Subgroups — C₁₃×#26485 #15712824

Order 3328.

782 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#500	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2451	C₂	1	2	yes	maximal
4	C₁₃×#2068	C₂	1	2	yes	maximal
5	C₁₃×#2024	C₂	1	2	yes	maximal
6	C₁₃×#1969	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1969	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1942	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1942	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1863	C₂	1	2	yes	maximal
11	C₈×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
15	C₁₃×#500	—	2	4	no	—
16	C₄×C₁₃×Q₁₆	—	2	4	no	—
17	C₂×C₁₃×#107	C₂²	1	2	yes	—
18	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#103	C₂²	1	2	yes	—
23	C₂×C₁₃×#103	C₂²	1	2	yes	—
24	C₂×C₁₃×#103	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₁₃×#398	—	2	2	no	—
29	C₁₃×#395	—	2	2	no	—
30	C₁₃×#391	—	2	2	no	—
31	C₁₃×#391	C₂²	1	2	yes	—
32	C₁₃×#391	C₂²	1	2	yes	—
33	C₁₃×#389	C₂²	1	2	yes	—
34	C₁₃×#389	C₂²	1	2	yes	—
35	C₁₃×#387	—	2	2	no	—
36	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	C₂²×Q₈×C₁₃	—	2	2	no	—
42	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
43	C₂×C₁₃×Q₁₆	—	2	2	no	—
44	C₂×C₁₃×Q₁₆	—	2	2	no	—
45	C₂×C₁₃×Q₁₆	Q₈	1	4	yes	complemented
46	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₁₃×C₄⋊Q₈	—	2	4	no	—
51	C₁₃×C₄⋊Q₈	—	4	2	no	—
52	C₄×Q₈×C₁₃	—	2	4	no	—
53	C₄×Q₈×C₁₃	—	4	2	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
58	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
59	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
63	C₂×C₄²×C₁₃	—	2	2	no	—
64	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
67	C₁₃×#107	—	2	2	no	—
68	C₁₃×#107	—	2	2	no	—
69	C₁₃×#107	—	2	4	no	—
70	C₁₃×#107	D₄	1	4	yes	—
71	C₁₃×C₄⋊C₈	—	2	2	no	—
72	C₁₃×#103	—	2	4	no	—
73	C₁₃×#103	—	2	4	no	—
74	C₁₃×#103	—	4	2	no	—
75	C₄×C₈×C₁₃	—	2	2	no	—
76	C₄×C₈×C₁₃	—	2	2	no	—
77	C₄×C₈×C₁₃	—	2	2	no	—
78	C₁₃×#95	—	2	2	no	—
79	C₁₃×#95	—	2	2	no	—
80	C₁₃×#95	—	2	2	no	—
81	C₁₃×#95	—	2	2	no	—
82	C₁₃×#95	—	2	2	no	—
83	C₁₃×#95	—	2	2	no	—
84	C₁₃×#95	D₄	1	1	yes	characteristic
85	C₁₃×#95	D₄	1	1	yes	characteristic
86	#26485	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
87	C₂×Q₈×C₁₃	—	2	2	no	—
88	C₂×Q₈×C₁₃	—	2	2	no	—
89	C₂×Q₈×C₁₃	—	2	2	no	—
90	C₂×Q₈×C₁₃	—	2	2	no	—
91	C₂×Q₈×C₁₃	—	2	2	no	—
92	C₂×Q₈×C₁₃	—	4	4	no	—
93	C₂×Q₈×C₁₃	—	4	4	no	—
94	C₂×Q₈×C₁₃	—	8	2	no	—
95	C₂×Q₈×C₁₃	C₂×Q₈	1	4	yes	—
96	C₂²×C₄×C₁₃	—	2	2	no	—
97	C₂²×C₄×C₁₃	—	2	2	no	—
98	C₂²×C₄×C₁₃	—	2	2	no	—
99	C₂²×C₄×C₁₃	—	2	2	no	—
100	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
107	C₁₃×Q₁₆	—	2	8	no	—
108	C₂×C₈×C₁₃	—	2	1	no	—
109	C₂×C₈×C₁₃	—	2	1	no	—
110	C₂×C₈×C₁₃	—	2	1	no	—
111	C₂×C₈×C₁₃	—	2	1	no	—
112	C₂×C₈×C₁₃	—	2	1	no	—
113	C₂×C₈×C₁₃	—	2	1	no	—
114	C₂×C₈×C₁₃	—	2	1	no	—
115	C₂×C₈×C₁₃	—	2	1	no	—
116	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
117	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
118	C₂×C₈×C₁₃	#41	1	2	yes	—
119	C₂×C₈×C₁₃	#41	1	2	yes	—
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	—	2	2	no	—
125	C₁₃×C₄⋊C₄	—	2	2	no	—
126	C₁₃×C₄⋊C₄	—	4	4	no	—
127	C₁₃×C₄⋊C₄	—	4	4	no	—
128	C₁₃×C₄⋊C₄	—	8	2	no	—
129	C₁₃×C₄⋊C₄	—	8	2	no	—
130	C₁₃×C₄⋊C₄	Q₁₆	1	4	yes	complemented
131	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
132	C₄²×C₁₃	—	2	1	no	—
133	C₄²×C₁₃	—	2	1	no	—
134	C₄²×C₁₃	—	2	1	no	—
135	C₄²×C₁₃	—	2	1	no	—
136	C₄²×C₁₃	—	2	1	no	—
137	C₄²×C₁₃	—	2	1	no	—
138	C₄²×C₁₃	—	4	4	no	—
139	C₂×#500	C₂×C₁₃	1	1	yes	characteristic
140	C₂×C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic
141	#2451	C₂×C₁₃	1	2	yes	—
142	#2068	C₂×C₁₃	1	2	yes	—
143	#2024	C₂×C₁₃	1	2	yes	—
144	#1969	C₂×C₁₃	1	1	yes	characteristic
145	#1969	C₂×C₁₃	1	1	yes	characteristic
146	#1942	C₂×C₁₃	1	1	yes	characteristic
147	#1942	C₂×C₁₃	1	1	yes	characteristic
148	#1863	C₂×C₁₃	1	2	yes	—
149	C₈×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
150	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
151	Q₈×C₁₃	—	2	4	no	—
152	Q₈×C₁₃	—	2	4	no	—
153	Q₈×C₁₃	—	4	2	no	—
154	Q₈×C₁₃	—	4	2	no	—
155	Q₈×C₁₃	—	8	8	no	—
156	C₂×C₄×C₁₃	—	2	1	no	—
157	C₂×C₄×C₁₃	—	2	1	no	—
158	C₂×C₄×C₁₃	—	2	1	no	—
159	C₂×C₄×C₁₃	—	2	1	no	—
160	C₂×C₄×C₁₃	—	2	1	no	—
161	C₂×C₄×C₁₃	—	2	1	no	—
162	C₂×C₄×C₁₃	—	2	1	no	—
163	C₂×C₄×C₁₃	—	2	1	no	—
164	C₂×C₄×C₁₃	—	2	1	no	—
165	C₂×C₄×C₁₃	—	2	1	no	—
166	C₂×C₄×C₁₃	—	2	4	no	—
167	C₂×C₄×C₁₃	—	2	4	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	—	4	2	no	—
173	C₂×C₄×C₁₃	—	4	2	no	—
174	C₂×C₄×C₁₃	—	4	2	no	—
175	C₂×C₄×C₁₃	—	4	2	no	—
176	C₂×C₄×C₁₃	—	4	2	no	—
177	C₂×C₄×C₁₃	—	4	2	no	—
178	C₂×C₄×C₁₃	—	4	2	no	—
179	C₂×C₄×C₁₃	—	4	2	no	—
180	C₂×C₄×C₁₃	—	4	2	no	—
181	C₂×C₄×C₁₃	—	4	2	no	—
182	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
183	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
184	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
185	C₂×C₄×C₁₃	#135	1	2	yes	—
186	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
188	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
191	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
192	C₈×C₁₃	—	2	2	no	—
193	C₈×C₁₃	—	4	1	no	—
194	C₈×C₁₃	—	4	1	no	—
195	C₈×C₁₃	C₂²⋊Q₈	1	4	yes	—
196	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
197	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
198	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
199	#500	—	2	4	no	—
200	C₄×Q₁₆	—	2	4	no	—
201	C₂×#107	C₂²×C₁₃	1	2	yes	—
202	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
203	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
204	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
205	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
206	C₂×#103	C₂²×C₁₃	1	2	yes	—
207	C₂×#103	C₂²×C₁₃	1	2	yes	—
208	C₂×#103	C₂²×C₁₃	1	2	yes	—
209	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
210	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
211	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
212	#398	—	2	2	no	—
213	#395	—	2	2	no	—
214	#391	—	2	2	no	—
215	#391	C₂²×C₁₃	1	2	yes	—
216	#391	C₂²×C₁₃	1	2	yes	—
217	#389	C₂²×C₁₃	1	2	yes	—
218	#389	C₂²×C₁₃	1	2	yes	—
219	#387	—	2	2	no	—
220	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
221	#340	C₂²×C₁₃	1	2	yes	—
222	#340	C₂²×C₁₃	1	2	yes	—
223	#336	C₂²×C₁₃	1	1	yes	characteristic
224	#336	C₂²×C₁₃	1	1	yes	characteristic
225	C₂²×C₁₃	#532	1	1	yes	characteristic
226	C₂²×C₁₃	D₄²	1	1	yes	characteristic
227	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
228	C₂²×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
229	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
230	C₂²×C₁₃	#576	1	1	yes	characteristic
231	C₂²×C₁₃	#578	1	1	yes	characteristic
232	C₄×C₁₃	—	2	2	no	—
233	C₄×C₁₃	—	2	2	no	—
234	C₄×C₁₃	—	2	2	no	—
235	C₄×C₁₃	—	2	2	no	—
236	C₄×C₁₃	—	4	1	no	—
237	C₄×C₁₃	—	4	4	no	—
238	C₄×C₁₃	—	4	1	no	—
239	C₄×C₁₃	—	4	4	no	—
240	C₄×C₁₃	—	8	2	no	—
241	C₄×C₁₃	—	8	2	no	—
242	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
243	C₄×C₁₃	#542	1	1	yes	characteristic
244	C₄×C₁₃	#548	1	1	yes	characteristic
245	C₄×C₁₃	#554	1	1	yes	characteristic
246	C₂²×Q₈	—	2	2	no	—
247	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
248	C₂×Q₁₆	—	2	2	no	—
249	C₂×Q₁₆	—	2	2	no	—
250	C₂×Q₁₆	Q₈×C₁₃	1	4	yes	complemented
251	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
252	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
253	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
254	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
255	C₄⋊Q₈	—	2	4	no	—
256	C₄⋊Q₈	—	4	2	no	—
257	C₄×Q₈	—	2	4	no	—
258	C₄×Q₈	—	4	2	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
264	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
265	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
266	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
267	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
268	C₂×C₄²	—	2	2	no	—
269	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
270	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
271	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
272	#107	—	2	2	no	—
273	#107	—	2	2	no	—
274	#107	—	2	4	no	—
275	#107	D₄×C₁₃	1	4	yes	—
276	C₄⋊C₈	—	2	2	no	—
277	#103	—	2	4	no	—
278	#103	—	2	4	no	—
279	#103	—	4	2	no	—
280	C₄×C₈	—	2	2	no	—
281	C₄×C₈	—	2	2	no	—
282	C₄×C₈	—	2	2	no	—
283	#95	—	2	2	no	—
284	#95	—	2	2	no	—
285	#95	—	2	2	no	—
286	#95	—	2	2	no	—
287	#95	—	2	2	no	—
288	#95	—	2	2	no	—
289	#95	D₄×C₁₃	1	1	yes	characteristic
290	#95	D₄×C₁₃	1	1	yes	characteristic
291	C₂×C₁₃	#2452	1	1	yes	characteristic
292	C₂×C₁₃	#3170	1	1	yes	characteristic
293	C₂×C₁₃	#3175	1	1	yes	characteristic
294	C₂×C₁₃	#3280	1	1	yes	characteristic
295	C₂×C₁₃	D₄×Q₁₆	1	1	yes	characteristic
296	C₂×C₁₃	Q₈×Q₁₆	1	1	yes	characteristic
297	C₂×C₁₃	#3383	1	1	yes	characteristic
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	—	4	4	no	—
304	C₂×Q₈	—	4	4	no	—
305	C₂×Q₈	—	8	2	no	—
306	C₂×Q₈	C₂×Q₈×C₁₃	1	4	yes	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
312	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
313	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
314	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
315	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
316	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
317	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
318	Q₁₆	—	2	8	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
328	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
329	C₂×C₈	C₁₃×#41	1	2	yes	—
330	C₂×C₈	C₁₃×#41	1	2	yes	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	4	4	no	—
338	C₄⋊C₄	—	4	4	no	—
339	C₄⋊C₄	—	8	2	no	—
340	C₄⋊C₄	—	8	2	no	—
341	C₄⋊C₄	C₁₃×Q₁₆	1	4	yes	complemented
342	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
343	C₄²	—	2	1	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	2	1	no	—
346	C₄²	—	2	1	no	—
347	C₄²	—	2	1	no	—
348	C₄²	—	2	1	no	—
349	C₄²	—	4	4	no	—
350	C₁₃	#26485	1	1	yes	characteristic, direct product factor, Sylow
351	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
352	Q₈	—	2	4	no	—
353	Q₈	—	2	4	no	—
354	Q₈	—	4	2	no	—
355	Q₈	—	4	2	no	—
356	Q₈	—	8	8	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
384	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
385	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
386	C₂×C₄	C₁₃×#135	1	2	yes	—
387	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
388	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
389	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
390	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
391	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
392	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
393	C₈	—	2	2	no	—
394	C₈	—	4	1	no	—
395	C₈	—	4	1	no	—
396	C₈	C₁₃×C₂²⋊Q₈	1	4	yes	—
397	C₂²	C₁₃×#532	1	1	yes	characteristic
398	C₂²	D₄²×C₁₃	1	1	yes	characteristic
399	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
400	C₂²	C₂²×C₁₃×Q₁₆	1	1	yes	characteristic
401	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
402	C₂²	C₁₃×#576	1	1	yes	characteristic
403	C₂²	C₁₃×#578	1	1	yes	characteristic
404	C₄	—	2	2	no	—
405	C₄	—	2	2	no	—
406	C₄	—	2	2	no	—
407	C₄	—	2	2	no	—
408	C₄	—	4	1	no	—
409	C₄	—	4	4	no	—
410	C₄	—	4	1	no	—
411	C₄	—	4	4	no	—
412	C₄	—	8	2	no	—
413	C₄	—	8	2	no	—
414	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
415	C₄	C₁₃×#542	1	1	yes	characteristic
416	C₄	C₁₃×#548	1	1	yes	characteristic
417	C₄	C₁₃×#554	1	1	yes	characteristic
418	C₂	C₁₃×#2452	1	1	yes	characteristic
419	C₂	C₁₃×#3170	1	1	yes	characteristic
420	C₂	C₁₃×#3175	1	1	yes	characteristic
421	C₂	C₁₃×#3280	1	1	yes	characteristic
422	C₂	D₄×C₁₃×Q₁₆	1	1	yes	characteristic
423	C₂	Q₈×C₁₃×Q₁₆	1	1	yes	characteristic
424	C₂	C₁₃×#3383	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
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
45. C₂×C₁₃×Q₁₆	Q₈	semidirect
86. #26485	C₁₃	direct (N × H)
130. C₁₃×C₄⋊C₄	Q₁₆	semidirect
250. C₂×Q₁₆	Q₈×C₁₃	semidirect
341. C₄⋊C₄	C₁₃×Q₁₆	semidirect
350. C₁₃	#26485	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×#500	2
C₂×C₄×C₁₃×Q₁₆	2
C₁₃×#2451	2
C₁₃×#2068	2
C₁₃×#2024	2
C₁₃×#1969	2
C₁₃×#1942	2
C₁₃×#1863	2
C₈×C₁₃×C₄⋊C₄	2
#26485	13

Subgroups — C13×#26485 #15712824

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26485 #15712824