Subgroups — C₁₃×#25057 #15711396

Order 3328.

722 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2538	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2355	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2092	C₂	1	2	yes	maximal
4	C₁₃×#2085	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1984	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1948	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1925	C₂	1	2	yes	maximal
8	C₁₃×#1921	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1845	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1802	C₂	1	1	yes	maximal, characteristic
11	C₄×C₁₃×#102	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
13	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#107	C₂²	1	2	yes	—
16	C₂×C₁₃×#107	C₂²	1	2	yes	—
17	C₂×C₁₃×#106	C₂²	1	2	yes	—
18	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#102	C₂²	1	2	yes	—
21	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₁₃×#396	—	2	2	no	—
24	C₁₃×#391	—	2	1	no	—
25	C₁₃×#390	C₂²	1	2	yes	—
26	C₁₃×#389	C₂²	1	2	yes	—
27	C₁₃×#387	—	2	2	no	—
28	C₁₃×#384	C₂²	1	1	yes	characteristic
29	C₁₃×#384	C₂²	1	1	yes	characteristic
30	C₁₃×#382	C₂²	1	2	yes	—
31	C₁₃×#380	—	2	1	no	—
32	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
33	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
35	C₁₃×#340	C₂²	1	1	yes	characteristic
36	C₁₃×#340	C₂²	1	1	yes	characteristic
37	C₁₃×#340	C₂²	1	2	yes	—
38	C₁₃×#340	C₂²	1	2	yes	—
39	C₁₃×#336	C₂²	1	2	yes	—
40	C₁₃×#336	C₂²	1	2	yes	—
41	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
42	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₁₃	—	2	1	no	—
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×C₂²⋊Q₈	—	4	4	no	—
48	C₄×Q₈×C₁₃	—	2	2	no	—
49	C₄×Q₈×C₁₃	—	2	2	no	—
50	C₄×D₄×C₁₃	—	2	2	no	—
51	C₄×D₄×C₁₃	—	2	2	no	—
52	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
57	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
58	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
59	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
64	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
65	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
66	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
67	C₂×C₄²×C₁₃	—	2	1	no	—
68	C₂×C₄²×C₁₃	—	2	2	no	—
69	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
70	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
71	C₁₃×#107	—	2	4	no	—
72	C₁₃×#107	—	4	2	no	—
73	C₁₃×#106	—	4	2	no	—
74	C₁₃×C₄⋊C₈	—	2	2	no	—
75	C₁₃×#102	—	2	2	no	—
76	C₁₃×#102	—	4	2	no	—
77	C₁₃×#102	Q₈	1	4	yes	complemented
78	C₄×C₈×C₁₃	—	2	2	no	—
79	C₁₃×#95	—	2	2	no	—
80	C₁₃×#95	—	2	1	no	—
81	C₁₃×#95	—	2	2	no	—
82	C₁₃×#95	—	2	2	no	—
83	C₁₃×#95	—	2	2	no	—
84	#25057	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
85	C₂⁴×C₁₃	—	2	1	no	—
86	C₂×Q₈×C₁₃	—	2	2	no	—
87	C₂×Q₈×C₁₃	—	2	2	no	—
88	C₂×Q₈×C₁₃	—	2	2	no	—
89	C₂×D₄×C₁₃	—	2	1	no	—
90	C₂×D₄×C₁₃	—	2	1	no	—
91	C₂×D₄×C₁₃	—	2	1	no	—
92	C₂×D₄×C₁₃	—	2	1	no	—
93	C₂×D₄×C₁₃	—	2	1	no	—
94	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
95	C₂²×C₄×C₁₃	—	2	1	no	—
96	C₂²×C₄×C₁₃	—	2	1	no	—
97	C₂²×C₄×C₁₃	—	2	2	no	—
98	C₂²×C₄×C₁₃	—	2	1	no	—
99	C₂²×C₄×C₁₃	—	2	2	no	—
100	C₂²×C₄×C₁₃	—	4	2	no	—
101	C₂²×C₄×C₁₃	—	4	2	no	—
102	C₂²×C₄×C₁₃	—	4	2	no	—
103	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
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	1	yes	characteristic
107	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
108	C₂×C₈×C₁₃	—	2	1	no	—
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	2	no	—
113	C₂×C₈×C₁₃	—	2	2	no	—
114	C₂×C₈×C₁₃	—	2	2	no	—
115	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
116	C₂×C₈×C₁₃	#41	1	2	yes	—
117	C₁₃×C₄⋊C₄	—	2	2	no	—
118	C₁₃×C₄⋊C₄	—	2	4	no	—
119	C₁₃×C₄⋊C₄	—	2	1	no	—
120	C₁₃×C₄⋊C₄	—	2	1	no	—
121	C₁₃×C₄⋊C₄	—	2	2	no	—
122	C₁₃×C₄⋊C₄	—	2	2	no	—
123	C₁₃×C₄⋊C₄	—	2	1	no	—
124	C₁₃×C₄⋊C₄	—	2	1	no	—
125	C₁₃×C₄⋊C₄	—	2	2	no	—
126	C₁₃×C₄⋊C₄	—	2	1	no	—
127	C₁₃×C₄⋊C₄	—	2	2	no	—
128	C₁₃×C₄⋊C₄	—	4	4	no	—
129	C₁₃×C₄⋊C₄	—	4	2	no	—
130	C₁₃×C₄⋊C₄	—	4	2	no	—
131	C₁₃×C₄⋊C₄	—	8	1	no	—
132	C₁₃×C₄⋊C₄	—	8	1	no	—
133	C₁₃×C₄⋊C₄	C₂×Q₈	1	2	yes	—
134	C₁₃×C₂²⋊C₄	—	4	4	no	—
135	C₁₃×C₂²⋊C₄	—	4	2	no	—
136	C₁₃×C₂²⋊C₄	—	8	2	no	—
137	C₄²×C₁₃	—	2	2	no	—
138	C₄²×C₁₃	—	2	2	no	—
139	C₄²×C₁₃	—	4	2	no	—
140	C₄²×C₁₃	—	8	2	no	—
141	C₄²×C₁₃	#41	1	2	yes	—
142	C₄²×C₁₃	#41	1	2	yes	—
143	#2538	C₂×C₁₃	1	1	yes	characteristic
144	#2355	C₂×C₁₃	1	1	yes	characteristic, complemented
145	#2092	C₂×C₁₃	1	2	yes	—
146	#2085	C₂×C₁₃	1	2	yes	complemented
147	#1984	C₂×C₁₃	1	1	yes	characteristic, complemented
148	#1948	C₂×C₁₃	1	1	yes	characteristic, complemented
149	#1925	C₂×C₁₃	1	2	yes	—
150	#1921	C₂×C₁₃	1	2	yes	complemented
151	#1845	C₂×C₁₃	1	1	yes	characteristic, complemented
152	#1802	C₂×C₁₃	1	1	yes	characteristic
153	C₄×#102	C₂×C₁₃	1	1	yes	characteristic
154	C₂³×C₁₃	—	2	2	no	—
155	C₂³×C₁₃	—	4	1	no	—
156	C₂³×C₁₃	—	4	1	no	—
157	C₂³×C₁₃	—	4	1	no	—
158	C₂³×C₁₃	—	4	1	no	—
159	C₂³×C₁₃	—	4	1	no	—
160	C₂³×C₁₃	—	4	1	no	—
161	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
162	Q₈×C₁₃	—	4	4	no	—
163	D₄×C₁₃	—	2	2	no	—
164	D₄×C₁₃	—	2	2	no	—
165	D₄×C₁₃	—	4	1	no	—
166	D₄×C₁₃	—	4	1	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	2	no	—
181	C₂×C₄×C₁₃	—	4	2	no	—
182	C₂×C₄×C₁₃	—	4	1	no	—
183	C₂×C₄×C₁₃	—	4	1	no	—
184	C₂×C₄×C₁₃	—	4	2	no	—
185	C₂×C₄×C₁₃	—	4	1	no	—
186	C₂×C₄×C₁₃	—	4	2	no	—
187	C₂×C₄×C₁₃	—	4	2	no	—
188	C₂×C₄×C₁₃	—	4	2	no	—
189	C₂×C₄×C₁₃	—	4	1	no	—
190	C₂×C₄×C₁₃	—	8	4	no	—
191	C₂×C₄×C₁₃	#123	1	2	yes	—
192	C₂×C₄×C₁₃	#123	1	2	yes	—
193	C₂×C₄×C₁₃	#135	1	2	yes	—
194	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
195	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
196	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
200	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
201	C₈×C₁₃	—	2	2	no	—
202	C₈×C₁₃	—	2	2	no	—
203	C₈×C₁₃	—	4	2	no	—
204	C₂×C₂²⋊Q₈	—	2	1	no	—
205	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
206	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
207	C₂×#107	C₂²×C₁₃	1	2	yes	—
208	C₂×#107	C₂²×C₁₃	1	2	yes	—
209	C₂×#106	C₂²×C₁₃	1	2	yes	—
210	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
211	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
212	C₂×#102	C₂²×C₁₃	1	2	yes	—
213	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
214	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
215	#396	—	2	2	no	—
216	#391	—	2	1	no	—
217	#390	C₂²×C₁₃	1	2	yes	—
218	#389	C₂²×C₁₃	1	2	yes	—
219	#387	—	2	2	no	—
220	#384	C₂²×C₁₃	1	1	yes	characteristic
221	#384	C₂²×C₁₃	1	1	yes	characteristic
222	#382	C₂²×C₁₃	1	2	yes	—
223	#380	—	2	1	no	—
224	C₄×C₄⋊C₄	—	2	1	no	—
225	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
226	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
227	#340	C₂²×C₁₃	1	2	yes	—
228	#340	C₂²×C₁₃	1	1	yes	characteristic
229	#340	C₂²×C₁₃	1	1	yes	characteristic
230	#340	C₂²×C₁₃	1	2	yes	—
231	#336	C₂²×C₁₃	1	2	yes	—
232	#336	C₂²×C₁₃	1	2	yes	—
233	C₂²×C₁₃	—	4	2	no	—
234	C₂²×C₁₃	—	4	2	no	—
235	C₂²×C₁₃	—	4	2	no	—
236	C₂²×C₁₃	—	8	1	no	—
237	C₂²×C₁₃	—	8	1	no	—
238	C₂²×C₁₃	—	8	1	no	—
239	C₂²×C₁₃	—	8	1	no	—
240	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
241	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
242	C₂²×C₁₃	#550	1	1	yes	characteristic
243	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
244	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
245	C₂²×C₁₃	#576	1	1	yes	characteristic
246	C₂²×C₁₃	#578	1	1	yes	characteristic
247	C₄×C₁₃	—	2	2	no	—
248	C₄×C₁₃	—	4	2	no	—
249	C₄×C₁₃	—	4	2	no	—
250	C₄×C₁₃	—	4	2	no	—
251	C₄×C₁₃	—	8	1	no	—
252	C₄×C₁₃	—	8	1	no	—
253	C₄×C₁₃	—	8	2	no	—
254	C₄×C₁₃	—	8	2	no	—
255	C₄×C₁₃	#482	1	4	yes	—
256	C₄×C₁₃	#533	1	1	yes	characteristic
257	C₄×C₁₃	#542	1	1	yes	characteristic
258	C₄×C₁₃	#552	1	1	yes	characteristic
259	C₄×C₁₃	#554	1	1	yes	characteristic
260	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
261	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
262	C₂³×C₄	—	2	1	no	—
263	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
264	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
265	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
266	C₂²⋊Q₈	—	4	4	no	—
267	C₄×Q₈	—	2	2	no	—
268	C₄×Q₈	—	2	2	no	—
269	C₄×D₄	—	2	2	no	—
270	C₄×D₄	—	2	2	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	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	D₄×C₁₃	1	1	yes	characteristic
277	C₂×C₄⋊C₄	D₄×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	2	yes	—
281	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
282	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
283	C₂×C₂²⋊C₄	—	2	1	no	—
284	C₂×C₂²⋊C₄	—	2	2	no	—
285	C₂×C₂²⋊C₄	—	2	2	no	—
286	C₂×C₄²	—	2	1	no	—
287	C₂×C₄²	—	2	2	no	—
288	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
289	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
290	#107	—	2	4	no	—
291	#107	—	4	2	no	—
292	#106	—	4	2	no	—
293	C₄⋊C₈	—	2	2	no	—
294	#102	—	2	2	no	—
295	#102	—	4	2	no	—
296	#102	Q₈×C₁₃	1	4	yes	complemented
297	C₄×C₈	—	2	2	no	—
298	#95	—	2	2	no	—
299	#95	—	2	1	no	—
300	#95	—	2	2	no	—
301	#95	—	2	2	no	—
302	#95	—	2	2	no	—
303	C₂×C₁₃	—	8	2	no	—
304	C₂×C₁₃	#2423	1	1	yes	characteristic
305	C₂×C₁₃	C₂×#482	1	1	yes	characteristic
306	C₂×C₁₃	#3098	1	1	yes	characteristic
307	C₂×C₁₃	#3380	1	1	yes	characteristic
308	C₂×C₁₃	#3386	1	1	yes	characteristic
309	C₂×C₁₃	#3393	1	1	yes	characteristic
310	C₂×C₁₃	#3399	1	1	yes	characteristic
311	C₂⁴	—	2	1	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	2	2	no	—
314	C₂×Q₈	—	2	2	no	—
315	C₂×D₄	—	2	1	no	—
316	C₂×D₄	—	2	1	no	—
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	4	2	no	—
327	C₂²×C₄	—	4	2	no	—
328	C₂²×C₄	—	4	2	no	—
329	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
330	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
331	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
333	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
342	C₂×C₈	C₁₃×#41	1	2	yes	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	4	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	4	4	no	—
355	C₄⋊C₄	—	4	2	no	—
356	C₄⋊C₄	—	4	2	no	—
357	C₄⋊C₄	—	8	1	no	—
358	C₄⋊C₄	—	8	1	no	—
359	C₄⋊C₄	C₂×Q₈×C₁₃	1	2	yes	—
360	C₂²⋊C₄	—	4	4	no	—
361	C₂²⋊C₄	—	4	2	no	—
362	C₂²⋊C₄	—	8	2	no	—
363	C₄²	—	2	2	no	—
364	C₄²	—	2	2	no	—
365	C₄²	—	4	2	no	—
366	C₄²	—	8	2	no	—
367	C₄²	C₁₃×#41	1	2	yes	—
368	C₄²	C₁₃×#41	1	2	yes	—
369	C₁₃	#25057	1	1	yes	characteristic, direct product factor, Sylow
370	C₂³	—	2	2	no	—
371	C₂³	—	4	1	no	—
372	C₂³	—	4	1	no	—
373	C₂³	—	4	1	no	—
374	C₂³	—	4	1	no	—
375	C₂³	—	4	1	no	—
376	C₂³	—	4	1	no	—
377	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
378	Q₈	—	4	4	no	—
379	D₄	—	2	2	no	—
380	D₄	—	2	2	no	—
381	D₄	—	4	1	no	—
382	D₄	—	4	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	8	4	no	—
407	C₂×C₄	C₁₃×#123	1	2	yes	—
408	C₂×C₄	C₁₃×#123	1	2	yes	—
409	C₂×C₄	C₁₃×#135	1	2	yes	—
410	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
411	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
412	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
413	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
414	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
415	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
416	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
417	C₈	—	2	2	no	—
418	C₈	—	2	2	no	—
419	C₈	—	4	2	no	—
420	C₂²	—	4	2	no	—
421	C₂²	—	4	2	no	—
422	C₂²	—	4	2	no	—
423	C₂²	—	8	1	no	—
424	C₂²	—	8	1	no	—
425	C₂²	—	8	1	no	—
426	C₂²	—	8	1	no	—
427	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
428	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
429	C₂²	C₁₃×#550	1	1	yes	characteristic
430	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
431	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
432	C₂²	C₁₃×#576	1	1	yes	characteristic
433	C₂²	C₁₃×#578	1	1	yes	characteristic
434	C₄	—	2	2	no	—
435	C₄	—	4	2	no	—
436	C₄	—	4	2	no	—
437	C₄	—	4	2	no	—
438	C₄	—	8	1	no	—
439	C₄	—	8	1	no	—
440	C₄	—	8	2	no	—
441	C₄	—	8	2	no	—
442	C₄	C₁₃×#482	1	4	yes	—
443	C₄	C₁₃×#533	1	1	yes	characteristic
444	C₄	C₁₃×#542	1	1	yes	characteristic
445	C₄	C₁₃×#552	1	1	yes	characteristic
446	C₄	C₁₃×#554	1	1	yes	characteristic
447	C₂	—	8	2	no	—
448	C₂	C₁₃×#2423	1	1	yes	characteristic
449	C₂	C₂×C₁₃×#482	1	1	yes	characteristic
450	C₂	C₁₃×#3098	1	1	yes	characteristic
451	C₂	C₁₃×#3380	1	1	yes	characteristic
452	C₂	C₁₃×#3386	1	1	yes	characteristic
453	C₂	C₁₃×#3393	1	1	yes	characteristic
454	C₂	C₁₃×#3399	1	1	yes	characteristic

	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. C₁₃×#2355	C₂	semidirect
4. C₁₃×#2085	C₂	semidirect
5. C₁₃×#1984	C₂	semidirect
6. C₁₃×#1948	C₂	semidirect
8. C₁₃×#1921	C₂	semidirect
9. C₁₃×#1845	C₂	semidirect
77. C₁₃×#102	Q₈	semidirect
84. #25057	C₁₃	direct (N × H)
144. #2355	C₂×C₁₃	semidirect
146. #2085	C₂×C₁₃	semidirect
147. #1984	C₂×C₁₃	semidirect
148. #1948	C₂×C₁₃	semidirect
150. #1921	C₂×C₁₃	semidirect
151. #1845	C₂×C₁₃	semidirect
296. #102	Q₈×C₁₃	semidirect
369. C₁₃	#25057	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×#2538	2
C₁₃×#2355	2
C₁₃×#2092	2
C₁₃×#2085	2
C₁₃×#1984	2
C₁₃×#1948	2
C₁₃×#1925	2
C₁₃×#1921	2
C₁₃×#1845	2
C₁₃×#1802	2
C₄×C₁₃×#102	2
#25057	13

Subgroups — C13×#25057 #15711396

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25057 #15711396