Subgroups — C₁₃×#18717 #15705056

Order 3328.

984 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×#3548	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3230	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3227	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3152	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1632	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1631	C₂	1	4	yes	maximal, complemented
7	C₁₃×#1543	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1485	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1484	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#137	—	2	2	no	—
11	C₁₃×#562	—	2	2	no	—
12	C₁₃×#554	—	2	1	no	—
13	C₁₃×#554	C₂²	1	2	yes	—
14	C₁₃×#550	—	2	1	no	—
15	C₁₃×#550	C₂²	1	2	yes	—
16	C₁₃×#547	—	2	1	no	—
17	C₁₃×#547	—	2	1	no	—
18	C₁₃×#540	—	2	2	no	—
19	C₁₃×#537	—	2	2	no	—
20	C₁₃×#537	—	2	2	no	—
21	C₁₃×#533	C₂²	1	1	yes	characteristic
22	C₁₃×#532	C₂²	1	1	yes	characteristic
23	C₁₃×#532	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₁₃×#500	—	2	1	no	—
26	C₁₃×#498	—	2	1	no	—
27	C₁₃×#497	—	2	2	no	—
28	C₁₃×#494	C₂²	1	2	yes	—
29	C₁₃×#492	C₂²	1	2	yes	—
30	C₁₃×#487	—	2	1	no	—
31	C₁₃×#486	—	2	1	no	—
32	C₁₃×#484	—	2	2	no	—
33	C₁₃×#481	—	2	2	no	—
34	C₁₃×#477	C₂²	1	4	yes	—
35	C₁₃×#476	C₂²	1	4	yes	—
36	C₁₃×#431	C₂²	1	1	yes	characteristic
37	C₁₃×#431	C₂²	1	1	yes	characteristic
38	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
39	C₁₃×#333	C₂²	1	2	yes	—
40	C₁₃×#331	C₂²	1	2	yes	—
41	C₁₃×Q₈⋊C₈	C₂²	1	4	yes	—
42	C₁₃×D₄⋊C₈	C₂²	1	4	yes	—
43	C₂×C₁₃×#41	—	2	2	no	—
44	C₂×C₁₃×#41	—	2	2	no	—
45	C₂×C₁₃×#41	—	2	1	no	—
46	C₂×C₁₃×#41	D₄	1	2	yes	—
47	C₂²×Q₈×C₁₃	—	2	1	no	—
48	C₁₃×#137	—	4	8	no	—
49	C₂×C₁₃×Q₁₆	—	2	4	no	—
50	C₂×C₁₃×SD₁₆	—	2	4	no	—
51	C₂×C₁₃×M₁₆	—	2	1	no	—
52	C₁₃×C₄⋊Q₈	—	2	1	no	—
53	C₁₃×C₄⋊Q₈	—	2	1	no	—
54	C₁₃×C₄⋊Q₈	—	2	1	no	—
55	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
56	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
57	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
58	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
59	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
60	C₁₃×#127	—	2	2	no	—
61	C₁₃×#127	D₄	1	1	yes	characteristic
62	C₁₃×#127	C₂³	1	1	yes	characteristic
63	C₁₃×#125	—	2	2	no	—
64	C₁₃×#125	—	2	1	no	—
65	C₁₃×#124	—	2	1	no	—
66	C₁₃×#124	D₄	1	2	yes	—
67	C₁₃×#123	—	2	4	no	—
68	C₁₃×#123	—	2	4	no	—
69	C₁₃×C₂²⋊Q₈	—	2	2	no	—
70	C₁₃×C₂²⋊Q₈	—	2	4	no	—
71	C₁₃×C₂²⋊Q₈	—	2	2	no	—
72	C₁₃×C₂²⋊Q₈	—	2	4	no	—
73	C₁₃×C₂²⋊Q₈	—	2	1	no	—
74	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
75	C₁₃×#121	—	2	4	no	—
76	C₁₃×#121	—	2	4	no	—
77	C₁₃×#121	—	2	2	no	—
78	C₁₃×#121	—	2	4	no	—
79	C₁₃×#121	—	2	4	no	—
80	C₁₃×#121	—	2	1	no	—
81	C₁₃×#121	—	2	1	no	—
82	C₁₃×#121	—	2	1	no	—
83	C₁₃×#121	—	2	2	no	—
84	C₁₃×#121	D₄	1	2	yes	—
85	C₄×Q₈×C₁₃	—	2	1	no	—
86	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
87	C₄×D₄×C₁₃	—	2	2	no	—
88	C₄×D₄×C₁₃	—	2	2	no	—
89	C₄×D₄×C₁₃	—	2	1	no	—
90	C₄×D₄×C₁₃	—	2	1	no	—
91	C₄×D₄×C₁₃	—	2	1	no	—
92	C₄×D₄×C₁₃	C₂³	1	2	yes	—
93	C₁₃×#117	—	2	1	no	—
94	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
95	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
96	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
97	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
98	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
99	C₁₃×#107	—	2	4	no	—
100	C₁₃×#106	—	2	4	no	—
101	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
102	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
103	C₁₃×#103	—	2	4	no	—
104	C₁₃×#102	—	2	4	no	—
105	C₁₃×C₂²⋊C₈	—	2	1	no	—
106	C₁₃×C₂²⋊C₈	—	2	1	no	—
107	C₁₃×#97	—	2	1	no	—
108	C₄×C₈×C₁₃	—	2	1	no	—
109	C₄×C₈×C₁₃	—	2	1	no	—
110	C₄×C₈×C₁₃	C₂³	1	2	yes	—
111	#18717	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
112	C₁₃×#41	—	4	4	no	—
113	C₁₃×#41	—	8	2	no	—
114	C₁₃×#41	—	8	4	no	—
115	C₁₃×#41	—	8	4	no	—
116	C₂×Q₈×C₁₃	—	2	1	no	—
117	C₂×Q₈×C₁₃	—	2	1	no	—
118	C₂×Q₈×C₁₃	—	2	2	no	—
119	C₂×Q₈×C₁₃	—	4	4	no	—
120	C₂×Q₈×C₁₃	—	4	1	no	—
121	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
122	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
123	C₂×D₄×C₁₃	—	2	4	no	—
124	C₂×D₄×C₁₃	—	2	4	no	—
125	C₂×D₄×C₁₃	—	2	2	no	—
126	C₂×D₄×C₁₃	—	2	2	no	—
127	C₂×D₄×C₁₃	—	2	1	no	—
128	C₂×D₄×C₁₃	—	2	1	no	—
129	C₂×D₄×C₁₃	—	2	1	no	—
130	C₂×D₄×C₁₃	—	2	1	no	—
131	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
132	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₁₃	—	2	4	no	—
134	C₂²×C₄×C₁₃	—	2	4	no	—
135	C₂²×C₄×C₁₃	—	2	2	no	—
136	C₂²×C₄×C₁₃	—	2	2	no	—
137	C₂²×C₄×C₁₃	—	4	1	no	—
138	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₁₃×Q₁₆	—	4	8	no	—
142	C₁₃×SD₁₆	—	4	8	no	—
143	C₁₃×M₁₆	—	2	4	no	—
144	C₂×C₈×C₁₃	—	2	2	no	—
145	C₂×C₈×C₁₃	—	2	2	no	—
146	C₂×C₈×C₁₃	—	2	2	no	—
147	C₁₃×C₄⋊C₄	—	2	4	no	—
148	C₁₃×C₄⋊C₄	—	2	4	no	—
149	C₁₃×C₄⋊C₄	—	2	1	no	—
150	C₁₃×C₄⋊C₄	—	2	1	no	—
151	C₁₃×C₄⋊C₄	—	2	1	no	—
152	C₁₃×C₄⋊C₄	—	2	1	no	—
153	C₁₃×C₄⋊C₄	—	2	2	no	—
154	C₁₃×C₄⋊C₄	—	2	1	no	—
155	C₁₃×C₄⋊C₄	—	2	1	no	—
156	C₁₃×C₄⋊C₄	—	2	2	no	—
157	C₁₃×C₄⋊C₄	—	2	2	no	—
158	C₁₃×C₄⋊C₄	—	2	2	no	—
159	C₁₃×C₄⋊C₄	—	4	1	no	—
160	C₁₃×C₄⋊C₄	—	4	1	no	—
161	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
162	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
163	C₁₃×C₂²⋊C₄	—	2	4	no	—
164	C₁₃×C₂²⋊C₄	—	2	4	no	—
165	C₁₃×C₂²⋊C₄	—	2	2	no	—
166	C₁₃×C₂²⋊C₄	—	2	2	no	—
167	C₁₃×C₂²⋊C₄	—	2	2	no	—
168	C₁₃×C₂²⋊C₄	—	2	2	no	—
169	C₁₃×C₂²⋊C₄	—	2	2	no	—
170	C₄²×C₁₃	—	2	2	no	—
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	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
175	#3548	C₂×C₁₃	1	1	yes	characteristic
176	#3230	C₂×C₁₃	1	1	yes	characteristic, complemented
177	#3227	C₂×C₁₃	1	1	yes	characteristic, complemented
178	#3152	C₂×C₁₃	1	1	yes	characteristic, complemented
179	#1632	C₂×C₁₃	1	4	yes	complemented
180	#1631	C₂×C₁₃	1	4	yes	complemented
181	#1543	C₂×C₁₃	1	1	yes	characteristic, complemented
182	#1485	C₂×C₁₃	1	1	yes	characteristic, complemented
183	#1484	C₂×C₁₃	1	1	yes	characteristic, complemented
184	C₂³×C₁₃	—	2	2	no	—
185	C₂³×C₁₃	—	2	2	no	—
186	C₂³×C₁₃	#120	1	1	yes	characteristic
187	Q₈×C₁₃	—	2	4	no	—
188	Q₈×C₁₃	—	4	2	no	—
189	Q₈×C₁₃	—	4	4	no	—
190	Q₈×C₁₃	—	4	2	no	—
191	Q₈×C₁₃	—	8	1	no	—
192	Q₈×C₁₃	—	8	2	no	—
193	D₄×C₁₃	—	2	4	no	—
194	D₄×C₁₃	—	4	2	no	—
195	D₄×C₁₃	—	4	2	no	—
196	D₄×C₁₃	—	4	2	no	—
197	D₄×C₁₃	—	4	2	no	—
198	D₄×C₁₃	—	8	1	no	—
199	D₄×C₁₃	—	8	2	no	—
200	D₄×C₁₃	—	8	2	no	—
201	D₄×C₁₃	—	8	4	no	—
202	D₄×C₁₃	—	8	4	no	—
203	C₂×C₄×C₁₃	—	2	2	no	—
204	C₂×C₄×C₁₃	—	2	2	no	—
205	C₂×C₄×C₁₃	—	2	2	no	—
206	C₂×C₄×C₁₃	—	2	2	no	—
207	C₂×C₄×C₁₃	—	2	2	no	—
208	C₂×C₄×C₁₃	—	2	2	no	—
209	C₂×C₄×C₁₃	—	2	2	no	—
210	C₂×C₄×C₁₃	—	4	4	no	—
211	C₂×C₄×C₁₃	—	4	4	no	—
212	C₂×C₄×C₁₃	—	4	2	no	—
213	C₂×C₄×C₁₃	—	8	4	no	—
214	C₂×C₄×C₁₃	—	8	4	no	—
215	C₂×C₄×C₁₃	—	8	2	no	—
216	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
217	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
218	C₂×C₄×C₁₃	#120	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	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
222	C₈×C₁₃	—	2	4	no	—
223	C₈×C₁₃	—	4	2	no	—
224	C₈×C₁₃	—	4	2	no	—
225	C₂×#137	—	2	2	no	—
226	#562	—	2	2	no	—
227	#554	—	2	1	no	—
228	#554	C₂²×C₁₃	1	2	yes	—
229	#550	—	2	1	no	—
230	#550	C₂²×C₁₃	1	2	yes	—
231	#547	—	2	1	no	—
232	#547	—	2	1	no	—
233	#540	—	2	2	no	—
234	#537	—	2	2	no	—
235	#537	—	2	2	no	—
236	#533	C₂²×C₁₃	1	1	yes	characteristic
237	#532	C₂²×C₁₃	1	1	yes	characteristic
238	#532	C₂²×C₁₃	1	1	yes	characteristic
239	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
240	#500	—	2	1	no	—
241	#498	—	2	1	no	—
242	#497	—	2	2	no	—
243	#494	C₂²×C₁₃	1	2	yes	—
244	#492	C₂²×C₁₃	1	2	yes	—
245	#487	—	2	1	no	—
246	#486	—	2	1	no	—
247	#484	—	2	2	no	—
248	#481	—	2	2	no	—
249	#477	C₂²×C₁₃	1	4	yes	—
250	#476	C₂²×C₁₃	1	4	yes	—
251	#431	C₂²×C₁₃	1	1	yes	characteristic
252	#431	C₂²×C₁₃	1	1	yes	characteristic
253	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
254	#333	C₂²×C₁₃	1	2	yes	—
255	#331	C₂²×C₁₃	1	2	yes	—
256	Q₈⋊C₈	C₂²×C₁₃	1	4	yes	—
257	D₄⋊C₈	C₂²×C₁₃	1	4	yes	—
258	C₂²×C₁₃	—	2	1	no	—
259	C₂²×C₁₃	—	2	1	no	—
260	C₂²×C₁₃	—	2	1	no	—
261	C₂²×C₁₃	—	4	2	no	—
262	C₂²×C₁₃	—	4	2	no	—
263	C₂²×C₁₃	—	4	2	no	—
264	C₂²×C₁₃	—	4	2	no	—
265	C₂²×C₁₃	—	4	2	no	—
266	C₂²×C₁₃	—	4	2	no	—
267	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
268	C₄×C₁₃	—	2	1	no	—
269	C₄×C₁₃	—	2	1	no	—
270	C₄×C₁₃	—	2	1	no	—
271	C₄×C₁₃	—	4	2	no	—
272	C₄×C₁₃	—	4	2	no	—
273	C₄×C₁₃	—	4	2	no	—
274	C₄×C₁₃	—	4	2	no	—
275	C₄×C₁₃	—	8	2	no	—
276	C₄×C₁₃	#453	1	2	yes	—
277	C₄×C₁₃	#577	1	2	yes	—
278	C₄×C₁₃	#578	1	2	yes	—
279	C₂×#41	—	2	2	no	—
280	C₂×#41	—	2	2	no	—
281	C₂×#41	—	2	1	no	—
282	C₂×#41	D₄×C₁₃	1	2	yes	—
283	C₂²×Q₈	—	2	1	no	—
284	#137	—	4	8	no	—
285	C₂×Q₁₆	—	2	4	no	—
286	C₂×SD₁₆	—	2	4	no	—
287	C₂×M₁₆	—	2	1	no	—
288	C₄⋊Q₈	—	2	1	no	—
289	C₄⋊Q₈	—	2	1	no	—
290	C₄⋊Q₈	—	2	1	no	—
291	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
292	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
293	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
294	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
295	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
296	#127	—	2	2	no	—
297	#127	D₄×C₁₃	1	1	yes	characteristic
298	#127	C₂³×C₁₃	1	1	yes	characteristic
299	#125	—	2	2	no	—
300	#125	—	2	1	no	—
301	#124	—	2	1	no	—
302	#124	D₄×C₁₃	1	2	yes	—
303	#123	—	2	4	no	—
304	#123	—	2	4	no	—
305	C₂²⋊Q₈	—	2	2	no	—
306	C₂²⋊Q₈	—	2	4	no	—
307	C₂²⋊Q₈	—	2	2	no	—
308	C₂²⋊Q₈	—	2	4	no	—
309	C₂²⋊Q₈	—	2	1	no	—
310	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
311	#121	—	2	4	no	—
312	#121	—	2	4	no	—
313	#121	—	2	2	no	—
314	#121	—	2	4	no	—
315	#121	—	2	4	no	—
316	#121	—	2	1	no	—
317	#121	—	2	1	no	—
318	#121	—	2	1	no	—
319	#121	—	2	2	no	—
320	#121	D₄×C₁₃	1	2	yes	—
321	C₄×Q₈	—	2	1	no	—
322	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
323	C₄×D₄	—	2	2	no	—
324	C₄×D₄	—	2	2	no	—
325	C₄×D₄	—	2	1	no	—
326	C₄×D₄	—	2	1	no	—
327	C₄×D₄	—	2	1	no	—
328	C₄×D₄	C₂³×C₁₃	1	2	yes	—
329	#117	—	2	1	no	—
330	C₂×C₄⋊C₄	—	2	2	no	—
331	C₂×C₄⋊C₄	—	2	2	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
335	#107	—	2	4	no	—
336	#106	—	2	4	no	—
337	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
338	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
339	#103	—	2	4	no	—
340	#102	—	2	4	no	—
341	C₂²⋊C₈	—	2	1	no	—
342	C₂²⋊C₈	—	2	1	no	—
343	#97	—	2	1	no	—
344	C₄×C₈	—	2	1	no	—
345	C₄×C₈	—	2	1	no	—
346	C₄×C₈	C₂³×C₁₃	1	2	yes	—
347	C₂×C₁₃	—	4	1	no	—
348	C₂×C₁₃	—	8	2	no	—
349	C₂×C₁₃	—	8	2	no	—
350	C₂×C₁₃	#3009	1	1	yes	characteristic
351	C₂×C₁₃	#3011	1	1	yes	characteristic
352	C₂×C₁₃	C₂×#453	1	1	yes	characteristic
353	#41	—	4	4	no	—
354	#41	—	8	2	no	—
355	#41	—	8	4	no	—
356	#41	—	8	4	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	—	2	1	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	4	4	no	—
361	C₂×Q₈	—	4	1	no	—
362	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
363	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
364	C₂×D₄	—	2	4	no	—
365	C₂×D₄	—	2	4	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	2	1	no	—
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	—	2	1	no	—
372	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
373	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
374	C₂²×C₄	—	2	4	no	—
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	4	1	no	—
379	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
380	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
381	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
382	Q₁₆	—	4	8	no	—
383	SD₁₆	—	4	8	no	—
384	M₁₆	—	2	4	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	2	no	—
388	C₄⋊C₄	—	2	4	no	—
389	C₄⋊C₄	—	2	4	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	4	1	no	—
401	C₄⋊C₄	—	4	1	no	—
402	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
403	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
404	C₂²⋊C₄	—	2	4	no	—
405	C₂²⋊C₄	—	2	4	no	—
406	C₂²⋊C₄	—	2	2	no	—
407	C₂²⋊C₄	—	2	2	no	—
408	C₂²⋊C₄	—	2	2	no	—
409	C₂²⋊C₄	—	2	2	no	—
410	C₂²⋊C₄	—	2	2	no	—
411	C₄²	—	2	2	no	—
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	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
416	C₁₃	#18717	1	1	yes	characteristic, direct product factor, Sylow
417	C₂³	—	2	2	no	—
418	C₂³	—	2	2	no	—
419	C₂³	C₁₃×#120	1	1	yes	characteristic
420	Q₈	—	2	4	no	—
421	Q₈	—	4	2	no	—
422	Q₈	—	4	4	no	—
423	Q₈	—	4	2	no	—
424	Q₈	—	8	1	no	—
425	Q₈	—	8	2	no	—
426	D₄	—	2	4	no	—
427	D₄	—	4	2	no	—
428	D₄	—	4	2	no	—
429	D₄	—	4	2	no	—
430	D₄	—	4	2	no	—
431	D₄	—	8	1	no	—
432	D₄	—	8	2	no	—
433	D₄	—	8	2	no	—
434	D₄	—	8	4	no	—
435	D₄	—	8	4	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	4	4	no	—
444	C₂×C₄	—	4	4	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	8	4	no	—
447	C₂×C₄	—	8	4	no	—
448	C₂×C₄	—	8	2	no	—
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	C₂²×D₄×C₁₃	1	1	yes	characteristic
453	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
454	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
455	C₈	—	2	4	no	—
456	C₈	—	4	2	no	—
457	C₈	—	4	2	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	4	2	no	—
462	C₂²	—	4	2	no	—
463	C₂²	—	4	2	no	—
464	C₂²	—	4	2	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	4	2	no	—
467	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
468	C₄	—	2	1	no	—
469	C₄	—	2	1	no	—
470	C₄	—	2	1	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×#453	1	2	yes	—
477	C₄	C₁₃×#577	1	2	yes	—
478	C₄	C₁₃×#578	1	2	yes	—
479	C₂	—	4	1	no	—
480	C₂	—	8	2	no	—
481	C₂	—	8	2	no	—
482	C₂	C₁₃×#3009	1	1	yes	characteristic
483	C₂	C₁₃×#3011	1	1	yes	characteristic
484	C₂	C₂×C₁₃×#453	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#3548	C₂
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×#3227	C₂	semidirect
4. C₁₃×#3152	C₂	semidirect
5. C₁₃×#1632	C₂	semidirect
6. C₁₃×#1631	C₂	semidirect
7. C₁₃×#1543	C₂	semidirect
8. C₁₃×#1485	C₂	semidirect
9. C₁₃×#1484	C₂	semidirect
111. #18717	C₁₃	direct (N × H)
176. #3230	C₂×C₁₃	semidirect
177. #3227	C₂×C₁₃	semidirect
178. #3152	C₂×C₁₃	semidirect
179. #1632	C₂×C₁₃	semidirect
180. #1631	C₂×C₁₃	semidirect
181. #1543	C₂×C₁₃	semidirect
182. #1485	C₂×C₁₃	semidirect
183. #1484	C₂×C₁₃	semidirect
416. C₁₃	#18717	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×#3548	2
C₁₃×#3230	2
C₁₃×#3227	2
C₁₃×#3152	2
C₁₃×#1632	2
C₁₃×#1631	2
C₁₃×#1543	2
C₁₃×#1485	2
C₁₃×#1484	2
#18717	13

Subgroups — C13×#18717 #15705056

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18717 #15705056