Subgroups — C₁₃×#34255 #15720594

Order 3328.

2682 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#518	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2357	C₂	1	4	yes	maximal, complemented
3	C₁₃×#2354	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2342	C₂	1	8	yes	maximal, complemented
5	C₁₃×#2319	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2317	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2309	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#2296	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2293	C₂	1	4	yes	maximal, complemented
10	C₂×C₁₃×#390	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#2274	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₁₃×#518	C₄	1	16	yes	complemented
15	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
16	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
17	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#117	C₂²	1	8	yes	complemented
22	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
24	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
25	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
26	C₁₃×#390	C₂²	1	2	yes	—
27	C₁₃×#390	C₂²	1	2	yes	—
28	C₁₃×#390	C₂²	1	4	yes	—
29	C₁₃×#390	C₂²	1	4	yes	—
30	C₁₃×#390	C₂²	1	2	yes	—
31	C₁₃×#390	C₂²	1	2	yes	—
32	C₁₃×#389	C₂²	1	2	yes	complemented
33	C₁₃×#389	C₂²	1	4	yes	complemented
34	C₁₃×#389	C₂²	1	2	yes	complemented
35	C₁₃×#388	C₂²	1	8	yes	complemented
36	C₁₃×#388	C₂²	1	8	yes	complemented
37	C₁₃×#388	C₂²	1	8	yes	complemented
38	C₁₃×#388	C₂²	1	8	yes	complemented
39	C₁₃×#385	C₂²	1	4	yes	—
40	C₁₃×#385	C₂²	1	4	yes	—
41	C₁₃×#384	C₂²	1	2	yes	complemented
42	C₁₃×#382	C₂²	1	2	yes	complemented
43	C₁₃×#381	C₂²	1	8	yes	complemented
44	C₁₃×#380	C₂²	1	8	yes	complemented
45	C₁₃×#379	C₂²	1	4	yes	—
46	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
47	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
48	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
49	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
50	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
51	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
52	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
53	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
54	C₁₃×#376	C₂²	1	2	yes	complemented
55	C₄³×C₁₃	C₂²	1	2	yes	complemented
56	C₂⁵×C₁₃	C₂³	1	2	yes	—
57	C₂²×D₄×C₁₃	—	2	4	no	—
58	C₂²×D₄×C₁₃	—	2	4	no	—
59	C₂²×D₄×C₁₃	C₂×C₄	1	8	yes	—
60	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
61	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
62	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
63	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
64	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
65	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₄×D₄×C₁₃	C₂×C₄	1	32	yes	complemented
67	C₄×D₄×C₁₃	C₂×C₄	1	32	yes	complemented
68	C₁₃×#117	—	2	4	no	—
69	C₁₃×#117	—	2	4	no	—
70	C₁₃×#117	—	4	16	no	—
71	C₁₃×#117	C₂×C₄	1	8	yes	—
72	C₁₃×#117	C₂×C₄	1	8	yes	—
73	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
74	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
75	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
76	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
84	C₂×C₁₃×C₂²⋊C₄	—	4	8	no	—
85	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	32	yes	—
86	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
87	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
88	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
89	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
90	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
91	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
92	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
93	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
94	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
95	C₂×C₄²×C₁₃	—	2	4	no	—
96	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
97	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
98	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
99	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
102	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
103	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
104	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
105	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
106	C₁₃×#95	C₂³	1	8	yes	—
107	C₁₃×#95	C₂³	1	4	yes	—
108	C₁₃×#95	C₂³	1	4	yes	—
109	C₁₃×#95	C₂³	1	4	yes	—
110	C₁₃×#95	C₂³	1	8	yes	—
111	C₁₃×#95	C₂³	1	4	yes	—
112	#34255	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
113	C₂⁴×C₁₃	—	2	4	no	—
114	C₂⁴×C₁₃	—	2	4	no	—
115	C₂⁴×C₁₃	—	4	4	no	—
116	C₂⁴×C₁₃	—	4	4	no	—
117	C₂⁴×C₁₃	C₂²×C₄	1	8	yes	—
118	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
119	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
120	C₂×D₄×C₁₃	—	2	32	no	—
121	C₂×D₄×C₁₃	—	2	4	no	—
122	C₂×D₄×C₁₃	—	2	4	no	—
123	C₂×D₄×C₁₃	—	2	4	no	—
124	C₂×D₄×C₁₃	—	2	4	no	—
125	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
126	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
127	C₂²×C₄×C₁₃	—	2	4	no	—
128	C₂²×C₄×C₁₃	—	2	4	no	—
129	C₂²×C₄×C₁₃	—	2	4	no	—
130	C₂²×C₄×C₁₃	—	4	8	no	—
131	C₂²×C₄×C₁₃	—	4	2	no	—
132	C₂²×C₄×C₁₃	—	4	8	no	—
133	C₂²×C₄×C₁₃	—	4	4	no	—
134	C₂²×C₄×C₁₃	C₂²×C₄	1	32	yes	—
135	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
136	C₂²×C₄×C₁₃	#41	1	4	yes	—
137	C₂²×C₄×C₁₃	#41	1	4	yes	—
138	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
139	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
140	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
141	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
142	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
143	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
144	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
145	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
146	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
147	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
148	C₁₃×C₄⋊C₄	—	2	4	no	—
149	C₁₃×C₄⋊C₄	—	2	4	no	—
150	C₁₃×C₄⋊C₄	—	2	4	no	—
151	C₁₃×C₄⋊C₄	—	2	2	no	—
152	C₁₃×C₄⋊C₄	—	2	2	no	—
153	C₁₃×C₄⋊C₄	—	2	8	no	—
154	C₁₃×C₄⋊C₄	—	4	4	no	—
155	C₁₃×C₄⋊C₄	—	4	8	no	—
156	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
157	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
158	C₁₃×C₂²⋊C₄	—	2	4	no	—
159	C₁₃×C₂²⋊C₄	—	2	4	no	—
160	C₁₃×C₂²⋊C₄	—	2	16	no	—
161	C₁₃×C₂²⋊C₄	—	4	8	no	—
162	C₁₃×C₂²⋊C₄	—	4	8	no	—
163	C₁₃×C₂²⋊C₄	—	4	8	no	—
164	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
165	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
166	C₁₃×C₂²⋊C₄	C₂²×C₄	1	32	yes	—
167	C₄²×C₁₃	—	2	2	no	—
168	C₄²×C₁₃	—	2	4	no	—
169	C₄²×C₁₃	—	2	2	no	—
170	C₄²×C₁₃	—	2	4	no	—
171	C₄²×C₁₃	—	2	4	no	—
172	C₄²×C₁₃	—	2	8	no	—
173	C₄²×C₁₃	—	4	4	no	—
174	C₄²×C₁₃	—	4	8	no	—
175	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
176	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
177	C₂×#518	C₂×C₁₃	1	1	yes	characteristic
178	#2357	C₂×C₁₃	1	4	yes	complemented
179	#2354	C₂×C₁₃	1	4	yes	complemented
180	#2342	C₂×C₁₃	1	8	yes	complemented
181	#2319	C₂×C₁₃	1	4	yes	complemented
182	#2317	C₂×C₁₃	1	1	yes	characteristic, complemented
183	#2309	C₂×C₁₃	1	1	yes	characteristic
184	#2296	C₂×C₁₃	1	1	yes	characteristic, complemented
185	#2293	C₂×C₁₃	1	4	yes	complemented
186	C₂×#390	C₂×C₁₃	1	1	yes	characteristic
187	#2274	C₂×C₁₃	1	1	yes	characteristic, complemented
188	C₄×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
189	C₂³×C₁₃	—	2	2	no	—
190	C₂³×C₁₃	—	2	2	no	—
191	C₂³×C₁₃	—	2	4	no	—
192	C₂³×C₁₃	—	2	4	no	—
193	C₂³×C₁₃	—	2	8	no	—
194	C₂³×C₁₃	—	2	8	no	—
195	C₂³×C₁₃	—	2	16	no	—
196	C₂³×C₁₃	—	4	16	no	—
197	C₂³×C₁₃	—	8	8	no	—
198	C₂³×C₁₃	—	8	4	no	—
199	C₂³×C₁₃	—	8	4	no	—
200	C₂³×C₁₃	C₂³×C₄	1	8	yes	—
201	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
202	C₂³×C₁₃	C₂×#41	1	2	yes	—
203	C₂³×C₁₃	C₂×#41	1	2	yes	—
204	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
205	D₄×C₁₃	—	2	16	no	—
206	D₄×C₁₃	—	2	16	no	—
207	C₂×C₄×C₁₃	—	2	2	no	—
208	C₂×C₄×C₁₃	—	2	4	no	—
209	C₂×C₄×C₁₃	—	2	4	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	2	4	no	—
212	C₂×C₄×C₁₃	—	2	4	no	—
213	C₂×C₄×C₁₃	—	2	2	no	—
214	C₂×C₄×C₁₃	—	2	4	no	—
215	C₂×C₄×C₁₃	—	2	2	no	—
216	C₂×C₄×C₁₃	—	2	2	no	—
217	C₂×C₄×C₁₃	—	2	4	no	—
218	C₂×C₄×C₁₃	—	2	4	no	—
219	C₂×C₄×C₁₃	—	2	4	no	—
220	C₂×C₄×C₁₃	—	2	8	no	—
221	C₂×C₄×C₁₃	—	2	2	no	—
222	C₂×C₄×C₁₃	—	2	4	no	—
223	C₂×C₄×C₁₃	—	2	4	no	—
224	C₂×C₄×C₁₃	—	2	2	no	—
225	C₂×C₄×C₁₃	—	4	32	no	—
226	C₂×C₄×C₁₃	—	4	8	no	—
227	C₂×C₄×C₁₃	—	8	4	no	—
228	C₂×C₄×C₁₃	#117	1	16	yes	complemented
229	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
230	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
231	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
232	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
233	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
234	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
235	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
236	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
237	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
238	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
239	#518	C₄×C₁₃	1	16	yes	complemented
240	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
241	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
242	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
243	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
244	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
245	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
246	C₂×#117	C₂²×C₁₃	1	8	yes	complemented
247	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
248	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
249	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
250	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
251	#390	C₂²×C₁₃	1	4	yes	—
252	#390	C₂²×C₁₃	1	2	yes	—
253	#390	C₂²×C₁₃	1	2	yes	—
254	#390	C₂²×C₁₃	1	2	yes	—
255	#390	C₂²×C₁₃	1	4	yes	—
256	#390	C₂²×C₁₃	1	2	yes	—
257	#389	C₂²×C₁₃	1	4	yes	complemented
258	#389	C₂²×C₁₃	1	2	yes	complemented
259	#389	C₂²×C₁₃	1	2	yes	complemented
260	#388	C₂²×C₁₃	1	8	yes	complemented
261	#388	C₂²×C₁₃	1	8	yes	complemented
262	#388	C₂²×C₁₃	1	8	yes	complemented
263	#388	C₂²×C₁₃	1	8	yes	complemented
264	#385	C₂²×C₁₃	1	4	yes	—
265	#385	C₂²×C₁₃	1	4	yes	—
266	#384	C₂²×C₁₃	1	2	yes	complemented
267	#382	C₂²×C₁₃	1	2	yes	complemented
268	#381	C₂²×C₁₃	1	8	yes	complemented
269	#380	C₂²×C₁₃	1	8	yes	complemented
270	#379	C₂²×C₁₃	1	4	yes	—
271	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
272	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
273	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
274	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
275	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
276	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
277	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
278	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
279	#376	C₂²×C₁₃	1	2	yes	complemented
280	C₄³	C₂²×C₁₃	1	2	yes	complemented
281	C₂²×C₁₃	—	2	4	no	—
282	C₂²×C₁₃	—	2	4	no	—
283	C₂²×C₁₃	—	2	2	no	—
284	C₂²×C₁₃	—	2	2	no	—
285	C₂²×C₁₃	—	2	8	no	—
286	C₂²×C₁₃	—	2	16	no	—
287	C₂²×C₁₃	—	4	8	no	—
288	C₂²×C₁₃	—	4	4	no	—
289	C₂²×C₁₃	—	4	4	no	—
290	C₂²×C₁₃	—	8	16	no	—
291	C₂²×C₁₃	C₂×#117	1	4	yes	—
292	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
293	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
294	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
295	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
296	C₂²×C₁₃	#585	1	2	yes	—
297	C₄×C₁₃	—	2	8	no	—
298	C₄×C₁₃	—	2	8	no	—
299	C₄×C₁₃	—	2	4	no	—
300	C₄×C₁₃	—	4	4	no	—
301	C₄×C₁₃	—	4	2	no	—
302	C₄×C₁₃	—	4	2	no	—
303	C₄×C₁₃	—	4	4	no	—
304	C₄×C₁₃	—	4	2	no	—
305	C₄×C₁₃	C₂×#117	1	4	yes	—
306	C₄×C₁₃	C₂×#117	1	4	yes	—
307	C₂⁵	C₂³×C₁₃	1	2	yes	—
308	C₂²×D₄	—	2	4	no	—
309	C₂²×D₄	—	2	4	no	—
310	C₂²×D₄	C₂×C₄×C₁₃	1	8	yes	—
311	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
312	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
313	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
314	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
315	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
316	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
317	C₄×D₄	C₂×C₄×C₁₃	1	32	yes	complemented
318	C₄×D₄	C₂×C₄×C₁₃	1	32	yes	complemented
319	#117	—	2	4	no	—
320	#117	—	2	4	no	—
321	#117	—	4	16	no	—
322	#117	C₂×C₄×C₁₃	1	8	yes	—
323	#117	C₂×C₄×C₁₃	1	8	yes	—
324	C₂×C₄⋊C₄	—	2	4	no	—
325	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
326	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
327	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
328	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
329	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
330	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
331	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
332	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
333	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
334	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
335	C₂×C₂²⋊C₄	—	4	8	no	—
336	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	32	yes	—
337	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
338	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
339	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
340	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
341	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
342	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
343	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
344	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
345	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
346	C₂×C₄²	—	2	4	no	—
347	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
348	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
349	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
350	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
351	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
352	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
353	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
354	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
355	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
356	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
357	#95	C₂³×C₁₃	1	4	yes	—
358	#95	C₂³×C₁₃	1	4	yes	—
359	#95	C₂³×C₁₃	1	8	yes	—
360	#95	C₂³×C₁₃	1	4	yes	—
361	#95	C₂³×C₁₃	1	8	yes	—
362	#95	C₂³×C₁₃	1	4	yes	—
363	C₂×C₁₃	—	2	4	no	—
364	C₂×C₁₃	—	4	8	no	—
365	C₂×C₁₃	C₂²×#117	1	1	yes	characteristic
366	C₂×C₁₃	C₄×H(5,𝔽₂)	1	2	yes	—
367	C₂×C₁₃	#3494	1	2	yes	—
368	C₂×C₁₃	#3508	1	1	yes	characteristic
369	C₂×C₁₃	#3510	1	1	yes	characteristic
370	C₂⁴	—	2	4	no	—
371	C₂⁴	—	2	4	no	—
372	C₂⁴	—	4	4	no	—
373	C₂⁴	—	4	4	no	—
374	C₂⁴	C₂²×C₄×C₁₃	1	8	yes	—
375	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
376	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
377	C₂×D₄	—	2	32	no	—
378	C₂×D₄	—	2	4	no	—
379	C₂×D₄	—	2	4	no	—
380	C₂×D₄	—	2	4	no	—
381	C₂×D₄	—	2	4	no	—
382	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
383	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
384	C₂²×C₄	—	2	4	no	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	2	4	no	—
387	C₂²×C₄	—	4	8	no	—
388	C₂²×C₄	—	4	2	no	—
389	C₂²×C₄	—	4	8	no	—
390	C₂²×C₄	—	4	4	no	—
391	C₂²×C₄	C₂²×C₄×C₁₃	1	32	yes	—
392	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
393	C₂²×C₄	C₁₃×#41	1	4	yes	—
394	C₂²×C₄	C₁₃×#41	1	4	yes	—
395	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
396	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
397	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
398	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
399	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
400	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
401	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
402	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
403	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
404	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
405	C₄⋊C₄	—	2	4	no	—
406	C₄⋊C₄	—	2	4	no	—
407	C₄⋊C₄	—	2	4	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	8	no	—
411	C₄⋊C₄	—	4	8	no	—
412	C₄⋊C₄	—	4	4	no	—
413	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
414	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
415	C₂²⋊C₄	—	2	4	no	—
416	C₂²⋊C₄	—	2	4	no	—
417	C₂²⋊C₄	—	2	16	no	—
418	C₂²⋊C₄	—	4	8	no	—
419	C₂²⋊C₄	—	4	8	no	—
420	C₂²⋊C₄	—	4	8	no	—
421	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
422	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
423	C₂²⋊C₄	C₂²×C₄×C₁₃	1	32	yes	—
424	C₄²	—	2	2	no	—
425	C₄²	—	2	4	no	—
426	C₄²	—	2	2	no	—
427	C₄²	—	2	4	no	—
428	C₄²	—	2	4	no	—
429	C₄²	—	2	8	no	—
430	C₄²	—	4	8	no	—
431	C₄²	—	4	4	no	—
432	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
433	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
434	C₁₃	#34255	1	1	yes	characteristic, direct product factor, Sylow
435	C₂³	—	2	2	no	—
436	C₂³	—	2	2	no	—
437	C₂³	—	2	4	no	—
438	C₂³	—	2	4	no	—
439	C₂³	—	2	8	no	—
440	C₂³	—	2	8	no	—
441	C₂³	—	2	16	no	—
442	C₂³	—	4	16	no	—
443	C₂³	—	8	8	no	—
444	C₂³	—	8	4	no	—
445	C₂³	—	8	4	no	—
446	C₂³	C₂³×C₄×C₁₃	1	8	yes	—
447	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
448	C₂³	C₂×C₁₃×#41	1	2	yes	—
449	C₂³	C₂×C₁₃×#41	1	2	yes	—
450	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
451	D₄	—	2	16	no	—
452	D₄	—	2	16	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	8	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	4	32	no	—
472	C₂×C₄	—	4	8	no	—
473	C₂×C₄	—	8	4	no	—
474	C₂×C₄	C₁₃×#117	1	16	yes	complemented
475	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
476	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
477	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
478	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
479	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
480	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
481	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
482	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
483	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
484	C₂²	—	2	4	no	—
485	C₂²	—	2	4	no	—
486	C₂²	—	2	2	no	—
487	C₂²	—	2	2	no	—
488	C₂²	—	2	8	no	—
489	C₂²	—	2	16	no	—
490	C₂²	—	4	8	no	—
491	C₂²	—	4	4	no	—
492	C₂²	—	4	4	no	—
493	C₂²	—	8	16	no	—
494	C₂²	C₂×C₁₃×#117	1	4	yes	—
495	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
496	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
497	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
498	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
499	C₂²	C₁₃×#585	1	2	yes	—
500	C₄	—	2	8	no	—
501	C₄	—	2	8	no	—
502	C₄	—	2	4	no	—
503	C₄	—	4	4	no	—
504	C₄	—	4	2	no	—
505	C₄	—	4	2	no	—
506	C₄	—	4	4	no	—
507	C₄	—	4	2	no	—
508	C₄	C₂×C₁₃×#117	1	4	yes	—
509	C₄	C₂×C₁₃×#117	1	4	yes	—
510	C₂	—	2	4	no	—
511	C₂	—	4	8	no	—
512	C₂	C₂²×C₁₃×#117	1	1	yes	characteristic
513	C₂	C₄×C₁₃×H(5,𝔽₂)	1	2	yes	—
514	C₂	C₁₃×#3494	1	2	yes	—
515	C₂	C₁₃×#3508	1	1	yes	characteristic
516	C₂	C₁₃×#3510	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂³×D₄×C₁₃	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2357	C₂	semidirect
3. C₁₃×#2354	C₂	semidirect
4. C₁₃×#2342	C₂	semidirect
5. C₁₃×#2319	C₂	semidirect
6. C₁₃×#2317	C₂	semidirect
8. C₁₃×#2296	C₂	semidirect
9. C₁₃×#2293	C₂	semidirect
11. C₁₃×#2274	C₂	semidirect
12. C₄×C₁₃×#117	C₂	semidirect
14. C₁₃×#518	C₄	semidirect
21. C₂×C₁₃×#117	C₂²	semidirect
32. C₁₃×#389	C₂²	semidirect
33. C₁₃×#389	C₂²	semidirect
34. C₁₃×#389	C₂²	semidirect
35. C₁₃×#388	C₂²	semidirect
36. C₁₃×#388	C₂²	semidirect
37. C₁₃×#388	C₂²	semidirect
38. C₁₃×#388	C₂²	semidirect
41. C₁₃×#384	C₂²	semidirect
42. C₁₃×#382	C₂²	semidirect
43. C₁₃×#381	C₂²	semidirect
44. C₁₃×#380	C₂²	semidirect
46. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
47. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
48. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
49. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
50. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
53. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
54. C₁₃×#376	C₂²	semidirect
55. C₄³×C₁₃	C₂²	semidirect
66. C₄×D₄×C₁₃	C₂×C₄	semidirect
67. C₄×D₄×C₁₃	C₂×C₄	semidirect
112. #34255	C₁₃	direct (N × H)
178. #2357	C₂×C₁₃	semidirect
179. #2354	C₂×C₁₃	semidirect
180. #2342	C₂×C₁₃	semidirect
181. #2319	C₂×C₁₃	semidirect
182. #2317	C₂×C₁₃	semidirect
184. #2296	C₂×C₁₃	semidirect
185. #2293	C₂×C₁₃	semidirect
187. #2274	C₂×C₁₃	semidirect
188. C₄×#117	C₂×C₁₃	semidirect
228. C₂×C₄×C₁₃	#117	semidirect
239. #518	C₄×C₁₃	semidirect
246. C₂×#117	C₂²×C₁₃	semidirect
257. #389	C₂²×C₁₃	semidirect
258. #389	C₂²×C₁₃	semidirect
259. #389	C₂²×C₁₃	semidirect
260. #388	C₂²×C₁₃	semidirect
261. #388	C₂²×C₁₃	semidirect
262. #388	C₂²×C₁₃	semidirect
263. #388	C₂²×C₁₃	semidirect
266. #384	C₂²×C₁₃	semidirect
267. #382	C₂²×C₁₃	semidirect
268. #381	C₂²×C₁₃	semidirect
269. #380	C₂²×C₁₃	semidirect
271. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
272. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
273. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
274. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
275. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
278. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
279. #376	C₂²×C₁₃	semidirect
280. C₄³	C₂²×C₁₃	semidirect
317. C₄×D₄	C₂×C₄×C₁₃	semidirect
318. C₄×D₄	C₂×C₄×C₁₃	semidirect
434. C₁₃	#34255	direct (N × H)
474. C₂×C₄	C₁₃×#117	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#518	2
C₁₃×#2357	2
C₁₃×#2354	2
C₁₃×#2342	2
C₁₃×#2319	2
C₁₃×#2317	2
C₁₃×#2309	2
C₁₃×#2296	2
C₁₃×#2293	2
C₂×C₁₃×#390	2
C₁₃×#2274	2
C₄×C₁₃×#117	2
#34255	13

Subgroups — C13×#34255 #15720594

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34255 #15720594