Subgroups — C₁₃×#8424 #15694763

Order 3328.

734 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3503	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1987	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#1806	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1550	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1549	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1503	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1477	C₂	1	1	yes	maximal, characteristic
8	Q₈²×C₁₃	—	2	1	no	—
9	C₁₃×#557	C₄	1	2	yes	complemented
10	C₁₃×#554	—	2	1	no	—
11	C₁₃×#554	—	2	2	no	—
12	D₄×Q₈×C₁₃	—	2	2	no	—
13	D₄×Q₈×C₁₃	C₄	1	2	yes	complemented
14	C₁₃×#544	—	2	2	no	—
15	C₁₃×#544	—	2	1	no	—
16	C₁₃×#533	—	2	1	no	—
17	C₁₃×#533	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
19	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₁₃×#520	—	2	1	no	—
21	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
22	C₁₃×#431	C₂²	1	1	yes	characteristic
23	C₁₃×#423	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#104	—	2	1	no	—
26	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₁₃×#340	—	2	2	no	—
28	C₁₃×#339	—	2	1	no	—
29	C₁₃×#333	—	2	1	no	—
30	C₁₃×#332	—	2	2	no	—
31	C₁₃×#332	—	2	1	no	—
32	C₁₃×#328	—	2	2	no	—
33	C₁₃×Q₈⋊C₈	—	2	1	no	—
34	C₁₃×D₄⋊C₈	—	2	1	no	—
35	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
36	C₂²×Q₈×C₁₃	—	2	2	no	—
37	C₂²×Q₈×C₁₃	—	2	1	no	—
38	C₂×C₁₃×M₁₆	—	2	1	no	—
39	C₂²×C₈×C₁₃	—	2	1	no	—
40	C₁₃×C₄⋊Q₈	—	2	2	no	—
41	C₁₃×C₄⋊Q₈	—	2	2	no	—
42	C₁₃×C₄⋊Q₈	—	2	4	no	—
43	C₁₃×C₄⋊Q₈	—	2	2	no	—
44	C₁₃×C₄⋊Q₈	—	2	2	no	—
45	C₁₃×C₄⋊Q₈	—	2	1	no	—
46	C₁₃×C₄⋊Q₈	—	2	1	no	—
47	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
48	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
49	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
50	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
51	C₁₃×#125	—	2	2	no	—
52	C₁₃×#125	—	2	4	no	—
53	C₁₃×#125	—	2	2	no	—
54	C₁₃×#125	—	2	1	no	—
55	C₁₃×C₂²⋊Q₈	—	2	2	no	—
56	C₁₃×C₂²⋊Q₈	—	2	4	no	—
57	C₁₃×C₂²⋊Q₈	—	2	4	no	—
58	C₁₃×C₂²⋊Q₈	—	2	1	no	—
59	C₁₃×C₂²⋊Q₈	—	2	2	no	—
60	C₁₃×C₂²⋊Q₈	—	2	4	no	—
61	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
62	C₄×Q₈×C₁₃	—	2	2	no	—
63	C₄×Q₈×C₁₃	—	2	2	no	—
64	C₄×Q₈×C₁₃	—	2	2	no	—
65	C₄×Q₈×C₁₃	—	2	1	no	—
66	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
67	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	—
68	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
69	C₄×D₄×C₁₃	—	2	4	no	—
70	C₄×D₄×C₁₃	—	2	2	no	—
71	C₄×D₄×C₁₃	—	2	1	no	—
72	C₄×D₄×C₁₃	—	2	1	no	—
73	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
74	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
75	C₁₃×#117	—	2	2	no	—
76	C₁₃×#117	—	2	1	no	—
77	C₁₃×#117	—	2	1	no	—
78	C₁₃×#117	D₄	1	1	yes	characteristic
79	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
80	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
81	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
83	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
84	C₂×C₄²×C₁₃	—	2	1	no	—
85	C₂×C₄²×C₁₃	—	2	1	no	—
86	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
87	C₁₃×C₄⋊C₈	—	2	1	no	—
88	C₁₃×C₄⋊C₈	—	2	1	no	—
89	C₁₃×C₄⋊C₈	—	2	1	no	—
90	C₁₃×C₄⋊C₈	—	2	1	no	—
91	C₁₃×C₄⋊C₈	—	2	1	no	—
92	C₁₃×#104	—	4	2	no	—
93	C₁₃×C₂²⋊C₈	—	2	1	no	—
94	C₄×C₈×C₁₃	—	2	1	no	—
95	C₁₃×#95	—	2	1	no	—
96	#8424	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
97	C₁₃×#41	—	2	1	no	—
98	C₁₃×#41	—	2	1	no	—
99	C₁₃×#41	SD₁₆	1	2	yes	—
100	C₁₃×#41	Q₁₆	1	2	yes	—
101	C₂×Q₈×C₁₃	—	2	4	no	—
102	C₂×Q₈×C₁₃	—	2	2	no	—
103	C₂×Q₈×C₁₃	—	2	1	no	—
104	C₂×Q₈×C₁₃	—	2	2	no	—
105	C₂×Q₈×C₁₃	—	8	2	no	—
106	C₂×Q₈×C₁₃	—	8	4	no	—
107	C₂×Q₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
108	C₂×Q₈×C₁₃	C₂²⋊C₄	1	2	yes	—
109	C₂×D₄×C₁₃	—	2	1	no	—
110	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	—	2	1	no	—
112	C₂²×C₄×C₁₃	—	2	4	no	—
113	C₂²×C₄×C₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₃	—	2	1	no	—
115	C₂²×C₄×C₁₃	—	2	1	no	—
116	C₂²×C₄×C₁₃	—	4	1	no	—
117	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₁₃×M₁₆	—	4	1	no	—
121	C₁₃×M₁₆	—	4	1	no	—
122	C₂×C₈×C₁₃	—	4	2	no	—
123	C₂×C₈×C₁₃	—	4	1	no	—
124	C₂×C₈×C₁₃	—	4	1	no	—
125	C₂×C₈×C₁₃	—	4	1	no	—
126	C₁₃×C₄⋊C₄	—	2	4	no	—
127	C₁₃×C₄⋊C₄	—	2	4	no	—
128	C₁₃×C₄⋊C₄	—	2	4	no	—
129	C₁₃×C₄⋊C₄	—	2	4	no	—
130	C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₁₃×C₄⋊C₄	—	2	1	no	—
132	C₁₃×C₄⋊C₄	—	2	2	no	—
133	C₁₃×C₄⋊C₄	—	2	1	no	—
134	C₁₃×C₄⋊C₄	—	2	2	no	—
135	C₁₃×C₄⋊C₄	—	2	1	no	—
136	C₁₃×C₄⋊C₄	—	2	2	no	—
137	C₁₃×C₄⋊C₄	—	2	1	no	—
138	C₁₃×C₄⋊C₄	—	2	1	no	—
139	C₁₃×C₄⋊C₄	—	2	2	no	—
140	C₁₃×C₄⋊C₄	—	2	2	no	—
141	C₁₃×C₄⋊C₄	—	4	1	no	—
142	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	4	yes	—
143	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
144	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
145	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
146	C₁₃×C₂²⋊C₄	—	2	4	no	—
147	C₁₃×C₂²⋊C₄	—	2	2	no	—
148	C₁₃×C₂²⋊C₄	—	2	1	no	—
149	C₁₃×C₂²⋊C₄	—	2	1	no	—
150	C₁₃×C₂²⋊C₄	—	2	1	no	—
151	C₄²×C₁₃	—	2	4	no	—
152	C₄²×C₁₃	—	2	1	no	—
153	C₄²×C₁₃	—	2	2	no	—
154	C₄²×C₁₃	—	2	1	no	—
155	C₄²×C₁₃	—	2	1	no	—
156	C₄²×C₁₃	—	4	1	no	—
157	C₄²×C₁₃	—	4	1	no	—
158	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
159	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
161	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
162	#3503	C₂×C₁₃	1	1	yes	characteristic
163	#1987	C₂×C₁₃	1	1	yes	characteristic, complemented
164	#1806	C₂×C₁₃	1	1	yes	characteristic
165	#1550	C₂×C₁₃	1	1	yes	characteristic, complemented
166	#1549	C₂×C₁₃	1	1	yes	characteristic, complemented
167	#1503	C₂×C₁₃	1	1	yes	characteristic, complemented
168	#1477	C₂×C₁₃	1	1	yes	characteristic
169	C₂³×C₁₃	—	2	1	no	—
170	C₂³×C₁₃	#120	1	1	yes	characteristic
171	Q₈×C₁₃	—	2	1	no	—
172	Q₈×C₁₃	—	4	4	no	—
173	Q₈×C₁₃	—	4	2	no	—
174	Q₈×C₁₃	—	4	1	no	—
175	Q₈×C₁₃	—	4	1	no	—
176	Q₈×C₁₃	—	8	2	no	—
177	Q₈×C₁₃	—	8	4	no	—
178	Q₈×C₁₃	#103	1	2	yes	—
179	D₄×C₁₃	—	2	2	no	—
180	D₄×C₁₃	—	2	2	no	—
181	D₄×C₁₃	—	2	1	no	—
182	D₄×C₁₃	#103	1	2	yes	—
183	C₂×C₄×C₁₃	—	2	1	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	1	no	—
187	C₂×C₄×C₁₃	—	2	1	no	—
188	C₂×C₄×C₁₃	—	2	2	no	—
189	C₂×C₄×C₁₃	—	2	1	no	—
190	C₂×C₄×C₁₃	—	2	1	no	—
191	C₂×C₄×C₁₃	—	2	2	no	—
192	C₂×C₄×C₁₃	—	2	4	no	—
193	C₂×C₄×C₁₃	—	4	1	no	—
194	C₂×C₄×C₁₃	—	4	2	no	—
195	C₂×C₄×C₁₃	—	4	1	no	—
196	C₂×C₄×C₁₃	—	4	1	no	—
197	C₂×C₄×C₁₃	—	4	2	no	—
198	C₂×C₄×C₁₃	—	8	2	no	—
199	C₂×C₄×C₁₃	—	8	4	no	—
200	C₂×C₄×C₁₃	—	8	1	no	—
201	C₂×C₄×C₁₃	—	8	1	no	—
202	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
203	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
204	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
205	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
206	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
207	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
208	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
209	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
210	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
211	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
212	C₈×C₁₃	—	8	1	no	—
213	C₈×C₁₃	—	8	1	no	—
214	C₈×C₁₃	—	8	1	no	—
215	Q₈²	—	2	1	no	—
216	#557	C₄×C₁₃	1	2	yes	complemented
217	#554	—	2	1	no	—
218	#554	—	2	2	no	—
219	D₄×Q₈	—	2	2	no	—
220	D₄×Q₈	C₄×C₁₃	1	2	yes	complemented
221	#544	—	2	2	no	—
222	#544	—	2	1	no	—
223	#533	—	2	1	no	—
224	#533	C₂²×C₁₃	1	1	yes	characteristic
225	C₂×C₄⋊Q₈	—	2	1	no	—
226	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
227	#520	—	2	1	no	—
228	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
229	#431	C₂²×C₁₃	1	1	yes	characteristic
230	#423	C₂²×C₁₃	1	1	yes	characteristic
231	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
232	C₂×#104	—	2	1	no	—
233	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
234	#340	—	2	2	no	—
235	#339	—	2	1	no	—
236	#333	—	2	1	no	—
237	#332	—	2	2	no	—
238	#332	—	2	1	no	—
239	#328	—	2	2	no	—
240	Q₈⋊C₈	—	2	1	no	—
241	D₄⋊C₈	—	2	1	no	—
242	C₂²×C₁₃	—	2	1	no	—
243	C₂²×C₁₃	—	2	1	no	—
244	C₂²×C₁₃	—	2	2	no	—
245	C₂²×C₁₃	—	4	1	no	—
246	C₂²×C₁₃	—	4	1	no	—
247	C₂²×C₁₃	#379	1	1	yes	characteristic
248	C₂²×C₁₃	#448	1	1	yes	characteristic
249	C₂²×C₁₃	#451	1	1	yes	characteristic
250	C₄×C₁₃	—	2	1	no	—
251	C₄×C₁₃	—	2	1	no	—
252	C₄×C₁₃	—	2	1	no	—
253	C₄×C₁₃	—	2	2	no	—
254	C₄×C₁₃	—	4	1	no	—
255	C₄×C₁₃	—	4	2	no	—
256	C₄×C₁₃	—	4	1	no	—
257	C₄×C₁₃	—	4	4	no	—
258	C₄×C₁₃	—	4	2	no	—
259	C₄×C₁₃	—	8	2	no	—
260	C₄×C₁₃	C₂×#103	1	1	yes	characteristic
261	C₄×C₁₃	#419	1	1	yes	characteristic
262	C₄×C₁₃	#448	1	1	yes	characteristic
263	C₄×C₁₃	#451	1	1	yes	characteristic
264	C₄×C₁₃	#454	1	1	yes	characteristic
265	C₄×C₁₃	#456	1	1	yes	characteristic
266	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
267	C₂²×Q₈	—	2	2	no	—
268	C₂²×Q₈	—	2	1	no	—
269	C₂×M₁₆	—	2	1	no	—
270	C₂²×C₈	—	2	1	no	—
271	C₄⋊Q₈	—	2	2	no	—
272	C₄⋊Q₈	—	2	2	no	—
273	C₄⋊Q₈	—	2	4	no	—
274	C₄⋊Q₈	—	2	2	no	—
275	C₄⋊Q₈	—	2	2	no	—
276	C₄⋊Q₈	—	2	1	no	—
277	C₄⋊Q₈	—	2	1	no	—
278	C₄⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
279	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
280	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
281	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
282	#125	—	2	2	no	—
283	#125	—	2	4	no	—
284	#125	—	2	2	no	—
285	#125	—	2	1	no	—
286	C₂²⋊Q₈	—	2	2	no	—
287	C₂²⋊Q₈	—	2	4	no	—
288	C₂²⋊Q₈	—	2	4	no	—
289	C₂²⋊Q₈	—	2	1	no	—
290	C₂²⋊Q₈	—	2	2	no	—
291	C₂²⋊Q₈	—	2	4	no	—
292	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
293	C₄×Q₈	—	2	2	no	—
294	C₄×Q₈	—	2	2	no	—
295	C₄×Q₈	—	2	2	no	—
296	C₄×Q₈	—	2	1	no	—
297	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
298	C₄×Q₈	C₂×C₄×C₁₃	1	2	yes	—
299	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
300	C₄×D₄	—	2	4	no	—
301	C₄×D₄	—	2	2	no	—
302	C₄×D₄	—	2	1	no	—
303	C₄×D₄	—	2	1	no	—
304	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
305	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
306	#117	—	2	2	no	—
307	#117	—	2	1	no	—
308	#117	—	2	1	no	—
309	#117	D₄×C₁₃	1	1	yes	characteristic
310	C₂×C₄⋊C₄	—	2	2	no	—
311	C₂×C₄⋊C₄	—	2	2	no	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
315	C₂×C₄²	—	2	1	no	—
316	C₂×C₄²	—	2	1	no	—
317	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
318	C₄⋊C₈	—	2	1	no	—
319	C₄⋊C₈	—	2	1	no	—
320	C₄⋊C₈	—	2	1	no	—
321	C₄⋊C₈	—	2	1	no	—
322	C₄⋊C₈	—	2	1	no	—
323	#104	—	4	2	no	—
324	C₂²⋊C₈	—	2	1	no	—
325	C₄×C₈	—	2	1	no	—
326	#95	—	2	1	no	—
327	C₂×C₁₃	—	2	1	no	—
328	C₂×C₁₃	—	2	1	no	—
329	C₂×C₁₃	—	4	2	no	—
330	C₂×C₁₃	#1787	1	1	yes	characteristic
331	C₂×C₁₃	#1793	1	1	yes	characteristic
332	C₂×C₁₃	#1795	1	1	yes	characteristic
333	#41	—	2	1	no	—
334	#41	—	2	1	no	—
335	#41	C₁₃×SD₁₆	1	2	yes	—
336	#41	C₁₃×Q₁₆	1	2	yes	—
337	C₂×Q₈	—	2	4	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	8	2	no	—
342	C₂×Q₈	—	8	4	no	—
343	C₂×Q₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
344	C₂×Q₈	C₁₃×C₂²⋊C₄	1	2	yes	—
345	C₂×D₄	—	2	1	no	—
346	C₂×D₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	4	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	4	1	no	—
353	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
356	M₁₆	—	4	1	no	—
357	M₁₆	—	4	1	no	—
358	C₂×C₈	—	4	2	no	—
359	C₂×C₈	—	4	1	no	—
360	C₂×C₈	—	4	1	no	—
361	C₂×C₈	—	4	1	no	—
362	C₄⋊C₄	—	2	4	no	—
363	C₄⋊C₄	—	2	4	no	—
364	C₄⋊C₄	—	2	4	no	—
365	C₄⋊C₄	—	2	4	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	4	1	no	—
378	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	4	yes	—
379	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
380	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
381	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
382	C₂²⋊C₄	—	2	4	no	—
383	C₂²⋊C₄	—	2	2	no	—
384	C₂²⋊C₄	—	2	1	no	—
385	C₂²⋊C₄	—	2	1	no	—
386	C₂²⋊C₄	—	2	1	no	—
387	C₄²	—	2	4	no	—
388	C₄²	—	2	1	no	—
389	C₄²	—	2	2	no	—
390	C₄²	—	2	1	no	—
391	C₄²	—	2	1	no	—
392	C₄²	—	4	1	no	—
393	C₄²	—	4	1	no	—
394	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
395	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
396	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
397	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
398	C₁₃	#8424	1	1	yes	characteristic, direct product factor, Sylow
399	C₂³	—	2	1	no	—
400	C₂³	C₁₃×#120	1	1	yes	characteristic
401	Q₈	—	2	1	no	—
402	Q₈	—	4	2	no	—
403	Q₈	—	4	4	no	—
404	Q₈	—	4	1	no	—
405	Q₈	—	4	1	no	—
406	Q₈	—	8	2	no	—
407	Q₈	—	8	4	no	—
408	Q₈	C₁₃×#103	1	2	yes	—
409	D₄	—	2	2	no	—
410	D₄	—	2	2	no	—
411	D₄	—	2	1	no	—
412	D₄	C₁₃×#103	1	2	yes	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	8	2	no	—
429	C₂×C₄	—	8	4	no	—
430	C₂×C₄	—	8	1	no	—
431	C₂×C₄	—	8	1	no	—
432	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
433	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
434	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
435	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
436	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
437	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
438	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
439	C₂×C₄	C₂×C₁₃×Q₁₆	1	1	yes	characteristic
440	C₂×C₄	C₁₃×#137	1	1	yes	characteristic
441	C₂×C₄	C₁₃×#137	1	1	yes	characteristic
442	C₈	—	8	1	no	—
443	C₈	—	8	1	no	—
444	C₈	—	8	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	2	1	no	—
447	C₂²	—	2	2	no	—
448	C₂²	—	4	1	no	—
449	C₂²	—	4	1	no	—
450	C₂²	C₁₃×#379	1	1	yes	characteristic
451	C₂²	C₁₃×#448	1	1	yes	characteristic
452	C₂²	C₁₃×#451	1	1	yes	characteristic
453	C₄	—	2	2	no	—
454	C₄	—	2	1	no	—
455	C₄	—	2	1	no	—
456	C₄	—	2	1	no	—
457	C₄	—	4	1	no	—
458	C₄	—	4	2	no	—
459	C₄	—	4	1	no	—
460	C₄	—	4	4	no	—
461	C₄	—	4	2	no	—
462	C₄	—	8	2	no	—
463	C₄	C₂×C₁₃×#103	1	1	yes	characteristic
464	C₄	C₁₃×#419	1	1	yes	characteristic
465	C₄	C₁₃×#448	1	1	yes	characteristic
466	C₄	C₁₃×#451	1	1	yes	characteristic
467	C₄	C₁₃×#454	1	1	yes	characteristic
468	C₄	C₁₃×#456	1	1	yes	characteristic
469	C₂	—	2	1	no	—
470	C₂	—	2	1	no	—
471	C₂	—	4	2	no	—
472	C₂	C₁₃×#1787	1	1	yes	characteristic
473	C₂	C₁₃×#1793	1	1	yes	characteristic
474	C₂	C₁₃×#1795	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	#379
commutator	C₄²	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂×C₁₃×#41	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#1987	C₂	semidirect
4. C₁₃×#1550	C₂	semidirect
5. C₁₃×#1549	C₂	semidirect
6. C₁₃×#1503	C₂	semidirect
9. C₁₃×#557	C₄	semidirect
13. D₄×Q₈×C₁₃	C₄	semidirect
96. #8424	C₁₃	direct (N × H)
163. #1987	C₂×C₁₃	semidirect
165. #1550	C₂×C₁₃	semidirect
166. #1549	C₂×C₁₃	semidirect
167. #1503	C₂×C₁₃	semidirect
216. #557	C₄×C₁₃	semidirect
220. D₄×Q₈	C₄×C₁₃	semidirect
398. C₁₃	#8424	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×#3503	2
C₁₃×#1987	2
C₁₃×#1806	2
C₁₃×#1550	2
C₁₃×#1549	2
C₁₃×#1503	2
C₁₃×#1477	2
#8424	13

Subgroups — C13×#8424 #15694763

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#8424 #15694763