Subgroups — C₁₃×#26061 #15712400

Order 3328.

794 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#498	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#427	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2439	C₂	1	2	yes	maximal
4	C₁₃×#2085	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2057	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1941	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1941	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1854	C₂	1	2	yes	maximal
9	C₁₃×#1846	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1807	C₂	1	1	yes	maximal, characteristic
11	C₈×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₁₃×#117	C₂²	1	2	yes	—
15	C₁₃×#498	—	2	4	no	—
16	C₁₃×#427	—	2	4	no	—
17	C₂×C₁₃×#107	C₂²	1	2	yes	—
18	C₂×C₁₃×#107	C₂²	1	2	yes	—
19	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#106	C₂²	1	2	yes	—
22	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₁₃×#396	—	2	2	no	—
28	C₁₃×#393	—	2	2	no	—
29	C₁₃×#391	—	2	2	no	—
30	C₁₃×#389	C₂²	1	2	yes	—
31	C₁₃×#389	C₂²	1	2	yes	—
32	C₁₃×#387	—	2	2	no	—
33	C₁₃×#382	C₂²	1	2	yes	—
34	C₁₃×#380	C₂²	1	2	yes	—
35	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
36	C₁₃×#340	C₂²	1	2	yes	—
37	C₁₃×#340	C₂²	1	2	yes	—
38	C₁₃×#340	C₂²	1	2	yes	—
39	C₁₃×#336	C₂²	1	1	yes	characteristic
40	C₁₃×#336	C₂²	1	1	yes	characteristic
41	C₂²×Q₈×C₁₃	—	2	2	no	—
42	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₁₃	—	2	2	no	—
44	C₂²×C₈×C₁₃	—	2	2	no	—
45	C₂²×C₈×C₁₃	Q₈	1	4	yes	complemented
46	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₁₃×C₄⋊Q₈	—	2	4	no	—
51	C₁₃×C₄⋊Q₈	—	4	2	no	—
52	C₁₃×#117	—	2	4	no	—
53	C₁₃×#117	—	4	2	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
57	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
58	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
59	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
61	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
62	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
63	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
64	C₂×C₄²×C₁₃	—	2	2	no	—
65	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
67	C₁₃×#107	—	2	4	no	—
68	C₁₃×#107	—	4	2	no	—
69	C₁₃×#106	—	2	2	no	—
70	C₁₃×#106	—	2	2	no	—
71	C₁₃×#106	—	2	2	no	—
72	C₁₃×#106	—	2	4	no	—
73	C₁₃×#106	D₄	1	4	yes	—
74	C₁₃×C₂²⋊C₈	Q₈	1	4	yes	complemented
75	C₄×C₈×C₁₃	—	2	2	no	—
76	C₄×C₈×C₁₃	—	2	2	no	—
77	C₁₃×#95	—	2	2	no	—
78	C₁₃×#95	—	2	2	no	—
79	C₁₃×#95	—	2	2	no	—
80	C₁₃×#95	—	2	2	no	—
81	C₁₃×#95	—	2	2	no	—
82	C₁₃×#95	D₄	1	2	yes	—
83	#26061	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
84	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
85	C₂×Q₈×C₁₃	—	4	4	no	—
86	C₂×Q₈×C₁₃	—	4	4	no	—
87	C₂×Q₈×C₁₃	—	8	2	no	—
88	C₂²×C₄×C₁₃	—	2	1	no	—
89	C₂²×C₄×C₁₃	—	2	1	no	—
90	C₂²×C₄×C₁₃	—	2	1	no	—
91	C₂²×C₄×C₁₃	—	2	1	no	—
92	C₂²×C₄×C₁₃	—	2	2	no	—
93	C₂²×C₄×C₁₃	—	2	2	no	—
94	C₂²×C₄×C₁₃	—	2	2	no	—
95	C₂²×C₄×C₁₃	—	2	2	no	—
96	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
100	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
101	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
102	C₂×C₈×C₁₃	—	2	1	no	—
103	C₂×C₈×C₁₃	—	2	1	no	—
104	C₂×C₈×C₁₃	—	2	1	no	—
105	C₂×C₈×C₁₃	—	2	1	no	—
106	C₂×C₈×C₁₃	—	2	1	no	—
107	C₂×C₈×C₁₃	—	2	1	no	—
108	C₂×C₈×C₁₃	—	2	8	no	—
109	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
110	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
111	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
112	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
113	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
114	C₂×C₈×C₁₃	#41	1	2	yes	—
115	C₁₃×C₄⋊C₄	—	2	2	no	—
116	C₁₃×C₄⋊C₄	—	2	2	no	—
117	C₁₃×C₄⋊C₄	—	2	2	no	—
118	C₁₃×C₄⋊C₄	—	2	2	no	—
119	C₁₃×C₄⋊C₄	—	2	2	no	—
120	C₁₃×C₄⋊C₄	—	2	2	no	—
121	C₁₃×C₄⋊C₄	—	2	2	no	—
122	C₁₃×C₄⋊C₄	—	4	4	no	—
123	C₁₃×C₄⋊C₄	—	4	4	no	—
124	C₁₃×C₄⋊C₄	—	8	2	no	—
125	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
126	C₁₃×C₂²⋊C₄	—	2	4	no	—
127	C₁₃×C₂²⋊C₄	—	4	4	no	—
128	C₁₃×C₂²⋊C₄	—	8	2	no	—
129	C₄²×C₁₃	—	2	1	no	—
130	C₄²×C₁₃	—	2	1	no	—
131	C₄²×C₁₃	—	2	1	no	—
132	C₄²×C₁₃	—	2	1	no	—
133	C₄²×C₁₃	—	4	4	no	—
134	C₂×#498	C₂×C₁₃	1	1	yes	characteristic, complemented
135	C₂×#427	C₂×C₁₃	1	1	yes	characteristic
136	#2439	C₂×C₁₃	1	2	yes	—
137	#2085	C₂×C₁₃	1	2	yes	complemented
138	#2057	C₂×C₁₃	1	2	yes	complemented
139	#1941	C₂×C₁₃	1	1	yes	characteristic, complemented
140	#1941	C₂×C₁₃	1	1	yes	characteristic, complemented
141	#1854	C₂×C₁₃	1	2	yes	—
142	#1846	C₂×C₁₃	1	1	yes	characteristic, complemented
143	#1807	C₂×C₁₃	1	1	yes	characteristic
144	C₈×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic
145	C₂³×C₁₃	—	2	1	no	—
146	C₂³×C₁₃	—	2	1	no	—
147	C₂³×C₁₃	—	2	2	no	—
148	C₂³×C₁₃	—	2	2	no	—
149	C₂³×C₁₃	C₄⋊Q₈	1	2	yes	—
150	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
151	Q₈×C₁₃	—	8	8	no	—
152	C₂×C₄×C₁₃	—	2	2	no	—
153	C₂×C₄×C₁₃	—	2	1	no	—
154	C₂×C₄×C₁₃	—	2	1	no	—
155	C₂×C₄×C₁₃	—	2	2	no	—
156	C₂×C₄×C₁₃	—	2	2	no	—
157	C₂×C₄×C₁₃	—	2	2	no	—
158	C₂×C₄×C₁₃	—	2	2	no	—
159	C₂×C₄×C₁₃	—	2	2	no	—
160	C₂×C₄×C₁₃	—	2	4	no	—
161	C₂×C₄×C₁₃	—	2	2	no	—
162	C₂×C₄×C₁₃	—	2	2	no	—
163	C₂×C₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	—	4	2	no	—
165	C₂×C₄×C₁₃	—	4	2	no	—
166	C₂×C₄×C₁₃	—	4	2	no	—
167	C₂×C₄×C₁₃	—	4	2	no	—
168	C₂×C₄×C₁₃	—	4	2	no	—
169	C₂×C₄×C₁₃	—	4	2	no	—
170	C₂×C₄×C₁₃	—	4	2	no	—
171	C₂×C₄×C₁₃	—	4	2	no	—
172	C₂×C₄×C₁₃	—	4	2	no	—
173	C₂×C₄×C₁₃	—	4	2	no	—
174	C₂×C₄×C₁₃	—	4	2	no	—
175	C₂×C₄×C₁₃	C₄⋊Q₈	1	2	yes	—
176	C₂×C₄×C₁₃	#135	1	4	yes	—
177	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
181	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
182	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
183	C₈×C₁₃	—	2	2	no	—
184	C₈×C₁₃	—	2	2	no	—
185	C₈×C₁₃	—	2	2	no	—
186	C₈×C₁₃	C₂²⋊Q₈	1	4	yes	—
187	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
188	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
189	C₂×#117	C₂²×C₁₃	1	2	yes	—
190	#498	—	2	4	no	—
191	#427	—	2	4	no	—
192	C₂×#107	C₂²×C₁₃	1	2	yes	—
193	C₂×#107	C₂²×C₁₃	1	2	yes	—
194	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
195	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
196	C₂×#106	C₂²×C₁₃	1	2	yes	—
197	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
198	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
199	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
200	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
201	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
202	#396	—	2	2	no	—
203	#393	—	2	2	no	—
204	#391	—	2	2	no	—
205	#389	C₂²×C₁₃	1	2	yes	—
206	#389	C₂²×C₁₃	1	2	yes	—
207	#387	—	2	2	no	—
208	#382	C₂²×C₁₃	1	2	yes	—
209	#380	C₂²×C₁₃	1	2	yes	—
210	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
211	#340	C₂²×C₁₃	1	2	yes	—
212	#340	C₂²×C₁₃	1	2	yes	—
213	#340	C₂²×C₁₃	1	2	yes	—
214	#336	C₂²×C₁₃	1	1	yes	characteristic
215	#336	C₂²×C₁₃	1	1	yes	characteristic
216	C₂²×C₁₃	—	2	2	no	—
217	C₂²×C₁₃	—	2	2	no	—
218	C₂²×C₁₃	—	2	2	no	—
219	C₂²×C₁₃	—	4	2	no	—
220	C₂²×C₁₃	—	4	2	no	—
221	C₂²×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
222	C₂²×C₁₃	D₄²	1	1	yes	characteristic
223	C₂²×C₁₃	#547	1	1	yes	characteristic
224	C₂²×C₁₃	C₂×#135	1	2	yes	—
225	C₂²×C₁₃	#577	1	2	yes	—
226	C₄×C₁₃	—	2	2	no	—
227	C₄×C₁₃	—	2	4	no	—
228	C₄×C₁₃	—	4	2	no	—
229	C₄×C₁₃	—	4	4	no	—
230	C₄×C₁₃	—	8	2	no	—
231	C₄×C₁₃	—	8	2	no	—
232	C₄×C₁₃	—	8	2	no	—
233	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
234	C₄×C₁₃	#544	1	1	yes	characteristic
235	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
236	C₄×C₁₃	#554	1	1	yes	characteristic
237	C₂²×Q₈	—	2	2	no	—
238	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
239	C₂²×C₈	—	2	2	no	—
240	C₂²×C₈	—	2	2	no	—
241	C₂²×C₈	Q₈×C₁₃	1	4	yes	complemented
242	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
243	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
244	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
245	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
246	C₄⋊Q₈	—	2	4	no	—
247	C₄⋊Q₈	—	4	2	no	—
248	#117	—	2	4	no	—
249	#117	—	4	2	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
254	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
255	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
256	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
257	C₂×C₂²⋊C₄	—	2	2	no	—
258	C₂×C₂²⋊C₄	—	2	2	no	—
259	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
260	C₂×C₄²	—	2	2	no	—
261	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
262	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
263	#107	—	2	4	no	—
264	#107	—	4	2	no	—
265	#106	—	2	2	no	—
266	#106	—	2	2	no	—
267	#106	—	2	2	no	—
268	#106	—	2	4	no	—
269	#106	D₄×C₁₃	1	4	yes	—
270	C₂²⋊C₈	Q₈×C₁₃	1	4	yes	complemented
271	C₄×C₈	—	2	2	no	—
272	C₄×C₈	—	2	2	no	—
273	#95	—	2	2	no	—
274	#95	—	2	2	no	—
275	#95	—	2	2	no	—
276	#95	—	2	2	no	—
277	#95	—	2	2	no	—
278	#95	D₄×C₁₃	1	2	yes	—
279	C₂×C₁₃	—	4	2	no	—
280	C₂×C₁₃	#2440	1	1	yes	characteristic
281	C₂×C₁₃	#3160	1	1	yes	characteristic
282	C₂×C₁₃	#3163	1	1	yes	characteristic
283	C₂×C₁₃	#3282	1	2	yes	—
284	C₂×C₁₃	#3340	1	2	yes	—
285	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
286	C₂×Q₈	—	4	4	no	—
287	C₂×Q₈	—	4	4	no	—
288	C₂×Q₈	—	8	2	no	—
289	C₂²×C₄	—	2	1	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
298	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
299	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
300	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
301	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
302	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	2	8	no	—
310	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
311	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
312	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
313	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
314	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
315	C₂×C₈	C₁₃×#41	1	2	yes	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	4	4	no	—
324	C₄⋊C₄	—	4	4	no	—
325	C₄⋊C₄	—	8	2	no	—
326	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
327	C₂²⋊C₄	—	2	4	no	—
328	C₂²⋊C₄	—	4	4	no	—
329	C₂²⋊C₄	—	8	2	no	—
330	C₄²	—	2	1	no	—
331	C₄²	—	2	1	no	—
332	C₄²	—	2	1	no	—
333	C₄²	—	2	1	no	—
334	C₄²	—	4	4	no	—
335	C₁₃	#26061	1	1	yes	characteristic, direct product factor, Sylow
336	C₂³	—	2	1	no	—
337	C₂³	—	2	1	no	—
338	C₂³	—	2	2	no	—
339	C₂³	—	2	2	no	—
340	C₂³	C₁₃×C₄⋊Q₈	1	2	yes	—
341	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
342	Q₈	—	8	8	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	C₁₃×C₄⋊Q₈	1	2	yes	—
367	C₂×C₄	C₁₃×#135	1	4	yes	—
368	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
369	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
370	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
371	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
372	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
373	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
374	C₈	—	2	2	no	—
375	C₈	—	2	2	no	—
376	C₈	—	2	2	no	—
377	C₈	C₁₃×C₂²⋊Q₈	1	4	yes	—
378	C₂²	—	2	2	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	4	2	no	—
382	C₂²	—	4	2	no	—
383	C₂²	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
384	C₂²	D₄²×C₁₃	1	1	yes	characteristic
385	C₂²	C₁₃×#547	1	1	yes	characteristic
386	C₂²	C₂×C₁₃×#135	1	2	yes	—
387	C₂²	C₁₃×#577	1	2	yes	—
388	C₄	—	2	4	no	—
389	C₄	—	2	2	no	—
390	C₄	—	4	4	no	—
391	C₄	—	4	2	no	—
392	C₄	—	8	2	no	—
393	C₄	—	8	2	no	—
394	C₄	—	8	2	no	—
395	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
396	C₄	C₁₃×#544	1	1	yes	characteristic
397	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
398	C₄	C₁₃×#554	1	1	yes	characteristic
399	C₂	—	4	2	no	—
400	C₂	C₁₃×#2440	1	1	yes	characteristic
401	C₂	C₁₃×#3160	1	1	yes	characteristic
402	C₂	C₁₃×#3163	1	1	yes	characteristic
403	C₂	C₁₃×#3282	1	2	yes	—
404	C₂	C₁₃×#3340	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂⁴×C₁₃	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄×C₁₃×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#498	C₂	semidirect
4. C₁₃×#2085	C₂	semidirect
5. C₁₃×#2057	C₂	semidirect
6. C₁₃×#1941	C₂	semidirect
7. C₁₃×#1941	C₂	semidirect
9. C₁₃×#1846	C₂	semidirect
45. C₂²×C₈×C₁₃	Q₈	semidirect
74. C₁₃×C₂²⋊C₈	Q₈	semidirect
83. #26061	C₁₃	direct (N × H)
134. C₂×#498	C₂×C₁₃	semidirect
137. #2085	C₂×C₁₃	semidirect
138. #2057	C₂×C₁₃	semidirect
139. #1941	C₂×C₁₃	semidirect
140. #1941	C₂×C₁₃	semidirect
142. #1846	C₂×C₁₃	semidirect
241. C₂²×C₈	Q₈×C₁₃	semidirect
270. C₂²⋊C₈	Q₈×C₁₃	semidirect
335. C₁₃	#26061	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#498	2
C₂×C₁₃×#427	2
C₁₃×#2439	2
C₁₃×#2085	2
C₁₃×#2057	2
C₁₃×#1941	2
C₁₃×#1854	2
C₁₃×#1846	2
C₁₃×#1807	2
C₈×C₁₃×C₂²⋊C₄	2
#26061	13

Subgroups — C13×#26061 #15712400

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26061 #15712400