Subgroups — C₁₃×#34493 #15720832

Order 3328.

3076 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄²×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2375	C₂	1	4	yes	maximal, complemented
3	C₁₃×#2366	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2363	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2354	C₂	1	2	yes	maximal, complemented
6	D₄×C₁₃×C₂²⋊C₄	C₂	1	4	yes	maximal, complemented
7	C₁₃×#2324	C₂	1	4	yes	maximal, complemented
8	C₁₃×#2321	C₂	1	4	yes	maximal, complemented
9	C₁₃×#2309	C₂	1	4	yes	maximal, complemented
10	C₄×C₁₃×#127	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2293	C₂	1	2	yes	maximal, complemented
12	C₂³×D₄×C₁₃	C₂²	1	4	yes	—
13	D₄²×C₁₃	C₄	1	16	yes	complemented
14	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#121	C₂²	1	4	yes	—
16	C₂×C₁₃×#120	C₂²	1	4	yes	—
17	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
18	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
19	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
20	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
21	C₂×C₁₃×#117	C₂²	1	4	yes	complemented
22	C₂×C₁₃×#117	C₂²	1	4	yes	complemented
23	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
24	C₁₃×#390	C₂²	1	2	yes	—
25	C₁₃×#390	C₂²	1	2	yes	—
26	C₁₃×#390	C₂²	1	4	yes	—
27	C₁₃×#390	C₂²	1	4	yes	complemented
28	C₁₃×#390	C₂²	1	2	yes	complemented
29	C₁₃×#390	C₂²	1	8	yes	complemented
30	C₁₃×#390	C₂²	1	4	yes	complemented
31	C₁₃×#390	C₂²	1	8	yes	complemented
32	C₁₃×#389	C₂²	1	2	yes	complemented
33	C₁₃×#389	C₂²	1	2	yes	complemented
34	C₁₃×#388	C₂²	1	4	yes	complemented
35	C₁₃×#388	C₂²	1	4	yes	complemented
36	C₁₃×#388	C₂²	1	8	yes	complemented
37	C₁₃×#388	C₂²	1	8	yes	complemented
38	C₁₃×#386	C₂²	1	8	yes	complemented
39	C₁₃×#386	C₂²	1	4	yes	complemented
40	C₁₃×#386	C₂²	1	8	yes	complemented
41	C₁₃×#385	C₂²	1	4	yes	complemented
42	C₁₃×#384	C₂²	1	1	yes	characteristic, complemented
43	C₁₃×#380	C₂²	1	4	yes	complemented
44	C₁₃×#379	C₂²	1	4	yes	complemented
45	C₁₃×#379	C₂²	1	8	yes	complemented
46	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
47	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
48	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
49	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
50	C₄³×C₁₃	C₂²	1	1	yes	characteristic, complemented
51	C₂⁵×C₁₃	C₂³	1	4	yes	—
52	C₂²×D₄×C₁₃	—	4	8	no	—
53	C₂²×D₄×C₁₃	—	4	8	no	—
54	C₂²×D₄×C₁₃	C₂×C₄	1	32	yes	complemented
55	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
56	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
57	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
58	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
59	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
60	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
61	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
62	C₁₃×#127	C₂×C₄	1	8	yes	—
63	C₁₃×#121	C₂×C₄	1	32	yes	complemented
64	C₁₃×#120	C₂×C₄	1	32	yes	complemented
65	C₄×D₄×C₁₃	—	4	8	no	—
66	C₄×D₄×C₁₃	—	4	8	no	—
67	C₄×D₄×C₁₃	—	4	4	no	—
68	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
69	C₁₃×#117	—	4	8	no	—
70	C₁₃×#117	—	4	8	no	—
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
73	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
74	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
75	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
76	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
78	C₂×C₁₃×C₂²⋊C₄	—	4	8	no	—
79	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
80	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
81	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
82	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
83	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
84	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
85	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
86	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
87	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
88	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
89	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
90	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
91	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
92	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
93	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
95	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
96	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
98	C₁₃×#95	C₂³	1	4	yes	—
99	C₁₃×#95	C₂³	1	4	yes	—
100	C₁₃×#95	C₂³	1	8	yes	—
101	C₁₃×#95	C₂³	1	4	yes	—
102	#34493	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
103	C₂⁴×C₁₃	—	4	4	no	—
104	C₂⁴×C₁₃	—	4	8	no	—
105	C₂⁴×C₁₃	—	4	8	no	—
106	C₂⁴×C₁₃	—	4	4	no	—
107	C₂⁴×C₁₃	C₂²×C₄	1	16	yes	—
108	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
109	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
110	C₂×D₄×C₁₃	—	2	8	no	—
111	C₂×D₄×C₁₃	—	2	8	no	—
112	C₂×D₄×C₁₃	—	2	4	no	—
113	C₂×D₄×C₁₃	—	2	4	no	—
114	C₂×D₄×C₁₃	—	4	64	no	—
115	C₂×D₄×C₁₃	—	4	2	no	—
116	C₂×D₄×C₁₃	—	4	8	no	—
117	C₂×D₄×C₁₃	—	4	8	no	—
118	C₂×D₄×C₁₃	—	4	2	no	—
119	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
120	C₂×D₄×C₁₃	C₂²×C₄	1	16	yes	—
121	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
122	C₂×D₄×C₁₃	C₂²×C₄	1	32	yes	—
123	C₂²×C₄×C₁₃	—	2	8	no	—
124	C₂²×C₄×C₁₃	—	2	8	no	—
125	C₂²×C₄×C₁₃	—	2	8	no	—
126	C₂²×C₄×C₁₃	—	4	4	no	—
127	C₂²×C₄×C₁₃	—	4	8	no	—
128	C₂²×C₄×C₁₃	—	4	8	no	—
129	C₂²×C₄×C₁₃	C₂²×C₄	1	16	yes	—
130	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
131	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
132	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
133	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
134	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
137	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
138	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
139	C₁₃×C₄⋊C₄	—	2	4	no	—
140	C₁₃×C₄⋊C₄	—	2	8	no	—
141	C₁₃×C₄⋊C₄	—	2	4	no	—
142	C₁₃×C₄⋊C₄	—	4	4	no	—
143	C₁₃×C₄⋊C₄	—	4	4	no	—
144	C₁₃×C₄⋊C₄	—	4	2	no	—
145	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
146	C₁₃×C₂²⋊C₄	—	2	8	no	—
147	C₁₃×C₂²⋊C₄	—	4	8	no	—
148	C₁₃×C₂²⋊C₄	—	4	4	no	—
149	C₁₃×C₂²⋊C₄	—	4	4	no	—
150	C₁₃×C₂²⋊C₄	—	4	4	no	—
151	C₁₃×C₂²⋊C₄	—	4	4	no	—
152	C₁₃×C₂²⋊C₄	—	4	8	no	—
153	C₁₃×C₂²⋊C₄	—	4	8	no	—
154	C₁₃×C₂²⋊C₄	—	4	4	no	—
155	C₁₃×C₂²⋊C₄	—	4	8	no	—
156	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
157	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
158	C₄²×C₁₃	—	2	4	no	—
159	C₄²×C₁₃	—	2	8	no	—
160	C₄²×C₁₃	—	2	2	no	—
161	C₄²×C₁₃	—	2	4	no	—
162	C₄²×C₁₃	—	4	1	no	—
163	C₄²×C₁₃	—	4	8	no	—
164	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
165	C₂×D₄²	C₂×C₁₃	1	1	yes	characteristic
166	#2375	C₂×C₁₃	1	4	yes	complemented
167	#2366	C₂×C₁₃	1	1	yes	characteristic, complemented
168	#2363	C₂×C₁₃	1	4	yes	complemented
169	#2354	C₂×C₁₃	1	2	yes	complemented
170	D₄×C₂²⋊C₄	C₂×C₁₃	1	4	yes	complemented
171	#2324	C₂×C₁₃	1	4	yes	complemented
172	#2321	C₂×C₁₃	1	4	yes	complemented
173	#2309	C₂×C₁₃	1	4	yes	complemented
174	C₄×#127	C₂×C₁₃	1	1	yes	characteristic, complemented
175	#2293	C₂×C₁₃	1	2	yes	complemented
176	C₂³×C₁₃	—	2	4	no	—
177	C₂³×C₁₃	—	2	4	no	—
178	C₂³×C₁₃	—	2	4	no	—
179	C₂³×C₁₃	—	2	4	no	—
180	C₂³×C₁₃	—	2	8	no	—
181	C₂³×C₁₃	—	2	8	no	—
182	C₂³×C₁₃	—	2	4	no	—
183	C₂³×C₁₃	—	2	4	no	—
184	C₂³×C₁₃	—	2	4	no	—
185	C₂³×C₁₃	—	2	4	no	—
186	C₂³×C₁₃	—	4	32	no	—
187	C₂³×C₁₃	—	4	16	no	—
188	C₂³×C₁₃	—	8	8	no	—
189	C₂³×C₁₃	—	8	16	no	—
190	C₂³×C₁₃	—	8	8	no	—
191	C₂³×C₁₃	C₂³×C₄	1	8	yes	—
192	C₂³×C₁₃	C₂³×C₄	1	8	yes	—
193	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
194	D₄×C₁₃	—	2	16	no	—
195	D₄×C₁₃	—	2	32	no	—
196	D₄×C₁₃	—	4	32	no	—
197	D₄×C₁₃	—	4	8	no	—
198	C₂×C₄×C₁₃	—	2	1	no	—
199	C₂×C₄×C₁₃	—	2	2	no	—
200	C₂×C₄×C₁₃	—	2	4	no	—
201	C₂×C₄×C₁₃	—	2	4	no	—
202	C₂×C₄×C₁₃	—	2	1	no	—
203	C₂×C₄×C₁₃	—	2	32	no	—
204	C₂×C₄×C₁₃	—	2	2	no	—
205	C₂×C₄×C₁₃	—	2	1	no	—
206	C₂×C₄×C₁₃	—	2	4	no	—
207	C₂×C₄×C₁₃	—	2	2	no	—
208	C₂×C₄×C₁₃	—	2	2	no	—
209	C₂×C₄×C₁₃	—	2	4	no	—
210	C₂×C₄×C₁₃	—	2	4	no	—
211	C₂×C₄×C₁₃	—	2	8	no	—
212	C₂×C₄×C₁₃	—	2	4	no	—
213	C₂×C₄×C₁₃	—	2	4	no	—
214	C₂×C₄×C₁₃	—	2	4	no	—
215	C₂×C₄×C₁₃	—	2	2	no	—
216	C₂×C₄×C₁₃	—	2	4	no	—
217	C₂×C₄×C₁₃	—	8	8	no	—
218	C₂×C₄×C₁₃	—	8	8	no	—
219	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
220	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
221	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
222	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
223	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
224	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
225	C₂³×D₄	C₂²×C₁₃	1	4	yes	—
226	D₄²	C₄×C₁₃	1	16	yes	complemented
227	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
228	C₂×#121	C₂²×C₁₃	1	4	yes	—
229	C₂×#120	C₂²×C₁₃	1	4	yes	—
230	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
231	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
232	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
233	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
234	C₂×#117	C₂²×C₁₃	1	4	yes	complemented
235	C₂×#117	C₂²×C₁₃	1	4	yes	complemented
236	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
237	#390	C₂²×C₁₃	1	2	yes	—
238	#390	C₂²×C₁₃	1	4	yes	—
239	#390	C₂²×C₁₃	1	2	yes	—
240	#390	C₂²×C₁₃	1	4	yes	complemented
241	#390	C₂²×C₁₃	1	2	yes	complemented
242	#390	C₂²×C₁₃	1	8	yes	complemented
243	#390	C₂²×C₁₃	1	4	yes	complemented
244	#390	C₂²×C₁₃	1	8	yes	complemented
245	#389	C₂²×C₁₃	1	2	yes	complemented
246	#389	C₂²×C₁₃	1	2	yes	complemented
247	#388	C₂²×C₁₃	1	4	yes	complemented
248	#388	C₂²×C₁₃	1	8	yes	complemented
249	#388	C₂²×C₁₃	1	8	yes	complemented
250	#388	C₂²×C₁₃	1	4	yes	complemented
251	#386	C₂²×C₁₃	1	8	yes	complemented
252	#386	C₂²×C₁₃	1	4	yes	complemented
253	#386	C₂²×C₁₃	1	8	yes	complemented
254	#385	C₂²×C₁₃	1	4	yes	complemented
255	#384	C₂²×C₁₃	1	1	yes	characteristic, complemented
256	#380	C₂²×C₁₃	1	4	yes	complemented
257	#379	C₂²×C₁₃	1	4	yes	complemented
258	#379	C₂²×C₁₃	1	8	yes	complemented
259	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
260	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
261	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
262	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
263	C₄³	C₂²×C₁₃	1	1	yes	characteristic, complemented
264	C₂²×C₁₃	—	2	8	no	—
265	C₂²×C₁₃	—	2	8	no	—
266	C₂²×C₁₃	—	2	16	no	—
267	C₂²×C₁₃	—	2	8	no	—
268	C₂²×C₁₃	—	2	8	no	—
269	C₂²×C₁₃	—	4	4	no	—
270	C₂²×C₁₃	—	4	4	no	—
271	C₂²×C₁₃	—	4	8	no	—
272	C₂²×C₁₃	—	4	4	no	—
273	C₂²×C₁₃	—	4	4	no	—
274	C₂²×C₁₃	—	4	4	no	—
275	C₂²×C₁₃	—	4	4	no	—
276	C₂²×C₁₃	—	8	32	no	—
277	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
278	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
279	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
280	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
281	C₂²×C₁₃	#585	1	1	yes	characteristic
282	C₄×C₁₃	—	2	8	no	—
283	C₄×C₁₃	—	2	2	no	—
284	C₄×C₁₃	—	2	2	no	—
285	C₄×C₁₃	—	4	4	no	—
286	C₄×C₁₃	—	4	2	no	—
287	C₄×C₁₃	—	4	4	no	—
288	C₄×C₁₃	—	4	1	no	—
289	C₄×C₁₃	—	4	4	no	—
290	C₄×C₁₃	#518	1	8	yes	—
291	C₂⁵	C₂³×C₁₃	1	4	yes	—
292	C₂²×D₄	—	4	8	no	—
293	C₂²×D₄	—	4	8	no	—
294	C₂²×D₄	C₂×C₄×C₁₃	1	32	yes	complemented
295	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
296	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
297	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
298	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
299	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
300	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
301	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
302	#127	C₂×C₄×C₁₃	1	8	yes	—
303	#121	C₂×C₄×C₁₃	1	32	yes	complemented
304	#120	C₂×C₄×C₁₃	1	32	yes	complemented
305	C₄×D₄	—	4	8	no	—
306	C₄×D₄	—	4	8	no	—
307	C₄×D₄	—	4	4	no	—
308	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
309	#117	—	4	8	no	—
310	#117	—	4	8	no	—
311	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
312	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
313	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
314	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
315	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
316	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
317	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
318	C₂×C₂²⋊C₄	—	4	8	no	—
319	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
320	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
321	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
322	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
323	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
324	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
325	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
326	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
327	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
328	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
329	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
330	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
331	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
332	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
333	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
334	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
335	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
336	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
337	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
338	#95	C₂³×C₁₃	1	4	yes	—
339	#95	C₂³×C₁₃	1	4	yes	—
340	#95	C₂³×C₁₃	1	8	yes	—
341	#95	C₂³×C₁₃	1	4	yes	—
342	C₂×C₁₃	—	4	8	no	—
343	C₂×C₁₃	—	4	8	no	—
344	C₂×C₁₃	C₂×#518	1	2	yes	—
345	C₂×C₁₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
346	C₂×C₁₃	#3543	1	1	yes	characteristic
347	C₂×C₁₃	#3546	1	2	yes	—
348	C₂×C₁₃	#3549	1	1	yes	characteristic
349	C₂⁴	—	4	4	no	—
350	C₂⁴	—	4	8	no	—
351	C₂⁴	—	4	8	no	—
352	C₂⁴	—	4	4	no	—
353	C₂⁴	C₂²×C₄×C₁₃	1	16	yes	—
354	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
355	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
356	C₂×D₄	—	2	8	no	—
357	C₂×D₄	—	2	8	no	—
358	C₂×D₄	—	2	4	no	—
359	C₂×D₄	—	2	4	no	—
360	C₂×D₄	—	4	64	no	—
361	C₂×D₄	—	4	2	no	—
362	C₂×D₄	—	4	8	no	—
363	C₂×D₄	—	4	8	no	—
364	C₂×D₄	—	4	2	no	—
365	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
366	C₂×D₄	C₂²×C₄×C₁₃	1	16	yes	—
367	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
368	C₂×D₄	C₂²×C₄×C₁₃	1	32	yes	—
369	C₂²×C₄	—	2	8	no	—
370	C₂²×C₄	—	2	8	no	—
371	C₂²×C₄	—	2	8	no	—
372	C₂²×C₄	—	4	4	no	—
373	C₂²×C₄	—	4	8	no	—
374	C₂²×C₄	—	4	8	no	—
375	C₂²×C₄	C₂²×C₄×C₁₃	1	16	yes	—
376	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
377	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
378	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
379	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
380	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
381	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
382	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
383	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
384	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
385	C₄⋊C₄	—	2	4	no	—
386	C₄⋊C₄	—	2	8	no	—
387	C₄⋊C₄	—	2	4	no	—
388	C₄⋊C₄	—	4	4	no	—
389	C₄⋊C₄	—	4	4	no	—
390	C₄⋊C₄	—	4	2	no	—
391	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
392	C₂²⋊C₄	—	2	8	no	—
393	C₂²⋊C₄	—	4	8	no	—
394	C₂²⋊C₄	—	4	4	no	—
395	C₂²⋊C₄	—	4	4	no	—
396	C₂²⋊C₄	—	4	8	no	—
397	C₂²⋊C₄	—	4	8	no	—
398	C₂²⋊C₄	—	4	4	no	—
399	C₂²⋊C₄	—	4	8	no	—
400	C₂²⋊C₄	—	4	4	no	—
401	C₂²⋊C₄	—	4	4	no	—
402	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
403	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
404	C₄²	—	2	4	no	—
405	C₄²	—	2	8	no	—
406	C₄²	—	2	2	no	—
407	C₄²	—	2	4	no	—
408	C₄²	—	4	8	no	—
409	C₄²	—	4	1	no	—
410	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
411	C₁₃	#34493	1	1	yes	characteristic, direct product factor, Sylow
412	C₂³	—	2	4	no	—
413	C₂³	—	2	4	no	—
414	C₂³	—	2	4	no	—
415	C₂³	—	2	4	no	—
416	C₂³	—	2	8	no	—
417	C₂³	—	2	8	no	—
418	C₂³	—	2	4	no	—
419	C₂³	—	2	4	no	—
420	C₂³	—	2	4	no	—
421	C₂³	—	2	4	no	—
422	C₂³	—	4	32	no	—
423	C₂³	—	4	16	no	—
424	C₂³	—	8	8	no	—
425	C₂³	—	8	16	no	—
426	C₂³	—	8	8	no	—
427	C₂³	C₂³×C₄×C₁₃	1	8	yes	—
428	C₂³	C₂³×C₄×C₁₃	1	8	yes	—
429	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
430	D₄	—	2	16	no	—
431	D₄	—	2	32	no	—
432	D₄	—	4	32	no	—
433	D₄	—	4	8	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	32	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	8	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	8	8	no	—
454	C₂×C₄	—	8	8	no	—
455	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
456	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
457	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
458	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
459	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
460	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
461	C₂²	—	2	8	no	—
462	C₂²	—	2	8	no	—
463	C₂²	—	2	16	no	—
464	C₂²	—	2	8	no	—
465	C₂²	—	2	8	no	—
466	C₂²	—	4	4	no	—
467	C₂²	—	4	4	no	—
468	C₂²	—	4	8	no	—
469	C₂²	—	4	4	no	—
470	C₂²	—	4	4	no	—
471	C₂²	—	4	4	no	—
472	C₂²	—	4	4	no	—
473	C₂²	—	8	32	no	—
474	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
475	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
476	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
477	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
478	C₂²	C₁₃×#585	1	1	yes	characteristic
479	C₄	—	2	2	no	—
480	C₄	—	2	8	no	—
481	C₄	—	2	2	no	—
482	C₄	—	4	4	no	—
483	C₄	—	4	2	no	—
484	C₄	—	4	4	no	—
485	C₄	—	4	1	no	—
486	C₄	—	4	4	no	—
487	C₄	C₁₃×#518	1	8	yes	—
488	C₂	—	4	8	no	—
489	C₂	—	4	8	no	—
490	C₂	C₂×C₁₃×#518	1	2	yes	—
491	C₂	C₄×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
492	C₂	C₁₃×#3543	1	1	yes	characteristic
493	C₂	C₁₃×#3546	1	2	yes	—
494	C₂	C₁₃×#3549	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂×D₄²×C₁₃	C₂
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×#2375	C₂	semidirect
3. C₁₃×#2366	C₂	semidirect
4. C₁₃×#2363	C₂	semidirect
5. C₁₃×#2354	C₂	semidirect
6. D₄×C₁₃×C₂²⋊C₄	C₂	semidirect
7. C₁₃×#2324	C₂	semidirect
8. C₁₃×#2321	C₂	semidirect
9. C₁₃×#2309	C₂	semidirect
10. C₄×C₁₃×#127	C₂	semidirect
11. C₁₃×#2293	C₂	semidirect
13. D₄²×C₁₃	C₄	semidirect
18. C₂×C₄×D₄×C₁₃	C₂²	semidirect
19. C₂×C₄×D₄×C₁₃	C₂²	semidirect
20. C₂×C₄×D₄×C₁₃	C₂²	semidirect
21. C₂×C₁₃×#117	C₂²	semidirect
22. C₂×C₁₃×#117	C₂²	semidirect
23. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
27. C₁₃×#390	C₂²	semidirect
28. C₁₃×#390	C₂²	semidirect
29. C₁₃×#390	C₂²	semidirect
30. C₁₃×#390	C₂²	semidirect
31. C₁₃×#390	C₂²	semidirect
32. C₁₃×#389	C₂²	semidirect
33. C₁₃×#389	C₂²	semidirect
34. C₁₃×#388	C₂²	semidirect
35. C₁₃×#388	C₂²	semidirect
36. C₁₃×#388	C₂²	semidirect
37. C₁₃×#388	C₂²	semidirect
38. C₁₃×#386	C₂²	semidirect
39. C₁₃×#386	C₂²	semidirect
40. C₁₃×#386	C₂²	semidirect
41. C₁₃×#385	C₂²	semidirect
42. C₁₃×#384	C₂²	semidirect
43. C₁₃×#380	C₂²	semidirect
44. C₁₃×#379	C₂²	semidirect
45. C₁₃×#379	C₂²	semidirect
46. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
47. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
48. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
49. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
50. C₄³×C₁₃	C₂²	semidirect
54. C₂²×D₄×C₁₃	C₂×C₄	semidirect
63. C₁₃×#121	C₂×C₄	semidirect
64. C₁₃×#120	C₂×C₄	semidirect
68. C₄×D₄×C₁₃	C₂×C₄	semidirect
102. #34493	C₁₃	direct (N × H)
166. #2375	C₂×C₁₃	semidirect
167. #2366	C₂×C₁₃	semidirect
168. #2363	C₂×C₁₃	semidirect
169. #2354	C₂×C₁₃	semidirect
170. D₄×C₂²⋊C₄	C₂×C₁₃	semidirect
171. #2324	C₂×C₁₃	semidirect
172. #2321	C₂×C₁₃	semidirect
173. #2309	C₂×C₁₃	semidirect
174. C₄×#127	C₂×C₁₃	semidirect
175. #2293	C₂×C₁₃	semidirect
226. D₄²	C₄×C₁₃	semidirect
231. C₂×C₄×D₄	C₂²×C₁₃	semidirect
232. C₂×C₄×D₄	C₂²×C₁₃	semidirect
233. C₂×C₄×D₄	C₂²×C₁₃	semidirect
234. C₂×#117	C₂²×C₁₃	semidirect
235. C₂×#117	C₂²×C₁₃	semidirect
236. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
240. #390	C₂²×C₁₃	semidirect
241. #390	C₂²×C₁₃	semidirect
242. #390	C₂²×C₁₃	semidirect
243. #390	C₂²×C₁₃	semidirect
244. #390	C₂²×C₁₃	semidirect
245. #389	C₂²×C₁₃	semidirect
246. #389	C₂²×C₁₃	semidirect
247. #388	C₂²×C₁₃	semidirect
248. #388	C₂²×C₁₃	semidirect
249. #388	C₂²×C₁₃	semidirect
250. #388	C₂²×C₁₃	semidirect
251. #386	C₂²×C₁₃	semidirect
252. #386	C₂²×C₁₃	semidirect
253. #386	C₂²×C₁₃	semidirect
254. #385	C₂²×C₁₃	semidirect
255. #384	C₂²×C₁₃	semidirect
256. #380	C₂²×C₁₃	semidirect
257. #379	C₂²×C₁₃	semidirect
258. #379	C₂²×C₁₃	semidirect
259. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
260. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
261. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
262. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
263. C₄³	C₂²×C₁₃	semidirect
294. C₂²×D₄	C₂×C₄×C₁₃	semidirect
303. #121	C₂×C₄×C₁₃	semidirect
304. #120	C₂×C₄×C₁₃	semidirect
308. C₄×D₄	C₂×C₄×C₁₃	semidirect
411. C₁₃	#34493	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×D₄²×C₁₃	2
C₁₃×#2375	2
C₁₃×#2366	2
C₁₃×#2363	2
C₁₃×#2354	2
D₄×C₁₃×C₂²⋊C₄	2
C₁₃×#2324	2
C₁₃×#2321	2
C₁₃×#2309	2
C₄×C₁₃×#127	2
C₁₃×#2293	2
#34493	13

Subgroups — C13×#34493 #15720832

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34493 #15720832