Subgroups — C₁₃×#26066 #15712405

Order 3328.

778 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#499	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#427	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2441	C₂	1	2	yes	maximal
4	C₁₃×#2084	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2059	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1942	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1942	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1854	C₂	1	2	yes	maximal
9	C₁₃×#1845	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1808	C₂	1	1	yes	maximal, characteristic
11	C₈×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#125	C₂²	1	2	yes	—
14	C₂×C₁₃×#117	C₂²	1	2	yes	—
15	C₁₃×#499	—	2	4	no	—
16	C₁₃×#427	—	2	4	no	—
17	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#107	C₂²	1	2	yes	—
21	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#106	C₂²	1	2	yes	—
23	C₂×C₁₃×#106	C₂²	1	2	yes	—
24	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₁₃×#399	—	2	2	no	—
28	C₁₃×#396	—	2	2	no	—
29	C₁₃×#389	—	2	2	no	—
30	C₁₃×#389	C₂²	1	2	yes	—
31	C₁₃×#389	C₂²	1	2	yes	—
32	C₁₃×#387	—	2	2	no	—
33	C₁₃×#384	C₂²	1	2	yes	—
34	C₁₃×#380	C₂²	1	2	yes	—
35	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
36	C₁₃×#340	C₂²	1	2	yes	—
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	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₁₃	—	2	2	no	—
43	C₂²×C₈×C₁₃	—	2	2	no	—
44	C₂²×C₈×C₁₃	Q₈	1	4	yes	—
45	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
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	C₁₃×#125	—	2	4	no	—
50	C₁₃×#125	—	4	2	no	—
51	C₁₃×#117	—	2	4	no	—
52	C₁₃×#117	—	4	2	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	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	—	2	2	no	—
59	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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×C₁₃×C₂²⋊C₄	—	2	2	no	—
64	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
65	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
66	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₁₃	—	2	2	no	—
68	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
70	C₁₃×#107	—	2	2	no	—
71	C₁₃×#107	—	2	2	no	—
72	C₁₃×#107	—	2	2	no	—
73	C₁₃×#107	—	4	2	no	—
74	C₁₃×#107	D₄	1	4	yes	—
75	C₁₃×#106	—	2	4	no	—
76	C₁₃×#106	—	2	4	no	—
77	C₁₃×C₂²⋊C₈	Q₈	1	4	yes	—
78	C₄×C₈×C₁₃	—	2	2	no	—
79	C₄×C₈×C₁₃	—	2	2	no	—
80	C₁₃×#95	—	2	2	no	—
81	C₁₃×#95	—	2	2	no	—
82	C₁₃×#95	—	2	2	no	—
83	C₁₃×#95	D₄	1	1	yes	characteristic
84	C₁₃×#95	D₄	1	1	yes	characteristic
85	#26066	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
86	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	—	2	1	no	—
88	C₂²×C₄×C₁₃	—	2	1	no	—
89	C₂²×C₄×C₁₃	—	2	1	no	—
90	C₂²×C₄×C₁₃	—	2	1	no	—
91	C₂²×C₄×C₁₃	—	2	2	no	—
92	C₂²×C₄×C₁₃	—	2	2	no	—
93	C₂²×C₄×C₁₃	—	2	2	no	—
94	C₂²×C₄×C₁₃	—	2	2	no	—
95	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
101	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
102	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
103	C₂×C₈×C₁₃	—	2	1	no	—
104	C₂×C₈×C₁₃	—	2	1	no	—
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	8	no	—
110	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
111	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
112	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
113	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
114	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
115	C₂×C₈×C₁₃	#41	1	2	yes	—
116	C₁₃×C₄⋊C₄	—	2	2	no	—
117	C₁₃×C₄⋊C₄	—	2	2	no	—
118	C₁₃×C₄⋊C₄	—	2	2	no	—
119	C₁₃×C₄⋊C₄	—	2	2	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	—	4	4	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	—	8	2	no	—
128	C₁₃×C₄⋊C₄	—	8	2	no	—
129	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
130	C₁₃×C₂²⋊C₄	—	2	2	no	—
131	C₁₃×C₂²⋊C₄	—	2	2	no	—
132	C₁₃×C₂²⋊C₄	—	4	4	no	—
133	C₁₃×C₂²⋊C₄	—	8	2	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×#499	C₂×C₁₃	1	1	yes	characteristic, complemented
140	C₂×#427	C₂×C₁₃	1	1	yes	characteristic
141	#2441	C₂×C₁₃	1	2	yes	—
142	#2084	C₂×C₁₃	1	2	yes	complemented
143	#2059	C₂×C₁₃	1	2	yes	complemented
144	#1942	C₂×C₁₃	1	1	yes	characteristic, complemented
145	#1942	C₂×C₁₃	1	1	yes	characteristic, complemented
146	#1854	C₂×C₁₃	1	2	yes	—
147	#1845	C₂×C₁₃	1	1	yes	characteristic, complemented
148	#1808	C₂×C₁₃	1	1	yes	characteristic
149	C₈×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic
150	C₂³×C₁₃	—	2	1	no	—
151	C₂³×C₁₃	—	2	1	no	—
152	C₂³×C₁₃	—	2	1	no	—
153	C₂³×C₁₃	—	2	1	no	—
154	C₂³×C₁₃	—	2	1	no	—
155	C₂³×C₁₃	—	2	1	no	—
156	C₂³×C₁₃	C₄⋊Q₈	1	2	yes	—
157	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
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	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	1	no	—
169	C₂×C₄×C₁₃	—	2	1	no	—
170	C₂×C₄×C₁₃	—	2	4	no	—
171	C₂×C₄×C₁₃	—	2	1	no	—
172	C₂×C₄×C₁₃	—	2	1	no	—
173	C₂×C₄×C₁₃	—	2	1	no	—
174	C₂×C₄×C₁₃	—	2	1	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	—	4	2	no	—
183	C₂×C₄×C₁₃	—	4	2	no	—
184	C₂×C₄×C₁₃	—	4	2	no	—
185	C₂×C₄×C₁₃	—	4	2	no	—
186	C₂×C₄×C₁₃	C₄⋊Q₈	1	2	yes	—
187	C₂×C₄×C₁₃	#135	1	2	yes	—
188	C₂×C₄×C₁₃	#135	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	—	2	2	no	—
198	C₈×C₁₃	C₂²⋊Q₈	1	4	yes	—
199	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
200	C₂×#125	C₂²×C₁₃	1	2	yes	—
201	C₂×#117	C₂²×C₁₃	1	2	yes	—
202	#499	—	2	4	no	—
203	#427	—	2	4	no	—
204	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
205	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
206	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
207	C₂×#107	C₂²×C₁₃	1	2	yes	—
208	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
209	C₂×#106	C₂²×C₁₃	1	2	yes	—
210	C₂×#106	C₂²×C₁₃	1	2	yes	—
211	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
212	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
213	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
214	#399	—	2	2	no	—
215	#396	—	2	2	no	—
216	#389	—	2	2	no	—
217	#389	C₂²×C₁₃	1	2	yes	—
218	#389	C₂²×C₁₃	1	2	yes	—
219	#387	—	2	2	no	—
220	#384	C₂²×C₁₃	1	2	yes	—
221	#380	C₂²×C₁₃	1	2	yes	—
222	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
223	#340	C₂²×C₁₃	1	2	yes	—
224	#340	C₂²×C₁₃	1	2	yes	—
225	#340	C₂²×C₁₃	1	2	yes	—
226	#336	C₂²×C₁₃	1	1	yes	characteristic
227	#336	C₂²×C₁₃	1	1	yes	characteristic
228	C₂²×C₁₃	—	2	2	no	—
229	C₂²×C₁₃	—	2	2	no	—
230	C₂²×C₁₃	—	2	2	no	—
231	C₂²×C₁₃	—	4	1	no	—
232	C₂²×C₁₃	—	4	1	no	—
233	C₂²×C₁₃	—	4	1	no	—
234	C₂²×C₁₃	—	4	1	no	—
235	C₂²×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
236	C₂²×C₁₃	D₄²	1	1	yes	characteristic
237	C₂²×C₁₃	#547	1	1	yes	characteristic
238	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
239	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
240	C₂²×C₁₃	#576	1	1	yes	characteristic
241	C₂²×C₁₃	#578	1	1	yes	characteristic
242	C₄×C₁₃	—	2	2	no	—
243	C₄×C₁₃	—	2	2	no	—
244	C₄×C₁₃	—	2	2	no	—
245	C₄×C₁₃	—	4	1	no	—
246	C₄×C₁₃	—	4	4	no	—
247	C₄×C₁₃	—	4	1	no	—
248	C₄×C₁₃	—	8	2	no	—
249	C₄×C₁₃	—	8	2	no	—
250	C₄×C₁₃	—	8	2	no	—
251	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
252	C₄×C₁₃	#544	1	1	yes	characteristic
253	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
254	C₄×C₁₃	#554	1	1	yes	characteristic
255	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
256	C₂²×C₈	—	2	2	no	—
257	C₂²×C₈	—	2	2	no	—
258	C₂²×C₈	Q₈×C₁₃	1	4	yes	—
259	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
260	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
261	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
262	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
263	#125	—	2	4	no	—
264	#125	—	4	2	no	—
265	#117	—	2	4	no	—
266	#117	—	4	2	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	—	2	2	no	—
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₄⋊C₄	—	2	2	no	—
273	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
274	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
275	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
276	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
277	C₂×C₂²⋊C₄	—	2	2	no	—
278	C₂×C₂²⋊C₄	—	2	2	no	—
279	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
280	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
281	C₂×C₄²	—	2	2	no	—
282	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
283	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
284	#107	—	2	2	no	—
285	#107	—	2	2	no	—
286	#107	—	2	2	no	—
287	#107	—	4	2	no	—
288	#107	D₄×C₁₃	1	4	yes	—
289	#106	—	2	4	no	—
290	#106	—	2	4	no	—
291	C₂²⋊C₈	Q₈×C₁₃	1	4	yes	—
292	C₄×C₈	—	2	2	no	—
293	C₄×C₈	—	2	2	no	—
294	#95	—	2	2	no	—
295	#95	—	2	2	no	—
296	#95	—	2	2	no	—
297	#95	D₄×C₁₃	1	1	yes	characteristic
298	#95	D₄×C₁₃	1	1	yes	characteristic
299	C₂×C₁₃	—	4	2	no	—
300	C₂×C₁₃	#2440	1	1	yes	characteristic
301	C₂×C₁₃	#3160	1	1	yes	characteristic
302	C₂×C₁₃	#3164	1	1	yes	characteristic
303	C₂×C₁₃	#3283	1	1	yes	characteristic
304	C₂×C₁₃	#3287	1	1	yes	characteristic
305	C₂×C₁₃	#3336	1	1	yes	characteristic
306	C₂×C₁₃	#3339	1	1	yes	characteristic
307	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
317	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
318	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
320	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
321	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
322	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
323	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	8	no	—
331	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
332	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
333	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
334	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
335	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
336	C₂×C₈	C₁₃×#41	1	2	yes	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	4	4	no	—
345	C₄⋊C₄	—	4	4	no	—
346	C₄⋊C₄	—	4	4	no	—
347	C₄⋊C₄	—	4	4	no	—
348	C₄⋊C₄	—	8	2	no	—
349	C₄⋊C₄	—	8	2	no	—
350	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
351	C₂²⋊C₄	—	2	2	no	—
352	C₂²⋊C₄	—	2	2	no	—
353	C₂²⋊C₄	—	4	4	no	—
354	C₂²⋊C₄	—	8	2	no	—
355	C₄²	—	2	1	no	—
356	C₄²	—	2	1	no	—
357	C₄²	—	2	1	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	4	4	no	—
360	C₁₃	#26066	1	1	yes	characteristic, direct product factor, Sylow
361	C₂³	—	2	1	no	—
362	C₂³	—	2	1	no	—
363	C₂³	—	2	1	no	—
364	C₂³	—	2	1	no	—
365	C₂³	—	2	1	no	—
366	C₂³	—	2	1	no	—
367	C₂³	C₁₃×C₄⋊Q₈	1	2	yes	—
368	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
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	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	C₁₃×C₄⋊Q₈	1	2	yes	—
398	C₂×C₄	C₁₃×#135	1	2	yes	—
399	C₂×C₄	C₁₃×#135	1	2	yes	—
400	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
401	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
402	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
403	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
404	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
405	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
406	C₈	—	2	2	no	—
407	C₈	—	2	2	no	—
408	C₈	—	2	2	no	—
409	C₈	C₁₃×C₂²⋊Q₈	1	4	yes	—
410	C₂²	—	2	2	no	—
411	C₂²	—	2	2	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	4	1	no	—
414	C₂²	—	4	1	no	—
415	C₂²	—	4	1	no	—
416	C₂²	—	4	1	no	—
417	C₂²	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
418	C₂²	D₄²×C₁₃	1	1	yes	characteristic
419	C₂²	C₁₃×#547	1	1	yes	characteristic
420	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
421	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
422	C₂²	C₁₃×#576	1	1	yes	characteristic
423	C₂²	C₁₃×#578	1	1	yes	characteristic
424	C₄	—	2	2	no	—
425	C₄	—	2	2	no	—
426	C₄	—	2	2	no	—
427	C₄	—	4	1	no	—
428	C₄	—	4	4	no	—
429	C₄	—	4	1	no	—
430	C₄	—	8	2	no	—
431	C₄	—	8	2	no	—
432	C₄	—	8	2	no	—
433	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
434	C₄	C₁₃×#544	1	1	yes	characteristic
435	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
436	C₄	C₁₃×#554	1	1	yes	characteristic
437	C₂	—	4	2	no	—
438	C₂	C₁₃×#2440	1	1	yes	characteristic
439	C₂	C₁₃×#3160	1	1	yes	characteristic
440	C₂	C₁₃×#3164	1	1	yes	characteristic
441	C₂	C₁₃×#3283	1	1	yes	characteristic
442	C₂	C₁₃×#3287	1	1	yes	characteristic
443	C₂	C₁₃×#3336	1	1	yes	characteristic
444	C₂	C₁₃×#3339	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#499	C₂	semidirect
4. C₁₃×#2084	C₂	semidirect
5. C₁₃×#2059	C₂	semidirect
6. C₁₃×#1942	C₂	semidirect
7. C₁₃×#1942	C₂	semidirect
9. C₁₃×#1845	C₂	semidirect
85. #26066	C₁₃	direct (N × H)
139. C₂×#499	C₂×C₁₃	semidirect
142. #2084	C₂×C₁₃	semidirect
143. #2059	C₂×C₁₃	semidirect
144. #1942	C₂×C₁₃	semidirect
145. #1942	C₂×C₁₃	semidirect
147. #1845	C₂×C₁₃	semidirect
360. C₁₃	#26066	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×#499	2
C₂×C₁₃×#427	2
C₁₃×#2441	2
C₁₃×#2084	2
C₁₃×#2059	2
C₁₃×#1942	2
C₁₃×#1854	2
C₁₃×#1845	2
C₁₃×#1808	2
C₈×C₁₃×C₂²⋊C₄	2
#26066	13

Subgroups — C13×#26066 #15712405

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26066 #15712405