Subgroups — C₁₃×#34984 #15721323

Order 3328.

3690 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#534	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₃×#534	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2854	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2847	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2618	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2617	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2425	C₂	1	8	yes	maximal, complemented
9	C₁₃×#2424	C₂	1	8	yes	maximal, complemented
10	C₁₃×#2315	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#386	C₂	1	2	yes	maximal, complemented
12	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
13	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
16	C₁₃×#534	—	2	16	no	—
17	C₁₃×#534	—	2	8	no	—
18	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
19	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
20	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
21	C₂×C₁₃×#121	C₂²	1	2	yes	—
22	C₂×C₁₃×#121	C₂²	1	2	yes	—
23	C₂×C₁₃×#121	C₂²	1	8	yes	—
24	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
25	C₂×C₁₃×#120	C₂²	1	4	yes	complemented
26	C₂×C₁₃×#120	C₂²	1	4	yes	complemented
27	C₂×C₁₃×#120	C₂²	1	4	yes	complemented
28	C₂×C₄×D₄×C₁₃	—	2	8	no	—
29	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	complemented
30	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
34	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
35	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#398	C₂²	1	4	yes	complemented
37	C₁₃×#397	C₂²	1	4	yes	complemented
38	C₁₃×#396	C₂²	1	8	yes	complemented
39	C₁₃×#394	C₂²	1	8	yes	complemented
40	C₁₃×#394	C₂²	1	4	yes	complemented
41	C₁₃×#392	C₂²	1	4	yes	complemented
42	C₁₃×#390	C₂²	1	4	yes	complemented
43	C₁₃×#389	C₂²	1	4	yes	complemented
44	C₁₃×#388	C₂²	1	8	yes	complemented
45	C₁₃×#386	C₂²	1	4	yes	complemented
46	C₁₃×#386	C₂²	1	4	yes	complemented
47	C₁₃×#386	C₂²	1	8	yes	complemented
48	C₁₃×#386	C₂²	1	8	yes	complemented
49	C₁₃×#385	C₂²	1	8	yes	complemented
50	C₁₃×#380	C₂²	1	2	yes	complemented
51	C₁₃×#380	C₂²	1	2	yes	complemented
52	C₁₃×#380	C₂²	1	4	yes	complemented
53	C₂×C₁₃×#95	C₂²	1	4	yes	complemented
54	C₂⁵×C₁₃	C₂³	1	2	yes	—
55	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
56	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
57	C₂²×D₄×C₁₃	—	2	4	no	—
58	C₂²×D₄×C₁₃	—	2	4	no	—
59	C₂²×D₄×C₁₃	—	2	8	no	—
60	C₂²×D₄×C₁₃	—	2	8	no	—
61	C₂²×D₄×C₁₃	—	2	8	no	—
62	C₂²×D₄×C₁₃	D₄	1	8	yes	complemented
63	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
64	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
65	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
66	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
67	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
68	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
69	C₂³×C₄×C₁₃	—	2	4	no	—
70	C₂³×C₄×C₁₃	—	2	4	no	—
71	C₂³×C₄×C₁₃	—	4	4	no	—
72	C₂³×C₄×C₁₃	—	4	4	no	—
73	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
75	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
76	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
77	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
79	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
82	C₁₃×#123	—	2	16	no	—
83	C₁₃×#123	—	2	16	no	—
84	C₁₃×#123	—	2	16	no	—
85	C₁₃×#121	—	2	32	no	—
86	C₁₃×#121	—	2	8	no	—
87	C₁₃×#121	—	2	8	no	—
88	C₁₃×#121	—	4	8	no	—
89	C₁₃×#120	—	2	16	no	—
90	C₁₃×#120	—	2	16	no	—
91	C₁₃×#120	—	2	16	no	—
92	C₄×D₄×C₁₃	—	2	32	no	—
93	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
94	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
95	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
96	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
97	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
98	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
100	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
101	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
102	C₂×C₁₃×C₂²⋊C₄	—	4	8	no	—
103	C₂×C₁₃×C₂²⋊C₄	D₄	1	8	yes	complemented
104	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
105	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
106	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
107	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
108	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
109	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
110	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
111	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
112	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
113	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
114	C₂×C₄²×C₁₃	—	2	4	no	—
115	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
116	C₁₃×#95	C₂³	1	4	yes	—
117	C₁₃×#95	C₂³	1	4	yes	—
118	C₁₃×#95	C₂³	1	8	yes	—
119	C₁₃×#95	C₂³	1	8	yes	—
120	#34984	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
121	C₂⁴×C₁₃	—	2	2	no	—
122	C₂⁴×C₁₃	—	2	2	no	—
123	C₂⁴×C₁₃	—	2	4	no	—
124	C₂⁴×C₁₃	—	2	4	no	—
125	C₂⁴×C₁₃	—	2	4	no	—
126	C₂⁴×C₁₃	—	4	2	no	—
127	C₂⁴×C₁₃	—	4	2	no	—
128	C₂⁴×C₁₃	—	4	2	no	—
129	C₂⁴×C₁₃	—	4	2	no	—
130	C₂⁴×C₁₃	—	4	4	no	—
131	C₂⁴×C₁₃	—	4	4	no	—
132	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
133	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
134	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
135	C₂⁴×C₁₃	#41	1	4	yes	—
136	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
137	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
138	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
139	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
140	C₂×D₄×C₁₃	—	2	32	no	—
141	C₂×D₄×C₁₃	—	2	8	no	—
142	C₂×D₄×C₁₃	—	2	8	no	—
143	C₂×D₄×C₁₃	—	2	8	no	—
144	C₂×D₄×C₁₃	—	2	8	no	—
145	C₂×D₄×C₁₃	—	2	8	no	—
146	C₂×D₄×C₁₃	—	2	8	no	—
147	C₂×D₄×C₁₃	—	2	8	no	—
148	C₂×D₄×C₁₃	—	2	8	no	—
149	C₂×D₄×C₁₃	—	2	16	no	—
150	C₂×D₄×C₁₃	—	2	4	no	—
151	C₂×D₄×C₁₃	—	2	4	no	—
152	C₂×D₄×C₁₃	—	4	4	no	—
153	C₂×D₄×C₁₃	—	4	8	no	—
154	C₂×D₄×C₁₃	—	4	4	no	—
155	C₂×D₄×C₁₃	—	4	8	no	—
156	C₂×D₄×C₁₃	—	4	32	no	—
157	C₂×D₄×C₁₃	C₂×D₄	1	16	yes	—
158	C₂²×C₄×C₁₃	—	2	2	no	—
159	C₂²×C₄×C₁₃	—	2	2	no	—
160	C₂²×C₄×C₁₃	—	2	2	no	—
161	C₂²×C₄×C₁₃	—	2	4	no	—
162	C₂²×C₄×C₁₃	—	2	2	no	—
163	C₂²×C₄×C₁₃	—	2	8	no	—
164	C₂²×C₄×C₁₃	—	2	4	no	—
165	C₂²×C₄×C₁₃	—	2	4	no	—
166	C₂²×C₄×C₁₃	—	2	4	no	—
167	C₂²×C₄×C₁₃	—	2	8	no	—
168	C₂²×C₄×C₁₃	—	2	8	no	—
169	C₂²×C₄×C₁₃	—	2	8	no	—
170	C₂²×C₄×C₁₃	—	2	8	no	—
171	C₂²×C₄×C₁₃	—	4	2	no	—
172	C₂²×C₄×C₁₃	—	4	4	no	—
173	C₂²×C₄×C₁₃	—	4	4	no	—
174	C₂²×C₄×C₁₃	—	4	2	no	—
175	C₂²×C₄×C₁₃	—	4	2	no	—
176	C₂²×C₄×C₁₃	—	4	4	no	—
177	C₂²×C₄×C₁₃	—	4	4	no	—
178	C₂²×C₄×C₁₃	—	4	16	no	—
179	C₂²×C₄×C₁₃	—	4	16	no	—
180	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
181	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
182	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
183	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
184	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
185	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
186	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
187	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
190	C₁₃×C₄⋊C₄	—	2	8	no	—
191	C₁₃×C₄⋊C₄	—	2	16	no	—
192	C₁₃×C₄⋊C₄	—	2	4	no	—
193	C₁₃×C₄⋊C₄	—	2	4	no	—
194	C₁₃×C₄⋊C₄	—	4	4	no	—
195	C₁₃×C₄⋊C₄	—	4	4	no	—
196	C₁₃×C₂²⋊C₄	—	2	8	no	—
197	C₁₃×C₂²⋊C₄	—	2	8	no	—
198	C₁₃×C₂²⋊C₄	—	2	16	no	—
199	C₁₃×C₂²⋊C₄	—	2	8	no	—
200	C₁₃×C₂²⋊C₄	—	2	16	no	—
201	C₁₃×C₂²⋊C₄	—	2	8	no	—
202	C₁₃×C₂²⋊C₄	—	2	8	no	—
203	C₁₃×C₂²⋊C₄	—	2	16	no	—
204	C₁₃×C₂²⋊C₄	—	4	8	no	—
205	C₁₃×C₂²⋊C₄	C₂×D₄	1	16	yes	—
206	C₄²×C₁₃	—	2	8	no	—
207	C₂×#534	C₂×C₁₃	1	2	yes	complemented
208	C₂×#534	C₂×C₁₃	1	1	yes	characteristic, complemented
209	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
210	#2854	C₂×C₁₃	1	2	yes	complemented
211	#2847	C₂×C₁₃	1	2	yes	complemented
212	#2618	C₂×C₁₃	1	2	yes	complemented
213	#2617	C₂×C₁₃	1	2	yes	complemented
214	#2425	C₂×C₁₃	1	8	yes	complemented
215	#2424	C₂×C₁₃	1	8	yes	complemented
216	#2315	C₂×C₁₃	1	1	yes	characteristic, complemented
217	C₂×#386	C₂×C₁₃	1	2	yes	complemented
218	C₂³×C₁₃	—	2	2	no	—
219	C₂³×C₁₃	—	2	4	no	—
220	C₂³×C₁₃	—	2	2	no	—
221	C₂³×C₁₃	—	2	4	no	—
222	C₂³×C₁₃	—	2	8	no	—
223	C₂³×C₁₃	—	2	2	no	—
224	C₂³×C₁₃	—	2	2	no	—
225	C₂³×C₁₃	—	2	4	no	—
226	C₂³×C₁₃	—	2	4	no	—
227	C₂³×C₁₃	—	2	4	no	—
228	C₂³×C₁₃	—	2	4	no	—
229	C₂³×C₁₃	—	2	4	no	—
230	C₂³×C₁₃	—	2	8	no	—
231	C₂³×C₁₃	—	2	8	no	—
232	C₂³×C₁₃	—	4	4	no	—
233	C₂³×C₁₃	—	4	4	no	—
234	C₂³×C₁₃	—	4	8	no	—
235	C₂³×C₁₃	—	4	8	no	—
236	C₂³×C₁₃	—	4	8	no	—
237	C₂³×C₁₃	—	4	4	no	—
238	C₂³×C₁₃	—	4	8	no	—
239	C₂³×C₁₃	—	4	4	no	—
240	C₂³×C₁₃	—	4	16	no	—
241	C₂³×C₁₃	—	4	8	no	—
242	C₂³×C₁₃	—	8	4	no	—
243	C₂³×C₁₃	—	8	4	no	—
244	C₂³×C₁₃	—	8	8	no	—
245	C₂³×C₁₃	#121	1	16	yes	complemented
246	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
247	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
248	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
249	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
250	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
251	C₂³×C₁₃	C₂×#41	1	2	yes	—
252	C₂³×C₁₃	C₂×#41	1	4	yes	—
253	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
254	D₄×C₁₃	—	2	32	no	—
255	D₄×C₁₃	—	4	16	no	—
256	D₄×C₁₃	—	4	16	no	—
257	D₄×C₁₃	—	8	4	no	—
258	D₄×C₁₃	—	8	4	no	—
259	D₄×C₁₃	—	8	16	no	—
260	C₂×C₄×C₁₃	—	2	8	no	—
261	C₂×C₄×C₁₃	—	2	8	no	—
262	C₂×C₄×C₁₃	—	2	2	no	—
263	C₂×C₄×C₁₃	—	2	2	no	—
264	C₂×C₄×C₁₃	—	2	2	no	—
265	C₂×C₄×C₁₃	—	2	4	no	—
266	C₂×C₄×C₁₃	—	2	2	no	—
267	C₂×C₄×C₁₃	—	2	4	no	—
268	C₂×C₄×C₁₃	—	2	8	no	—
269	C₂×C₄×C₁₃	—	2	2	no	—
270	C₂×C₄×C₁₃	—	2	4	no	—
271	C₂×C₄×C₁₃	—	2	4	no	—
272	C₂×C₄×C₁₃	—	2	4	no	—
273	C₂×C₄×C₁₃	—	2	8	no	—
274	C₂×C₄×C₁₃	—	2	4	no	—
275	C₂×C₄×C₁₃	—	2	8	no	—
276	C₂×C₄×C₁₃	—	4	4	no	—
277	C₂×C₄×C₁₃	—	4	4	no	—
278	C₂×C₄×C₁₃	—	4	16	no	—
279	C₂×C₄×C₁₃	—	4	16	no	—
280	C₂×C₄×C₁₃	—	4	4	no	—
281	C₂×C₄×C₁₃	—	4	8	no	—
282	C₂×C₄×C₁₃	—	8	8	no	—
283	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
284	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
285	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
286	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
287	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
288	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
289	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
290	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
291	#534	—	2	16	no	—
292	#534	—	2	8	no	—
293	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
294	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
295	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
296	C₂×#121	C₂²×C₁₃	1	2	yes	—
297	C₂×#121	C₂²×C₁₃	1	2	yes	—
298	C₂×#121	C₂²×C₁₃	1	8	yes	—
299	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
300	C₂×#120	C₂²×C₁₃	1	4	yes	complemented
301	C₂×#120	C₂²×C₁₃	1	4	yes	complemented
302	C₂×#120	C₂²×C₁₃	1	4	yes	complemented
303	C₂×C₄×D₄	—	2	8	no	—
304	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	complemented
305	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
306	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
307	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
308	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
309	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
310	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
311	#398	C₂²×C₁₃	1	4	yes	complemented
312	#397	C₂²×C₁₃	1	4	yes	complemented
313	#396	C₂²×C₁₃	1	8	yes	complemented
314	#394	C₂²×C₁₃	1	8	yes	complemented
315	#394	C₂²×C₁₃	1	4	yes	complemented
316	#392	C₂²×C₁₃	1	4	yes	complemented
317	#390	C₂²×C₁₃	1	4	yes	complemented
318	#389	C₂²×C₁₃	1	4	yes	complemented
319	#388	C₂²×C₁₃	1	8	yes	complemented
320	#386	C₂²×C₁₃	1	4	yes	complemented
321	#386	C₂²×C₁₃	1	8	yes	complemented
322	#386	C₂²×C₁₃	1	4	yes	complemented
323	#386	C₂²×C₁₃	1	8	yes	complemented
324	#385	C₂²×C₁₃	1	8	yes	complemented
325	#380	C₂²×C₁₃	1	2	yes	complemented
326	#380	C₂²×C₁₃	1	2	yes	complemented
327	#380	C₂²×C₁₃	1	4	yes	complemented
328	C₂×#95	C₂²×C₁₃	1	4	yes	complemented
329	C₂²×C₁₃	—	2	4	no	—
330	C₂²×C₁₃	—	2	8	no	—
331	C₂²×C₁₃	—	2	2	no	—
332	C₂²×C₁₃	—	2	4	no	—
333	C₂²×C₁₃	—	2	2	no	—
334	C₂²×C₁₃	—	2	4	no	—
335	C₂²×C₁₃	—	2	8	no	—
336	C₂²×C₁₃	—	2	4	no	—
337	C₂²×C₁₃	—	2	4	no	—
338	C₂²×C₁₃	—	2	8	no	—
339	C₂²×C₁₃	—	4	16	no	—
340	C₂²×C₁₃	—	4	16	no	—
341	C₂²×C₁₃	—	4	4	no	—
342	C₂²×C₁₃	—	4	2	no	—
343	C₂²×C₁₃	—	4	2	no	—
344	C₂²×C₁₃	—	4	4	no	—
345	C₂²×C₁₃	—	4	8	no	—
346	C₂²×C₁₃	—	4	4	no	—
347	C₂²×C₁₃	—	4	4	no	—
348	C₂²×C₁₃	—	4	8	no	—
349	C₂²×C₁₃	—	8	16	no	—
350	C₂²×C₁₃	C₂×#121	1	4	yes	—
351	C₂²×C₁₃	C₂×#121	1	8	yes	—
352	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
353	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
354	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
355	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
356	C₂²×C₁₃	#585	1	2	yes	—
357	C₄×C₁₃	—	2	4	no	—
358	C₄×C₁₃	—	2	4	no	—
359	C₄×C₁₃	—	2	4	no	—
360	C₄×C₁₃	—	2	4	no	—
361	C₄×C₁₃	—	4	4	no	—
362	C₄×C₁₃	—	4	2	no	—
363	C₄×C₁₃	—	4	8	no	—
364	C₂⁵	C₂³×C₁₃	1	2	yes	—
365	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
366	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
367	C₂²×D₄	—	2	4	no	—
368	C₂²×D₄	—	2	4	no	—
369	C₂²×D₄	—	2	8	no	—
370	C₂²×D₄	—	2	8	no	—
371	C₂²×D₄	—	2	8	no	—
372	C₂²×D₄	D₄×C₁₃	1	8	yes	complemented
373	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
374	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
375	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
376	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
377	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
378	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
379	C₂³×C₄	—	2	4	no	—
380	C₂³×C₄	—	2	4	no	—
381	C₂³×C₄	—	4	4	no	—
382	C₂³×C₄	—	4	4	no	—
383	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
384	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
385	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
386	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
387	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
388	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
389	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
390	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
391	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
392	#123	—	2	16	no	—
393	#123	—	2	16	no	—
394	#123	—	2	16	no	—
395	#121	—	2	32	no	—
396	#121	—	2	8	no	—
397	#121	—	2	8	no	—
398	#121	—	4	8	no	—
399	#120	—	2	16	no	—
400	#120	—	2	16	no	—
401	#120	—	2	16	no	—
402	C₄×D₄	—	2	32	no	—
403	C₂×C₄⋊C₄	—	2	4	no	—
404	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
405	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
406	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
407	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
408	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
409	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
410	C₂×C₂²⋊C₄	—	2	8	no	—
411	C₂×C₂²⋊C₄	—	2	4	no	—
412	C₂×C₂²⋊C₄	—	4	8	no	—
413	C₂×C₂²⋊C₄	D₄×C₁₃	1	8	yes	complemented
414	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
415	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
416	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
417	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
418	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
419	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
420	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
421	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
422	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
423	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
424	C₂×C₄²	—	2	4	no	—
425	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
426	#95	C₂³×C₁₃	1	8	yes	—
427	#95	C₂³×C₁₃	1	8	yes	—
428	#95	C₂³×C₁₃	1	4	yes	—
429	#95	C₂³×C₁₃	1	4	yes	—
430	C₂×C₁₃	—	2	4	no	—
431	C₂×C₁₃	—	2	8	no	—
432	C₂×C₁₃	—	4	4	no	—
433	C₂×C₁₃	—	8	4	no	—
434	C₂×C₁₃	C₂²×#121	1	1	yes	characteristic
435	C₂×C₁₃	#3459	1	2	yes	—
436	C₂×C₁₃	#3484	1	1	yes	characteristic
437	C₂×C₁₃	#3485	1	1	yes	characteristic
438	C₂×C₁₃	#3496	1	2	yes	—
439	C₂⁴	—	2	2	no	—
440	C₂⁴	—	2	2	no	—
441	C₂⁴	—	2	4	no	—
442	C₂⁴	—	2	4	no	—
443	C₂⁴	—	2	4	no	—
444	C₂⁴	—	4	2	no	—
445	C₂⁴	—	4	2	no	—
446	C₂⁴	—	4	2	no	—
447	C₂⁴	—	4	2	no	—
448	C₂⁴	—	4	4	no	—
449	C₂⁴	—	4	4	no	—
450	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
451	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
452	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
453	C₂⁴	C₁₃×#41	1	4	yes	—
454	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
455	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
456	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
457	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
458	C₂×D₄	—	2	32	no	—
459	C₂×D₄	—	2	8	no	—
460	C₂×D₄	—	2	8	no	—
461	C₂×D₄	—	2	8	no	—
462	C₂×D₄	—	2	8	no	—
463	C₂×D₄	—	2	8	no	—
464	C₂×D₄	—	2	8	no	—
465	C₂×D₄	—	2	8	no	—
466	C₂×D₄	—	2	8	no	—
467	C₂×D₄	—	2	16	no	—
468	C₂×D₄	—	2	4	no	—
469	C₂×D₄	—	2	4	no	—
470	C₂×D₄	—	4	4	no	—
471	C₂×D₄	—	4	8	no	—
472	C₂×D₄	—	4	4	no	—
473	C₂×D₄	—	4	8	no	—
474	C₂×D₄	—	4	32	no	—
475	C₂×D₄	C₂×D₄×C₁₃	1	16	yes	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	4	no	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	—	2	8	no	—
482	C₂²×C₄	—	2	4	no	—
483	C₂²×C₄	—	2	4	no	—
484	C₂²×C₄	—	2	4	no	—
485	C₂²×C₄	—	2	8	no	—
486	C₂²×C₄	—	2	8	no	—
487	C₂²×C₄	—	2	8	no	—
488	C₂²×C₄	—	2	8	no	—
489	C₂²×C₄	—	4	2	no	—
490	C₂²×C₄	—	4	4	no	—
491	C₂²×C₄	—	4	4	no	—
492	C₂²×C₄	—	4	2	no	—
493	C₂²×C₄	—	4	2	no	—
494	C₂²×C₄	—	4	4	no	—
495	C₂²×C₄	—	4	4	no	—
496	C₂²×C₄	—	4	16	no	—
497	C₂²×C₄	—	4	16	no	—
498	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
499	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
500	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
501	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
502	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
503	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
504	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
505	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
506	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
507	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
508	C₄⋊C₄	—	2	8	no	—
509	C₄⋊C₄	—	2	16	no	—
510	C₄⋊C₄	—	2	4	no	—
511	C₄⋊C₄	—	2	4	no	—
512	C₄⋊C₄	—	4	4	no	—
513	C₄⋊C₄	—	4	4	no	—
514	C₂²⋊C₄	—	2	8	no	—
515	C₂²⋊C₄	—	2	8	no	—
516	C₂²⋊C₄	—	2	16	no	—
517	C₂²⋊C₄	—	2	8	no	—
518	C₂²⋊C₄	—	2	16	no	—
519	C₂²⋊C₄	—	2	8	no	—
520	C₂²⋊C₄	—	2	8	no	—
521	C₂²⋊C₄	—	2	16	no	—
522	C₂²⋊C₄	—	4	8	no	—
523	C₂²⋊C₄	C₂×D₄×C₁₃	1	16	yes	—
524	C₄²	—	2	8	no	—
525	C₁₃	#34984	1	1	yes	characteristic, direct product factor, Sylow
526	C₂³	—	2	2	no	—
527	C₂³	—	2	4	no	—
528	C₂³	—	2	2	no	—
529	C₂³	—	2	4	no	—
530	C₂³	—	2	8	no	—
531	C₂³	—	2	2	no	—
532	C₂³	—	2	2	no	—
533	C₂³	—	2	4	no	—
534	C₂³	—	2	4	no	—
535	C₂³	—	2	4	no	—
536	C₂³	—	2	4	no	—
537	C₂³	—	2	4	no	—
538	C₂³	—	2	8	no	—
539	C₂³	—	2	8	no	—
540	C₂³	—	4	4	no	—
541	C₂³	—	4	4	no	—
542	C₂³	—	4	8	no	—
543	C₂³	—	4	8	no	—
544	C₂³	—	4	8	no	—
545	C₂³	—	4	4	no	—
546	C₂³	—	4	8	no	—
547	C₂³	—	4	4	no	—
548	C₂³	—	4	16	no	—
549	C₂³	—	4	8	no	—
550	C₂³	—	8	4	no	—
551	C₂³	—	8	4	no	—
552	C₂³	—	8	8	no	—
553	C₂³	C₁₃×#121	1	16	yes	complemented
554	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
555	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
556	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
557	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
558	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
559	C₂³	C₂×C₁₃×#41	1	2	yes	—
560	C₂³	C₂×C₁₃×#41	1	4	yes	—
561	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
562	D₄	—	2	32	no	—
563	D₄	—	4	16	no	—
564	D₄	—	4	16	no	—
565	D₄	—	8	4	no	—
566	D₄	—	8	4	no	—
567	D₄	—	8	16	no	—
568	C₂×C₄	—	2	8	no	—
569	C₂×C₄	—	2	8	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	4	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	4	no	—
576	C₂×C₄	—	2	8	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	4	no	—
579	C₂×C₄	—	2	4	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	2	8	no	—
582	C₂×C₄	—	2	4	no	—
583	C₂×C₄	—	2	8	no	—
584	C₂×C₄	—	4	4	no	—
585	C₂×C₄	—	4	4	no	—
586	C₂×C₄	—	4	16	no	—
587	C₂×C₄	—	4	16	no	—
588	C₂×C₄	—	4	4	no	—
589	C₂×C₄	—	4	8	no	—
590	C₂×C₄	—	8	8	no	—
591	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
592	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
593	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
594	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
595	C₂²	—	2	4	no	—
596	C₂²	—	2	8	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	2	4	no	—
599	C₂²	—	2	2	no	—
600	C₂²	—	2	4	no	—
601	C₂²	—	2	8	no	—
602	C₂²	—	2	4	no	—
603	C₂²	—	2	4	no	—
604	C₂²	—	2	8	no	—
605	C₂²	—	4	16	no	—
606	C₂²	—	4	16	no	—
607	C₂²	—	4	4	no	—
608	C₂²	—	4	2	no	—
609	C₂²	—	4	2	no	—
610	C₂²	—	4	4	no	—
611	C₂²	—	4	8	no	—
612	C₂²	—	4	4	no	—
613	C₂²	—	4	4	no	—
614	C₂²	—	4	8	no	—
615	C₂²	—	8	16	no	—
616	C₂²	C₂×C₁₃×#121	1	4	yes	—
617	C₂²	C₂×C₁₃×#121	1	8	yes	—
618	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
619	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
620	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
621	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
622	C₂²	C₁₃×#585	1	2	yes	—
623	C₄	—	2	4	no	—
624	C₄	—	2	4	no	—
625	C₄	—	2	4	no	—
626	C₄	—	2	4	no	—
627	C₄	—	4	4	no	—
628	C₄	—	4	2	no	—
629	C₄	—	4	8	no	—
630	C₂	—	2	4	no	—
631	C₂	—	2	8	no	—
632	C₂	—	4	4	no	—
633	C₂	—	8	4	no	—
634	C₂	C₂²×C₁₃×#121	1	1	yes	characteristic
635	C₂	C₁₃×#3459	1	2	yes	—
636	C₂	C₁₃×#3484	1	1	yes	characteristic
637	C₂	C₁₃×#3485	1	1	yes	characteristic
638	C₂	C₁₃×#3496	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#534	C₂	semidirect
2. C₂×C₁₃×#534	C₂	semidirect
3. C₂²×C₄×D₄×C₁₃	C₂	semidirect
4. C₁₃×#2854	C₂	semidirect
5. C₁₃×#2847	C₂	semidirect
6. C₁₃×#2618	C₂	semidirect
7. C₁₃×#2617	C₂	semidirect
8. C₁₃×#2425	C₂	semidirect
9. C₁₃×#2424	C₂	semidirect
10. C₁₃×#2315	C₂	semidirect
11. C₂×C₁₃×#386	C₂	semidirect
15. C₂⁴×C₄×C₁₃	C₂²	semidirect
18. C₂×C₁₃×#123	C₂²	semidirect
19. C₂×C₁₃×#123	C₂²	semidirect
20. C₂×C₁₃×#123	C₂²	semidirect
24. C₂×C₁₃×#121	C₂²	semidirect
25. C₂×C₁₃×#120	C₂²	semidirect
26. C₂×C₁₃×#120	C₂²	semidirect
27. C₂×C₁₃×#120	C₂²	semidirect
29. C₂×C₄×D₄×C₁₃	C₂²	semidirect
30. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
33. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
34. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
35. C₂²×C₄²×C₁₃	C₂²	semidirect
36. C₁₃×#398	C₂²	semidirect
37. C₁₃×#397	C₂²	semidirect
38. C₁₃×#396	C₂²	semidirect
39. C₁₃×#394	C₂²	semidirect
40. C₁₃×#394	C₂²	semidirect
41. C₁₃×#392	C₂²	semidirect
42. C₁₃×#390	C₂²	semidirect
43. C₁₃×#389	C₂²	semidirect
44. C₁₃×#388	C₂²	semidirect
45. C₁₃×#386	C₂²	semidirect
46. C₁₃×#386	C₂²	semidirect
47. C₁₃×#386	C₂²	semidirect
48. C₁₃×#386	C₂²	semidirect
49. C₁₃×#385	C₂²	semidirect
50. C₁₃×#380	C₂²	semidirect
51. C₁₃×#380	C₂²	semidirect
52. C₁₃×#380	C₂²	semidirect
53. C₂×C₁₃×#95	C₂²	semidirect
62. C₂²×D₄×C₁₃	D₄	semidirect
103. C₂×C₁₃×C₂²⋊C₄	D₄	semidirect
120. #34984	C₁₃	direct (N × H)
207. C₂×#534	C₂×C₁₃	semidirect
208. C₂×#534	C₂×C₁₃	semidirect
209. C₂²×C₄×D₄	C₂×C₁₃	semidirect
210. #2854	C₂×C₁₃	semidirect
211. #2847	C₂×C₁₃	semidirect
212. #2618	C₂×C₁₃	semidirect
213. #2617	C₂×C₁₃	semidirect
214. #2425	C₂×C₁₃	semidirect
215. #2424	C₂×C₁₃	semidirect
216. #2315	C₂×C₁₃	semidirect
217. C₂×#386	C₂×C₁₃	semidirect
245. C₂³×C₁₃	#121	semidirect
290. C₂⁴×C₄	C₂²×C₁₃	semidirect
293. C₂×#123	C₂²×C₁₃	semidirect
294. C₂×#123	C₂²×C₁₃	semidirect
295. C₂×#123	C₂²×C₁₃	semidirect
299. C₂×#121	C₂²×C₁₃	semidirect
300. C₂×#120	C₂²×C₁₃	semidirect
301. C₂×#120	C₂²×C₁₃	semidirect
302. C₂×#120	C₂²×C₁₃	semidirect
304. C₂×C₄×D₄	C₂²×C₁₃	semidirect
305. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
308. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
309. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
310. C₂²×C₄²	C₂²×C₁₃	semidirect
311. #398	C₂²×C₁₃	semidirect
312. #397	C₂²×C₁₃	semidirect
313. #396	C₂²×C₁₃	semidirect
314. #394	C₂²×C₁₃	semidirect
315. #394	C₂²×C₁₃	semidirect
316. #392	C₂²×C₁₃	semidirect
317. #390	C₂²×C₁₃	semidirect
318. #389	C₂²×C₁₃	semidirect
319. #388	C₂²×C₁₃	semidirect
320. #386	C₂²×C₁₃	semidirect
321. #386	C₂²×C₁₃	semidirect
322. #386	C₂²×C₁₃	semidirect
323. #386	C₂²×C₁₃	semidirect
324. #385	C₂²×C₁₃	semidirect
325. #380	C₂²×C₁₃	semidirect
326. #380	C₂²×C₁₃	semidirect
327. #380	C₂²×C₁₃	semidirect
328. C₂×#95	C₂²×C₁₃	semidirect
372. C₂²×D₄	D₄×C₁₃	semidirect
413. C₂×C₂²⋊C₄	D₄×C₁₃	semidirect
525. C₁₃	#34984	direct (N × H)
553. C₂³	C₁₃×#121	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#534	2
C₂²×C₄×D₄×C₁₃	2
C₁₃×#2854	2
C₁₃×#2847	2
C₁₃×#2618	2
C₁₃×#2617	2
C₁₃×#2425	2
C₁₃×#2424	2
C₁₃×#2315	2
C₂×C₁₃×#386	2
#34984	13

Subgroups — C13×#34984 #15721323

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34984 #15721323