Subgroups — C₁₃×#34210 #15720549

Order 3328.

4006 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#127	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#518	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2366	C₂	1	8	yes	maximal, complemented
4	D₄×C₁₃×C₂²⋊C₄	C₂	1	8	yes	maximal, complemented
5	C₁₃×#2328	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2309	C₂	1	2	yes	maximal, complemented
7	C₄×C₁₃×#127	C₂	1	4	yes	maximal, complemented
8	C₁₃×#2285	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
11	C₂³×D₄×C₁₃	C₂²	1	4	yes	—
12	C₂×C₁₃×#127	C₄	1	16	yes	complemented
13	C₂×C₁₃×#127	C₂²	1	2	yes	—
14	C₂×C₁₃×#127	C₂²	1	2	yes	—
15	C₂×C₁₃×#127	C₂²	1	4	yes	—
16	C₁₃×#518	—	2	16	no	—
17	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	complemented
18	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	complemented
19	C₂×C₄×D₄×C₁₃	C₂²	1	16	yes	complemented
20	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#117	C₂²	1	2	yes	—
22	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
24	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
25	C₁₃×#390	C₂²	1	8	yes	complemented
26	C₁₃×#390	C₂²	1	16	yes	complemented
27	C₁₃×#390	C₂²	1	8	yes	complemented
28	C₁₃×#386	C₂²	1	32	yes	complemented
29	C₁₃×#384	C₂²	1	2	yes	complemented
30	C₁₃×#382	C₂²	1	2	yes	complemented
31	C₁₃×#380	C₂²	1	4	yes	—
32	C₁₃×#379	C₂²	1	8	yes	—
33	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
34	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
35	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
36	C₁₃×#376	C₂²	1	2	yes	complemented
37	C₄³×C₁₃	C₂²	1	2	yes	complemented
38	C₂⁵×C₁₃	C₂³	1	4	yes	—
39	C₂²×D₄×C₁₃	—	2	8	no	—
40	C₂²×D₄×C₁₃	—	2	8	no	—
41	C₂²×D₄×C₁₃	—	4	16	no	—
42	C₂²×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
43	C₂²×D₄×C₁₃	C₂×C₄	1	32	yes	complemented
44	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
45	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
46	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
47	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
48	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
49	C₂³×C₄×C₁₃	C₂³	1	16	yes	—
50	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
51	C₁₃×#127	C₂×C₄	1	16	yes	complemented
52	C₁₃×#127	C₂×C₄	1	32	yes	complemented
53	C₁₃×#127	C₂×C₄	1	16	yes	complemented
54	C₄×D₄×C₁₃	—	2	32	no	—
55	C₄×D₄×C₁₃	—	2	32	no	—
56	C₄×D₄×C₁₃	—	4	32	no	—
57	C₁₃×#117	—	2	8	no	—
58	C₁₃×#117	—	2	4	no	—
59	C₁₃×#117	D₄	1	8	yes	complemented
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
64	C₂×C₁₃×C₂²⋊C₄	—	2	32	no	—
65	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
66	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
67	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
68	C₂×C₁₃×C₂²⋊C₄	C₂³	1	32	yes	—
69	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
70	C₂×C₄²×C₁₃	C₂×C₄	1	8	yes	complemented
71	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
72	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
73	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
74	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
75	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
78	C₁₃×#95	C₂³	1	8	yes	—
79	C₁₃×#95	C₂³	1	8	yes	—
80	#34210	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
81	C₂⁴×C₁₃	—	2	8	no	—
82	C₂⁴×C₁₃	—	2	8	no	—
83	C₂⁴×C₁₃	—	4	16	no	—
84	C₂⁴×C₁₃	C₂²×C₄	1	16	yes	—
85	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
86	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
87	C₂×D₄×C₁₃	—	2	64	no	—
88	C₂×D₄×C₁₃	—	2	8	no	—
89	C₂×D₄×C₁₃	—	2	8	no	—
90	C₂×D₄×C₁₃	—	2	8	no	—
91	C₂×D₄×C₁₃	—	2	8	no	—
92	C₂×D₄×C₁₃	—	2	32	no	—
93	C₂×D₄×C₁₃	—	4	64	no	—
94	C₂×D₄×C₁₃	—	4	16	no	—
95	C₂×D₄×C₁₃	C₂²×C₄	1	16	yes	—
96	C₂×D₄×C₁₃	C₂²×C₄	1	16	yes	—
97	C₂×D₄×C₁₃	C₂²×C₄	1	32	yes	—
98	C₂×D₄×C₁₃	C₂²×C₄	1	32	yes	—
99	C₂²×C₄×C₁₃	—	2	8	no	—
100	C₂²×C₄×C₁₃	—	2	32	no	—
101	C₂²×C₄×C₁₃	—	4	32	no	—
102	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
103	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
104	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
105	C₂²×C₄×C₁₃	#41	1	4	yes	—
106	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
107	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
108	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
109	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
110	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
113	C₁₃×C₄⋊C₄	—	2	8	no	—
114	C₁₃×C₄⋊C₄	—	2	4	no	—
115	C₁₃×C₄⋊C₄	—	2	16	no	—
116	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	complemented
117	C₁₃×C₂²⋊C₄	—	2	8	no	—
118	C₁₃×C₂²⋊C₄	—	2	4	no	—
119	C₁₃×C₂²⋊C₄	—	2	32	no	—
120	C₁₃×C₂²⋊C₄	—	4	32	no	—
121	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
122	C₄²×C₁₃	—	2	8	no	—
123	C₄²×C₁₃	—	2	4	no	—
124	C₄²×C₁₃	—	2	16	no	—
125	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
126	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
127	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
128	C₄²×C₁₃	C₂×D₄	1	8	yes	complemented
129	C₂²×#127	C₂×C₁₃	1	1	yes	characteristic
130	C₂×#518	C₂×C₁₃	1	2	yes	complemented
131	#2366	C₂×C₁₃	1	8	yes	complemented
132	D₄×C₂²⋊C₄	C₂×C₁₃	1	8	yes	complemented
133	#2328	C₂×C₁₃	1	4	yes	complemented
134	#2309	C₂×C₁₃	1	2	yes	complemented
135	C₄×#127	C₂×C₁₃	1	4	yes	complemented
136	#2285	C₂×C₁₃	1	1	yes	characteristic, complemented
137	C₄×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
138	C₂³×C₁₃	—	2	4	no	—
139	C₂³×C₁₃	—	2	8	no	—
140	C₂³×C₁₃	—	2	8	no	—
141	C₂³×C₁₃	—	2	32	no	—
142	C₂³×C₁₃	—	2	32	no	—
143	C₂³×C₁₃	—	4	32	no	—
144	C₂³×C₁₃	—	8	16	no	—
145	C₂³×C₁₃	—	8	16	no	—
146	C₂³×C₁₃	C₂³×C₄	1	16	yes	—
147	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
148	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
149	C₂³×C₁₃	C₂×#41	1	2	yes	—
150	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
151	D₄×C₁₃	—	2	32	no	—
152	D₄×C₁₃	—	2	32	no	—
153	D₄×C₁₃	—	2	64	no	—
154	D₄×C₁₃	—	4	32	no	—
155	C₂×C₄×C₁₃	—	2	8	no	—
156	C₂×C₄×C₁₃	—	2	4	no	—
157	C₂×C₄×C₁₃	—	2	16	no	—
158	C₂×C₄×C₁₃	—	2	8	no	—
159	C₂×C₄×C₁₃	—	2	4	no	—
160	C₂×C₄×C₁₃	—	2	8	no	—
161	C₂×C₄×C₁₃	—	2	16	no	—
162	C₂×C₄×C₁₃	—	8	32	no	—
163	C₂×C₄×C₁₃	C₄×D₄	1	16	yes	complemented
164	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
165	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
166	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
167	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
168	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
169	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
170	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
171	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
172	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
173	C₂×C₄×C₁₃	H(5,𝔽₂)	1	8	yes	—
174	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
175	C₂³×D₄	C₂²×C₁₃	1	4	yes	—
176	C₂×#127	C₄×C₁₃	1	16	yes	complemented
177	C₂×#127	C₂²×C₁₃	1	2	yes	—
178	C₂×#127	C₂²×C₁₃	1	2	yes	—
179	C₂×#127	C₂²×C₁₃	1	4	yes	—
180	#518	—	2	16	no	—
181	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	complemented
182	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	complemented
183	C₂×C₄×D₄	C₂²×C₁₃	1	16	yes	complemented
184	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
185	C₂×#117	C₂²×C₁₃	1	2	yes	—
186	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
187	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
188	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
189	#390	C₂²×C₁₃	1	8	yes	complemented
190	#390	C₂²×C₁₃	1	16	yes	complemented
191	#390	C₂²×C₁₃	1	8	yes	complemented
192	#386	C₂²×C₁₃	1	32	yes	complemented
193	#384	C₂²×C₁₃	1	2	yes	complemented
194	#382	C₂²×C₁₃	1	2	yes	complemented
195	#380	C₂²×C₁₃	1	4	yes	—
196	#379	C₂²×C₁₃	1	8	yes	—
197	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
198	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
199	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
200	#376	C₂²×C₁₃	1	2	yes	complemented
201	C₄³	C₂²×C₁₃	1	2	yes	complemented
202	C₂²×C₁₃	—	2	4	no	—
203	C₂²×C₁₃	—	2	4	no	—
204	C₂²×C₁₃	—	2	4	no	—
205	C₂²×C₁₃	—	2	16	no	—
206	C₂²×C₁₃	—	2	32	no	—
207	C₂²×C₁₃	—	4	16	no	—
208	C₂²×C₁₃	—	4	16	no	—
209	C₂²×C₁₃	—	8	32	no	—
210	C₂²×C₁₃	C₂×C₄×D₄	1	4	yes	—
211	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
212	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
213	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
214	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
215	C₄×C₁₃	—	2	4	no	—
216	C₄×C₁₃	—	2	8	no	—
217	C₄×C₁₃	—	4	8	no	—
218	C₄×C₁₃	—	4	4	no	—
219	C₄×C₁₃	C₂×C₄×D₄	1	4	yes	—
220	C₄×C₁₃	C₂×C₄×D₄	1	4	yes	—
221	C₄×C₁₃	#518	1	8	yes	complemented
222	C₂⁵	C₂³×C₁₃	1	4	yes	—
223	C₂²×D₄	—	2	8	no	—
224	C₂²×D₄	—	2	8	no	—
225	C₂²×D₄	—	4	16	no	—
226	C₂²×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
227	C₂²×D₄	C₂×C₄×C₁₃	1	32	yes	complemented
228	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
229	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
230	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
231	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
232	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
233	C₂³×C₄	C₂³×C₁₃	1	16	yes	—
234	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
235	#127	C₂×C₄×C₁₃	1	16	yes	complemented
236	#127	C₂×C₄×C₁₃	1	32	yes	complemented
237	#127	C₂×C₄×C₁₃	1	16	yes	complemented
238	C₄×D₄	—	2	32	no	—
239	C₄×D₄	—	2	32	no	—
240	C₄×D₄	—	4	32	no	—
241	#117	—	2	8	no	—
242	#117	—	2	4	no	—
243	#117	D₄×C₁₃	1	8	yes	complemented
244	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
245	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
246	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
247	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
248	C₂×C₂²⋊C₄	—	2	32	no	—
249	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
250	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
251	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
252	C₂×C₂²⋊C₄	C₂³×C₁₃	1	32	yes	—
253	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
254	C₂×C₄²	C₂×C₄×C₁₃	1	8	yes	complemented
255	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
256	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
257	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
258	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
259	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
260	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
261	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
262	#95	C₂³×C₁₃	1	8	yes	—
263	#95	C₂³×C₁₃	1	8	yes	—
264	C₂×C₁₃	—	2	4	no	—
265	C₂×C₁₃	—	4	16	no	—
266	C₂×C₁₃	C₂²×C₄×D₄	1	1	yes	characteristic
267	C₂×C₁₃	C₂×#518	1	2	yes	—
268	C₂×C₁₃	#3498	1	2	yes	—
269	C₂×C₁₃	#3508	1	2	yes	—
270	C₂⁴	—	2	8	no	—
271	C₂⁴	—	2	8	no	—
272	C₂⁴	—	4	16	no	—
273	C₂⁴	C₂²×C₄×C₁₃	1	16	yes	—
274	C₂⁴	C₂⁴×C₁₃	1	8	yes	—
275	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
276	C₂×D₄	—	2	64	no	—
277	C₂×D₄	—	2	8	no	—
278	C₂×D₄	—	2	8	no	—
279	C₂×D₄	—	2	8	no	—
280	C₂×D₄	—	2	8	no	—
281	C₂×D₄	—	2	32	no	—
282	C₂×D₄	—	4	64	no	—
283	C₂×D₄	—	4	16	no	—
284	C₂×D₄	C₂²×C₄×C₁₃	1	16	yes	—
285	C₂×D₄	C₂²×C₄×C₁₃	1	16	yes	—
286	C₂×D₄	C₂²×C₄×C₁₃	1	32	yes	—
287	C₂×D₄	C₂²×C₄×C₁₃	1	32	yes	—
288	C₂²×C₄	—	2	8	no	—
289	C₂²×C₄	—	2	32	no	—
290	C₂²×C₄	—	4	32	no	—
291	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
292	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
293	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
294	C₂²×C₄	C₁₃×#41	1	4	yes	—
295	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
296	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
297	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
298	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
299	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
300	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
301	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
302	C₄⋊C₄	—	2	8	no	—
303	C₄⋊C₄	—	2	4	no	—
304	C₄⋊C₄	—	2	16	no	—
305	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	complemented
306	C₂²⋊C₄	—	2	8	no	—
307	C₂²⋊C₄	—	2	4	no	—
308	C₂²⋊C₄	—	2	32	no	—
309	C₂²⋊C₄	—	4	32	no	—
310	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
311	C₄²	—	2	8	no	—
312	C₄²	—	2	4	no	—
313	C₄²	—	2	16	no	—
314	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
315	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
316	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
317	C₄²	C₂×D₄×C₁₃	1	8	yes	complemented
318	C₁₃	#34210	1	1	yes	characteristic, direct product factor, Sylow
319	C₂³	—	2	4	no	—
320	C₂³	—	2	8	no	—
321	C₂³	—	2	8	no	—
322	C₂³	—	2	32	no	—
323	C₂³	—	2	32	no	—
324	C₂³	—	4	32	no	—
325	C₂³	—	8	16	no	—
326	C₂³	—	8	16	no	—
327	C₂³	C₂³×C₄×C₁₃	1	16	yes	—
328	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
329	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
330	C₂³	C₂×C₁₃×#41	1	2	yes	—
331	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
332	D₄	—	2	32	no	—
333	D₄	—	2	32	no	—
334	D₄	—	2	64	no	—
335	D₄	—	4	32	no	—
336	C₂×C₄	—	2	8	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	16	no	—
339	C₂×C₄	—	2	8	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	8	no	—
342	C₂×C₄	—	2	16	no	—
343	C₂×C₄	—	8	32	no	—
344	C₂×C₄	C₄×D₄×C₁₃	1	16	yes	complemented
345	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
346	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
347	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
348	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
349	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
350	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
351	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
352	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
353	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
354	C₂×C₄	C₁₃×H(5,𝔽₂)	1	8	yes	—
355	C₂²	—	2	4	no	—
356	C₂²	—	2	4	no	—
357	C₂²	—	2	4	no	—
358	C₂²	—	2	16	no	—
359	C₂²	—	2	32	no	—
360	C₂²	—	4	16	no	—
361	C₂²	—	4	16	no	—
362	C₂²	—	8	32	no	—
363	C₂²	C₂×C₄×D₄×C₁₃	1	4	yes	—
364	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
365	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
366	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
367	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
368	C₄	—	2	4	no	—
369	C₄	—	2	8	no	—
370	C₄	—	4	8	no	—
371	C₄	—	4	4	no	—
372	C₄	C₂×C₄×D₄×C₁₃	1	4	yes	—
373	C₄	C₂×C₄×D₄×C₁₃	1	4	yes	—
374	C₄	C₁₃×#518	1	8	yes	complemented
375	C₂	—	2	4	no	—
376	C₂	—	4	16	no	—
377	C₂	C₂²×C₄×D₄×C₁₃	1	1	yes	characteristic
378	C₂	C₂×C₁₃×#518	1	2	yes	—
379	C₂	C₁₃×#3498	1	2	yes	—
380	C₂	C₁₃×#3508	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂²×C₁₃×#127	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. C₂×C₁₃×#518	C₂	semidirect
3. C₁₃×#2366	C₂	semidirect
4. D₄×C₁₃×C₂²⋊C₄	C₂	semidirect
5. C₁₃×#2328	C₂	semidirect
6. C₁₃×#2309	C₂	semidirect
7. C₄×C₁₃×#127	C₂	semidirect
8. C₁₃×#2285	C₂	semidirect
9. C₄×C₁₃×#117	C₂	semidirect
12. C₂×C₁₃×#127	C₄	semidirect
17. C₂×C₄×D₄×C₁₃	C₂²	semidirect
18. C₂×C₄×D₄×C₁₃	C₂²	semidirect
19. C₂×C₄×D₄×C₁₃	C₂²	semidirect
25. C₁₃×#390	C₂²	semidirect
26. C₁₃×#390	C₂²	semidirect
27. C₁₃×#390	C₂²	semidirect
28. C₁₃×#386	C₂²	semidirect
29. C₁₃×#384	C₂²	semidirect
30. C₁₃×#382	C₂²	semidirect
33. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
34. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
36. C₁₃×#376	C₂²	semidirect
37. C₄³×C₁₃	C₂²	semidirect
42. C₂²×D₄×C₁₃	C₂×C₄	semidirect
43. C₂²×D₄×C₁₃	C₂×C₄	semidirect
51. C₁₃×#127	C₂×C₄	semidirect
52. C₁₃×#127	C₂×C₄	semidirect
53. C₁₃×#127	C₂×C₄	semidirect
59. C₁₃×#117	D₄	semidirect
70. C₂×C₄²×C₁₃	C₂×C₄	semidirect
80. #34210	C₁₃	direct (N × H)
116. C₁₃×C₄⋊C₄	C₂×D₄	semidirect
128. C₄²×C₁₃	C₂×D₄	semidirect
130. C₂×#518	C₂×C₁₃	semidirect
131. #2366	C₂×C₁₃	semidirect
132. D₄×C₂²⋊C₄	C₂×C₁₃	semidirect
133. #2328	C₂×C₁₃	semidirect
134. #2309	C₂×C₁₃	semidirect
135. C₄×#127	C₂×C₁₃	semidirect
136. #2285	C₂×C₁₃	semidirect
137. C₄×#117	C₂×C₁₃	semidirect
163. C₂×C₄×C₁₃	C₄×D₄	semidirect
176. C₂×#127	C₄×C₁₃	semidirect
181. C₂×C₄×D₄	C₂²×C₁₃	semidirect
182. C₂×C₄×D₄	C₂²×C₁₃	semidirect
183. C₂×C₄×D₄	C₂²×C₁₃	semidirect
189. #390	C₂²×C₁₃	semidirect
190. #390	C₂²×C₁₃	semidirect
191. #390	C₂²×C₁₃	semidirect
192. #386	C₂²×C₁₃	semidirect
193. #384	C₂²×C₁₃	semidirect
194. #382	C₂²×C₁₃	semidirect
197. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
198. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
200. #376	C₂²×C₁₃	semidirect
201. C₄³	C₂²×C₁₃	semidirect
221. C₄×C₁₃	#518	semidirect
226. C₂²×D₄	C₂×C₄×C₁₃	semidirect
227. C₂²×D₄	C₂×C₄×C₁₃	semidirect
235. #127	C₂×C₄×C₁₃	semidirect
236. #127	C₂×C₄×C₁₃	semidirect
237. #127	C₂×C₄×C₁₃	semidirect
243. #117	D₄×C₁₃	semidirect
254. C₂×C₄²	C₂×C₄×C₁₃	semidirect
305. C₄⋊C₄	C₂×D₄×C₁₃	semidirect
317. C₄²	C₂×D₄×C₁₃	semidirect
318. C₁₃	#34210	direct (N × H)
344. C₂×C₄	C₄×D₄×C₁₃	semidirect
374. C₄	C₁₃×#518	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×#127	2
C₂×C₁₃×#518	2
C₁₃×#2366	2
D₄×C₁₃×C₂²⋊C₄	2
C₁₃×#2328	2
C₁₃×#2309	2
C₄×C₁₃×#127	2
C₁₃×#2285	2
C₄×C₁₃×#117	2
#34210	13

Subgroups — C13×#34210 #15720549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34210 #15720549