Subgroups — C₁₃×#29159 #15715498

Order 3328.

828 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2857	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2099	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2096	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2058	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2024	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1919	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1892	C₂	1	2	yes	maximal
9	C₁₃×#1865	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1807	C₂	1	2	yes	maximal
11	C₂×C₁₃×#336	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
15	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#106	C₂²	1	2	yes	—
19	C₂×C₁₃×#106	C₂²	1	2	yes	—
20	C₂×C₁₃×#103	C₂²	1	2	yes	—
21	C₂×C₁₃×#103	C₂²	1	2	yes	—
22	C₁₃×#391	—	2	1	no	—
23	C₁₃×#391	C₂²	1	1	yes	characteristic
24	C₁₃×#389	—	2	1	no	—
25	C₁₃×#389	C₂²	1	1	yes	characteristic
26	C₁₃×#389	C₂²	1	2	yes	—
27	C₁₃×#387	—	2	1	no	—
28	C₁₃×#385	—	2	1	no	—
29	C₁₃×#384	C₂²	1	1	yes	characteristic
30	C₁₃×#380	—	2	1	no	—
31	C₁₃×#380	C₂²	1	1	yes	characteristic
32	C₁₃×#380	C₂²	1	2	yes	—
33	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
34	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
36	C₁₃×#340	C₂²	1	2	yes	—
37	C₁₃×#340	C₂²	1	2	yes	—
38	C₁₃×#340	C₂²	1	2	yes	—
39	C₁₃×#340	C₂²	1	2	yes	—
40	C₁₃×#336	C₂²	1	1	yes	characteristic
41	C₁₃×#336	C₂²	1	1	yes	characteristic
42	C₁₃×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃	—	2	1	no	—
44	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₃	—	2	4	no	—
49	C₂²×C₈×C₁₃	—	2	4	no	—
50	C₂²×C₈×C₁₃	—	4	2	no	—
51	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
53	C₁₃×C₄⋊Q₈	—	4	2	no	—
54	C₁₃×C₂²⋊Q₈	—	2	2	no	—
55	C₁₃×C₂²⋊Q₈	—	4	4	no	—
56	C₁₃×C₂²⋊Q₈	Q₈	1	4	yes	complemented
57	C₄×Q₈×C₁₃	—	4	2	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
71	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
72	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
73	C₂×C₄²×C₁₃	—	2	1	no	—
74	C₂×C₄²×C₁₃	—	2	1	no	—
75	C₂×C₄²×C₁₃	—	4	2	no	—
76	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
80	C₁₃×#106	—	2	4	no	—
81	C₁₃×#106	—	4	2	no	—
82	C₁₃×#103	—	2	4	no	—
83	C₁₃×#103	—	4	2	no	—
84	C₁₃×#95	—	2	1	no	—
85	C₁₃×#95	—	2	1	no	—
86	C₁₃×#95	—	2	1	no	—
87	C₁₃×#95	—	2	1	no	—
88	C₁₃×#95	—	2	1	no	—
89	C₁₃×#95	—	2	2	no	—
90	C₁₃×#95	—	2	2	no	—
91	#29159	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
92	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
93	C₂×Q₈×C₁₃	—	2	1	no	—
94	C₂×Q₈×C₁₃	—	2	2	no	—
95	C₂×Q₈×C₁₃	—	2	2	no	—
96	C₂×Q₈×C₁₃	—	4	2	no	—
97	C₂×Q₈×C₁₃	—	4	2	no	—
98	C₂×Q₈×C₁₃	—	4	2	no	—
99	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
100	C₂²×C₄×C₁₃	—	2	2	no	—
101	C₂²×C₄×C₁₃	—	2	2	no	—
102	C₂²×C₄×C₁₃	—	2	2	no	—
103	C₂²×C₄×C₁₃	—	2	1	no	—
104	C₂²×C₄×C₁₃	—	2	1	no	—
105	C₂²×C₄×C₁₃	—	2	2	no	—
106	C₂²×C₄×C₁₃	—	2	1	no	—
107	C₂²×C₄×C₁₃	—	2	1	no	—
108	C₂²×C₄×C₁₃	—	2	2	no	—
109	C₂²×C₄×C₁₃	—	2	2	no	—
110	C₂²×C₄×C₁₃	—	4	1	no	—
111	C₂²×C₄×C₁₃	—	4	1	no	—
112	C₂²×C₄×C₁₃	—	4	1	no	—
113	C₂²×C₄×C₁₃	SD₁₆	1	4	yes	—
114	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
120	C₂²×C₄×C₁₃	#41	1	2	yes	—
121	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	—	2	2	no	—
125	C₂×C₈×C₁₃	—	2	2	no	—
126	C₂×C₈×C₁₃	—	2	2	no	—
127	C₂×C₈×C₁₃	—	4	8	no	—
128	C₂×C₈×C₁₃	#41	1	4	yes	—
129	C₁₃×C₄⋊C₄	—	2	4	no	—
130	C₁₃×C₄⋊C₄	—	2	1	no	—
131	C₁₃×C₄⋊C₄	—	2	2	no	—
132	C₁₃×C₄⋊C₄	—	2	2	no	—
133	C₁₃×C₄⋊C₄	—	2	2	no	—
134	C₁₃×C₄⋊C₄	—	2	2	no	—
135	C₁₃×C₄⋊C₄	—	2	2	no	—
136	C₁₃×C₄⋊C₄	—	2	2	no	—
137	C₁₃×C₄⋊C₄	—	4	2	no	—
138	C₁₃×C₄⋊C₄	—	4	2	no	—
139	C₁₃×C₄⋊C₄	—	4	2	no	—
140	C₁₃×C₄⋊C₄	—	4	4	no	—
141	C₁₃×C₄⋊C₄	—	4	2	no	—
142	C₁₃×C₄⋊C₄	—	4	2	no	—
143	C₁₃×C₄⋊C₄	C₂×Q₈	1	2	yes	—
144	C₁₃×C₂²⋊C₄	—	2	4	no	—
145	C₁₃×C₂²⋊C₄	—	4	4	no	—
146	C₁₃×C₂²⋊C₄	—	4	2	no	—
147	C₄²×C₁₃	—	2	2	no	—
148	C₄²×C₁₃	—	2	2	no	—
149	C₄²×C₁₃	—	4	1	no	—
150	C₄²×C₁₃	—	4	1	no	—
151	C₄²×C₁₃	—	4	2	no	—
152	C₄²×C₁₃	—	4	2	no	—
153	#2857	C₂×C₁₃	1	1	yes	characteristic
154	C₄×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic
155	#2099	C₂×C₁₃	1	1	yes	characteristic, complemented
156	#2096	C₂×C₁₃	1	1	yes	characteristic, complemented
157	#2058	C₂×C₁₃	1	1	yes	characteristic, complemented
158	#2024	C₂×C₁₃	1	1	yes	characteristic, complemented
159	#1919	C₂×C₁₃	1	2	yes	complemented
160	#1892	C₂×C₁₃	1	2	yes	—
161	#1865	C₂×C₁₃	1	2	yes	complemented
162	#1807	C₂×C₁₃	1	2	yes	—
163	C₂×#336	C₂×C₁₃	1	1	yes	characteristic
164	C₂³×C₁₃	—	2	1	no	—
165	C₂³×C₁₃	—	2	1	no	—
166	C₂³×C₁₃	—	2	1	no	—
167	C₂³×C₁₃	—	2	1	no	—
168	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
169	C₂³×C₁₃	C₂×SD₁₆	1	2	yes	—
170	C₂³×C₁₃	#137	1	2	yes	—
171	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
172	Q₈×C₁₃	—	2	4	no	—
173	Q₈×C₁₃	—	4	2	no	—
174	Q₈×C₁₃	—	8	4	no	—
175	C₂×C₄×C₁₃	—	2	1	no	—
176	C₂×C₄×C₁₃	—	2	1	no	—
177	C₂×C₄×C₁₃	—	2	1	no	—
178	C₂×C₄×C₁₃	—	2	1	no	—
179	C₂×C₄×C₁₃	—	2	1	no	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	2	1	no	—
183	C₂×C₄×C₁₃	—	2	4	no	—
184	C₂×C₄×C₁₃	—	2	4	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	2	no	—
187	C₂×C₄×C₁₃	—	2	1	no	—
188	C₂×C₄×C₁₃	—	2	1	no	—
189	C₂×C₄×C₁₃	—	2	1	no	—
190	C₂×C₄×C₁₃	—	4	4	no	—
191	C₂×C₄×C₁₃	—	4	4	no	—
192	C₂×C₄×C₁₃	—	4	1	no	—
193	C₂×C₄×C₁₃	—	4	1	no	—
194	C₂×C₄×C₁₃	—	4	1	no	—
195	C₂×C₄×C₁₃	—	4	1	no	—
196	C₂×C₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	—	4	1	no	—
198	C₂×C₄×C₁₃	—	4	1	no	—
199	C₂×C₄×C₁₃	—	4	2	no	—
200	C₂×C₄×C₁₃	—	4	2	no	—
201	C₂×C₄×C₁₃	—	4	2	no	—
202	C₂×C₄×C₁₃	—	4	2	no	—
203	C₂×C₄×C₁₃	—	4	1	no	—
204	C₂×C₄×C₁₃	—	4	1	no	—
205	C₂×C₄×C₁₃	—	4	1	no	—
206	C₂×C₄×C₁₃	—	4	1	no	—
207	C₂×C₄×C₁₃	—	4	2	no	—
208	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
209	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
210	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
211	C₂×C₄×C₁₃	#135	1	2	yes	—
212	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
213	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
214	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
215	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
216	C₈×C₁₃	—	2	4	no	—
217	C₈×C₁₃	—	4	2	no	—
218	C₂³×C₈	C₂²×C₁₃	1	2	yes	—
219	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
220	C₂×C₂²⋊Q₈	—	2	1	no	—
221	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
222	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
223	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
224	C₂×#106	C₂²×C₁₃	1	2	yes	—
225	C₂×#106	C₂²×C₁₃	1	2	yes	—
226	C₂×#103	C₂²×C₁₃	1	2	yes	—
227	C₂×#103	C₂²×C₁₃	1	2	yes	—
228	#391	—	2	1	no	—
229	#391	C₂²×C₁₃	1	1	yes	characteristic
230	#389	—	2	1	no	—
231	#389	C₂²×C₁₃	1	1	yes	characteristic
232	#389	C₂²×C₁₃	1	2	yes	—
233	#387	—	2	1	no	—
234	#385	—	2	1	no	—
235	#384	C₂²×C₁₃	1	1	yes	characteristic
236	#380	—	2	1	no	—
237	#380	C₂²×C₁₃	1	1	yes	characteristic
238	#380	C₂²×C₁₃	1	2	yes	—
239	C₄×C₄⋊C₄	—	2	1	no	—
240	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
241	C₄×C₂²⋊C₄	—	2	1	no	—
242	#340	C₂²×C₁₃	1	2	yes	—
243	#340	C₂²×C₁₃	1	2	yes	—
244	#340	C₂²×C₁₃	1	2	yes	—
245	#340	C₂²×C₁₃	1	2	yes	—
246	#336	C₂²×C₁₃	1	1	yes	characteristic
247	#336	C₂²×C₁₃	1	1	yes	characteristic
248	#336	C₂²×C₁₃	1	2	yes	—
249	C₂²×C₁₃	—	2	2	no	—
250	C₂²×C₁₃	—	2	2	no	—
251	C₂²×C₁₃	—	2	2	no	—
252	C₂²×C₁₃	—	2	2	no	—
253	C₂²×C₁₃	—	2	2	no	—
254	C₂²×C₁₃	—	2	2	no	—
255	C₂²×C₁₃	#475	1	4	yes	—
256	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
257	C₂²×C₁₃	#532	1	1	yes	characteristic
258	C₂²×C₁₃	#534	1	1	yes	characteristic
259	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
260	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
261	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
262	C₂²×C₁₃	#575	1	1	yes	characteristic
263	C₄×C₁₃	—	2	2	no	—
264	C₄×C₁₃	—	2	2	no	—
265	C₄×C₁₃	—	2	2	no	—
266	C₄×C₁₃	—	2	2	no	—
267	C₄×C₁₃	—	4	2	no	—
268	C₄×C₁₃	—	4	2	no	—
269	C₄×C₁₃	—	4	1	no	—
270	C₄×C₁₃	—	8	2	no	—
271	C₄×C₁₃	—	8	1	no	—
272	C₄×C₁₃	—	8	2	no	—
273	C₄×C₁₃	—	8	1	no	—
274	C₄×C₁₃	#551	1	2	yes	—
275	C₄×C₁₃	#554	1	2	yes	—
276	C₂²×Q₈	—	2	1	no	—
277	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
278	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
279	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
280	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
281	C₂²×C₈	—	2	4	no	—
282	C₂²×C₈	—	2	4	no	—
283	C₂²×C₈	—	4	2	no	—
284	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
285	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
286	C₄⋊Q₈	—	4	2	no	—
287	C₂²⋊Q₈	—	2	2	no	—
288	C₂²⋊Q₈	—	4	4	no	—
289	C₂²⋊Q₈	Q₈×C₁₃	1	4	yes	complemented
290	C₄×Q₈	—	4	2	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	—	2	1	no	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	—	2	2	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
299	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
300	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
301	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
302	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
303	C₂×C₂²⋊C₄	—	2	1	no	—
304	C₂×C₂²⋊C₄	—	2	2	no	—
305	C₂×C₂²⋊C₄	—	2	1	no	—
306	C₂×C₄²	—	2	1	no	—
307	C₂×C₄²	—	2	1	no	—
308	C₂×C₄²	—	4	2	no	—
309	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
310	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
311	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
312	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
313	#106	—	2	4	no	—
314	#106	—	4	2	no	—
315	#103	—	2	4	no	—
316	#103	—	4	2	no	—
317	#95	—	2	1	no	—
318	#95	—	2	1	no	—
319	#95	—	2	1	no	—
320	#95	—	2	1	no	—
321	#95	—	2	1	no	—
322	#95	—	2	2	no	—
323	#95	—	2	2	no	—
324	C₂×C₁₃	—	2	4	no	—
325	C₂×C₁₃	#2564	1	1	yes	characteristic
326	C₂×C₁₃	C₂×#475	1	1	yes	characteristic
327	C₂×C₁₃	#3076	1	1	yes	characteristic
328	C₂×C₁₃	#3167	1	1	yes	characteristic
329	C₂×C₁₃	#3181	1	1	yes	characteristic
330	C₂×C₁₃	#3187	1	1	yes	characteristic
331	C₂×C₁₃	#3190	1	1	yes	characteristic
332	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	4	2	no	—
337	C₂×Q₈	—	4	2	no	—
338	C₂×Q₈	—	4	2	no	—
339	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	4	1	no	—
351	C₂²×C₄	—	4	1	no	—
352	C₂²×C₄	—	4	1	no	—
353	C₂²×C₄	C₁₃×SD₁₆	1	4	yes	—
354	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
356	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
357	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
358	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
359	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
360	C₂²×C₄	C₁₃×#41	1	2	yes	—
361	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	4	8	no	—
368	C₂×C₈	C₁₃×#41	1	4	yes	—
369	C₄⋊C₄	—	2	4	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	4	2	no	—
378	C₄⋊C₄	—	4	2	no	—
379	C₄⋊C₄	—	4	2	no	—
380	C₄⋊C₄	—	4	4	no	—
381	C₄⋊C₄	—	4	2	no	—
382	C₄⋊C₄	—	4	2	no	—
383	C₄⋊C₄	C₂×Q₈×C₁₃	1	2	yes	—
384	C₂²⋊C₄	—	2	4	no	—
385	C₂²⋊C₄	—	4	4	no	—
386	C₂²⋊C₄	—	4	2	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	2	2	no	—
389	C₄²	—	4	1	no	—
390	C₄²	—	4	1	no	—
391	C₄²	—	4	2	no	—
392	C₄²	—	4	2	no	—
393	C₁₃	#29159	1	1	yes	characteristic, direct product factor, Sylow
394	C₂³	—	2	1	no	—
395	C₂³	—	2	1	no	—
396	C₂³	—	2	1	no	—
397	C₂³	—	2	1	no	—
398	C₂³	C₁₃×C₂²⋊Q₈	1	2	yes	—
399	C₂³	C₂×C₁₃×SD₁₆	1	2	yes	—
400	C₂³	C₁₃×#137	1	2	yes	—
401	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
402	Q₈	—	2	4	no	—
403	Q₈	—	4	2	no	—
404	Q₈	—	8	4	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	4	4	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
439	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
440	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
441	C₂×C₄	C₁₃×#135	1	2	yes	—
442	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
443	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
444	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
445	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
446	C₈	—	2	4	no	—
447	C₈	—	4	2	no	—
448	C₂²	—	2	2	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	2	2	no	—
451	C₂²	—	2	2	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	2	2	no	—
454	C₂²	C₁₃×#475	1	4	yes	—
455	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
456	C₂²	C₁₃×#532	1	1	yes	characteristic
457	C₂²	C₁₃×#534	1	1	yes	characteristic
458	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
459	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
460	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
461	C₂²	C₁₃×#575	1	1	yes	characteristic
462	C₄	—	2	2	no	—
463	C₄	—	2	2	no	—
464	C₄	—	2	2	no	—
465	C₄	—	2	2	no	—
466	C₄	—	4	2	no	—
467	C₄	—	4	2	no	—
468	C₄	—	4	1	no	—
469	C₄	—	8	2	no	—
470	C₄	—	8	1	no	—
471	C₄	—	8	2	no	—
472	C₄	—	8	1	no	—
473	C₄	C₁₃×#551	1	2	yes	—
474	C₄	C₁₃×#554	1	2	yes	—
475	C₂	—	2	4	no	—
476	C₂	C₁₃×#2564	1	1	yes	characteristic
477	C₂	C₂×C₁₃×#475	1	1	yes	characteristic
478	C₂	C₁₃×#3076	1	1	yes	characteristic
479	C₂	C₁₃×#3167	1	1	yes	characteristic
480	C₂	C₁₃×#3181	1	1	yes	characteristic
481	C₂	C₁₃×#3187	1	1	yes	characteristic
482	C₂	C₁₃×#3190	1	1	yes	characteristic

	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 ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#2099	C₂	semidirect
4. C₁₃×#2096	C₂	semidirect
5. C₁₃×#2058	C₂	semidirect
6. C₁₃×#2024	C₂	semidirect
7. C₁₃×#1919	C₂	semidirect
9. C₁₃×#1865	C₂	semidirect
56. C₁₃×C₂²⋊Q₈	Q₈	semidirect
91. #29159	C₁₃	direct (N × H)
155. #2099	C₂×C₁₃	semidirect
156. #2096	C₂×C₁₃	semidirect
157. #2058	C₂×C₁₃	semidirect
158. #2024	C₂×C₁₃	semidirect
159. #1919	C₂×C₁₃	semidirect
161. #1865	C₂×C₁₃	semidirect
289. C₂²⋊Q₈	Q₈×C₁₃	semidirect
393. C₁₃	#29159	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×#2857	2
C₄×C₁₃×C₂²⋊Q₈	2
C₁₃×#2099	2
C₁₃×#2096	2
C₁₃×#2058	2
C₁₃×#2024	2
C₁₃×#1919	2
C₁₃×#1892	2
C₁₃×#1865	2
C₁₃×#1807	2
C₂×C₁₃×#336	2
#29159	13

Subgroups — C13×#29159 #15715498

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#29159 #15715498