Subgroups — C₁₃×#34070 #15720409

Order 3328.

3102 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₁₃×#41	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2328	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2327	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2326	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2325	C₂	1	8	yes	maximal, complemented
7	C₁₃×#2297	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2290	C₂	1	8	yes	maximal, complemented
9	C₁₃×#2285	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#376	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₁₃×#41	C₂²	1	2	yes	—
12	C₁₃×#532	C₄	1	16	yes	complemented
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#124	C₂²	1	2	yes	—
16	C₂×C₁₃×#121	C₂²	1	4	yes	—
17	C₄×C₁₃×#41	—	2	16	no	—
18	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	—
19	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	—
20	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
21	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
22	C₂×C₁₃×#117	C₂²	1	2	yes	—
23	C₂×C₁₃×#117	C₂²	1	4	yes	—
24	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
25	C₂²×C₄²×C₁₃	C₂²	1	4	yes	—
26	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
27	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
28	C₁₃×#391	C₂²	1	4	yes	—
29	C₁₃×#390	C₂²	1	4	yes	—
30	C₁₃×#388	C₂²	1	16	yes	—
31	C₁₃×#387	C₂²	1	16	yes	—
32	C₁₃×#386	C₂²	1	16	yes	—
33	C₁₃×#386	C₂²	1	8	yes	—
34	C₁₃×#385	C₂²	1	16	yes	—
35	C₁₃×#384	C₂²	1	2	yes	—
36	C₁₃×#382	C₂²	1	2	yes	—
37	C₁₃×#380	C₂²	1	4	yes	—
38	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
39	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
40	C₁₃×#376	C₂²	1	4	yes	—
41	C₁₃×#376	C₂²	1	2	yes	—
42	C₁₃×#376	C₂²	1	2	yes	—
43	C₂×C₁₃×#95	C₂²	1	4	yes	—
44	C₂×C₁₃×#41	—	2	8	no	—
45	C₂×C₁₃×#41	—	2	8	no	—
46	C₂×C₁₃×#41	C₂×C₄	1	16	yes	complemented
47	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
48	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
49	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
50	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
51	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
52	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
53	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
54	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
55	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
56	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
57	C₁₃×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
58	C₁₃×#127	C₂×C₄	1	8	yes	complemented
59	C₁₃×#124	C₂×C₄	1	16	yes	complemented
60	C₁₃×#121	C₂×C₄	1	32	yes	complemented
61	C₄×Q₈×C₁₃	—	2	16	no	—
62	C₄×D₄×C₁₃	—	2	32	no	—
63	C₄×D₄×C₁₃	—	2	16	no	—
64	C₄×D₄×C₁₃	C₂×C₄	1	32	yes	complemented
65	C₁₃×#117	—	2	8	no	—
66	C₁₃×#117	—	2	16	no	—
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
71	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
72	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
73	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
74	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
75	C₂×C₄²×C₁₃	—	2	4	no	—
76	C₂×C₄²×C₁₃	—	2	16	no	—
77	C₂×C₄²×C₁₃	C₂×C₄	1	8	yes	complemented
78	C₂×C₄²×C₁₃	D₄	1	8	yes	complemented
79	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
80	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
81	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
82	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
83	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
86	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
87	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
88	C₁₃×#95	C₂³	1	16	yes	—
89	C₁₃×#95	C₂³	1	8	yes	—
90	C₁₃×#95	C₂³	1	8	yes	—
91	C₁₃×#95	C₂³	1	8	yes	—
92	#34070	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
94	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
95	C₁₃×#41	—	2	64	no	—
96	C₂×Q₈×C₁₃	—	2	4	no	—
97	C₂×Q₈×C₁₃	—	2	4	no	—
98	C₂×Q₈×C₁₃	C₂²×C₄	1	8	yes	—
99	C₂×D₄×C₁₃	—	2	8	no	—
100	C₂×D₄×C₁₃	—	2	8	no	—
101	C₂×D₄×C₁₃	—	2	4	no	—
102	C₂×D₄×C₁₃	—	2	4	no	—
103	C₂×D₄×C₁₃	—	4	8	no	—
104	C₂×D₄×C₁₃	C₂²×C₄	1	16	yes	—
105	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
106	C₂×D₄×C₁₃	C₂²×C₄	1	16	yes	—
107	C₂²×C₄×C₁₃	—	2	8	no	—
108	C₂²×C₄×C₁₃	—	2	8	no	—
109	C₂²×C₄×C₁₃	—	2	4	no	—
110	C₂²×C₄×C₁₃	—	2	16	no	—
111	C₂²×C₄×C₁₃	—	4	4	no	—
112	C₂²×C₄×C₁₃	—	4	4	no	—
113	C₂²×C₄×C₁₃	—	4	16	no	—
114	C₂²×C₄×C₁₃	—	4	4	no	—
115	C₂²×C₄×C₁₃	C₂²×C₄	1	16	yes	—
116	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
117	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
118	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
119	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
120	C₂²×C₄×C₁₃	#41	1	4	yes	—
121	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
122	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
123	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
124	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
125	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
126	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
127	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
129	C₁₃×C₄⋊C₄	—	2	16	no	—
130	C₁₃×C₄⋊C₄	—	2	8	no	—
131	C₁₃×C₄⋊C₄	—	4	8	no	—
132	C₁₃×C₄⋊C₄	C₂²×C₄	1	16	yes	—
133	C₁₃×C₂²⋊C₄	—	2	8	no	—
134	C₁₃×C₂²⋊C₄	—	2	16	no	—
135	C₁₃×C₂²⋊C₄	—	4	16	no	—
136	C₁₃×C₂²⋊C₄	C₂²×C₄	1	32	yes	—
137	C₄²×C₁₃	—	2	8	no	—
138	C₄²×C₁₃	—	2	16	no	—
139	C₄²×C₁₃	—	2	4	no	—
140	C₄²×C₁₃	—	2	4	no	—
141	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
142	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
143	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
144	C₄²×C₁₃	C₂×D₄	1	8	yes	—
145	C₄²×C₁₃	C₂×D₄	1	8	yes	—
146	C₂×#532	C₂×C₁₃	1	1	yes	characteristic
147	C₂×C₄×#41	C₂×C₁₃	1	2	yes	complemented
148	#2328	C₂×C₁₃	1	2	yes	complemented
149	#2327	C₂×C₁₃	1	2	yes	complemented
150	#2326	C₂×C₁₃	1	4	yes	complemented
151	#2325	C₂×C₁₃	1	8	yes	complemented
152	#2297	C₂×C₁₃	1	2	yes	complemented
153	#2290	C₂×C₁₃	1	8	yes	complemented
154	#2285	C₂×C₁₃	1	1	yes	characteristic, complemented
155	C₂×#376	C₂×C₁₃	1	1	yes	characteristic, complemented
156	C₂³×C₁₃	—	2	4	no	—
157	C₂³×C₁₃	—	2	4	no	—
158	C₂³×C₁₃	—	2	4	no	—
159	C₂³×C₁₃	—	2	16	no	—
160	C₂³×C₁₃	C₂³×C₄	1	8	yes	—
161	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
162	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
163	C₂³×C₁₃	C₂×#41	1	2	yes	—
164	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
165	Q₈×C₁₃	—	2	16	no	—
166	D₄×C₁₃	—	2	32	no	—
167	D₄×C₁₃	—	2	16	no	—
168	D₄×C₁₃	—	4	16	no	—
169	C₂×C₄×C₁₃	—	2	4	no	—
170	C₂×C₄×C₁₃	—	2	4	no	—
171	C₂×C₄×C₁₃	—	2	4	no	—
172	C₂×C₄×C₁₃	—	2	8	no	—
173	C₂×C₄×C₁₃	—	2	4	no	—
174	C₂×C₄×C₁₃	—	2	32	no	—
175	C₂×C₄×C₁₃	—	2	8	no	—
176	C₂×C₄×C₁₃	—	2	4	no	—
177	C₂×C₄×C₁₃	—	2	8	no	—
178	C₂×C₄×C₁₃	—	2	16	no	—
179	C₂×C₄×C₁₃	—	4	8	no	—
180	C₂×C₄×C₁₃	—	4	8	no	—
181	C₂×C₄×C₁₃	—	4	32	no	—
182	C₂×C₄×C₁₃	—	4	8	no	—
183	C₂×C₄×C₁₃	C₄×D₄	1	16	yes	—
184	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
185	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
186	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
187	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
188	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
189	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
190	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
191	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
192	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
193	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
194	C₂²×#41	C₂²×C₁₃	1	2	yes	—
195	#532	C₄×C₁₃	1	16	yes	complemented
196	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
197	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
198	C₂×#124	C₂²×C₁₃	1	2	yes	—
199	C₂×#121	C₂²×C₁₃	1	4	yes	—
200	C₄×#41	—	2	16	no	—
201	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	—
202	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	—
203	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
204	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
205	C₂×#117	C₂²×C₁₃	1	2	yes	—
206	C₂×#117	C₂²×C₁₃	1	4	yes	—
207	C₂²×C₄²	C₂²×C₁₃	1	4	yes	—
208	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
209	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
210	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
211	#391	C₂²×C₁₃	1	4	yes	—
212	#390	C₂²×C₁₃	1	4	yes	—
213	#388	C₂²×C₁₃	1	16	yes	—
214	#387	C₂²×C₁₃	1	16	yes	—
215	#386	C₂²×C₁₃	1	8	yes	—
216	#386	C₂²×C₁₃	1	16	yes	—
217	#385	C₂²×C₁₃	1	16	yes	—
218	#384	C₂²×C₁₃	1	2	yes	—
219	#382	C₂²×C₁₃	1	2	yes	—
220	#380	C₂²×C₁₃	1	4	yes	—
221	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
222	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
223	#376	C₂²×C₁₃	1	2	yes	—
224	#376	C₂²×C₁₃	1	2	yes	—
225	#376	C₂²×C₁₃	1	4	yes	—
226	C₂×#95	C₂²×C₁₃	1	4	yes	—
227	C₂²×C₁₃	—	2	4	no	—
228	C₂²×C₁₃	—	2	4	no	—
229	C₂²×C₁₃	—	2	4	no	—
230	C₂²×C₁₃	—	2	8	no	—
231	C₂²×C₁₃	—	2	16	no	—
232	C₂²×C₁₃	—	4	8	no	—
233	C₂²×C₁₃	—	4	8	no	—
234	C₂²×C₁₃	C₂×C₄×D₄	1	4	yes	—
235	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
236	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
237	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
238	C₂²×C₁₃	#585	1	4	yes	—
239	C₄×C₁₃	—	2	8	no	—
240	C₄×C₁₃	—	2	4	no	—
241	C₄×C₁₃	—	2	4	no	—
242	C₄×C₁₃	—	2	8	no	—
243	C₄×C₁₃	—	4	8	no	—
244	C₄×C₁₃	—	4	4	no	—
245	C₄×C₁₃	C₂×C₄×D₄	1	4	yes	—
246	C₄×C₁₃	C₂×C₄×D₄	1	4	yes	—
247	C₂×#41	—	2	8	no	—
248	C₂×#41	—	2	8	no	—
249	C₂×#41	C₂×C₄×C₁₃	1	16	yes	complemented
250	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
251	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
252	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
253	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
254	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
255	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
256	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
257	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
258	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
259	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
260	C₄⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
261	#127	C₂×C₄×C₁₃	1	8	yes	complemented
262	#124	C₂×C₄×C₁₃	1	16	yes	complemented
263	#121	C₂×C₄×C₁₃	1	32	yes	complemented
264	C₄×Q₈	—	2	16	no	—
265	C₄×D₄	—	2	32	no	—
266	C₄×D₄	—	2	16	no	—
267	C₄×D₄	C₂×C₄×C₁₃	1	32	yes	complemented
268	#117	—	2	8	no	—
269	#117	—	2	16	no	—
270	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
271	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
272	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
273	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
274	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
275	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
276	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
277	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
278	C₂×C₄²	—	2	4	no	—
279	C₂×C₄²	—	2	16	no	—
280	C₂×C₄²	C₂×C₄×C₁₃	1	8	yes	complemented
281	C₂×C₄²	D₄×C₁₃	1	8	yes	complemented
282	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
283	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
284	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
285	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
286	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
287	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
288	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
289	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
290	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
291	#95	C₂³×C₁₃	1	8	yes	—
292	#95	C₂³×C₁₃	1	8	yes	—
293	#95	C₂³×C₁₃	1	16	yes	—
294	#95	C₂³×C₁₃	1	8	yes	—
295	C₂×C₁₃	—	2	4	no	—
296	C₂×C₁₃	—	4	8	no	—
297	C₂×C₁₃	C₂²×C₄×D₄	1	1	yes	characteristic
298	C₂×C₁₃	#3428	1	2	yes	—
299	C₂×C₁₃	#3449	1	2	yes	—
300	C₂×C₁₃	#3455	1	2	yes	—
301	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
302	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
303	#41	—	2	64	no	—
304	C₂×Q₈	—	2	4	no	—
305	C₂×Q₈	—	2	4	no	—
306	C₂×Q₈	C₂²×C₄×C₁₃	1	8	yes	—
307	C₂×D₄	—	2	8	no	—
308	C₂×D₄	—	2	8	no	—
309	C₂×D₄	—	2	4	no	—
310	C₂×D₄	—	2	4	no	—
311	C₂×D₄	—	4	8	no	—
312	C₂×D₄	C₂²×C₄×C₁₃	1	16	yes	—
313	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
314	C₂×D₄	C₂²×C₄×C₁₃	1	16	yes	—
315	C₂²×C₄	—	2	8	no	—
316	C₂²×C₄	—	2	8	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	16	no	—
319	C₂²×C₄	—	4	4	no	—
320	C₂²×C₄	—	4	4	no	—
321	C₂²×C₄	—	4	16	no	—
322	C₂²×C₄	—	4	4	no	—
323	C₂²×C₄	C₂²×C₄×C₁₃	1	16	yes	—
324	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
325	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
326	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
327	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
328	C₂²×C₄	C₁₃×#41	1	4	yes	—
329	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
330	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
331	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
332	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
333	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
334	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
335	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
336	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
337	C₄⋊C₄	—	2	16	no	—
338	C₄⋊C₄	—	2	8	no	—
339	C₄⋊C₄	—	4	8	no	—
340	C₄⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
341	C₂²⋊C₄	—	2	8	no	—
342	C₂²⋊C₄	—	2	16	no	—
343	C₂²⋊C₄	—	4	16	no	—
344	C₂²⋊C₄	C₂²×C₄×C₁₃	1	32	yes	—
345	C₄²	—	2	8	no	—
346	C₄²	—	2	16	no	—
347	C₄²	—	2	4	no	—
348	C₄²	—	2	4	no	—
349	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
350	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
351	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
352	C₄²	C₂×D₄×C₁₃	1	8	yes	—
353	C₄²	C₂×D₄×C₁₃	1	8	yes	—
354	C₁₃	#34070	1	1	yes	characteristic, direct product factor, Sylow
355	C₂³	—	2	4	no	—
356	C₂³	—	2	4	no	—
357	C₂³	—	2	4	no	—
358	C₂³	—	2	16	no	—
359	C₂³	C₂³×C₄×C₁₃	1	8	yes	—
360	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
361	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
362	C₂³	C₂×C₁₃×#41	1	2	yes	—
363	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
364	Q₈	—	2	16	no	—
365	D₄	—	2	32	no	—
366	D₄	—	2	16	no	—
367	D₄	—	4	16	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	8	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	32	no	—
374	C₂×C₄	—	2	8	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	2	8	no	—
377	C₂×C₄	—	2	16	no	—
378	C₂×C₄	—	4	8	no	—
379	C₂×C₄	—	4	8	no	—
380	C₂×C₄	—	4	32	no	—
381	C₂×C₄	—	4	8	no	—
382	C₂×C₄	C₄×D₄×C₁₃	1	16	yes	—
383	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
384	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
385	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
386	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
387	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
388	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
389	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
390	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
391	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
392	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
393	C₂²	—	2	4	no	—
394	C₂²	—	2	4	no	—
395	C₂²	—	2	4	no	—
396	C₂²	—	2	8	no	—
397	C₂²	—	2	16	no	—
398	C₂²	—	4	8	no	—
399	C₂²	—	4	8	no	—
400	C₂²	C₂×C₄×D₄×C₁₃	1	4	yes	—
401	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
402	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
403	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
404	C₂²	C₁₃×#585	1	4	yes	—
405	C₄	—	2	8	no	—
406	C₄	—	2	4	no	—
407	C₄	—	2	4	no	—
408	C₄	—	2	8	no	—
409	C₄	—	4	8	no	—
410	C₄	—	4	4	no	—
411	C₄	C₂×C₄×D₄×C₁₃	1	4	yes	—
412	C₄	C₂×C₄×D₄×C₁₃	1	4	yes	—
413	C₂	—	2	4	no	—
414	C₂	—	4	8	no	—
415	C₂	C₂²×C₄×D₄×C₁₃	1	1	yes	characteristic
416	C₂	C₁₃×#3428	1	2	yes	—
417	C₂	C₁₃×#3449	1	2	yes	—
418	C₂	C₁₃×#3455	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
prime radical	C₂×C₁₃×#532	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₁₃×#41	C₂	semidirect
3. C₁₃×#2328	C₂	semidirect
4. C₁₃×#2327	C₂	semidirect
5. C₁₃×#2326	C₂	semidirect
6. C₁₃×#2325	C₂	semidirect
7. C₁₃×#2297	C₂	semidirect
8. C₁₃×#2290	C₂	semidirect
9. C₁₃×#2285	C₂	semidirect
10. C₂×C₁₃×#376	C₂	semidirect
12. C₁₃×#532	C₄	semidirect
46. C₂×C₁₃×#41	C₂×C₄	semidirect
57. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
58. C₁₃×#127	C₂×C₄	semidirect
59. C₁₃×#124	C₂×C₄	semidirect
60. C₁₃×#121	C₂×C₄	semidirect
64. C₄×D₄×C₁₃	C₂×C₄	semidirect
77. C₂×C₄²×C₁₃	C₂×C₄	semidirect
78. C₂×C₄²×C₁₃	D₄	semidirect
92. #34070	C₁₃	direct (N × H)
147. C₂×C₄×#41	C₂×C₁₃	semidirect
148. #2328	C₂×C₁₃	semidirect
149. #2327	C₂×C₁₃	semidirect
150. #2326	C₂×C₁₃	semidirect
151. #2325	C₂×C₁₃	semidirect
152. #2297	C₂×C₁₃	semidirect
153. #2290	C₂×C₁₃	semidirect
154. #2285	C₂×C₁₃	semidirect
155. C₂×#376	C₂×C₁₃	semidirect
195. #532	C₄×C₁₃	semidirect
249. C₂×#41	C₂×C₄×C₁₃	semidirect
260. C₄⋊Q₈	C₂×C₄×C₁₃	semidirect
261. #127	C₂×C₄×C₁₃	semidirect
262. #124	C₂×C₄×C₁₃	semidirect
263. #121	C₂×C₄×C₁₃	semidirect
267. C₄×D₄	C₂×C₄×C₁₃	semidirect
280. C₂×C₄²	C₂×C₄×C₁₃	semidirect
281. C₂×C₄²	D₄×C₁₃	semidirect
354. C₁₃	#34070	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×C₁₃×#532	2
C₂×C₄×C₁₃×#41	2
C₁₃×#2328	2
C₁₃×#2327	2
C₁₃×#2326	2
C₁₃×#2325	2
C₁₃×#2297	2
C₁₃×#2290	2
C₁₃×#2285	2
C₂×C₁₃×#376	2
#34070	13

Subgroups — C13×#34070 #15720409

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34070 #15720409