Subgroups — C₁₃×#18759 #15705098

Order 3328.

1138 conjugacy classes of subgroups.

The subgroup lattice has 482 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	C₁₃×#3230	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3104	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3077	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1649	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1637	C₂	1	4	yes	maximal, complemented
7	C₁₃×#1549	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1487	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1478	C₂	1	1	yes	maximal, characteristic
10	C₂³×Q₈×C₁₃	—	2	1	no	—
11	D₄×Q₈×C₁₃	—	2	2	no	—
12	D₄×Q₈×C₁₃	—	2	2	no	—
13	D₄×Q₈×C₁₃	—	2	2	no	—
14	D₄×Q₈×C₁₃	C₂²	1	4	yes	—
15	C₁₃×#533	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
19	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
20	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₃	—	2	1	no	—
22	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
23	C₁₃×#500	C₂²	1	2	yes	complemented
24	C₁₃×#487	C₂²	1	2	yes	complemented
25	C₁₃×#484	—	2	1	no	—
26	C₁₃×#484	—	2	2	no	—
27	C₁₃×#478	—	2	2	no	—
28	C₁₃×#477	—	2	2	no	—
29	C₁₃×#477	C₂²	1	2	yes	complemented
30	C₁₃×#476	C₂²	1	2	yes	—
31	C₁₃×#474	C₂²	1	2	yes	—
32	C₁₃×#462	C₂²	1	2	yes	complemented
33	C₁₃×#451	—	2	1	no	—
34	C₄×C₁₃×Q₁₆	—	2	2	no	—
35	C₁₃×#431	C₂²	1	1	yes	characteristic
36	C₁₃×#431	C₂²	1	1	yes	characteristic
37	C₁₃×#428	—	2	1	no	—
38	C₁₃×#423	C₂²	1	1	yes	characteristic
39	C₁₃×#418	—	2	1	no	—
40	C₁₃×#332	C₂²	1	4	yes	complemented
41	C₁₃×Q₈⋊C₈	C₂²	1	4	yes	complemented
42	C₁₃×D₄⋊C₈	C₂²	1	4	yes	—
43	C₂²×Q₈×C₁₃	—	2	2	no	—
44	C₂²×Q₈×C₁₃	—	2	4	no	—
45	C₂²×Q₈×C₁₃	—	2	4	no	—
46	C₂²×Q₈×C₁₃	—	2	1	no	—
47	C₂²×Q₈×C₁₃	—	4	8	no	—
48	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
49	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₁₃	—	2	2	no	—
51	C₂³×C₄×C₁₃	—	2	1	no	—
52	C₂×C₁₃×Q₁₆	—	2	2	no	—
53	C₂×C₁₃×M₁₆	—	2	1	no	—
54	C₁₃×C₄⋊Q₈	—	2	4	no	—
55	C₁₃×C₄⋊Q₈	—	2	4	no	—
56	C₁₃×C₄⋊Q₈	—	2	1	no	—
57	C₁₃×C₄⋊Q₈	—	2	1	no	—
58	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
59	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
60	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
61	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
62	C₁₃×#125	—	2	1	no	—
63	C₁₃×C₂²⋊Q₈	—	2	4	no	—
64	C₁₃×C₂²⋊Q₈	—	2	8	no	—
65	C₁₃×C₂²⋊Q₈	—	2	4	no	—
66	C₁₃×C₂²⋊Q₈	—	2	8	no	—
67	C₁₃×C₂²⋊Q₈	—	2	1	no	—
68	C₁₃×C₂²⋊Q₈	—	2	1	no	—
69	C₄×Q₈×C₁₃	—	2	1	no	—
70	C₄×Q₈×C₁₃	—	2	1	no	—
71	C₄×Q₈×C₁₃	—	2	1	no	—
72	C₄×Q₈×C₁₃	—	2	1	no	—
73	C₄×Q₈×C₁₃	D₄	1	2	yes	—
74	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
75	C₄×D₄×C₁₃	—	2	4	no	—
76	C₄×D₄×C₁₃	—	2	4	no	—
77	C₄×D₄×C₁₃	—	2	1	no	—
78	C₄×D₄×C₁₃	—	2	1	no	—
79	C₄×D₄×C₁₃	D₄	1	2	yes	—
80	C₄×D₄×C₁₃	C₂³	1	2	yes	—
81	C₁₃×#117	—	2	1	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
83	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
84	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
85	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
86	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
87	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
88	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
89	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
90	C₂×C₄²×C₁₃	—	2	1	no	—
91	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
92	C₁₃×#107	—	2	2	no	—
93	C₁₃×#107	—	2	2	no	—
94	C₁₃×#107	—	2	4	no	—
95	C₁₃×#106	—	2	2	no	—
96	C₁₃×C₄⋊C₈	—	2	1	no	—
97	C₁₃×C₄⋊C₈	—	2	1	no	—
98	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
99	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
100	C₁₃×#103	—	2	2	no	—
101	C₁₃×#103	—	2	2	no	—
102	C₁₃×#103	—	2	4	no	—
103	C₁₃×#102	—	2	2	no	—
104	C₁₃×#102	—	2	2	no	—
105	C₁₃×C₂²⋊C₈	—	2	1	no	—
106	C₁₃×C₂²⋊C₈	—	2	1	no	—
107	C₄×C₈×C₁₃	—	2	1	no	—
108	C₄×C₈×C₁₃	C₂³	1	2	yes	—
109	#18759	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
110	C₂⁴×C₁₃	—	2	1	no	—
111	C₂×Q₈×C₁₃	—	2	4	no	—
112	C₂×Q₈×C₁₃	—	2	8	no	—
113	C₂×Q₈×C₁₃	—	2	1	no	—
114	C₂×Q₈×C₁₃	—	2	2	no	—
115	C₂×Q₈×C₁₃	—	2	2	no	—
116	C₂×Q₈×C₁₃	—	2	1	no	—
117	C₂×Q₈×C₁₃	—	2	1	no	—
118	C₂×Q₈×C₁₃	—	4	8	no	—
119	C₂×Q₈×C₁₃	—	4	4	no	—
120	C₂×Q₈×C₁₃	—	4	16	no	—
121	C₂×Q₈×C₁₃	—	4	8	no	—
122	C₂×Q₈×C₁₃	—	4	8	no	—
123	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
124	C₂×D₄×C₁₃	—	2	1	no	—
125	C₂×D₄×C₁₃	—	2	2	no	—
126	C₂×D₄×C₁₃	Q₁₆	1	4	yes	complemented
127	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₃	—	2	1	no	—
129	C₂²×C₄×C₁₃	—	2	8	no	—
130	C₂²×C₄×C₁₃	—	2	1	no	—
131	C₂²×C₄×C₁₃	—	2	2	no	—
132	C₂²×C₄×C₁₃	—	2	1	no	—
133	C₂²×C₄×C₁₃	—	2	2	no	—
134	C₂²×C₄×C₁₃	—	2	2	no	—
135	C₂²×C₄×C₁₃	—	4	8	no	—
136	C₂²×C₄×C₁₃	—	4	4	no	—
137	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₁₃×Q₁₆	—	4	4	no	—
141	C₁₃×M₁₆	—	4	2	no	—
142	C₂×C₈×C₁₃	—	2	2	no	—
143	C₂×C₈×C₁₃	—	2	2	no	—
144	C₂×C₈×C₁₃	—	2	2	no	—
145	C₁₃×C₄⋊C₄	—	2	8	no	—
146	C₁₃×C₄⋊C₄	—	2	2	no	—
147	C₁₃×C₄⋊C₄	—	2	2	no	—
148	C₁₃×C₄⋊C₄	—	2	1	no	—
149	C₁₃×C₄⋊C₄	—	2	1	no	—
150	C₁₃×C₄⋊C₄	—	2	2	no	—
151	C₁₃×C₄⋊C₄	—	2	2	no	—
152	C₁₃×C₄⋊C₄	—	2	2	no	—
153	C₁₃×C₄⋊C₄	—	2	1	no	—
154	C₁₃×C₄⋊C₄	—	2	1	no	—
155	C₁₃×C₄⋊C₄	—	2	1	no	—
156	C₁₃×C₄⋊C₄	—	2	1	no	—
157	C₁₃×C₄⋊C₄	—	4	1	no	—
158	C₁₃×C₄⋊C₄	—	4	1	no	—
159	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
160	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
161	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
162	C₁₃×C₂²⋊C₄	—	2	8	no	—
163	C₁₃×C₂²⋊C₄	—	2	2	no	—
164	C₁₃×C₂²⋊C₄	—	2	2	no	—
165	C₁₃×C₂²⋊C₄	—	4	1	no	—
166	C₄²×C₁₃	—	2	2	no	—
167	C₄²×C₁₃	—	2	2	no	—
168	C₄²×C₁₃	—	4	1	no	—
169	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
173	C₂×D₄×Q₈	C₂×C₁₃	1	1	yes	characteristic
174	#3230	C₂×C₁₃	1	1	yes	characteristic, complemented
175	#3104	C₂×C₁₃	1	1	yes	characteristic, complemented
176	#3077	C₂×C₁₃	1	1	yes	characteristic
177	#1649	C₂×C₁₃	1	4	yes	complemented
178	#1637	C₂×C₁₃	1	4	yes	complemented
179	#1549	C₂×C₁₃	1	1	yes	characteristic, complemented
180	#1487	C₂×C₁₃	1	1	yes	characteristic, complemented
181	#1478	C₂×C₁₃	1	1	yes	characteristic
182	C₂³×C₁₃	—	2	2	no	—
183	C₂³×C₁₃	—	2	4	no	—
184	C₂³×C₁₃	—	4	2	no	—
185	C₂³×C₁₃	—	4	2	no	—
186	C₂³×C₁₃	#120	1	1	yes	characteristic
187	Q₈×C₁₃	—	2	4	no	—
188	Q₈×C₁₃	—	2	2	no	—
189	Q₈×C₁₃	—	4	16	no	—
190	Q₈×C₁₃	—	4	4	no	—
191	Q₈×C₁₃	—	4	2	no	—
192	Q₈×C₁₃	—	4	4	no	—
193	Q₈×C₁₃	—	4	2	no	—
194	Q₈×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
195	D₄×C₁₃	—	2	2	no	—
196	D₄×C₁₃	—	2	4	no	—
197	D₄×C₁₃	C₂×Q₁₆	1	4	yes	—
198	C₂×C₄×C₁₃	—	2	4	no	—
199	C₂×C₄×C₁₃	—	2	2	no	—
200	C₂×C₄×C₁₃	—	2	2	no	—
201	C₂×C₄×C₁₃	—	2	2	no	—
202	C₂×C₄×C₁₃	—	2	4	no	—
203	C₂×C₄×C₁₃	—	2	2	no	—
204	C₂×C₄×C₁₃	—	4	1	no	—
205	C₂×C₄×C₁₃	—	4	16	no	—
206	C₂×C₄×C₁₃	—	4	4	no	—
207	C₂×C₄×C₁₃	—	4	2	no	—
208	C₂×C₄×C₁₃	—	4	4	no	—
209	C₂×C₄×C₁₃	—	4	2	no	—
210	C₂×C₄×C₁₃	—	4	4	no	—
211	C₂×C₄×C₁₃	—	4	1	no	—
212	C₂×C₄×C₁₃	—	4	1	no	—
213	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
214	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
215	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
216	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
217	C₂×C₄×C₁₃	#137	1	2	yes	—
218	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
221	C₈×C₁₃	—	4	2	no	—
222	C₈×C₁₃	—	4	2	no	—
223	C₈×C₁₃	—	4	2	no	—
224	C₂³×Q₈	—	2	1	no	—
225	D₄×Q₈	—	2	2	no	—
226	D₄×Q₈	—	2	2	no	—
227	D₄×Q₈	—	2	2	no	—
228	D₄×Q₈	C₂²×C₁₃	1	4	yes	—
229	#533	C₂²×C₁₃	1	1	yes	characteristic
230	C₂×C₄⋊Q₈	—	2	1	no	—
231	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
232	C₂×C₂²⋊Q₈	—	2	1	no	—
233	C₂×C₂²⋊Q₈	—	2	2	no	—
234	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
235	C₂×C₄×D₄	—	2	1	no	—
236	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
237	#500	C₂²×C₁₃	1	2	yes	complemented
238	#487	C₂²×C₁₃	1	2	yes	complemented
239	#484	—	2	1	no	—
240	#484	—	2	2	no	—
241	#478	—	2	2	no	—
242	#477	—	2	2	no	—
243	#477	C₂²×C₁₃	1	2	yes	complemented
244	#476	C₂²×C₁₃	1	2	yes	—
245	#474	C₂²×C₁₃	1	2	yes	—
246	#462	C₂²×C₁₃	1	2	yes	complemented
247	#451	—	2	1	no	—
248	C₄×Q₁₆	—	2	2	no	—
249	#431	C₂²×C₁₃	1	1	yes	characteristic
250	#431	C₂²×C₁₃	1	1	yes	characteristic
251	#428	—	2	1	no	—
252	#423	C₂²×C₁₃	1	1	yes	characteristic
253	#418	—	2	1	no	—
254	#332	C₂²×C₁₃	1	4	yes	complemented
255	Q₈⋊C₈	C₂²×C₁₃	1	4	yes	complemented
256	D₄⋊C₈	C₂²×C₁₃	1	4	yes	—
257	C₂²×C₁₃	—	2	1	no	—
258	C₂²×C₁₃	—	2	1	no	—
259	C₂²×C₁₃	—	2	4	no	—
260	C₂²×C₁₃	—	4	8	no	—
261	C₂²×C₁₃	—	4	2	no	—
262	C₂²×C₁₃	—	4	2	no	—
263	C₂²×C₁₃	#451	1	2	yes	—
264	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
265	C₄×C₁₃	—	2	4	no	—
266	C₄×C₁₃	—	2	1	no	—
267	C₄×C₁₃	—	2	1	no	—
268	C₄×C₁₃	—	2	1	no	—
269	C₄×C₁₃	—	4	4	no	—
270	C₄×C₁₃	—	4	2	no	—
271	C₄×C₁₃	—	4	2	no	—
272	C₄×C₁₃	—	8	1	no	—
273	C₄×C₁₃	—	8	1	no	—
274	C₄×C₁₃	#451	1	2	yes	—
275	C₄×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
276	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
277	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
278	C₂²×Q₈	—	2	2	no	—
279	C₂²×Q₈	—	2	4	no	—
280	C₂²×Q₈	—	2	4	no	—
281	C₂²×Q₈	—	2	1	no	—
282	C₂²×Q₈	—	4	8	no	—
283	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
284	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
285	C₂³×C₄	—	2	2	no	—
286	C₂³×C₄	—	2	1	no	—
287	C₂×Q₁₆	—	2	2	no	—
288	C₂×M₁₆	—	2	1	no	—
289	C₄⋊Q₈	—	2	4	no	—
290	C₄⋊Q₈	—	2	4	no	—
291	C₄⋊Q₈	—	2	1	no	—
292	C₄⋊Q₈	—	2	1	no	—
293	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
294	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
295	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
296	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
297	#125	—	2	1	no	—
298	C₂²⋊Q₈	—	2	4	no	—
299	C₂²⋊Q₈	—	2	8	no	—
300	C₂²⋊Q₈	—	2	4	no	—
301	C₂²⋊Q₈	—	2	8	no	—
302	C₂²⋊Q₈	—	2	1	no	—
303	C₂²⋊Q₈	—	2	1	no	—
304	C₄×Q₈	—	2	1	no	—
305	C₄×Q₈	—	2	1	no	—
306	C₄×Q₈	—	2	1	no	—
307	C₄×Q₈	—	2	1	no	—
308	C₄×Q₈	D₄×C₁₃	1	2	yes	—
309	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
310	C₄×D₄	—	2	4	no	—
311	C₄×D₄	—	2	4	no	—
312	C₄×D₄	—	2	1	no	—
313	C₄×D₄	—	2	1	no	—
314	C₄×D₄	D₄×C₁₃	1	2	yes	—
315	C₄×D₄	C₂³×C₁₃	1	2	yes	—
316	#117	—	2	1	no	—
317	C₂×C₄⋊C₄	—	2	2	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
321	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
322	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
323	C₂×C₂²⋊C₄	—	2	2	no	—
324	C₂×C₂²⋊C₄	—	2	1	no	—
325	C₂×C₄²	—	2	1	no	—
326	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
327	#107	—	2	2	no	—
328	#107	—	2	2	no	—
329	#107	—	2	4	no	—
330	#106	—	2	2	no	—
331	C₄⋊C₈	—	2	1	no	—
332	C₄⋊C₈	—	2	1	no	—
333	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
334	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
335	#103	—	2	2	no	—
336	#103	—	2	2	no	—
337	#103	—	2	4	no	—
338	#102	—	2	2	no	—
339	#102	—	2	2	no	—
340	C₂²⋊C₈	—	2	1	no	—
341	C₂²⋊C₈	—	2	1	no	—
342	C₄×C₈	—	2	1	no	—
343	C₄×C₈	C₂³×C₁₃	1	2	yes	—
344	C₂×C₁₃	—	2	2	no	—
345	C₂×C₁₃	—	4	4	no	—
346	C₂×C₁₃	C₂×#451	1	1	yes	characteristic
347	C₂×C₁₃	#3003	1	1	yes	characteristic
348	C₂×C₁₃	#3020	1	1	yes	characteristic
349	C₂⁴	—	2	1	no	—
350	C₂×Q₈	—	2	4	no	—
351	C₂×Q₈	—	2	8	no	—
352	C₂×Q₈	—	2	1	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	2	2	no	—
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	4	8	no	—
358	C₂×Q₈	—	4	4	no	—
359	C₂×Q₈	—	4	16	no	—
360	C₂×Q₈	—	4	8	no	—
361	C₂×Q₈	—	4	8	no	—
362	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	C₁₃×Q₁₆	1	4	yes	complemented
366	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	8	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	4	8	no	—
375	C₂²×C₄	—	4	4	no	—
376	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
377	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
378	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
379	Q₁₆	—	4	4	no	—
380	M₁₆	—	4	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	2	no	—
384	C₄⋊C₄	—	2	8	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	4	1	no	—
397	C₄⋊C₄	—	4	1	no	—
398	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
399	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
400	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
401	C₂²⋊C₄	—	2	8	no	—
402	C₂²⋊C₄	—	2	2	no	—
403	C₂²⋊C₄	—	2	2	no	—
404	C₂²⋊C₄	—	4	1	no	—
405	C₄²	—	2	2	no	—
406	C₄²	—	2	2	no	—
407	C₄²	—	4	1	no	—
408	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
409	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
410	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
411	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
412	C₁₃	#18759	1	1	yes	characteristic, direct product factor, Sylow
413	C₂³	—	2	4	no	—
414	C₂³	—	2	2	no	—
415	C₂³	—	4	2	no	—
416	C₂³	—	4	2	no	—
417	C₂³	C₁₃×#120	1	1	yes	characteristic
418	Q₈	—	2	4	no	—
419	Q₈	—	2	2	no	—
420	Q₈	—	4	16	no	—
421	Q₈	—	4	4	no	—
422	Q₈	—	4	2	no	—
423	Q₈	—	4	4	no	—
424	Q₈	—	4	2	no	—
425	Q₈	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
426	D₄	—	2	4	no	—
427	D₄	—	2	2	no	—
428	D₄	C₂×C₁₃×Q₁₆	1	4	yes	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	16	no	—
437	C₂×C₄	—	4	4	no	—
438	C₂×C₄	—	4	4	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	4	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
445	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
446	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
447	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
448	C₂×C₄	C₁₃×#137	1	2	yes	—
449	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
450	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
451	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
452	C₈	—	4	2	no	—
453	C₈	—	4	2	no	—
454	C₈	—	4	2	no	—
455	C₂²	—	2	1	no	—
456	C₂²	—	2	1	no	—
457	C₂²	—	2	4	no	—
458	C₂²	—	4	8	no	—
459	C₂²	—	4	2	no	—
460	C₂²	—	4	2	no	—
461	C₂²	C₁₃×#451	1	2	yes	—
462	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
463	C₄	—	2	1	no	—
464	C₄	—	2	1	no	—
465	C₄	—	2	4	no	—
466	C₄	—	2	1	no	—
467	C₄	—	4	2	no	—
468	C₄	—	4	4	no	—
469	C₄	—	4	2	no	—
470	C₄	—	8	1	no	—
471	C₄	—	8	1	no	—
472	C₄	C₁₃×#451	1	2	yes	—
473	C₄	C₂²×C₁₃×Q₁₆	1	1	yes	characteristic
474	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
475	C₄	C₂×C₁₃×#137	1	1	yes	characteristic
476	C₂	—	2	2	no	—
477	C₂	—	4	4	no	—
478	C₂	C₂×C₁₃×#451	1	1	yes	characteristic
479	C₂	C₁₃×#3003	1	1	yes	characteristic
480	C₂	C₁₃×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#3230	C₂	semidirect
3. C₁₃×#3104	C₂	semidirect
5. C₁₃×#1649	C₂	semidirect
6. C₁₃×#1637	C₂	semidirect
7. C₁₃×#1549	C₂	semidirect
8. C₁₃×#1487	C₂	semidirect
23. C₁₃×#500	C₂²	semidirect
24. C₁₃×#487	C₂²	semidirect
29. C₁₃×#477	C₂²	semidirect
32. C₁₃×#462	C₂²	semidirect
40. C₁₃×#332	C₂²	semidirect
41. C₁₃×Q₈⋊C₈	C₂²	semidirect
109. #18759	C₁₃	direct (N × H)
126. C₂×D₄×C₁₃	Q₁₆	semidirect
174. #3230	C₂×C₁₃	semidirect
175. #3104	C₂×C₁₃	semidirect
177. #1649	C₂×C₁₃	semidirect
178. #1637	C₂×C₁₃	semidirect
179. #1549	C₂×C₁₃	semidirect
180. #1487	C₂×C₁₃	semidirect
237. #500	C₂²×C₁₃	semidirect
238. #487	C₂²×C₁₃	semidirect
243. #477	C₂²×C₁₃	semidirect
246. #462	C₂²×C₁₃	semidirect
254. #332	C₂²×C₁₃	semidirect
255. Q₈⋊C₈	C₂²×C₁₃	semidirect
365. C₂×D₄	C₁₃×Q₁₆	semidirect
412. C₁₃	#18759	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×D₄×Q₈×C₁₃	2
C₁₃×#3230	2
C₁₃×#3104	2
C₁₃×#3077	2
C₁₃×#1649	2
C₁₃×#1637	2
C₁₃×#1549	2
C₁₃×#1487	2
C₁₃×#1478	2
#18759	13

Subgroups — C13×#18759 #15705098

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18759 #15705098