Subgroups — C₁₃×#18656 #15704995

Order 3328.

960 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3511	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3226	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#498	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3039	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1654	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1652	C₂	1	4	yes	maximal, complemented
7	C₁₃×#1549	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1492	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1476	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#137	—	2	1	no	—
11	C₁₃×#556	C₂²	1	2	yes	—
12	C₁₃×#555	—	2	1	no	—
13	C₁₃×#554	—	2	1	no	—
14	C₁₃×#553	—	2	2	no	—
15	C₁₃×#548	—	2	2	no	—
16	C₁₃×#547	C₂²	1	2	yes	—
17	C₁₃×#542	—	2	2	no	—
18	C₁₃×#537	—	2	1	no	—
19	C₁₃×#533	—	2	1	no	—
20	C₁₃×#532	—	2	1	no	—
21	C₁₃×#532	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₁₃×#520	—	2	1	no	—
25	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
26	C₁₃×#500	—	2	1	no	—
27	C₁₃×#498	—	2	2	no	—
28	C₁₃×#498	C₂²	1	4	yes	—
29	C₁₃×#486	—	2	1	no	—
30	C₁₃×#480	—	2	2	no	—
31	C₁₃×#474	C₂²	1	4	yes	—
32	C₁₃×#462	—	2	1	no	—
33	C₁₃×#462	C₂²	1	2	yes	—
34	C₁₃×#461	—	2	1	no	—
35	C₁₃×#461	C₂²	1	2	yes	—
36	C₁₃×#431	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#106	—	2	2	no	—
38	C₁₃×#423	C₂²	1	1	yes	characteristic
39	C₁₃×#419	—	2	1	no	—
40	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
41	C₁₃×#332	C₂²	1	4	yes	—
42	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
43	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
44	C₁₃×D₄⋊C₈	C₂²	1	4	yes	—
45	C₂×C₁₃×#41	—	2	2	no	—
46	C₂×C₁₃×#41	—	2	1	no	—
47	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
48	C₂²×Q₈×C₁₃	—	2	1	no	—
49	C₂²×Q₈×C₁₃	—	2	1	no	—
50	C₁₃×#137	—	4	4	no	—
51	C₂×C₁₃×Q₁₆	—	2	2	no	—
52	C₂×C₁₃×SD₁₆	—	2	2	no	—
53	C₂×C₁₃×M₁₆	—	2	1	no	—
54	C₂²×C₈×C₁₃	—	2	1	no	—
55	C₁₃×C₄⋊Q₈	—	2	1	no	—
56	C₁₃×C₄⋊Q₈	—	2	1	no	—
57	C₁₃×C₄⋊Q₈	—	2	1	no	—
58	C₁₃×C₄⋊Q₈	—	2	1	no	—
59	C₁₃×C₄⋊Q₈	—	2	1	no	—
60	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
61	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
62	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
63	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
64	C₁₃×#127	D₄	1	1	yes	characteristic
65	C₁₃×#126	—	2	4	no	—
66	C₁₃×#125	—	2	2	no	—
67	C₁₃×#124	—	2	4	no	—
68	C₁₃×#124	—	2	2	no	—
69	C₁₃×#124	—	2	1	no	—
70	C₁₃×#123	—	2	4	no	—
71	C₁₃×C₂²⋊Q₈	—	2	2	no	—
72	C₁₃×C₂²⋊Q₈	—	2	4	no	—
73	C₁₃×C₂²⋊Q₈	—	2	2	no	—
74	C₁₃×C₂²⋊Q₈	—	2	2	no	—
75	C₁₃×#121	—	2	2	no	—
76	C₁₃×#121	—	2	2	no	—
77	C₁₃×#121	—	2	4	no	—
78	C₁₃×#121	—	2	2	no	—
79	C₁₃×#121	—	2	1	no	—
80	C₁₃×#121	D₄	1	2	yes	—
81	C₄×Q₈×C₁₃	—	2	2	no	—
82	C₄×Q₈×C₁₃	—	2	2	no	—
83	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
84	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₄×D₄×C₁₃	—	2	2	no	—
86	C₄×D₄×C₁₃	—	2	4	no	—
87	C₄×D₄×C₁₃	—	2	2	no	—
88	C₄×D₄×C₁₃	—	2	1	no	—
89	C₄×D₄×C₁₃	—	2	1	no	—
90	C₄×D₄×C₁₃	—	2	1	no	—
91	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
92	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
93	C₄×D₄×C₁₃	C₂³	1	2	yes	—
94	C₁₃×#117	—	2	2	no	—
95	C₁₃×#117	—	2	2	no	—
96	C₁₃×#117	—	2	1	no	—
97	C₁₃×#117	D₄	1	1	yes	characteristic
98	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
100	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
101	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
102	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
103	C₂×C₄²×C₁₃	—	2	1	no	—
104	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
105	C₁₃×#107	—	2	4	no	—
106	C₁₃×#106	—	2	8	no	—
107	C₁₃×C₄⋊C₈	—	2	1	no	—
108	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
109	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
110	C₁₃×#103	—	2	2	no	—
111	C₁₃×#103	—	2	2	no	—
112	C₁₃×#102	—	2	4	no	—
113	C₁₃×C₂²⋊C₈	—	2	1	no	—
114	C₄×C₈×C₁₃	—	2	1	no	—
115	C₄×C₈×C₁₃	—	2	1	no	—
116	C₄×C₈×C₁₃	C₂³	1	2	yes	—
117	#18656	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
118	C₁₃×#41	—	2	2	no	—
119	C₁₃×#41	—	2	2	no	—
120	C₁₃×#41	—	4	2	no	—
121	C₁₃×#41	—	4	2	no	—
122	C₁₃×#41	—	8	4	no	—
123	C₂×Q₈×C₁₃	—	2	1	no	—
124	C₂×Q₈×C₁₃	—	2	2	no	—
125	C₂×Q₈×C₁₃	—	2	2	no	—
126	C₂×Q₈×C₁₃	—	2	2	no	—
127	C₂×Q₈×C₁₃	—	4	1	no	—
128	C₂×Q₈×C₁₃	—	4	2	no	—
129	C₂×Q₈×C₁₃	—	4	2	no	—
130	C₂×Q₈×C₁₃	—	8	2	no	—
131	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂×D₄×C₁₃	—	2	1	no	—
133	C₂×D₄×C₁₃	—	2	2	no	—
134	C₂×D₄×C₁₃	—	2	4	no	—
135	C₂×D₄×C₁₃	—	2	1	no	—
136	C₂×D₄×C₁₃	—	2	1	no	—
137	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
138	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	—	2	4	no	—
140	C₂²×C₄×C₁₃	—	2	2	no	—
141	C₂²×C₄×C₁₃	—	2	1	no	—
142	C₂²×C₄×C₁₃	—	2	1	no	—
143	C₂²×C₄×C₁₃	—	2	1	no	—
144	C₂²×C₄×C₁₃	—	2	2	no	—
145	C₂²×C₄×C₁₃	—	4	1	no	—
146	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
149	C₁₃×Q₁₆	—	4	4	no	—
150	C₁₃×SD₁₆	—	4	4	no	—
151	C₁₃×M₁₆	—	4	2	no	—
152	C₂×C₈×C₁₃	—	2	4	no	—
153	C₂×C₈×C₁₃	—	2	2	no	—
154	C₂×C₈×C₁₃	—	2	2	no	—
155	C₂×C₈×C₁₃	—	2	2	no	—
156	C₁₃×C₄⋊C₄	—	2	4	no	—
157	C₁₃×C₄⋊C₄	—	2	4	no	—
158	C₁₃×C₄⋊C₄	—	2	2	no	—
159	C₁₃×C₄⋊C₄	—	2	2	no	—
160	C₁₃×C₄⋊C₄	—	2	1	no	—
161	C₁₃×C₄⋊C₄	—	2	1	no	—
162	C₁₃×C₄⋊C₄	—	2	2	no	—
163	C₁₃×C₄⋊C₄	—	2	1	no	—
164	C₁₃×C₄⋊C₄	—	2	2	no	—
165	C₁₃×C₄⋊C₄	—	2	2	no	—
166	C₁₃×C₄⋊C₄	—	4	1	no	—
167	C₁₃×C₄⋊C₄	—	4	1	no	—
168	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
169	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
170	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
171	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
172	C₁₃×C₂²⋊C₄	—	2	4	no	—
173	C₁₃×C₂²⋊C₄	—	2	4	no	—
174	C₁₃×C₂²⋊C₄	—	2	4	no	—
175	C₁₃×C₂²⋊C₄	—	2	1	no	—
176	C₁₃×C₂²⋊C₄	—	2	1	no	—
177	C₁₃×C₂²⋊C₄	—	2	2	no	—
178	C₁₃×C₂²⋊C₄	—	2	1	no	—
179	C₁₃×C₂²⋊C₄	—	2	2	no	—
180	C₄²×C₁₃	—	2	4	no	—
181	C₄²×C₁₃	—	2	1	no	—
182	C₄²×C₁₃	—	2	1	no	—
183	C₄²×C₁₃	—	2	1	no	—
184	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
185	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
186	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
187	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
188	#3511	C₂×C₁₃	1	1	yes	characteristic
189	#3226	C₂×C₁₃	1	1	yes	characteristic, complemented
190	C₂×#498	C₂×C₁₃	1	1	yes	characteristic, complemented
191	#3039	C₂×C₁₃	1	1	yes	characteristic, complemented
192	#1654	C₂×C₁₃	1	4	yes	complemented
193	#1652	C₂×C₁₃	1	4	yes	complemented
194	#1549	C₂×C₁₃	1	1	yes	characteristic, complemented
195	#1492	C₂×C₁₃	1	1	yes	characteristic, complemented
196	#1476	C₂×C₁₃	1	1	yes	characteristic, complemented
197	C₂³×C₁₃	—	2	1	no	—
198	C₂³×C₁₃	—	2	2	no	—
199	C₂³×C₁₃	#120	1	1	yes	characteristic
200	Q₈×C₁₃	—	2	1	no	—
201	Q₈×C₁₃	—	2	1	no	—
202	Q₈×C₁₃	—	4	4	no	—
203	Q₈×C₁₃	—	4	2	no	—
204	Q₈×C₁₃	—	4	2	no	—
205	Q₈×C₁₃	—	4	2	no	—
206	Q₈×C₁₃	—	8	2	no	—
207	Q₈×C₁₃	—	8	2	no	—
208	D₄×C₁₃	—	2	1	no	—
209	D₄×C₁₃	—	2	1	no	—
210	D₄×C₁₃	—	2	4	no	—
211	D₄×C₁₃	—	4	2	no	—
212	D₄×C₁₃	—	4	4	no	—
213	D₄×C₁₃	—	4	2	no	—
214	D₄×C₁₃	—	4	2	no	—
215	D₄×C₁₃	—	8	4	no	—
216	C₂×C₄×C₁₃	—	2	2	no	—
217	C₂×C₄×C₁₃	—	2	2	no	—
218	C₂×C₄×C₁₃	—	2	1	no	—
219	C₂×C₄×C₁₃	—	2	1	no	—
220	C₂×C₄×C₁₃	—	2	2	no	—
221	C₂×C₄×C₁₃	—	2	1	no	—
222	C₂×C₄×C₁₃	—	2	4	no	—
223	C₂×C₄×C₁₃	—	4	2	no	—
224	C₂×C₄×C₁₃	—	4	2	no	—
225	C₂×C₄×C₁₃	—	4	2	no	—
226	C₂×C₄×C₁₃	—	4	2	no	—
227	C₂×C₄×C₁₃	—	4	2	no	—
228	C₂×C₄×C₁₃	—	4	2	no	—
229	C₂×C₄×C₁₃	—	8	2	no	—
230	C₂×C₄×C₁₃	—	8	4	no	—
231	C₂×C₄×C₁₃	—	8	2	no	—
232	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
233	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
234	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
235	C₂×C₄×C₁₃	#135	1	2	yes	—
236	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
237	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
240	C₈×C₁₃	—	2	4	no	—
241	C₈×C₁₃	—	4	2	no	—
242	C₈×C₁₃	—	4	2	no	—
243	C₂×#137	—	2	1	no	—
244	#556	C₂²×C₁₃	1	2	yes	—
245	#555	—	2	1	no	—
246	#554	—	2	1	no	—
247	#553	—	2	2	no	—
248	#548	—	2	2	no	—
249	#547	C₂²×C₁₃	1	2	yes	—
250	#542	—	2	2	no	—
251	#537	—	2	1	no	—
252	#533	—	2	1	no	—
253	#532	—	2	1	no	—
254	#532	C₂²×C₁₃	1	1	yes	characteristic
255	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
256	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
257	#520	—	2	1	no	—
258	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
259	#500	—	2	1	no	—
260	#498	—	2	2	no	—
261	#498	C₂²×C₁₃	1	4	yes	—
262	#486	—	2	1	no	—
263	#480	—	2	2	no	—
264	#474	C₂²×C₁₃	1	4	yes	—
265	#462	—	2	1	no	—
266	#462	C₂²×C₁₃	1	2	yes	—
267	#461	—	2	1	no	—
268	#461	C₂²×C₁₃	1	2	yes	—
269	#431	C₂²×C₁₃	1	1	yes	characteristic
270	C₂×#106	—	2	2	no	—
271	#423	C₂²×C₁₃	1	1	yes	characteristic
272	#419	—	2	1	no	—
273	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
274	#332	C₂²×C₁₃	1	4	yes	—
275	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
276	D₄⋊C₈	C₂²×C₁₃	1	4	yes	—
277	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
278	C₂²×C₁₃	—	2	1	no	—
279	C₂²×C₁₃	—	2	1	no	—
280	C₂²×C₁₃	—	4	1	no	—
281	C₂²×C₁₃	—	4	2	no	—
282	C₂²×C₁₃	—	4	1	no	—
283	C₂²×C₁₃	—	4	2	no	—
284	C₂²×C₁₃	—	4	1	no	—
285	C₂²×C₁₃	—	4	2	no	—
286	C₂²×C₁₃	#449	1	2	yes	—
287	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
288	C₄×C₁₃	—	2	1	no	—
289	C₄×C₁₃	—	2	1	no	—
290	C₄×C₁₃	—	4	1	no	—
291	C₄×C₁₃	—	4	2	no	—
292	C₄×C₁₃	—	4	1	no	—
293	C₄×C₁₃	—	4	4	no	—
294	C₄×C₁₃	—	4	1	no	—
295	C₄×C₁₃	—	8	2	no	—
296	C₄×C₁₃	#449	1	2	yes	—
297	C₄×C₁₃	#456	1	2	yes	—
298	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
299	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
300	C₄×C₁₃	#577	1	2	yes	—
301	C₂×#41	—	2	2	no	—
302	C₂×#41	—	2	1	no	—
303	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
304	C₂²×Q₈	—	2	1	no	—
305	C₂²×Q₈	—	2	1	no	—
306	#137	—	4	4	no	—
307	C₂×Q₁₆	—	2	2	no	—
308	C₂×SD₁₆	—	2	2	no	—
309	C₂×M₁₆	—	2	1	no	—
310	C₂²×C₈	—	2	1	no	—
311	C₄⋊Q₈	—	2	1	no	—
312	C₄⋊Q₈	—	2	1	no	—
313	C₄⋊Q₈	—	2	1	no	—
314	C₄⋊Q₈	—	2	1	no	—
315	C₄⋊Q₈	—	2	1	no	—
316	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
317	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
318	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
319	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
320	#127	D₄×C₁₃	1	1	yes	characteristic
321	#126	—	2	4	no	—
322	#125	—	2	2	no	—
323	#124	—	2	4	no	—
324	#124	—	2	2	no	—
325	#124	—	2	1	no	—
326	#123	—	2	4	no	—
327	C₂²⋊Q₈	—	2	2	no	—
328	C₂²⋊Q₈	—	2	4	no	—
329	C₂²⋊Q₈	—	2	2	no	—
330	C₂²⋊Q₈	—	2	2	no	—
331	#121	—	2	2	no	—
332	#121	—	2	2	no	—
333	#121	—	2	4	no	—
334	#121	—	2	2	no	—
335	#121	—	2	1	no	—
336	#121	D₄×C₁₃	1	2	yes	—
337	C₄×Q₈	—	2	2	no	—
338	C₄×Q₈	—	2	2	no	—
339	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
340	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
341	C₄×D₄	—	2	2	no	—
342	C₄×D₄	—	2	4	no	—
343	C₄×D₄	—	2	2	no	—
344	C₄×D₄	—	2	1	no	—
345	C₄×D₄	—	2	1	no	—
346	C₄×D₄	—	2	1	no	—
347	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
348	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
349	C₄×D₄	C₂³×C₁₃	1	2	yes	—
350	#117	—	2	2	no	—
351	#117	—	2	2	no	—
352	#117	—	2	1	no	—
353	#117	D₄×C₁₃	1	1	yes	characteristic
354	C₂×C₄⋊C₄	—	2	1	no	—
355	C₂×C₄⋊C₄	—	2	2	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
359	C₂×C₄²	—	2	1	no	—
360	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
361	#107	—	2	4	no	—
362	#106	—	2	8	no	—
363	C₄⋊C₈	—	2	1	no	—
364	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
365	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
366	#103	—	2	2	no	—
367	#103	—	2	2	no	—
368	#102	—	2	4	no	—
369	C₂²⋊C₈	—	2	1	no	—
370	C₄×C₈	—	2	1	no	—
371	C₄×C₈	—	2	1	no	—
372	C₄×C₈	C₂³×C₁₃	1	2	yes	—
373	C₂×C₁₃	—	2	2	no	—
374	C₂×C₁₃	—	8	1	no	—
375	C₂×C₁₃	—	8	2	no	—
376	C₂×C₁₃	C₂×#449	1	1	yes	characteristic
377	C₂×C₁₃	#3009	1	1	yes	characteristic
378	C₂×C₁₃	C₂×#456	1	1	yes	characteristic
379	#41	—	2	2	no	—
380	#41	—	2	2	no	—
381	#41	—	4	2	no	—
382	#41	—	4	2	no	—
383	#41	—	8	4	no	—
384	C₂×Q₈	—	2	1	no	—
385	C₂×Q₈	—	2	2	no	—
386	C₂×Q₈	—	2	2	no	—
387	C₂×Q₈	—	2	2	no	—
388	C₂×Q₈	—	4	1	no	—
389	C₂×Q₈	—	4	2	no	—
390	C₂×Q₈	—	4	2	no	—
391	C₂×Q₈	—	8	2	no	—
392	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
393	C₂×D₄	—	2	1	no	—
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	—	2	4	no	—
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
399	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
400	C₂²×C₄	—	2	4	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	4	1	no	—
407	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
408	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
409	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
410	Q₁₆	—	4	4	no	—
411	SD₁₆	—	4	4	no	—
412	M₁₆	—	4	2	no	—
413	C₂×C₈	—	2	4	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₄⋊C₄	—	2	4	no	—
418	C₄⋊C₄	—	2	4	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	4	1	no	—
428	C₄⋊C₄	—	4	1	no	—
429	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
430	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
431	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
432	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
433	C₂²⋊C₄	—	2	4	no	—
434	C₂²⋊C₄	—	2	4	no	—
435	C₂²⋊C₄	—	2	4	no	—
436	C₂²⋊C₄	—	2	1	no	—
437	C₂²⋊C₄	—	2	1	no	—
438	C₂²⋊C₄	—	2	2	no	—
439	C₂²⋊C₄	—	2	1	no	—
440	C₂²⋊C₄	—	2	2	no	—
441	C₄²	—	2	4	no	—
442	C₄²	—	2	1	no	—
443	C₄²	—	2	1	no	—
444	C₄²	—	2	1	no	—
445	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
446	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
447	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
448	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
449	C₁₃	#18656	1	1	yes	characteristic, direct product factor, Sylow
450	C₂³	—	2	1	no	—
451	C₂³	—	2	2	no	—
452	C₂³	C₁₃×#120	1	1	yes	characteristic
453	Q₈	—	2	1	no	—
454	Q₈	—	2	1	no	—
455	Q₈	—	4	2	no	—
456	Q₈	—	4	4	no	—
457	Q₈	—	4	2	no	—
458	Q₈	—	4	2	no	—
459	Q₈	—	8	2	no	—
460	Q₈	—	8	2	no	—
461	D₄	—	2	1	no	—
462	D₄	—	2	1	no	—
463	D₄	—	2	4	no	—
464	D₄	—	4	2	no	—
465	D₄	—	4	4	no	—
466	D₄	—	4	2	no	—
467	D₄	—	4	2	no	—
468	D₄	—	8	4	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	8	2	no	—
483	C₂×C₄	—	8	4	no	—
484	C₂×C₄	—	8	2	no	—
485	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
486	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
487	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
488	C₂×C₄	C₁₃×#135	1	2	yes	—
489	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
490	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
491	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
492	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
493	C₈	—	2	4	no	—
494	C₈	—	4	2	no	—
495	C₈	—	4	2	no	—
496	C₂²	—	2	1	no	—
497	C₂²	—	2	1	no	—
498	C₂²	—	4	1	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	4	1	no	—
501	C₂²	—	4	2	no	—
502	C₂²	—	4	1	no	—
503	C₂²	—	4	2	no	—
504	C₂²	C₁₃×#449	1	2	yes	—
505	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
506	C₄	—	2	1	no	—
507	C₄	—	2	1	no	—
508	C₄	—	4	1	no	—
509	C₄	—	4	4	no	—
510	C₄	—	4	1	no	—
511	C₄	—	4	1	no	—
512	C₄	—	4	2	no	—
513	C₄	—	8	2	no	—
514	C₄	C₁₃×#449	1	2	yes	—
515	C₄	C₁₃×#456	1	2	yes	—
516	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
517	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
518	C₄	C₁₃×#577	1	2	yes	—
519	C₂	—	2	2	no	—
520	C₂	—	8	1	no	—
521	C₂	—	8	2	no	—
522	C₂	C₂×C₁₃×#449	1	1	yes	characteristic
523	C₂	C₁₃×#3009	1	1	yes	characteristic
524	C₂	C₂×C₁₃×#456	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#3511	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×#3226	C₂	semidirect
3. C₂×C₁₃×#498	C₂	semidirect
4. C₁₃×#3039	C₂	semidirect
5. C₁₃×#1654	C₂	semidirect
6. C₁₃×#1652	C₂	semidirect
7. C₁₃×#1549	C₂	semidirect
8. C₁₃×#1492	C₂	semidirect
9. C₁₃×#1476	C₂	semidirect
117. #18656	C₁₃	direct (N × H)
189. #3226	C₂×C₁₃	semidirect
190. C₂×#498	C₂×C₁₃	semidirect
191. #3039	C₂×C₁₃	semidirect
192. #1654	C₂×C₁₃	semidirect
193. #1652	C₂×C₁₃	semidirect
194. #1549	C₂×C₁₃	semidirect
195. #1492	C₂×C₁₃	semidirect
196. #1476	C₂×C₁₃	semidirect
449. C₁₃	#18656	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×#3511	2
C₁₃×#3226	2
C₂×C₁₃×#498	2
C₁₃×#3039	2
C₁₃×#1654	2
C₁₃×#1652	2
C₁₃×#1549	2
C₁₃×#1492	2
C₁₃×#1476	2
#18656	13

Subgroups — C13×#18656 #15704995

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18656 #15704995