Subgroups — C₁₃×#24696 #15711035

Order 3328.

796 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#474	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#440	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2567	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2357	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2071	C₂	1	2	yes	maximal
6	C₁₃×#2055	C₂	1	2	yes	maximal
7	C₁₃×#1993	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1947	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1940	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1928	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1805	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₁₃×#474	—	2	4	no	—
17	C₁₃×#440	—	2	4	no	—
18	C₂×C₁₃×#107	C₂²	1	2	yes	—
19	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
22	C₂×C₁₃×#103	C₂²	1	2	yes	—
23	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#102	C₂²	1	2	yes	—
25	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
27	C₁₃×#395	—	2	1	no	—
28	C₁₃×#395	—	2	1	no	—
29	C₁₃×#391	C₂²	1	2	yes	—
30	C₁₃×#390	C₂²	1	2	yes	—
31	C₁₃×#389	—	2	2	no	—
32	C₁₃×#388	—	2	2	no	—
33	C₁₃×#384	C₂²	1	2	yes	—
34	C₁₃×#382	C₂²	1	1	yes	characteristic
35	C₁₃×#381	—	2	1	no	—
36	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
37	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
39	C₁₃×#340	C₂²	1	2	yes	—
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#340	C₂²	1	2	yes	—
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	C₂×C₁₃×SD₁₆	—	2	2	no	—
48	C₂×C₁₃×SD₁₆	—	2	2	no	—
49	C₂×C₁₃×SD₁₆	—	2	2	no	—
50	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₁₃×C₄⋊Q₈	—	2	2	no	—
54	C₁₃×C₄⋊Q₈	—	2	2	no	—
55	C₄×Q₈×C₁₃	—	2	2	no	—
56	C₄×Q₈×C₁₃	—	2	2	no	—
57	C₄×D₄×C₁₃	—	2	2	no	—
58	C₄×D₄×C₁₃	D₄	1	4	yes	—
59	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
63	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
68	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
69	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
70	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
71	C₂×C₄²×C₁₃	—	2	1	no	—
72	C₂×C₄²×C₁₃	—	2	2	no	—
73	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
74	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
75	C₁₃×#107	—	2	2	no	—
76	C₁₃×#107	—	2	4	no	—
77	C₁₃×C₄⋊C₈	—	2	4	no	—
78	C₁₃×C₄⋊C₈	—	2	2	no	—
79	C₁₃×#103	—	2	4	no	—
80	C₁₃×#103	—	2	2	no	—
81	C₁₃×#102	—	2	2	no	—
82	C₁₃×#102	—	2	4	no	—
83	C₁₃×#97	—	2	2	no	—
84	C₁₃×#95	—	2	1	no	—
85	C₁₃×#95	—	2	2	no	—
86	C₁₃×#95	—	2	1	no	—
87	C₁₃×#95	—	2	2	no	—
88	C₁₃×#95	—	2	2	no	—
89	C₁₃×#95	D₄	1	1	yes	characteristic
90	C₁₃×#95	D₄	1	1	yes	characteristic
91	#24696	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
92	C₂⁴×C₁₃	—	2	1	no	—
93	C₂×Q₈×C₁₃	—	2	1	no	—
94	C₂×Q₈×C₁₃	—	2	1	no	—
95	C₂×Q₈×C₁₃	—	2	1	no	—
96	C₂×Q₈×C₁₃	—	2	1	no	—
97	C₂×Q₈×C₁₃	—	2	1	no	—
98	C₂×Q₈×C₁₃	—	4	2	no	—
99	C₂×Q₈×C₁₃	—	8	2	no	—
100	C₂×Q₈×C₁₃	#41	1	2	yes	—
101	C₂×D₄×C₁₃	—	2	1	no	—
102	C₂×D₄×C₁₃	—	2	1	no	—
103	C₂×D₄×C₁₃	—	2	1	no	—
104	C₂×D₄×C₁₃	—	2	1	no	—
105	C₂×D₄×C₁₃	—	2	1	no	—
106	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₃	—	2	1	no	—
108	C₂²×C₄×C₁₃	—	2	1	no	—
109	C₂²×C₄×C₁₃	—	2	4	no	—
110	C₂²×C₄×C₁₃	—	2	2	no	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	—	2	1	no	—
113	C₂²×C₄×C₁₃	—	8	2	no	—
114	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
119	C₁₃×SD₁₆	—	2	8	no	—
120	C₂×C₈×C₁₃	—	2	1	no	—
121	C₂×C₈×C₁₃	—	2	1	no	—
122	C₂×C₈×C₁₃	—	2	1	no	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	—	2	2	no	—
125	C₂×C₈×C₁₃	—	2	2	no	—
126	C₂×C₈×C₁₃	—	2	1	no	—
127	C₂×C₈×C₁₃	—	2	1	no	—
128	C₂×C₈×C₁₃	#41	1	2	yes	—
129	C₁₃×C₄⋊C₄	—	2	4	no	—
130	C₁₃×C₄⋊C₄	—	2	1	no	—
131	C₁₃×C₄⋊C₄	—	2	1	no	—
132	C₁₃×C₄⋊C₄	—	2	2	no	—
133	C₁₃×C₄⋊C₄	—	2	2	no	—
134	C₁₃×C₄⋊C₄	—	2	1	no	—
135	C₁₃×C₄⋊C₄	—	2	2	no	—
136	C₁₃×C₄⋊C₄	—	2	2	no	—
137	C₁₃×C₄⋊C₄	—	4	2	no	—
138	C₁₃×C₄⋊C₄	—	4	2	no	—
139	C₁₃×C₄⋊C₄	—	8	2	no	—
140	C₁₃×C₄⋊C₄	—	8	2	no	—
141	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
142	C₁₃×C₂²⋊C₄	—	2	4	no	—
143	C₁₃×C₂²⋊C₄	—	4	4	no	—
144	C₁₃×C₂²⋊C₄	—	8	2	no	—
145	C₄²×C₁₃	—	2	2	no	—
146	C₄²×C₁₃	—	2	2	no	—
147	C₄²×C₁₃	—	4	2	no	—
148	C₄²×C₁₃	—	8	2	no	—
149	C₄²×C₁₃	C₂×D₄	1	2	yes	—
150	C₄²×C₁₃	#41	1	2	yes	—
151	C₂×#474	C₂×C₁₃	1	1	yes	characteristic
152	C₂×#440	C₂×C₁₃	1	1	yes	characteristic
153	#2567	C₂×C₁₃	1	1	yes	characteristic, complemented
154	#2357	C₂×C₁₃	1	1	yes	characteristic
155	#2071	C₂×C₁₃	1	2	yes	—
156	#2055	C₂×C₁₃	1	2	yes	—
157	#1993	C₂×C₁₃	1	1	yes	characteristic, complemented
158	#1947	C₂×C₁₃	1	2	yes	complemented
159	#1940	C₂×C₁₃	1	1	yes	characteristic, complemented
160	#1928	C₂×C₁₃	1	2	yes	complemented
161	#1805	C₂×C₁₃	1	1	yes	characteristic, complemented
162	C₂³×C₁₃	—	2	2	no	—
163	C₂³×C₁₃	—	4	1	no	—
164	C₂³×C₁₃	—	4	1	no	—
165	C₂³×C₁₃	—	4	2	no	—
166	C₂³×C₁₃	—	4	2	no	—
167	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
168	Q₈×C₁₃	—	2	2	no	—
169	Q₈×C₁₃	—	2	2	no	—
170	Q₈×C₁₃	—	4	1	no	—
171	Q₈×C₁₃	—	4	1	no	—
172	Q₈×C₁₃	—	8	4	no	—
173	D₄×C₁₃	—	2	2	no	—
174	D₄×C₁₃	—	2	2	no	—
175	D₄×C₁₃	—	4	1	no	—
176	D₄×C₁₃	—	4	1	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	2	no	—
180	C₂×C₄×C₁₃	—	2	2	no	—
181	C₂×C₄×C₁₃	—	2	2	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	4	1	no	—
187	C₂×C₄×C₁₃	—	4	1	no	—
188	C₂×C₄×C₁₃	—	4	2	no	—
189	C₂×C₄×C₁₃	—	4	1	no	—
190	C₂×C₄×C₁₃	—	4	2	no	—
191	C₂×C₄×C₁₃	—	4	2	no	—
192	C₂×C₄×C₁₃	—	4	2	no	—
193	C₂×C₄×C₁₃	—	4	2	no	—
194	C₂×C₄×C₁₃	—	4	2	no	—
195	C₂×C₄×C₁₃	—	4	2	no	—
196	C₂×C₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	—	8	4	no	—
198	C₂×C₄×C₁₃	#121	1	2	yes	—
199	C₂×C₄×C₁₃	#121	1	2	yes	—
200	C₂×C₄×C₁₃	#137	1	4	yes	—
201	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
204	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
206	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
207	C₈×C₁₃	—	2	2	no	—
208	C₈×C₁₃	—	4	2	no	—
209	C₈×C₁₃	—	4	1	no	—
210	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
211	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
212	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
213	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
214	#474	—	2	4	no	—
215	#440	—	2	4	no	—
216	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
217	C₂×#107	C₂²×C₁₃	1	2	yes	—
218	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
219	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
220	C₂×#103	C₂²×C₁₃	1	2	yes	—
221	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
222	C₂×#102	C₂²×C₁₃	1	2	yes	—
223	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
224	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
225	#395	—	2	1	no	—
226	#395	—	2	1	no	—
227	#391	C₂²×C₁₃	1	2	yes	—
228	#390	C₂²×C₁₃	1	2	yes	—
229	#389	—	2	2	no	—
230	#388	—	2	2	no	—
231	#384	C₂²×C₁₃	1	2	yes	—
232	#382	C₂²×C₁₃	1	1	yes	characteristic
233	#381	—	2	1	no	—
234	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
235	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
236	C₄×C₂²⋊C₄	—	2	1	no	—
237	#340	C₂²×C₁₃	1	2	yes	—
238	#340	C₂²×C₁₃	1	2	yes	—
239	#340	C₂²×C₁₃	1	2	yes	—
240	#336	C₂²×C₁₃	1	2	yes	—
241	C₂²×C₁₃	—	4	2	no	—
242	C₂²×C₁₃	—	4	2	no	—
243	C₂²×C₁₃	—	4	2	no	—
244	C₂²×C₁₃	—	8	2	no	—
245	C₂²×C₁₃	—	8	2	no	—
246	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
247	C₂²×C₁₃	#547	1	1	yes	characteristic
248	C₂²×C₁₃	#548	1	1	yes	characteristic
249	C₂²×C₁₃	C₂×#137	1	2	yes	—
250	C₂²×C₁₃	#576	1	2	yes	—
251	C₄×C₁₃	—	2	4	no	—
252	C₄×C₁₃	—	2	2	no	—
253	C₄×C₁₃	—	2	2	no	—
254	C₄×C₁₃	—	4	2	no	—
255	C₄×C₁₃	—	4	2	no	—
256	C₄×C₁₃	—	4	2	no	—
257	C₄×C₁₃	—	8	2	no	—
258	C₄×C₁₃	—	8	1	no	—
259	C₄×C₁₃	—	8	2	no	—
260	C₄×C₁₃	#525	1	1	yes	characteristic
261	C₄×C₁₃	#536	1	1	yes	characteristic
262	C₄×C₁₃	#552	1	1	yes	characteristic
263	C₄×C₁₃	#556	1	1	yes	characteristic
264	C₂²×Q₈	—	2	1	no	—
265	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
266	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
267	C₂³×C₄	—	2	1	no	—
268	C₂×SD₁₆	—	2	2	no	—
269	C₂×SD₁₆	—	2	2	no	—
270	C₂×SD₁₆	—	2	2	no	—
271	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
272	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
273	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
274	C₄⋊Q₈	—	2	2	no	—
275	C₄⋊Q₈	—	2	2	no	—
276	C₄×Q₈	—	2	2	no	—
277	C₄×Q₈	—	2	2	no	—
278	C₄×D₄	—	2	2	no	—
279	C₄×D₄	D₄×C₁₃	1	4	yes	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
285	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
287	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
288	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
289	C₂×C₂²⋊C₄	—	2	1	no	—
290	C₂×C₂²⋊C₄	—	2	2	no	—
291	C₂×C₂²⋊C₄	—	2	2	no	—
292	C₂×C₄²	—	2	1	no	—
293	C₂×C₄²	—	2	2	no	—
294	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
295	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
296	#107	—	2	2	no	—
297	#107	—	2	4	no	—
298	C₄⋊C₈	—	2	4	no	—
299	C₄⋊C₈	—	2	2	no	—
300	#103	—	2	4	no	—
301	#103	—	2	2	no	—
302	#102	—	2	2	no	—
303	#102	—	2	4	no	—
304	#97	—	2	2	no	—
305	#95	—	2	1	no	—
306	#95	—	2	2	no	—
307	#95	—	2	1	no	—
308	#95	—	2	2	no	—
309	#95	—	2	2	no	—
310	#95	D₄×C₁₃	1	1	yes	characteristic
311	#95	D₄×C₁₃	1	1	yes	characteristic
312	C₂×C₁₃	—	8	2	no	—
313	C₂×C₁₃	#2415	1	1	yes	characteristic
314	C₂×C₁₃	#3039	1	1	yes	characteristic
315	C₂×C₁₃	#3041	1	1	yes	characteristic
316	C₂×C₁₃	#3346	1	2	yes	—
317	C₂×C₁₃	#3375	1	2	yes	—
318	C₂⁴	—	2	1	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	2	1	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	4	2	no	—
325	C₂×Q₈	—	8	2	no	—
326	C₂×Q₈	C₁₃×#41	1	2	yes	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	4	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	8	2	no	—
340	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
341	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
342	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
344	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
345	SD₁₆	—	2	8	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	C₁₃×#41	1	2	yes	—
355	C₄⋊C₄	—	2	4	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	4	2	no	—
364	C₄⋊C₄	—	4	2	no	—
365	C₄⋊C₄	—	8	2	no	—
366	C₄⋊C₄	—	8	2	no	—
367	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
368	C₂²⋊C₄	—	2	4	no	—
369	C₂²⋊C₄	—	4	4	no	—
370	C₂²⋊C₄	—	8	2	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	4	2	no	—
374	C₄²	—	8	2	no	—
375	C₄²	C₂×D₄×C₁₃	1	2	yes	—
376	C₄²	C₁₃×#41	1	2	yes	—
377	C₁₃	#24696	1	1	yes	characteristic, direct product factor, Sylow
378	C₂³	—	2	2	no	—
379	C₂³	—	4	1	no	—
380	C₂³	—	4	1	no	—
381	C₂³	—	4	2	no	—
382	C₂³	—	4	2	no	—
383	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
384	Q₈	—	2	2	no	—
385	Q₈	—	2	2	no	—
386	Q₈	—	4	1	no	—
387	Q₈	—	4	1	no	—
388	Q₈	—	8	4	no	—
389	D₄	—	2	2	no	—
390	D₄	—	2	2	no	—
391	D₄	—	4	1	no	—
392	D₄	—	4	1	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	8	4	no	—
414	C₂×C₄	C₁₃×#121	1	2	yes	—
415	C₂×C₄	C₁₃×#121	1	2	yes	—
416	C₂×C₄	C₁₃×#137	1	4	yes	—
417	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
418	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
419	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
420	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
421	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
422	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
423	C₈	—	2	2	no	—
424	C₈	—	4	2	no	—
425	C₈	—	4	1	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	8	2	no	—
430	C₂²	—	8	2	no	—
431	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
432	C₂²	C₁₃×#547	1	1	yes	characteristic
433	C₂²	C₁₃×#548	1	1	yes	characteristic
434	C₂²	C₂×C₁₃×#137	1	2	yes	—
435	C₂²	C₁₃×#576	1	2	yes	—
436	C₄	—	2	2	no	—
437	C₄	—	2	2	no	—
438	C₄	—	2	4	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	2	no	—
441	C₄	—	4	2	no	—
442	C₄	—	8	1	no	—
443	C₄	—	8	2	no	—
444	C₄	—	8	2	no	—
445	C₄	C₁₃×#525	1	1	yes	characteristic
446	C₄	C₁₃×#536	1	1	yes	characteristic
447	C₄	C₁₃×#552	1	1	yes	characteristic
448	C₄	C₁₃×#556	1	1	yes	characteristic
449	C₂	—	8	2	no	—
450	C₂	C₁₃×#2415	1	1	yes	characteristic
451	C₂	C₁₃×#3039	1	1	yes	characteristic
452	C₂	C₁₃×#3041	1	1	yes	characteristic
453	C₂	C₁₃×#3346	1	2	yes	—
454	C₂	C₁₃×#3375	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 ◁ C₄×C₁₃×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#2567	C₂	semidirect
7. C₁₃×#1993	C₂	semidirect
8. C₁₃×#1947	C₂	semidirect
9. C₁₃×#1940	C₂	semidirect
10. C₁₃×#1928	C₂	semidirect
11. C₁₃×#1805	C₂	semidirect
91. #24696	C₁₃	direct (N × H)
153. #2567	C₂×C₁₃	semidirect
157. #1993	C₂×C₁₃	semidirect
158. #1947	C₂×C₁₃	semidirect
159. #1940	C₂×C₁₃	semidirect
160. #1928	C₂×C₁₃	semidirect
161. #1805	C₂×C₁₃	semidirect
377. C₁₃	#24696	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×C₁₃×#474	2
C₂×C₁₃×#440	2
C₁₃×#2567	2
C₁₃×#2357	2
C₁₃×#2071	2
C₁₃×#2055	2
C₁₃×#1993	2
C₁₃×#1947	2
C₁₃×#1940	2
C₁₃×#1928	2
C₁₃×#1805	2
#24696	13

Subgroups — C13×#24696 #15711035

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24696 #15711035