Subgroups — C₁₃×#23817 #15710156

Order 3328.

810 conjugacy classes of subgroups.

The subgroup lattice has 474 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	C₄×C₁₃×#124	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2101	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2072	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2071	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#2042	C₂	1	2	yes	maximal
7	C₁₃×#2024	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2023	C₂	1	1	yes	maximal, characteristic
9	C₄×C₁₃×#103	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₃×#102	C₂	1	2	yes	maximal
11	C₁₃×#1744	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
15	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#103	C₂²	1	2	yes	—
18	C₂×C₁₃×#103	C₂²	1	2	yes	—
19	C₂×C₁₃×#102	C₂²	1	2	yes	—
20	C₂×C₁₃×#102	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
22	C₁₃×#391	—	2	1	no	—
23	C₁₃×#391	C₂²	1	1	yes	characteristic
24	C₁₃×#390	C₂²	1	1	yes	characteristic
25	C₁₃×#389	—	2	1	no	—
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	C₁₃×#382	C₂²	1	1	yes	characteristic
31	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
32	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
33	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
34	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
35	C₄³×C₁₃	C₂²	1	1	yes	characteristic
36	C₁₃×#340	C₂²	1	2	yes	—
37	C₁₃×#340	C₂²	1	2	yes	—
38	C₁₃×#340	C₂²	1	2	yes	—
39	C₁₃×#340	C₂²	1	2	yes	—
40	C₁₃×#336	C₂²	1	1	yes	characteristic
41	C₁₃×#336	C₂²	1	1	yes	characteristic
42	C₁₃×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃	—	2	1	no	—
44	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	—	2	1	no	—
47	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
49	C₁₃×C₄⋊Q₈	—	2	4	no	—
50	C₁₃×#124	—	2	2	no	—
51	C₁₃×#124	—	2	2	no	—
52	C₄×Q₈×C₁₃	—	2	4	no	—
53	C₄×Q₈×C₁₃	—	4	4	no	—
54	C₄×D₄×C₁₃	—	2	4	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	1	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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×#103	—	2	4	no	—
79	C₁₃×#103	—	2	4	no	—
80	C₁₃×#102	—	2	4	no	—
81	C₁₃×#102	—	2	4	no	—
82	C₄×C₈×C₁₃	—	2	4	no	—
83	C₁₃×#95	—	2	1	no	—
84	C₁₃×#95	—	2	1	no	—
85	C₁₃×#95	—	2	1	no	—
86	C₁₃×#95	—	2	1	no	—
87	C₁₃×#95	—	2	2	no	—
88	C₁₃×#95	—	2	2	no	—
89	#23817	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂⁴×C₁₃	—	2	1	no	—
91	C₂×Q₈×C₁₃	—	2	4	no	—
92	C₂×Q₈×C₁₃	—	2	1	no	—
93	C₂×Q₈×C₁₃	—	2	2	no	—
94	C₂×Q₈×C₁₃	—	2	2	no	—
95	C₂×Q₈×C₁₃	—	4	2	no	—
96	C₂×Q₈×C₁₃	—	4	2	no	—
97	C₂×Q₈×C₁₃	#41	1	2	yes	—
98	C₂×D₄×C₁₃	—	2	2	no	—
99	C₂×D₄×C₁₃	—	2	2	no	—
100	C₂×D₄×C₁₃	—	2	1	no	—
101	C₂×D₄×C₁₃	#41	1	2	yes	—
102	C₂²×C₄×C₁₃	—	2	1	no	—
103	C₂²×C₄×C₁₃	—	2	2	no	—
104	C₂²×C₄×C₁₃	—	2	1	no	—
105	C₂²×C₄×C₁₃	—	2	1	no	—
106	C₂²×C₄×C₁₃	—	2	2	no	—
107	C₂²×C₄×C₁₃	—	4	2	no	—
108	C₂²×C₄×C₁₃	—	4	2	no	—
109	C₂²×C₄×C₁₃	—	4	2	no	—
110	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
117	C₂×C₈×C₁₃	—	2	2	no	—
118	C₂×C₈×C₁₃	—	2	2	no	—
119	C₂×C₈×C₁₃	—	2	2	no	—
120	C₂×C₈×C₁₃	—	2	2	no	—
121	C₂×C₈×C₁₃	—	2	2	no	—
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₁₃×C₄⋊C₄	—	2	4	no	—
124	C₁₃×C₄⋊C₄	—	2	2	no	—
125	C₁₃×C₄⋊C₄	—	2	2	no	—
126	C₁₃×C₄⋊C₄	—	2	2	no	—
127	C₁₃×C₄⋊C₄	—	2	2	no	—
128	C₁₃×C₄⋊C₄	—	2	2	no	—
129	C₁₃×C₄⋊C₄	—	4	2	no	—
130	C₁₃×C₄⋊C₄	—	4	4	no	—
131	C₁₃×C₄⋊C₄	—	4	2	no	—
132	C₁₃×C₄⋊C₄	—	4	2	no	—
133	C₁₃×C₄⋊C₄	#41	1	4	yes	—
134	C₁₃×C₂²⋊C₄	—	2	4	no	—
135	C₁₃×C₂²⋊C₄	—	2	4	no	—
136	C₁₃×C₂²⋊C₄	—	4	2	no	—
137	C₁₃×C₂²⋊C₄	—	4	2	no	—
138	C₁₃×C₂²⋊C₄	—	4	2	no	—
139	C₄²×C₁₃	—	2	2	no	—
140	C₄²×C₁₃	—	2	2	no	—
141	C₄²×C₁₃	—	2	2	no	—
142	C₄²×C₁₃	—	2	2	no	—
143	C₄²×C₁₃	—	2	1	no	—
144	C₄²×C₁₃	—	2	1	no	—
145	C₄²×C₁₃	—	2	2	no	—
146	C₄²×C₁₃	—	4	2	no	—
147	C₄²×C₁₃	—	4	4	no	—
148	C₄²×C₁₃	#41	1	4	yes	—
149	C₄×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
150	C₄×#124	C₂×C₁₃	1	1	yes	characteristic
151	#2101	C₂×C₁₃	1	2	yes	complemented
152	#2072	C₂×C₁₃	1	1	yes	characteristic, complemented
153	#2071	C₂×C₁₃	1	1	yes	characteristic
154	#2042	C₂×C₁₃	1	2	yes	—
155	#2024	C₂×C₁₃	1	1	yes	characteristic, complemented
156	#2023	C₂×C₁₃	1	1	yes	characteristic
157	C₄×#103	C₂×C₁₃	1	2	yes	complemented
158	C₄×#102	C₂×C₁₃	1	2	yes	—
159	#1744	C₂×C₁₃	1	1	yes	characteristic, complemented
160	C₂³×C₁₃	—	2	2	no	—
161	C₂³×C₁₃	—	4	1	no	—
162	C₂³×C₁₃	—	4	1	no	—
163	C₂³×C₁₃	—	4	1	no	—
164	C₂³×C₁₃	—	4	1	no	—
165	C₂³×C₁₃	—	4	1	no	—
166	C₂³×C₁₃	—	4	1	no	—
167	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
168	Q₈×C₁₃	—	2	4	no	—
169	Q₈×C₁₃	—	4	8	no	—
170	Q₈×C₁₃	—	4	2	no	—
171	D₄×C₁₃	—	2	4	no	—
172	D₄×C₁₃	—	4	2	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	1	no	—
178	C₂×C₄×C₁₃	—	2	1	no	—
179	C₂×C₄×C₁₃	—	2	1	no	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	2	2	no	—
182	C₂×C₄×C₁₃	—	2	4	no	—
183	C₂×C₄×C₁₃	—	2	1	no	—
184	C₂×C₄×C₁₃	—	2	1	no	—
185	C₂×C₄×C₁₃	—	2	1	no	—
186	C₂×C₄×C₁₃	—	2	1	no	—
187	C₂×C₄×C₁₃	—	4	1	no	—
188	C₂×C₄×C₁₃	—	4	1	no	—
189	C₂×C₄×C₁₃	—	4	2	no	—
190	C₂×C₄×C₁₃	—	4	2	no	—
191	C₂×C₄×C₁₃	—	4	2	no	—
192	C₂×C₄×C₁₃	—	4	1	no	—
193	C₂×C₄×C₁₃	—	4	1	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	2	no	—
198	C₂×C₄×C₁₃	—	4	1	no	—
199	C₂×C₄×C₁₃	—	4	1	no	—
200	C₂×C₄×C₁₃	—	8	4	no	—
201	C₂×C₄×C₁₃	#124	1	2	yes	—
202	C₂×C₄×C₁₃	#124	1	2	yes	—
203	C₂×C₄×C₁₃	#135	1	2	yes	—
204	C₂×C₄×C₁₃	#135	1	2	yes	—
205	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
206	C₂×C₄×C₁₃	#137	1	2	yes	—
207	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
210	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
211	C₈×C₁₃	—	4	2	no	—
212	C₈×C₁₃	—	4	2	no	—
213	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
214	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
215	C₂×C₄×Q₈	—	2	1	no	—
216	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
217	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
218	C₂×#103	C₂²×C₁₃	1	2	yes	—
219	C₂×#103	C₂²×C₁₃	1	2	yes	—
220	C₂×#102	C₂²×C₁₃	1	2	yes	—
221	C₂×#102	C₂²×C₁₃	1	2	yes	—
222	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
223	#391	—	2	1	no	—
224	#391	C₂²×C₁₃	1	1	yes	characteristic
225	#390	C₂²×C₁₃	1	1	yes	characteristic
226	#389	—	2	1	no	—
227	#389	C₂²×C₁₃	1	2	yes	—
228	#388	—	2	1	no	—
229	#388	—	2	1	no	—
230	#384	C₂²×C₁₃	1	1	yes	characteristic
231	#382	C₂²×C₁₃	1	1	yes	characteristic
232	C₄×C₄⋊C₄	—	2	1	no	—
233	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
234	C₄×C₂²⋊C₄	—	2	1	no	—
235	C₄×C₂²⋊C₄	—	2	1	no	—
236	C₄³	C₂²×C₁₃	1	1	yes	characteristic
237	#340	C₂²×C₁₃	1	2	yes	—
238	#340	C₂²×C₁₃	1	2	yes	—
239	#340	C₂²×C₁₃	1	2	yes	—
240	#340	C₂²×C₁₃	1	2	yes	—
241	#336	C₂²×C₁₃	1	1	yes	characteristic
242	#336	C₂²×C₁₃	1	1	yes	characteristic
243	#336	C₂²×C₁₃	1	2	yes	—
244	C₂²×C₁₃	—	4	2	no	—
245	C₂²×C₁₃	—	4	2	no	—
246	C₂²×C₁₃	—	4	2	no	—
247	C₂²×C₁₃	—	8	1	no	—
248	C₂²×C₁₃	—	8	1	no	—
249	C₂²×C₁₃	—	8	1	no	—
250	C₂²×C₁₃	—	8	1	no	—
251	C₂²×C₁₃	#525	1	1	yes	characteristic
252	C₂²×C₁₃	#525	1	1	yes	characteristic
253	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
254	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
255	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
256	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
257	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
258	C₄×C₁₃	—	2	2	no	—
259	C₄×C₁₃	—	2	2	no	—
260	C₄×C₁₃	—	2	2	no	—
261	C₄×C₁₃	—	4	4	no	—
262	C₄×C₁₃	—	4	1	no	—
263	C₄×C₁₃	—	4	1	no	—
264	C₄×C₁₃	—	4	2	no	—
265	C₄×C₁₃	—	8	2	no	—
266	C₄×C₁₃	—	8	1	no	—
267	C₄×C₁₃	—	8	1	no	—
268	C₄×C₁₃	#489	1	4	yes	—
269	C₄×C₁₃	#529	1	2	yes	—
270	C₄×C₁₃	#529	1	2	yes	—
271	C₂²×Q₈	—	2	1	no	—
272	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
273	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
274	C₂³×C₄	—	2	1	no	—
275	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
276	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
277	C₄⋊Q₈	—	2	4	no	—
278	#124	—	2	2	no	—
279	#124	—	2	2	no	—
280	C₄×Q₈	—	2	4	no	—
281	C₄×Q₈	—	4	4	no	—
282	C₄×D₄	—	2	4	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
291	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
292	C₂×C₂²⋊C₄	—	2	1	no	—
293	C₂×C₂²⋊C₄	—	2	1	no	—
294	C₂×C₂²⋊C₄	—	2	1	no	—
295	C₂×C₂²⋊C₄	—	2	1	no	—
296	C₂×C₂²⋊C₄	—	2	1	no	—
297	C₂×C₄²	—	2	2	no	—
298	C₂×C₄²	—	2	1	no	—
299	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
300	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
301	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
302	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
303	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
304	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
305	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
306	#103	—	2	4	no	—
307	#103	—	2	4	no	—
308	#102	—	2	4	no	—
309	#102	—	2	4	no	—
310	C₄×C₈	—	2	4	no	—
311	#95	—	2	1	no	—
312	#95	—	2	1	no	—
313	#95	—	2	1	no	—
314	#95	—	2	1	no	—
315	#95	—	2	2	no	—
316	#95	—	2	2	no	—
317	C₂×C₁₃	—	8	2	no	—
318	C₂×C₁₃	#2398	1	1	yes	characteristic
319	C₂×C₁₃	#3105	1	1	yes	characteristic
320	C₂×C₁₃	#3106	1	1	yes	characteristic
321	C₂×C₁₃	#3107	1	1	yes	characteristic
322	C₂×C₁₃	#3108	1	1	yes	characteristic
323	C₂×C₁₃	#3131	1	1	yes	characteristic
324	C₂×C₁₃	C₂×#489	1	1	yes	characteristic
325	C₂⁴	—	2	1	no	—
326	C₂×Q₈	—	2	4	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	4	2	no	—
331	C₂×Q₈	—	4	2	no	—
332	C₂×Q₈	C₁₃×#41	1	2	yes	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	C₁₃×#41	1	2	yes	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	4	2	no	—
343	C₂²×C₄	—	4	2	no	—
344	C₂²×C₄	—	4	2	no	—
345	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
346	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
347	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
348	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
351	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₄⋊C₄	—	2	4	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	4	2	no	—
365	C₄⋊C₄	—	4	4	no	—
366	C₄⋊C₄	—	4	2	no	—
367	C₄⋊C₄	—	4	2	no	—
368	C₄⋊C₄	C₁₃×#41	1	4	yes	—
369	C₂²⋊C₄	—	2	4	no	—
370	C₂²⋊C₄	—	2	4	no	—
371	C₂²⋊C₄	—	4	2	no	—
372	C₂²⋊C₄	—	4	2	no	—
373	C₂²⋊C₄	—	4	2	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	2	1	no	—
379	C₄²	—	2	1	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	4	2	no	—
382	C₄²	—	4	4	no	—
383	C₄²	C₁₃×#41	1	4	yes	—
384	C₁₃	#23817	1	1	yes	characteristic, direct product factor, Sylow
385	C₂³	—	2	2	no	—
386	C₂³	—	4	1	no	—
387	C₂³	—	4	1	no	—
388	C₂³	—	4	1	no	—
389	C₂³	—	4	1	no	—
390	C₂³	—	4	1	no	—
391	C₂³	—	4	1	no	—
392	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
393	Q₈	—	2	4	no	—
394	Q₈	—	4	8	no	—
395	Q₈	—	4	2	no	—
396	D₄	—	2	4	no	—
397	D₄	—	4	2	no	—
398	C₂×C₄	—	2	1	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	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	8	4	no	—
426	C₂×C₄	C₁₃×#124	1	2	yes	—
427	C₂×C₄	C₁₃×#124	1	2	yes	—
428	C₂×C₄	C₁₃×#135	1	2	yes	—
429	C₂×C₄	C₁₃×#135	1	2	yes	—
430	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
431	C₂×C₄	C₁₃×#137	1	2	yes	—
432	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
433	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
434	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
435	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
436	C₈	—	4	2	no	—
437	C₈	—	4	2	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	8	1	no	—
442	C₂²	—	8	1	no	—
443	C₂²	—	8	1	no	—
444	C₂²	—	8	1	no	—
445	C₂²	C₁₃×#525	1	1	yes	characteristic
446	C₂²	C₁₃×#525	1	1	yes	characteristic
447	C₂²	C₂×C₁₃×#124	1	1	yes	characteristic
448	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
449	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
450	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
451	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
452	C₄	—	2	2	no	—
453	C₄	—	2	2	no	—
454	C₄	—	2	2	no	—
455	C₄	—	4	4	no	—
456	C₄	—	4	1	no	—
457	C₄	—	4	1	no	—
458	C₄	—	4	2	no	—
459	C₄	—	8	2	no	—
460	C₄	—	8	1	no	—
461	C₄	—	8	1	no	—
462	C₄	C₁₃×#489	1	4	yes	—
463	C₄	C₁₃×#529	1	2	yes	—
464	C₄	C₁₃×#529	1	2	yes	—
465	C₂	—	8	2	no	—
466	C₂	C₁₃×#2398	1	1	yes	characteristic
467	C₂	C₁₃×#3105	1	1	yes	characteristic
468	C₂	C₁₃×#3106	1	1	yes	characteristic
469	C₂	C₁₃×#3107	1	1	yes	characteristic
470	C₂	C₁₃×#3108	1	1	yes	characteristic
471	C₂	C₁₃×#3131	1	1	yes	characteristic
472	C₂	C₂×C₁₃×#489	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂³×C₁₃	C₂²×D₄
prime radical	C₂²×D₄×C₁₃	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×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×#2101	C₂	semidirect
4. C₁₃×#2072	C₂	semidirect
7. C₁₃×#2024	C₂	semidirect
9. C₄×C₁₃×#103	C₂	semidirect
11. C₁₃×#1744	C₂	semidirect
89. #23817	C₁₃	direct (N × H)
149. C₄×C₄⋊Q₈	C₂×C₁₃	semidirect
151. #2101	C₂×C₁₃	semidirect
152. #2072	C₂×C₁₃	semidirect
155. #2024	C₂×C₁₃	semidirect
157. C₄×#103	C₂×C₁₃	semidirect
159. #1744	C₂×C₁₃	semidirect
384. C₁₃	#23817	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
C₄×C₁₃×#124	2
C₁₃×#2101	2
C₁₃×#2072	2
C₁₃×#2071	2
C₁₃×#2042	2
C₁₃×#2024	2
C₁₃×#2023	2
C₄×C₁₃×#103	2
C₄×C₁₃×#102	2
C₁₃×#1744	2
#23817	13

Subgroups — C13×#23817 #15710156

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23817 #15710156