Subgroups — C₂×C₁₃×#1542 #15704036

Order 3328.

1050 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#431	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1542	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₁₃×#333	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#332	C₂	1	2	yes	maximal, complemented
7	C₂³×C₈×C₁₃	—	2	1	no	—
8	C₁₃×#533	—	2	2	no	—
9	C₁₃×#533	—	2	2	no	—
10	C₁₃×#533	C₄	1	4	yes	—
11	C₁₃×#533	C₂²	1	4	yes	—
12	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#125	—	2	1	no	—
15	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
16	C₂×C₁₃×C₂²⋊Q₈	C₄	1	2	yes	—
17	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
18	C₂×C₄×Q₈×C₁₃	C₄	1	2	yes	—
19	C₂×C₁₃×#117	—	2	1	no	—
20	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
21	C₁₃×#431	—	2	2	no	—
22	C₁₃×#431	C₂²	1	4	yes	—
23	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
24	C₂×C₁₃×C₄⋊C₈	—	2	2	no	—
25	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
26	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
27	C₂×C₁₃×C₄⋊C₈	C₂²	1	4	yes	—
28	C₂×C₁₃×C₂²⋊C₈	—	2	1	no	—
29	C₂×C₄×C₈×C₁₃	—	2	1	no	—
30	C₁₃×#333	C₂²	1	8	yes	complemented
31	C₁₃×#332	C₂²	1	8	yes	complemented
32	C₂²×Q₈×C₁₃	—	2	1	no	—
33	C₂²×Q₈×C₁₃	C₂×C₄	1	2	yes	—
34	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
37	C₂²×C₈×C₁₃	—	2	2	no	—
38	C₂²×C₈×C₁₃	—	2	2	no	—
39	C₂²×C₈×C₁₃	—	2	4	no	—
40	C₂²×C₈×C₁₃	—	4	4	no	—
41	C₁₃×C₄⋊Q₈	—	2	1	no	—
42	C₁₃×C₄⋊Q₈	—	2	1	no	—
43	C₁₃×C₄⋊Q₈	—	2	1	no	—
44	C₁₃×C₄⋊Q₈	—	2	1	no	—
45	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
46	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
47	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
48	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
49	C₁₃×#125	—	2	4	no	—
50	C₁₃×#125	—	2	4	no	—
51	C₁₃×C₂²⋊Q₈	—	2	4	no	—
52	C₁₃×C₂²⋊Q₈	—	2	4	no	—
53	C₁₃×C₂²⋊Q₈	—	2	4	no	—
54	C₁₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
55	C₄×Q₈×C₁₃	—	2	4	no	—
56	C₄×Q₈×C₁₃	—	2	4	no	—
57	C₄×Q₈×C₁₃	—	2	4	no	—
58	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	—
59	C₁₃×#117	—	2	4	no	—
60	C₁₃×#117	—	2	4	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
66	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
67	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
68	C₂×C₄²×C₁₃	—	2	2	no	—
69	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
70	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₁₃	D₄	1	2	yes	—
73	C₂×C₄²×C₁₃	D₄	1	2	yes	—
74	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
77	C₁₃×C₄⋊C₈	—	2	4	no	—
78	C₁₃×C₄⋊C₈	—	2	2	no	—
79	C₁₃×C₄⋊C₈	—	2	2	no	—
80	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
81	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
82	C₁₃×C₂²⋊C₈	—	2	4	no	—
83	C₄×C₈×C₁₃	—	2	4	no	—
84	C₂×#1542	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
85	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
86	C₂×Q₈×C₁₃	—	2	2	no	—
87	C₂×Q₈×C₁₃	—	2	2	no	—
88	C₂×Q₈×C₁₃	—	2	2	no	—
89	C₂×Q₈×C₁₃	—	4	4	no	—
90	C₂×Q₈×C₁₃	—	4	4	no	—
91	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
92	C₂²×C₄×C₁₃	—	2	4	no	—
93	C₂²×C₄×C₁₃	—	2	2	no	—
94	C₂²×C₄×C₁₃	—	2	2	no	—
95	C₂²×C₄×C₁₃	—	4	2	no	—
96	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
98	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
100	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
101	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	SD₁₆	1	4	yes	—
103	C₂²×C₄×C₁₃	Q₁₆	1	4	yes	—
104	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂×C₈×C₁₃	—	2	4	no	—
111	C₂×C₈×C₁₃	—	2	4	no	—
112	C₂×C₈×C₁₃	—	4	8	no	—
113	C₂×C₈×C₁₃	—	4	4	no	—
114	C₂×C₈×C₁₃	—	4	4	no	—
115	C₁₃×C₄⋊C₄	—	2	2	no	—
116	C₁₃×C₄⋊C₄	—	2	2	no	—
117	C₁₃×C₄⋊C₄	—	2	2	no	—
118	C₁₃×C₄⋊C₄	—	2	8	no	—
119	C₁₃×C₄⋊C₄	—	2	8	no	—
120	C₁₃×C₄⋊C₄	—	2	2	no	—
121	C₁₃×C₄⋊C₄	—	2	2	no	—
122	C₁₃×C₄⋊C₄	—	2	2	no	—
123	C₁₃×C₄⋊C₄	—	2	2	no	—
124	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
125	C₁₃×C₂²⋊C₄	—	2	8	no	—
126	C₄²×C₁₃	—	2	8	no	—
127	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
128	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
129	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
130	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
131	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₄²×C₁₃	C₂×D₄	1	2	yes	—
133	C₄²×C₁₃	C₂×D₄	1	2	yes	—
134	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
137	C₂×#533	C₂×C₁₃	1	1	yes	characteristic
138	C₂×#431	C₂×C₁₃	1	1	yes	characteristic
139	C₂²×C₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic
140	#1542	C₂×C₁₃	1	8	yes	direct product factor
141	C₂×#333	C₂×C₁₃	1	2	yes	complemented
142	C₂×#332	C₂×C₁₃	1	2	yes	complemented
143	C₂³×C₁₃	—	2	2	no	—
144	C₂³×C₁₃	—	2	2	no	—
145	C₂³×C₁₃	#103	1	4	yes	—
146	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
147	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
148	Q₈×C₁₃	—	4	4	no	—
149	Q₈×C₁₃	—	4	4	no	—
150	Q₈×C₁₃	—	4	4	no	—
151	Q₈×C₁₃	—	4	4	no	—
152	C₂×C₄×C₁₃	—	2	2	no	—
153	C₂×C₄×C₁₃	—	2	2	no	—
154	C₂×C₄×C₁₃	—	2	2	no	—
155	C₂×C₄×C₁₃	—	2	4	no	—
156	C₂×C₄×C₁₃	—	2	4	no	—
157	C₂×C₄×C₁₃	—	2	4	no	—
158	C₂×C₄×C₁₃	—	2	4	no	—
159	C₂×C₄×C₁₃	—	4	2	no	—
160	C₂×C₄×C₁₃	—	4	2	no	—
161	C₂×C₄×C₁₃	—	4	4	no	—
162	C₂×C₄×C₁₃	—	4	4	no	—
163	C₂×C₄×C₁₃	#103	1	8	yes	—
164	C₂×C₄×C₁₃	#103	1	4	yes	—
165	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
166	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
167	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
169	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	—
172	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
173	C₂×C₄×C₁₃	C₂×Q₁₆	1	4	yes	—
174	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
175	C₂×C₄×C₁₃	#135	1	4	yes	—
176	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
177	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
179	C₈×C₁₃	—	4	4	no	—
180	C₈×C₁₃	—	4	4	no	—
181	C₂³×C₈	—	2	1	no	—
182	#533	—	2	2	no	—
183	#533	—	2	2	no	—
184	#533	C₄×C₁₃	1	4	yes	—
185	#533	C₂²×C₁₃	1	4	yes	—
186	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
187	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
188	C₂×#125	—	2	1	no	—
189	C₂×C₂²⋊Q₈	—	2	1	no	—
190	C₂×C₂²⋊Q₈	C₄×C₁₃	1	2	yes	—
191	C₂×C₄×Q₈	—	2	1	no	—
192	C₂×C₄×Q₈	C₄×C₁₃	1	2	yes	—
193	C₂×#117	—	2	1	no	—
194	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
195	#431	—	2	2	no	—
196	#431	C₂²×C₁₃	1	4	yes	—
197	C₂×C₄⋊C₈	—	2	1	no	—
198	C₂×C₄⋊C₈	—	2	2	no	—
199	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
200	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
201	C₂×C₄⋊C₈	C₂²×C₁₃	1	4	yes	—
202	C₂×C₂²⋊C₈	—	2	1	no	—
203	C₂×C₄×C₈	—	2	1	no	—
204	#333	C₂²×C₁₃	1	8	yes	complemented
205	#332	C₂²×C₁₃	1	8	yes	complemented
206	C₂²×C₁₃	—	2	8	no	—
207	C₂²×C₁₃	—	2	2	no	—
208	C₂²×C₁₃	—	2	2	no	—
209	C₂²×C₁₃	#413	1	2	yes	—
210	C₂²×C₁₃	C₂×#103	1	4	yes	—
211	C₂²×C₁₃	C₂×#103	1	2	yes	—
212	C₂²×C₁₃	#416	1	2	yes	—
213	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
214	C₄×C₁₃	—	2	2	no	—
215	C₄×C₁₃	—	2	1	no	—
216	C₄×C₁₃	—	2	1	no	—
217	C₄×C₁₃	—	2	2	no	—
218	C₄×C₁₃	—	4	4	no	—
219	C₄×C₁₃	—	4	4	no	—
220	C₄×C₁₃	C₂×#103	1	2	yes	—
221	C₄×C₁₃	C₂×#103	1	4	yes	—
222	C₄×C₁₃	#416	1	2	yes	—
223	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
224	C₄×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
225	C₄×C₁₃	C₂×#135	1	2	yes	—
226	C₂²×Q₈	—	2	1	no	—
227	C₂²×Q₈	C₂×C₄×C₁₃	1	2	yes	—
228	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
229	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
230	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
231	C₂²×C₈	—	2	2	no	—
232	C₂²×C₈	—	2	4	no	—
233	C₂²×C₈	—	2	2	no	—
234	C₂²×C₈	—	4	4	no	—
235	C₄⋊Q₈	—	2	1	no	—
236	C₄⋊Q₈	—	2	1	no	—
237	C₄⋊Q₈	—	2	1	no	—
238	C₄⋊Q₈	—	2	1	no	—
239	C₄⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
240	C₄⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
241	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
242	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
243	#125	—	2	4	no	—
244	#125	—	2	4	no	—
245	C₂²⋊Q₈	—	2	4	no	—
246	C₂²⋊Q₈	—	2	4	no	—
247	C₂²⋊Q₈	—	2	4	no	—
248	C₂²⋊Q₈	C₂×C₄×C₁₃	1	8	yes	—
249	C₄×Q₈	—	2	4	no	—
250	C₄×Q₈	—	2	4	no	—
251	C₄×Q₈	—	2	4	no	—
252	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	—
253	#117	—	2	4	no	—
254	#117	—	2	4	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
261	C₂×C₂²⋊C₄	—	2	2	no	—
262	C₂×C₄²	—	2	2	no	—
263	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
264	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
265	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
266	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
267	C₂×C₄²	D₄×C₁₃	1	2	yes	—
268	C₂×C₄²	D₄×C₁₃	1	2	yes	—
269	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
270	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
271	C₄⋊C₈	—	2	4	no	—
272	C₄⋊C₈	—	2	2	no	—
273	C₄⋊C₈	—	2	2	no	—
274	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
275	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
276	C₂²⋊C₈	—	2	4	no	—
277	C₄×C₈	—	2	4	no	—
278	C₂×C₁₃	—	2	4	no	—
279	C₂×C₁₃	#1542	1	4	yes	direct product factor
280	C₂×C₁₃	C₂×#413	1	1	yes	characteristic
281	C₂×C₁₃	C₂²×#103	1	1	yes	characteristic
282	C₂×C₁₃	C₂×#416	1	1	yes	characteristic
283	C₂⁴	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	4	4	no	—
288	C₂×Q₈	—	4	4	no	—
289	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
290	C₂²×C₄	—	2	4	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	4	2	no	—
294	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
295	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
296	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
297	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
298	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
299	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
300	C₂²×C₄	C₁₃×SD₁₆	1	4	yes	—
301	C₂²×C₄	C₁₃×Q₁₆	1	4	yes	—
302	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
303	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
304	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
305	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
306	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
307	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
308	C₂×C₈	—	2	4	no	—
309	C₂×C₈	—	2	4	no	—
310	C₂×C₈	—	4	8	no	—
311	C₂×C₈	—	4	4	no	—
312	C₂×C₈	—	4	4	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	8	no	—
317	C₄⋊C₄	—	2	8	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
323	C₂²⋊C₄	—	2	8	no	—
324	C₄²	—	2	8	no	—
325	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
326	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
327	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
328	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
329	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
330	C₄²	C₂×D₄×C₁₃	1	2	yes	—
331	C₄²	C₂×D₄×C₁₃	1	2	yes	—
332	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
333	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
334	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
335	C₁₃	C₂×#1542	1	1	yes	characteristic, direct product factor, Sylow
336	C₂³	—	2	2	no	—
337	C₂³	—	2	2	no	—
338	C₂³	C₁₃×#103	1	4	yes	—
339	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
340	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
341	Q₈	—	4	4	no	—
342	Q₈	—	4	4	no	—
343	Q₈	—	4	4	no	—
344	Q₈	—	4	4	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	4	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	C₁₃×#103	1	8	yes	—
357	C₂×C₄	C₁₃×#103	1	4	yes	—
358	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
359	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
360	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
361	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
362	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
363	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
364	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	—
365	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
366	C₂×C₄	C₂×C₁₃×Q₁₆	1	4	yes	—
367	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
368	C₂×C₄	C₁₃×#135	1	4	yes	—
369	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
370	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
371	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
372	C₈	—	4	4	no	—
373	C₈	—	4	4	no	—
374	C₂²	—	2	8	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	2	2	no	—
377	C₂²	C₁₃×#413	1	2	yes	—
378	C₂²	C₂×C₁₃×#103	1	4	yes	—
379	C₂²	C₂×C₁₃×#103	1	2	yes	—
380	C₂²	C₁₃×#416	1	2	yes	—
381	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
382	C₄	—	2	2	no	—
383	C₄	—	2	1	no	—
384	C₄	—	2	1	no	—
385	C₄	—	2	2	no	—
386	C₄	—	4	4	no	—
387	C₄	—	4	4	no	—
388	C₄	C₂×C₁₃×#103	1	4	yes	—
389	C₄	C₂×C₁₃×#103	1	2	yes	—
390	C₄	C₁₃×#416	1	2	yes	—
391	C₄	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
392	C₄	C₂²×C₁₃×Q₁₆	1	1	yes	characteristic
393	C₄	C₂×C₁₃×#135	1	2	yes	—
394	C₂	—	2	4	no	—
395	C₂	C₁₃×#1542	1	4	yes	direct product factor
396	C₂	C₂×C₁₃×#413	1	1	yes	characteristic
397	C₂	C₂²×C₁₃×#103	1	1	yes	characteristic
398	C₂	C₂×C₁₃×#416	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₃
socle	C₂³×C₁₃	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₃	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₃×#1542	C₂	direct (N × H)
5. C₂×C₁₃×#333	C₂	semidirect
6. C₂×C₁₃×#332	C₂	semidirect
30. C₁₃×#333	C₂²	semidirect
31. C₁₃×#332	C₂²	semidirect
84. C₂×#1542	C₁₃	direct (N × H)
140. #1542	C₂×C₁₃	direct (N × H)
141. C₂×#333	C₂×C₁₃	semidirect
142. C₂×#332	C₂×C₁₃	semidirect
204. #333	C₂²×C₁₃	semidirect
205. #332	C₂²×C₁₃	semidirect
279. C₂×C₁₃	#1542	direct (N × H)
335. C₁₃	C₂×#1542	direct (N × H)
395. C₂	C₁₃×#1542	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×#533	2
C₂×C₁₃×#431	2
C₂²×C₁₃×C₄⋊C₈	2
C₁₃×#1542	2
C₂×C₁₃×#333	2
C₂×C₁₃×#332	2
C₂×#1542	13

Subgroups — C2×C13×#1542 #15704036

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#1542 #15704036