Subgroups — C₁₃×#26042 #15712381

Order 3328.

810 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	C₂×C₁₃×#475	C₂	1	2	yes	maximal
2	C₁₃×#2551	C₂	1	1	yes	maximal, characteristic
3	Q₈×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2088	C₂	1	2	yes	maximal
5	C₁₃×#2058	C₂	1	2	yes	maximal
6	C₁₃×#1948	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1939	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1865	C₂	1	2	yes	maximal
9	C₁₃×#1844	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1803	C₂	1	1	yes	maximal, characteristic
11	C₄×C₁₃×#103	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₁₃×#475	—	2	8	no	—
17	C₂×C₁₃×#106	C₂²	1	2	yes	—
18	C₂×C₁₃×#106	C₂²	1	2	yes	—
19	C₂×C₁₃×#106	C₂²	1	2	yes	—
20	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#103	C₂²	1	2	yes	—
23	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₁₃×#395	—	2	2	no	—
27	C₁₃×#389	—	2	1	no	—
28	C₁₃×#389	—	2	2	no	—
29	C₁₃×#389	C₂²	1	2	yes	—
30	C₁₃×#389	C₂²	1	2	yes	—
31	C₁₃×#384	—	2	1	no	—
32	C₁₃×#384	C₂²	1	1	yes	characteristic
33	C₁₃×#384	C₂²	1	1	yes	characteristic
34	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
35	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₁₃×#340	C₂²	1	1	yes	characteristic
38	C₁₃×#340	C₂²	1	1	yes	characteristic
39	C₁₃×#340	C₂²	1	2	yes	—
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#336	C₂²	1	2	yes	—
42	C₂²×Q₈×C₁₃	—	2	2	no	—
43	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
47	C₁₃×C₄⋊Q₈	—	2	4	no	—
48	C₁₃×C₄⋊Q₈	—	4	2	no	—
49	C₁₃×C₄⋊Q₈	—	4	4	no	—
50	C₄×Q₈×C₁₃	—	2	2	no	—
51	C₄×Q₈×C₁₃	—	2	4	no	—
52	C₄×Q₈×C₁₃	—	4	2	no	—
53	C₄×Q₈×C₁₃	Q₈	1	4	yes	complemented
54	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	1	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	—	2	1	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
63	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
64	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₁₃	—	2	1	no	—
71	C₂×C₄²×C₁₃	—	2	2	no	—
72	C₂×C₄²×C₁₃	—	2	1	no	—
73	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
74	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
75	C₁₃×#106	—	2	4	no	—
76	C₁₃×#106	—	2	4	no	—
77	C₁₃×#106	—	4	2	no	—
78	C₁₃×C₄⋊C₈	—	2	4	no	—
79	C₁₃×C₄⋊C₈	—	2	2	no	—
80	C₁₃×#103	—	2	4	no	—
81	C₁₃×#103	D₄	1	4	yes	—
82	C₁₃×#103	Q₈	1	4	yes	complemented
83	C₄×C₈×C₁₃	—	2	2	no	—
84	C₁₃×#95	—	2	2	no	—
85	C₁₃×#95	—	2	1	no	—
86	C₁₃×#95	—	2	2	no	—
87	C₁₃×#95	D₄	1	2	yes	—
88	#26042	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
89	C₂×Q₈×C₁₃	—	2	1	no	—
90	C₂×Q₈×C₁₃	—	2	1	no	—
91	C₂×Q₈×C₁₃	—	2	1	no	—
92	C₂×Q₈×C₁₃	—	4	4	no	—
93	C₂×Q₈×C₁₃	—	4	4	no	—
94	C₂×Q₈×C₁₃	—	8	2	no	—
95	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
96	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
97	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
98	C₂²×C₄×C₁₃	—	2	1	no	—
99	C₂²×C₄×C₁₃	—	2	1	no	—
100	C₂²×C₄×C₁₃	—	2	1	no	—
101	C₂²×C₄×C₁₃	—	2	1	no	—
102	C₂²×C₄×C₁₃	—	2	2	no	—
103	C₂²×C₄×C₁₃	—	2	2	no	—
104	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	1	no	—
113	C₂×C₈×C₁₃	—	2	2	no	—
114	C₂×C₈×C₁₃	—	2	2	no	—
115	C₂×C₈×C₁₃	—	2	2	no	—
116	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
117	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
118	C₁₃×C₄⋊C₄	—	2	4	no	—
119	C₁₃×C₄⋊C₄	—	2	2	no	—
120	C₁₃×C₄⋊C₄	—	2	1	no	—
121	C₁₃×C₄⋊C₄	—	2	1	no	—
122	C₁₃×C₄⋊C₄	—	2	1	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	—	2	2	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	2	no	—
131	C₁₃×C₄⋊C₄	—	4	2	no	—
132	C₁₃×C₄⋊C₄	—	8	1	no	—
133	C₁₃×C₄⋊C₄	—	8	1	no	—
134	C₁₃×C₄⋊C₄	—	8	2	no	—
135	C₁₃×C₄⋊C₄	SD₁₆	1	4	yes	—
136	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
137	C₁₃×C₄⋊C₄	C₂×Q₈	1	2	yes	—
138	C₁₃×C₄⋊C₄	C₂×Q₈	1	2	yes	—
139	C₄²×C₁₃	—	2	4	no	—
140	C₄²×C₁₃	—	2	2	no	—
141	C₄²×C₁₃	—	2	2	no	—
142	C₄²×C₁₃	—	4	4	no	—
143	C₄²×C₁₃	—	4	2	no	—
144	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
145	C₄²×C₁₃	#41	1	2	yes	—
146	C₂×#475	C₂×C₁₃	1	2	yes	—
147	#2551	C₂×C₁₃	1	1	yes	characteristic
148	Q₈×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
149	#2088	C₂×C₁₃	1	2	yes	—
150	#2058	C₂×C₁₃	1	2	yes	—
151	#1948	C₂×C₁₃	1	1	yes	characteristic
152	#1939	C₂×C₁₃	1	1	yes	characteristic
153	#1865	C₂×C₁₃	1	2	yes	—
154	#1844	C₂×C₁₃	1	1	yes	characteristic
155	#1803	C₂×C₁₃	1	1	yes	characteristic
156	C₄×#103	C₂×C₁₃	1	1	yes	characteristic
157	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
158	Q₈×C₁₃	—	2	2	no	—
159	Q₈×C₁₃	—	2	2	no	—
160	Q₈×C₁₃	—	2	2	no	—
161	Q₈×C₁₃	—	8	8	no	—
162	Q₈×C₁₃	C₄⋊Q₈	1	4	yes	complemented
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	1	no	—
168	C₂×C₄×C₁₃	—	2	1	no	—
169	C₂×C₄×C₁₃	—	2	2	no	—
170	C₂×C₄×C₁₃	—	2	2	no	—
171	C₂×C₄×C₁₃	—	2	2	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	2	2	no	—
174	C₂×C₄×C₁₃	—	2	2	no	—
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	4	1	no	—
177	C₂×C₄×C₁₃	—	4	1	no	—
178	C₂×C₄×C₁₃	—	4	1	no	—
179	C₂×C₄×C₁₃	—	4	1	no	—
180	C₂×C₄×C₁₃	—	4	1	no	—
181	C₂×C₄×C₁₃	—	4	1	no	—
182	C₂×C₄×C₁₃	—	4	2	no	—
183	C₂×C₄×C₁₃	—	4	2	no	—
184	C₂×C₄×C₁₃	—	4	2	no	—
185	C₂×C₄×C₁₃	—	4	2	no	—
186	C₂×C₄×C₁₃	—	4	2	no	—
187	C₂×C₄×C₁₃	—	4	2	no	—
188	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
189	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
190	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	—
191	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
192	C₂×C₄×C₁₃	#137	1	2	yes	—
193	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
195	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
196	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
198	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
199	C₈×C₁₃	—	2	2	no	—
200	C₈×C₁₃	—	2	2	no	—
201	C₈×C₁₃	—	4	2	no	—
202	C₂×C₄⋊Q₈	—	2	1	no	—
203	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
204	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
205	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
206	#475	—	2	8	no	—
207	C₂×#106	C₂²×C₁₃	1	2	yes	—
208	C₂×#106	C₂²×C₁₃	1	2	yes	—
209	C₂×#106	C₂²×C₁₃	1	2	yes	—
210	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
211	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
212	C₂×#103	C₂²×C₁₃	1	2	yes	—
213	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
214	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
215	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
216	#395	—	2	2	no	—
217	#389	—	2	1	no	—
218	#389	—	2	2	no	—
219	#389	C₂²×C₁₃	1	2	yes	—
220	#389	C₂²×C₁₃	1	2	yes	—
221	#384	—	2	1	no	—
222	#384	C₂²×C₁₃	1	1	yes	characteristic
223	#384	C₂²×C₁₃	1	1	yes	characteristic
224	C₄×C₄⋊C₄	—	2	1	no	—
225	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
226	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
227	#340	C₂²×C₁₃	1	1	yes	characteristic
228	#340	C₂²×C₁₃	1	2	yes	—
229	#340	C₂²×C₁₃	1	1	yes	characteristic
230	#340	C₂²×C₁₃	1	2	yes	—
231	#336	C₂²×C₁₃	1	2	yes	—
232	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
233	C₂²×C₁₃	D₄²	1	1	yes	characteristic
234	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
235	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
236	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
237	C₂²×C₁₃	#577	1	1	yes	characteristic
238	C₂²×C₁₃	#577	1	1	yes	characteristic
239	C₄×C₁₃	—	2	2	no	—
240	C₄×C₁₃	—	2	4	no	—
241	C₄×C₁₃	—	2	4	no	—
242	C₄×C₁₃	—	4	2	no	—
243	C₄×C₁₃	—	4	2	no	—
244	C₄×C₁₃	—	4	2	no	—
245	C₄×C₁₃	—	4	2	no	—
246	C₄×C₁₃	—	8	2	no	—
247	C₄×C₁₃	—	8	2	no	—
248	C₄×C₁₃	#475	1	4	yes	complemented
249	C₄×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
250	C₄×C₁₃	#544	1	1	yes	characteristic
251	C₄×C₁₃	#547	1	1	yes	characteristic
252	C₄×C₁₃	#554	1	1	yes	characteristic
253	C₂²×Q₈	—	2	2	no	—
254	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
255	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
256	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
257	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
258	C₄⋊Q₈	—	2	4	no	—
259	C₄⋊Q₈	—	4	2	no	—
260	C₄⋊Q₈	—	4	4	no	—
261	C₄×Q₈	—	2	2	no	—
262	C₄×Q₈	—	2	4	no	—
263	C₄×Q₈	—	4	2	no	—
264	C₄×Q₈	Q₈×C₁₃	1	4	yes	complemented
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
275	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
276	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
277	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
278	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
279	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
280	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
281	C₂×C₄²	—	2	1	no	—
282	C₂×C₄²	—	2	2	no	—
283	C₂×C₄²	—	2	1	no	—
284	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
285	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
286	#106	—	2	4	no	—
287	#106	—	2	4	no	—
288	#106	—	4	2	no	—
289	C₄⋊C₈	—	2	4	no	—
290	C₄⋊C₈	—	2	2	no	—
291	#103	—	2	4	no	—
292	#103	D₄×C₁₃	1	4	yes	—
293	#103	Q₈×C₁₃	1	4	yes	complemented
294	C₄×C₈	—	2	2	no	—
295	#95	—	2	2	no	—
296	#95	—	2	1	no	—
297	#95	—	2	2	no	—
298	#95	D₄×C₁₃	1	2	yes	—
299	C₂×C₁₃	#2440	1	1	yes	characteristic
300	C₂×C₁₃	C₂×#475	1	1	yes	characteristic
301	C₂×C₁₃	#3084	1	1	yes	characteristic
302	C₂×C₁₃	#3278	1	1	yes	characteristic
303	C₂×C₁₃	D₄×SD₁₆	1	1	yes	characteristic
304	C₂×C₁₃	Q₈×SD₁₆	1	1	yes	characteristic
305	C₂×C₁₃	#3387	1	1	yes	characteristic
306	C₂×Q₈	—	2	1	no	—
307	C₂×Q₈	—	2	1	no	—
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	—	4	4	no	—
310	C₂×Q₈	—	4	4	no	—
311	C₂×Q₈	—	8	2	no	—
312	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
313	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
314	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
322	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
323	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
324	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
325	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
334	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
335	C₄⋊C₄	—	2	4	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	4	4	no	—
345	C₄⋊C₄	—	4	4	no	—
346	C₄⋊C₄	—	4	4	no	—
347	C₄⋊C₄	—	4	2	no	—
348	C₄⋊C₄	—	4	2	no	—
349	C₄⋊C₄	—	8	1	no	—
350	C₄⋊C₄	—	8	1	no	—
351	C₄⋊C₄	—	8	2	no	—
352	C₄⋊C₄	C₁₃×SD₁₆	1	4	yes	—
353	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
354	C₄⋊C₄	C₂×Q₈×C₁₃	1	2	yes	—
355	C₄⋊C₄	C₂×Q₈×C₁₃	1	2	yes	—
356	C₄²	—	2	4	no	—
357	C₄²	—	2	2	no	—
358	C₄²	—	2	2	no	—
359	C₄²	—	4	4	no	—
360	C₄²	—	4	2	no	—
361	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
362	C₄²	C₁₃×#41	1	2	yes	—
363	C₁₃	#26042	1	1	yes	characteristic, direct product factor, Sylow
364	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
365	Q₈	—	2	2	no	—
366	Q₈	—	2	2	no	—
367	Q₈	—	2	2	no	—
368	Q₈	—	8	8	no	—
369	Q₈	C₁₃×C₄⋊Q₈	1	4	yes	complemented
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
396	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
397	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	—
398	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
399	C₂×C₄	C₁₃×#137	1	2	yes	—
400	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
401	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
402	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
403	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
404	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
405	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
406	C₈	—	2	2	no	—
407	C₈	—	2	2	no	—
408	C₈	—	4	2	no	—
409	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
410	C₂²	D₄²×C₁₃	1	1	yes	characteristic
411	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
412	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
413	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
414	C₂²	C₁₃×#577	1	1	yes	characteristic
415	C₂²	C₁₃×#577	1	1	yes	characteristic
416	C₄	—	2	4	no	—
417	C₄	—	2	2	no	—
418	C₄	—	2	4	no	—
419	C₄	—	4	2	no	—
420	C₄	—	4	2	no	—
421	C₄	—	4	2	no	—
422	C₄	—	4	2	no	—
423	C₄	—	8	2	no	—
424	C₄	—	8	2	no	—
425	C₄	C₁₃×#475	1	4	yes	complemented
426	C₄	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
427	C₄	C₁₃×#544	1	1	yes	characteristic
428	C₄	C₁₃×#547	1	1	yes	characteristic
429	C₄	C₁₃×#554	1	1	yes	characteristic
430	C₂	C₁₃×#2440	1	1	yes	characteristic
431	C₂	C₂×C₁₃×#475	1	1	yes	characteristic
432	C₂	C₁₃×#3084	1	1	yes	characteristic
433	C₂	C₁₃×#3278	1	1	yes	characteristic
434	C₂	D₄×C₁₃×SD₁₆	1	1	yes	characteristic
435	C₂	Q₈×C₁₃×SD₁₆	1	1	yes	characteristic
436	C₂	C₁₃×#3387	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
53. C₄×Q₈×C₁₃	Q₈	semidirect
82. C₁₃×#103	Q₈	semidirect
88. #26042	C₁₃	direct (N × H)
162. Q₈×C₁₃	C₄⋊Q₈	semidirect
248. C₄×C₁₃	#475	semidirect
264. C₄×Q₈	Q₈×C₁₃	semidirect
293. #103	Q₈×C₁₃	semidirect
363. C₁₃	#26042	direct (N × H)
369. Q₈	C₁₃×C₄⋊Q₈	semidirect
425. C₄	C₁₃×#475	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#475	2
C₁₃×#2551	2
Q₈×C₁₃×C₄⋊C₄	2
C₁₃×#2088	2
C₁₃×#2058	2
C₁₃×#1948	2
C₁₃×#1939	2
C₁₃×#1865	2
C₁₃×#1844	2
C₁₃×#1803	2
C₄×C₁₃×#103	2
#26042	13

Subgroups — C13×#26042 #15712381

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26042 #15712381