Subgroups — C₁₃×#25845 #15712184

Order 3328.

1040 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#554	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#478	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2584	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2059	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2059	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1988	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1985	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1864	C₂	1	2	yes	maximal
10	C₁₃×#1862	C₂	1	2	yes	maximal
11	C₁₃×#1762	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#554	—	2	4	no	—
13	C₁₃×#554	—	2	4	no	—
14	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#125	C₂²	1	2	yes	—
17	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
18	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
19	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
21	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
23	C₁₃×#501	—	2	4	no	—
24	C₁₃×#478	—	2	4	no	—
25	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#107	C₂²	1	2	yes	—
27	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#106	C₂²	1	2	yes	—
29	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#102	C₂²	1	2	yes	—
33	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
34	C₁₃×#398	—	2	1	no	—
35	C₁₃×#395	—	2	1	no	—
36	C₁₃×#389	—	2	2	no	—
37	C₁₃×#389	C₂²	1	2	yes	—
38	C₁₃×#389	C₂²	1	2	yes	—
39	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#340	C₂²	1	2	yes	—
43	C₁₃×#336	C₂²	1	2	yes	—
44	C₁₃×#336	C₂²	1	2	yes	—
45	C₂²×Q₈×C₁₃	—	2	1	no	—
46	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
47	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₁₃	—	2	1	no	—
49	C₂³×C₄×C₁₃	—	2	2	no	—
50	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
53	C₁₃×C₄⋊Q₈	—	2	2	no	—
54	C₁₃×C₄⋊Q₈	D₄	1	4	yes	—
55	C₁₃×#125	—	2	4	no	—
56	C₁₃×#125	—	2	4	no	—
57	C₁₃×#125	—	2	2	no	—
58	C₁₃×#125	—	2	2	no	—
59	C₁₃×C₂²⋊Q₈	—	2	8	no	—
60	C₁₃×C₂²⋊Q₈	—	2	16	no	—
61	C₄×Q₈×C₁₃	—	2	2	no	—
62	C₄×Q₈×C₁₃	—	2	2	no	—
63	C₄×D₄×C₁₃	—	2	4	no	—
64	C₄×D₄×C₁₃	—	2	4	no	—
65	C₄×D₄×C₁₃	—	2	2	no	—
66	C₄×D₄×C₁₃	D₄	1	4	yes	—
67	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
73	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
75	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
76	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
82	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
83	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
84	C₂×C₄²×C₁₃	—	2	1	no	—
85	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
86	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
87	C₁₃×#107	—	2	2	no	—
88	C₁₃×#107	—	2	4	no	—
89	C₁₃×#106	—	2	2	no	—
90	C₁₃×#106	—	2	4	no	—
91	C₁₃×C₄⋊C₈	—	2	2	no	—
92	C₁₃×#102	—	2	2	no	—
93	C₁₃×#102	—	2	2	no	—
94	C₁₃×#102	Q₈	1	8	yes	complemented
95	C₁₃×#97	—	2	2	no	—
96	C₁₃×#95	—	2	1	no	—
97	C₁₃×#95	—	2	2	no	—
98	C₁₃×#95	—	2	2	no	—
99	#25845	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
100	C₂⁴×C₁₃	—	2	1	no	—
101	C₂×Q₈×C₁₃	—	2	2	no	—
102	C₂×Q₈×C₁₃	—	2	4	no	—
103	C₂×Q₈×C₁₃	—	4	2	no	—
104	C₂×Q₈×C₁₃	—	8	1	no	—
105	C₂×Q₈×C₁₃	—	8	1	no	—
106	C₂×D₄×C₁₃	—	2	1	no	—
107	C₂×D₄×C₁₃	—	2	2	no	—
108	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
109	C₂×D₄×C₁₃	C₂×Q₈	1	4	yes	—
110	C₂²×C₄×C₁₃	—	2	2	no	—
111	C₂²×C₄×C₁₃	—	2	1	no	—
112	C₂²×C₄×C₁₃	—	2	2	no	—
113	C₂²×C₄×C₁₃	—	2	8	no	—
114	C₂²×C₄×C₁₃	—	2	4	no	—
115	C₂²×C₄×C₁₃	—	2	1	no	—
116	C₂²×C₄×C₁₃	—	2	1	no	—
117	C₂²×C₄×C₁₃	—	4	4	no	—
118	C₂²×C₄×C₁₃	—	8	2	no	—
119	C₂²×C₄×C₁₃	—	8	2	no	—
120	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
125	C₂×C₈×C₁₃	—	2	2	no	—
126	C₂×C₈×C₁₃	—	2	2	no	—
127	C₂×C₈×C₁₃	—	2	1	no	—
128	C₂×C₈×C₁₃	—	2	1	no	—
129	C₂×C₈×C₁₃	—	2	2	no	—
130	C₂×C₈×C₁₃	—	2	2	no	—
131	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	—
132	C₁₃×C₄⋊C₄	—	2	8	no	—
133	C₁₃×C₄⋊C₄	—	2	8	no	—
134	C₁₃×C₄⋊C₄	—	2	2	no	—
135	C₁₃×C₄⋊C₄	—	2	4	no	—
136	C₁₃×C₄⋊C₄	—	2	4	no	—
137	C₁₃×C₄⋊C₄	—	2	1	no	—
138	C₁₃×C₄⋊C₄	—	2	2	no	—
139	C₁₃×C₄⋊C₄	—	2	2	no	—
140	C₁₃×C₄⋊C₄	—	2	1	no	—
141	C₁₃×C₄⋊C₄	—	2	1	no	—
142	C₁₃×C₄⋊C₄	—	2	1	no	—
143	C₁₃×C₄⋊C₄	—	2	1	no	—
144	C₁₃×C₄⋊C₄	—	4	4	no	—
145	C₁₃×C₄⋊C₄	—	4	2	no	—
146	C₁₃×C₄⋊C₄	—	4	2	no	—
147	C₁₃×C₄⋊C₄	—	8	2	no	—
148	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
149	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
150	C₁₃×C₄⋊C₄	C₂×Q₈	1	4	yes	—
151	C₁₃×C₂²⋊C₄	—	2	8	no	—
152	C₁₃×C₂²⋊C₄	—	2	4	no	—
153	C₄²×C₁₃	—	2	2	no	—
154	C₄²×C₁₃	—	2	2	no	—
155	C₄²×C₁₃	—	8	1	no	—
156	C₄²×C₁₃	C₂×D₄	1	2	yes	—
157	C₄²×C₁₃	C₂×D₄	1	2	yes	—
158	C₂×#554	C₂×C₁₃	1	1	yes	characteristic
159	C₂×#501	C₂×C₁₃	1	1	yes	characteristic, complemented
160	C₂×#478	C₂×C₁₃	1	1	yes	characteristic
161	#2584	C₂×C₁₃	1	1	yes	characteristic, complemented
162	#2059	C₂×C₁₃	1	2	yes	complemented
163	#2059	C₂×C₁₃	1	2	yes	complemented
164	#1988	C₂×C₁₃	1	1	yes	characteristic, complemented
165	#1985	C₂×C₁₃	1	1	yes	characteristic, complemented
166	#1864	C₂×C₁₃	1	2	yes	—
167	#1862	C₂×C₁₃	1	2	yes	—
168	#1762	C₂×C₁₃	1	1	yes	characteristic
169	C₂³×C₁₃	—	2	2	no	—
170	C₂³×C₁₃	—	2	4	no	—
171	C₂³×C₁₃	—	4	2	no	—
172	C₂³×C₁₃	—	4	1	no	—
173	C₂³×C₁₃	—	4	1	no	—
174	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
175	Q₈×C₁₃	—	4	4	no	—
176	Q₈×C₁₃	—	8	4	no	—
177	D₄×C₁₃	—	2	2	no	—
178	D₄×C₁₃	—	2	4	no	—
179	D₄×C₁₃	C₄⋊Q₈	1	4	yes	—
180	C₂×C₄×C₁₃	—	2	2	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	2	1	no	—
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	4	no	—
187	C₂×C₄×C₁₃	—	2	4	no	—
188	C₂×C₄×C₁₃	—	2	2	no	—
189	C₂×C₄×C₁₃	—	2	2	no	—
190	C₂×C₄×C₁₃	—	2	2	no	—
191	C₂×C₄×C₁₃	—	2	2	no	—
192	C₂×C₄×C₁₃	—	4	8	no	—
193	C₂×C₄×C₁₃	—	4	2	no	—
194	C₂×C₄×C₁₃	—	4	2	no	—
195	C₂×C₄×C₁₃	—	4	2	no	—
196	C₂×C₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	—	4	2	no	—
198	C₂×C₄×C₁₃	—	4	1	no	—
199	C₂×C₄×C₁₃	—	4	1	no	—
200	C₂×C₄×C₁₃	—	4	2	no	—
201	C₂×C₄×C₁₃	—	4	1	no	—
202	C₂×C₄×C₁₃	—	4	1	no	—
203	C₂×C₄×C₁₃	—	8	8	no	—
204	C₂×C₄×C₁₃	#120	1	2	yes	—
205	C₂×C₄×C₁₃	#120	1	2	yes	—
206	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
209	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
210	C₈×C₁₃	—	2	4	no	—
211	C₈×C₁₃	—	4	1	no	—
212	C₈×C₁₃	—	4	1	no	—
213	#554	—	2	4	no	—
214	#554	—	2	4	no	—
215	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
216	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
217	C₂×#125	C₂²×C₁₃	1	2	yes	—
218	C₂×C₂²⋊Q₈	—	2	1	no	—
219	C₂×C₂²⋊Q₈	—	2	2	no	—
220	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
221	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
222	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
223	C₂²×C₄⋊C₄	—	2	1	no	—
224	#501	—	2	4	no	—
225	#478	—	2	4	no	—
226	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
227	C₂×#107	C₂²×C₁₃	1	2	yes	—
228	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
229	C₂×#106	C₂²×C₁₃	1	2	yes	—
230	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
231	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
232	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
233	C₂×#102	C₂²×C₁₃	1	2	yes	—
234	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
235	#398	—	2	1	no	—
236	#395	—	2	1	no	—
237	#389	—	2	2	no	—
238	#389	C₂²×C₁₃	1	2	yes	—
239	#389	C₂²×C₁₃	1	2	yes	—
240	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
241	#340	C₂²×C₁₃	1	2	yes	—
242	#340	C₂²×C₁₃	1	2	yes	—
243	#340	C₂²×C₁₃	1	2	yes	—
244	#336	C₂²×C₁₃	1	2	yes	—
245	#336	C₂²×C₁₃	1	2	yes	—
246	C₂²×C₁₃	—	2	4	no	—
247	C₂²×C₁₃	—	4	4	no	—
248	C₂²×C₁₃	—	4	4	no	—
249	C₂²×C₁₃	—	4	2	no	—
250	C₂²×C₁₃	—	4	2	no	—
251	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
252	C₂²×C₁₃	D₄×Q₈	1	2	yes	—
253	C₂²×C₁₃	#575	1	2	yes	—
254	C₂²×C₁₃	#576	1	1	yes	characteristic
255	C₂²×C₁₃	#577	1	1	yes	characteristic
256	C₄×C₁₃	—	2	2	no	—
257	C₄×C₁₃	—	2	2	no	—
258	C₄×C₁₃	—	4	4	no	—
259	C₄×C₁₃	—	4	2	no	—
260	C₄×C₁₃	—	4	2	no	—
261	C₄×C₁₃	—	4	2	no	—
262	C₄×C₁₃	—	4	4	no	—
263	C₄×C₁₃	—	8	1	no	—
264	C₄×C₁₃	—	8	1	no	—
265	C₄×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
266	C₄×C₁₃	#536	1	1	yes	characteristic
267	C₄×C₁₃	D₄×Q₈	1	2	yes	—
268	C₂²×Q₈	—	2	1	no	—
269	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
270	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
271	C₂³×C₄	—	2	1	no	—
272	C₂³×C₄	—	2	2	no	—
273	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
274	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
275	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
276	C₄⋊Q₈	—	2	2	no	—
277	C₄⋊Q₈	D₄×C₁₃	1	4	yes	—
278	#125	—	2	4	no	—
279	#125	—	2	4	no	—
280	#125	—	2	2	no	—
281	#125	—	2	2	no	—
282	C₂²⋊Q₈	—	2	8	no	—
283	C₂²⋊Q₈	—	2	16	no	—
284	C₄×Q₈	—	2	2	no	—
285	C₄×Q₈	—	2	2	no	—
286	C₄×D₄	—	2	4	no	—
287	C₄×D₄	—	2	4	no	—
288	C₄×D₄	—	2	2	no	—
289	C₄×D₄	D₄×C₁₃	1	4	yes	—
290	C₂×C₄⋊C₄	—	2	8	no	—
291	C₂×C₄⋊C₄	—	2	2	no	—
292	C₂×C₄⋊C₄	—	2	1	no	—
293	C₂×C₄⋊C₄	—	2	2	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	2	2	no	—
297	C₂×C₄⋊C₄	—	2	2	no	—
298	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
299	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
300	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
301	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
302	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
304	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
305	C₂×C₂²⋊C₄	—	2	2	no	—
306	C₂×C₂²⋊C₄	—	2	1	no	—
307	C₂×C₄²	—	2	1	no	—
308	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
309	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
310	#107	—	2	2	no	—
311	#107	—	2	4	no	—
312	#106	—	2	2	no	—
313	#106	—	2	4	no	—
314	C₄⋊C₈	—	2	2	no	—
315	#102	—	2	2	no	—
316	#102	—	2	2	no	—
317	#102	Q₈×C₁₃	1	8	yes	complemented
318	#97	—	2	2	no	—
319	#95	—	2	1	no	—
320	#95	—	2	2	no	—
321	#95	—	2	2	no	—
322	C₂×C₁₃	—	4	4	no	—
323	C₂×C₁₃	#2434	1	1	yes	characteristic
324	C₂×C₁₃	#3005	1	1	yes	characteristic
325	C₂×C₁₃	#3012	1	1	yes	characteristic
326	C₂×C₁₃	#3388	1	2	yes	—
327	C₂×C₁₃	#3389	1	2	yes	—
328	C₂⁴	—	2	1	no	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	2	4	no	—
331	C₂×Q₈	—	4	2	no	—
332	C₂×Q₈	—	8	1	no	—
333	C₂×Q₈	—	8	1	no	—
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
337	C₂×D₄	C₂×Q₈×C₁₃	1	4	yes	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	8	no	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	4	4	no	—
346	C₂²×C₄	—	8	2	no	—
347	C₂²×C₄	—	8	2	no	—
348	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
349	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
350	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
352	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	C₂×Q₈×C₁₃	1	4	yes	—
360	C₄⋊C₄	—	2	8	no	—
361	C₄⋊C₄	—	2	8	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	4	no	—
364	C₄⋊C₄	—	2	4	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	4	4	no	—
373	C₄⋊C₄	—	4	2	no	—
374	C₄⋊C₄	—	4	2	no	—
375	C₄⋊C₄	—	8	2	no	—
376	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
377	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
378	C₄⋊C₄	C₂×Q₈×C₁₃	1	4	yes	—
379	C₂²⋊C₄	—	2	8	no	—
380	C₂²⋊C₄	—	2	4	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	2	2	no	—
383	C₄²	—	8	1	no	—
384	C₄²	C₂×D₄×C₁₃	1	2	yes	—
385	C₄²	C₂×D₄×C₁₃	1	2	yes	—
386	C₁₃	#25845	1	1	yes	characteristic, direct product factor, Sylow
387	C₂³	—	2	2	no	—
388	C₂³	—	2	4	no	—
389	C₂³	—	4	2	no	—
390	C₂³	—	4	1	no	—
391	C₂³	—	4	1	no	—
392	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
393	Q₈	—	4	4	no	—
394	Q₈	—	8	4	no	—
395	D₄	—	2	2	no	—
396	D₄	—	2	4	no	—
397	D₄	C₁₃×C₄⋊Q₈	1	4	yes	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	4	8	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	8	8	no	—
422	C₂×C₄	C₁₃×#120	1	2	yes	—
423	C₂×C₄	C₁₃×#120	1	2	yes	—
424	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
425	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
426	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
427	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
428	C₈	—	2	4	no	—
429	C₈	—	4	1	no	—
430	C₈	—	4	1	no	—
431	C₂²	—	2	4	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	4	no	—
434	C₂²	—	4	4	no	—
435	C₂²	—	4	2	no	—
436	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
437	C₂²	D₄×Q₈×C₁₃	1	2	yes	—
438	C₂²	C₁₃×#575	1	2	yes	—
439	C₂²	C₁₃×#576	1	1	yes	characteristic
440	C₂²	C₁₃×#577	1	1	yes	characteristic
441	C₄	—	2	2	no	—
442	C₄	—	2	2	no	—
443	C₄	—	4	2	no	—
444	C₄	—	4	4	no	—
445	C₄	—	4	4	no	—
446	C₄	—	4	2	no	—
447	C₄	—	4	2	no	—
448	C₄	—	8	1	no	—
449	C₄	—	8	1	no	—
450	C₄	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
451	C₄	C₁₃×#536	1	1	yes	characteristic
452	C₄	D₄×Q₈×C₁₃	1	2	yes	—
453	C₂	—	4	4	no	—
454	C₂	C₁₃×#2434	1	1	yes	characteristic
455	C₂	C₁₃×#3005	1	1	yes	characteristic
456	C₂	C₁₃×#3012	1	1	yes	characteristic
457	C₂	C₁₃×#3388	1	2	yes	—
458	C₂	C₁₃×#3389	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#501	C₂	semidirect
4. C₁₃×#2584	C₂	semidirect
5. C₁₃×#2059	C₂	semidirect
6. C₁₃×#2059	C₂	semidirect
7. C₁₃×#1988	C₂	semidirect
8. C₁₃×#1985	C₂	semidirect
94. C₁₃×#102	Q₈	semidirect
99. #25845	C₁₃	direct (N × H)
159. C₂×#501	C₂×C₁₃	semidirect
161. #2584	C₂×C₁₃	semidirect
162. #2059	C₂×C₁₃	semidirect
163. #2059	C₂×C₁₃	semidirect
164. #1988	C₂×C₁₃	semidirect
165. #1985	C₂×C₁₃	semidirect
317. #102	Q₈×C₁₃	semidirect
386. C₁₃	#25845	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×#554	2
C₂×C₁₃×#501	2
C₂×C₁₃×#478	2
C₁₃×#2584	2
C₁₃×#2059	2
C₁₃×#1988	2
C₁₃×#1985	2
C₁₃×#1864	2
C₁₃×#1862	2
C₁₃×#1762	2
#25845	13

Subgroups — C13×#25845 #15712184

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25845 #15712184