Subgroups — C₁₃×#17916 #15704255

Order 3328.

624 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3107	C₂	1	1	yes	maximal, characteristic
2	C₈×C₁₃×#41	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2960	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1584	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1582	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1579	C₂	1	2	yes	maximal, complemented
7	C₁₃×SD₁₆⋊C₈	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1574	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1489	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1485	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#533	C₂²	1	1	yes	characteristic
13	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
14	C₁₃×#485	C₄	1	2	yes	—
15	C₁₃×#475	C₄	1	1	yes	characteristic
16	C₁₃×#474	C₄	1	1	yes	characteristic
17	C₁₃×#462	C₄	1	1	yes	characteristic
18	C₁₃×#461	C₄	1	1	yes	characteristic
19	C₁₃×#452	C₄	1	2	yes	—
20	C₁₃×#446	—	2	1	no	—
21	C₁₃×#446	C₂²	1	2	yes	—
22	C₈×Q₈×C₁₃	—	2	1	no	—
23	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
24	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
25	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
27	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
28	C₈×D₄×C₁₃	—	2	1	no	—
29	C₈×D₄×C₁₃	—	2	1	no	—
30	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
31	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
32	C₁₃×#431	—	2	1	no	—
33	C₁₃×#431	C₂²	1	1	yes	characteristic
34	C₁₃×#431	C₂²	1	1	yes	characteristic
35	C₁₃×#424	—	2	1	no	—
36	C₁₃×#423	C₂²	1	1	yes	characteristic
37	C₁₃×#405	—	2	1	no	—
38	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₁₃	—	2	1	no	—
40	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
41	C₁₃×#335	C₂²	1	2	yes	—
42	C₁₃×#334	C₂²	1	2	yes	—
43	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
44	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
45	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
46	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
47	C₁₃×#322	C₂²	1	2	yes	—
48	C₁₃×#322	C₂²	1	2	yes	—
49	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
50	C₂×C₁₃×Q₁₆	C₂×C₄	1	2	yes	—
51	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
52	C₂×C₁₃×M₁₆	—	2	1	no	—
53	C₂×C₁₃×M₁₆	—	2	1	no	—
54	C₂²×C₈×C₁₃	—	2	1	no	—
55	C₂²×C₈×C₁₃	—	2	1	no	—
56	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
57	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
58	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
59	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
60	C₁₃×#125	—	2	1	no	—
61	C₁₃×C₂²⋊Q₈	—	2	1	no	—
62	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
63	C₄×Q₈×C₁₃	—	2	1	no	—
64	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
65	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
66	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
67	C₄×D₄×C₁₃	—	2	1	no	—
68	C₄×D₄×C₁₃	—	2	1	no	—
69	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
70	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₁₃×#117	—	2	1	no	—
72	C₁₃×#117	—	2	1	no	—
73	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₁₃	—	2	1	no	—
75	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
76	C₁₃×#107	C₂×C₄	1	2	yes	—
77	C₁₃×#106	C₂×C₄	1	2	yes	—
78	C₁₃×C₄⋊C₈	—	2	2	no	—
79	C₁₃×C₄⋊C₈	—	2	2	no	—
80	C₁₃×C₄⋊C₈	—	2	1	no	—
81	C₁₃×C₄⋊C₈	—	2	1	no	—
82	C₁₃×C₄⋊C₈	—	2	1	no	—
83	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
84	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
85	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
86	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
87	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
88	C₁₃×#103	C₂×C₄	1	2	yes	—
89	C₁₃×#103	C₂×C₄	1	2	yes	—
90	C₁₃×#103	C₂×C₄	1	2	yes	—
91	C₁₃×#102	C₂×C₄	1	2	yes	—
92	C₁₃×C₂²⋊C₈	—	2	1	no	—
93	C₁₃×C₂²⋊C₈	—	2	1	no	—
94	C₁₃×C₂²⋊C₈	—	2	1	no	—
95	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
96	C₁₃×#97	—	2	2	no	—
97	C₁₃×#97	—	2	1	no	—
98	C₄×C₈×C₁₃	—	2	1	no	—
99	C₄×C₈×C₁₃	—	2	1	no	—
100	C₄×C₈×C₁₃	—	2	2	no	—
101	C₄×C₈×C₁₃	—	2	1	no	—
102	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
103	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
104	C₄×C₈×C₁₃	C₂³	1	2	yes	—
105	C₄×C₈×C₁₃	C₂³	1	2	yes	—
106	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
107	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
108	#17916	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
109	C₁₃×#41	—	2	2	no	—
110	C₁₃×#41	—	2	2	no	—
111	C₂×Q₈×C₁₃	—	2	1	no	—
112	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
113	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₂×D₄×C₁₃	—	2	1	no	—
115	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	—	2	1	no	—
117	C₂²×C₄×C₁₃	—	2	1	no	—
118	C₂²×C₄×C₁₃	—	2	1	no	—
119	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
122	C₁₃×Q₁₆	—	2	4	no	—
123	C₁₃×SD₁₆	—	2	4	no	—
124	C₁₃×M₁₆	—	4	2	no	—
125	C₁₃×M₁₆	—	4	2	no	—
126	C₂×C₈×C₁₃	—	2	2	no	—
127	C₂×C₈×C₁₃	—	2	1	no	—
128	C₂×C₈×C₁₃	—	2	1	no	—
129	C₂×C₈×C₁₃	—	2	2	no	—
130	C₂×C₈×C₁₃	—	2	2	no	—
131	C₂×C₈×C₁₃	—	4	1	no	—
132	C₂×C₈×C₁₃	—	4	2	no	—
133	C₂×C₈×C₁₃	—	4	2	no	—
134	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
135	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
136	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₁₃×C₄⋊C₄	—	2	1	no	—
141	C₁₃×C₄⋊C₄	—	2	1	no	—
142	C₁₃×C₄⋊C₄	—	2	1	no	—
143	C₁₃×C₄⋊C₄	—	2	1	no	—
144	C₁₃×C₄⋊C₄	—	2	2	no	—
145	C₁₃×C₄⋊C₄	—	2	1	no	—
146	C₁₃×C₄⋊C₄	—	2	2	no	—
147	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
148	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
149	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
150	C₁₃×C₂²⋊C₄	—	2	2	no	—
151	C₁₃×C₂²⋊C₄	—	2	1	no	—
152	C₁₃×C₂²⋊C₄	—	2	1	no	—
153	C₁₃×C₂²⋊C₄	—	2	1	no	—
154	C₄²×C₁₃	—	2	1	no	—
155	C₄²×C₁₃	—	2	1	no	—
156	C₄²×C₁₃	—	2	1	no	—
157	C₄²×C₁₃	—	2	2	no	—
158	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
159	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₁₃	#41	1	1	yes	characteristic
161	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
162	#3107	C₂×C₁₃	1	1	yes	characteristic
163	C₈×#41	C₂×C₁₃	1	1	yes	characteristic
164	#2960	C₂×C₁₃	1	1	yes	characteristic, complemented
165	#1584	C₂×C₁₃	1	2	yes	complemented
166	#1582	C₂×C₁₃	1	2	yes	complemented
167	#1579	C₂×C₁₃	1	2	yes	complemented
168	SD₁₆⋊C₈	C₂×C₁₃	1	2	yes	complemented
169	#1574	C₂×C₁₃	1	1	yes	characteristic, complemented
170	#1489	C₂×C₁₃	1	1	yes	characteristic
171	#1485	C₂×C₁₃	1	1	yes	characteristic, complemented
172	#1451	C₂×C₁₃	1	1	yes	characteristic, complemented
173	C₂³×C₁₃	—	2	1	no	—
174	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
175	Q₈×C₁₃	—	2	1	no	—
176	Q₈×C₁₃	—	2	2	no	—
177	Q₈×C₁₃	—	2	2	no	—
178	Q₈×C₁₃	—	4	2	no	—
179	Q₈×C₁₃	#131	1	2	yes	—
180	D₄×C₁₃	—	2	4	no	—
181	D₄×C₁₃	—	2	1	no	—
182	D₄×C₁₃	#131	1	2	yes	—
183	C₂×C₄×C₁₃	—	2	4	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	—	2	1	no	—
188	C₂×C₄×C₁₃	—	2	1	no	—
189	C₂×C₄×C₁₃	—	2	2	no	—
190	C₂×C₄×C₁₃	—	2	1	no	—
191	C₂×C₄×C₁₃	—	2	1	no	—
192	C₂×C₄×C₁₃	—	2	2	no	—
193	C₂×C₄×C₁₃	—	2	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	C₄×D₄	1	1	yes	characteristic
198	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
199	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
201	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
203	C₈×C₁₃	—	2	2	no	—
204	C₈×C₁₃	—	2	2	no	—
205	C₈×C₁₃	—	2	1	no	—
206	C₈×C₁₃	—	2	1	no	—
207	C₈×C₁₃	—	2	1	no	—
208	C₈×C₁₃	—	4	2	no	—
209	C₈×C₁₃	—	4	1	no	—
210	C₈×C₁₃	—	4	1	no	—
211	C₈×C₁₃	—	4	2	no	—
212	C₈×C₁₃	#137	1	2	yes	—
213	#533	C₂²×C₁₃	1	1	yes	characteristic
214	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
215	#485	C₄×C₁₃	1	2	yes	—
216	#475	C₄×C₁₃	1	1	yes	characteristic
217	#474	C₄×C₁₃	1	1	yes	characteristic
218	#462	C₄×C₁₃	1	1	yes	characteristic
219	#461	C₄×C₁₃	1	1	yes	characteristic
220	#452	C₄×C₁₃	1	2	yes	—
221	#446	—	2	1	no	—
222	#446	C₂²×C₁₃	1	2	yes	—
223	C₈×Q₈	—	2	1	no	—
224	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
225	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
226	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
227	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
228	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
229	C₈×D₄	—	2	1	no	—
230	C₈×D₄	—	2	1	no	—
231	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
232	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
233	#431	—	2	1	no	—
234	#431	C₂²×C₁₃	1	1	yes	characteristic
235	#431	C₂²×C₁₃	1	1	yes	characteristic
236	#424	—	2	1	no	—
237	#423	C₂²×C₁₃	1	1	yes	characteristic
238	#405	—	2	1	no	—
239	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
240	C₂×C₄×C₈	—	2	1	no	—
241	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
242	#335	C₂²×C₁₃	1	2	yes	—
243	#334	C₂²×C₁₃	1	2	yes	—
244	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
245	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
246	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
247	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
248	#322	C₂²×C₁₃	1	2	yes	—
249	#322	C₂²×C₁₃	1	2	yes	—
250	C₂²×C₁₃	—	2	1	no	—
251	C₂²×C₁₃	—	2	2	no	—
252	C₂²×C₁₃	—	2	1	no	—
253	C₂²×C₁₃	—	2	1	no	—
254	C₂²×C₁₃	—	4	1	no	—
255	C₂²×C₁₃	—	4	1	no	—
256	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
257	C₄×C₁₃	—	2	1	no	—
258	C₄×C₁₃	—	2	2	no	—
259	C₄×C₁₃	—	2	1	no	—
260	C₄×C₁₃	—	2	1	no	—
261	C₄×C₁₃	—	4	2	no	—
262	C₄×C₁₃	—	4	1	no	—
263	C₄×C₁₃	—	4	1	no	—
264	C₄×C₁₃	—	4	2	no	—
265	C₄×C₁₃	#444	1	2	yes	—
266	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
267	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
268	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
269	C₄×C₁₃	#575	1	1	yes	characteristic
270	C₂×#41	C₂×C₄×C₁₃	1	1	yes	characteristic
271	C₂×Q₁₆	C₂×C₄×C₁₃	1	2	yes	—
272	C₂×SD₁₆	C₂×C₄×C₁₃	1	2	yes	—
273	C₂×M₁₆	—	2	1	no	—
274	C₂×M₁₆	—	2	1	no	—
275	C₂²×C₈	—	2	1	no	—
276	C₂²×C₈	—	2	1	no	—
277	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
278	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
279	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
280	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
281	#125	—	2	1	no	—
282	C₂²⋊Q₈	—	2	1	no	—
283	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
284	C₄×Q₈	—	2	1	no	—
285	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
286	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
287	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
288	C₄×D₄	—	2	1	no	—
289	C₄×D₄	—	2	1	no	—
290	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
291	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
292	#117	—	2	1	no	—
293	#117	—	2	1	no	—
294	#117	C₂×C₄×C₁₃	1	1	yes	characteristic
295	C₂×C₄²	—	2	1	no	—
296	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
297	#107	C₂×C₄×C₁₃	1	2	yes	—
298	#106	C₂×C₄×C₁₃	1	2	yes	—
299	C₄⋊C₈	—	2	2	no	—
300	C₄⋊C₈	—	2	2	no	—
301	C₄⋊C₈	—	2	1	no	—
302	C₄⋊C₈	—	2	1	no	—
303	C₄⋊C₈	—	2	1	no	—
304	C₄⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
305	C₄⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
306	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
307	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
308	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
309	#103	C₂×C₄×C₁₃	1	2	yes	—
310	#103	C₂×C₄×C₁₃	1	2	yes	—
311	#103	C₂×C₄×C₁₃	1	2	yes	—
312	#102	C₂×C₄×C₁₃	1	2	yes	—
313	C₂²⋊C₈	—	2	1	no	—
314	C₂²⋊C₈	—	2	1	no	—
315	C₂²⋊C₈	—	2	1	no	—
316	C₂²⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
317	#97	—	2	2	no	—
318	#97	—	2	1	no	—
319	C₄×C₈	—	2	1	no	—
320	C₄×C₈	—	2	1	no	—
321	C₄×C₈	—	2	2	no	—
322	C₄×C₈	—	2	1	no	—
323	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
324	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
325	C₄×C₈	C₂³×C₁₃	1	2	yes	—
326	C₄×C₈	C₂³×C₁₃	1	2	yes	—
327	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
328	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
329	C₂×C₁₃	—	4	1	no	—
330	C₂×C₁₃	—	4	2	no	—
331	C₂×C₁₃	#2929	1	1	yes	characteristic
332	C₂×C₁₃	C₄×#137	1	1	yes	characteristic
333	C₂×C₁₃	C₂×#444	1	1	yes	characteristic
334	#41	—	2	2	no	—
335	#41	—	2	2	no	—
336	C₂×Q₈	—	2	1	no	—
337	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
338	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
345	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
346	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
347	Q₁₆	—	2	4	no	—
348	SD₁₆	—	2	4	no	—
349	M₁₆	—	4	2	no	—
350	M₁₆	—	4	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	4	1	no	—
357	C₂×C₈	—	4	2	no	—
358	C₂×C₈	—	4	2	no	—
359	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
360	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
361	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
362	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
363	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
364	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
373	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
374	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
375	C₂²⋊C₄	—	2	2	no	—
376	C₂²⋊C₄	—	2	1	no	—
377	C₂²⋊C₄	—	2	1	no	—
378	C₂²⋊C₄	—	2	1	no	—
379	C₄²	—	2	1	no	—
380	C₄²	—	2	1	no	—
381	C₄²	—	2	1	no	—
382	C₄²	—	2	2	no	—
383	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
384	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
385	C₄²	C₁₃×#41	1	1	yes	characteristic
386	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
387	C₁₃	#17916	1	1	yes	characteristic, direct product factor, Sylow
388	C₂³	—	2	1	no	—
389	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
390	Q₈	—	2	1	no	—
391	Q₈	—	2	2	no	—
392	Q₈	—	2	2	no	—
393	Q₈	—	4	2	no	—
394	Q₈	C₁₃×#131	1	2	yes	—
395	D₄	—	2	4	no	—
396	D₄	—	2	1	no	—
397	D₄	C₁₃×#131	1	2	yes	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	2	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	1	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
413	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
414	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
415	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
417	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
418	C₈	—	2	2	no	—
419	C₈	—	2	2	no	—
420	C₈	—	2	1	no	—
421	C₈	—	2	1	no	—
422	C₈	—	2	1	no	—
423	C₈	—	4	2	no	—
424	C₈	—	4	1	no	—
425	C₈	—	4	1	no	—
426	C₈	—	4	2	no	—
427	C₈	C₁₃×#137	1	2	yes	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	4	1	no	—
433	C₂²	—	4	1	no	—
434	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
435	C₄	—	2	1	no	—
436	C₄	—	2	2	no	—
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	1	no	—
441	C₄	—	4	1	no	—
442	C₄	—	4	2	no	—
443	C₄	C₁₃×#444	1	2	yes	—
444	C₄	C₂×C₁₃×#131	1	1	yes	characteristic
445	C₄	C₂×C₁₃×#131	1	1	yes	characteristic
446	C₄	C₂×C₁₃×#137	1	1	yes	characteristic
447	C₄	C₁₃×#575	1	1	yes	characteristic
448	C₂	—	4	1	no	—
449	C₂	—	4	2	no	—
450	C₂	C₁₃×#2929	1	1	yes	characteristic
451	C₂	C₄×C₁₃×#137	1	1	yes	characteristic
452	C₂	C₂×C₁₃×#444	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂×C₁₃×#41	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#2960	C₂	semidirect
4. C₁₃×#1584	C₂	semidirect
5. C₁₃×#1582	C₂	semidirect
6. C₁₃×#1579	C₂	semidirect
7. C₁₃×SD₁₆⋊C₈	C₂	semidirect
8. C₁₃×#1574	C₂	semidirect
10. C₁₃×#1485	C₂	semidirect
11. C₁₃×#1451	C₂	semidirect
108. #17916	C₁₃	direct (N × H)
164. #2960	C₂×C₁₃	semidirect
165. #1584	C₂×C₁₃	semidirect
166. #1582	C₂×C₁₃	semidirect
167. #1579	C₂×C₁₃	semidirect
168. SD₁₆⋊C₈	C₂×C₁₃	semidirect
169. #1574	C₂×C₁₃	semidirect
171. #1485	C₂×C₁₃	semidirect
172. #1451	C₂×C₁₃	semidirect
387. C₁₃	#17916	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×#3107	2
C₈×C₁₃×#41	2
C₁₃×#2960	2
C₁₃×#1584	2
C₁₃×#1582	2
C₁₃×#1579	2
C₁₃×SD₁₆⋊C₈	2
C₁₃×#1574	2
C₁₃×#1489	2
C₁₃×#1485	2
C₁₃×#1451	2
#17916	13

Subgroups — C13×#17916 #15704255

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17916 #15704255