₁₃	1	4	yes	—
506	#125	C₂³×C₁₃	1	4	yes	—
507	C₂²⋊Q₈	—	2	2	no	—
508	C₂²⋊Q₈	—	2	1	no	—
509	C₂²⋊Q₈	—	2	1	no	—
510	C₂²⋊Q₈	—	2	2	no	—
511	C₂²⋊Q₈	—	2	4	no	—
512	C₂²⋊Q₈	—	2	4	no	—
513	C₂²⋊Q₈	—	2	4	no	—
514	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
515	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
516	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
517	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
518	C₄×Q₈	—	2	2	no	—
519	C₄×Q₈	—	2	2	no	—
520	C₄×Q₈	—	2	2	no	—
521	C₄×Q₈	—	2	2	no	—
522	C₄×Q₈	—	2	2	no	—
523	C₄×Q₈	—	2	2	no	—
524	C₄×Q₈	—	2	1	no	—
525	C₄×Q₈	—	2	1	no	—
526	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
527	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
528	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
529	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
530	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
531	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
532	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
533	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
534	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
535	C₄×D₄	—	2	1	no	—
536	C₄×D₄	—	2	1	no	—
537	C₄×D₄	—	2	4	no	—
538	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
539	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
540	C₄×D₄	C₂³×C₁₃	1	4	yes	—
541	#117	—	2	1	no	—
542	#117	—	2	1	no	—
543	#117	—	2	2	no	—
544	#117	—	2	1	no	—
545	#117	C₂³×C₁₃	1	1	yes	characteristic
546	#117	C₂³×C₁₃	1	2	yes	—
547	C₂×C₄⋊C₄	—	2	1	no	—
548	C₂×C₄⋊C₄	—	2	2	no	—
549	C₂×C₄⋊C₄	—	2	2	no	—
550	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
551	C₂×C₄²	—	2	1	no	—
552	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
553	#107	C₂³×C₁₃	1	2	yes	—
554	#107	C₂³×C₁₃	1	2	yes	—
555	#107	C₂³×C₁₃	1	4	yes	—
556	#107	C₂³×C₁₃	1	4	yes	—
557	#106	C₂³×C₁₃	1	2	yes	—
558	#106	C₂³×C₁₃	1	4	yes	—
559	#106	C₂³×C₁₃	1	2	yes	—
560	#106	C₂³×C₁₃	1	4	yes	—
561	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
562	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
563	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
564	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
565	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
566	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
567	#103	C₂³×C₁₃	1	2	yes	—
568	#103	C₂³×C₁₃	1	4	yes	—
569	#103	C₂³×C₁₃	1	2	yes	—
570	#103	C₂³×C₁₃	1	2	yes	—
571	#103	C₂³×C₁₃	1	2	yes	—
572	#103	C₂³×C₁₃	1	2	yes	—
573	#103	C₂³×C₁₃	1	4	yes	—
574	#103	C₂³×C₁₃	1	2	yes	—
575	#103	C₂³×C₁₃	1	4	yes	—
576	#103	C₂³×C₁₃	1	4	yes	—
577	#102	C₂³×C₁₃	1	2	yes	—
578	#102	C₂³×C₁₃	1	2	yes	—
579	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
580	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
581	#97	C₂³×C₁₃	1	4	yes	—
582	C₄×C₈	C₂³×C₁₃	1	2	yes	—
583	C₄×C₈	C₂³×C₁₃	1	2	yes	—
584	C₄×C₈	C₂³×C₁₃	1	4	yes	—
585	C₂×C₁₃	—	4	1	no	—
586	C₂×C₁₃	—	4	2	no	—
587	C₂×C₁₃	#3486	1	1	yes	characteristic
588	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
589	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
590	#41	—	2	2	no	—
591	#41	—	2	2	no	—
592	C₂×Q₈	—	2	1	no	—
593	C₂×Q₈	—	2	1	no	—
594	C₂×Q₈	—	2	2	no	—
595	C₂×Q₈	—	2	4	no	—
596	C₂×Q₈	—	2	2	no	—
597	C₂×Q₈	—	8	2	no	—
598	C₂×Q₈	—	8	4	no	—
599	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
600	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
601	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
602	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
603	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
604	C₂×D₄	—	2	1	no	—
605	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
606	C₂²×C₄	—	2	1	no	—
607	C₂²×C₄	—	2	2	no	—
608	C₂²×C₄	—	2	1	no	—
609	C₂²×C₄	—	2	1	no	—
610	C₂²×C₄	—	2	4	no	—
611	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
612	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
613	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
614	Q₁₆	—	2	4	no	—
615	Q₁₆	—	2	4	no	—
616	SD₁₆	—	2	4	no	—
617	SD₁₆	—	2	4	no	—
618	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
619	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
620	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
621	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
622	C₄⋊C₄	—	2	2	no	—
623	C₄⋊C₄	—	2	2	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	2	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	—	2	1	no	—
629	C₄⋊C₄	—	2	1	no	—
630	C₄⋊C₄	—	2	1	no	—
631	C₄⋊C₄	—	2	1	no	—
632	C₄⋊C₄	—	2	1	no	—
633	C₄⋊C₄	—	2	1	no	—
634	C₄⋊C₄	—	2	1	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	2	2	no	—
638	C₄⋊C₄	—	2	2	no	—
639	C₄⋊C₄	—	2	4	no	—
640	C₄⋊C₄	—	2	4	no	—
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	2	2	no	—
644	C₄⋊C₄	—	2	2	no	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
648	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
649	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
650	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
651	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
652	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
653	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
654	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
655	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
656	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
657	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
658	C₂²⋊C₄	—	2	2	no	—
659	C₂²⋊C₄	—	2	2	no	—
660	C₂²⋊C₄	—	2	1	no	—
661	C₂²⋊C₄	—	2	1	no	—
662	C₂²⋊C₄	—	2	1	no	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
665	C₄²	—	2	1	no	—
666	C₄²	—	2	1	no	—
667	C₄²	—	2	1	no	—
668	C₄²	—	2	4	no	—
669	C₄²	—	2	2	no	—
670	C₄²	—	2	2	no	—
671	C₄²	—	2	4	no	—
672	C₄²	—	2	4	no	—
673	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
674	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
675	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
676	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
677	C₄²	C₂⁴×C₁₃	1	4	yes	—
678	C₁₃	#61869	1	1	yes	characteristic, direct product factor, Sylow
679	C₂³	—	2	1	no	—
680	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
681	Q₈	—	2	4	no	—
682	Q₈	—	2	4	no	—
683	Q₈	—	2	1	no	—
684	Q₈	—	2	2	no	—
685	Q₈	—	2	2	no	—
686	Q₈	—	2	2	no	—
687	Q₈	—	2	2	no	—
688	Q₈	—	4	4	no	—
689	Q₈	—	4	2	no	—
690	Q₈	—	4	2	no	—
691	Q₈	—	8	2	no	—
692	Q₈	—	8	4	no	—
693	Q₈	C₁₃×2₋¹⁺⁴	1	2	yes	—
694	D₄	—	2	4	no	—
695	D₄	—	2	1	no	—
696	D₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	4	no	—
710	C₂×C₄	—	4	2	no	—
711	C₂×C₄	—	4	2	no	—
712	C₂×C₄	—	8	4	no	—
713	C₂×C₄	—	8	2	no	—
714	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
715	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
716	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
717	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
718	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
719	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
720	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
721	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
722	C₈	—	2	2	no	—
723	C₈	—	2	2	no	—
724	C₈	—	2	2	no	—
725	C₈	—	2	2	no	—
726	C₂²	—	2	1	no	—
727	C₂²	—	2	1	no	—
728	C₂²	—	2	1	no	—
729	C₂²	—	2	2	no	—
730	C₂²	—	4	1	no	—
731	C₂²	—	4	1	no	—
732	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
733	C₄	—	2	1	no	—
734	C₄	—	2	4	no	—
735	C₄	—	2	1	no	—
736	C₄	—	2	4	no	—
737	C₄	—	2	1	no	—
738	C₄	—	2	2	no	—
739	C₄	—	4	1	no	—
740	C₄	—	4	4	no	—
741	C₄	—	4	2	no	—
742	C₄	—	4	1	no	—
743	C₄	—	4	2	no	—
744	C₄	—	4	2	no	—
745	C₄	—	4	2	no	—
746	C₄	C₁₃×#577	1	2	yes	—
747	C₄	C₁₃×#578	1	2	yes	—
748	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
749	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
750	C₂	—	4	1	no	—
751	C₂	—	4	2	no	—
752	C₂	C₁₃×#3486	1	1	yes	characteristic
753	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
754	C₂	C₂×C₁₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#41	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3556	C₂	semidirect
3. C₁₃×#3387	C₂	semidirect
4. C₁₃×#3386	C₂	semidirect
5. C₁₃×#3383	C₂	semidirect
6. C₁₃×#3381	C₂	semidirect
7. C₁₃×#3374	C₂	semidirect
8. C₁₃×#3372	C₂	semidirect
9. C₁₃×#3363	C₂	semidirect
10. C₁₃×#3359	C₂	semidirect
11. C₁₃×#3242	C₂	semidirect
12. C₁₃×#3230	C₂	semidirect
13. C₁₃×#3229	C₂	semidirect
17. C₁₃×#2986	C₂	semidirect
213. #61869	C₁₃	direct (N × H)
302. #3556	C₂×C₁₃	semidirect
304. #3387	C₂×C₁₃	semidirect
305. #3386	C₂×C₁₃	semidirect
306. #3383	C₂×C₁₃	semidirect
307. #3381	C₂×C₁₃	semidirect
308. #3374	C₂×C₁₃	semidirect
309. #3372	C₂×C₁₃	semidirect
310. #3363	C₂×C₁₃	semidirect
311. #3359	C₂×C₁₃	semidirect
312. #3242	C₂×C₁₃	semidirect
313. #3230	C₂×C₁₃	semidirect
314. #3229	C₂×C₁₃	semidirect
318. #2986	C₂×C₁₃	semidirect
678. C₁₃	#61869	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3556	2
C₁₃×#3503	2
C₁₃×#3387	2
C₁₃×#3386	2
C₁₃×#3383	2
C₁₃×#3381	2
C₁₃×#3374	2
C₁₃×#3372	2
C₁₃×#3363	2
C₁₃×#3359	2
C₁₃×#3242	2
C₁₃×#3230	2
C₁₃×#3229	2
C₁₃×#3120	2
C₁₃×#3107	2
C₁₃×#2986	2
#61869	13

Subgroups — C13×#61869 #15748208

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61869 #15748208