Subgroups — C₂×C₁₃×#1553 #15704050

Order 3328.

1254 conjugacy classes of subgroups.

The subgroup lattice has 426 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×#432	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1553	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	C₁₃×#532	—	2	2	no	—
9	C₁₃×#532	—	2	2	no	—
10	C₁₃×#532	C₄	1	4	yes	—
11	C₁₃×#532	C₂²	1	4	yes	—
12	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#124	—	2	1	no	—
15	C₂×C₁₃×#121	—	2	1	no	—
16	C₂×C₁₃×#121	C₄	1	2	yes	—
17	C₂×C₄×D₄×C₁₃	—	2	1	no	—
18	C₂×C₄×D₄×C₁₃	C₄	1	2	yes	—
19	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#432	—	2	2	no	—
21	C₁₃×#432	C₂²	1	4	yes	complemented
22	C₁₃×#431	—	2	2	no	—
23	C₁₃×#431	C₂²	1	4	yes	complemented
24	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
25	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
26	C₂×C₁₃×C₂²⋊C₈	—	2	1	no	—
27	C₂×C₁₃×C₂²⋊C₈	—	2	1	no	—
28	C₂×C₁₃×#97	—	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	8	no	—
35	C₂²×Q₈×C₁₃	—	2	1	no	—
36	C₂²×D₄×C₁₃	—	2	2	no	—
37	C₂²×D₄×C₁₃	—	2	1	no	—
38	C₂²×D₄×C₁₃	—	2	1	no	—
39	C₂²×D₄×C₁₃	C₂×C₄	1	2	yes	—
40	C₂³×C₄×C₁₃	—	2	2	no	—
41	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
44	C₂²×C₈×C₁₃	—	2	2	no	—
45	C₂²×C₈×C₁₃	—	2	2	no	—
46	C₁₃×C₄⋊Q₈	—	2	1	no	—
47	C₁₃×C₄⋊Q₈	—	2	1	no	—
48	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
49	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
50	C₁₃×#127	—	2	1	no	—
51	C₁₃×#127	—	2	1	no	—
52	C₁₃×#127	C₂×C₄	1	2	yes	—
53	C₁₃×#127	C₂³	1	2	yes	—
54	C₁₃×#124	—	2	4	no	—
55	C₁₃×#124	—	2	4	no	—
56	C₁₃×#121	—	2	4	no	—
57	C₁₃×#121	—	2	4	no	—
58	C₁₃×#121	—	2	4	no	—
59	C₁₃×#121	C₂×C₄	1	8	yes	—
60	C₄×D₄×C₁₃	—	2	4	no	—
61	C₄×D₄×C₁₃	—	2	4	no	—
62	C₄×D₄×C₁₃	—	2	4	no	—
63	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	—
64	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
65	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
66	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
67	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
68	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
70	C₂×C₄²×C₁₃	D₄	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	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
76	C₁₃×C₄⋊C₈	—	2	2	no	—
77	C₁₃×C₄⋊C₈	—	2	2	no	—
78	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
79	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
80	C₁₃×C₂²⋊C₈	—	2	4	no	—
81	C₁₃×C₂²⋊C₈	—	2	4	no	—
82	C₁₃×#97	—	2	4	no	—
83	C₄×C₈×C₁₃	—	2	4	no	—
84	C₂×#1553	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
85	C₂⁴×C₁₃	—	2	2	no	—
86	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
87	C₁₃×#41	—	4	16	no	—
88	C₁₃×#41	—	4	16	no	—
89	C₂×Q₈×C₁₃	—	2	2	no	—
90	C₂×Q₈×C₁₃	—	2	2	no	—
91	C₂×Q₈×C₁₃	—	4	4	no	—
92	C₂×D₄×C₁₃	—	2	8	no	—
93	C₂×D₄×C₁₃	—	2	2	no	—
94	C₂×D₄×C₁₃	—	2	2	no	—
95	C₂×D₄×C₁₃	—	2	2	no	—
96	C₂×D₄×C₁₃	—	2	2	no	—
97	C₂×D₄×C₁₃	—	2	2	no	—
98	C₂×D₄×C₁₃	—	4	4	no	—
99	C₂×D₄×C₁₃	—	4	8	no	—
100	C₂×D₄×C₁₃	—	4	4	no	—
101	C₂×D₄×C₁₃	—	4	4	no	—
102	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
103	C₂²×C₄×C₁₃	—	2	4	no	—
104	C₂²×C₄×C₁₃	—	2	4	no	—
105	C₂²×C₄×C₁₃	—	2	2	no	—
106	C₂²×C₄×C₁₃	—	2	8	no	—
107	C₂²×C₄×C₁₃	—	4	2	no	—
108	C₂²×C₄×C₁₃	—	4	8	no	—
109	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
110	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
111	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
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	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₁₃	—	2	4	no	—
122	C₂×C₈×C₁₃	—	2	4	no	—
123	C₂×C₈×C₁₃	—	4	4	no	—
124	C₂×C₈×C₁₃	—	4	4	no	—
125	C₁₃×C₄⋊C₄	—	2	2	no	—
126	C₁₃×C₄⋊C₄	—	2	2	no	—
127	C₁₃×C₄⋊C₄	—	2	2	no	—
128	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
129	C₁₃×C₂²⋊C₄	—	2	8	no	—
130	C₁₃×C₂²⋊C₄	—	2	8	no	—
131	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
132	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
133	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
134	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
135	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
136	C₄²×C₁₃	C₂×D₄	1	2	yes	—
137	C₄²×C₁₃	C₂×D₄	1	2	yes	—
138	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
141	C₂×#532	C₂×C₁₃	1	1	yes	characteristic
142	C₂×#432	C₂×C₁₃	1	1	yes	characteristic, complemented
143	C₂×#431	C₂×C₁₃	1	1	yes	characteristic, complemented
144	#1553	C₂×C₁₃	1	8	yes	direct product factor
145	C₂×#332	C₂×C₁₃	1	2	yes	complemented
146	C₂×#331	C₂×C₁₃	1	2	yes	complemented
147	C₂³×C₁₃	—	2	2	no	—
148	C₂³×C₁₃	—	2	2	no	—
149	C₂³×C₁₃	—	2	2	no	—
150	C₂³×C₁₃	—	2	4	no	—
151	C₂³×C₁₃	—	4	4	no	—
152	C₂³×C₁₃	—	4	4	no	—
153	C₂³×C₁₃	—	4	4	no	—
154	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
155	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	Q₈×C₁₃	—	4	4	no	—
157	Q₈×C₁₃	—	4	4	no	—
158	D₄×C₁₃	—	4	4	no	—
159	D₄×C₁₃	—	4	4	no	—
160	D₄×C₁₃	—	4	16	no	—
161	D₄×C₁₃	—	4	4	no	—
162	D₄×C₁₃	—	4	4	no	—
163	D₄×C₁₃	—	4	4	no	—
164	D₄×C₁₃	—	4	4	no	—
165	C₂×C₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	—	2	2	no	—
167	C₂×C₄×C₁₃	—	2	2	no	—
168	C₂×C₄×C₁₃	—	2	2	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	4	no	—
173	C₂×C₄×C₁₃	—	2	4	no	—
174	C₂×C₄×C₁₃	—	4	2	no	—
175	C₂×C₄×C₁₃	—	4	2	no	—
176	C₂×C₄×C₁₃	—	4	16	no	—
177	C₂×C₄×C₁₃	—	4	4	no	—
178	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
179	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
180	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
181	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
183	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₁₃	#135	1	4	yes	—
185	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
186	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
187	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
189	C₈×C₁₃	—	4	4	no	—
190	C₈×C₁₃	—	4	4	no	—
191	C₂²×#41	—	2	1	no	—
192	#532	—	2	2	no	—
193	#532	—	2	2	no	—
194	#532	C₄×C₁₃	1	4	yes	—
195	#532	C₂²×C₁₃	1	4	yes	—
196	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
197	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
198	C₂×#124	—	2	1	no	—
199	C₂×#121	—	2	1	no	—
200	C₂×#121	C₄×C₁₃	1	2	yes	—
201	C₂×C₄×D₄	—	2	1	no	—
202	C₂×C₄×D₄	C₄×C₁₃	1	2	yes	—
203	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
204	#432	—	2	2	no	—
205	#432	C₂²×C₁₃	1	4	yes	complemented
206	#431	—	2	2	no	—
207	#431	C₂²×C₁₃	1	4	yes	complemented
208	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
209	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
210	C₂×C₂²⋊C₈	—	2	1	no	—
211	C₂×C₂²⋊C₈	—	2	1	no	—
212	C₂×#97	—	2	1	no	—
213	C₂×C₄×C₈	—	2	1	no	—
214	#332	C₂²×C₁₃	1	8	yes	complemented
215	#331	C₂²×C₁₃	1	8	yes	complemented
216	C₂²×C₁₃	—	2	2	no	—
217	C₂²×C₁₃	—	2	2	no	—
218	C₂²×C₁₃	—	2	2	no	—
219	C₂²×C₁₃	—	4	4	no	—
220	C₂²×C₁₃	—	4	4	no	—
221	C₂²×C₁₃	—	4	4	no	—
222	C₂²×C₁₃	—	4	4	no	—
223	C₂²×C₁₃	—	8	8	no	—
224	C₂²×C₁₃	#413	1	2	yes	—
225	C₂²×C₁₃	#416	1	2	yes	—
226	C₂²×C₁₃	#418	1	2	yes	—
227	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
228	C₄×C₁₃	—	2	2	no	—
229	C₄×C₁₃	—	2	1	no	—
230	C₄×C₁₃	—	2	1	no	—
231	C₄×C₁₃	—	2	2	no	—
232	C₄×C₁₃	—	2	2	no	—
233	C₄×C₁₃	—	4	4	no	—
234	C₄×C₁₃	#416	1	2	yes	—
235	C₄×C₁₃	#418	1	2	yes	—
236	C₄×C₁₃	C₂×#135	1	2	yes	—
237	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
238	C₂×#41	—	2	4	no	—
239	C₂×#41	—	2	4	no	—
240	C₂×#41	—	4	8	no	—
241	C₂²×Q₈	—	2	1	no	—
242	C₂²×D₄	—	2	2	no	—
243	C₂²×D₄	—	2	1	no	—
244	C₂²×D₄	—	2	1	no	—
245	C₂²×D₄	C₂×C₄×C₁₃	1	2	yes	—
246	C₂³×C₄	—	2	2	no	—
247	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
248	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
249	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
250	C₂²×C₈	—	2	2	no	—
251	C₂²×C₈	—	2	2	no	—
252	C₄⋊Q₈	—	2	1	no	—
253	C₄⋊Q₈	—	2	1	no	—
254	C₄⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
255	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
256	#127	—	2	1	no	—
257	#127	—	2	1	no	—
258	#127	C₂×C₄×C₁₃	1	2	yes	—
259	#127	C₂³×C₁₃	1	2	yes	—
260	#124	—	2	4	no	—
261	#124	—	2	4	no	—
262	#121	—	2	4	no	—
263	#121	—	2	4	no	—
264	#121	—	2	4	no	—
265	#121	C₂×C₄×C₁₃	1	8	yes	—
266	C₄×D₄	—	2	4	no	—
267	C₄×D₄	—	2	4	no	—
268	C₄×D₄	—	2	4	no	—
269	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
272	C₂×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₂²⋊C₄	—	2	2	no	—
274	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
275	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
276	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
277	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
278	C₂×C₄²	D₄×C₁₃	1	2	yes	—
279	C₂×C₄²	D₄×C₁₃	1	2	yes	—
280	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
281	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
282	C₄⋊C₈	—	2	2	no	—
283	C₄⋊C₈	—	2	2	no	—
284	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
285	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
286	C₂²⋊C₈	—	2	4	no	—
287	C₂²⋊C₈	—	2	4	no	—
288	#97	—	2	4	no	—
289	C₄×C₈	—	2	4	no	—
290	C₂×C₁₃	—	4	2	no	—
291	C₂×C₁₃	—	8	4	no	—
292	C₂×C₁₃	#1553	1	4	yes	direct product factor
293	C₂×C₁₃	C₂×#413	1	1	yes	characteristic
294	C₂×C₁₃	C₂×#416	1	1	yes	characteristic
295	C₂×C₁₃	C₂×#418	1	1	yes	characteristic
296	C₂⁴	—	2	2	no	—
297	C₂⁴	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
298	#41	—	4	16	no	—
299	#41	—	4	16	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	4	4	no	—
303	C₂×D₄	—	2	8	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	4	4	no	—
310	C₂×D₄	—	4	8	no	—
311	C₂×D₄	—	4	4	no	—
312	C₂×D₄	—	4	4	no	—
313	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	8	no	—
318	C₂²×C₄	—	4	2	no	—
319	C₂²×C₄	—	4	8	no	—
320	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
321	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
322	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
323	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
324	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
325	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
326	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
327	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
328	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
329	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
330	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
332	C₂×C₈	—	2	4	no	—
333	C₂×C₈	—	2	4	no	—
334	C₂×C₈	—	4	4	no	—
335	C₂×C₈	—	4	4	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
340	C₂²⋊C₄	—	2	8	no	—
341	C₂²⋊C₄	—	2	8	no	—
342	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
343	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
344	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
345	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
346	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
347	C₄²	C₂×D₄×C₁₃	1	2	yes	—
348	C₄²	C₂×D₄×C₁₃	1	2	yes	—
349	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
350	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
351	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
352	C₁₃	C₂×#1553	1	1	yes	characteristic, direct product factor, Sylow
353	C₂³	—	2	2	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	2	2	no	—
356	C₂³	—	2	4	no	—
357	C₂³	—	4	4	no	—
358	C₂³	—	4	4	no	—
359	C₂³	—	4	4	no	—
360	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
361	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
362	Q₈	—	4	4	no	—
363	Q₈	—	4	4	no	—
364	D₄	—	4	4	no	—
365	D₄	—	4	4	no	—
366	D₄	—	4	16	no	—
367	D₄	—	4	4	no	—
368	D₄	—	4	4	no	—
369	D₄	—	4	4	no	—
370	D₄	—	4	4	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	16	no	—
383	C₂×C₄	—	4	4	no	—
384	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
385	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
386	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
387	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
388	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
389	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
390	C₂×C₄	C₁₃×#135	1	4	yes	—
391	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
392	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
393	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
394	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
395	C₈	—	4	4	no	—
396	C₈	—	4	4	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	2	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	4	4	no	—
401	C₂²	—	4	4	no	—
402	C₂²	—	4	4	no	—
403	C₂²	—	4	4	no	—
404	C₂²	—	8	8	no	—
405	C₂²	C₁₃×#413	1	2	yes	—
406	C₂²	C₁₃×#416	1	2	yes	—
407	C₂²	C₁₃×#418	1	2	yes	—
408	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
409	C₄	—	2	2	no	—
410	C₄	—	2	1	no	—
411	C₄	—	2	1	no	—
412	C₄	—	2	2	no	—
413	C₄	—	2	2	no	—
414	C₄	—	4	4	no	—
415	C₄	C₁₃×#416	1	2	yes	—
416	C₄	C₁₃×#418	1	2	yes	—
417	C₄	C₂×C₁₃×#135	1	2	yes	—
418	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
419	C₂	—	4	2	no	—
420	C₂	—	8	4	no	—
421	C₂	C₁₃×#1553	1	4	yes	direct product factor
422	C₂	C₂×C₁₃×#413	1	1	yes	characteristic
423	C₂	C₂×C₁₃×#416	1	1	yes	characteristic
424	C₂	C₂×C₁₃×#418	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#432	C₂	semidirect
3. C₂×C₁₃×#431	C₂	semidirect
4. C₁₃×#1553	C₂	direct (N × H)
5. C₂×C₁₃×#332	C₂	semidirect
6. C₂×C₁₃×#331	C₂	semidirect
21. C₁₃×#432	C₂²	semidirect
23. C₁₃×#431	C₂²	semidirect
30. C₁₃×#332	C₂²	semidirect
31. C₁₃×#331	C₂²	semidirect
84. C₂×#1553	C₁₃	direct (N × H)
142. C₂×#432	C₂×C₁₃	semidirect
143. C₂×#431	C₂×C₁₃	semidirect
144. #1553	C₂×C₁₃	direct (N × H)
145. C₂×#332	C₂×C₁₃	semidirect
146. C₂×#331	C₂×C₁₃	semidirect
205. #432	C₂²×C₁₃	semidirect
207. #431	C₂²×C₁₃	semidirect
214. #332	C₂²×C₁₃	semidirect
215. #331	C₂²×C₁₃	semidirect
292. C₂×C₁₃	#1553	direct (N × H)
352. C₁₃	C₂×#1553	direct (N × H)
421. C₂	C₁₃×#1553	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×#432	2
C₂×C₁₃×#431	2
C₁₃×#1553	2
C₂×C₁₃×#332	2
C₂×C₁₃×#331	2
C₂×#1553	13

Subgroups — C2×C13×#1553 #15704050

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#1553 #15704050