Subgroups — C₁₃×#61892 #15748231

Order 3328.

1770 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3502	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#559	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3400	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3375	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3215	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3208	C₂	1	2	yes	maximal
7	C₁₃×#3110	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3104	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2983	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#559	—	2	4	no	—
11	C₁₃×#559	C₂²	1	8	yes	—
12	Q₈²×C₁₃	C₂²	1	4	yes	complemented
13	C₁₃×#557	—	2	4	no	—
14	C₁₃×#557	C₂²	1	4	yes	complemented
15	C₁₃×#544	—	2	1	no	—
16	C₁₃×#544	—	2	2	no	—
17	C₁₃×#533	C₂²	1	2	yes	—
18	C₁₃×#533	C₂²	1	4	yes	—
19	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#124	—	2	1	no	—
21	C₂×C₁₃×#124	C₂²	1	2	yes	—
22	C₂×C₁₃×#123	—	2	2	no	—
23	C₁₃×#519	—	2	1	no	—
24	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₁₃	—	2	1	no	—
27	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
28	C₁₃×#497	C₂²	1	8	yes	complemented
29	C₁₃×#492	C₂²	1	4	yes	—
30	C₁₃×#489	C₂²	1	8	yes	complemented
31	C₁₃×#486	C₂²	1	4	yes	—
32	C₁₃×#484	C₂²	1	4	yes	—
33	C₁₃×#477	C₂²	1	4	yes	complemented
34	C₁₃×#474	C₂²	1	8	yes	complemented
35	C₁₃×#464	C₂²	1	16	yes	complemented
36	C₁₃×#462	C₂²	1	4	yes	complemented
37	C₁₃×#461	C₂²	1	8	yes	complemented
38	C₁₃×#460	C₂²	1	8	yes	—
39	C₁₃×#451	C₂²	1	4	yes	—
40	C₁₃×#450	C₂²	1	8	yes	—
41	C₁₃×#446	C₂²	1	8	yes	complemented
42	C₁₃×#440	C₂²	1	16	yes	complemented
43	C₄×C₁₃×Q₁₆	C₂²	1	8	yes	complemented
44	C₁₃×#432	C₂²	1	4	yes	—
45	C₁₃×#431	C₂²	1	2	yes	—
46	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
47	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₁₃	—	2	1	no	—
49	C₂²×D₄×C₁₃	—	2	1	no	—
50	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
51	C₂³×C₄×C₁₃	—	2	2	no	—
52	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
53	C₂×C₁₃×SD₁₆	C₂³	1	16	yes	—
54	C₁₃×C₄⋊Q₈	—	2	4	no	—
55	C₁₃×C₄⋊Q₈	—	2	8	no	—
56	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
57	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
58	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
59	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
60	C₁₃×#127	—	2	2	no	—
61	C₁₃×#127	C₂³	1	4	yes	—
62	C₁₃×#125	—	2	4	no	—
63	C₁₃×#125	—	2	8	no	—
64	C₁₃×#125	—	2	4	no	—
65	C₁₃×#125	—	2	2	no	—
66	C₁₃×#124	—	2	8	no	—
67	C₁₃×#124	—	2	4	no	—
68	C₁₃×#124	C₂³	1	8	yes	—
69	C₁₃×#123	—	2	16	no	—
70	C₁₃×C₂²⋊Q₈	—	2	4	no	—
71	C₁₃×C₂²⋊Q₈	—	2	2	no	—
72	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
73	C₄×Q₈×C₁₃	—	2	4	no	—
74	C₄×Q₈×C₁₃	—	2	4	no	—
75	C₄×Q₈×C₁₃	—	2	2	no	—
76	C₄×Q₈×C₁₃	—	2	4	no	—
77	C₄×Q₈×C₁₃	—	2	2	no	—
78	C₄×Q₈×C₁₃	D₄	1	4	yes	—
79	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
80	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
81	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
82	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
83	C₄×D₄×C₁₃	—	2	8	no	—
84	C₄×D₄×C₁₃	—	2	4	no	—
85	C₄×D₄×C₁₃	C₂³	1	8	yes	—
86	C₁₃×#117	—	2	4	no	—
87	C₁₃×#117	—	2	2	no	—
88	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
89	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
90	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
92	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
93	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
94	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
95	C₂×C₄²×C₁₃	—	2	1	no	—
96	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
98	C₁₃×#107	C₂³	1	8	yes	—
99	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
100	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
101	C₁₃×#103	C₂³	1	8	yes	—
102	C₁₃×#103	C₂³	1	8	yes	—
103	C₁₃×#102	C₂³	1	16	yes	—
104	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
105	C₁₃×#97	C₂³	1	8	yes	—
106	C₄×C₈×C₁₃	C₂³	1	4	yes	—
107	#61892	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₂⁴×C₁₃	—	2	2	no	—
109	C₂×Q₈×C₁₃	—	2	4	no	—
110	C₂×Q₈×C₁₃	—	2	1	no	—
111	C₂×Q₈×C₁₃	—	2	4	no	—
112	C₂×Q₈×C₁₃	—	2	2	no	—
113	C₂×Q₈×C₁₃	—	4	2	no	—
114	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
115	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
116	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
117	C₂×D₄×C₁₃	—	2	2	no	—
118	C₂×D₄×C₁₃	—	2	4	no	—
119	C₂×D₄×C₁₃	—	2	4	no	—
120	C₂×D₄×C₁₃	—	4	4	no	—
121	C₂×D₄×C₁₃	—	4	4	no	—
122	C₂×D₄×C₁₃	—	8	2	no	—
123	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
124	C₂²×C₄×C₁₃	—	2	1	no	—
125	C₂²×C₄×C₁₃	—	2	1	no	—
126	C₂²×C₄×C₁₃	—	2	8	no	—
127	C₂²×C₄×C₁₃	—	8	4	no	—
128	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
133	C₁₃×Q₁₆	—	4	8	no	—
134	C₁₃×SD₁₆	—	4	16	no	—
135	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
136	C₁₃×C₄⋊C₄	—	2	4	no	—
137	C₁₃×C₄⋊C₄	—	2	1	no	—
138	C₁₃×C₄⋊C₄	—	2	4	no	—
139	C₁₃×C₄⋊C₄	—	2	2	no	—
140	C₁₃×C₄⋊C₄	—	2	4	no	—
141	C₁₃×C₄⋊C₄	—	2	2	no	—
142	C₁₃×C₄⋊C₄	—	2	4	no	—
143	C₁₃×C₄⋊C₄	—	2	4	no	—
144	C₁₃×C₄⋊C₄	—	2	2	no	—
145	C₁₃×C₄⋊C₄	—	2	8	no	—
146	C₁₃×C₄⋊C₄	—	2	4	no	—
147	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
148	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
149	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
150	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
151	C₁₃×C₂²⋊C₄	—	2	4	no	—
152	C₁₃×C₂²⋊C₄	—	2	8	no	—
153	C₁₃×C₂²⋊C₄	—	2	8	no	—
154	C₁₃×C₂²⋊C₄	—	2	8	no	—
155	C₄²×C₁₃	—	2	4	no	—
156	C₄²×C₁₃	—	2	8	no	—
157	C₄²×C₁₃	—	2	4	no	—
158	C₄²×C₁₃	C₂×D₄	1	4	yes	—
159	C₄²×C₁₃	C₂×D₄	1	2	yes	—
160	C₄²×C₁₃	C₂⁴	1	2	yes	—
161	C₄²×C₁₃	C₂⁴	1	4	yes	—
162	#3502	C₂×C₁₃	1	1	yes	characteristic, complemented
163	C₂×#559	C₂×C₁₃	1	1	yes	characteristic
164	#3400	C₂×C₁₃	1	8	yes	complemented
165	#3375	C₂×C₁₃	1	8	yes	complemented
166	#3215	C₂×C₁₃	1	4	yes	complemented
167	#3208	C₂×C₁₃	1	2	yes	—
168	#3110	C₂×C₁₃	1	4	yes	complemented
169	#3104	C₂×C₁₃	1	2	yes	complemented
170	#2983	C₂×C₁₃	1	1	yes	characteristic, complemented
171	C₂³×C₁₃	—	2	4	no	—
172	C₂³×C₁₃	—	4	4	no	—
173	C₂³×C₁₃	—	4	4	no	—
174	C₂³×C₁₃	—	4	4	no	—
175	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
176	Q₈×C₁₃	—	2	8	no	—
177	Q₈×C₁₃	—	2	8	no	—
178	Q₈×C₁₃	—	2	4	no	—
179	Q₈×C₁₃	—	4	2	no	—
180	Q₈×C₁₃	—	8	4	no	—
181	Q₈×C₁₃	—	8	2	no	—
182	D₄×C₁₃	—	2	8	no	—
183	D₄×C₁₃	—	4	4	no	—
184	D₄×C₁₃	—	4	8	no	—
185	D₄×C₁₃	—	8	4	no	—
186	C₂×C₄×C₁₃	—	2	4	no	—
187	C₂×C₄×C₁₃	—	2	2	no	—
188	C₂×C₄×C₁₃	—	2	4	no	—
189	C₂×C₄×C₁₃	—	2	4	no	—
190	C₂×C₄×C₁₃	—	2	2	no	—
191	C₂×C₄×C₁₃	—	2	2	no	—
192	C₂×C₄×C₁₃	—	4	2	no	—
193	C₂×C₄×C₁₃	—	4	1	no	—
194	C₂×C₄×C₁₃	—	4	2	no	—
195	C₂×C₄×C₁₃	—	4	2	no	—
196	C₂×C₄×C₁₃	—	8	8	no	—
197	C₂×C₄×C₁₃	#137	1	4	yes	—
198	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
199	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
201	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
202	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
203	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
204	C₈×C₁₃	—	2	8	no	—
205	#559	—	2	4	no	—
206	#559	C₂²×C₁₃	1	8	yes	—
207	Q₈²	C₂²×C₁₃	1	4	yes	complemented
208	#557	—	2	4	no	—
209	#557	C₂²×C₁₃	1	4	yes	complemented
210	#544	—	2	1	no	—
211	#544	—	2	2	no	—
212	#533	C₂²×C₁₃	1	2	yes	—
213	#533	C₂²×C₁₃	1	4	yes	—
214	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
215	C₂×#124	—	2	1	no	—
216	C₂×#124	C₂²×C₁₃	1	2	yes	—
217	C₂×#123	—	2	2	no	—
218	#519	—	2	1	no	—
219	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
220	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
221	C₂×C₄×D₄	—	2	1	no	—
222	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
223	#497	C₂²×C₁₃	1	8	yes	complemented
224	#492	C₂²×C₁₃	1	4	yes	—
225	#489	C₂²×C₁₃	1	8	yes	complemented
226	#486	C₂²×C₁₃	1	4	yes	—
227	#484	C₂²×C₁₃	1	4	yes	—
228	#477	C₂²×C₁₃	1	4	yes	complemented
229	#474	C₂²×C₁₃	1	8	yes	complemented
230	#464	C₂²×C₁₃	1	16	yes	complemented
231	#462	C₂²×C₁₃	1	4	yes	complemented
232	#461	C₂²×C₁₃	1	8	yes	complemented
233	#460	C₂²×C₁₃	1	8	yes	—
234	#451	C₂²×C₁₃	1	4	yes	—
235	#450	C₂²×C₁₃	1	8	yes	—
236	#446	C₂²×C₁₃	1	8	yes	complemented
237	#440	C₂²×C₁₃	1	16	yes	complemented
238	C₄×Q₁₆	C₂²×C₁₃	1	8	yes	complemented
239	#432	C₂²×C₁₃	1	4	yes	—
240	#431	C₂²×C₁₃	1	2	yes	—
241	C₂²×C₁₃	—	2	1	no	—
242	C₂²×C₁₃	—	2	1	no	—
243	C₂²×C₁₃	—	4	4	no	—
244	C₂²×C₁₃	—	4	4	no	—
245	C₂²×C₁₃	—	4	4	no	—
246	C₂²×C₁₃	—	8	8	no	—
247	C₂²×C₁₃	C₂×#137	1	2	yes	—
248	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
249	C₄×C₁₃	—	2	4	no	—
250	C₄×C₁₃	—	2	2	no	—
251	C₄×C₁₃	—	2	1	no	—
252	C₄×C₁₃	—	2	4	no	—
253	C₄×C₁₃	—	4	2	no	—
254	C₄×C₁₃	—	4	4	no	—
255	C₄×C₁₃	—	4	2	no	—
256	C₄×C₁₃	—	4	4	no	—
257	C₄×C₁₃	C₂×#137	1	4	yes	—
258	C₄×C₁₃	#585	1	2	yes	—
259	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
260	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
261	C₂²×D₄	—	2	1	no	—
262	C₂²×D₄	—	2	1	no	—
263	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
264	C₂³×C₄	—	2	2	no	—
265	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
266	C₂×SD₁₆	C₂³×C₁₃	1	16	yes	—
267	C₄⋊Q₈	—	2	4	no	—
268	C₄⋊Q₈	—	2	8	no	—
269	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
270	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
271	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
272	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
273	#127	—	2	2	no	—
274	#127	C₂³×C₁₃	1	4	yes	—
275	#125	—	2	4	no	—
276	#125	—	2	8	no	—
277	#125	—	2	4	no	—
278	#125	—	2	2	no	—
279	#124	—	2	8	no	—
280	#124	—	2	4	no	—
281	#124	C₂³×C₁₃	1	8	yes	—
282	#123	—	2	16	no	—
283	C₂²⋊Q₈	—	2	4	no	—
284	C₂²⋊Q₈	—	2	2	no	—
285	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
286	C₄×Q₈	—	2	4	no	—
287	C₄×Q₈	—	2	4	no	—
288	C₄×Q₈	—	2	2	no	—
289	C₄×Q₈	—	2	4	no	—
290	C₄×Q₈	—	2	2	no	—
291	C₄×Q₈	D₄×C₁₃	1	4	yes	—
292	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
293	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
294	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
295	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
296	C₄×D₄	—	2	8	no	—
297	C₄×D₄	—	2	4	no	—
298	C₄×D₄	C₂³×C₁₃	1	8	yes	—
299	#117	—	2	4	no	—
300	#117	—	2	2	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
303	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
304	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
305	C₂×C₂²⋊C₄	—	2	2	no	—
306	C₂×C₂²⋊C₄	—	2	2	no	—
307	C₂×C₂²⋊C₄	—	2	2	no	—
308	C₂×C₄²	—	2	1	no	—
309	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
310	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
311	#107	C₂³×C₁₃	1	8	yes	—
312	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
313	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
314	#103	C₂³×C₁₃	1	8	yes	—
315	#103	C₂³×C₁₃	1	8	yes	—
316	#102	C₂³×C₁₃	1	16	yes	—
317	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
318	#97	C₂³×C₁₃	1	8	yes	—
319	C₄×C₈	C₂³×C₁₃	1	4	yes	—
320	C₂×C₁₃	—	2	2	no	—
321	C₂×C₁₃	—	8	4	no	—
322	C₂×C₁₃	#3487	1	1	yes	characteristic
323	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
324	C₂×C₁₃	#3585	1	1	yes	characteristic
325	C₂⁴	—	2	2	no	—
326	C₂×Q₈	—	2	4	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	2	4	no	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	4	2	no	—
331	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
332	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
333	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	4	no	—
336	C₂×D₄	—	2	4	no	—
337	C₂×D₄	—	4	4	no	—
338	C₂×D₄	—	4	4	no	—
339	C₂×D₄	—	8	2	no	—
340	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	8	no	—
344	C₂²×C₄	—	8	4	no	—
345	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
346	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
347	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
348	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
349	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
350	Q₁₆	—	4	8	no	—
351	SD₁₆	—	4	16	no	—
352	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
353	C₄⋊C₄	—	2	4	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	4	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	4	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	4	no	—
360	C₄⋊C₄	—	2	4	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	8	no	—
363	C₄⋊C₄	—	2	4	no	—
364	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
365	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
366	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
367	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
368	C₂²⋊C₄	—	2	4	no	—
369	C₂²⋊C₄	—	2	8	no	—
370	C₂²⋊C₄	—	2	8	no	—
371	C₂²⋊C₄	—	2	8	no	—
372	C₄²	—	2	4	no	—
373	C₄²	—	2	8	no	—
374	C₄²	—	2	4	no	—
375	C₄²	C₂×D₄×C₁₃	1	4	yes	—
376	C₄²	C₂×D₄×C₁₃	1	2	yes	—
377	C₄²	C₂⁴×C₁₃	1	2	yes	—
378	C₄²	C₂⁴×C₁₃	1	4	yes	—
379	C₁₃	#61892	1	1	yes	characteristic, direct product factor, Sylow
380	C₂³	—	2	4	no	—
381	C₂³	—	4	4	no	—
382	C₂³	—	4	4	no	—
383	C₂³	—	4	4	no	—
384	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
385	Q₈	—	2	8	no	—
386	Q₈	—	2	8	no	—
387	Q₈	—	2	4	no	—
388	Q₈	—	4	2	no	—
389	Q₈	—	8	4	no	—
390	Q₈	—	8	2	no	—
391	D₄	—	2	8	no	—
392	D₄	—	4	4	no	—
393	D₄	—	4	8	no	—
394	D₄	—	8	4	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	8	8	no	—
406	C₂×C₄	C₁₃×#137	1	4	yes	—
407	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
408	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
409	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
410	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
411	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
412	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
413	C₈	—	2	8	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	4	4	no	—
417	C₂²	—	4	4	no	—
418	C₂²	—	4	4	no	—
419	C₂²	—	8	8	no	—
420	C₂²	C₂×C₁₃×#137	1	2	yes	—
421	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
422	C₄	—	2	4	no	—
423	C₄	—	2	4	no	—
424	C₄	—	2	2	no	—
425	C₄	—	2	1	no	—
426	C₄	—	4	2	no	—
427	C₄	—	4	4	no	—
428	C₄	—	4	2	no	—
429	C₄	—	4	4	no	—
430	C₄	C₂×C₁₃×#137	1	4	yes	—
431	C₄	C₁₃×#585	1	2	yes	—
432	C₂	—	2	2	no	—
433	C₂	—	8	4	no	—
434	C₂	C₁₃×#3487	1	1	yes	characteristic
435	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
436	C₂	C₁₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#127	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3502	C₂	semidirect
3. C₁₃×#3400	C₂	semidirect
4. C₁₃×#3375	C₂	semidirect
5. C₁₃×#3215	C₂	semidirect
7. C₁₃×#3110	C₂	semidirect
8. C₁₃×#3104	C₂	semidirect
9. C₁₃×#2983	C₂	semidirect
12. Q₈²×C₁₃	C₂²	semidirect
14. C₁₃×#557	C₂²	semidirect
28. C₁₃×#497	C₂²	semidirect
30. C₁₃×#489	C₂²	semidirect
33. C₁₃×#477	C₂²	semidirect
34. C₁₃×#474	C₂²	semidirect
35. C₁₃×#464	C₂²	semidirect
36. C₁₃×#462	C₂²	semidirect
37. C₁₃×#461	C₂²	semidirect
41. C₁₃×#446	C₂²	semidirect
42. C₁₃×#440	C₂²	semidirect
43. C₄×C₁₃×Q₁₆	C₂²	semidirect
107. #61892	C₁₃	direct (N × H)
162. #3502	C₂×C₁₃	semidirect
164. #3400	C₂×C₁₃	semidirect
165. #3375	C₂×C₁₃	semidirect
166. #3215	C₂×C₁₃	semidirect
168. #3110	C₂×C₁₃	semidirect
169. #3104	C₂×C₁₃	semidirect
170. #2983	C₂×C₁₃	semidirect
207. Q₈²	C₂²×C₁₃	semidirect
209. #557	C₂²×C₁₃	semidirect
223. #497	C₂²×C₁₃	semidirect
225. #489	C₂²×C₁₃	semidirect
228. #477	C₂²×C₁₃	semidirect
229. #474	C₂²×C₁₃	semidirect
230. #464	C₂²×C₁₃	semidirect
231. #462	C₂²×C₁₃	semidirect
232. #461	C₂²×C₁₃	semidirect
236. #446	C₂²×C₁₃	semidirect
237. #440	C₂²×C₁₃	semidirect
238. C₄×Q₁₆	C₂²×C₁₃	semidirect
379. C₁₃	#61892	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×#3502	2
C₂×C₁₃×#559	2
C₁₃×#3400	2
C₁₃×#3375	2
C₁₃×#3215	2
C₁₃×#3208	2
C₁₃×#3110	2
C₁₃×#3104	2
C₁₃×#2983	2
#61892	13

Subgroups — C13×#61892 #15748231

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61892 #15748231