Subgroups — C₁₃×#18713 #15705052

Order 3328.

956 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3247	C₂	1	2	yes	maximal, complemented
3	C₁₃×#3152	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1634	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1633	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1632	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1624	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1623	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1622	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#333	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1483	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₃×#137	—	2	2	no	—
13	C₁₃×#563	—	2	2	no	—
14	Q₈²×C₁₃	C₂²	1	1	yes	characteristic
15	C₁₃×#555	C₂²	1	1	yes	characteristic
16	C₁₃×#554	C₂²	1	2	yes	—
17	C₁₃×#552	—	2	2	no	—
18	C₁₃×#547	—	2	2	no	—
19	C₁₃×#544	—	2	2	no	—
20	C₁₃×#542	—	2	2	no	—
21	C₁₃×#536	—	2	2	no	—
22	C₁₃×#532	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₁₃×#529	C₂²	1	2	yes	—
25	C₁₃×#497	—	2	2	no	—
26	C₁₃×#494	C₂²	1	1	yes	characteristic
27	C₁₃×#494	C₂²	1	1	yes	characteristic
28	C₁₃×#492	C₂²	1	1	yes	characteristic
29	C₁₃×#492	C₂²	1	1	yes	characteristic
30	C₁₃×#478	—	2	2	no	—
31	C₁₃×#477	C₂²	1	2	yes	—
32	C₁₃×#476	C₂²	1	2	yes	—
33	C₁₃×#466	—	2	2	no	—
34	C₁₃×#465	—	2	2	no	—
35	C₁₃×#463	—	2	2	no	—
36	C₁₃×#460	C₂²	1	2	yes	—
37	C₁₃×#459	C₂²	1	2	yes	—
38	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
39	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
40	C₁₃×#333	C₂²	1	2	yes	—
41	C₁₃×#333	C₂²	1	1	yes	characteristic
42	C₁₃×#333	C₂²	1	1	yes	characteristic
43	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
44	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
45	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
46	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
47	C₂×C₁₃×#41	—	2	2	no	—
48	C₂×C₁₃×#41	—	2	1	no	—
49	C₂²×Q₈×C₁₃	D₄	1	2	yes	—
50	C₁₃×#137	—	4	8	no	—
51	C₂×C₁₃×Q₁₆	—	2	2	no	—
52	C₂×C₁₃×Q₁₆	—	2	2	no	—
53	C₂×C₁₃×SD₁₆	—	2	2	no	—
54	C₂×C₁₃×SD₁₆	—	2	2	no	—
55	C₂×C₁₃×SD₁₆	—	2	2	no	—
56	C₂×C₁₃×D₈	—	2	2	no	—
57	C₂×C₁₃×M₁₆	—	2	1	no	—
58	C₂²×C₈×C₁₃	—	2	2	no	—
59	C₁₃×C₄⋊Q₈	—	2	2	no	—
60	C₁₃×C₄⋊Q₈	—	2	2	no	—
61	C₁₃×C₄⋊Q₈	—	2	2	no	—
62	C₁₃×C₄⋊Q₈	—	2	2	no	—
63	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
64	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
65	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
66	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
67	C₁₃×#127	C₂³	1	1	yes	characteristic
68	C₁₃×#126	—	2	4	no	—
69	C₁₃×#126	—	2	2	no	—
70	C₁₃×#125	—	2	4	no	—
71	C₁₃×#125	—	2	2	no	—
72	C₁₃×#125	D₄	1	2	yes	—
73	C₁₃×#124	—	2	2	no	—
74	C₁₃×#124	—	2	2	no	—
75	C₁₃×#124	—	2	1	no	—
76	C₁₃×#124	D₄	1	2	yes	—
77	C₁₃×#123	—	2	4	no	—
78	C₁₃×#123	—	2	4	no	—
79	C₁₃×#123	—	2	2	no	—
80	C₁₃×C₂²⋊Q₈	—	2	4	no	—
81	C₁₃×C₂²⋊Q₈	—	2	4	no	—
82	C₁₃×C₂²⋊Q₈	—	2	4	no	—
83	C₁₃×C₂²⋊Q₈	—	2	2	no	—
84	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
85	C₁₃×#121	—	2	2	no	—
86	C₁₃×#121	—	2	2	no	—
87	C₁₃×#121	D₄	1	2	yes	—
88	C₄×Q₈×C₁₃	—	2	2	no	—
89	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
90	C₄×D₄×C₁₃	—	2	2	no	—
91	C₄×D₄×C₁₃	—	2	2	no	—
92	C₄×D₄×C₁₃	—	2	2	no	—
93	C₄×D₄×C₁₃	C₂³	1	2	yes	—
94	C₁₃×#117	—	2	2	no	—
95	C₁₃×#117	—	2	2	no	—
96	C₁₃×#117	—	2	2	no	—
97	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
98	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
99	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
100	C₁₃×#107	—	2	2	no	—
101	C₁₃×#106	—	2	2	no	—
102	C₁₃×C₄⋊C₈	—	2	2	no	—
103	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
104	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
105	C₁₃×#103	—	2	2	no	—
106	C₁₃×#102	—	2	2	no	—
107	C₁₃×#102	—	2	2	no	—
108	C₁₃×#102	—	2	2	no	—
109	C₁₃×#97	—	2	1	no	—
110	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
111	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
112	#18713	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
113	C₁₃×#41	—	4	4	no	—
114	C₁₃×#41	—	8	4	no	—
115	C₂×Q₈×C₁₃	—	2	2	no	—
116	C₂×Q₈×C₁₃	—	2	2	no	—
117	C₂×Q₈×C₁₃	—	2	1	no	—
118	C₂×Q₈×C₁₃	—	4	4	no	—
119	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
120	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
121	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
122	C₂×D₄×C₁₃	—	2	2	no	—
123	C₂×D₄×C₁₃	—	2	2	no	—
124	C₂×D₄×C₁₃	—	2	2	no	—
125	C₂×D₄×C₁₃	—	2	1	no	—
126	C₂×D₄×C₁₃	—	4	1	no	—
127	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₃	—	2	2	no	—
129	C₂²×C₄×C₁₃	—	2	4	no	—
130	C₂²×C₄×C₁₃	—	2	2	no	—
131	C₂²×C₄×C₁₃	—	4	1	no	—
132	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₁₃×Q₁₆	—	4	4	no	—
135	C₁₃×Q₁₆	—	4	4	no	—
136	C₁₃×SD₁₆	—	4	4	no	—
137	C₁₃×SD₁₆	—	4	4	no	—
138	C₁₃×SD₁₆	—	8	2	no	—
139	C₁₃×D₈	—	8	2	no	—
140	C₁₃×M₁₆	—	2	4	no	—
141	C₂×C₈×C₁₃	—	2	1	no	—
142	C₂×C₈×C₁₃	—	2	1	no	—
143	C₂×C₈×C₁₃	—	2	2	no	—
144	C₂×C₈×C₁₃	—	2	2	no	—
145	C₂×C₈×C₁₃	—	8	2	no	—
146	C₁₃×C₄⋊C₄	—	2	4	no	—
147	C₁₃×C₄⋊C₄	—	2	4	no	—
148	C₁₃×C₄⋊C₄	—	2	4	no	—
149	C₁₃×C₄⋊C₄	—	2	4	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	—	2	2	no	—
155	C₁₃×C₄⋊C₄	—	2	2	no	—
156	C₁₃×C₄⋊C₄	—	2	2	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	2	no	—
162	C₁₃×C₂²⋊C₄	—	2	2	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	—	4	2	no	—
167	C₄²×C₁₃	—	2	2	no	—
168	C₄²×C₁₃	—	2	2	no	—
169	C₄²×C₁₃	—	2	2	no	—
170	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₁₃	C₂×D₄	1	2	yes	—
172	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
173	#3544	C₂×C₁₃	1	1	yes	characteristic, complemented
174	#3247	C₂×C₁₃	1	2	yes	complemented
175	#3152	C₂×C₁₃	1	1	yes	characteristic, complemented
176	#1634	C₂×C₁₃	1	1	yes	characteristic, complemented
177	#1633	C₂×C₁₃	1	1	yes	characteristic, complemented
178	#1632	C₂×C₁₃	1	2	yes	complemented
179	#1624	C₂×C₁₃	1	1	yes	characteristic, complemented
180	#1623	C₂×C₁₃	1	1	yes	characteristic, complemented
181	#1622	C₂×C₁₃	1	2	yes	complemented
182	C₂×#333	C₂×C₁₃	1	1	yes	characteristic, complemented
183	#1483	C₂×C₁₃	1	2	yes	complemented
184	C₂³×C₁₃	—	2	2	no	—
185	C₂³×C₁₃	—	4	1	no	—
186	C₂³×C₁₃	#120	1	1	yes	characteristic
187	Q₈×C₁₃	—	2	2	no	—
188	Q₈×C₁₃	—	2	2	no	—
189	Q₈×C₁₃	—	4	2	no	—
190	Q₈×C₁₃	—	4	2	no	—
191	Q₈×C₁₃	—	4	2	no	—
192	Q₈×C₁₃	—	8	2	no	—
193	Q₈×C₁₃	—	8	2	no	—
194	D₄×C₁₃	—	2	2	no	—
195	D₄×C₁₃	—	2	2	no	—
196	D₄×C₁₃	—	4	2	no	—
197	D₄×C₁₃	—	4	4	no	—
198	D₄×C₁₃	—	4	2	no	—
199	D₄×C₁₃	—	4	2	no	—
200	D₄×C₁₃	—	8	2	no	—
201	D₄×C₁₃	—	8	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	—	2	2	no	—
209	C₂×C₄×C₁₃	—	2	2	no	—
210	C₂×C₄×C₁₃	—	4	4	no	—
211	C₂×C₄×C₁₃	—	4	2	no	—
212	C₂×C₄×C₁₃	—	4	2	no	—
213	C₂×C₄×C₁₃	—	4	1	no	—
214	C₂×C₄×C₁₃	—	8	2	no	—
215	C₂×C₄×C₁₃	—	8	4	no	—
216	C₂×C₄×C₁₃	#120	1	2	yes	—
217	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
218	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
220	C₈×C₁₃	—	2	2	no	—
221	C₈×C₁₃	—	2	2	no	—
222	C₈×C₁₃	—	4	2	no	—
223	C₈×C₁₃	—	4	2	no	—
224	C₂×#137	—	2	2	no	—
225	#563	—	2	2	no	—
226	Q₈²	C₂²×C₁₃	1	1	yes	characteristic
227	#555	C₂²×C₁₃	1	1	yes	characteristic
228	#554	C₂²×C₁₃	1	2	yes	—
229	#552	—	2	2	no	—
230	#547	—	2	2	no	—
231	#544	—	2	2	no	—
232	#542	—	2	2	no	—
233	#536	—	2	2	no	—
234	#532	C₂²×C₁₃	1	1	yes	characteristic
235	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
236	#529	C₂²×C₁₃	1	2	yes	—
237	#497	—	2	2	no	—
238	#494	C₂²×C₁₃	1	1	yes	characteristic
239	#494	C₂²×C₁₃	1	1	yes	characteristic
240	#492	C₂²×C₁₃	1	1	yes	characteristic
241	#492	C₂²×C₁₃	1	1	yes	characteristic
242	#478	—	2	2	no	—
243	#477	C₂²×C₁₃	1	2	yes	—
244	#476	C₂²×C₁₃	1	2	yes	—
245	#466	—	2	2	no	—
246	#465	—	2	2	no	—
247	#463	—	2	2	no	—
248	#460	C₂²×C₁₃	1	2	yes	—
249	#459	C₂²×C₁₃	1	2	yes	—
250	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
251	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
252	#333	C₂²×C₁₃	1	2	yes	—
253	#333	C₂²×C₁₃	1	1	yes	characteristic
254	#333	C₂²×C₁₃	1	1	yes	characteristic
255	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
256	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
257	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
258	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
259	C₂²×C₁₃	—	2	2	no	—
260	C₂²×C₁₃	—	4	2	no	—
261	C₂²×C₁₃	—	4	2	no	—
262	C₂²×C₁₃	—	4	2	no	—
263	C₂²×C₁₃	—	8	2	no	—
264	C₂²×C₁₃	—	8	1	no	—
265	C₂²×C₁₃	#453	1	2	yes	—
266	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
267	C₄×C₁₃	—	2	2	no	—
268	C₄×C₁₃	—	2	1	no	—
269	C₄×C₁₃	—	2	1	no	—
270	C₄×C₁₃	—	4	2	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	1	no	—
276	C₄×C₁₃	#577	1	2	yes	—
277	C₄×C₁₃	#578	1	2	yes	—
278	C₂×#41	—	2	2	no	—
279	C₂×#41	—	2	1	no	—
280	C₂²×Q₈	D₄×C₁₃	1	2	yes	—
281	#137	—	4	8	no	—
282	C₂×Q₁₆	—	2	2	no	—
283	C₂×Q₁₆	—	2	2	no	—
284	C₂×SD₁₆	—	2	2	no	—
285	C₂×SD₁₆	—	2	2	no	—
286	C₂×SD₁₆	—	2	2	no	—
287	C₂×D₈	—	2	2	no	—
288	C₂×M₁₆	—	2	1	no	—
289	C₂²×C₈	—	2	2	no	—
290	C₄⋊Q₈	—	2	2	no	—
291	C₄⋊Q₈	—	2	2	no	—
292	C₄⋊Q₈	—	2	2	no	—
293	C₄⋊Q₈	—	2	2	no	—
294	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
295	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
296	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
297	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
298	#127	C₂³×C₁₃	1	1	yes	characteristic
299	#126	—	2	4	no	—
300	#126	—	2	2	no	—
301	#125	—	2	4	no	—
302	#125	—	2	2	no	—
303	#125	D₄×C₁₃	1	2	yes	—
304	#124	—	2	2	no	—
305	#124	—	2	2	no	—
306	#124	—	2	1	no	—
307	#124	D₄×C₁₃	1	2	yes	—
308	#123	—	2	4	no	—
309	#123	—	2	4	no	—
310	#123	—	2	2	no	—
311	C₂²⋊Q₈	—	2	4	no	—
312	C₂²⋊Q₈	—	2	4	no	—
313	C₂²⋊Q₈	—	2	4	no	—
314	C₂²⋊Q₈	—	2	2	no	—
315	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
316	#121	—	2	2	no	—
317	#121	—	2	2	no	—
318	#121	D₄×C₁₃	1	2	yes	—
319	C₄×Q₈	—	2	2	no	—
320	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
321	C₄×D₄	—	2	2	no	—
322	C₄×D₄	—	2	2	no	—
323	C₄×D₄	—	2	2	no	—
324	C₄×D₄	C₂³×C₁₃	1	2	yes	—
325	#117	—	2	2	no	—
326	#117	—	2	2	no	—
327	#117	—	2	2	no	—
328	C₂×C₄⋊C₄	—	2	2	no	—
329	C₂×C₄⋊C₄	—	2	2	no	—
330	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
331	#107	—	2	2	no	—
332	#106	—	2	2	no	—
333	C₄⋊C₈	—	2	2	no	—
334	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
335	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
336	#103	—	2	2	no	—
337	#102	—	2	2	no	—
338	#102	—	2	2	no	—
339	#102	—	2	2	no	—
340	#97	—	2	1	no	—
341	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
342	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
343	C₂×C₁₃	—	2	2	no	—
344	C₂×C₁₃	—	8	2	no	—
345	C₂×C₁₃	—	16	1	no	—
346	C₂×C₁₃	#3013	1	2	yes	—
347	C₂×C₁₃	C₂×#453	1	1	yes	characteristic
348	#41	—	4	4	no	—
349	#41	—	8	4	no	—
350	C₂×Q₈	—	2	2	no	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	—	2	1	no	—
353	C₂×Q₈	—	4	4	no	—
354	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
355	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
356	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	4	1	no	—
362	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	4	1	no	—
367	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
368	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
369	Q₁₆	—	4	4	no	—
370	Q₁₆	—	4	4	no	—
371	SD₁₆	—	4	4	no	—
372	SD₁₆	—	4	4	no	—
373	SD₁₆	—	8	2	no	—
374	D₈	—	8	2	no	—
375	M₁₆	—	2	4	no	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	8	2	no	—
381	C₄⋊C₄	—	2	4	no	—
382	C₄⋊C₄	—	2	4	no	—
383	C₄⋊C₄	—	2	4	no	—
384	C₄⋊C₄	—	2	4	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
393	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
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	C₂²⋊C₄	—	2	2	no	—
400	C₂²⋊C₄	—	2	2	no	—
401	C₂²⋊C₄	—	4	2	no	—
402	C₄²	—	2	2	no	—
403	C₄²	—	2	2	no	—
404	C₄²	—	2	2	no	—
405	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
406	C₄²	C₂×D₄×C₁₃	1	2	yes	—
407	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
408	C₁₃	#18713	1	1	yes	characteristic, direct product factor, Sylow
409	C₂³	—	2	2	no	—
410	C₂³	—	4	1	no	—
411	C₂³	C₁₃×#120	1	1	yes	characteristic
412	Q₈	—	2	2	no	—
413	Q₈	—	2	2	no	—
414	Q₈	—	4	2	no	—
415	Q₈	—	4	2	no	—
416	Q₈	—	4	2	no	—
417	Q₈	—	8	2	no	—
418	Q₈	—	8	2	no	—
419	D₄	—	2	2	no	—
420	D₄	—	2	2	no	—
421	D₄	—	4	2	no	—
422	D₄	—	4	4	no	—
423	D₄	—	4	2	no	—
424	D₄	—	4	2	no	—
425	D₄	—	8	2	no	—
426	D₄	—	8	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	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	4	4	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	8	2	no	—
440	C₂×C₄	—	8	4	no	—
441	C₂×C₄	C₁₃×#120	1	2	yes	—
442	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
443	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
444	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
445	C₈	—	2	2	no	—
446	C₈	—	2	2	no	—
447	C₈	—	4	2	no	—
448	C₈	—	4	2	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	4	2	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	4	2	no	—
453	C₂²	—	8	2	no	—
454	C₂²	—	8	1	no	—
455	C₂²	C₁₃×#453	1	2	yes	—
456	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
457	C₄	—	2	2	no	—
458	C₄	—	2	1	no	—
459	C₄	—	2	1	no	—
460	C₄	—	4	2	no	—
461	C₄	—	4	2	no	—
462	C₄	—	4	2	no	—
463	C₄	—	4	2	no	—
464	C₄	—	4	2	no	—
465	C₄	—	8	1	no	—
466	C₄	C₁₃×#577	1	2	yes	—
467	C₄	C₁₃×#578	1	2	yes	—
468	C₂	—	2	2	no	—
469	C₂	—	8	2	no	—
470	C₂	—	16	1	no	—
471	C₂	C₁₃×#3013	1	2	yes	—
472	C₂	C₂×C₁₃×#453	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
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
1. C₁₃×#3544	C₂	semidirect
2. C₁₃×#3247	C₂	semidirect
3. C₁₃×#3152	C₂	semidirect
4. C₁₃×#1634	C₂	semidirect
5. C₁₃×#1633	C₂	semidirect
6. C₁₃×#1632	C₂	semidirect
7. C₁₃×#1624	C₂	semidirect
8. C₁₃×#1623	C₂	semidirect
9. C₁₃×#1622	C₂	semidirect
10. C₂×C₁₃×#333	C₂	semidirect
11. C₁₃×#1483	C₂	semidirect
112. #18713	C₁₃	direct (N × H)
173. #3544	C₂×C₁₃	semidirect
174. #3247	C₂×C₁₃	semidirect
175. #3152	C₂×C₁₃	semidirect
176. #1634	C₂×C₁₃	semidirect
177. #1633	C₂×C₁₃	semidirect
178. #1632	C₂×C₁₃	semidirect
179. #1624	C₂×C₁₃	semidirect
180. #1623	C₂×C₁₃	semidirect
181. #1622	C₂×C₁₃	semidirect
182. C₂×#333	C₂×C₁₃	semidirect
183. #1483	C₂×C₁₃	semidirect
408. C₁₃	#18713	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×#3544	2
C₁₃×#3247	2
C₁₃×#3152	2
C₁₃×#1634	2
C₁₃×#1633	2
C₁₃×#1632	2
C₁₃×#1624	2
C₁₃×#1623	2
C₁₃×#1622	2
C₂×C₁₃×#333	2
C₁₃×#1483	2
#18713	13

Subgroups — C13×#18713 #15705052

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18713 #15705052