Subgroups — C₁₃×#29393 #15715732

Order 3328.

774 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2293	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2084	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2071	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2057	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2023	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1925	C₂	1	2	yes	maximal
8	C₁₃×#1921	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1920	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1864	C₂	1	2	yes	maximal
11	C₁₃×#1839	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
14	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#117	—	2	1	no	—
16	C₂×C₁₃×#107	C₂²	1	2	yes	—
17	C₂×C₁₃×#106	C₂²	1	2	yes	—
18	C₂×C₁₃×#102	C₂²	1	2	yes	—
19	C₂×C₁₃×#102	C₂²	1	2	yes	—
20	C₁₃×#391	—	2	1	no	—
21	C₁₃×#390	C₂²	1	1	yes	characteristic
22	C₁₃×#390	C₂²	1	1	yes	characteristic
23	C₁₃×#389	—	2	1	no	—
24	C₁₃×#389	C₂²	1	1	yes	characteristic
25	C₁₃×#389	C₂²	1	1	yes	characteristic
26	C₁₃×#389	C₂²	1	2	yes	—
27	C₁₃×#388	—	2	1	no	—
28	C₁₃×#388	—	2	1	no	—
29	C₁₃×#384	C₂²	1	1	yes	characteristic
30	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
31	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
33	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
34	C₄³×C₁₃	C₂²	1	1	yes	characteristic
35	C₁₃×#340	C₂²	1	2	yes	—
36	C₁₃×#340	C₂²	1	2	yes	—
37	C₁₃×#340	C₂²	1	2	yes	—
38	C₁₃×#340	C₂²	1	2	yes	—
39	C₁₃×#336	C₂²	1	1	yes	characteristic
40	C₁₃×#336	C₂²	1	1	yes	characteristic
41	C₁₃×#336	C₂²	1	2	yes	—
42	C₁₃×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃	—	2	1	no	—
44	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₃	—	2	1	no	—
46	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
48	C₁₃×C₄⋊Q₈	—	2	4	no	—
49	C₄×Q₈×C₁₃	—	4	4	no	—
50	C₄×D₄×C₁₃	—	2	2	no	—
51	C₄×D₄×C₁₃	—	2	2	no	—
52	C₁₃×#117	—	4	4	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
59	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
64	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
65	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
66	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
67	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
68	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
69	C₂×C₄²×C₁₃	—	2	1	no	—
70	C₂×C₄²×C₁₃	—	2	2	no	—
71	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
78	C₁₃×#107	—	2	4	no	—
79	C₁₃×#106	—	2	4	no	—
80	C₁₃×#102	—	2	4	no	—
81	C₁₃×#102	—	2	4	no	—
82	C₁₃×#95	—	2	1	no	—
83	C₁₃×#95	—	2	1	no	—
84	C₁₃×#95	—	2	2	no	—
85	C₁₃×#95	—	2	1	no	—
86	C₁₃×#95	—	2	2	no	—
87	#29393	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
88	C₂⁴×C₁₃	—	2	1	no	—
89	C₂×Q₈×C₁₃	—	2	4	no	—
90	C₂×Q₈×C₁₃	—	4	2	no	—
91	C₂×Q₈×C₁₃	—	4	2	no	—
92	C₂×D₄×C₁₃	—	2	2	no	—
93	C₂×D₄×C₁₃	—	2	1	no	—
94	C₂×D₄×C₁₃	—	2	2	no	—
95	C₂×D₄×C₁₃	#41	1	2	yes	—
96	C₂²×C₄×C₁₃	—	2	4	no	—
97	C₂²×C₄×C₁₃	—	2	2	no	—
98	C₂²×C₄×C₁₃	—	2	1	no	—
99	C₂²×C₄×C₁₃	—	2	1	no	—
100	C₂²×C₄×C₁₃	—	2	1	no	—
101	C₂²×C₄×C₁₃	—	2	2	no	—
102	C₂²×C₄×C₁₃	—	4	2	no	—
103	C₂²×C₄×C₁₃	—	4	2	no	—
104	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
111	C₂×C₈×C₁₃	—	2	2	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	—	2	2	no	—
116	C₂×C₈×C₁₃	—	2	2	no	—
117	C₁₃×C₄⋊C₄	—	2	4	no	—
118	C₁₃×C₄⋊C₄	—	2	1	no	—
119	C₁₃×C₄⋊C₄	—	2	2	no	—
120	C₁₃×C₄⋊C₄	—	2	2	no	—
121	C₁₃×C₄⋊C₄	—	2	2	no	—
122	C₁₃×C₄⋊C₄	—	2	2	no	—
123	C₁₃×C₄⋊C₄	—	2	2	no	—
124	C₁₃×C₄⋊C₄	—	4	2	no	—
125	C₁₃×C₄⋊C₄	—	4	2	no	—
126	C₁₃×C₄⋊C₄	—	4	4	no	—
127	C₁₃×C₄⋊C₄	—	4	2	no	—
128	C₁₃×C₄⋊C₄	—	4	2	no	—
129	C₁₃×C₄⋊C₄	#41	1	4	yes	—
130	C₁₃×C₄⋊C₄	#41	1	2	yes	—
131	C₁₃×C₂²⋊C₄	—	2	4	no	—
132	C₁₃×C₂²⋊C₄	—	4	2	no	—
133	C₁₃×C₂²⋊C₄	—	4	2	no	—
134	C₁₃×C₂²⋊C₄	—	4	2	no	—
135	C₁₃×C₂²⋊C₄	—	4	2	no	—
136	C₄²×C₁₃	—	2	2	no	—
137	C₄²×C₁₃	—	2	2	no	—
138	C₄²×C₁₃	—	2	2	no	—
139	C₄²×C₁₃	—	2	2	no	—
140	C₄²×C₁₃	—	2	1	no	—
141	C₄²×C₁₃	—	2	1	no	—
142	C₄²×C₁₃	—	2	2	no	—
143	C₄²×C₁₃	—	2	2	no	—
144	C₄²×C₁₃	—	4	2	no	—
145	C₄²×C₁₃	—	4	4	no	—
146	C₄×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
147	#2293	C₂×C₁₃	1	1	yes	characteristic
148	#2084	C₂×C₁₃	1	1	yes	characteristic, complemented
149	#2071	C₂×C₁₃	1	1	yes	characteristic
150	#2057	C₂×C₁₃	1	1	yes	characteristic, complemented
151	#2023	C₂×C₁₃	1	1	yes	characteristic
152	#1925	C₂×C₁₃	1	2	yes	—
153	#1921	C₂×C₁₃	1	2	yes	complemented
154	#1920	C₂×C₁₃	1	2	yes	complemented
155	#1864	C₂×C₁₃	1	2	yes	—
156	#1839	C₂×C₁₃	1	1	yes	characteristic, complemented
157	C₂³×C₁₃	—	2	2	no	—
158	C₂³×C₁₃	—	4	1	no	—
159	C₂³×C₁₃	—	4	1	no	—
160	C₂³×C₁₃	—	4	1	no	—
161	C₂³×C₁₃	—	4	1	no	—
162	C₂³×C₁₃	—	4	1	no	—
163	C₂³×C₁₃	—	4	1	no	—
164	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
165	Q₈×C₁₃	—	4	8	no	—
166	D₄×C₁₃	—	2	4	no	—
167	D₄×C₁₃	—	4	2	no	—
168	C₂×C₄×C₁₃	—	2	1	no	—
169	C₂×C₄×C₁₃	—	2	1	no	—
170	C₂×C₄×C₁₃	—	2	1	no	—
171	C₂×C₄×C₁₃	—	2	1	no	—
172	C₂×C₄×C₁₃	—	2	1	no	—
173	C₂×C₄×C₁₃	—	2	1	no	—
174	C₂×C₄×C₁₃	—	2	1	no	—
175	C₂×C₄×C₁₃	—	2	1	no	—
176	C₂×C₄×C₁₃	—	2	1	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	4	no	—
179	C₂×C₄×C₁₃	—	2	1	no	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	2	1	no	—
183	C₂×C₄×C₁₃	—	2	1	no	—
184	C₂×C₄×C₁₃	—	4	8	no	—
185	C₂×C₄×C₁₃	—	4	2	no	—
186	C₂×C₄×C₁₃	—	4	1	no	—
187	C₂×C₄×C₁₃	—	4	2	no	—
188	C₂×C₄×C₁₃	—	4	1	no	—
189	C₂×C₄×C₁₃	—	4	2	no	—
190	C₂×C₄×C₁₃	—	4	1	no	—
191	C₂×C₄×C₁₃	—	4	1	no	—
192	C₂×C₄×C₁₃	—	4	1	no	—
193	C₂×C₄×C₁₃	—	4	2	no	—
194	C₂×C₄×C₁₃	—	4	1	no	—
195	C₂×C₄×C₁₃	—	4	1	no	—
196	C₂×C₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	—	4	1	no	—
198	C₂×C₄×C₁₃	#135	1	2	yes	—
199	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
200	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
201	C₂×C₄×C₁₃	#137	1	2	yes	—
202	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
204	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
206	C₈×C₁₃	—	4	2	no	—
207	C₈×C₁₃	—	4	2	no	—
208	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
209	C₂×C₄×Q₈	—	2	1	no	—
210	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
211	C₂×#117	—	2	1	no	—
212	C₂×#107	C₂²×C₁₃	1	2	yes	—
213	C₂×#106	C₂²×C₁₃	1	2	yes	—
214	C₂×#102	C₂²×C₁₃	1	2	yes	—
215	C₂×#102	C₂²×C₁₃	1	2	yes	—
216	#391	—	2	1	no	—
217	#390	C₂²×C₁₃	1	1	yes	characteristic
218	#390	C₂²×C₁₃	1	1	yes	characteristic
219	#389	—	2	1	no	—
220	#389	C₂²×C₁₃	1	2	yes	—
221	#389	C₂²×C₁₃	1	1	yes	characteristic
222	#389	C₂²×C₁₃	1	1	yes	characteristic
223	#388	—	2	1	no	—
224	#388	—	2	1	no	—
225	#384	C₂²×C₁₃	1	1	yes	characteristic
226	C₄×C₄⋊C₄	—	2	1	no	—
227	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
228	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
229	C₄×C₂²⋊C₄	—	2	1	no	—
230	C₄³	C₂²×C₁₃	1	1	yes	characteristic
231	#340	C₂²×C₁₃	1	2	yes	—
232	#340	C₂²×C₁₃	1	2	yes	—
233	#340	C₂²×C₁₃	1	2	yes	—
234	#340	C₂²×C₁₃	1	2	yes	—
235	#336	C₂²×C₁₃	1	1	yes	characteristic
236	#336	C₂²×C₁₃	1	1	yes	characteristic
237	#336	C₂²×C₁₃	1	2	yes	—
238	#336	C₂²×C₁₃	1	2	yes	—
239	C₂²×C₁₃	—	4	2	no	—
240	C₂²×C₁₃	—	4	2	no	—
241	C₂²×C₁₃	—	4	2	no	—
242	C₂²×C₁₃	—	8	1	no	—
243	C₂²×C₁₃	—	8	1	no	—
244	C₂²×C₁₃	—	8	1	no	—
245	C₂²×C₁₃	—	8	1	no	—
246	C₂²×C₁₃	#525	1	1	yes	characteristic
247	C₂²×C₁₃	#525	1	1	yes	characteristic
248	C₂²×C₁₃	#536	1	1	yes	characteristic
249	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
250	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
251	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
252	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
253	C₄×C₁₃	—	2	2	no	—
254	C₄×C₁₃	—	2	2	no	—
255	C₄×C₁₃	—	2	2	no	—
256	C₄×C₁₃	—	2	2	no	—
257	C₄×C₁₃	—	4	1	no	—
258	C₄×C₁₃	—	4	4	no	—
259	C₄×C₁₃	—	4	2	no	—
260	C₄×C₁₃	—	4	1	no	—
261	C₄×C₁₃	—	8	2	no	—
262	C₄×C₁₃	—	8	1	no	—
263	C₄×C₁₃	—	8	1	no	—
264	C₄×C₁₃	#552	1	2	yes	—
265	C₄×C₁₃	#556	1	2	yes	—
266	C₂²×Q₈	—	2	1	no	—
267	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
268	C₂³×C₄	—	2	1	no	—
269	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
270	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
271	C₄⋊Q₈	—	2	4	no	—
272	C₄×Q₈	—	4	4	no	—
273	C₄×D₄	—	2	2	no	—
274	C₄×D₄	—	2	2	no	—
275	#117	—	4	4	no	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
283	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
284	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
285	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
287	C₂×C₂²⋊C₄	—	2	1	no	—
288	C₂×C₂²⋊C₄	—	2	1	no	—
289	C₂×C₂²⋊C₄	—	2	1	no	—
290	C₂×C₂²⋊C₄	—	2	1	no	—
291	C₂×C₂²⋊C₄	—	2	1	no	—
292	C₂×C₄²	—	2	1	no	—
293	C₂×C₄²	—	2	2	no	—
294	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
295	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
296	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
297	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
298	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
299	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
300	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
301	#107	—	2	4	no	—
302	#106	—	2	4	no	—
303	#102	—	2	4	no	—
304	#102	—	2	4	no	—
305	#95	—	2	1	no	—
306	#95	—	2	1	no	—
307	#95	—	2	2	no	—
308	#95	—	2	1	no	—
309	#95	—	2	2	no	—
310	C₂×C₁₃	—	8	2	no	—
311	C₂×C₁₃	#2599	1	1	yes	characteristic
312	C₂×C₁₃	#3106	1	1	yes	characteristic
313	C₂×C₁₃	#3108	1	1	yes	characteristic
314	C₂×C₁₃	#3109	1	1	yes	characteristic
315	C₂×C₁₃	#3110	1	1	yes	characteristic
316	C₂×C₁₃	#3228	1	1	yes	characteristic
317	C₂×C₁₃	#3238	1	1	yes	characteristic
318	C₂⁴	—	2	1	no	—
319	C₂×Q₈	—	2	4	no	—
320	C₂×Q₈	—	4	2	no	—
321	C₂×Q₈	—	4	2	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	C₁₃×#41	1	2	yes	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	4	2	no	—
333	C₂²×C₄	—	4	2	no	—
334	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
338	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
339	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
340	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₄⋊C₄	—	2	4	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	—	2	2	no	—
354	C₄⋊C₄	—	4	2	no	—
355	C₄⋊C₄	—	4	2	no	—
356	C₄⋊C₄	—	4	4	no	—
357	C₄⋊C₄	—	4	2	no	—
358	C₄⋊C₄	—	4	2	no	—
359	C₄⋊C₄	C₁₃×#41	1	4	yes	—
360	C₄⋊C₄	C₁₃×#41	1	2	yes	—
361	C₂²⋊C₄	—	2	4	no	—
362	C₂²⋊C₄	—	4	2	no	—
363	C₂²⋊C₄	—	4	2	no	—
364	C₂²⋊C₄	—	4	2	no	—
365	C₂²⋊C₄	—	4	2	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	2	2	no	—
370	C₄²	—	2	1	no	—
371	C₄²	—	2	1	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	4	2	no	—
375	C₄²	—	4	4	no	—
376	C₁₃	#29393	1	1	yes	characteristic, direct product factor, Sylow
377	C₂³	—	2	2	no	—
378	C₂³	—	4	1	no	—
379	C₂³	—	4	1	no	—
380	C₂³	—	4	1	no	—
381	C₂³	—	4	1	no	—
382	C₂³	—	4	1	no	—
383	C₂³	—	4	1	no	—
384	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
385	Q₈	—	4	8	no	—
386	D₄	—	2	4	no	—
387	D₄	—	4	2	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	4	8	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	C₁₃×#135	1	2	yes	—
419	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
420	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
421	C₂×C₄	C₁₃×#137	1	2	yes	—
422	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
423	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
424	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
425	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
426	C₈	—	4	2	no	—
427	C₈	—	4	2	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	8	1	no	—
432	C₂²	—	8	1	no	—
433	C₂²	—	8	1	no	—
434	C₂²	—	8	1	no	—
435	C₂²	C₁₃×#525	1	1	yes	characteristic
436	C₂²	C₁₃×#525	1	1	yes	characteristic
437	C₂²	C₁₃×#536	1	1	yes	characteristic
438	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
439	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
440	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
441	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
442	C₄	—	2	2	no	—
443	C₄	—	2	2	no	—
444	C₄	—	2	2	no	—
445	C₄	—	2	2	no	—
446	C₄	—	4	1	no	—
447	C₄	—	4	4	no	—
448	C₄	—	4	2	no	—
449	C₄	—	4	1	no	—
450	C₄	—	8	2	no	—
451	C₄	—	8	1	no	—
452	C₄	—	8	1	no	—
453	C₄	C₁₃×#552	1	2	yes	—
454	C₄	C₁₃×#556	1	2	yes	—
455	C₂	—	8	2	no	—
456	C₂	C₁₃×#2599	1	1	yes	characteristic
457	C₂	C₁₃×#3106	1	1	yes	characteristic
458	C₂	C₁₃×#3108	1	1	yes	characteristic
459	C₂	C₁₃×#3109	1	1	yes	characteristic
460	C₂	C₁₃×#3110	1	1	yes	characteristic
461	C₂	C₁₃×#3228	1	1	yes	characteristic
462	C₂	C₁₃×#3238	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 ◁ C₄³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄×C₁₃×C₄⋊Q₈	C₂	semidirect
3. C₁₃×#2084	C₂	semidirect
5. C₁₃×#2057	C₂	semidirect
8. C₁₃×#1921	C₂	semidirect
9. C₁₃×#1920	C₂	semidirect
11. C₁₃×#1839	C₂	semidirect
87. #29393	C₁₃	direct (N × H)
146. C₄×C₄⋊Q₈	C₂×C₁₃	semidirect
148. #2084	C₂×C₁₃	semidirect
150. #2057	C₂×C₁₃	semidirect
153. #1921	C₂×C₁₃	semidirect
154. #1920	C₂×C₁₃	semidirect
156. #1839	C₂×C₁₃	semidirect
376. C₁₃	#29393	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄×C₁₃×C₄⋊Q₈	2
C₁₃×#2293	2
C₁₃×#2084	2
C₁₃×#2071	2
C₁₃×#2057	2
C₁₃×#2023	2
C₁₃×#1925	2
C₁₃×#1921	2
C₁₃×#1920	2
C₁₃×#1864	2
C₁₃×#1839	2
#29393	13

Subgroups — C13×#29393 #15715732

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#29393 #15715732