Subgroups — C₁₃×#25930 #15712269

Order 3328.

1182 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×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#486	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#459	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2548	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2025	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1987	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1984	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1879	C₂	1	4	yes	maximal, complemented
9	C₄×C₁₃×#102	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
11	C₁₃×#554	—	2	4	no	—
12	C₁₃×#554	—	2	4	no	—
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#125	C₂²	1	2	yes	—
16	C₂×C₁₃×#124	—	2	1	no	—
17	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
18	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
19	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
21	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
23	C₁₃×#486	—	2	4	no	—
24	C₁₃×#459	—	2	4	no	—
25	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#102	C₂²	1	2	yes	—
27	C₂×C₁₃×#102	C₂²	1	2	yes	—
28	C₂×C₁₃×#102	C₂²	1	4	yes	—
29	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×#394	—	2	2	no	—
31	C₁₃×#390	—	2	1	no	—
32	C₁₃×#390	C₂²	1	4	yes	—
33	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₁₃×#340	C₂²	1	4	yes	—
35	C₁₃×#340	C₂²	1	2	yes	—
36	C₁₃×#336	C₂²	1	4	yes	—
37	C₂²×Q₈×C₁₃	—	2	1	no	—
38	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
39	C₂²×D₄×C₁₃	—	2	1	no	—
40	C₂²×D₄×C₁₃	—	2	1	no	—
41	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
42	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₁₃	—	2	1	no	—
44	C₂³×C₄×C₁₃	—	2	2	no	—
45	C₂×C₁₃×D₈	—	2	4	no	—
46	C₂×C₁₃×D₈	—	2	8	no	—
47	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
49	C₁₃×C₄⋊Q₈	—	2	2	no	—
50	C₁₃×C₄⋊Q₈	D₄	1	4	yes	—
51	C₁₃×#127	—	2	2	no	—
52	C₁₃×#127	—	2	2	no	—
53	C₁₃×#125	—	2	4	no	—
54	C₁₃×#125	—	2	4	no	—
55	C₁₃×#124	—	4	4	no	—
56	C₁₃×C₂²⋊Q₈	—	2	8	no	—
57	C₁₃×C₂²⋊Q₈	—	2	16	no	—
58	C₄×Q₈×C₁₃	—	2	2	no	—
59	C₄×Q₈×C₁₃	—	2	2	no	—
60	C₄×D₄×C₁₃	—	2	4	no	—
61	C₄×D₄×C₁₃	—	2	4	no	—
62	C₄×D₄×C₁₃	—	2	2	no	—
63	C₄×D₄×C₁₃	D₄	1	4	yes	—
64	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
68	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
69	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
74	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
75	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
76	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
77	C₂×C₄²×C₁₃	—	2	1	no	—
78	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
79	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
80	C₁₃×C₄⋊C₈	—	2	2	no	—
81	C₁₃×#102	—	2	4	no	—
82	C₁₃×#102	—	2	4	no	—
83	C₁₃×#102	—	2	8	no	—
84	C₄×C₈×C₁₃	—	2	2	no	—
85	C₁₃×#95	—	2	1	no	—
86	#25930	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
87	C₂⁴×C₁₃	—	2	1	no	—
88	C₂⁴×C₁₃	—	2	2	no	—
89	C₂×Q₈×C₁₃	—	2	2	no	—
90	C₂×Q₈×C₁₃	—	2	4	no	—
91	C₂×Q₈×C₁₃	—	2	2	no	—
92	C₂×Q₈×C₁₃	—	2	2	no	—
93	C₂×Q₈×C₁₃	—	8	2	no	—
94	C₂×D₄×C₁₃	—	2	1	no	—
95	C₂×D₄×C₁₃	—	2	2	no	—
96	C₂×D₄×C₁₃	—	2	2	no	—
97	C₂×D₄×C₁₃	—	2	4	no	—
98	C₂×D₄×C₁₃	—	2	2	no	—
99	C₂×D₄×C₁₃	—	2	4	no	—
100	C₂×D₄×C₁₃	—	4	2	no	—
101	C₂×D₄×C₁₃	—	4	2	no	—
102	C₂×D₄×C₁₃	—	4	2	no	—
103	C₂×D₄×C₁₃	—	4	2	no	—
104	C₂×D₄×C₁₃	—	8	2	no	—
105	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
106	C₂×D₄×C₁₃	#41	1	4	yes	—
107	C₂²×C₄×C₁₃	—	2	1	no	—
108	C₂²×C₄×C₁₃	—	2	2	no	—
109	C₂²×C₄×C₁₃	—	2	8	no	—
110	C₂²×C₄×C₁₃	—	2	4	no	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	—	4	2	no	—
113	C₂²×C₄×C₁₃	—	4	2	no	—
114	C₂²×C₄×C₁₃	—	8	4	no	—
115	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
120	C₁₃×D₈	—	4	8	no	—
121	C₂×C₈×C₁₃	—	2	2	no	—
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	—	2	4	no	—
125	C₂×C₈×C₁₃	—	2	2	no	—
126	C₁₃×C₄⋊C₄	—	2	8	no	—
127	C₁₃×C₄⋊C₄	—	2	8	no	—
128	C₁₃×C₄⋊C₄	—	2	2	no	—
129	C₁₃×C₄⋊C₄	—	2	4	no	—
130	C₁₃×C₄⋊C₄	—	2	4	no	—
131	C₁₃×C₄⋊C₄	—	2	1	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	C₂×D₄	1	4	yes	—
136	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
137	C₁₃×C₂²⋊C₄	—	2	8	no	—
138	C₁₃×C₂²⋊C₄	—	2	4	no	—
139	C₁₃×C₂²⋊C₄	—	4	8	no	—
140	C₁₃×C₂²⋊C₄	—	8	4	no	—
141	C₄²×C₁₃	—	2	2	no	—
142	C₄²×C₁₃	—	2	2	no	—
143	C₄²×C₁₃	—	4	2	no	—
144	C₄²×C₁₃	C₂×D₄	1	2	yes	—
145	C₄²×C₁₃	C₂×D₄	1	2	yes	—
146	C₂×#554	C₂×C₁₃	1	1	yes	characteristic, complemented
147	C₂×#486	C₂×C₁₃	1	1	yes	characteristic, complemented
148	C₂×#459	C₂×C₁₃	1	1	yes	characteristic
149	#2548	C₂×C₁₃	1	1	yes	characteristic, complemented
150	#2025	C₂×C₁₃	1	4	yes	complemented
151	#1987	C₂×C₁₃	1	1	yes	characteristic, complemented
152	#1984	C₂×C₁₃	1	1	yes	characteristic, complemented
153	#1879	C₂×C₁₃	1	4	yes	complemented
154	C₄×#102	C₂×C₁₃	1	1	yes	characteristic, complemented
155	C₂³×C₁₃	—	2	2	no	—
156	C₂³×C₁₃	—	2	4	no	—
157	C₂³×C₁₃	—	4	1	no	—
158	C₂³×C₁₃	—	4	1	no	—
159	C₂³×C₁₃	—	4	2	no	—
160	C₂³×C₁₃	—	4	2	no	—
161	C₂³×C₁₃	—	4	4	no	—
162	C₂³×C₁₃	—	4	2	no	—
163	C₂³×C₁₃	—	4	2	no	—
164	C₂³×C₁₃	—	4	4	no	—
165	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
166	Q₈×C₁₃	—	4	4	no	—
167	Q₈×C₁₃	—	8	4	no	—
168	D₄×C₁₃	—	2	2	no	—
169	D₄×C₁₃	—	2	4	no	—
170	D₄×C₁₃	—	4	2	no	—
171	D₄×C₁₃	—	4	2	no	—
172	D₄×C₁₃	—	4	4	no	—
173	D₄×C₁₃	—	8	4	no	—
174	D₄×C₁₃	—	8	4	no	—
175	D₄×C₁₃	#124	1	4	yes	complemented
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	2	no	—
180	C₂×C₄×C₁₃	—	2	4	no	—
181	C₂×C₄×C₁₃	—	2	2	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	2	4	no	—
184	C₂×C₄×C₁₃	—	4	1	no	—
185	C₂×C₄×C₁₃	—	4	1	no	—
186	C₂×C₄×C₁₃	—	4	4	no	—
187	C₂×C₄×C₁₃	—	4	8	no	—
188	C₂×C₄×C₁₃	—	4	2	no	—
189	C₂×C₄×C₁₃	—	4	2	no	—
190	C₂×C₄×C₁₃	—	4	2	no	—
191	C₂×C₄×C₁₃	—	8	8	no	—
192	C₂×C₄×C₁₃	#120	1	2	yes	—
193	C₂×C₄×C₁₃	#120	1	2	yes	—
194	C₂×C₄×C₁₃	#135	1	2	yes	—
195	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
196	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
199	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
200	C₈×C₁₃	—	4	2	no	—
201	C₈×C₁₃	—	4	2	no	—
202	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
203	#554	—	2	4	no	—
204	#554	—	2	4	no	—
205	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
206	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
207	C₂×#125	C₂²×C₁₃	1	2	yes	—
208	C₂×#124	—	2	1	no	—
209	C₂×C₂²⋊Q₈	—	2	1	no	—
210	C₂×C₂²⋊Q₈	—	2	2	no	—
211	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
212	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
213	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
214	C₂²×C₄⋊C₄	—	2	1	no	—
215	#486	—	2	4	no	—
216	#459	—	2	4	no	—
217	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
218	C₂×#102	C₂²×C₁₃	1	4	yes	—
219	C₂×#102	C₂²×C₁₃	1	2	yes	—
220	C₂×#102	C₂²×C₁₃	1	2	yes	—
221	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
222	#394	—	2	2	no	—
223	#390	—	2	1	no	—
224	#390	C₂²×C₁₃	1	4	yes	—
225	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
226	#340	C₂²×C₁₃	1	4	yes	—
227	#340	C₂²×C₁₃	1	2	yes	—
228	#336	C₂²×C₁₃	1	4	yes	—
229	C₂²×C₁₃	—	2	4	no	—
230	C₂²×C₁₃	—	4	4	no	—
231	C₂²×C₁₃	—	4	4	no	—
232	C₂²×C₁₃	—	4	2	no	—
233	C₂²×C₁₃	—	4	2	no	—
234	C₂²×C₁₃	—	8	4	no	—
235	C₂²×C₁₃	—	8	4	no	—
236	C₂²×C₁₃	—	8	2	no	—
237	C₂²×C₁₃	—	8	2	no	—
238	C₂²×C₁₃	—	8	2	no	—
239	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
240	C₂²×C₁₃	#548	1	2	yes	—
241	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
242	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
243	C₂²×C₁₃	#576	1	2	yes	—
244	C₄×C₁₃	—	2	2	no	—
245	C₄×C₁₃	—	4	2	no	—
246	C₄×C₁₃	—	4	2	no	—
247	C₄×C₁₃	—	4	2	no	—
248	C₄×C₁₃	—	4	4	no	—
249	C₄×C₁₃	—	8	2	no	—
250	C₄×C₁₃	#449	1	4	yes	—
251	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
252	C₄×C₁₃	#536	1	1	yes	characteristic
253	C₄×C₁₃	#548	1	2	yes	—
254	C₂²×Q₈	—	2	1	no	—
255	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
256	C₂²×D₄	—	2	1	no	—
257	C₂²×D₄	—	2	1	no	—
258	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
259	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
260	C₂³×C₄	—	2	1	no	—
261	C₂³×C₄	—	2	2	no	—
262	C₂×D₈	—	2	4	no	—
263	C₂×D₈	—	2	8	no	—
264	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
265	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
266	C₄⋊Q₈	—	2	2	no	—
267	C₄⋊Q₈	D₄×C₁₃	1	4	yes	—
268	#127	—	2	2	no	—
269	#127	—	2	2	no	—
270	#125	—	2	4	no	—
271	#125	—	2	4	no	—
272	#124	—	4	4	no	—
273	C₂²⋊Q₈	—	2	8	no	—
274	C₂²⋊Q₈	—	2	16	no	—
275	C₄×Q₈	—	2	2	no	—
276	C₄×Q₈	—	2	2	no	—
277	C₄×D₄	—	2	4	no	—
278	C₄×D₄	—	2	4	no	—
279	C₄×D₄	—	2	2	no	—
280	C₄×D₄	D₄×C₁₃	1	4	yes	—
281	C₂×C₄⋊C₄	—	2	8	no	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
286	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
287	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
288	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
290	C₂×C₂²⋊C₄	—	2	2	no	—
291	C₂×C₂²⋊C₄	—	2	1	no	—
292	C₂×C₂²⋊C₄	—	2	4	no	—
293	C₂×C₂²⋊C₄	—	2	4	no	—
294	C₂×C₄²	—	2	1	no	—
295	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
296	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
297	C₄⋊C₈	—	2	2	no	—
298	#102	—	2	4	no	—
299	#102	—	2	4	no	—
300	#102	—	2	8	no	—
301	C₄×C₈	—	2	2	no	—
302	#95	—	2	1	no	—
303	C₂×C₁₃	—	4	4	no	—
304	C₂×C₁₃	—	16	2	no	—
305	C₂×C₁₃	#2436	1	1	yes	characteristic
306	C₂×C₁₃	C₂×#449	1	1	yes	characteristic
307	C₂×C₁₃	#3008	1	1	yes	characteristic
308	C₂×C₁₃	#3361	1	2	yes	—
309	C₂×C₁₃	#3366	1	2	yes	—
310	C₂⁴	—	2	1	no	—
311	C₂⁴	—	2	2	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	2	4	no	—
314	C₂×Q₈	—	2	2	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	—	8	2	no	—
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	4	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	4	no	—
323	C₂×D₄	—	4	2	no	—
324	C₂×D₄	—	4	2	no	—
325	C₂×D₄	—	4	2	no	—
326	C₂×D₄	—	4	2	no	—
327	C₂×D₄	—	8	2	no	—
328	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
329	C₂×D₄	C₁₃×#41	1	4	yes	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	8	no	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	4	2	no	—
336	C₂²×C₄	—	4	2	no	—
337	C₂²×C₄	—	8	4	no	—
338	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
339	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
340	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
341	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
342	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
343	D₈	—	4	8	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	4	no	—
348	C₂×C₈	—	2	2	no	—
349	C₄⋊C₄	—	2	8	no	—
350	C₄⋊C₄	—	2	8	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	4	no	—
353	C₄⋊C₄	—	2	4	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
359	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
360	C₂²⋊C₄	—	2	8	no	—
361	C₂²⋊C₄	—	2	4	no	—
362	C₂²⋊C₄	—	4	8	no	—
363	C₂²⋊C₄	—	8	4	no	—
364	C₄²	—	2	2	no	—
365	C₄²	—	2	2	no	—
366	C₄²	—	4	2	no	—
367	C₄²	C₂×D₄×C₁₃	1	2	yes	—
368	C₄²	C₂×D₄×C₁₃	1	2	yes	—
369	C₁₃	#25930	1	1	yes	characteristic, direct product factor, Sylow
370	C₂³	—	2	2	no	—
371	C₂³	—	2	4	no	—
372	C₂³	—	4	1	no	—
373	C₂³	—	4	1	no	—
374	C₂³	—	4	2	no	—
375	C₂³	—	4	2	no	—
376	C₂³	—	4	4	no	—
377	C₂³	—	4	2	no	—
378	C₂³	—	4	2	no	—
379	C₂³	—	4	4	no	—
380	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
381	Q₈	—	4	4	no	—
382	Q₈	—	8	4	no	—
383	D₄	—	2	2	no	—
384	D₄	—	2	4	no	—
385	D₄	—	4	2	no	—
386	D₄	—	4	2	no	—
387	D₄	—	4	4	no	—
388	D₄	—	8	4	no	—
389	D₄	—	8	4	no	—
390	D₄	C₁₃×#124	1	4	yes	complemented
391	C₂×C₄	—	2	2	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	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	4	no	—
402	C₂×C₄	—	4	8	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	8	8	no	—
407	C₂×C₄	C₁₃×#120	1	2	yes	—
408	C₂×C₄	C₁₃×#120	1	2	yes	—
409	C₂×C₄	C₁₃×#135	1	2	yes	—
410	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
411	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
412	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
413	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
414	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
415	C₈	—	4	2	no	—
416	C₈	—	4	2	no	—
417	C₂²	—	2	4	no	—
418	C₂²	—	4	2	no	—
419	C₂²	—	4	4	no	—
420	C₂²	—	4	4	no	—
421	C₂²	—	4	2	no	—
422	C₂²	—	8	2	no	—
423	C₂²	—	8	4	no	—
424	C₂²	—	8	4	no	—
425	C₂²	—	8	2	no	—
426	C₂²	—	8	2	no	—
427	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
428	C₂²	C₁₃×#548	1	2	yes	—
429	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
430	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
431	C₂²	C₁₃×#576	1	2	yes	—
432	C₄	—	2	2	no	—
433	C₄	—	4	2	no	—
434	C₄	—	4	4	no	—
435	C₄	—	4	2	no	—
436	C₄	—	4	2	no	—
437	C₄	—	8	2	no	—
438	C₄	C₁₃×#449	1	4	yes	—
439	C₄	C₂×C₁₃×#124	1	1	yes	characteristic
440	C₄	C₁₃×#536	1	1	yes	characteristic
441	C₄	C₁₃×#548	1	2	yes	—
442	C₂	—	4	4	no	—
443	C₂	—	16	2	no	—
444	C₂	C₁₃×#2436	1	1	yes	characteristic
445	C₂	C₂×C₁₃×#449	1	1	yes	characteristic
446	C₂	C₁₃×#3008	1	1	yes	characteristic
447	C₂	C₁₃×#3361	1	2	yes	—
448	C₂	C₁₃×#3366	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#459	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#554	C₂	semidirect
2. C₂×C₁₃×#486	C₂	semidirect
4. C₁₃×#2548	C₂	semidirect
5. C₁₃×#2025	C₂	semidirect
6. C₁₃×#1987	C₂	semidirect
7. C₁₃×#1984	C₂	semidirect
8. C₁₃×#1879	C₂	semidirect
9. C₄×C₁₃×#102	C₂	semidirect
86. #25930	C₁₃	direct (N × H)
146. C₂×#554	C₂×C₁₃	semidirect
147. C₂×#486	C₂×C₁₃	semidirect
149. #2548	C₂×C₁₃	semidirect
150. #2025	C₂×C₁₃	semidirect
151. #1987	C₂×C₁₃	semidirect
152. #1984	C₂×C₁₃	semidirect
153. #1879	C₂×C₁₃	semidirect
154. C₄×#102	C₂×C₁₃	semidirect
175. D₄×C₁₃	#124	semidirect
369. C₁₃	#25930	direct (N × H)
390. D₄	C₁₃×#124	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#554	2
C₂×C₁₃×#486	2
C₂×C₁₃×#459	2
C₁₃×#2548	2
C₁₃×#2025	2
C₁₃×#1987	2
C₁₃×#1984	2
C₁₃×#1879	2
C₄×C₁₃×#102	2
#25930	13

Subgroups — C13×#25930 #15712269

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25930 #15712269