Subgroups — C₁₃×#26060 #15712399

Order 3328.

894 conjugacy classes of subgroups.

The subgroup lattice has 418 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	C₂²×C₁₃×#106	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2440	C₂	1	2	yes	maximal
4	C₁₃×#2084	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2058	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×#1853	C₂	1	2	yes	maximal
9	C₁₃×#1844	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×C₂²⋊Q₈	—	2	2	no	—
15	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
16	C₁₃×#498	—	2	4	no	—
17	C₂×C₁₃×#106	—	2	4	no	—
18	C₂×C₁₃×#106	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	2	yes	—
24	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₁₃×#398	—	2	2	no	—
29	C₁₃×#395	—	2	2	no	—
30	C₁₃×#389	C₂²	1	2	yes	—
31	C₁₃×#389	C₂²	1	2	yes	—
32	C₁₃×#385	—	2	2	no	—
33	C₁₃×#384	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	—	2	2	no	—
43	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₃	—	2	2	no	—
45	C₂²×C₈×C₁₃	—	2	2	no	—
46	C₂²×C₈×C₁₃	Q₈	1	4	yes	complemented
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	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₁₃×C₄⋊Q₈	—	2	4	no	—
52	C₁₃×C₄⋊Q₈	—	4	2	no	—
53	C₁₃×C₂²⋊Q₈	—	4	8	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
61	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
66	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
67	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
68	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
70	C₁₃×#106	—	2	2	no	—
71	C₁₃×#106	—	2	2	no	—
72	C₁₃×#106	—	2	2	no	—
73	C₁₃×#106	—	2	4	no	—
74	C₁₃×#106	—	2	4	no	—
75	C₁₃×#106	—	4	2	no	—
76	C₁₃×#106	D₄	1	4	yes	—
77	C₁₃×C₂²⋊C₈	Q₈	1	4	yes	complemented
78	C₄×C₈×C₁₃	—	2	2	no	—
79	C₄×C₈×C₁₃	—	2	2	no	—
80	C₁₃×#95	—	2	2	no	—
81	C₁₃×#95	—	2	2	no	—
82	C₁₃×#95	—	2	2	no	—
83	C₁₃×#95	D₄	1	2	yes	—
84	#26060	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
85	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
86	C₂×Q₈×C₁₃	—	4	4	no	—
87	C₂×Q₈×C₁₃	—	4	4	no	—
88	C₂×Q₈×C₁₃	—	8	2	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	1	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	—	2	2	no	—
97	C₂²×C₄×C₁₃	—	4	4	no	—
98	C₂²×C₄×C₁₃	—	4	4	no	—
99	C₂²×C₄×C₁₃	—	8	2	no	—
100	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
104	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
105	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
106	C₂×C₈×C₁₃	—	2	1	no	—
107	C₂×C₈×C₁₃	—	2	1	no	—
108	C₂×C₈×C₁₃	—	2	1	no	—
109	C₂×C₈×C₁₃	—	2	1	no	—
110	C₂×C₈×C₁₃	—	2	1	no	—
111	C₂×C₈×C₁₃	—	2	1	no	—
112	C₂×C₈×C₁₃	—	2	8	no	—
113	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
114	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
115	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
116	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
117	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
118	C₂×C₈×C₁₃	#41	1	2	yes	—
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	—	2	2	no	—
123	C₁₃×C₄⋊C₄	—	2	2	no	—
124	C₁₃×C₄⋊C₄	—	2	2	no	—
125	C₁₃×C₄⋊C₄	—	2	2	no	—
126	C₁₃×C₄⋊C₄	—	4	4	no	—
127	C₁₃×C₄⋊C₄	—	4	4	no	—
128	C₁₃×C₄⋊C₄	—	4	4	no	—
129	C₁₃×C₄⋊C₄	—	4	4	no	—
130	C₁₃×C₄⋊C₄	—	4	4	no	—
131	C₁₃×C₄⋊C₄	—	8	2	no	—
132	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
133	C₁₃×C₂²⋊C₄	—	4	4	no	—
134	C₁₃×C₂²⋊C₄	SD₁₆	1	8	yes	—
135	C₄²×C₁₃	—	2	1	no	—
136	C₄²×C₁₃	—	2	1	no	—
137	C₄²×C₁₃	—	2	1	no	—
138	C₄²×C₁₃	—	2	1	no	—
139	C₂×#498	C₂×C₁₃	1	1	yes	characteristic, complemented
140	C₂²×#106	C₂×C₁₃	1	1	yes	characteristic
141	#2440	C₂×C₁₃	1	2	yes	—
142	#2084	C₂×C₁₃	1	2	yes	complemented
143	#2058	C₂×C₁₃	1	2	yes	complemented
144	#1941	C₂×C₁₃	1	1	yes	characteristic, complemented
145	#1941	C₂×C₁₃	1	1	yes	characteristic, complemented
146	#1853	C₂×C₁₃	1	2	yes	—
147	#1844	C₂×C₁₃	1	1	yes	characteristic, complemented
148	#1807	C₂×C₁₃	1	1	yes	characteristic
149	C₈×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic
150	C₂³×C₁₃	—	2	1	no	—
151	C₂³×C₁₃	—	2	1	no	—
152	C₂³×C₁₃	—	2	2	no	—
153	C₂³×C₁₃	C₄⋊Q₈	1	2	yes	—
154	C₂³×C₁₃	C₂×SD₁₆	1	4	yes	—
155	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
156	Q₈×C₁₃	—	8	8	no	—
157	C₂×C₄×C₁₃	—	2	2	no	—
158	C₂×C₄×C₁₃	—	2	1	no	—
159	C₂×C₄×C₁₃	—	2	2	no	—
160	C₂×C₄×C₁₃	—	2	1	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	—	2	2	no	—
165	C₂×C₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	—	2	2	no	—
167	C₂×C₄×C₁₃	—	2	4	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	—	4	2	no	—
176	C₂×C₄×C₁₃	—	4	2	no	—
177	C₂×C₄×C₁₃	—	4	2	no	—
178	C₂×C₄×C₁₃	—	4	2	no	—
179	C₂×C₄×C₁₃	—	8	8	no	—
180	C₂×C₄×C₁₃	C₄⋊Q₈	1	2	yes	—
181	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	—
182	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	—
183	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
188	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
189	C₈×C₁₃	—	2	2	no	—
190	C₈×C₁₃	—	2	2	no	—
191	C₈×C₁₃	—	2	2	no	—
192	C₈×C₁₃	C₂²⋊Q₈	1	4	yes	complemented
193	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
194	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
195	C₂×C₂²⋊Q₈	—	2	2	no	—
196	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
197	#498	—	2	4	no	—
198	C₂×#106	—	2	4	no	—
199	C₂×#106	C₂²×C₁₃	1	2	yes	—
200	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
201	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
202	C₂×#106	C₂²×C₁₃	1	2	yes	—
203	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
204	C₂×#106	C₂²×C₁₃	1	2	yes	—
205	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
206	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
207	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
208	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
209	#398	—	2	2	no	—
210	#395	—	2	2	no	—
211	#389	C₂²×C₁₃	1	2	yes	—
212	#389	C₂²×C₁₃	1	2	yes	—
213	#385	—	2	2	no	—
214	#384	C₂²×C₁₃	1	2	yes	—
215	#380	C₂²×C₁₃	1	2	yes	—
216	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
217	#340	C₂²×C₁₃	1	2	yes	—
218	#340	C₂²×C₁₃	1	2	yes	—
219	#340	C₂²×C₁₃	1	2	yes	—
220	#336	C₂²×C₁₃	1	1	yes	characteristic
221	#336	C₂²×C₁₃	1	1	yes	characteristic
222	C₂²×C₁₃	—	2	4	no	—
223	C₂²×C₁₃	—	2	2	no	—
224	C₂²×C₁₃	—	2	2	no	—
225	C₂²×C₁₃	—	2	4	no	—
226	C₂²×C₁₃	#498	1	4	yes	complemented
227	C₂²×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
228	C₂²×C₁₃	D₄²	1	1	yes	characteristic
229	C₂²×C₁₃	#547	1	1	yes	characteristic
230	C₂²×C₁₃	C₂²×SD₁₆	1	2	yes	—
231	C₂²×C₁₃	#577	1	2	yes	—
232	C₄×C₁₃	—	2	4	no	—
233	C₄×C₁₃	—	2	2	no	—
234	C₄×C₁₃	—	2	4	no	—
235	C₄×C₁₃	—	4	4	no	—
236	C₄×C₁₃	—	8	2	no	—
237	C₄×C₁₃	—	8	2	no	—
238	C₄×C₁₃	—	8	2	no	—
239	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
240	C₄×C₁₃	#544	1	1	yes	characteristic
241	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
242	C₄×C₁₃	#554	1	1	yes	characteristic
243	C₂²×Q₈	—	2	2	no	—
244	C₂³×C₄	—	2	2	no	—
245	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
246	C₂²×C₈	—	2	2	no	—
247	C₂²×C₈	—	2	2	no	—
248	C₂²×C₈	Q₈×C₁₃	1	4	yes	complemented
249	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
250	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
251	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
252	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
253	C₄⋊Q₈	—	2	4	no	—
254	C₄⋊Q₈	—	4	2	no	—
255	C₂²⋊Q₈	—	4	8	no	—
256	C₂×C₄⋊C₄	—	2	4	no	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	—	4	2	no	—
264	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
265	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
266	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
267	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
270	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
271	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
272	#106	—	2	2	no	—
273	#106	—	2	2	no	—
274	#106	—	2	2	no	—
275	#106	—	2	4	no	—
276	#106	—	2	4	no	—
277	#106	—	4	2	no	—
278	#106	D₄×C₁₃	1	4	yes	—
279	C₂²⋊C₈	Q₈×C₁₃	1	4	yes	complemented
280	C₄×C₈	—	2	2	no	—
281	C₄×C₈	—	2	2	no	—
282	#95	—	2	2	no	—
283	#95	—	2	2	no	—
284	#95	—	2	2	no	—
285	#95	D₄×C₁₃	1	2	yes	—
286	C₂×C₁₃	—	2	4	no	—
287	C₂×C₁₃	#2440	1	1	yes	characteristic
288	C₂×C₁₃	C₂×#498	1	1	yes	characteristic
289	C₂×C₁₃	#3163	1	1	yes	characteristic
290	C₂×C₁₃	D₄×SD₁₆	1	2	yes	—
291	C₂×C₁₃	#3335	1	2	yes	—
292	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
293	C₂×Q₈	—	4	4	no	—
294	C₂×Q₈	—	4	4	no	—
295	C₂×Q₈	—	8	2	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	4	4	no	—
305	C₂²×C₄	—	4	4	no	—
306	C₂²×C₄	—	8	2	no	—
307	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
308	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
309	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
310	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
311	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
312	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	8	no	—
320	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
321	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
322	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
323	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
324	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
325	C₂×C₈	C₁₃×#41	1	2	yes	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	4	4	no	—
334	C₄⋊C₄	—	4	4	no	—
335	C₄⋊C₄	—	4	4	no	—
336	C₄⋊C₄	—	4	4	no	—
337	C₄⋊C₄	—	4	4	no	—
338	C₄⋊C₄	—	8	2	no	—
339	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
340	C₂²⋊C₄	—	4	4	no	—
341	C₂²⋊C₄	C₁₃×SD₁₆	1	8	yes	—
342	C₄²	—	2	1	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	2	1	no	—
346	C₁₃	#26060	1	1	yes	characteristic, direct product factor, Sylow
347	C₂³	—	2	1	no	—
348	C₂³	—	2	1	no	—
349	C₂³	—	2	2	no	—
350	C₂³	C₁₃×C₄⋊Q₈	1	2	yes	—
351	C₂³	C₂×C₁₃×SD₁₆	1	4	yes	—
352	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
353	Q₈	—	8	8	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	8	8	no	—
377	C₂×C₄	C₁₃×C₄⋊Q₈	1	2	yes	—
378	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	—
379	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	—
380	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
381	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
382	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
383	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
384	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
385	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
386	C₈	—	2	2	no	—
387	C₈	—	2	2	no	—
388	C₈	—	2	2	no	—
389	C₈	C₁₃×C₂²⋊Q₈	1	4	yes	complemented
390	C₂²	—	2	4	no	—
391	C₂²	—	2	4	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	2	2	no	—
394	C₂²	C₁₃×#498	1	4	yes	complemented
395	C₂²	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
396	C₂²	D₄²×C₁₃	1	1	yes	characteristic
397	C₂²	C₁₃×#547	1	1	yes	characteristic
398	C₂²	C₂²×C₁₃×SD₁₆	1	2	yes	—
399	C₂²	C₁₃×#577	1	2	yes	—
400	C₄	—	2	4	no	—
401	C₄	—	2	4	no	—
402	C₄	—	2	2	no	—
403	C₄	—	4	4	no	—
404	C₄	—	8	2	no	—
405	C₄	—	8	2	no	—
406	C₄	—	8	2	no	—
407	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
408	C₄	C₁₃×#544	1	1	yes	characteristic
409	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
410	C₄	C₁₃×#554	1	1	yes	characteristic
411	C₂	—	2	4	no	—
412	C₂	C₁₃×#2440	1	1	yes	characteristic
413	C₂	C₂×C₁₃×#498	1	1	yes	characteristic
414	C₂	C₁₃×#3163	1	1	yes	characteristic
415	C₂	D₄×C₁₃×SD₁₆	1	2	yes	—
416	C₂	C₁₃×#3335	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×#2084	C₂	semidirect
5. C₁₃×#2058	C₂	semidirect
6. C₁₃×#1941	C₂	semidirect
7. C₁₃×#1941	C₂	semidirect
9. C₁₃×#1844	C₂	semidirect
46. C₂²×C₈×C₁₃	Q₈	semidirect
77. C₁₃×C₂²⋊C₈	Q₈	semidirect
84. #26060	C₁₃	direct (N × H)
139. C₂×#498	C₂×C₁₃	semidirect
142. #2084	C₂×C₁₃	semidirect
143. #2058	C₂×C₁₃	semidirect
144. #1941	C₂×C₁₃	semidirect
145. #1941	C₂×C₁₃	semidirect
147. #1844	C₂×C₁₃	semidirect
192. C₈×C₁₃	C₂²⋊Q₈	semidirect
226. C₂²×C₁₃	#498	semidirect
248. C₂²×C₈	Q₈×C₁₃	semidirect
279. C₂²⋊C₈	Q₈×C₁₃	semidirect
346. C₁₃	#26060	direct (N × H)
389. C₈	C₁₃×C₂²⋊Q₈	semidirect
394. C₂²	C₁₃×#498	semidirect

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
C₂²×C₁₃×#106	2
C₁₃×#2440	2
C₁₃×#2084	2
C₁₃×#2058	2
C₁₃×#1941	2
C₁₃×#1853	2
C₁₃×#1844	2
C₁₃×#1807	2
C₈×C₁₃×C₂²⋊C₄	2
#26060	13

Subgroups — C13×#26060 #15712399

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26060 #15712399