Subgroups — C₁₃×#26043 #15712382

Order 3328.

758 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#479	C₂	1	2	yes	maximal
2	C₁₃×#2552	C₂	1	1	yes	maximal, characteristic
3	Q₈×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2088	C₂	1	2	yes	maximal
5	C₁₃×#2059	C₂	1	2	yes	maximal
6	C₁₃×#1947	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1939	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1865	C₂	1	2	yes	maximal
9	C₁₃×#1844	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1803	C₂	1	1	yes	maximal, characteristic
11	C₄×C₁₃×#103	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×#125	C₂²	1	2	yes	—
13	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
14	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₁₃×#479	—	2	8	no	—
16	C₂×C₁₃×#107	C₂²	1	2	yes	—
17	C₂×C₁₃×#106	C₂²	1	2	yes	—
18	C₂×C₁₃×#106	C₂²	1	2	yes	—
19	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
20	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#103	C₂²	1	2	yes	—
22	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
25	C₁₃×#398	—	2	2	no	—
26	C₁₃×#389	—	2	1	no	—
27	C₁₃×#389	—	2	2	no	—
28	C₁₃×#389	C₂²	1	2	yes	—
29	C₁₃×#389	C₂²	1	2	yes	—
30	C₁₃×#384	—	2	1	no	—
31	C₁₃×#384	—	2	1	no	—
32	C₁₃×#384	C₂²	1	1	yes	characteristic
33	C₁₃×#384	C₂²	1	1	yes	characteristic
34	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
35	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₁₃×#340	C₂²	1	1	yes	characteristic
38	C₁₃×#340	C₂²	1	1	yes	characteristic
39	C₁₃×#340	C₂²	1	2	yes	—
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#336	C₂²	1	2	yes	—
42	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
44	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
46	C₁₃×#125	—	2	4	no	—
47	C₁₃×#125	—	4	2	no	—
48	C₄×Q₈×C₁₃	—	2	2	no	—
49	C₄×Q₈×C₁₃	—	2	4	no	—
50	C₄×Q₈×C₁₃	—	4	2	no	—
51	C₄×Q₈×C₁₃	Q₈	1	4	yes	—
52	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	1	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	—	2	2	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
62	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
63	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₁₃	—	2	1	no	—
70	C₂×C₄²×C₁₃	—	2	2	no	—
71	C₂×C₄²×C₁₃	—	2	1	no	—
72	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
73	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
74	C₁₃×#107	—	2	4	no	—
75	C₁₃×#106	—	2	4	no	—
76	C₁₃×#106	—	4	2	no	—
77	C₁₃×C₄⋊C₈	—	2	4	no	—
78	C₁₃×C₄⋊C₈	—	2	2	no	—
79	C₁₃×#103	—	2	4	no	—
80	C₁₃×#103	D₄	1	4	yes	—
81	C₁₃×#103	Q₈	1	4	yes	—
82	C₄×C₈×C₁₃	—	2	2	no	—
83	C₁₃×#95	—	2	2	no	—
84	C₁₃×#95	—	2	1	no	—
85	C₁₃×#95	—	2	2	no	—
86	C₁₃×#95	D₄	1	2	yes	—
87	#26043	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
88	C₂×Q₈×C₁₃	—	2	1	no	—
89	C₂×Q₈×C₁₃	—	2	1	no	—
90	C₂×Q₈×C₁₃	—	2	1	no	—
91	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
92	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
93	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
94	C₂²×C₄×C₁₃	—	2	1	no	—
95	C₂²×C₄×C₁₃	—	2	1	no	—
96	C₂²×C₄×C₁₃	—	2	1	no	—
97	C₂²×C₄×C₁₃	—	2	1	no	—
98	C₂²×C₄×C₁₃	—	2	2	no	—
99	C₂²×C₄×C₁₃	—	2	2	no	—
100	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
105	C₂×C₈×C₁₃	—	2	1	no	—
106	C₂×C₈×C₁₃	—	2	1	no	—
107	C₂×C₈×C₁₃	—	2	1	no	—
108	C₂×C₈×C₁₃	—	2	1	no	—
109	C₂×C₈×C₁₃	—	2	2	no	—
110	C₂×C₈×C₁₃	—	2	2	no	—
111	C₂×C₈×C₁₃	—	2	2	no	—
112	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
113	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
114	C₁₃×C₄⋊C₄	—	2	4	no	—
115	C₁₃×C₄⋊C₄	—	2	2	no	—
116	C₁₃×C₄⋊C₄	—	2	2	no	—
117	C₁₃×C₄⋊C₄	—	2	1	no	—
118	C₁₃×C₄⋊C₄	—	2	1	no	—
119	C₁₃×C₄⋊C₄	—	2	1	no	—
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	—	4	4	no	—
125	C₁₃×C₄⋊C₄	—	4	4	no	—
126	C₁₃×C₄⋊C₄	—	4	4	no	—
127	C₁₃×C₄⋊C₄	—	4	2	no	—
128	C₁₃×C₄⋊C₄	—	4	2	no	—
129	C₁₃×C₄⋊C₄	—	8	1	no	—
130	C₁₃×C₄⋊C₄	—	8	1	no	—
131	C₁₃×C₄⋊C₄	—	8	2	no	—
132	C₁₃×C₄⋊C₄	—	8	2	no	—
133	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
134	C₁₃×C₄⋊C₄	C₂×Q₈	1	2	yes	—
135	C₁₃×C₄⋊C₄	C₂×Q₈	1	2	yes	—
136	C₄²×C₁₃	—	2	4	no	—
137	C₄²×C₁₃	—	2	2	no	—
138	C₄²×C₁₃	—	2	2	no	—
139	C₄²×C₁₃	—	4	4	no	—
140	C₄²×C₁₃	—	4	2	no	—
141	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
142	C₄²×C₁₃	#41	1	2	yes	—
143	C₂×#479	C₂×C₁₃	1	2	yes	—
144	#2552	C₂×C₁₃	1	1	yes	characteristic
145	Q₈×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
146	#2088	C₂×C₁₃	1	2	yes	—
147	#2059	C₂×C₁₃	1	2	yes	—
148	#1947	C₂×C₁₃	1	1	yes	characteristic
149	#1939	C₂×C₁₃	1	1	yes	characteristic
150	#1865	C₂×C₁₃	1	2	yes	—
151	#1844	C₂×C₁₃	1	1	yes	characteristic
152	#1803	C₂×C₁₃	1	1	yes	characteristic
153	C₄×#103	C₂×C₁₃	1	1	yes	characteristic
154	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
155	Q₈×C₁₃	—	2	2	no	—
156	Q₈×C₁₃	—	2	2	no	—
157	Q₈×C₁₃	—	2	2	no	—
158	Q₈×C₁₃	C₄⋊Q₈	1	4	yes	—
159	C₂×C₄×C₁₃	—	2	2	no	—
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	—	2	2	no	—
162	C₂×C₄×C₁₃	—	2	1	no	—
163	C₂×C₄×C₁₃	—	2	1	no	—
164	C₂×C₄×C₁₃	—	2	2	no	—
165	C₂×C₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	—	2	2	no	—
167	C₂×C₄×C₁₃	—	2	2	no	—
168	C₂×C₄×C₁₃	—	2	2	no	—
169	C₂×C₄×C₁₃	—	2	2	no	—
170	C₂×C₄×C₁₃	—	2	2	no	—
171	C₂×C₄×C₁₃	—	2	2	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	4	1	no	—
174	C₂×C₄×C₁₃	—	4	1	no	—
175	C₂×C₄×C₁₃	—	4	1	no	—
176	C₂×C₄×C₁₃	—	4	1	no	—
177	C₂×C₄×C₁₃	—	4	1	no	—
178	C₂×C₄×C₁₃	—	4	1	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	—	4	2	no	—
183	C₂×C₄×C₁₃	—	4	2	no	—
184	C₂×C₄×C₁₃	—	4	2	no	—
185	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
186	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
187	C₂×C₄×C₁₃	#135	1	2	yes	—
188	C₂×C₄×C₁₃	#137	1	2	yes	—
189	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
191	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
192	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
193	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
194	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
195	C₈×C₁₃	—	2	2	no	—
196	C₈×C₁₃	—	2	2	no	—
197	C₈×C₁₃	—	4	2	no	—
198	C₂×#125	C₂²×C₁₃	1	2	yes	—
199	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
200	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
201	#479	—	2	8	no	—
202	C₂×#107	C₂²×C₁₃	1	2	yes	—
203	C₂×#106	C₂²×C₁₃	1	2	yes	—
204	C₂×#106	C₂²×C₁₃	1	2	yes	—
205	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
206	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
207	C₂×#103	C₂²×C₁₃	1	2	yes	—
208	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
209	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
210	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
211	#398	—	2	2	no	—
212	#389	—	2	1	no	—
213	#389	—	2	2	no	—
214	#389	C₂²×C₁₃	1	2	yes	—
215	#389	C₂²×C₁₃	1	2	yes	—
216	#384	—	2	1	no	—
217	#384	—	2	1	no	—
218	#384	C₂²×C₁₃	1	1	yes	characteristic
219	#384	C₂²×C₁₃	1	1	yes	characteristic
220	C₄×C₄⋊C₄	—	2	1	no	—
221	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
222	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
223	#340	C₂²×C₁₃	1	2	yes	—
224	#340	C₂²×C₁₃	1	1	yes	characteristic
225	#340	C₂²×C₁₃	1	1	yes	characteristic
226	#340	C₂²×C₁₃	1	2	yes	—
227	#336	C₂²×C₁₃	1	2	yes	—
228	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
229	C₂²×C₁₃	D₄²	1	1	yes	characteristic
230	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
231	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
232	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
233	C₂²×C₁₃	#577	1	1	yes	characteristic
234	C₂²×C₁₃	#577	1	1	yes	characteristic
235	C₄×C₁₃	—	2	2	no	—
236	C₄×C₁₃	—	2	4	no	—
237	C₄×C₁₃	—	4	2	no	—
238	C₄×C₁₃	—	4	2	no	—
239	C₄×C₁₃	—	4	2	no	—
240	C₄×C₁₃	—	4	2	no	—
241	C₄×C₁₃	—	4	2	no	—
242	C₄×C₁₃	—	8	2	no	—
243	C₄×C₁₃	—	8	2	no	—
244	C₄×C₁₃	#479	1	4	yes	complemented
245	C₄×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
246	C₄×C₁₃	#544	1	1	yes	characteristic
247	C₄×C₁₃	#547	1	1	yes	characteristic
248	C₄×C₁₃	#554	1	1	yes	characteristic
249	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
250	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
251	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
252	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
253	#125	—	2	4	no	—
254	#125	—	4	2	no	—
255	C₄×Q₈	—	2	2	no	—
256	C₄×Q₈	—	2	4	no	—
257	C₄×Q₈	—	4	2	no	—
258	C₄×Q₈	Q₈×C₁₃	1	4	yes	—
259	C₂×C₄⋊C₄	—	2	1	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	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
270	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
271	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
272	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
273	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
274	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
275	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
276	C₂×C₄²	—	2	1	no	—
277	C₂×C₄²	—	2	2	no	—
278	C₂×C₄²	—	2	1	no	—
279	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
280	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
281	#107	—	2	4	no	—
282	#106	—	2	4	no	—
283	#106	—	4	2	no	—
284	C₄⋊C₈	—	2	4	no	—
285	C₄⋊C₈	—	2	2	no	—
286	#103	—	2	4	no	—
287	#103	D₄×C₁₃	1	4	yes	—
288	#103	Q₈×C₁₃	1	4	yes	—
289	C₄×C₈	—	2	2	no	—
290	#95	—	2	2	no	—
291	#95	—	2	1	no	—
292	#95	—	2	2	no	—
293	#95	D₄×C₁₃	1	2	yes	—
294	C₂×C₁₃	#2440	1	1	yes	characteristic
295	C₂×C₁₃	C₂×#479	1	1	yes	characteristic
296	C₂×C₁₃	#3084	1	1	yes	characteristic
297	C₂×C₁₃	#3278	1	1	yes	characteristic
298	C₂×C₁₃	#3284	1	1	yes	characteristic
299	C₂×C₁₃	#3381	1	1	yes	characteristic
300	C₂×C₁₃	#3387	1	1	yes	characteristic
301	C₂×Q₈	—	2	1	no	—
302	C₂×Q₈	—	2	1	no	—
303	C₂×Q₈	—	2	1	no	—
304	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
305	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
306	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
314	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
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	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
326	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
327	C₄⋊C₄	—	2	4	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	2	1	no	—
332	C₄⋊C₄	—	2	1	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	—	4	4	no	—
340	C₄⋊C₄	—	4	2	no	—
341	C₄⋊C₄	—	4	2	no	—
342	C₄⋊C₄	—	8	1	no	—
343	C₄⋊C₄	—	8	1	no	—
344	C₄⋊C₄	—	8	2	no	—
345	C₄⋊C₄	—	8	2	no	—
346	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
347	C₄⋊C₄	C₂×Q₈×C₁₃	1	2	yes	—
348	C₄⋊C₄	C₂×Q₈×C₁₃	1	2	yes	—
349	C₄²	—	2	4	no	—
350	C₄²	—	2	2	no	—
351	C₄²	—	2	2	no	—
352	C₄²	—	4	4	no	—
353	C₄²	—	4	2	no	—
354	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
355	C₄²	C₁₃×#41	1	2	yes	—
356	C₁₃	#26043	1	1	yes	characteristic, direct product factor, Sylow
357	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
358	Q₈	—	2	2	no	—
359	Q₈	—	2	2	no	—
360	Q₈	—	2	2	no	—
361	Q₈	C₁₃×C₄⋊Q₈	1	4	yes	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
389	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
390	C₂×C₄	C₁₃×#135	1	2	yes	—
391	C₂×C₄	C₁₃×#137	1	2	yes	—
392	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
393	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
394	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
395	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
396	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
397	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
398	C₈	—	2	2	no	—
399	C₈	—	2	2	no	—
400	C₈	—	4	2	no	—
401	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
402	C₂²	D₄²×C₁₃	1	1	yes	characteristic
403	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
404	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
405	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
406	C₂²	C₁₃×#577	1	1	yes	characteristic
407	C₂²	C₁₃×#577	1	1	yes	characteristic
408	C₄	—	2	2	no	—
409	C₄	—	2	4	no	—
410	C₄	—	4	2	no	—
411	C₄	—	4	2	no	—
412	C₄	—	4	2	no	—
413	C₄	—	4	2	no	—
414	C₄	—	4	2	no	—
415	C₄	—	8	2	no	—
416	C₄	—	8	2	no	—
417	C₄	C₁₃×#479	1	4	yes	complemented
418	C₄	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
419	C₄	C₁₃×#544	1	1	yes	characteristic
420	C₄	C₁₃×#547	1	1	yes	characteristic
421	C₄	C₁₃×#554	1	1	yes	characteristic
422	C₂	C₁₃×#2440	1	1	yes	characteristic
423	C₂	C₂×C₁₃×#479	1	1	yes	characteristic
424	C₂	C₁₃×#3084	1	1	yes	characteristic
425	C₂	C₁₃×#3278	1	1	yes	characteristic
426	C₂	C₁₃×#3284	1	1	yes	characteristic
427	C₂	C₁₃×#3381	1	1	yes	characteristic
428	C₂	C₁₃×#3387	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
87. #26043	C₁₃	direct (N × H)
244. C₄×C₁₃	#479	semidirect
356. C₁₃	#26043	direct (N × H)
417. C₄	C₁₃×#479	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#479	2
C₁₃×#2552	2
Q₈×C₁₃×C₄⋊C₄	2
C₁₃×#2088	2
C₁₃×#2059	2
C₁₃×#1947	2
C₁₃×#1939	2
C₁₃×#1865	2
C₁₃×#1844	2
C₁₃×#1803	2
C₄×C₁₃×#103	2
#26043	13

Subgroups — C13×#26043 #15712382

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26043 #15712382