Subgroups — C₁₃×#18398 #15704737

Order 3328.

930 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3507	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3229	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3226	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2546	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1609	C₂	1	8	yes	maximal, complemented
6	C₁₃×#1503	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1502	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1461	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#559	—	2	1	no	—
10	C₁₃×#557	—	2	1	no	—
11	C₁₃×#556	—	2	1	no	—
12	C₁₃×#556	—	2	2	no	—
13	C₁₃×#554	—	2	1	no	—
14	C₁₃×#552	—	2	2	no	—
15	C₁₃×#539	C₂²	1	4	yes	—
16	C₁₃×#536	—	2	1	no	—
17	C₁₃×#533	C₂²	1	1	yes	characteristic
18	C₁₃×#532	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
20	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₁₃×#529	—	2	2	no	—
22	C₁₃×#520	—	2	1	no	—
23	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₁₃×#500	—	2	1	no	—
25	C₁₃×#498	—	2	1	no	—
26	C₁₃×#487	—	2	1	no	—
27	C₁₃×#486	—	2	1	no	—
28	C₁₃×#483	C₂²	1	4	yes	—
29	C₁₃×#480	C₂²	1	4	yes	—
30	C₁₃×#475	—	2	2	no	—
31	C₁₃×#474	—	2	2	no	—
32	C₁₃×#431	C₂²	1	1	yes	characteristic
33	C₁₃×#431	C₂²	1	1	yes	characteristic
34	C₁₃×#398	C₂²	1	4	yes	—
35	C₁₃×#391	—	2	1	no	—
36	C₁₃×#389	—	2	2	no	—
37	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₁₃×#328	C₂²	1	4	yes	—
39	C₁₃×#327	C₂²	1	4	yes	—
40	C₁₃×#324	C₂²	1	4	yes	—
41	C₂×C₁₃×#41	—	2	1	no	—
42	C₂²×Q₈×C₁₃	—	2	1	no	—
43	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
44	C₁₃×C₄⋊Q₈	—	2	2	no	—
45	C₁₃×C₄⋊Q₈	—	2	1	no	—
46	C₁₃×C₄⋊Q₈	—	2	1	no	—
47	C₁₃×C₄⋊Q₈	—	2	1	no	—
48	C₁₃×C₄⋊Q₈	—	2	1	no	—
49	C₁₃×C₄⋊Q₈	—	4	4	no	—
50	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
51	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
52	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
53	C₁₃×#127	D₄	1	1	yes	characteristic
54	C₁₃×#126	—	2	4	no	—
55	C₁₃×#126	—	2	4	no	—
56	C₁₃×#125	—	2	2	no	—
57	C₁₃×#125	—	2	4	no	—
58	C₁₃×#125	—	2	1	no	—
59	C₁₃×#124	—	2	2	no	—
60	C₁₃×#124	—	2	2	no	—
61	C₁₃×#124	—	2	1	no	—
62	C₁₃×#123	—	2	4	no	—
63	C₁₃×#123	—	2	4	no	—
64	C₁₃×C₂²⋊Q₈	—	2	2	no	—
65	C₁₃×C₂²⋊Q₈	—	2	2	no	—
66	C₁₃×C₂²⋊Q₈	—	2	4	no	—
67	C₁₃×C₂²⋊Q₈	—	2	1	no	—
68	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
69	C₁₃×#121	—	2	1	no	—
70	C₁₃×#121	C₂³	1	2	yes	—
71	C₄×Q₈×C₁₃	—	2	2	no	—
72	C₄×Q₈×C₁₃	—	2	2	no	—
73	C₄×Q₈×C₁₃	—	2	1	no	—
74	C₄×Q₈×C₁₃	—	2	1	no	—
75	C₄×Q₈×C₁₃	—	2	1	no	—
76	C₄×Q₈×C₁₃	—	2	1	no	—
77	C₄×Q₈×C₁₃	—	2	1	no	—
78	C₄×Q₈×C₁₃	D₄	1	2	yes	—
79	C₄×D₄×C₁₃	—	2	2	no	—
80	C₄×D₄×C₁₃	—	2	2	no	—
81	C₄×D₄×C₁₃	—	2	4	no	—
82	C₄×D₄×C₁₃	—	2	1	no	—
83	C₄×D₄×C₁₃	D₄	1	2	yes	—
84	C₁₃×#117	—	2	2	no	—
85	C₁₃×#117	—	2	4	no	—
86	C₁₃×#117	—	2	1	no	—
87	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
88	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
89	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
90	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
91	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
94	C₂×C₄²×C₁₃	—	2	1	no	—
95	C₂×C₄²×C₁₃	D₄	1	2	yes	—
96	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
97	C₁₃×#107	—	2	4	no	—
98	C₁₃×#106	—	2	4	no	—
99	C₁₃×C₄⋊C₈	—	2	1	no	—
100	C₁₃×C₄⋊C₈	—	2	1	no	—
101	C₁₃×#103	—	2	4	no	—
102	C₁₃×#102	—	2	4	no	—
103	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
104	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
105	C₄×C₈×C₁₃	—	2	1	no	—
106	C₄×C₈×C₁₃	—	2	1	no	—
107	C₁₃×#95	—	2	4	no	—
108	C₁₃×#95	C₂³	1	2	yes	—
109	#18398	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
110	C₁₃×#41	—	4	2	no	—
111	C₁₃×#41	—	4	2	no	—
112	C₂×Q₈×C₁₃	—	2	1	no	—
113	C₂×Q₈×C₁₃	—	2	1	no	—
114	C₂×Q₈×C₁₃	—	2	1	no	—
115	C₂×Q₈×C₁₃	—	2	1	no	—
116	C₂×Q₈×C₁₃	—	2	2	no	—
117	C₂×Q₈×C₁₃	—	2	2	no	—
118	C₂×Q₈×C₁₃	—	4	1	no	—
119	C₂×Q₈×C₁₃	—	4	1	no	—
120	C₂×Q₈×C₁₃	—	4	2	no	—
121	C₂×Q₈×C₁₃	—	4	2	no	—
122	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
123	C₂×D₄×C₁₃	—	2	2	no	—
124	C₂×D₄×C₁₃	—	2	1	no	—
125	C₂×D₄×C₁₃	—	2	1	no	—
126	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₃	—	2	2	no	—
128	C₂²×C₄×C₁₃	—	2	4	no	—
129	C₂²×C₄×C₁₃	—	2	2	no	—
130	C₂²×C₄×C₁₃	—	2	2	no	—
131	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
136	C₂×C₈×C₁₃	—	2	2	no	—
137	C₂×C₈×C₁₃	—	2	2	no	—
138	C₁₃×C₄⋊C₄	—	2	4	no	—
139	C₁₃×C₄⋊C₄	—	2	4	no	—
140	C₁₃×C₄⋊C₄	—	2	4	no	—
141	C₁₃×C₄⋊C₄	—	2	4	no	—
142	C₁₃×C₄⋊C₄	—	2	1	no	—
143	C₁₃×C₄⋊C₄	—	2	1	no	—
144	C₁₃×C₄⋊C₄	—	2	1	no	—
145	C₁₃×C₄⋊C₄	—	2	1	no	—
146	C₁₃×C₄⋊C₄	—	2	2	no	—
147	C₁₃×C₄⋊C₄	—	2	1	no	—
148	C₁₃×C₄⋊C₄	—	2	1	no	—
149	C₁₃×C₄⋊C₄	—	2	2	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	2	no	—
154	C₁₃×C₄⋊C₄	—	4	8	no	—
155	C₁₃×C₄⋊C₄	—	4	1	no	—
156	C₁₃×C₄⋊C₄	—	4	1	no	—
157	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
158	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
159	C₁₃×C₂²⋊C₄	—	2	4	no	—
160	C₁₃×C₂²⋊C₄	—	2	4	no	—
161	C₁₃×C₂²⋊C₄	—	2	4	no	—
162	C₁₃×C₂²⋊C₄	—	2	2	no	—
163	C₁₃×C₂²⋊C₄	—	2	2	no	—
164	C₁₃×C₂²⋊C₄	—	2	2	no	—
165	C₄²×C₁₃	—	2	4	no	—
166	C₄²×C₁₃	—	2	2	no	—
167	C₄²×C₁₃	—	2	2	no	—
168	C₄²×C₁₃	—	2	2	no	—
169	C₄²×C₁₃	—	4	2	no	—
170	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
174	#3507	C₂×C₁₃	1	1	yes	characteristic
175	#3229	C₂×C₁₃	1	1	yes	characteristic, complemented
176	#3226	C₂×C₁₃	1	1	yes	characteristic
177	#2546	C₂×C₁₃	1	1	yes	characteristic, complemented
178	#1609	C₂×C₁₃	1	8	yes	complemented
179	#1503	C₂×C₁₃	1	1	yes	characteristic, complemented
180	#1502	C₂×C₁₃	1	1	yes	characteristic
181	#1461	C₂×C₁₃	1	1	yes	characteristic, complemented
182	C₂³×C₁₃	—	2	2	no	—
183	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
184	Q₈×C₁₃	—	4	2	no	—
185	Q₈×C₁₃	—	4	2	no	—
186	Q₈×C₁₃	—	4	2	no	—
187	Q₈×C₁₃	—	4	2	no	—
188	Q₈×C₁₃	—	4	2	no	—
189	Q₈×C₁₃	—	8	2	no	—
190	Q₈×C₁₃	—	8	2	no	—
191	D₄×C₁₃	—	4	2	no	—
192	D₄×C₁₃	—	4	2	no	—
193	D₄×C₁₃	—	4	2	no	—
194	D₄×C₁₃	—	4	2	no	—
195	D₄×C₁₃	—	4	2	no	—
196	C₂×C₄×C₁₃	—	2	2	no	—
197	C₂×C₄×C₁₃	—	2	4	no	—
198	C₂×C₄×C₁₃	—	2	2	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	2	no	—
203	C₂×C₄×C₁₃	—	2	2	no	—
204	C₂×C₄×C₁₃	—	2	2	no	—
205	C₂×C₄×C₁₃	—	4	1	no	—
206	C₂×C₄×C₁₃	—	4	2	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	2	no	—
211	C₂×C₄×C₁₃	—	4	2	no	—
212	C₂×C₄×C₁₃	—	4	2	no	—
213	C₂×C₄×C₁₃	—	8	4	no	—
214	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
215	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
216	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
217	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
218	C₂×C₄×C₁₃	#135	1	2	yes	—
219	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
220	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
222	C₈×C₁₃	—	4	2	no	—
223	C₈×C₁₃	—	4	2	no	—
224	#559	—	2	1	no	—
225	#557	—	2	1	no	—
226	#556	—	2	1	no	—
227	#556	—	2	2	no	—
228	#554	—	2	1	no	—
229	#552	—	2	2	no	—
230	#539	C₂²×C₁₃	1	4	yes	—
231	#536	—	2	1	no	—
232	#533	C₂²×C₁₃	1	1	yes	characteristic
233	#532	C₂²×C₁₃	1	1	yes	characteristic
234	C₂×C₄⋊Q₈	—	2	1	no	—
235	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
236	#529	—	2	2	no	—
237	#520	—	2	1	no	—
238	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
239	#500	—	2	1	no	—
240	#498	—	2	1	no	—
241	#487	—	2	1	no	—
242	#486	—	2	1	no	—
243	#483	C₂²×C₁₃	1	4	yes	—
244	#480	C₂²×C₁₃	1	4	yes	—
245	#475	—	2	2	no	—
246	#474	—	2	2	no	—
247	#431	C₂²×C₁₃	1	1	yes	characteristic
248	#431	C₂²×C₁₃	1	1	yes	characteristic
249	#398	C₂²×C₁₃	1	4	yes	—
250	#391	—	2	1	no	—
251	#389	—	2	2	no	—
252	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
253	#328	C₂²×C₁₃	1	4	yes	—
254	#327	C₂²×C₁₃	1	4	yes	—
255	#324	C₂²×C₁₃	1	4	yes	—
256	C₂²×C₁₃	—	2	1	no	—
257	C₂²×C₁₃	—	2	1	no	—
258	C₂²×C₁₃	—	4	2	no	—
259	C₂²×C₁₃	—	4	2	no	—
260	C₂²×C₁₃	—	4	2	no	—
261	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
262	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
263	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
264	C₄×C₁₃	—	2	1	no	—
265	C₄×C₁₃	—	2	1	no	—
266	C₄×C₁₃	—	2	1	no	—
267	C₄×C₁₃	—	4	4	no	—
268	C₄×C₁₃	—	4	2	no	—
269	C₄×C₁₃	—	4	2	no	—
270	C₄×C₁₃	—	4	2	no	—
271	C₄×C₁₃	—	4	2	no	—
272	C₄×C₁₃	—	4	2	no	—
273	C₄×C₁₃	—	8	2	no	—
274	C₄×C₁₃	#449	1	2	yes	—
275	C₄×C₁₃	#449	1	2	yes	—
276	C₄×C₁₃	#456	1	2	yes	—
277	C₂×#41	—	2	1	no	—
278	C₂²×Q₈	—	2	1	no	—
279	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
280	C₄⋊Q₈	—	2	2	no	—
281	C₄⋊Q₈	—	2	1	no	—
282	C₄⋊Q₈	—	2	1	no	—
283	C₄⋊Q₈	—	2	1	no	—
284	C₄⋊Q₈	—	2	1	no	—
285	C₄⋊Q₈	—	4	4	no	—
286	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
287	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
288	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
289	#127	D₄×C₁₃	1	1	yes	characteristic
290	#126	—	2	4	no	—
291	#126	—	2	4	no	—
292	#125	—	2	2	no	—
293	#125	—	2	4	no	—
294	#125	—	2	1	no	—
295	#124	—	2	2	no	—
296	#124	—	2	2	no	—
297	#124	—	2	1	no	—
298	#123	—	2	4	no	—
299	#123	—	2	4	no	—
300	C₂²⋊Q₈	—	2	2	no	—
301	C₂²⋊Q₈	—	2	2	no	—
302	C₂²⋊Q₈	—	2	4	no	—
303	C₂²⋊Q₈	—	2	1	no	—
304	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
305	#121	—	2	1	no	—
306	#121	C₂³×C₁₃	1	2	yes	—
307	C₄×Q₈	—	2	2	no	—
308	C₄×Q₈	—	2	2	no	—
309	C₄×Q₈	—	2	1	no	—
310	C₄×Q₈	—	2	1	no	—
311	C₄×Q₈	—	2	1	no	—
312	C₄×Q₈	—	2	1	no	—
313	C₄×Q₈	—	2	1	no	—
314	C₄×Q₈	D₄×C₁₃	1	2	yes	—
315	C₄×D₄	—	2	2	no	—
316	C₄×D₄	—	2	2	no	—
317	C₄×D₄	—	2	4	no	—
318	C₄×D₄	—	2	1	no	—
319	C₄×D₄	D₄×C₁₃	1	2	yes	—
320	#117	—	2	2	no	—
321	#117	—	2	4	no	—
322	#117	—	2	1	no	—
323	C₂×C₄⋊C₄	—	2	2	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	—	2	4	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
328	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
329	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
330	C₂×C₄²	—	2	1	no	—
331	C₂×C₄²	D₄×C₁₃	1	2	yes	—
332	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
333	#107	—	2	4	no	—
334	#106	—	2	4	no	—
335	C₄⋊C₈	—	2	1	no	—
336	C₄⋊C₈	—	2	1	no	—
337	#103	—	2	4	no	—
338	#102	—	2	4	no	—
339	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
340	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
341	C₄×C₈	—	2	1	no	—
342	C₄×C₈	—	2	1	no	—
343	#95	—	2	4	no	—
344	#95	C₂³×C₁₃	1	2	yes	—
345	C₂×C₁₃	—	2	1	no	—
346	C₂×C₁₃	—	2	1	no	—
347	C₂×C₁₃	—	8	2	no	—
348	C₂×C₁₃	C₂×#449	1	1	yes	characteristic
349	C₂×C₁₃	C₂×#456	1	1	yes	characteristic
350	C₂×C₁₃	#3028	1	1	yes	characteristic
351	#41	—	4	2	no	—
352	#41	—	4	2	no	—
353	C₂×Q₈	—	2	1	no	—
354	C₂×Q₈	—	2	1	no	—
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	2	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	4	1	no	—
360	C₂×Q₈	—	4	1	no	—
361	C₂×Q₈	—	4	2	no	—
362	C₂×Q₈	—	4	2	no	—
363	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	4	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
373	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
374	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
375	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
376	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₄⋊C₄	—	2	4	no	—
380	C₄⋊C₄	—	2	4	no	—
381	C₄⋊C₄	—	2	4	no	—
382	C₄⋊C₄	—	2	4	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	4	8	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	2	yes	—
400	C₂²⋊C₄	—	2	4	no	—
401	C₂²⋊C₄	—	2	4	no	—
402	C₂²⋊C₄	—	2	4	no	—
403	C₂²⋊C₄	—	2	2	no	—
404	C₂²⋊C₄	—	2	2	no	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₄²	—	2	4	no	—
407	C₄²	—	2	2	no	—
408	C₄²	—	2	2	no	—
409	C₄²	—	2	2	no	—
410	C₄²	—	4	2	no	—
411	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
412	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
413	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
414	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
415	C₁₃	#18398	1	1	yes	characteristic, direct product factor, Sylow
416	C₂³	—	2	2	no	—
417	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
418	Q₈	—	4	2	no	—
419	Q₈	—	4	2	no	—
420	Q₈	—	4	2	no	—
421	Q₈	—	4	2	no	—
422	Q₈	—	4	2	no	—
423	Q₈	—	8	2	no	—
424	Q₈	—	8	2	no	—
425	D₄	—	4	2	no	—
426	D₄	—	4	2	no	—
427	D₄	—	4	2	no	—
428	D₄	—	4	2	no	—
429	D₄	—	4	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	4	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	8	4	no	—
448	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
449	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
450	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
451	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
452	C₂×C₄	C₁₃×#135	1	2	yes	—
453	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
454	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
455	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
456	C₈	—	4	2	no	—
457	C₈	—	4	2	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	4	2	no	—
461	C₂²	—	4	2	no	—
462	C₂²	—	4	2	no	—
463	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
464	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
465	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
466	C₄	—	2	1	no	—
467	C₄	—	2	1	no	—
468	C₄	—	2	1	no	—
469	C₄	—	4	4	no	—
470	C₄	—	4	2	no	—
471	C₄	—	4	2	no	—
472	C₄	—	4	2	no	—
473	C₄	—	4	2	no	—
474	C₄	—	4	2	no	—
475	C₄	—	8	2	no	—
476	C₄	C₁₃×#449	1	2	yes	—
477	C₄	C₁₃×#449	1	2	yes	—
478	C₄	C₁₃×#456	1	2	yes	—
479	C₂	—	2	1	no	—
480	C₂	—	2	1	no	—
481	C₂	—	8	2	no	—
482	C₂	C₂×C₁₃×#449	1	1	yes	characteristic
483	C₂	C₂×C₁₃×#456	1	1	yes	characteristic
484	C₂	C₁₃×#3028	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#532	C₂²
LCS	G ▷ C₂²×C₄ ▷ 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×#3229	C₂	semidirect
4. C₁₃×#2546	C₂	semidirect
5. C₁₃×#1609	C₂	semidirect
6. C₁₃×#1503	C₂	semidirect
8. C₁₃×#1461	C₂	semidirect
109. #18398	C₁₃	direct (N × H)
175. #3229	C₂×C₁₃	semidirect
177. #2546	C₂×C₁₃	semidirect
178. #1609	C₂×C₁₃	semidirect
179. #1503	C₂×C₁₃	semidirect
181. #1461	C₂×C₁₃	semidirect
415. C₁₃	#18398	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3507	2
C₁₃×#3229	2
C₁₃×#3226	2
C₁₃×#2546	2
C₁₃×#1609	2
C₁₃×#1503	2
C₁₃×#1502	2
C₁₃×#1461	2
#18398	13

Subgroups — C13×#18398 #15704737

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18398 #15704737