Subgroups — C₁₃×#34643 #15720982

Order 3328.

2234 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#529	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2664	C₂	1	4	yes	maximal, complemented
3	C₁₃×#2663	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2662	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2661	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2399	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2398	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2397	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2392	C₂	1	4	yes	maximal, complemented
10	C₁₃×#2293	C₂	1	4	yes	maximal, complemented
11	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#529	—	2	16	no	—
13	C₂×C₁₃×#126	C₂²	1	4	yes	—
14	C₂×C₁₃×#125	C₂²	1	2	yes	—
15	C₂×C₁₃×#124	C₂²	1	2	yes	—
16	C₂×C₁₃×#123	C₂²	1	4	yes	—
17	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₁₃×#121	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
20	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
21	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
22	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
23	C₂×C₁₃×#117	C₂²	1	2	yes	—
24	C₂×C₁₃×#117	C₂²	1	4	yes	—
25	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
26	C₁₃×#400	C₂²	1	4	yes	—
27	C₁₃×#399	C₂²	1	4	yes	—
28	C₁₃×#398	C₂²	1	4	yes	—
29	C₁₃×#398	C₂²	1	4	yes	—
30	C₁₃×#397	C₂²	1	4	yes	—
31	C₁₃×#397	C₂²	1	4	yes	—
32	C₁₃×#396	C₂²	1	8	yes	—
33	C₁₃×#395	C₂²	1	4	yes	—
34	C₁₃×#394	C₂²	1	8	yes	—
35	C₁₃×#394	C₂²	1	4	yes	—
36	C₁₃×#394	C₂²	1	4	yes	—
37	C₁₃×#393	C₂²	1	4	yes	—
38	C₁₃×#392	C₂²	1	4	yes	—
39	C₁₃×#392	C₂²	1	4	yes	—
40	C₁₃×#390	C₂²	1	8	yes	—
41	C₁₃×#389	C₂²	1	8	yes	—
42	C₁₃×#388	C₂²	1	8	yes	—
43	C₁₃×#388	C₂²	1	8	yes	—
44	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
45	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
46	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
47	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
48	C₁₃×#376	C₂²	1	1	yes	characteristic
49	C₁₃×#376	C₂²	1	1	yes	characteristic
50	C₄³×C₁₃	C₂²	1	2	yes	—
51	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
52	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
53	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
54	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
55	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
56	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
58	C₁₃×#126	—	2	16	no	—
59	C₁₃×#125	—	2	8	no	—
60	C₁₃×#124	—	2	8	no	—
61	C₁₃×#123	—	2	16	no	—
62	C₁₃×C₂²⋊Q₈	—	2	8	no	—
63	C₁₃×#121	—	2	8	no	—
64	C₄×Q₈×C₁₃	—	2	8	no	—
65	C₄×D₄×C₁₃	—	2	16	no	—
66	C₄×D₄×C₁₃	—	2	8	no	—
67	C₄×D₄×C₁₃	—	2	16	no	—
68	C₁₃×#117	—	2	16	no	—
69	C₁₃×#117	—	2	8	no	—
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
73	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
74	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
75	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
76	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
79	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
80	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
81	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
82	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
83	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
84	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
85	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
86	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
87	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
88	C₂×C₄²×C₁₃	D₄	1	8	yes	complemented
89	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
90	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
91	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
92	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
93	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
96	C₁₃×#95	C₂³	1	4	yes	—
97	C₁₃×#95	C₂³	1	4	yes	—
98	C₁₃×#95	C₂³	1	8	yes	—
99	C₁₃×#95	C₂³	1	8	yes	—
100	C₁₃×#95	C₂³	1	4	yes	—
101	C₁₃×#95	C₂³	1	4	yes	—
102	#34643	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
103	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
104	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
105	C₂×Q₈×C₁₃	—	2	4	no	—
106	C₂×Q₈×C₁₃	—	4	4	no	—
107	C₂×D₄×C₁₃	—	2	8	no	—
108	C₂×D₄×C₁₃	—	2	4	no	—
109	C₂×D₄×C₁₃	—	2	8	no	—
110	C₂×D₄×C₁₃	—	4	8	no	—
111	C₂×D₄×C₁₃	—	4	4	no	—
112	C₂×D₄×C₁₃	—	4	8	no	—
113	C₂²×C₄×C₁₃	—	2	4	no	—
114	C₂²×C₄×C₁₃	—	2	8	no	—
115	C₂²×C₄×C₁₃	—	2	16	no	—
116	C₂²×C₄×C₁₃	—	4	4	no	—
117	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
118	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
119	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
120	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
121	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
122	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
123	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
124	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
125	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
127	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
128	C₁₃×C₄⋊C₄	—	2	8	no	—
129	C₁₃×C₄⋊C₄	—	2	8	no	—
130	C₁₃×C₄⋊C₄	—	2	4	no	—
131	C₁₃×C₄⋊C₄	—	2	8	no	—
132	C₁₃×C₄⋊C₄	—	2	4	no	—
133	C₁₃×C₄⋊C₄	—	2	8	no	—
134	C₁₃×C₄⋊C₄	—	2	8	no	—
135	C₁₃×C₄⋊C₄	—	2	8	no	—
136	C₁₃×C₄⋊C₄	—	4	8	no	—
137	C₁₃×C₂²⋊C₄	—	2	8	no	—
138	C₁₃×C₂²⋊C₄	—	2	8	no	—
139	C₁₃×C₂²⋊C₄	—	2	8	no	—
140	C₁₃×C₂²⋊C₄	—	2	8	no	—
141	C₁₃×C₂²⋊C₄	—	2	8	no	—
142	C₁₃×C₂²⋊C₄	—	2	8	no	—
143	C₁₃×C₂²⋊C₄	—	2	16	no	—
144	C₁₃×C₂²⋊C₄	—	4	8	no	—
145	C₁₃×C₂²⋊C₄	—	4	8	no	—
146	C₄²×C₁₃	—	2	8	no	—
147	C₄²×C₁₃	—	2	4	no	—
148	C₄²×C₁₃	—	4	8	no	—
149	C₄²×C₁₃	C₂×D₄	1	4	yes	—
150	C₄²×C₁₃	C₂×D₄	1	4	yes	—
151	C₄²×C₁₃	C₂×D₄	1	8	yes	—
152	C₄²×C₁₃	#41	1	8	yes	—
153	C₂×#529	C₂×C₁₃	1	2	yes	complemented
154	#2664	C₂×C₁₃	1	4	yes	complemented
155	#2663	C₂×C₁₃	1	4	yes	complemented
156	#2662	C₂×C₁₃	1	4	yes	complemented
157	#2661	C₂×C₁₃	1	4	yes	complemented
158	#2399	C₂×C₁₃	1	1	yes	characteristic, complemented
159	#2398	C₂×C₁₃	1	2	yes	complemented
160	#2397	C₂×C₁₃	1	1	yes	characteristic, complemented
161	#2392	C₂×C₁₃	1	4	yes	complemented
162	#2293	C₂×C₁₃	1	4	yes	complemented
163	C₄×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
164	C₂³×C₁₃	—	2	2	no	—
165	C₂³×C₁₃	—	2	4	no	—
166	C₂³×C₁₃	—	2	4	no	—
167	C₂³×C₁₃	—	2	8	no	—
168	C₂³×C₁₃	—	2	4	no	—
169	C₂³×C₁₃	—	2	8	no	—
170	C₂³×C₁₃	—	2	4	no	—
171	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
172	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
173	Q₈×C₁₃	—	4	8	no	—
174	D₄×C₁₃	—	4	8	no	—
175	D₄×C₁₃	—	4	16	no	—
176	D₄×C₁₃	—	4	16	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	4	no	—
179	C₂×C₄×C₁₃	—	2	8	no	—
180	C₂×C₄×C₁₃	—	2	4	no	—
181	C₂×C₄×C₁₃	—	2	8	no	—
182	C₂×C₄×C₁₃	—	2	4	no	—
183	C₂×C₄×C₁₃	—	2	4	no	—
184	C₂×C₄×C₁₃	—	2	4	no	—
185	C₂×C₄×C₁₃	—	2	4	no	—
186	C₂×C₄×C₁₃	—	2	8	no	—
187	C₂×C₄×C₁₃	—	2	8	no	—
188	C₂×C₄×C₁₃	—	2	4	no	—
189	C₂×C₄×C₁₃	—	2	8	no	—
190	C₂×C₄×C₁₃	—	2	4	no	—
191	C₂×C₄×C₁₃	—	4	8	no	—
192	C₂×C₄×C₁₃	—	4	16	no	—
193	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
194	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
195	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
196	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
197	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
198	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
199	#529	—	2	16	no	—
200	C₂×#126	C₂²×C₁₃	1	4	yes	—
201	C₂×#125	C₂²×C₁₃	1	2	yes	—
202	C₂×#124	C₂²×C₁₃	1	2	yes	—
203	C₂×#123	C₂²×C₁₃	1	4	yes	—
204	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
205	C₂×#121	C₂²×C₁₃	1	2	yes	—
206	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
207	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
208	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
209	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
210	C₂×#117	C₂²×C₁₃	1	2	yes	—
211	C₂×#117	C₂²×C₁₃	1	4	yes	—
212	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
213	#400	C₂²×C₁₃	1	4	yes	—
214	#399	C₂²×C₁₃	1	4	yes	—
215	#398	C₂²×C₁₃	1	4	yes	—
216	#398	C₂²×C₁₃	1	4	yes	—
217	#397	C₂²×C₁₃	1	4	yes	—
218	#397	C₂²×C₁₃	1	4	yes	—
219	#396	C₂²×C₁₃	1	8	yes	—
220	#395	C₂²×C₁₃	1	4	yes	—
221	#394	C₂²×C₁₃	1	8	yes	—
222	#394	C₂²×C₁₃	1	4	yes	—
223	#394	C₂²×C₁₃	1	4	yes	—
224	#393	C₂²×C₁₃	1	4	yes	—
225	#392	C₂²×C₁₃	1	4	yes	—
226	#392	C₂²×C₁₃	1	4	yes	—
227	#390	C₂²×C₁₃	1	8	yes	—
228	#389	C₂²×C₁₃	1	8	yes	—
229	#388	C₂²×C₁₃	1	8	yes	—
230	#388	C₂²×C₁₃	1	8	yes	—
231	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
232	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
233	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
234	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
235	#376	C₂²×C₁₃	1	1	yes	characteristic
236	#376	C₂²×C₁₃	1	1	yes	characteristic
237	C₄³	C₂²×C₁₃	1	2	yes	—
238	C₂²×C₁₃	—	2	2	no	—
239	C₂²×C₁₃	—	2	4	no	—
240	C₂²×C₁₃	—	4	4	no	—
241	C₂²×C₁₃	—	4	4	no	—
242	C₂²×C₁₃	—	4	4	no	—
243	C₂²×C₁₃	—	4	4	no	—
244	C₂²×C₁₃	—	4	8	no	—
245	C₂²×C₁₃	—	4	8	no	—
246	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
247	C₂²×C₁₃	C₂²×#41	1	2	yes	—
248	C₂²×C₁₃	#585	1	4	yes	—
249	C₄×C₁₃	—	2	2	no	—
250	C₄×C₁₃	—	2	4	no	—
251	C₄×C₁₃	—	2	4	no	—
252	C₄×C₁₃	—	2	8	no	—
253	C₄×C₁₃	—	4	4	no	—
254	C₄×C₁₃	—	4	4	no	—
255	C₄×C₁₃	—	4	4	no	—
256	C₄×C₁₃	—	4	4	no	—
257	C₄×C₁₃	#532	1	4	yes	—
258	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
259	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
260	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
261	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
262	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
263	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
264	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
265	#126	—	2	16	no	—
266	#125	—	2	8	no	—
267	#124	—	2	8	no	—
268	#123	—	2	16	no	—
269	C₂²⋊Q₈	—	2	8	no	—
270	#121	—	2	8	no	—
271	C₄×Q₈	—	2	8	no	—
272	C₄×D₄	—	2	16	no	—
273	C₄×D₄	—	2	8	no	—
274	C₄×D₄	—	2	16	no	—
275	#117	—	2	16	no	—
276	#117	—	2	8	no	—
277	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
278	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
279	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
280	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
281	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
282	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
283	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
284	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
285	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
286	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
287	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
288	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
289	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
290	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
291	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
292	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
293	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
294	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
295	C₂×C₄²	D₄×C₁₃	1	8	yes	complemented
296	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
297	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
298	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
299	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
300	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
301	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
302	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
303	#95	C₂³×C₁₃	1	4	yes	—
304	#95	C₂³×C₁₃	1	4	yes	—
305	#95	C₂³×C₁₃	1	8	yes	—
306	#95	C₂³×C₁₃	1	8	yes	—
307	#95	C₂³×C₁₃	1	4	yes	—
308	#95	C₂³×C₁₃	1	4	yes	—
309	C₂×C₁₃	—	4	2	no	—
310	C₂×C₁₃	—	8	4	no	—
311	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
312	C₂×C₁₃	#3449	1	2	yes	—
313	C₂×C₁₃	#3455	1	4	yes	—
314	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
315	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
316	C₂×Q₈	—	2	4	no	—
317	C₂×Q₈	—	4	4	no	—
318	C₂×D₄	—	2	8	no	—
319	C₂×D₄	—	2	4	no	—
320	C₂×D₄	—	2	8	no	—
321	C₂×D₄	—	4	8	no	—
322	C₂×D₄	—	4	4	no	—
323	C₂×D₄	—	4	8	no	—
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	—	2	8	no	—
326	C₂²×C₄	—	2	16	no	—
327	C₂²×C₄	—	4	4	no	—
328	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
329	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
330	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
331	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
332	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
333	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
334	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
335	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
336	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
337	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
338	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
339	C₄⋊C₄	—	2	8	no	—
340	C₄⋊C₄	—	2	8	no	—
341	C₄⋊C₄	—	2	4	no	—
342	C₄⋊C₄	—	2	8	no	—
343	C₄⋊C₄	—	2	4	no	—
344	C₄⋊C₄	—	2	8	no	—
345	C₄⋊C₄	—	2	8	no	—
346	C₄⋊C₄	—	2	8	no	—
347	C₄⋊C₄	—	4	8	no	—
348	C₂²⋊C₄	—	2	8	no	—
349	C₂²⋊C₄	—	2	8	no	—
350	C₂²⋊C₄	—	2	8	no	—
351	C₂²⋊C₄	—	2	8	no	—
352	C₂²⋊C₄	—	2	8	no	—
353	C₂²⋊C₄	—	2	8	no	—
354	C₂²⋊C₄	—	2	16	no	—
355	C₂²⋊C₄	—	4	8	no	—
356	C₂²⋊C₄	—	4	8	no	—
357	C₄²	—	2	8	no	—
358	C₄²	—	2	4	no	—
359	C₄²	—	4	8	no	—
360	C₄²	C₂×D₄×C₁₃	1	4	yes	—
361	C₄²	C₂×D₄×C₁₃	1	4	yes	—
362	C₄²	C₂×D₄×C₁₃	1	8	yes	—
363	C₄²	C₁₃×#41	1	8	yes	—
364	C₁₃	#34643	1	1	yes	characteristic, direct product factor, Sylow
365	C₂³	—	2	2	no	—
366	C₂³	—	2	4	no	—
367	C₂³	—	2	4	no	—
368	C₂³	—	2	8	no	—
369	C₂³	—	2	4	no	—
370	C₂³	—	2	8	no	—
371	C₂³	—	2	4	no	—
372	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
373	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
374	Q₈	—	4	8	no	—
375	D₄	—	4	8	no	—
376	D₄	—	4	16	no	—
377	D₄	—	4	16	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	8	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	8	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	8	no	—
388	C₂×C₄	—	2	8	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	8	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	4	8	no	—
393	C₂×C₄	—	4	16	no	—
394	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
395	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
396	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
397	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
398	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
399	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	4	no	—
402	C₂²	—	4	4	no	—
403	C₂²	—	4	4	no	—
404	C₂²	—	4	4	no	—
405	C₂²	—	4	4	no	—
406	C₂²	—	4	8	no	—
407	C₂²	—	4	8	no	—
408	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
409	C₂²	C₂²×C₁₃×#41	1	2	yes	—
410	C₂²	C₁₃×#585	1	4	yes	—
411	C₄	—	2	2	no	—
412	C₄	—	2	4	no	—
413	C₄	—	2	4	no	—
414	C₄	—	2	8	no	—
415	C₄	—	4	4	no	—
416	C₄	—	4	4	no	—
417	C₄	—	4	4	no	—
418	C₄	—	4	4	no	—
419	C₄	C₁₃×#532	1	4	yes	—
420	C₂	—	4	2	no	—
421	C₂	—	8	4	no	—
422	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
423	C₂	C₁₃×#3449	1	2	yes	—
424	C₂	C₁₃×#3455	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#529	C₂	semidirect
2. C₁₃×#2664	C₂	semidirect
3. C₁₃×#2663	C₂	semidirect
4. C₁₃×#2662	C₂	semidirect
5. C₁₃×#2661	C₂	semidirect
6. C₁₃×#2399	C₂	semidirect
7. C₁₃×#2398	C₂	semidirect
8. C₁₃×#2397	C₂	semidirect
9. C₁₃×#2392	C₂	semidirect
10. C₁₃×#2293	C₂	semidirect
11. C₄×C₁₃×#117	C₂	semidirect
88. C₂×C₄²×C₁₃	D₄	semidirect
102. #34643	C₁₃	direct (N × H)
153. C₂×#529	C₂×C₁₃	semidirect
154. #2664	C₂×C₁₃	semidirect
155. #2663	C₂×C₁₃	semidirect
156. #2662	C₂×C₁₃	semidirect
157. #2661	C₂×C₁₃	semidirect
158. #2399	C₂×C₁₃	semidirect
159. #2398	C₂×C₁₃	semidirect
160. #2397	C₂×C₁₃	semidirect
161. #2392	C₂×C₁₃	semidirect
162. #2293	C₂×C₁₃	semidirect
163. C₄×#117	C₂×C₁₃	semidirect
295. C₂×C₄²	D₄×C₁₃	semidirect
364. C₁₃	#34643	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×#529	2
C₁₃×#2664	2
C₁₃×#2663	2
C₁₃×#2662	2
C₁₃×#2661	2
C₁₃×#2399	2
C₁₃×#2398	2
C₁₃×#2397	2
C₁₃×#2392	2
C₁₃×#2293	2
C₄×C₁₃×#117	2
#34643	13

Subgroups — C13×#34643 #15720982

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34643 #15720982