Subgroups — C₁₃×#25838 #15712177

Order 3328.

1266 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#500	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#474	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2546	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2057	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1988	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1984	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1862	C₂	1	4	yes	maximal
9	C₄×C₁₃×#102	C₂	1	1	yes	maximal, characteristic
10	C₂³×Q₈×C₁₃	—	2	1	no	—
11	D₄×Q₈×C₁₃	—	2	4	no	—
12	D₄×Q₈×C₁₃	—	2	4	no	—
13	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
14	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
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	C₁₃×#500	—	2	4	no	—
23	C₁₃×#474	—	2	4	no	—
24	C₂×C₁₃×#107	C₂²	1	2	yes	—
25	C₂×C₁₃×#107	C₂²	1	4	yes	—
26	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#102	C₂²	1	2	yes	—
28	C₂×C₁₃×#102	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×#398	—	2	2	no	—
31	C₁₃×#391	—	2	1	no	—
32	C₁₃×#389	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	8	no	—
38	C₂²×Q₈×C₁₃	—	2	2	no	—
39	C₂²×Q₈×C₁₃	—	2	1	no	—
40	C₂²×Q₈×C₁₃	—	2	1	no	—
41	C₂²×Q₈×C₁₃	—	4	4	no	—
42	C₂²×Q₈×C₁₃	—	4	4	no	—
43	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
44	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₃	—	2	2	no	—
46	C₂³×C₄×C₁₃	—	2	1	no	—
47	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
49	C₁₃×C₄⋊Q₈	—	2	4	no	—
50	C₁₃×C₄⋊Q₈	—	2	4	no	—
51	C₁₃×C₄⋊Q₈	—	2	2	no	—
52	C₁₃×C₄⋊Q₈	—	2	2	no	—
53	C₁₃×C₄⋊Q₈	—	2	2	no	—
54	C₁₃×C₄⋊Q₈	—	4	4	no	—
55	C₁₃×C₄⋊Q₈	D₄	1	4	yes	—
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	2	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	1	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	2	yes	—
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
73	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
74	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
75	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
76	C₂×C₄²×C₁₃	—	2	1	no	—
77	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
78	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
79	C₁₃×#107	—	2	4	no	—
80	C₁₃×#107	—	2	8	no	—
81	C₁₃×C₄⋊C₈	—	2	2	no	—
82	C₁₃×#102	—	2	4	no	—
83	C₁₃×#102	Q₈	1	8	yes	complemented
84	C₄×C₈×C₁₃	—	2	2	no	—
85	C₁₃×#95	—	2	1	no	—
86	C₁₃×#95	—	2	4	no	—
87	#25838	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
88	C₂⁴×C₁₃	—	2	1	no	—
89	C₂×Q₈×C₁₃	—	2	8	no	—
90	C₂×Q₈×C₁₃	—	2	2	no	—
91	C₂×Q₈×C₁₃	—	2	4	no	—
92	C₂×Q₈×C₁₃	—	2	2	no	—
93	C₂×Q₈×C₁₃	—	4	4	no	—
94	C₂×Q₈×C₁₃	—	4	32	no	—
95	C₂×Q₈×C₁₃	—	4	2	no	—
96	C₂×Q₈×C₁₃	—	4	4	no	—
97	C₂×Q₈×C₁₃	—	4	2	no	—
98	C₂×Q₈×C₁₃	—	4	2	no	—
99	C₂×Q₈×C₁₃	—	4	2	no	—
100	C₂×Q₈×C₁₃	—	4	2	no	—
101	C₂×Q₈×C₁₃	D₈	1	4	yes	—
102	C₂×D₄×C₁₃	—	2	1	no	—
103	C₂×D₄×C₁₃	—	2	2	no	—
104	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
105	C₂×D₄×C₁₃	C₂×Q₈	1	4	yes	—
106	C₂²×C₄×C₁₃	—	2	8	no	—
107	C₂²×C₄×C₁₃	—	2	2	no	—
108	C₂²×C₄×C₁₃	—	2	2	no	—
109	C₂²×C₄×C₁₃	—	2	1	no	—
110	C₂²×C₄×C₁₃	—	2	4	no	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	—	4	4	no	—
113	C₂²×C₄×C₁₃	—	4	4	no	—
114	C₂²×C₄×C₁₃	—	4	2	no	—
115	C₂²×C₄×C₁₃	—	4	2	no	—
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	2	yes	—
119	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	C₂×Q₈	1	4	yes	complemented
126	C₁₃×C₄⋊C₄	—	2	8	no	—
127	C₁₃×C₄⋊C₄	—	2	4	no	—
128	C₁₃×C₄⋊C₄	—	2	4	no	—
129	C₁₃×C₄⋊C₄	—	2	2	no	—
130	C₁₃×C₄⋊C₄	—	2	2	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	—	4	2	no	—
136	C₁₃×C₄⋊C₄	—	4	8	no	—
137	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
138	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
139	C₁₃×C₄⋊C₄	C₂×Q₈	1	4	yes	complemented
140	C₁₃×C₂²⋊C₄	—	2	8	no	—
141	C₁₃×C₂²⋊C₄	—	2	4	no	—
142	C₄²×C₁₃	—	2	2	no	—
143	C₄²×C₁₃	—	2	2	no	—
144	C₄²×C₁₃	—	4	2	no	—
145	C₄²×C₁₃	C₂×D₄	1	2	yes	—
146	C₄²×C₁₃	C₂×D₄	1	2	yes	—
147	C₂×D₄×Q₈	C₂×C₁₃	1	1	yes	characteristic
148	C₂×#500	C₂×C₁₃	1	1	yes	characteristic, complemented
149	C₂×#474	C₂×C₁₃	1	1	yes	characteristic
150	#2546	C₂×C₁₃	1	1	yes	characteristic, complemented
151	#2057	C₂×C₁₃	1	4	yes	complemented
152	#1988	C₂×C₁₃	1	1	yes	characteristic, complemented
153	#1984	C₂×C₁₃	1	1	yes	characteristic, complemented
154	#1862	C₂×C₁₃	1	4	yes	—
155	C₄×#102	C₂×C₁₃	1	1	yes	characteristic
156	C₂³×C₁₃	—	2	2	no	—
157	C₂³×C₁₃	—	2	4	no	—
158	C₂³×C₁₃	—	4	1	no	—
159	C₂³×C₁₃	—	4	1	no	—
160	C₂³×C₁₃	—	4	2	no	—
161	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
162	Q₈×C₁₃	—	2	8	no	—
163	Q₈×C₁₃	—	4	16	no	—
164	Q₈×C₁₃	—	4	8	no	—
165	Q₈×C₁₃	—	8	4	no	—
166	D₄×C₁₃	—	2	2	no	—
167	D₄×C₁₃	—	2	4	no	—
168	D₄×C₁₃	C₄⋊Q₈	1	4	yes	complemented
169	C₂×C₄×C₁₃	—	2	2	no	—
170	C₂×C₄×C₁₃	—	2	2	no	—
171	C₂×C₄×C₁₃	—	2	2	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	2	4	no	—
174	C₂×C₄×C₁₃	—	2	2	no	—
175	C₂×C₄×C₁₃	—	2	4	no	—
176	C₂×C₄×C₁₃	—	2	4	no	—
177	C₂×C₄×C₁₃	—	4	16	no	—
178	C₂×C₄×C₁₃	—	4	2	no	—
179	C₂×C₄×C₁₃	—	4	2	no	—
180	C₂×C₄×C₁₃	—	4	1	no	—
181	C₂×C₄×C₁₃	—	4	2	no	—
182	C₂×C₄×C₁₃	—	4	1	no	—
183	C₂×C₄×C₁₃	—	4	2	no	—
184	C₂×C₄×C₁₃	—	4	8	no	—
185	C₂×C₄×C₁₃	—	4	2	no	—
186	C₂×C₄×C₁₃	—	4	2	no	—
187	C₂×C₄×C₁₃	—	4	2	no	—
188	C₂×C₄×C₁₃	#120	1	2	yes	—
189	C₂×C₄×C₁₃	#120	1	2	yes	—
190	C₂×C₄×C₁₃	C₂×D₈	1	4	yes	—
191	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
192	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
193	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
196	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
197	C₈×C₁₃	—	2	4	no	—
198	C₈×C₁₃	—	4	2	no	—
199	C₂³×Q₈	—	2	1	no	—
200	D₄×Q₈	—	2	4	no	—
201	D₄×Q₈	—	2	4	no	—
202	C₂×C₄⋊Q₈	—	2	1	no	—
203	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
204	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
205	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
206	C₂×C₂²⋊Q₈	—	2	1	no	—
207	C₂×C₂²⋊Q₈	—	2	2	no	—
208	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
209	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
210	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
211	#500	—	2	4	no	—
212	#474	—	2	4	no	—
213	C₂×#107	C₂²×C₁₃	1	2	yes	—
214	C₂×#107	C₂²×C₁₃	1	4	yes	—
215	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
216	C₂×#102	C₂²×C₁₃	1	2	yes	—
217	C₂×#102	C₂²×C₁₃	1	2	yes	—
218	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
219	#398	—	2	2	no	—
220	#391	—	2	1	no	—
221	#389	C₂²×C₁₃	1	4	yes	—
222	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
223	#340	C₂²×C₁₃	1	2	yes	—
224	#340	C₂²×C₁₃	1	4	yes	—
225	#336	C₂²×C₁₃	1	4	yes	—
226	C₂²×C₁₃	—	2	4	no	—
227	C₂²×C₁₃	—	4	4	no	—
228	C₂²×C₁₃	—	4	4	no	—
229	C₂²×C₁₃	—	4	2	no	—
230	C₂²×C₁₃	—	4	2	no	—
231	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
232	C₂²×C₁₃	D₄×Q₈	1	2	yes	—
233	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
234	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
235	C₂²×C₁₃	#578	1	2	yes	—
236	C₄×C₁₃	—	2	4	no	—
237	C₄×C₁₃	—	2	2	no	—
238	C₄×C₁₃	—	4	4	no	—
239	C₄×C₁₃	—	4	4	no	—
240	C₄×C₁₃	—	4	2	no	—
241	C₄×C₁₃	—	4	2	no	—
242	C₄×C₁₃	—	8	2	no	—
243	C₄×C₁₃	#447	1	4	yes	—
244	C₄×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
245	C₄×C₁₃	#536	1	1	yes	characteristic
246	C₄×C₁₃	D₄×Q₈	1	2	yes	—
247	C₂²×Q₈	—	2	8	no	—
248	C₂²×Q₈	—	2	2	no	—
249	C₂²×Q₈	—	2	1	no	—
250	C₂²×Q₈	—	2	1	no	—
251	C₂²×Q₈	—	4	4	no	—
252	C₂²×Q₈	—	4	4	no	—
253	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
254	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
255	C₂³×C₄	—	2	2	no	—
256	C₂³×C₄	—	2	1	no	—
257	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
258	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
259	C₄⋊Q₈	—	2	4	no	—
260	C₄⋊Q₈	—	2	4	no	—
261	C₄⋊Q₈	—	2	2	no	—
262	C₄⋊Q₈	—	2	2	no	—
263	C₄⋊Q₈	—	2	2	no	—
264	C₄⋊Q₈	—	4	4	no	—
265	C₄⋊Q₈	D₄×C₁₃	1	4	yes	—
266	C₂²⋊Q₈	—	2	8	no	—
267	C₂²⋊Q₈	—	2	16	no	—
268	C₄×Q₈	—	2	2	no	—
269	C₄×Q₈	—	2	2	no	—
270	C₄×D₄	—	2	4	no	—
271	C₄×D₄	—	2	4	no	—
272	C₄×D₄	—	2	2	no	—
273	C₄×D₄	D₄×C₁₃	1	4	yes	—
274	C₂×C₄⋊C₄	—	2	2	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	—	2	4	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
279	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
280	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
281	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
282	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
283	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
284	C₂×C₂²⋊C₄	—	2	2	no	—
285	C₂×C₂²⋊C₄	—	2	1	no	—
286	C₂×C₄²	—	2	1	no	—
287	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
288	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
289	#107	—	2	4	no	—
290	#107	—	2	8	no	—
291	C₄⋊C₈	—	2	2	no	—
292	#102	—	2	4	no	—
293	#102	Q₈×C₁₃	1	8	yes	complemented
294	C₄×C₈	—	2	2	no	—
295	#95	—	2	1	no	—
296	#95	—	2	4	no	—
297	C₂×C₁₃	—	4	4	no	—
298	C₂×C₁₃	#2434	1	1	yes	characteristic
299	C₂×C₁₃	C₂×#447	1	1	yes	characteristic
300	C₂×C₁₃	#3011	1	1	yes	characteristic
301	C₂×C₁₃	Q₈×D₈	1	2	yes	—
302	C₂×C₁₃	#3386	1	2	yes	—
303	C₂⁴	—	2	1	no	—
304	C₂×Q₈	—	2	8	no	—
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	—	2	4	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	4	4	no	—
309	C₂×Q₈	—	4	32	no	—
310	C₂×Q₈	—	4	2	no	—
311	C₂×Q₈	—	4	4	no	—
312	C₂×Q₈	—	4	2	no	—
313	C₂×Q₈	—	4	2	no	—
314	C₂×Q₈	—	4	2	no	—
315	C₂×Q₈	—	4	2	no	—
316	C₂×Q₈	C₁₃×D₈	1	4	yes	—
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
320	C₂×D₄	C₂×Q₈×C₁₃	1	4	yes	—
321	C₂²×C₄	—	2	8	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	4	4	no	—
328	C₂²×C₄	—	4	4	no	—
329	C₂²×C₄	—	4	2	no	—
330	C₂²×C₄	—	4	2	no	—
331	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
332	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
334	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
335	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	4	no	—
340	C₂×C₈	C₂×Q₈×C₁₃	1	4	yes	complemented
341	C₄⋊C₄	—	2	8	no	—
342	C₄⋊C₄	—	2	4	no	—
343	C₄⋊C₄	—	2	4	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	4	2	no	—
351	C₄⋊C₄	—	4	8	no	—
352	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
353	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
354	C₄⋊C₄	C₂×Q₈×C₁₃	1	4	yes	complemented
355	C₂²⋊C₄	—	2	8	no	—
356	C₂²⋊C₄	—	2	4	no	—
357	C₄²	—	2	2	no	—
358	C₄²	—	2	2	no	—
359	C₄²	—	4	2	no	—
360	C₄²	C₂×D₄×C₁₃	1	2	yes	—
361	C₄²	C₂×D₄×C₁₃	1	2	yes	—
362	C₁₃	#25838	1	1	yes	characteristic, direct product factor, Sylow
363	C₂³	—	2	2	no	—
364	C₂³	—	2	4	no	—
365	C₂³	—	4	1	no	—
366	C₂³	—	4	1	no	—
367	C₂³	—	4	2	no	—
368	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
369	Q₈	—	2	8	no	—
370	Q₈	—	4	16	no	—
371	Q₈	—	4	8	no	—
372	Q₈	—	8	4	no	—
373	D₄	—	2	2	no	—
374	D₄	—	2	4	no	—
375	D₄	C₁₃×C₄⋊Q₈	1	4	yes	complemented
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	4	16	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	8	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	C₁₃×#120	1	2	yes	—
396	C₂×C₄	C₁₃×#120	1	2	yes	—
397	C₂×C₄	C₂×C₁₃×D₈	1	4	yes	—
398	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
399	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
400	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
401	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
402	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
403	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
404	C₈	—	2	4	no	—
405	C₈	—	4	2	no	—
406	C₂²	—	2	4	no	—
407	C₂²	—	4	2	no	—
408	C₂²	—	4	4	no	—
409	C₂²	—	4	4	no	—
410	C₂²	—	4	2	no	—
411	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
412	C₂²	D₄×Q₈×C₁₃	1	2	yes	—
413	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
414	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
415	C₂²	C₁₃×#578	1	2	yes	—
416	C₄	—	2	2	no	—
417	C₄	—	2	4	no	—
418	C₄	—	4	2	no	—
419	C₄	—	4	4	no	—
420	C₄	—	4	4	no	—
421	C₄	—	4	2	no	—
422	C₄	—	8	2	no	—
423	C₄	C₁₃×#447	1	4	yes	—
424	C₄	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
425	C₄	C₁₃×#536	1	1	yes	characteristic
426	C₄	D₄×Q₈×C₁₃	1	2	yes	—
427	C₂	—	4	4	no	—
428	C₂	C₁₃×#2434	1	1	yes	characteristic
429	C₂	C₂×C₁₃×#447	1	1	yes	characteristic
430	C₂	C₁₃×#3011	1	1	yes	characteristic
431	C₂	Q₈×C₁₃×D₈	1	2	yes	—
432	C₂	C₁₃×#3386	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂³
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
2. C₂×C₁₃×#500	C₂	semidirect
4. C₁₃×#2546	C₂	semidirect
5. C₁₃×#2057	C₂	semidirect
6. C₁₃×#1988	C₂	semidirect
7. C₁₃×#1984	C₂	semidirect
83. C₁₃×#102	Q₈	semidirect
87. #25838	C₁₃	direct (N × H)
125. C₂×C₈×C₁₃	C₂×Q₈	semidirect
139. C₁₃×C₄⋊C₄	C₂×Q₈	semidirect
148. C₂×#500	C₂×C₁₃	semidirect
150. #2546	C₂×C₁₃	semidirect
151. #2057	C₂×C₁₃	semidirect
152. #1988	C₂×C₁₃	semidirect
153. #1984	C₂×C₁₃	semidirect
168. D₄×C₁₃	C₄⋊Q₈	semidirect
293. #102	Q₈×C₁₃	semidirect
340. C₂×C₈	C₂×Q₈×C₁₃	semidirect
354. C₄⋊C₄	C₂×Q₈×C₁₃	semidirect
362. C₁₃	#25838	direct (N × H)
375. D₄	C₁₃×C₄⋊Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×Q₈×C₁₃	2
C₂×C₁₃×#500	2
C₂×C₁₃×#474	2
C₁₃×#2546	2
C₁₃×#2057	2
C₁₃×#1988	2
C₁₃×#1984	2
C₁₃×#1862	2
C₄×C₁₃×#102	2
#25838	13

Subgroups — C13×#25838 #15712177

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25838 #15712177