Subgroups — C₁₃×#26460 #15712799

Order 3328.

950 conjugacy classes of subgroups.

The subgroup lattice has 482 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	2	yes	maximal, complemented
2	C₁₃×#2551	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2366	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2067	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2023	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1982	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1957	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1947	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1939	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1862	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₃	—	2	1	no	—
16	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
17	C₁₃×#474	—	2	8	no	—
18	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#107	C₂²	1	2	yes	—
20	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
23	C₂×C₁₃×#102	C₂²	1	2	yes	—
24	C₂×C₁₃×#102	C₂²	1	2	yes	—
25	C₂×C₁₃×#102	C₂²	1	2	yes	—
26	C₂×C₁₃×#102	C₂²	1	2	yes	—
27	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₁₃×#395	—	2	2	no	—
29	C₁₃×#390	—	2	1	no	—
30	C₁₃×#390	C₂²	1	2	yes	—
31	C₁₃×#389	—	2	1	no	—
32	C₁₃×#389	C₂²	1	2	yes	—
33	C₁₃×#386	—	2	2	no	—
34	C₁₃×#384	C₂²	1	1	yes	characteristic
35	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₄×C₁₃×C₄⋊C₄	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	1	yes	characteristic
41	C₁₃×#336	C₂²	1	2	yes	—
42	C₂²×Q₈×C₁₃	—	2	2	no	—
43	C₂²×D₄×C₁₃	—	2	1	no	—
44	C₂²×D₄×C₁₃	—	2	1	no	—
45	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
46	C₂³×C₄×C₁₃	—	2	2	no	—
47	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₁₃×C₄⋊Q₈	—	2	4	no	—
51	C₁₃×C₄⋊Q₈	—	4	2	no	—
52	C₁₃×C₄⋊Q₈	—	4	4	no	—
53	C₁₃×#127	—	2	2	no	—
54	C₁₃×#127	Q₈	1	4	yes	complemented
55	C₄×D₄×C₁₃	—	2	4	no	—
56	C₄×D₄×C₁₃	—	4	2	no	—
57	C₄×D₄×C₁₃	—	4	4	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	2	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	1	yes	characteristic
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×C₁₃×C₂²⋊C₄	—	2	2	no	—
70	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
71	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
72	C₂×C₄²×C₁₃	—	2	1	no	—
73	C₂×C₄²×C₁₃	—	2	1	no	—
74	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
75	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
76	C₁₃×#107	—	2	4	no	—
77	C₁₃×#107	—	2	2	no	—
78	C₁₃×#107	D₄	1	4	yes	complemented
79	C₁₃×C₄⋊C₈	—	2	4	no	—
80	C₁₃×C₄⋊C₈	—	2	2	no	—
81	C₁₃×#102	—	2	4	no	—
82	C₁₃×#102	—	2	4	no	—
83	C₁₃×#102	—	2	4	no	—
84	C₁₃×#102	—	4	2	no	—
85	C₄×C₈×C₁₃	—	2	2	no	—
86	C₁₃×#95	—	2	1	no	—
87	C₁₃×#95	—	2	1	no	—
88	C₁₃×#95	—	2	2	no	—
89	C₁₃×#95	D₄	1	2	yes	—
90	#26460	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
91	C₂⁴×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×D₄×C₁₃	—	2	4	no	—
96	C₂×D₄×C₁₃	—	2	4	no	—
97	C₂×D₄×C₁₃	—	2	2	no	—
98	C₂×D₄×C₁₃	—	2	2	no	—
99	C₂×D₄×C₁₃	—	2	2	no	—
100	C₂×D₄×C₁₃	—	2	2	no	—
101	C₂×D₄×C₁₃	—	2	2	no	—
102	C₂×D₄×C₁₃	—	4	2	no	—
103	C₂×D₄×C₁₃	—	4	2	no	—
104	C₂×D₄×C₁₃	—	8	1	no	—
105	C₂×D₄×C₁₃	—	8	1	no	—
106	C₂×D₄×C₁₃	C₂×Q₈	1	4	yes	—
107	C₂²×C₄×C₁₃	—	2	1	no	—
108	C₂²×C₄×C₁₃	—	2	1	no	—
109	C₂²×C₄×C₁₃	—	2	1	no	—
110	C₂²×C₄×C₁₃	—	2	1	no	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	—	4	4	no	—
113	C₂²×C₄×C₁₃	—	4	4	no	—
114	C₂²×C₄×C₁₃	—	8	2	no	—
115	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
120	C₂×C₈×C₁₃	—	2	1	no	—
121	C₂×C₈×C₁₃	—	2	1	no	—
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₂×C₈×C₁₃	—	2	1	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	C₂×D₄	1	2	yes	—
129	C₁₃×C₄⋊C₄	—	2	2	no	—
130	C₁₃×C₄⋊C₄	—	2	1	no	—
131	C₁₃×C₄⋊C₄	—	2	1	no	—
132	C₁₃×C₄⋊C₄	—	2	1	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	1	no	—
137	C₁₃×C₄⋊C₄	—	4	4	no	—
138	C₁₃×C₄⋊C₄	—	4	4	no	—
139	C₁₃×C₄⋊C₄	—	4	2	no	—
140	C₁₃×C₄⋊C₄	—	8	1	no	—
141	C₁₃×C₄⋊C₄	D₈	1	4	yes	—
142	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
143	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
144	C₁₃×C₄⋊C₄	#41	1	2	yes	—
145	C₁₃×C₂²⋊C₄	—	4	4	no	—
146	C₁₃×C₂²⋊C₄	—	4	4	no	—
147	C₁₃×C₂²⋊C₄	—	8	2	no	—
148	C₄²×C₁₃	—	2	2	no	—
149	C₄²×C₁₃	—	2	2	no	—
150	C₄²×C₁₃	—	4	2	no	—
151	C₄²×C₁₃	—	4	2	no	—
152	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
153	C₄²×C₁₃	#41	1	2	yes	—
154	C₂×#474	C₂×C₁₃	1	2	yes	complemented
155	#2551	C₂×C₁₃	1	1	yes	characteristic, complemented
156	#2366	C₂×C₁₃	1	1	yes	characteristic
157	#2067	C₂×C₁₃	1	2	yes	complemented
158	#2023	C₂×C₁₃	1	2	yes	complemented
159	#1982	C₂×C₁₃	1	1	yes	characteristic
160	#1957	C₂×C₁₃	1	1	yes	characteristic
161	#1947	C₂×C₁₃	1	1	yes	characteristic, complemented
162	#1939	C₂×C₁₃	1	1	yes	characteristic, complemented
163	#1862	C₂×C₁₃	1	2	yes	complemented
164	C₄×#107	C₂×C₁₃	1	1	yes	characteristic, complemented
165	C₂³×C₁₃	—	2	4	no	—
166	C₂³×C₁₃	—	4	2	no	—
167	C₂³×C₁₃	—	4	2	no	—
168	C₂³×C₁₃	—	4	2	no	—
169	C₂³×C₁₃	—	4	2	no	—
170	C₂³×C₁₃	—	4	2	no	—
171	C₂³×C₁₃	—	4	2	no	—
172	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
173	Q₈×C₁₃	—	8	8	no	—
174	D₄×C₁₃	—	2	4	no	—
175	D₄×C₁₃	—	2	4	no	—
176	D₄×C₁₃	—	4	2	no	—
177	D₄×C₁₃	—	4	2	no	—
178	D₄×C₁₃	—	4	8	no	—
179	D₄×C₁₃	—	8	4	no	—
180	C₂×C₄×C₁₃	—	2	2	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	2	1	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	2	no	—
187	C₂×C₄×C₁₃	—	2	2	no	—
188	C₂×C₄×C₁₃	—	2	2	no	—
189	C₂×C₄×C₁₃	—	2	2	no	—
190	C₂×C₄×C₁₃	—	4	1	no	—
191	C₂×C₄×C₁₃	—	4	1	no	—
192	C₂×C₄×C₁₃	—	4	1	no	—
193	C₂×C₄×C₁₃	—	4	1	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	—	4	1	no	—
198	C₂×C₄×C₁₃	—	4	1	no	—
199	C₂×C₄×C₁₃	—	4	2	no	—
200	C₂×C₄×C₁₃	—	4	2	no	—
201	C₂×C₄×C₁₃	—	4	1	no	—
202	C₂×C₄×C₁₃	—	8	8	no	—
203	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
204	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
205	C₂×C₄×C₁₃	C₂×D₈	1	4	yes	—
206	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
207	C₂×C₄×C₁₃	#137	1	2	yes	—
208	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
210	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
211	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
212	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
213	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
214	C₈×C₁₃	—	2	2	no	—
215	C₈×C₁₃	—	4	2	no	—
216	C₈×C₁₃	—	4	1	no	—
217	C₂×C₄⋊Q₈	—	2	1	no	—
218	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
219	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
220	C₂×C₄×D₄	—	2	1	no	—
221	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
222	#474	—	2	8	no	—
223	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
224	C₂×#107	C₂²×C₁₃	1	2	yes	—
225	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
226	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
227	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
228	C₂×#102	C₂²×C₁₃	1	2	yes	—
229	C₂×#102	C₂²×C₁₃	1	2	yes	—
230	C₂×#102	C₂²×C₁₃	1	2	yes	—
231	C₂×#102	C₂²×C₁₃	1	2	yes	—
232	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
233	#395	—	2	2	no	—
234	#390	—	2	1	no	—
235	#390	C₂²×C₁₃	1	2	yes	—
236	#389	—	2	1	no	—
237	#389	C₂²×C₁₃	1	2	yes	—
238	#386	—	2	2	no	—
239	#384	C₂²×C₁₃	1	1	yes	characteristic
240	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
241	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
242	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
243	#340	C₂²×C₁₃	1	2	yes	—
244	#340	C₂²×C₁₃	1	1	yes	characteristic
245	#340	C₂²×C₁₃	1	1	yes	characteristic
246	#336	C₂²×C₁₃	1	2	yes	—
247	C₂²×C₁₃	—	4	4	no	—
248	C₂²×C₁₃	—	4	4	no	—
249	C₂²×C₁₃	—	4	4	no	—
250	C₂²×C₁₃	—	8	2	no	—
251	C₂²×C₁₃	—	8	2	no	—
252	C₂²×C₁₃	—	8	2	no	—
253	C₂²×C₁₃	—	8	2	no	—
254	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
255	C₂²×C₁₃	D₄²	1	1	yes	characteristic
256	C₂²×C₁₃	#548	1	1	yes	characteristic
257	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
258	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
259	C₂²×C₁₃	#576	1	1	yes	characteristic
260	C₂²×C₁₃	#577	1	1	yes	characteristic
261	C₄×C₁₃	—	2	2	no	—
262	C₄×C₁₃	—	2	4	no	—
263	C₄×C₁₃	—	4	2	no	—
264	C₄×C₁₃	—	4	2	no	—
265	C₄×C₁₃	—	4	2	no	—
266	C₄×C₁₃	—	4	2	no	—
267	C₄×C₁₃	—	8	1	no	—
268	C₄×C₁₃	—	8	2	no	—
269	C₄×C₁₃	#474	1	4	yes	complemented
270	C₄×C₁₃	#532	1	1	yes	characteristic
271	C₄×C₁₃	#542	1	1	yes	characteristic
272	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
273	C₄×C₁₃	#554	1	1	yes	characteristic
274	C₂²×Q₈	—	2	2	no	—
275	C₂²×D₄	—	2	1	no	—
276	C₂²×D₄	—	2	1	no	—
277	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
278	C₂³×C₄	—	2	2	no	—
279	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
280	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
281	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
282	C₄⋊Q₈	—	2	4	no	—
283	C₄⋊Q₈	—	4	2	no	—
284	C₄⋊Q₈	—	4	4	no	—
285	#127	—	2	2	no	—
286	#127	Q₈×C₁₃	1	4	yes	complemented
287	C₄×D₄	—	2	4	no	—
288	C₄×D₄	—	4	2	no	—
289	C₄×D₄	—	4	4	no	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	—	2	2	no	—
292	C₂×C₄⋊C₄	—	2	2	no	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
295	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
296	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
297	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
298	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
299	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
300	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
301	C₂×C₂²⋊C₄	—	2	2	no	—
302	C₂×C₂²⋊C₄	—	2	2	no	—
303	C₂×C₂²⋊C₄	—	2	2	no	—
304	C₂×C₄²	—	2	1	no	—
305	C₂×C₄²	—	2	1	no	—
306	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
307	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
308	#107	—	2	4	no	—
309	#107	—	2	2	no	—
310	#107	D₄×C₁₃	1	4	yes	complemented
311	C₄⋊C₈	—	2	4	no	—
312	C₄⋊C₈	—	2	2	no	—
313	#102	—	2	4	no	—
314	#102	—	2	4	no	—
315	#102	—	2	4	no	—
316	#102	—	4	2	no	—
317	C₄×C₈	—	2	2	no	—
318	#95	—	2	1	no	—
319	#95	—	2	1	no	—
320	#95	—	2	2	no	—
321	#95	D₄×C₁₃	1	2	yes	—
322	C₂×C₁₃	—	8	4	no	—
323	C₂×C₁₃	#2452	1	1	yes	characteristic
324	C₂×C₁₃	C₂×#474	1	1	yes	characteristic
325	C₂×C₁₃	#3081	1	1	yes	characteristic
326	C₂×C₁₃	#3278	1	1	yes	characteristic
327	C₂×C₁₃	D₄×D₈	1	1	yes	characteristic
328	C₂×C₁₃	#3358	1	1	yes	characteristic
329	C₂×C₁₃	#3375	1	1	yes	characteristic
330	C₂⁴	—	2	2	no	—
331	C₂×Q₈	—	4	4	no	—
332	C₂×Q₈	—	4	4	no	—
333	C₂×Q₈	—	8	2	no	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	—	2	4	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	4	2	no	—
342	C₂×D₄	—	4	2	no	—
343	C₂×D₄	—	8	1	no	—
344	C₂×D₄	—	8	1	no	—
345	C₂×D₄	C₂×Q₈×C₁₃	1	4	yes	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	4	4	no	—
352	C₂²×C₄	—	4	4	no	—
353	C₂²×C₄	—	8	2	no	—
354	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
355	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
356	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
357	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
358	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	4	4	no	—
377	C₄⋊C₄	—	4	4	no	—
378	C₄⋊C₄	—	4	2	no	—
379	C₄⋊C₄	—	8	1	no	—
380	C₄⋊C₄	C₁₃×D₈	1	4	yes	—
381	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
382	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
383	C₄⋊C₄	C₁₃×#41	1	2	yes	—
384	C₂²⋊C₄	—	4	4	no	—
385	C₂²⋊C₄	—	4	4	no	—
386	C₂²⋊C₄	—	8	2	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	2	2	no	—
389	C₄²	—	4	2	no	—
390	C₄²	—	4	2	no	—
391	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
392	C₄²	C₁₃×#41	1	2	yes	—
393	C₁₃	#26460	1	1	yes	characteristic, direct product factor, Sylow
394	C₂³	—	2	4	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	4	2	no	—
397	C₂³	—	4	2	no	—
398	C₂³	—	4	2	no	—
399	C₂³	—	4	2	no	—
400	C₂³	—	4	2	no	—
401	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
402	Q₈	—	8	8	no	—
403	D₄	—	2	4	no	—
404	D₄	—	2	4	no	—
405	D₄	—	4	8	no	—
406	D₄	—	4	2	no	—
407	D₄	—	4	2	no	—
408	D₄	—	8	4	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	8	8	no	—
432	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
433	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
434	C₂×C₄	C₂×C₁₃×D₈	1	4	yes	—
435	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
436	C₂×C₄	C₁₃×#137	1	2	yes	—
437	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
438	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
439	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
440	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
441	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
442	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
443	C₈	—	2	2	no	—
444	C₈	—	4	2	no	—
445	C₈	—	4	1	no	—
446	C₂²	—	4	4	no	—
447	C₂²	—	4	4	no	—
448	C₂²	—	4	4	no	—
449	C₂²	—	8	2	no	—
450	C₂²	—	8	2	no	—
451	C₂²	—	8	2	no	—
452	C₂²	—	8	2	no	—
453	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
454	C₂²	D₄²×C₁₃	1	1	yes	characteristic
455	C₂²	C₁₃×#548	1	1	yes	characteristic
456	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
457	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
458	C₂²	C₁₃×#576	1	1	yes	characteristic
459	C₂²	C₁₃×#577	1	1	yes	characteristic
460	C₄	—	2	4	no	—
461	C₄	—	2	2	no	—
462	C₄	—	4	2	no	—
463	C₄	—	4	2	no	—
464	C₄	—	4	2	no	—
465	C₄	—	4	2	no	—
466	C₄	—	8	2	no	—
467	C₄	—	8	1	no	—
468	C₄	C₁₃×#474	1	4	yes	complemented
469	C₄	C₁₃×#532	1	1	yes	characteristic
470	C₄	C₁₃×#542	1	1	yes	characteristic
471	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
472	C₄	C₁₃×#554	1	1	yes	characteristic
473	C₂	—	8	4	no	—
474	C₂	C₁₃×#2452	1	1	yes	characteristic
475	C₂	C₂×C₁₃×#474	1	1	yes	characteristic
476	C₂	C₁₃×#3081	1	1	yes	characteristic
477	C₂	C₁₃×#3278	1	1	yes	characteristic
478	C₂	D₄×C₁₃×D₈	1	1	yes	characteristic
479	C₂	C₁₃×#3358	1	1	yes	characteristic
480	C₂	C₁₃×#3375	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#127	C₂²
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
1. C₂×C₁₃×#474	C₂	semidirect
2. C₁₃×#2551	C₂	semidirect
4. C₁₃×#2067	C₂	semidirect
5. C₁₃×#2023	C₂	semidirect
8. C₁₃×#1947	C₂	semidirect
9. C₁₃×#1939	C₂	semidirect
10. C₁₃×#1862	C₂	semidirect
11. C₄×C₁₃×#107	C₂	semidirect
54. C₁₃×#127	Q₈	semidirect
78. C₁₃×#107	D₄	semidirect
90. #26460	C₁₃	direct (N × H)
154. C₂×#474	C₂×C₁₃	semidirect
155. #2551	C₂×C₁₃	semidirect
157. #2067	C₂×C₁₃	semidirect
158. #2023	C₂×C₁₃	semidirect
161. #1947	C₂×C₁₃	semidirect
162. #1939	C₂×C₁₃	semidirect
163. #1862	C₂×C₁₃	semidirect
164. C₄×#107	C₂×C₁₃	semidirect
269. C₄×C₁₃	#474	semidirect
286. #127	Q₈×C₁₃	semidirect
310. #107	D₄×C₁₃	semidirect
393. C₁₃	#26460	direct (N × H)
468. C₄	C₁₃×#474	semidirect

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
C₁₃×#2551	2
C₁₃×#2366	2
C₁₃×#2067	2
C₁₃×#2023	2
C₁₃×#1982	2
C₁₃×#1957	2
C₁₃×#1947	2
C₁₃×#1939	2
C₁₃×#1862	2
C₄×C₁₃×#107	2
#26460	13

Subgroups — C13×#26460 #15712799

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26460 #15712799