Subgroups — C₁₃×#18723 #15705062

Order 3328.

932 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	C₁₃×#3548	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3229	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3206	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3141	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1643	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1642	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	C₁₃×#562	—	2	2	no	—
11	C₁₃×#554	—	2	1	no	—
12	C₁₃×#554	C₂²	1	2	yes	—
13	C₁₃×#550	—	2	1	no	—
14	C₁₃×#550	C₂²	1	2	yes	—
15	C₁₃×#547	—	2	1	no	—
16	C₁₃×#547	—	2	1	no	—
17	C₁₃×#540	—	2	2	no	—
18	C₁₃×#537	—	2	2	no	—
19	C₁₃×#537	—	2	2	no	—
20	C₁₃×#533	C₂²	1	1	yes	characteristic
21	C₁₃×#532	C₂²	1	1	yes	characteristic
22	C₁₃×#532	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₁₃×#498	—	2	1	no	—
25	C₁₃×#492	—	2	1	no	—
26	C₁₃×#489	—	2	2	no	—
27	C₁₃×#487	—	2	1	no	—
28	C₁₃×#487	—	2	1	no	—
29	C₁₃×#487	C₂²	1	2	yes	—
30	C₁₃×#486	C₂²	1	2	yes	—
31	C₁₃×#483	—	2	2	no	—
32	C₁₃×#475	C₂²	1	4	yes	—
33	C₁₃×#461	C₂²	1	4	yes	—
34	C₁₃×#448	—	2	2	no	—
35	C₁₃×#431	C₂²	1	1	yes	characteristic
36	C₁₃×#431	C₂²	1	1	yes	characteristic
37	C₁₃×#417	—	2	2	no	—
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	C₂×C₁₃×SD₁₆	—	2	4	no	—
49	C₂×C₁₃×M₁₆	—	2	1	no	—
50	C₁₃×C₄⋊Q₈	—	2	1	no	—
51	C₁₃×C₄⋊Q₈	—	2	1	no	—
52	C₁₃×C₄⋊Q₈	—	2	1	no	—
53	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
54	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
55	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
56	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
57	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
58	C₁₃×#127	—	2	2	no	—
59	C₁₃×#127	D₄	1	1	yes	characteristic
60	C₁₃×#127	C₂³	1	1	yes	characteristic
61	C₁₃×#125	—	2	2	no	—
62	C₁₃×#125	—	2	1	no	—
63	C₁₃×#124	—	2	1	no	—
64	C₁₃×#124	D₄	1	2	yes	—
65	C₁₃×#123	—	2	4	no	—
66	C₁₃×#123	—	2	4	no	—
67	C₁₃×C₂²⋊Q₈	—	2	2	no	—
68	C₁₃×C₂²⋊Q₈	—	2	4	no	—
69	C₁₃×C₂²⋊Q₈	—	2	2	no	—
70	C₁₃×C₂²⋊Q₈	—	2	4	no	—
71	C₁₃×C₂²⋊Q₈	—	2	1	no	—
72	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
73	C₁₃×#121	—	2	4	no	—
74	C₁₃×#121	—	2	4	no	—
75	C₁₃×#121	—	2	2	no	—
76	C₁₃×#121	—	2	4	no	—
77	C₁₃×#121	—	2	4	no	—
78	C₁₃×#121	—	2	1	no	—
79	C₁₃×#121	—	2	1	no	—
80	C₁₃×#121	—	2	1	no	—
81	C₁₃×#121	—	2	2	no	—
82	C₁₃×#121	D₄	1	2	yes	—
83	C₄×Q₈×C₁₃	—	2	1	no	—
84	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
85	C₄×D₄×C₁₃	—	2	2	no	—
86	C₄×D₄×C₁₃	—	2	2	no	—
87	C₄×D₄×C₁₃	—	2	1	no	—
88	C₄×D₄×C₁₃	—	2	1	no	—
89	C₄×D₄×C₁₃	—	2	1	no	—
90	C₄×D₄×C₁₃	C₂³	1	2	yes	—
91	C₁₃×#117	—	2	1	no	—
92	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
93	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
94	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
95	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
96	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
97	C₁₃×#106	—	2	4	no	—
98	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
99	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
100	C₁₃×#103	—	2	4	no	—
101	C₁₃×#103	—	2	4	no	—
102	C₁₃×#103	—	2	4	no	—
103	C₁₃×#102	—	2	4	no	—
104	C₁₃×C₂²⋊C₈	—	2	1	no	—
105	C₁₃×C₂²⋊C₈	—	2	1	no	—
106	C₁₃×#97	—	2	1	no	—
107	C₄×C₈×C₁₃	—	2	1	no	—
108	C₄×C₈×C₁₃	—	2	1	no	—
109	C₄×C₈×C₁₃	C₂³	1	2	yes	—
110	#18723	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
111	C₁₃×#41	—	4	4	no	—
112	C₁₃×#41	—	8	2	no	—
113	C₁₃×#41	—	8	4	no	—
114	C₁₃×#41	—	8	4	no	—
115	C₂×Q₈×C₁₃	—	2	1	no	—
116	C₂×Q₈×C₁₃	—	2	1	no	—
117	C₂×Q₈×C₁₃	—	2	2	no	—
118	C₂×Q₈×C₁₃	—	4	1	no	—
119	C₂×Q₈×C₁₃	—	8	2	no	—
120	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
121	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
122	C₂×D₄×C₁₃	—	2	4	no	—
123	C₂×D₄×C₁₃	—	2	4	no	—
124	C₂×D₄×C₁₃	—	2	2	no	—
125	C₂×D₄×C₁₃	—	2	2	no	—
126	C₂×D₄×C₁₃	—	2	1	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	C₂×D₄	1	2	yes	—
131	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₁₃	—	2	4	no	—
133	C₂²×C₄×C₁₃	—	2	4	no	—
134	C₂²×C₄×C₁₃	—	2	2	no	—
135	C₂²×C₄×C₁₃	—	2	2	no	—
136	C₂²×C₄×C₁₃	—	4	1	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×SD₁₆	—	8	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	4	no	—
146	C₁₃×C₄⋊C₄	—	2	4	no	—
147	C₁₃×C₄⋊C₄	—	2	1	no	—
148	C₁₃×C₄⋊C₄	—	2	1	no	—
149	C₁₃×C₄⋊C₄	—	2	1	no	—
150	C₁₃×C₄⋊C₄	—	2	1	no	—
151	C₁₃×C₄⋊C₄	—	2	2	no	—
152	C₁₃×C₄⋊C₄	—	2	1	no	—
153	C₁₃×C₄⋊C₄	—	2	1	no	—
154	C₁₃×C₄⋊C₄	—	2	2	no	—
155	C₁₃×C₄⋊C₄	—	2	2	no	—
156	C₁₃×C₄⋊C₄	—	2	2	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	2	yes	—
161	C₁₃×C₂²⋊C₄	—	2	4	no	—
162	C₁₃×C₂²⋊C₄	—	2	4	no	—
163	C₁₃×C₂²⋊C₄	—	2	2	no	—
164	C₁₃×C₂²⋊C₄	—	2	2	no	—
165	C₁₃×C₂²⋊C₄	—	2	2	no	—
166	C₁₃×C₂²⋊C₄	—	2	2	no	—
167	C₁₃×C₂²⋊C₄	—	2	2	no	—
168	C₄²×C₁₃	—	2	2	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	#3548	C₂×C₁₃	1	1	yes	characteristic
174	#3229	C₂×C₁₃	1	1	yes	characteristic, complemented
175	#3206	C₂×C₁₃	1	1	yes	characteristic, complemented
176	#3141	C₂×C₁₃	1	1	yes	characteristic, complemented
177	#1643	C₂×C₁₃	1	4	yes	complemented
178	#1642	C₂×C₁₃	1	4	yes	complemented
179	#1543	C₂×C₁₃	1	1	yes	characteristic, complemented
180	#1485	C₂×C₁₃	1	1	yes	characteristic, complemented
181	#1484	C₂×C₁₃	1	1	yes	characteristic, complemented
182	C₂³×C₁₃	—	2	2	no	—
183	C₂³×C₁₃	—	2	2	no	—
184	C₂³×C₁₃	#120	1	1	yes	characteristic
185	Q₈×C₁₃	—	2	4	no	—
186	Q₈×C₁₃	—	4	2	no	—
187	Q₈×C₁₃	—	4	2	no	—
188	Q₈×C₁₃	—	4	4	no	—
189	Q₈×C₁₃	—	8	1	no	—
190	Q₈×C₁₃	—	8	2	no	—
191	D₄×C₁₃	—	2	4	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	D₄×C₁₃	—	8	1	no	—
197	D₄×C₁₃	—	8	2	no	—
198	D₄×C₁₃	—	8	2	no	—
199	D₄×C₁₃	—	8	4	no	—
200	D₄×C₁₃	—	8	4	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	—	2	2	no	—
206	C₂×C₄×C₁₃	—	2	2	no	—
207	C₂×C₄×C₁₃	—	2	2	no	—
208	C₂×C₄×C₁₃	—	4	4	no	—
209	C₂×C₄×C₁₃	—	4	4	no	—
210	C₂×C₄×C₁₃	—	4	2	no	—
211	C₂×C₄×C₁₃	—	8	4	no	—
212	C₂×C₄×C₁₃	—	8	4	no	—
213	C₂×C₄×C₁₃	—	8	2	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	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
220	C₈×C₁₃	—	4	2	no	—
221	C₈×C₁₃	—	4	2	no	—
222	C₈×C₁₃	—	4	2	no	—
223	#562	—	2	2	no	—
224	#554	—	2	1	no	—
225	#554	C₂²×C₁₃	1	2	yes	—
226	#550	—	2	1	no	—
227	#550	C₂²×C₁₃	1	2	yes	—
228	#547	—	2	1	no	—
229	#547	—	2	1	no	—
230	#540	—	2	2	no	—
231	#537	—	2	2	no	—
232	#537	—	2	2	no	—
233	#533	C₂²×C₁₃	1	1	yes	characteristic
234	#532	C₂²×C₁₃	1	1	yes	characteristic
235	#532	C₂²×C₁₃	1	1	yes	characteristic
236	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
237	#498	—	2	1	no	—
238	#492	—	2	1	no	—
239	#489	—	2	2	no	—
240	#487	—	2	1	no	—
241	#487	—	2	1	no	—
242	#487	C₂²×C₁₃	1	2	yes	—
243	#486	C₂²×C₁₃	1	2	yes	—
244	#483	—	2	2	no	—
245	#475	C₂²×C₁₃	1	4	yes	—
246	#461	C₂²×C₁₃	1	4	yes	—
247	#448	—	2	2	no	—
248	#431	C₂²×C₁₃	1	1	yes	characteristic
249	#431	C₂²×C₁₃	1	1	yes	characteristic
250	#417	—	2	2	no	—
251	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
252	#333	C₂²×C₁₃	1	2	yes	—
253	#331	C₂²×C₁₃	1	2	yes	—
254	Q₈⋊C₈	C₂²×C₁₃	1	4	yes	—
255	D₄⋊C₈	C₂²×C₁₃	1	4	yes	—
256	C₂²×C₁₃	—	2	1	no	—
257	C₂²×C₁₃	—	2	1	no	—
258	C₂²×C₁₃	—	2	1	no	—
259	C₂²×C₁₃	—	4	2	no	—
260	C₂²×C₁₃	—	4	2	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	C₂×#120	1	1	yes	characteristic
266	C₄×C₁₃	—	2	1	no	—
267	C₄×C₁₃	—	2	1	no	—
268	C₄×C₁₃	—	2	1	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	#455	1	2	yes	—
275	C₄×C₁₃	#577	1	2	yes	—
276	C₄×C₁₃	#577	1	2	yes	—
277	C₂×#41	—	2	2	no	—
278	C₂×#41	—	2	2	no	—
279	C₂×#41	—	2	1	no	—
280	C₂×#41	D₄×C₁₃	1	2	yes	—
281	C₂²×Q₈	—	2	1	no	—
282	C₂×SD₁₆	—	2	4	no	—
283	C₂×M₁₆	—	2	1	no	—
284	C₄⋊Q₈	—	2	1	no	—
285	C₄⋊Q₈	—	2	1	no	—
286	C₄⋊Q₈	—	2	1	no	—
287	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
288	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
289	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
290	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
291	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
292	#127	—	2	2	no	—
293	#127	D₄×C₁₃	1	1	yes	characteristic
294	#127	C₂³×C₁₃	1	1	yes	characteristic
295	#125	—	2	2	no	—
296	#125	—	2	1	no	—
297	#124	—	2	1	no	—
298	#124	D₄×C₁₃	1	2	yes	—
299	#123	—	2	4	no	—
300	#123	—	2	4	no	—
301	C₂²⋊Q₈	—	2	2	no	—
302	C₂²⋊Q₈	—	2	4	no	—
303	C₂²⋊Q₈	—	2	2	no	—
304	C₂²⋊Q₈	—	2	4	no	—
305	C₂²⋊Q₈	—	2	1	no	—
306	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
307	#121	—	2	4	no	—
308	#121	—	2	4	no	—
309	#121	—	2	2	no	—
310	#121	—	2	4	no	—
311	#121	—	2	4	no	—
312	#121	—	2	1	no	—
313	#121	—	2	1	no	—
314	#121	—	2	1	no	—
315	#121	—	2	2	no	—
316	#121	D₄×C₁₃	1	2	yes	—
317	C₄×Q₈	—	2	1	no	—
318	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
319	C₄×D₄	—	2	2	no	—
320	C₄×D₄	—	2	2	no	—
321	C₄×D₄	—	2	1	no	—
322	C₄×D₄	—	2	1	no	—
323	C₄×D₄	—	2	1	no	—
324	C₄×D₄	C₂³×C₁₃	1	2	yes	—
325	#117	—	2	1	no	—
326	C₂×C₄⋊C₄	—	2	2	no	—
327	C₂×C₄⋊C₄	—	2	2	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
331	#106	—	2	4	no	—
332	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
333	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
334	#103	—	2	4	no	—
335	#103	—	2	4	no	—
336	#103	—	2	4	no	—
337	#102	—	2	4	no	—
338	C₂²⋊C₈	—	2	1	no	—
339	C₂²⋊C₈	—	2	1	no	—
340	#97	—	2	1	no	—
341	C₄×C₈	—	2	1	no	—
342	C₄×C₈	—	2	1	no	—
343	C₄×C₈	C₂³×C₁₃	1	2	yes	—
344	C₂×C₁₃	—	4	1	no	—
345	C₂×C₁₃	—	8	2	no	—
346	C₂×C₁₃	—	8	2	no	—
347	C₂×C₁₃	#3009	1	1	yes	characteristic
348	C₂×C₁₃	#3010	1	1	yes	characteristic
349	C₂×C₁₃	C₂×#455	1	1	yes	characteristic
350	#41	—	4	4	no	—
351	#41	—	8	2	no	—
352	#41	—	8	4	no	—
353	#41	—	8	4	no	—
354	C₂×Q₈	—	2	1	no	—
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	2	2	no	—
357	C₂×Q₈	—	4	1	no	—
358	C₂×Q₈	—	8	2	no	—
359	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
360	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
361	C₂×D₄	—	2	4	no	—
362	C₂×D₄	—	2	4	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
370	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
371	C₂²×C₄	—	2	4	no	—
372	C₂²×C₄	—	2	4	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	4	1	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	SD₁₆	—	8	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	4	no	—
385	C₄⋊C₄	—	2	4	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	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	2	no	—
403	C₂²⋊C₄	—	2	2	no	—
404	C₂²⋊C₄	—	2	2	no	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	2	2	no	—
407	C₄²	—	2	2	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	#18723	1	1	yes	characteristic, direct product factor, Sylow
413	C₂³	—	2	2	no	—
414	C₂³	—	2	2	no	—
415	C₂³	C₁₃×#120	1	1	yes	characteristic
416	Q₈	—	2	4	no	—
417	Q₈	—	4	2	no	—
418	Q₈	—	4	2	no	—
419	Q₈	—	4	4	no	—
420	Q₈	—	8	1	no	—
421	Q₈	—	8	2	no	—
422	D₄	—	2	4	no	—
423	D₄	—	4	2	no	—
424	D₄	—	4	2	no	—
425	D₄	—	4	2	no	—
426	D₄	—	4	2	no	—
427	D₄	—	8	1	no	—
428	D₄	—	8	2	no	—
429	D₄	—	8	2	no	—
430	D₄	—	8	4	no	—
431	D₄	—	8	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	4	no	—
440	C₂×C₄	—	4	4	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	8	4	no	—
443	C₂×C₄	—	8	4	no	—
444	C₂×C₄	—	8	2	no	—
445	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
446	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
447	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
448	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
449	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
450	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
451	C₈	—	4	2	no	—
452	C₈	—	4	2	no	—
453	C₈	—	4	2	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	2	1	no	—
456	C₂²	—	2	1	no	—
457	C₂²	—	4	2	no	—
458	C₂²	—	4	2	no	—
459	C₂²	—	4	2	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	C₄	—	2	1	no	—
465	C₄	—	2	1	no	—
466	C₄	—	2	1	no	—
467	C₄	—	4	2	no	—
468	C₄	—	4	2	no	—
469	C₄	—	4	2	no	—
470	C₄	—	4	2	no	—
471	C₄	—	8	2	no	—
472	C₄	C₁₃×#455	1	2	yes	—
473	C₄	C₁₃×#577	1	2	yes	—
474	C₄	C₁₃×#577	1	2	yes	—
475	C₂	—	4	1	no	—
476	C₂	—	8	2	no	—
477	C₂	—	8	2	no	—
478	C₂	C₁₃×#3009	1	1	yes	characteristic
479	C₂	C₁₃×#3010	1	1	yes	characteristic
480	C₂	C₂×C₁₃×#455	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×#3229	C₂	semidirect
3. C₁₃×#3206	C₂	semidirect
4. C₁₃×#3141	C₂	semidirect
5. C₁₃×#1643	C₂	semidirect
6. C₁₃×#1642	C₂	semidirect
7. C₁₃×#1543	C₂	semidirect
8. C₁₃×#1485	C₂	semidirect
9. C₁₃×#1484	C₂	semidirect
110. #18723	C₁₃	direct (N × H)
174. #3229	C₂×C₁₃	semidirect
175. #3206	C₂×C₁₃	semidirect
176. #3141	C₂×C₁₃	semidirect
177. #1643	C₂×C₁₃	semidirect
178. #1642	C₂×C₁₃	semidirect
179. #1543	C₂×C₁₃	semidirect
180. #1485	C₂×C₁₃	semidirect
181. #1484	C₂×C₁₃	semidirect
412. C₁₃	#18723	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×#3229	2
C₁₃×#3206	2
C₁₃×#3141	2
C₁₃×#1643	2
C₁₃×#1642	2
C₁₃×#1543	2
C₁₃×#1485	2
C₁₃×#1484	2
#18723	13

Subgroups — C13×#18723 #15705062

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18723 #15705062