Subgroups — C₁₃×#18399 #15704738

Order 3328.

894 conjugacy classes of subgroups.

The subgroup lattice has 478 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×#3230	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3227	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2568	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1615	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	C₂²	1	1	yes	characteristic
20	C₁₃×#529	—	2	2	no	—
21	C₁₃×#520	—	2	1	no	—
22	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₁₃×#500	—	2	1	no	—
24	C₁₃×#498	—	2	1	no	—
25	C₁₃×#487	—	2	1	no	—
26	C₁₃×#486	—	2	1	no	—
27	C₁₃×#484	C₂²	1	4	yes	—
28	C₁₃×#481	C₂²	1	4	yes	—
29	C₁₃×#477	—	2	2	no	—
30	C₁₃×#476	—	2	2	no	—
31	C₁₃×#431	C₂²	1	1	yes	characteristic
32	C₁₃×#431	C₂²	1	1	yes	characteristic
33	C₁₃×#400	C₂²	1	4	yes	—
34	C₁₃×#391	—	2	1	no	—
35	C₁₃×#391	—	2	2	no	—
36	C₁₃×#382	—	2	1	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	D₄	1	1	yes	characteristic
50	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
51	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
52	C₁₃×#127	D₄	1	1	yes	characteristic
53	C₁₃×#126	—	2	4	no	—
54	C₁₃×#126	—	2	4	no	—
55	C₁₃×#125	—	2	2	no	—
56	C₁₃×#125	—	2	4	no	—
57	C₁₃×#125	—	2	1	no	—
58	C₁₃×#124	—	2	2	no	—
59	C₁₃×#124	—	2	2	no	—
60	C₁₃×#124	—	2	1	no	—
61	C₁₃×#123	—	2	4	no	—
62	C₁₃×#123	—	2	4	no	—
63	C₁₃×C₂²⋊Q₈	—	2	2	no	—
64	C₁₃×C₂²⋊Q₈	—	2	2	no	—
65	C₁₃×C₂²⋊Q₈	—	2	4	no	—
66	C₁₃×C₂²⋊Q₈	—	2	1	no	—
67	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
68	C₁₃×#121	—	2	1	no	—
69	C₁₃×#121	C₂³	1	2	yes	—
70	C₄×Q₈×C₁₃	—	2	2	no	—
71	C₄×Q₈×C₁₃	—	2	2	no	—
72	C₄×Q₈×C₁₃	—	2	1	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	D₄	1	2	yes	—
78	C₄×D₄×C₁₃	—	2	2	no	—
79	C₄×D₄×C₁₃	—	2	2	no	—
80	C₄×D₄×C₁₃	—	2	4	no	—
81	C₄×D₄×C₁₃	—	2	1	no	—
82	C₄×D₄×C₁₃	D₄	1	2	yes	—
83	C₁₃×#117	—	2	2	no	—
84	C₁₃×#117	—	2	4	no	—
85	C₁₃×#117	—	2	1	no	—
86	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
87	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
88	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
89	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
92	C₂×C₄²×C₁₃	—	2	1	no	—
93	C₂×C₄²×C₁₃	D₄	1	2	yes	—
94	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
95	C₁₃×#107	—	2	4	no	—
96	C₁₃×#106	—	2	4	no	—
97	C₁₃×C₄⋊C₈	—	2	1	no	—
98	C₁₃×C₄⋊C₈	—	2	1	no	—
99	C₁₃×#103	—	2	4	no	—
100	C₁₃×#102	—	2	4	no	—
101	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
102	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
103	C₄×C₈×C₁₃	—	2	1	no	—
104	C₄×C₈×C₁₃	—	2	1	no	—
105	C₁₃×#95	—	2	4	no	—
106	C₁₃×#95	—	2	4	no	—
107	C₁₃×#95	C₂³	1	2	yes	—
108	#18399	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
109	C₁₃×#41	—	4	2	no	—
110	C₁₃×#41	—	4	2	no	—
111	C₂×Q₈×C₁₃	—	2	1	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	2	no	—
116	C₂×Q₈×C₁₃	—	2	2	no	—
117	C₂×Q₈×C₁₃	—	4	4	no	—
118	C₂×Q₈×C₁₃	—	4	1	no	—
119	C₂×Q₈×C₁₃	—	4	1	no	—
120	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
121	C₂×D₄×C₁₃	—	2	2	no	—
122	C₂×D₄×C₁₃	—	2	1	no	—
123	C₂×D₄×C₁₃	—	2	1	no	—
124	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₃	—	2	4	no	—
126	C₂²×C₄×C₁₃	—	2	2	no	—
127	C₂²×C₄×C₁₃	—	2	2	no	—
128	C₂²×C₄×C₁₃	—	2	2	no	—
129	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
134	C₂×C₈×C₁₃	—	2	2	no	—
135	C₂×C₈×C₁₃	—	2	2	no	—
136	C₁₃×C₄⋊C₄	—	2	4	no	—
137	C₁₃×C₄⋊C₄	—	2	4	no	—
138	C₁₃×C₄⋊C₄	—	2	4	no	—
139	C₁₃×C₄⋊C₄	—	2	1	no	—
140	C₁₃×C₄⋊C₄	—	2	1	no	—
141	C₁₃×C₄⋊C₄	—	2	1	no	—
142	C₁₃×C₄⋊C₄	—	2	1	no	—
143	C₁₃×C₄⋊C₄	—	2	2	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	2	no	—
148	C₁₃×C₄⋊C₄	—	2	2	no	—
149	C₁₃×C₄⋊C₄	—	2	2	no	—
150	C₁₃×C₄⋊C₄	—	2	2	no	—
151	C₁₃×C₄⋊C₄	—	4	2	no	—
152	C₁₃×C₄⋊C₄	—	4	1	no	—
153	C₁₃×C₄⋊C₄	—	4	1	no	—
154	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
155	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
156	C₁₃×C₂²⋊C₄	—	2	4	no	—
157	C₁₃×C₂²⋊C₄	—	2	4	no	—
158	C₁₃×C₂²⋊C₄	—	2	4	no	—
159	C₁₃×C₂²⋊C₄	—	2	2	no	—
160	C₁₃×C₂²⋊C₄	—	2	2	no	—
161	C₁₃×C₂²⋊C₄	—	2	2	no	—
162	C₄²×C₁₃	—	2	4	no	—
163	C₄²×C₁₃	—	2	2	no	—
164	C₄²×C₁₃	—	2	2	no	—
165	C₄²×C₁₃	—	2	2	no	—
166	C₄²×C₁₃	—	4	2	no	—
167	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
168	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
171	#3507	C₂×C₁₃	1	1	yes	characteristic
172	#3230	C₂×C₁₃	1	1	yes	characteristic, complemented
173	#3227	C₂×C₁₃	1	1	yes	characteristic
174	#2568	C₂×C₁₃	1	1	yes	characteristic, complemented
175	#1615	C₂×C₁₃	1	8	yes	complemented
176	#1503	C₂×C₁₃	1	1	yes	characteristic, complemented
177	#1502	C₂×C₁₃	1	1	yes	characteristic
178	#1461	C₂×C₁₃	1	1	yes	characteristic, complemented
179	C₂³×C₁₃	—	2	2	no	—
180	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
181	Q₈×C₁₃	—	4	2	no	—
182	Q₈×C₁₃	—	4	2	no	—
183	Q₈×C₁₃	—	4	2	no	—
184	Q₈×C₁₃	—	4	2	no	—
185	Q₈×C₁₃	—	4	2	no	—
186	Q₈×C₁₃	—	8	2	no	—
187	Q₈×C₁₃	—	8	2	no	—
188	D₄×C₁₃	—	4	2	no	—
189	D₄×C₁₃	—	4	2	no	—
190	D₄×C₁₃	—	4	2	no	—
191	D₄×C₁₃	—	4	2	no	—
192	D₄×C₁₃	—	4	2	no	—
193	C₂×C₄×C₁₃	—	2	2	no	—
194	C₂×C₄×C₁₃	—	2	2	no	—
195	C₂×C₄×C₁₃	—	2	2	no	—
196	C₂×C₄×C₁₃	—	2	2	no	—
197	C₂×C₄×C₁₃	—	2	2	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	—	4	1	no	—
202	C₂×C₄×C₁₃	—	4	4	no	—
203	C₂×C₄×C₁₃	—	4	2	no	—
204	C₂×C₄×C₁₃	—	4	2	no	—
205	C₂×C₄×C₁₃	—	4	2	no	—
206	C₂×C₄×C₁₃	—	4	4	no	—
207	C₂×C₄×C₁₃	—	4	2	no	—
208	C₂×C₄×C₁₃	—	4	2	no	—
209	C₂×C₄×C₁₃	—	8	4	no	—
210	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
211	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
212	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
213	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
214	C₂×C₄×C₁₃	#135	1	2	yes	—
215	C₂×C₄×C₁₃	#137	1	2	yes	—
216	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
218	C₈×C₁₃	—	4	2	no	—
219	C₈×C₁₃	—	4	2	no	—
220	#559	—	2	1	no	—
221	#557	—	2	1	no	—
222	#556	—	2	1	no	—
223	#556	—	2	2	no	—
224	#554	—	2	1	no	—
225	#552	—	2	2	no	—
226	#539	C₂²×C₁₃	1	4	yes	—
227	#536	—	2	1	no	—
228	#533	C₂²×C₁₃	1	1	yes	characteristic
229	#532	C₂²×C₁₃	1	1	yes	characteristic
230	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
231	#529	—	2	2	no	—
232	#520	—	2	1	no	—
233	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
234	#500	—	2	1	no	—
235	#498	—	2	1	no	—
236	#487	—	2	1	no	—
237	#486	—	2	1	no	—
238	#484	C₂²×C₁₃	1	4	yes	—
239	#481	C₂²×C₁₃	1	4	yes	—
240	#477	—	2	2	no	—
241	#476	—	2	2	no	—
242	#431	C₂²×C₁₃	1	1	yes	characteristic
243	#431	C₂²×C₁₃	1	1	yes	characteristic
244	#400	C₂²×C₁₃	1	4	yes	—
245	#391	—	2	1	no	—
246	#391	—	2	2	no	—
247	#382	—	2	1	no	—
248	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
249	#328	C₂²×C₁₃	1	4	yes	—
250	#327	C₂²×C₁₃	1	4	yes	—
251	#324	C₂²×C₁₃	1	4	yes	—
252	C₂²×C₁₃	—	2	1	no	—
253	C₂²×C₁₃	—	2	1	no	—
254	C₂²×C₁₃	—	4	2	no	—
255	C₂²×C₁₃	—	4	2	no	—
256	C₂²×C₁₃	—	4	2	no	—
257	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
258	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
259	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
260	C₄×C₁₃	—	2	1	no	—
261	C₄×C₁₃	—	2	1	no	—
262	C₄×C₁₃	—	2	1	no	—
263	C₄×C₁₃	—	4	2	no	—
264	C₄×C₁₃	—	4	2	no	—
265	C₄×C₁₃	—	4	2	no	—
266	C₄×C₁₃	—	4	2	no	—
267	C₄×C₁₃	—	4	2	no	—
268	C₄×C₁₃	—	8	2	no	—
269	C₄×C₁₃	—	8	2	no	—
270	C₄×C₁₃	#452	1	2	yes	—
271	C₄×C₁₃	#452	1	2	yes	—
272	C₄×C₁₃	#454	1	2	yes	—
273	C₂×#41	—	2	1	no	—
274	C₂²×Q₈	—	2	1	no	—
275	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
276	C₄⋊Q₈	—	2	2	no	—
277	C₄⋊Q₈	—	2	1	no	—
278	C₄⋊Q₈	—	2	1	no	—
279	C₄⋊Q₈	—	2	1	no	—
280	C₄⋊Q₈	—	2	1	no	—
281	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
282	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
283	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
284	#127	D₄×C₁₃	1	1	yes	characteristic
285	#126	—	2	4	no	—
286	#126	—	2	4	no	—
287	#125	—	2	2	no	—
288	#125	—	2	4	no	—
289	#125	—	2	1	no	—
290	#124	—	2	2	no	—
291	#124	—	2	2	no	—
292	#124	—	2	1	no	—
293	#123	—	2	4	no	—
294	#123	—	2	4	no	—
295	C₂²⋊Q₈	—	2	2	no	—
296	C₂²⋊Q₈	—	2	2	no	—
297	C₂²⋊Q₈	—	2	4	no	—
298	C₂²⋊Q₈	—	2	1	no	—
299	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
300	#121	—	2	1	no	—
301	#121	C₂³×C₁₃	1	2	yes	—
302	C₄×Q₈	—	2	2	no	—
303	C₄×Q₈	—	2	2	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	—	2	1	no	—
309	C₄×Q₈	D₄×C₁₃	1	2	yes	—
310	C₄×D₄	—	2	2	no	—
311	C₄×D₄	—	2	2	no	—
312	C₄×D₄	—	2	4	no	—
313	C₄×D₄	—	2	1	no	—
314	C₄×D₄	D₄×C₁₃	1	2	yes	—
315	#117	—	2	2	no	—
316	#117	—	2	4	no	—
317	#117	—	2	1	no	—
318	C₂×C₄⋊C₄	—	2	2	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
322	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
323	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
324	C₂×C₄²	—	2	1	no	—
325	C₂×C₄²	D₄×C₁₃	1	2	yes	—
326	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
327	#107	—	2	4	no	—
328	#106	—	2	4	no	—
329	C₄⋊C₈	—	2	1	no	—
330	C₄⋊C₈	—	2	1	no	—
331	#103	—	2	4	no	—
332	#102	—	2	4	no	—
333	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
334	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
335	C₄×C₈	—	2	1	no	—
336	C₄×C₈	—	2	1	no	—
337	#95	—	2	4	no	—
338	#95	—	2	4	no	—
339	#95	C₂³×C₁₃	1	2	yes	—
340	C₂×C₁₃	—	2	1	no	—
341	C₂×C₁₃	—	2	1	no	—
342	C₂×C₁₃	—	8	2	no	—
343	C₂×C₁₃	C₂×#452	1	1	yes	characteristic
344	C₂×C₁₃	C₂×#454	1	1	yes	characteristic
345	C₂×C₁₃	#3028	1	1	yes	characteristic
346	#41	—	4	2	no	—
347	#41	—	4	2	no	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	—	2	1	no	—
350	C₂×Q₈	—	2	1	no	—
351	C₂×Q₈	—	2	1	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	4	4	no	—
355	C₂×Q₈	—	4	1	no	—
356	C₂×Q₈	—	4	1	no	—
357	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
362	C₂²×C₄	—	2	4	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
367	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
369	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
370	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₄⋊C₄	—	2	4	no	—
374	C₄⋊C₄	—	2	4	no	—
375	C₄⋊C₄	—	2	4	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	4	2	no	—
389	C₄⋊C₄	—	4	1	no	—
390	C₄⋊C₄	—	4	1	no	—
391	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
392	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
393	C₂²⋊C₄	—	2	4	no	—
394	C₂²⋊C₄	—	2	4	no	—
395	C₂²⋊C₄	—	2	4	no	—
396	C₂²⋊C₄	—	2	2	no	—
397	C₂²⋊C₄	—	2	2	no	—
398	C₂²⋊C₄	—	2	2	no	—
399	C₄²	—	2	4	no	—
400	C₄²	—	2	2	no	—
401	C₄²	—	2	2	no	—
402	C₄²	—	2	2	no	—
403	C₄²	—	4	2	no	—
404	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
405	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
406	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
407	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
408	C₁₃	#18399	1	1	yes	characteristic, direct product factor, Sylow
409	C₂³	—	2	2	no	—
410	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
411	Q₈	—	4	2	no	—
412	Q₈	—	4	2	no	—
413	Q₈	—	4	2	no	—
414	Q₈	—	4	2	no	—
415	Q₈	—	4	2	no	—
416	Q₈	—	8	2	no	—
417	Q₈	—	8	2	no	—
418	D₄	—	4	2	no	—
419	D₄	—	4	2	no	—
420	D₄	—	4	2	no	—
421	D₄	—	4	2	no	—
422	D₄	—	4	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	4	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	4	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	8	4	no	—
440	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
441	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
442	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
443	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
444	C₂×C₄	C₁₃×#135	1	2	yes	—
445	C₂×C₄	C₁₃×#137	1	2	yes	—
446	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
447	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
448	C₈	—	4	2	no	—
449	C₈	—	4	2	no	—
450	C₂²	—	2	1	no	—
451	C₂²	—	2	1	no	—
452	C₂²	—	4	2	no	—
453	C₂²	—	4	2	no	—
454	C₂²	—	4	2	no	—
455	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
456	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
457	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
458	C₄	—	2	1	no	—
459	C₄	—	2	1	no	—
460	C₄	—	2	1	no	—
461	C₄	—	4	2	no	—
462	C₄	—	4	2	no	—
463	C₄	—	4	2	no	—
464	C₄	—	4	2	no	—
465	C₄	—	4	2	no	—
466	C₄	—	8	2	no	—
467	C₄	—	8	2	no	—
468	C₄	C₁₃×#452	1	2	yes	—
469	C₄	C₁₃×#452	1	2	yes	—
470	C₄	C₁₃×#454	1	2	yes	—
471	C₂	—	2	1	no	—
472	C₂	—	2	1	no	—
473	C₂	—	8	2	no	—
474	C₂	C₂×C₁₃×#452	1	1	yes	characteristic
475	C₂	C₂×C₁₃×#454	1	1	yes	characteristic
476	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×#3230	C₂	semidirect
4. C₁₃×#2568	C₂	semidirect
5. C₁₃×#1615	C₂	semidirect
6. C₁₃×#1503	C₂	semidirect
8. C₁₃×#1461	C₂	semidirect
108. #18399	C₁₃	direct (N × H)
172. #3230	C₂×C₁₃	semidirect
174. #2568	C₂×C₁₃	semidirect
175. #1615	C₂×C₁₃	semidirect
176. #1503	C₂×C₁₃	semidirect
178. #1461	C₂×C₁₃	semidirect
408. C₁₃	#18399	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×#3230	2
C₁₃×#3227	2
C₁₃×#2568	2
C₁₃×#1615	2
C₁₃×#1503	2
C₁₃×#1502	2
C₁₃×#1461	2
#18399	13

Subgroups — C13×#18399 #15704738

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18399 #15704738