Subgroups — C₂×C₁₃×#1540 #15704034

Order 3328.

1330 conjugacy classes of subgroups.

The subgroup lattice has 450 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×C₁₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1540	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₁₃×#332	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#331	C₂	1	2	yes	maximal, complemented
7	C₂²×C₁₃×#41	—	2	1	no	—
8	C₂³×C₈×C₁₃	—	2	1	no	—
9	C₁₃×#532	—	2	2	no	—
10	C₁₃×#532	—	2	2	no	—
11	C₁₃×#532	C₄	1	4	yes	—
12	C₁₃×#532	C₂²	1	4	yes	—
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#124	—	2	1	no	—
16	C₂×C₁₃×#121	—	2	1	no	—
17	C₂×C₁₃×#121	C₄	1	2	yes	—
18	C₂×C₄×D₄×C₁₃	—	2	1	no	—
19	C₂×C₄×D₄×C₁₃	C₄	1	2	yes	—
20	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
21	C₁₃×#431	—	2	2	no	—
22	C₁₃×#431	C₂²	1	4	yes	complemented
23	C₂×C₁₃×C₄⋊C₈	—	2	2	no	—
24	C₂×C₁₃×C₄⋊C₈	—	2	1	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	complemented
28	C₂×C₁₃×C₂²⋊C₈	—	2	1	no	—
29	C₂×C₄×C₈×C₁₃	—	2	1	no	—
30	C₁₃×#332	C₂²	1	8	yes	complemented
31	C₁₃×#331	C₂²	1	8	yes	complemented
32	C₂×C₁₃×#41	—	2	4	no	—
33	C₂×C₁₃×#41	—	2	4	no	—
34	C₂×C₁₃×#41	—	4	4	no	—
35	C₂×C₁₃×#41	—	4	4	no	—
36	C₂²×Q₈×C₁₃	—	2	1	no	—
37	C₂²×D₄×C₁₃	—	2	2	no	—
38	C₂²×D₄×C₁₃	—	2	1	no	—
39	C₂²×D₄×C₁₃	—	2	1	no	—
40	C₂²×D₄×C₁₃	C₂×C₄	1	2	yes	—
41	C₂³×C₄×C₁₃	—	2	2	no	—
42	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
45	C₂²×C₈×C₁₃	—	2	2	no	—
46	C₂²×C₈×C₁₃	—	2	2	no	—
47	C₂²×C₈×C₁₃	—	2	4	no	—
48	C₂²×C₈×C₁₃	—	4	4	no	—
49	C₁₃×C₄⋊Q₈	—	2	1	no	—
50	C₁₃×C₄⋊Q₈	—	2	1	no	—
51	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
52	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
53	C₁₃×#127	—	2	1	no	—
54	C₁₃×#127	—	2	1	no	—
55	C₁₃×#127	C₂×C₄	1	2	yes	—
56	C₁₃×#127	C₂³	1	2	yes	—
57	C₁₃×#124	—	2	4	no	—
58	C₁₃×#124	—	2	4	no	—
59	C₁₃×#121	—	2	4	no	—
60	C₁₃×#121	—	2	4	no	—
61	C₁₃×#121	—	2	4	no	—
62	C₁₃×#121	C₂×C₄	1	8	yes	—
63	C₄×D₄×C₁₃	—	2	4	no	—
64	C₄×D₄×C₁₃	—	2	4	no	—
65	C₄×D₄×C₁₃	—	2	4	no	—
66	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	—
67	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
68	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
69	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
70	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
71	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
72	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₁₃	D₄	1	2	yes	—
75	C₂×C₄²×C₁₃	D₄	1	2	yes	—
76	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
79	C₁₃×C₄⋊C₈	—	2	2	no	—
80	C₁₃×C₄⋊C₈	—	2	4	no	—
81	C₁₃×C₄⋊C₈	—	2	2	no	—
82	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
83	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
84	C₁₃×C₂²⋊C₈	—	2	4	no	—
85	C₄×C₈×C₁₃	—	2	4	no	—
86	C₂×#1540	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
87	C₂⁴×C₁₃	—	2	2	no	—
88	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
89	C₁₃×#41	—	4	16	no	—
90	C₁₃×#41	—	4	8	no	—
91	C₁₃×#41	—	4	8	no	—
92	C₂×Q₈×C₁₃	—	2	2	no	—
93	C₂×Q₈×C₁₃	—	2	2	no	—
94	C₂×Q₈×C₁₃	—	4	2	no	—
95	C₂×Q₈×C₁₃	—	4	2	no	—
96	C₂×D₄×C₁₃	—	2	8	no	—
97	C₂×D₄×C₁₃	—	2	2	no	—
98	C₂×D₄×C₁₃	—	2	2	no	—
99	C₂×D₄×C₁₃	—	2	2	no	—
100	C₂×D₄×C₁₃	—	2	2	no	—
101	C₂×D₄×C₁₃	—	2	2	no	—
102	C₂×D₄×C₁₃	—	4	4	no	—
103	C₂×D₄×C₁₃	—	4	8	no	—
104	C₂×D₄×C₁₃	—	4	2	no	—
105	C₂×D₄×C₁₃	—	4	2	no	—
106	C₂×D₄×C₁₃	—	4	4	no	—
107	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
108	C₂²×C₄×C₁₃	—	2	4	no	—
109	C₂²×C₄×C₁₃	—	2	2	no	—
110	C₂²×C₄×C₁₃	—	2	8	no	—
111	C₂²×C₄×C₁₃	—	4	2	no	—
112	C₂²×C₄×C₁₃	—	4	8	no	—
113	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
115	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
117	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
118	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	D₈	1	4	yes	—
120	C₂²×C₄×C₁₃	SD₁₆	1	4	yes	—
121	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
123	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₁₃	—	2	4	no	—
128	C₂×C₈×C₁₃	—	2	4	no	—
129	C₂×C₈×C₁₃	—	4	4	no	—
130	C₂×C₈×C₁₃	—	4	8	no	—
131	C₂×C₈×C₁₃	—	4	4	no	—
132	C₁₃×C₄⋊C₄	—	2	2	no	—
133	C₁₃×C₄⋊C₄	—	2	2	no	—
134	C₁₃×C₄⋊C₄	—	2	2	no	—
135	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
136	C₁₃×C₂²⋊C₄	—	2	8	no	—
137	C₁₃×C₂²⋊C₄	—	2	8	no	—
138	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
139	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
140	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
141	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
142	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
143	C₄²×C₁₃	C₂×D₄	1	2	yes	—
144	C₄²×C₁₃	C₂×D₄	1	2	yes	—
145	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
148	C₂×#532	C₂×C₁₃	1	1	yes	characteristic
149	C₂×#431	C₂×C₁₃	1	1	yes	characteristic, complemented
150	C₂²×C₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
151	#1540	C₂×C₁₃	1	8	yes	direct product factor
152	C₂×#332	C₂×C₁₃	1	2	yes	complemented
153	C₂×#331	C₂×C₁₃	1	2	yes	complemented
154	C₂³×C₁₃	—	2	2	no	—
155	C₂³×C₁₃	—	2	2	no	—
156	C₂³×C₁₃	—	2	4	no	—
157	C₂³×C₁₃	—	4	4	no	—
158	C₂³×C₁₃	—	4	4	no	—
159	C₂³×C₁₃	—	4	4	no	—
160	C₂³×C₁₃	#102	1	4	yes	—
161	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
162	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	Q₈×C₁₃	—	4	2	no	—
164	Q₈×C₁₃	—	4	2	no	—
165	Q₈×C₁₃	—	4	4	no	—
166	D₄×C₁₃	—	4	4	no	—
167	D₄×C₁₃	—	4	4	no	—
168	D₄×C₁₃	—	4	16	no	—
169	D₄×C₁₃	—	4	2	no	—
170	D₄×C₁₃	—	4	2	no	—
171	D₄×C₁₃	—	4	4	no	—
172	D₄×C₁₃	—	4	4	no	—
173	D₄×C₁₃	—	4	4	no	—
174	C₂×C₄×C₁₃	—	2	2	no	—
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	2	4	no	—
178	C₂×C₄×C₁₃	—	2	4	no	—
179	C₂×C₄×C₁₃	—	2	4	no	—
180	C₂×C₄×C₁₃	—	4	2	no	—
181	C₂×C₄×C₁₃	—	4	2	no	—
182	C₂×C₄×C₁₃	—	4	4	no	—
183	C₂×C₄×C₁₃	—	4	16	no	—
184	C₂×C₄×C₁₃	#102	1	4	yes	—
185	C₂×C₄×C₁₃	#102	1	8	yes	—
186	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
187	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
188	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
189	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
190	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
191	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
192	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
193	C₂×C₄×C₁₃	C₂×D₈	1	4	yes	—
194	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
195	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	—
196	C₂×C₄×C₁₃	#135	1	4	yes	—
197	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
198	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
200	C₈×C₁₃	—	4	4	no	—
201	C₈×C₁₃	—	4	4	no	—
202	C₂²×#41	—	2	1	no	—
203	C₂³×C₈	—	2	1	no	—
204	#532	—	2	2	no	—
205	#532	—	2	2	no	—
206	#532	C₄×C₁₃	1	4	yes	—
207	#532	C₂²×C₁₃	1	4	yes	—
208	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
209	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
210	C₂×#124	—	2	1	no	—
211	C₂×#121	—	2	1	no	—
212	C₂×#121	C₄×C₁₃	1	2	yes	—
213	C₂×C₄×D₄	—	2	1	no	—
214	C₂×C₄×D₄	C₄×C₁₃	1	2	yes	—
215	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
216	#431	—	2	2	no	—
217	#431	C₂²×C₁₃	1	4	yes	complemented
218	C₂×C₄⋊C₈	—	2	2	no	—
219	C₂×C₄⋊C₈	—	2	1	no	—
220	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
221	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
222	C₂×C₄⋊C₈	C₂²×C₁₃	1	4	yes	complemented
223	C₂×C₂²⋊C₈	—	2	1	no	—
224	C₂×C₄×C₈	—	2	1	no	—
225	#332	C₂²×C₁₃	1	8	yes	complemented
226	#331	C₂²×C₁₃	1	8	yes	complemented
227	C₂²×C₁₃	—	2	8	no	—
228	C₂²×C₁₃	—	2	2	no	—
229	C₂²×C₁₃	—	2	2	no	—
230	C₂²×C₁₃	—	4	4	no	—
231	C₂²×C₁₃	—	4	4	no	—
232	C₂²×C₁₃	—	4	4	no	—
233	C₂²×C₁₃	—	8	8	no	—
234	C₂²×C₁₃	#413	1	2	yes	—
235	C₂²×C₁₃	C₂×#102	1	4	yes	—
236	C₂²×C₁₃	C₂×#102	1	2	yes	—
237	C₂²×C₁₃	#416	1	2	yes	—
238	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
239	C₄×C₁₃	—	2	2	no	—
240	C₄×C₁₃	—	2	1	no	—
241	C₄×C₁₃	—	2	1	no	—
242	C₄×C₁₃	—	2	2	no	—
243	C₄×C₁₃	—	4	4	no	—
244	C₄×C₁₃	C₂×#102	1	4	yes	—
245	C₄×C₁₃	C₂×#102	1	2	yes	—
246	C₄×C₁₃	#416	1	2	yes	—
247	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
248	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
249	C₄×C₁₃	C₂×#135	1	2	yes	—
250	C₂×#41	—	2	4	no	—
251	C₂×#41	—	2	4	no	—
252	C₂×#41	—	4	4	no	—
253	C₂×#41	—	4	4	no	—
254	C₂²×Q₈	—	2	1	no	—
255	C₂²×D₄	—	2	2	no	—
256	C₂²×D₄	—	2	1	no	—
257	C₂²×D₄	—	2	1	no	—
258	C₂²×D₄	C₂×C₄×C₁₃	1	2	yes	—
259	C₂³×C₄	—	2	2	no	—
260	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
261	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
262	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
263	C₂²×C₈	—	2	2	no	—
264	C₂²×C₈	—	2	4	no	—
265	C₂²×C₈	—	2	2	no	—
266	C₂²×C₈	—	4	4	no	—
267	C₄⋊Q₈	—	2	1	no	—
268	C₄⋊Q₈	—	2	1	no	—
269	C₄⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
270	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
271	#127	—	2	1	no	—
272	#127	—	2	1	no	—
273	#127	C₂×C₄×C₁₃	1	2	yes	—
274	#127	C₂³×C₁₃	1	2	yes	—
275	#124	—	2	4	no	—
276	#124	—	2	4	no	—
277	#121	—	2	4	no	—
278	#121	—	2	4	no	—
279	#121	—	2	4	no	—
280	#121	C₂×C₄×C₁₃	1	8	yes	—
281	C₄×D₄	—	2	4	no	—
282	C₄×D₄	—	2	4	no	—
283	C₄×D₄	—	2	4	no	—
284	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
287	C₂×C₂²⋊C₄	—	2	2	no	—
288	C₂×C₂²⋊C₄	—	2	2	no	—
289	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
290	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
291	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
292	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
293	C₂×C₄²	D₄×C₁₃	1	2	yes	—
294	C₂×C₄²	D₄×C₁₃	1	2	yes	—
295	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
296	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
297	C₄⋊C₈	—	2	2	no	—
298	C₄⋊C₈	—	2	4	no	—
299	C₄⋊C₈	—	2	2	no	—
300	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
301	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
302	C₂²⋊C₈	—	2	4	no	—
303	C₄×C₈	—	2	4	no	—
304	C₂×C₁₃	—	2	4	no	—
305	C₂×C₁₃	—	8	4	no	—
306	C₂×C₁₃	#1540	1	4	yes	direct product factor
307	C₂×C₁₃	C₂×#413	1	1	yes	characteristic
308	C₂×C₁₃	C₂²×#102	1	1	yes	characteristic
309	C₂×C₁₃	C₂×#416	1	1	yes	characteristic
310	C₂⁴	—	2	2	no	—
311	C₂⁴	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
312	#41	—	4	16	no	—
313	#41	—	4	8	no	—
314	#41	—	4	8	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	4	2	no	—
318	C₂×Q₈	—	4	2	no	—
319	C₂×D₄	—	2	8	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	4	4	no	—
326	C₂×D₄	—	4	8	no	—
327	C₂×D₄	—	4	2	no	—
328	C₂×D₄	—	4	2	no	—
329	C₂×D₄	—	4	4	no	—
330	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	8	no	—
334	C₂²×C₄	—	4	2	no	—
335	C₂²×C₄	—	4	8	no	—
336	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
337	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
338	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
339	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
340	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
341	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
342	C₂²×C₄	C₁₃×D₈	1	4	yes	—
343	C₂²×C₄	C₁₃×SD₁₆	1	4	yes	—
344	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
345	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
346	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
347	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
348	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
349	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
350	C₂×C₈	—	2	4	no	—
351	C₂×C₈	—	2	4	no	—
352	C₂×C₈	—	4	4	no	—
353	C₂×C₈	—	4	8	no	—
354	C₂×C₈	—	4	4	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
359	C₂²⋊C₄	—	2	8	no	—
360	C₂²⋊C₄	—	2	8	no	—
361	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
362	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
363	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
364	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
365	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
366	C₄²	C₂×D₄×C₁₃	1	2	yes	—
367	C₄²	C₂×D₄×C₁₃	1	2	yes	—
368	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
369	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
370	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
371	C₁₃	C₂×#1540	1	1	yes	characteristic, direct product factor, Sylow
372	C₂³	—	2	2	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	2	4	no	—
375	C₂³	—	4	4	no	—
376	C₂³	—	4	4	no	—
377	C₂³	—	4	4	no	—
378	C₂³	C₁₃×#102	1	4	yes	—
379	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
380	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
381	Q₈	—	4	4	no	—
382	Q₈	—	4	2	no	—
383	Q₈	—	4	2	no	—
384	D₄	—	4	4	no	—
385	D₄	—	4	4	no	—
386	D₄	—	4	16	no	—
387	D₄	—	4	4	no	—
388	D₄	—	4	4	no	—
389	D₄	—	4	2	no	—
390	D₄	—	4	2	no	—
391	D₄	—	4	4	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	4	no	—
401	C₂×C₄	—	4	16	no	—
402	C₂×C₄	C₁₃×#102	1	4	yes	—
403	C₂×C₄	C₁₃×#102	1	8	yes	—
404	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
405	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
406	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
407	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
408	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
409	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
410	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
411	C₂×C₄	C₂×C₁₃×D₈	1	4	yes	—
412	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
413	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	—
414	C₂×C₄	C₁₃×#135	1	4	yes	—
415	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
417	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
418	C₈	—	4	4	no	—
419	C₈	—	4	4	no	—
420	C₂²	—	2	8	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	2	2	no	—
423	C₂²	—	4	4	no	—
424	C₂²	—	4	4	no	—
425	C₂²	—	4	4	no	—
426	C₂²	—	8	8	no	—
427	C₂²	C₁₃×#413	1	2	yes	—
428	C₂²	C₂×C₁₃×#102	1	4	yes	—
429	C₂²	C₂×C₁₃×#102	1	2	yes	—
430	C₂²	C₁₃×#416	1	2	yes	—
431	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
432	C₄	—	2	2	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	2	2	no	—
436	C₄	—	4	4	no	—
437	C₄	C₂×C₁₃×#102	1	4	yes	—
438	C₄	C₂×C₁₃×#102	1	2	yes	—
439	C₄	C₁₃×#416	1	2	yes	—
440	C₄	C₂²×C₁₃×D₈	1	1	yes	characteristic
441	C₄	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
442	C₄	C₂×C₁₃×#135	1	2	yes	—
443	C₂	—	2	4	no	—
444	C₂	—	8	4	no	—
445	C₂	C₁₃×#1540	1	4	yes	direct product factor
446	C₂	C₂×C₁₃×#413	1	1	yes	characteristic
447	C₂	C₂²×C₁₃×#102	1	1	yes	characteristic
448	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	C₂×C₁₃×#532	C₂
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
2. C₂×C₁₃×#431	C₂	semidirect
3. C₂²×C₁₃×C₄⋊C₈	C₂	semidirect
4. C₁₃×#1540	C₂	direct (N × H)
5. C₂×C₁₃×#332	C₂	semidirect
6. C₂×C₁₃×#331	C₂	semidirect
22. C₁₃×#431	C₂²	semidirect
27. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
30. C₁₃×#332	C₂²	semidirect
31. C₁₃×#331	C₂²	semidirect
86. C₂×#1540	C₁₃	direct (N × H)
149. C₂×#431	C₂×C₁₃	semidirect
150. C₂²×C₄⋊C₈	C₂×C₁₃	semidirect
151. #1540	C₂×C₁₃	direct (N × H)
152. C₂×#332	C₂×C₁₃	semidirect
153. C₂×#331	C₂×C₁₃	semidirect
217. #431	C₂²×C₁₃	semidirect
222. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
225. #332	C₂²×C₁₃	semidirect
226. #331	C₂²×C₁₃	semidirect
306. C₂×C₁₃	#1540	direct (N × H)
371. C₁₃	C₂×#1540	direct (N × H)
445. C₂	C₁₃×#1540	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×C₁₃×#431	2
C₂²×C₁₃×C₄⋊C₈	2
C₁₃×#1540	2
C₂×C₁₃×#332	2
C₂×C₁₃×#331	2
C₂×#1540	13

Subgroups — C2×C13×#1540 #15704034

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#1540 #15704034