Subgroups — C₁₃×#25888 #15712227

Order 3328.

1282 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#487	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#477	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2563	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2036	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1981	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1954	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1787	C₂	1	4	yes	maximal, complemented
9	C₄×C₁₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
11	D₄×Q₈×C₁₃	—	2	4	no	—
12	D₄×Q₈×C₁₃	—	2	4	no	—
13	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
14	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
17	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₃	—	2	1	no	—
20	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₁₃×#487	—	2	4	no	—
22	C₁₃×#477	—	2	4	no	—
23	C₂×C₁₃×#107	C₂²	1	2	yes	—
24	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#103	C₂²	1	2	yes	—
26	C₂×C₁₃×#103	C₂²	1	4	yes	—
27	C₂×C₁₃×#103	C₂²	1	2	yes	—
28	C₂×C₁₃×#103	C₂²	1	4	yes	—
29	C₂×C₁₃×C₂²⋊C₈	C₂²	1	4	yes	—
30	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
31	C₁₃×#393	—	2	2	no	—
32	C₁₃×#390	—	2	1	no	—
33	C₁₃×#382	—	2	1	no	—
34	C₁₃×#380	C₂²	1	4	yes	—
35	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₁₃×#340	C₂²	1	2	yes	—
37	C₂²×Q₈×C₁₃	—	2	4	no	—
38	C₂²×Q₈×C₁₃	—	2	4	no	—
39	C₂²×Q₈×C₁₃	—	2	2	no	—
40	C₂²×Q₈×C₁₃	—	2	1	no	—
41	C₂²×Q₈×C₁₃	—	2	8	no	—
42	C₂²×Q₈×C₁₃	—	4	4	no	—
43	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
44	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	—	2	2	no	—
47	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
50	C₁₃×C₄⋊Q₈	—	2	8	no	—
51	C₁₃×C₄⋊Q₈	—	2	2	no	—
52	C₁₃×C₄⋊Q₈	—	2	2	no	—
53	C₁₃×C₄⋊Q₈	—	2	2	no	—
54	C₁₃×C₄⋊Q₈	D₄	1	4	yes	—
55	C₁₃×C₂²⋊Q₈	—	2	16	no	—
56	C₁₃×C₂²⋊Q₈	—	2	4	no	—
57	C₁₃×C₂²⋊Q₈	—	2	4	no	—
58	C₄×Q₈×C₁₃	—	2	2	no	—
59	C₄×Q₈×C₁₃	D₄	1	4	yes	—
60	C₄×D₄×C₁₃	—	2	8	no	—
61	C₄×D₄×C₁₃	—	2	2	no	—
62	C₄×D₄×C₁₃	—	2	2	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
68	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
72	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
74	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
75	C₂×C₄²×C₁₃	—	2	1	no	—
76	C₂×C₄²×C₁₃	—	2	1	no	—
77	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
78	C₁₃×#107	—	2	4	no	—
79	C₁₃×C₄⋊C₈	—	2	2	no	—
80	C₁₃×#103	—	2	4	no	—
81	C₁₃×#103	—	2	8	no	—
82	C₁₃×#103	—	2	4	no	—
83	C₁₃×#103	—	4	4	no	—
84	C₁₃×C₂²⋊C₈	—	4	4	no	—
85	C₄×C₈×C₁₃	—	2	2	no	—
86	C₁₃×#95	—	2	1	no	—
87	C₁₃×#95	—	2	4	no	—
88	#25888	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
89	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
90	C₂×Q₈×C₁₃	—	2	8	no	—
91	C₂×Q₈×C₁₃	—	2	1	no	—
92	C₂×Q₈×C₁₃	—	2	2	no	—
93	C₂×Q₈×C₁₃	—	2	2	no	—
94	C₂×Q₈×C₁₃	—	2	4	no	—
95	C₂×Q₈×C₁₃	—	2	4	no	—
96	C₂×Q₈×C₁₃	—	4	8	no	—
97	C₂×Q₈×C₁₃	—	4	16	no	—
98	C₂×Q₈×C₁₃	—	4	8	no	—
99	C₂×Q₈×C₁₃	—	4	8	no	—
100	C₂×Q₈×C₁₃	—	4	2	no	—
101	C₂×Q₈×C₁₃	—	8	2	no	—
102	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
103	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
104	C₂×Q₈×C₁₃	#41	1	4	yes	—
105	C₂×D₄×C₁₃	—	2	2	no	—
106	C₂×D₄×C₁₃	—	2	2	no	—
107	C₂×D₄×C₁₃	Q₁₆	1	4	yes	—
108	C₂²×C₄×C₁₃	—	2	1	no	—
109	C₂²×C₄×C₁₃	—	2	8	no	—
110	C₂²×C₄×C₁₃	—	2	1	no	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	—	2	2	no	—
113	C₂²×C₄×C₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₃	—	2	4	no	—
115	C₂²×C₄×C₁₃	—	2	4	no	—
116	C₂²×C₄×C₁₃	—	2	2	no	—
117	C₂²×C₄×C₁₃	—	2	2	no	—
118	C₂²×C₄×C₁₃	—	4	8	no	—
119	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	—	2	4	no	—
128	C₁₃×C₄⋊C₄	—	2	8	no	—
129	C₁₃×C₄⋊C₄	—	2	4	no	—
130	C₁₃×C₄⋊C₄	—	2	4	no	—
131	C₁₃×C₄⋊C₄	—	2	4	no	—
132	C₁₃×C₄⋊C₄	—	2	2	no	—
133	C₁₃×C₄⋊C₄	—	2	1	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	—	2	2	no	—
138	C₁₃×C₄⋊C₄	—	4	2	no	—
139	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
140	C₁₃×C₂²⋊C₄	—	2	8	no	—
141	C₁₃×C₂²⋊C₄	—	2	4	no	—
142	C₁₃×C₂²⋊C₄	—	8	4	no	—
143	C₄²×C₁₃	—	2	4	no	—
144	C₄²×C₁₃	—	4	2	no	—
145	C₄²×C₁₃	C₂×D₄	1	2	yes	—
146	C₄²×C₁₃	C₂×D₄	1	2	yes	—
147	C₂×D₄×Q₈	C₂×C₁₃	1	1	yes	characteristic
148	C₂×#487	C₂×C₁₃	1	1	yes	characteristic, complemented
149	C₂×#477	C₂×C₁₃	1	1	yes	characteristic, complemented
150	#2563	C₂×C₁₃	1	1	yes	characteristic
151	#2036	C₂×C₁₃	1	4	yes	complemented
152	#1981	C₂×C₁₃	1	1	yes	characteristic, complemented
153	#1954	C₂×C₁₃	1	1	yes	characteristic
154	#1787	C₂×C₁₃	1	4	yes	complemented
155	C₄×#103	C₂×C₁₃	1	1	yes	characteristic, complemented
156	C₂³×C₁₃	—	2	2	no	—
157	C₂³×C₁₃	—	2	4	no	—
158	C₂³×C₁₃	—	2	2	no	—
159	C₂³×C₁₃	—	2	4	no	—
160	C₂³×C₁₃	C₂×Q₁₆	1	4	yes	—
161	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
162	Q₈×C₁₃	—	2	2	no	—
163	Q₈×C₁₃	—	2	4	no	—
164	Q₈×C₁₃	—	2	8	no	—
165	Q₈×C₁₃	—	4	16	no	—
166	Q₈×C₁₃	—	4	2	no	—
167	Q₈×C₁₃	—	4	2	no	—
168	Q₈×C₁₃	—	8	4	no	—
169	Q₈×C₁₃	#124	1	4	yes	—
170	D₄×C₁₃	—	2	8	no	—
171	C₂×C₄×C₁₃	—	2	2	no	—
172	C₂×C₄×C₁₃	—	2	4	no	—
173	C₂×C₄×C₁₃	—	2	2	no	—
174	C₂×C₄×C₁₃	—	2	2	no	—
175	C₂×C₄×C₁₃	—	2	4	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	2	4	no	—
178	C₂×C₄×C₁₃	—	4	16	no	—
179	C₂×C₄×C₁₃	—	4	4	no	—
180	C₂×C₄×C₁₃	—	4	2	no	—
181	C₂×C₄×C₁₃	—	4	2	no	—
182	C₂×C₄×C₁₃	—	4	2	no	—
183	C₂×C₄×C₁₃	—	4	4	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	—	4	4	no	—
189	C₂×C₄×C₁₃	#120	1	2	yes	—
190	C₂×C₄×C₁₃	#120	1	2	yes	—
191	C₂×C₄×C₁₃	C₂×Q₁₆	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×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
196	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
197	C₈×C₁₃	—	4	2	no	—
198	C₈×C₁₃	—	4	2	no	—
199	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
200	D₄×Q₈	—	2	4	no	—
201	D₄×Q₈	—	2	4	no	—
202	C₂×C₄⋊Q₈	—	2	1	no	—
203	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
204	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
205	C₂×C₂²⋊Q₈	—	2	2	no	—
206	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
207	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
208	C₂×C₄×D₄	—	2	1	no	—
209	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
210	#487	—	2	4	no	—
211	#477	—	2	4	no	—
212	C₂×#107	C₂²×C₁₃	1	2	yes	—
213	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
214	C₂×#103	C₂²×C₁₃	1	2	yes	—
215	C₂×#103	C₂²×C₁₃	1	4	yes	—
216	C₂×#103	C₂²×C₁₃	1	2	yes	—
217	C₂×#103	C₂²×C₁₃	1	4	yes	—
218	C₂×C₂²⋊C₈	C₂²×C₁₃	1	4	yes	—
219	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
220	#393	—	2	2	no	—
221	#390	—	2	1	no	—
222	#382	—	2	1	no	—
223	#380	C₂²×C₁₃	1	4	yes	—
224	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
225	#340	C₂²×C₁₃	1	2	yes	—
226	C₂²×C₁₃	—	2	4	no	—
227	C₂²×C₁₃	—	2	8	no	—
228	C₂²×C₁₃	—	4	4	no	—
229	C₂²×C₁₃	—	4	2	no	—
230	C₂²×C₁₃	—	4	2	no	—
231	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
232	C₂²×C₁₃	#546	1	2	yes	—
233	C₂²×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
234	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
235	C₂²×C₁₃	#577	1	2	yes	—
236	C₄×C₁₃	—	2	4	no	—
237	C₄×C₁₃	—	2	2	no	—
238	C₄×C₁₃	—	4	2	no	—
239	C₄×C₁₃	—	4	4	no	—
240	C₄×C₁₃	—	4	2	no	—
241	C₄×C₁₃	—	8	2	no	—
242	C₄×C₁₃	—	8	2	no	—
243	C₄×C₁₃	#451	1	4	yes	—
244	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
245	C₄×C₁₃	#535	1	1	yes	characteristic
246	C₄×C₁₃	#546	1	2	yes	—
247	C₂²×Q₈	—	2	4	no	—
248	C₂²×Q₈	—	2	4	no	—
249	C₂²×Q₈	—	2	2	no	—
250	C₂²×Q₈	—	2	1	no	—
251	C₂²×Q₈	—	2	8	no	—
252	C₂²×Q₈	—	4	4	no	—
253	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
254	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
255	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
256	C₂³×C₄	—	2	2	no	—
257	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
258	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
259	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
260	C₄⋊Q₈	—	2	8	no	—
261	C₄⋊Q₈	—	2	2	no	—
262	C₄⋊Q₈	—	2	2	no	—
263	C₄⋊Q₈	—	2	2	no	—
264	C₄⋊Q₈	D₄×C₁₃	1	4	yes	—
265	C₂²⋊Q₈	—	2	16	no	—
266	C₂²⋊Q₈	—	2	4	no	—
267	C₂²⋊Q₈	—	2	4	no	—
268	C₄×Q₈	—	2	2	no	—
269	C₄×Q₈	D₄×C₁₃	1	4	yes	—
270	C₄×D₄	—	2	8	no	—
271	C₄×D₄	—	2	2	no	—
272	C₄×D₄	—	2	2	no	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
279	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
280	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
281	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
282	C₂×C₂²⋊C₄	—	2	2	no	—
283	C₂×C₂²⋊C₄	—	2	4	no	—
284	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
285	C₂×C₄²	—	2	1	no	—
286	C₂×C₄²	—	2	1	no	—
287	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
288	#107	—	2	4	no	—
289	C₄⋊C₈	—	2	2	no	—
290	#103	—	2	4	no	—
291	#103	—	2	8	no	—
292	#103	—	2	4	no	—
293	#103	—	4	4	no	—
294	C₂²⋊C₈	—	4	4	no	—
295	C₄×C₈	—	2	2	no	—
296	#95	—	2	1	no	—
297	#95	—	2	4	no	—
298	C₂×C₁₃	—	4	4	no	—
299	C₂×C₁₃	#2435	1	1	yes	characteristic
300	C₂×C₁₃	C₂×#451	1	1	yes	characteristic
301	C₂×C₁₃	#3010	1	1	yes	characteristic
302	C₂×C₁₃	#3299	1	2	yes	—
303	C₂×C₁₃	#3329	1	2	yes	—
304	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
305	C₂×Q₈	—	2	8	no	—
306	C₂×Q₈	—	2	1	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	—	2	4	no	—
310	C₂×Q₈	—	2	4	no	—
311	C₂×Q₈	—	4	8	no	—
312	C₂×Q₈	—	4	16	no	—
313	C₂×Q₈	—	4	8	no	—
314	C₂×Q₈	—	4	8	no	—
315	C₂×Q₈	—	4	2	no	—
316	C₂×Q₈	—	8	2	no	—
317	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
318	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
319	C₂×Q₈	C₁₃×#41	1	4	yes	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	C₁₃×Q₁₆	1	4	yes	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	8	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	4	8	no	—
334	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
335	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
337	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	4	no	—
343	C₄⋊C₄	—	2	8	no	—
344	C₄⋊C₄	—	2	4	no	—
345	C₄⋊C₄	—	2	4	no	—
346	C₄⋊C₄	—	2	4	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	4	2	no	—
354	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
355	C₂²⋊C₄	—	2	8	no	—
356	C₂²⋊C₄	—	2	4	no	—
357	C₂²⋊C₄	—	8	4	no	—
358	C₄²	—	2	4	no	—
359	C₄²	—	4	2	no	—
360	C₄²	C₂×D₄×C₁₃	1	2	yes	—
361	C₄²	C₂×D₄×C₁₃	1	2	yes	—
362	C₁₃	#25888	1	1	yes	characteristic, direct product factor, Sylow
363	C₂³	—	2	2	no	—
364	C₂³	—	2	4	no	—
365	C₂³	—	2	2	no	—
366	C₂³	—	2	4	no	—
367	C₂³	C₂×C₁₃×Q₁₆	1	4	yes	—
368	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
369	Q₈	—	2	2	no	—
370	Q₈	—	2	4	no	—
371	Q₈	—	2	8	no	—
372	Q₈	—	4	16	no	—
373	Q₈	—	4	2	no	—
374	Q₈	—	4	2	no	—
375	Q₈	—	8	4	no	—
376	Q₈	C₁₃×#124	1	4	yes	—
377	D₄	—	2	8	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	4	16	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	4	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	—	4	4	no	—
396	C₂×C₄	C₁₃×#120	1	2	yes	—
397	C₂×C₄	C₁₃×#120	1	2	yes	—
398	C₂×C₄	C₂×C₁₃×Q₁₆	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×D₄×C₁₃	1	1	yes	characteristic
402	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
403	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
404	C₈	—	4	2	no	—
405	C₈	—	4	2	no	—
406	C₂²	—	2	8	no	—
407	C₂²	—	2	4	no	—
408	C₂²	—	4	2	no	—
409	C₂²	—	4	4	no	—
410	C₂²	—	4	2	no	—
411	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
412	C₂²	C₁₃×#546	1	2	yes	—
413	C₂²	C₂²×C₁₃×Q₁₆	1	1	yes	characteristic
414	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
415	C₂²	C₁₃×#577	1	2	yes	—
416	C₄	—	2	2	no	—
417	C₄	—	2	4	no	—
418	C₄	—	4	2	no	—
419	C₄	—	4	2	no	—
420	C₄	—	4	4	no	—
421	C₄	—	8	2	no	—
422	C₄	—	8	2	no	—
423	C₄	C₁₃×#451	1	4	yes	—
424	C₄	C₂×C₁₃×#124	1	1	yes	characteristic
425	C₄	C₁₃×#535	1	1	yes	characteristic
426	C₄	C₁₃×#546	1	2	yes	—
427	C₂	—	4	4	no	—
428	C₂	C₁₃×#2435	1	1	yes	characteristic
429	C₂	C₂×C₁₃×#451	1	1	yes	characteristic
430	C₂	C₁₃×#3010	1	1	yes	characteristic
431	C₂	C₁₃×#3299	1	2	yes	—
432	C₂	C₁₃×#3329	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#487	C₂	semidirect
3. C₂×C₁₃×#477	C₂	semidirect
5. C₁₃×#2036	C₂	semidirect
6. C₁₃×#1981	C₂	semidirect
8. C₁₃×#1787	C₂	semidirect
9. C₄×C₁₃×#103	C₂	semidirect
88. #25888	C₁₃	direct (N × H)
148. C₂×#487	C₂×C₁₃	semidirect
149. C₂×#477	C₂×C₁₃	semidirect
151. #2036	C₂×C₁₃	semidirect
152. #1981	C₂×C₁₃	semidirect
154. #1787	C₂×C₁₃	semidirect
155. C₄×#103	C₂×C₁₃	semidirect
362. C₁₃	#25888	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×D₄×Q₈×C₁₃	2
C₂×C₁₃×#487	2
C₂×C₁₃×#477	2
C₁₃×#2563	2
C₁₃×#2036	2
C₁₃×#1981	2
C₁₃×#1954	2
C₁₃×#1787	2
C₄×C₁₃×#103	2
#25888	13

Subgroups — C13×#25888 #15712227

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25888 #15712227