Subgroups — C₁₃×#25844 #15712183

Order 3328.

1224 conjugacy classes of subgroups.

The subgroup lattice has 468 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×#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×#2058	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2057	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1987	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	C₂³×Q₈×C₁₃	—	2	1	no	—
13	D₄×Q₈×C₁₃	—	2	4	no	—
14	D₄×Q₈×C₁₃	—	2	4	no	—
15	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
19	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
20	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
22	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
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	8	no	—
46	C₂²×Q₈×C₁₃	—	2	1	no	—
47	C₂²×Q₈×C₁₃	—	2	2	no	—
48	C₂²×Q₈×C₁₃	—	4	8	no	—
49	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
50	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₃	—	2	2	no	—
52	C₂³×C₄×C₁₃	—	2	1	no	—
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
56	C₁₃×C₄⋊Q₈	—	2	4	no	—
57	C₁₃×C₄⋊Q₈	—	2	4	no	—
58	C₁₃×C₄⋊Q₈	—	2	2	no	—
59	C₁₃×C₄⋊Q₈	D₄	1	4	yes	—
60	C₁₃×#125	—	2	2	no	—
61	C₁₃×#125	—	2	2	no	—
62	C₁₃×C₂²⋊Q₈	—	2	8	no	—
63	C₁₃×C₂²⋊Q₈	—	2	16	no	—
64	C₄×Q₈×C₁₃	—	2	2	no	—
65	C₄×Q₈×C₁₃	—	2	2	no	—
66	C₄×D₄×C₁₃	—	2	4	no	—
67	C₄×D₄×C₁₃	—	2	4	no	—
68	C₄×D₄×C₁₃	—	2	2	no	—
69	C₄×D₄×C₁₃	D₄	1	4	yes	—
70	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
73	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
76	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
77	C₂×C₁₃×C₄⋊C₄	D₄	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	1	yes	characteristic
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
83	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
84	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
85	C₂×C₄²×C₁₃	—	2	1	no	—
86	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
87	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
88	C₁₃×#107	—	2	2	no	—
89	C₁₃×#107	—	2	4	no	—
90	C₁₃×#106	—	2	2	no	—
91	C₁₃×#106	—	2	4	no	—
92	C₁₃×C₄⋊C₈	—	2	2	no	—
93	C₁₃×#102	—	2	2	no	—
94	C₁₃×#102	—	2	2	no	—
95	C₁₃×#102	Q₈	1	8	yes	complemented
96	C₁₃×#97	—	2	2	no	—
97	C₁₃×#95	—	2	1	no	—
98	C₁₃×#95	—	2	2	no	—
99	C₁₃×#95	—	2	2	no	—
100	#25844	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
101	C₂⁴×C₁₃	—	2	1	no	—
102	C₂×Q₈×C₁₃	—	2	8	no	—
103	C₂×Q₈×C₁₃	—	2	2	no	—
104	C₂×Q₈×C₁₃	—	2	4	no	—
105	C₂×Q₈×C₁₃	—	2	4	no	—
106	C₂×Q₈×C₁₃	—	4	4	no	—
107	C₂×Q₈×C₁₃	—	4	4	no	—
108	C₂×Q₈×C₁₃	—	4	32	no	—
109	C₂×Q₈×C₁₃	—	4	4	no	—
110	C₂×D₄×C₁₃	—	2	1	no	—
111	C₂×D₄×C₁₃	—	2	2	no	—
112	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
113	C₂×D₄×C₁₃	C₂×Q₈	1	4	yes	—
114	C₂²×C₄×C₁₃	—	2	8	no	—
115	C₂²×C₄×C₁₃	—	2	2	no	—
116	C₂²×C₄×C₁₃	—	2	2	no	—
117	C₂²×C₄×C₁₃	—	2	1	no	—
118	C₂²×C₄×C₁₃	—	2	4	no	—
119	C₂²×C₄×C₁₃	—	2	1	no	—
120	C₂²×C₄×C₁₃	—	2	1	no	—
121	C₂²×C₄×C₁₃	—	4	4	no	—
122	C₂²×C₄×C₁₃	—	4	4	no	—
123	C₂²×C₄×C₁₃	—	4	4	no	—
124	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
129	C₂×C₈×C₁₃	—	2	2	no	—
130	C₂×C₈×C₁₃	—	2	2	no	—
131	C₂×C₈×C₁₃	—	2	1	no	—
132	C₂×C₈×C₁₃	—	2	1	no	—
133	C₂×C₈×C₁₃	—	2	2	no	—
134	C₂×C₈×C₁₃	—	2	2	no	—
135	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	complemented
136	C₁₃×C₄⋊C₄	—	2	8	no	—
137	C₁₃×C₄⋊C₄	—	2	4	no	—
138	C₁₃×C₄⋊C₄	—	2	4	no	—
139	C₁₃×C₄⋊C₄	—	2	2	no	—
140	C₁₃×C₄⋊C₄	—	2	2	no	—
141	C₁₃×C₄⋊C₄	—	2	1	no	—
142	C₁₃×C₄⋊C₄	—	2	2	no	—
143	C₁₃×C₄⋊C₄	—	2	1	no	—
144	C₁₃×C₄⋊C₄	—	2	1	no	—
145	C₁₃×C₄⋊C₄	—	2	1	no	—
146	C₁₃×C₄⋊C₄	—	2	1	no	—
147	C₁₃×C₄⋊C₄	—	4	2	no	—
148	C₁₃×C₄⋊C₄	—	4	2	no	—
149	C₁₃×C₄⋊C₄	—	4	4	no	—
150	C₁₃×C₄⋊C₄	—	8	2	no	—
151	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
152	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
153	C₁₃×C₄⋊C₄	C₂×Q₈	1	4	yes	complemented
154	C₁₃×C₂²⋊C₄	—	2	8	no	—
155	C₁₃×C₂²⋊C₄	—	2	4	no	—
156	C₄²×C₁₃	—	2	2	no	—
157	C₄²×C₁₃	—	2	2	no	—
158	C₄²×C₁₃	—	8	1	no	—
159	C₄²×C₁₃	C₂×D₄	1	2	yes	—
160	C₄²×C₁₃	C₂×D₄	1	2	yes	—
161	C₂×D₄×Q₈	C₂×C₁₃	1	1	yes	characteristic
162	C₂×#501	C₂×C₁₃	1	1	yes	characteristic, complemented
163	C₂×#478	C₂×C₁₃	1	1	yes	characteristic
164	#2584	C₂×C₁₃	1	1	yes	characteristic, complemented
165	#2058	C₂×C₁₃	1	2	yes	complemented
166	#2057	C₂×C₁₃	1	2	yes	complemented
167	#1987	C₂×C₁₃	1	1	yes	characteristic, complemented
168	#1985	C₂×C₁₃	1	1	yes	characteristic, complemented
169	#1864	C₂×C₁₃	1	2	yes	—
170	#1862	C₂×C₁₃	1	2	yes	—
171	#1762	C₂×C₁₃	1	1	yes	characteristic
172	C₂³×C₁₃	—	2	2	no	—
173	C₂³×C₁₃	—	2	4	no	—
174	C₂³×C₁₃	—	4	2	no	—
175	C₂³×C₁₃	—	4	1	no	—
176	C₂³×C₁₃	—	4	1	no	—
177	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
178	Q₈×C₁₃	—	2	8	no	—
179	Q₈×C₁₃	—	4	8	no	—
180	Q₈×C₁₃	—	4	16	no	—
181	D₄×C₁₃	—	2	2	no	—
182	D₄×C₁₃	—	2	4	no	—
183	D₄×C₁₃	C₄⋊Q₈	1	4	yes	—
184	C₂×C₄×C₁₃	—	2	2	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	2	no	—
190	C₂×C₄×C₁₃	—	2	4	no	—
191	C₂×C₄×C₁₃	—	2	2	no	—
192	C₂×C₄×C₁₃	—	2	4	no	—
193	C₂×C₄×C₁₃	—	2	2	no	—
194	C₂×C₄×C₁₃	—	2	2	no	—
195	C₂×C₄×C₁₃	—	4	8	no	—
196	C₂×C₄×C₁₃	—	4	16	no	—
197	C₂×C₄×C₁₃	—	4	2	no	—
198	C₂×C₄×C₁₃	—	4	2	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	1	no	—
203	C₂×C₄×C₁₃	—	4	1	no	—
204	C₂×C₄×C₁₃	—	4	2	no	—
205	C₂×C₄×C₁₃	—	4	1	no	—
206	C₂×C₄×C₁₃	—	4	1	no	—
207	C₂×C₄×C₁₃	#120	1	2	yes	—
208	C₂×C₄×C₁₃	#120	1	2	yes	—
209	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
210	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
213	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
214	C₈×C₁₃	—	2	4	no	—
215	C₈×C₁₃	—	4	1	no	—
216	C₈×C₁₃	—	4	1	no	—
217	C₂³×Q₈	—	2	1	no	—
218	D₄×Q₈	—	2	4	no	—
219	D₄×Q₈	—	2	4	no	—
220	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
221	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
222	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
223	C₂×C₂²⋊Q₈	—	2	2	no	—
224	C₂×C₂²⋊Q₈	—	2	1	no	—
225	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
226	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
227	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
228	#501	—	2	4	no	—
229	#478	—	2	4	no	—
230	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
231	C₂×#107	C₂²×C₁₃	1	2	yes	—
232	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
233	C₂×#106	C₂²×C₁₃	1	2	yes	—
234	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
235	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
236	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
237	C₂×#102	C₂²×C₁₃	1	2	yes	—
238	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
239	#398	—	2	1	no	—
240	#395	—	2	1	no	—
241	#389	—	2	2	no	—
242	#389	C₂²×C₁₃	1	2	yes	—
243	#389	C₂²×C₁₃	1	2	yes	—
244	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
245	#340	C₂²×C₁₃	1	2	yes	—
246	#340	C₂²×C₁₃	1	2	yes	—
247	#340	C₂²×C₁₃	1	2	yes	—
248	#336	C₂²×C₁₃	1	2	yes	—
249	#336	C₂²×C₁₃	1	2	yes	—
250	C₂²×C₁₃	—	2	4	no	—
251	C₂²×C₁₃	—	4	4	no	—
252	C₂²×C₁₃	—	4	4	no	—
253	C₂²×C₁₃	—	4	2	no	—
254	C₂²×C₁₃	—	4	2	no	—
255	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
256	C₂²×C₁₃	D₄×Q₈	1	2	yes	—
257	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
258	C₂²×C₁₃	#577	1	1	yes	characteristic
259	C₂²×C₁₃	#578	1	1	yes	characteristic
260	C₄×C₁₃	—	2	2	no	—
261	C₄×C₁₃	—	2	4	no	—
262	C₄×C₁₃	—	2	2	no	—
263	C₄×C₁₃	—	4	4	no	—
264	C₄×C₁₃	—	4	4	no	—
265	C₄×C₁₃	—	4	2	no	—
266	C₄×C₁₃	—	4	2	no	—
267	C₄×C₁₃	—	8	1	no	—
268	C₄×C₁₃	—	8	1	no	—
269	C₄×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
270	C₄×C₁₃	#536	1	1	yes	characteristic
271	C₄×C₁₃	D₄×Q₈	1	2	yes	—
272	C₂²×Q₈	—	2	8	no	—
273	C₂²×Q₈	—	2	1	no	—
274	C₂²×Q₈	—	2	2	no	—
275	C₂²×Q₈	—	4	8	no	—
276	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
277	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
278	C₂³×C₄	—	2	2	no	—
279	C₂³×C₄	—	2	1	no	—
280	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
281	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
282	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
283	C₄⋊Q₈	—	2	4	no	—
284	C₄⋊Q₈	—	2	4	no	—
285	C₄⋊Q₈	—	2	2	no	—
286	C₄⋊Q₈	D₄×C₁₃	1	4	yes	—
287	#125	—	2	2	no	—
288	#125	—	2	2	no	—
289	C₂²⋊Q₈	—	2	8	no	—
290	C₂²⋊Q₈	—	2	16	no	—
291	C₄×Q₈	—	2	2	no	—
292	C₄×Q₈	—	2	2	no	—
293	C₄×D₄	—	2	4	no	—
294	C₄×D₄	—	2	4	no	—
295	C₄×D₄	—	2	2	no	—
296	C₄×D₄	D₄×C₁₃	1	4	yes	—
297	C₂×C₄⋊C₄	—	2	2	no	—
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	—	2	2	no	—
302	C₂×C₄⋊C₄	—	2	2	no	—
303	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
304	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
305	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
306	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
307	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
308	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
309	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
310	C₂×C₂²⋊C₄	—	2	2	no	—
311	C₂×C₂²⋊C₄	—	2	1	no	—
312	C₂×C₄²	—	2	1	no	—
313	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
314	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
315	#107	—	2	2	no	—
316	#107	—	2	4	no	—
317	#106	—	2	2	no	—
318	#106	—	2	4	no	—
319	C₄⋊C₈	—	2	2	no	—
320	#102	—	2	2	no	—
321	#102	—	2	2	no	—
322	#102	Q₈×C₁₃	1	8	yes	complemented
323	#97	—	2	2	no	—
324	#95	—	2	1	no	—
325	#95	—	2	2	no	—
326	#95	—	2	2	no	—
327	C₂×C₁₃	—	4	4	no	—
328	C₂×C₁₃	#2434	1	1	yes	characteristic
329	C₂×C₁₃	#3003	1	1	yes	characteristic
330	C₂×C₁₃	#3013	1	1	yes	characteristic
331	C₂×C₁₃	#3384	1	2	yes	—
332	C₂×C₁₃	#3386	1	2	yes	—
333	C₂⁴	—	2	1	no	—
334	C₂×Q₈	—	2	8	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	4	no	—
337	C₂×Q₈	—	2	4	no	—
338	C₂×Q₈	—	4	4	no	—
339	C₂×Q₈	—	4	4	no	—
340	C₂×Q₈	—	4	32	no	—
341	C₂×Q₈	—	4	4	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
345	C₂×D₄	C₂×Q₈×C₁₃	1	4	yes	—
346	C₂²×C₄	—	2	8	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	4	4	no	—
354	C₂²×C₄	—	4	4	no	—
355	C₂²×C₄	—	4	4	no	—
356	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
357	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
358	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
360	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	C₂×Q₈×C₁₃	1	4	yes	complemented
368	C₄⋊C₄	—	2	8	no	—
369	C₄⋊C₄	—	2	4	no	—
370	C₄⋊C₄	—	2	4	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	4	2	no	—
380	C₄⋊C₄	—	4	2	no	—
381	C₄⋊C₄	—	4	4	no	—
382	C₄⋊C₄	—	8	2	no	—
383	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
384	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
385	C₄⋊C₄	C₂×Q₈×C₁₃	1	4	yes	complemented
386	C₂²⋊C₄	—	2	8	no	—
387	C₂²⋊C₄	—	2	4	no	—
388	C₄²	—	2	2	no	—
389	C₄²	—	2	2	no	—
390	C₄²	—	8	1	no	—
391	C₄²	C₂×D₄×C₁₃	1	2	yes	—
392	C₄²	C₂×D₄×C₁₃	1	2	yes	—
393	C₁₃	#25844	1	1	yes	characteristic, direct product factor, Sylow
394	C₂³	—	2	2	no	—
395	C₂³	—	2	4	no	—
396	C₂³	—	4	2	no	—
397	C₂³	—	4	1	no	—
398	C₂³	—	4	1	no	—
399	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
400	Q₈	—	2	8	no	—
401	Q₈	—	4	8	no	—
402	Q₈	—	4	16	no	—
403	D₄	—	2	2	no	—
404	D₄	—	2	4	no	—
405	D₄	C₁₃×C₄⋊Q₈	1	4	yes	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	4	8	no	—
418	C₂×C₄	—	4	16	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	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	C₁₃×#120	1	2	yes	—
430	C₂×C₄	C₁₃×#120	1	2	yes	—
431	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
432	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
433	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
434	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
435	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
436	C₈	—	2	4	no	—
437	C₈	—	4	1	no	—
438	C₈	—	4	1	no	—
439	C₂²	—	2	4	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	4	no	—
442	C₂²	—	4	4	no	—
443	C₂²	—	4	2	no	—
444	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
445	C₂²	D₄×Q₈×C₁₃	1	2	yes	—
446	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
447	C₂²	C₁₃×#577	1	1	yes	characteristic
448	C₂²	C₁₃×#578	1	1	yes	characteristic
449	C₄	—	2	2	no	—
450	C₄	—	2	2	no	—
451	C₄	—	2	4	no	—
452	C₄	—	4	2	no	—
453	C₄	—	4	4	no	—
454	C₄	—	4	4	no	—
455	C₄	—	4	2	no	—
456	C₄	—	8	1	no	—
457	C₄	—	8	1	no	—
458	C₄	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
459	C₄	C₁₃×#536	1	1	yes	characteristic
460	C₄	D₄×Q₈×C₁₃	1	2	yes	—
461	C₂	—	4	4	no	—
462	C₂	C₁₃×#2434	1	1	yes	characteristic
463	C₂	C₁₃×#3003	1	1	yes	characteristic
464	C₂	C₁₃×#3013	1	1	yes	characteristic
465	C₂	C₁₃×#3384	1	2	yes	—
466	C₂	C₁₃×#3386	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×#2058	C₂	semidirect
6. C₁₃×#2057	C₂	semidirect
7. C₁₃×#1987	C₂	semidirect
8. C₁₃×#1985	C₂	semidirect
95. C₁₃×#102	Q₈	semidirect
100. #25844	C₁₃	direct (N × H)
135. C₂×C₈×C₁₃	C₂×Q₈	semidirect
153. C₁₃×C₄⋊C₄	C₂×Q₈	semidirect
162. C₂×#501	C₂×C₁₃	semidirect
164. #2584	C₂×C₁₃	semidirect
165. #2058	C₂×C₁₃	semidirect
166. #2057	C₂×C₁₃	semidirect
167. #1987	C₂×C₁₃	semidirect
168. #1985	C₂×C₁₃	semidirect
322. #102	Q₈×C₁₃	semidirect
367. C₂×C₈	C₂×Q₈×C₁₃	semidirect
385. C₄⋊C₄	C₂×Q₈×C₁₃	semidirect
393. C₁₃	#25844	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×#501	2
C₂×C₁₃×#478	2
C₁₃×#2584	2
C₁₃×#2058	2
C₁₃×#2057	2
C₁₃×#1987	2
C₁₃×#1985	2
C₁₃×#1864	2
C₁₃×#1862	2
C₁₃×#1762	2
#25844	13

Subgroups — C13×#25844 #15712183

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25844 #15712183