Subgroups — C₁₃×#7678 #15694017

Order 3328.

630 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2854	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1728	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#336	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1271	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1270	C₂	1	2	yes	maximal, complemented
6	C₂²×C₁₃×M₁₆	—	2	1	no	—
7	C₂³×C₈×C₁₃	—	2	1	no	—
8	C₂×C₁₃×#123	—	2	1	no	—
9	C₂×C₁₃×#121	C₄	1	1	yes	characteristic
10	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
11	C₁₃×#390	C₄	1	1	yes	characteristic
12	C₁₃×#390	C₂²	1	1	yes	characteristic
13	C₁₃×#389	C₄	1	1	yes	characteristic
14	C₁₃×#389	C₂²	1	1	yes	characteristic
15	C₁₃×#388	—	2	1	no	—
16	C₁₃×#388	—	2	1	no	—
17	C₁₃×#386	—	2	1	no	—
18	C₁₃×#380	C₄	1	1	yes	characteristic
19	C₁₃×#336	—	2	1	no	—
20	C₁₃×#336	—	2	1	no	—
21	C₁₃×#336	C₂²	1	2	yes	—
22	C₁₃×#336	C₂²	1	2	yes	—
23	C₂²×D₄×C₁₃	—	2	1	no	—
24	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
25	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
27	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
28	C₂×C₁₃×M₁₆	—	2	4	no	—
29	C₂×C₁₃×M₁₆	—	4	2	no	—
30	C₂×C₁₃×M₁₆	—	4	2	no	—
31	C₂²×C₈×C₁₃	—	2	4	no	—
32	C₂²×C₈×C₁₃	—	2	2	no	—
33	C₂²×C₈×C₁₃	—	2	2	no	—
34	C₂²×C₈×C₁₃	—	4	2	no	—
35	C₂²×C₈×C₁₃	—	4	2	no	—
36	C₁₃×#123	—	4	2	no	—
37	C₁₃×#123	—	4	2	no	—
38	C₁₃×#121	—	4	2	no	—
39	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
40	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
41	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
42	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
43	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
44	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
45	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
46	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
47	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
48	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
49	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
50	C₂×C₄²×C₁₃	—	4	2	no	—
51	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
53	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
54	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
55	C₁₃×#95	—	2	1	no	—
56	C₁₃×#95	—	2	1	no	—
57	C₁₃×#95	—	2	1	no	—
58	#7678	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
59	C₂⁴×C₁₃	—	2	1	no	—
60	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
61	C₂×D₄×C₁₃	—	2	2	no	—
62	C₂×D₄×C₁₃	—	4	1	no	—
63	C₂×D₄×C₁₃	—	4	1	no	—
64	C₂×D₄×C₁₃	—	4	2	no	—
65	C₂×D₄×C₁₃	—	4	2	no	—
66	C₂×D₄×C₁₃	—	4	2	no	—
67	C₂²×C₄×C₁₃	—	2	2	no	—
68	C₂²×C₄×C₁₃	—	2	2	no	—
69	C₂²×C₄×C₁₃	—	2	2	no	—
70	C₂²×C₄×C₁₃	—	2	2	no	—
71	C₂²×C₄×C₁₃	—	2	1	no	—
72	C₂²×C₄×C₁₃	—	2	1	no	—
73	C₂²×C₄×C₁₃	—	2	2	no	—
74	C₂²×C₄×C₁₃	—	2	2	no	—
75	C₂²×C₄×C₁₃	—	2	1	no	—
76	C₂²×C₄×C₁₃	—	2	1	no	—
77	C₂²×C₄×C₁₃	—	2	1	no	—
78	C₂²×C₄×C₁₃	—	4	1	no	—
79	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₃	D₈	1	2	yes	—
83	C₂²×C₄×C₁₃	SD₁₆	1	2	yes	—
84	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
87	C₁₃×M₁₆	—	4	8	no	—
88	C₂×C₈×C₁₃	—	2	4	no	—
89	C₂×C₈×C₁₃	—	2	4	no	—
90	C₂×C₈×C₁₃	—	4	8	no	—
91	C₂×C₈×C₁₃	—	4	2	no	—
92	C₂×C₈×C₁₃	—	4	2	no	—
93	C₂×C₈×C₁₃	—	4	2	no	—
94	C₂×C₈×C₁₃	—	4	2	no	—
95	C₁₃×C₄⋊C₄	—	2	2	no	—
96	C₁₃×C₄⋊C₄	—	4	1	no	—
97	C₁₃×C₄⋊C₄	—	4	1	no	—
98	C₁₃×C₄⋊C₄	—	4	2	no	—
99	C₁₃×C₄⋊C₄	—	4	1	no	—
100	C₁₃×C₄⋊C₄	—	4	1	no	—
101	C₁₃×C₂²⋊C₄	—	4	2	no	—
102	C₁₃×C₂²⋊C₄	—	4	2	no	—
103	C₁₃×C₂²⋊C₄	—	4	2	no	—
104	C₁₃×C₂²⋊C₄	—	4	2	no	—
105	C₁₃×C₂²⋊C₄	—	4	1	no	—
106	C₁₃×C₂²⋊C₄	—	4	1	no	—
107	C₁₃×C₂²⋊C₄	—	4	1	no	—
108	C₁₃×C₂²⋊C₄	—	4	1	no	—
109	C₄²×C₁₃	—	4	1	no	—
110	C₄²×C₁₃	—	4	1	no	—
111	C₄²×C₁₃	—	4	1	no	—
112	C₄²×C₁₃	—	4	1	no	—
113	#2854	C₂×C₁₃	1	1	yes	characteristic
114	#1728	C₂×C₁₃	1	1	yes	characteristic, complemented
115	C₂×#336	C₂×C₁₃	1	1	yes	characteristic, complemented
116	#1271	C₂×C₁₃	1	2	yes	complemented
117	#1270	C₂×C₁₃	1	2	yes	complemented
118	C₂³×C₁₃	—	2	1	no	—
119	C₂³×C₁₃	—	2	1	no	—
120	C₂³×C₁₃	—	2	1	no	—
121	C₂³×C₁₃	—	2	1	no	—
122	C₂³×C₁₃	—	4	1	no	—
123	C₂³×C₁₃	—	4	1	no	—
124	C₂³×C₁₃	—	4	1	no	—
125	C₂³×C₁₃	—	4	1	no	—
126	C₂³×C₁₃	—	4	1	no	—
127	C₂³×C₁₃	—	4	1	no	—
128	C₂³×C₁₃	—	4	1	no	—
129	C₂³×C₁₃	#99	1	2	yes	—
130	C₂³×C₁₃	#102	1	2	yes	—
131	C₂³×C₁₃	#104	1	2	yes	—
132	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
133	D₄×C₁₃	—	8	2	no	—
134	D₄×C₁₃	—	8	4	no	—
135	C₂×C₄×C₁₃	—	2	4	no	—
136	C₂×C₄×C₁₃	—	2	4	no	—
137	C₂×C₄×C₁₃	—	2	4	no	—
138	C₂×C₄×C₁₃	—	2	4	no	—
139	C₂×C₄×C₁₃	—	2	1	no	—
140	C₂×C₄×C₁₃	—	2	1	no	—
141	C₂×C₄×C₁₃	—	2	1	no	—
142	C₂×C₄×C₁₃	—	2	1	no	—
143	C₂×C₄×C₁₃	—	2	1	no	—
144	C₂×C₄×C₁₃	—	2	1	no	—
145	C₂×C₄×C₁₃	—	2	1	no	—
146	C₂×C₄×C₁₃	—	2	1	no	—
147	C₂×C₄×C₁₃	—	2	1	no	—
148	C₂×C₄×C₁₃	—	2	1	no	—
149	C₂×C₄×C₁₃	—	2	1	no	—
150	C₂×C₄×C₁₃	—	2	1	no	—
151	C₂×C₄×C₁₃	—	2	1	no	—
152	C₂×C₄×C₁₃	—	4	4	no	—
153	C₂×C₄×C₁₃	—	4	1	no	—
154	C₂×C₄×C₁₃	—	4	1	no	—
155	C₂×C₄×C₁₃	—	4	1	no	—
156	C₂×C₄×C₁₃	—	4	1	no	—
157	C₂×C₄×C₁₃	—	4	1	no	—
158	C₂×C₄×C₁₃	—	4	1	no	—
159	C₂×C₄×C₁₃	—	4	1	no	—
160	C₂×C₄×C₁₃	—	4	1	no	—
161	C₂×C₄×C₁₃	—	4	1	no	—
162	C₂×C₄×C₁₃	#102	1	2	yes	—
163	C₂×C₄×C₁₃	#104	1	2	yes	—
164	C₂×C₄×C₁₃	#131	1	2	yes	—
165	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
166	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
167	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
168	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
169	C₈×C₁₃	—	4	4	no	—
170	C₈×C₁₃	—	4	4	no	—
171	C₂²×M₁₆	—	2	1	no	—
172	C₂³×C₈	—	2	1	no	—
173	C₂×#123	—	2	1	no	—
174	C₂×#121	C₄×C₁₃	1	1	yes	characteristic
175	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
176	#390	C₄×C₁₃	1	1	yes	characteristic
177	#390	C₂²×C₁₃	1	1	yes	characteristic
178	#389	C₄×C₁₃	1	1	yes	characteristic
179	#389	C₂²×C₁₃	1	1	yes	characteristic
180	#388	—	2	1	no	—
181	#388	—	2	1	no	—
182	#386	—	2	1	no	—
183	#380	C₄×C₁₃	1	1	yes	characteristic
184	#336	—	2	1	no	—
185	#336	—	2	1	no	—
186	#336	C₂²×C₁₃	1	2	yes	—
187	#336	C₂²×C₁₃	1	2	yes	—
188	C₂²×C₁₃	—	2	2	no	—
189	C₂²×C₁₃	—	2	2	no	—
190	C₂²×C₁₃	—	2	2	no	—
191	C₂²×C₁₃	—	2	2	no	—
192	C₂²×C₁₃	—	2	2	no	—
193	C₂²×C₁₃	—	2	2	no	—
194	C₂²×C₁₃	—	8	1	no	—
195	C₂²×C₁₃	—	8	1	no	—
196	C₂²×C₁₃	—	8	1	no	—
197	C₂²×C₁₃	—	8	1	no	—
198	C₂²×C₁₃	—	8	1	no	—
199	C₂²×C₁₃	—	8	1	no	—
200	C₂²×C₁₃	—	8	1	no	—
201	C₂²×C₁₃	#327	1	4	yes	—
202	C₂²×C₁₃	#408	1	1	yes	characteristic
203	C₂²×C₁₃	C₂×#99	1	1	yes	characteristic
204	C₂²×C₁₃	#413	1	1	yes	characteristic
205	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
206	C₂²×C₁₃	#417	1	1	yes	characteristic
207	C₂²×C₁₃	C₂×#104	1	1	yes	characteristic
208	C₂²×C₁₃	C₂×#104	1	1	yes	characteristic
209	C₄×C₁₃	—	2	2	no	—
210	C₄×C₁₃	—	2	1	no	—
211	C₄×C₁₃	—	2	2	no	—
212	C₄×C₁₃	—	2	1	no	—
213	C₄×C₁₃	—	2	1	no	—
214	C₄×C₁₃	—	2	2	no	—
215	C₄×C₁₃	—	2	1	no	—
216	C₄×C₁₃	—	4	1	no	—
217	C₄×C₁₃	—	8	1	no	—
218	C₄×C₁₃	—	8	1	no	—
219	C₄×C₁₃	—	8	1	no	—
220	C₂²×D₄	—	2	1	no	—
221	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
222	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
223	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
224	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
225	C₂×M₁₆	—	2	4	no	—
226	C₂×M₁₆	—	4	2	no	—
227	C₂×M₁₆	—	4	2	no	—
228	C₂²×C₈	—	2	4	no	—
229	C₂²×C₈	—	2	2	no	—
230	C₂²×C₈	—	2	2	no	—
231	C₂²×C₈	—	4	2	no	—
232	C₂²×C₈	—	4	2	no	—
233	#123	—	4	2	no	—
234	#123	—	4	2	no	—
235	#121	—	4	2	no	—
236	C₂×C₄⋊C₄	—	2	1	no	—
237	C₂×C₄⋊C₄	—	2	1	no	—
238	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
239	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
240	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
241	C₂×C₂²⋊C₄	—	2	1	no	—
242	C₂×C₂²⋊C₄	—	2	1	no	—
243	C₂×C₂²⋊C₄	—	2	1	no	—
244	C₂×C₂²⋊C₄	—	2	1	no	—
245	C₂×C₂²⋊C₄	—	2	1	no	—
246	C₂×C₂²⋊C₄	—	2	1	no	—
247	C₂×C₄²	—	4	2	no	—
248	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
249	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
250	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
251	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
252	#95	—	2	1	no	—
253	#95	—	2	1	no	—
254	#95	—	2	1	no	—
255	C₂×C₁₃	—	2	4	no	—
256	C₂×C₁₃	—	16	1	no	—
257	C₂×C₁₃	#1468	1	1	yes	characteristic
258	C₂×C₁₃	#1483	1	1	yes	characteristic
259	C₂×C₁₃	#1492	1	1	yes	characteristic
260	C₂×C₁₃	C₂×#327	1	1	yes	characteristic
261	C₂×C₁₃	#1504	1	1	yes	characteristic
262	C₂×C₁₃	#1524	1	1	yes	characteristic
263	C₂×C₁₃	#1547	1	1	yes	characteristic
264	C₂⁴	—	2	1	no	—
265	C₂⁴	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
266	C₂×D₄	—	2	2	no	—
267	C₂×D₄	—	4	1	no	—
268	C₂×D₄	—	4	1	no	—
269	C₂×D₄	—	4	2	no	—
270	C₂×D₄	—	4	2	no	—
271	C₂×D₄	—	4	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	4	1	no	—
284	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
285	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
286	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
287	C₂²×C₄	C₁₃×D₈	1	2	yes	—
288	C₂²×C₄	C₁₃×SD₁₆	1	2	yes	—
289	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
292	M₁₆	—	4	8	no	—
293	C₂×C₈	—	2	4	no	—
294	C₂×C₈	—	2	4	no	—
295	C₂×C₈	—	4	8	no	—
296	C₂×C₈	—	4	2	no	—
297	C₂×C₈	—	4	2	no	—
298	C₂×C₈	—	4	2	no	—
299	C₂×C₈	—	4	2	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	4	1	no	—
302	C₄⋊C₄	—	4	1	no	—
303	C₄⋊C₄	—	4	2	no	—
304	C₄⋊C₄	—	4	1	no	—
305	C₄⋊C₄	—	4	1	no	—
306	C₂²⋊C₄	—	4	2	no	—
307	C₂²⋊C₄	—	4	2	no	—
308	C₂²⋊C₄	—	4	2	no	—
309	C₂²⋊C₄	—	4	2	no	—
310	C₂²⋊C₄	—	4	1	no	—
311	C₂²⋊C₄	—	4	1	no	—
312	C₂²⋊C₄	—	4	1	no	—
313	C₂²⋊C₄	—	4	1	no	—
314	C₄²	—	4	1	no	—
315	C₄²	—	4	1	no	—
316	C₄²	—	4	1	no	—
317	C₄²	—	4	1	no	—
318	C₁₃	#7678	1	1	yes	characteristic, direct product factor, Sylow
319	C₂³	—	2	1	no	—
320	C₂³	—	2	1	no	—
321	C₂³	—	2	1	no	—
322	C₂³	—	2	1	no	—
323	C₂³	—	4	1	no	—
324	C₂³	—	4	1	no	—
325	C₂³	—	4	1	no	—
326	C₂³	—	4	1	no	—
327	C₂³	—	4	1	no	—
328	C₂³	—	4	1	no	—
329	C₂³	—	4	1	no	—
330	C₂³	C₁₃×#99	1	2	yes	—
331	C₂³	C₁₃×#102	1	2	yes	—
332	C₂³	C₁₃×#104	1	2	yes	—
333	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
334	D₄	—	8	2	no	—
335	D₄	—	8	4	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	C₁₃×#102	1	2	yes	—
364	C₂×C₄	C₁₃×#104	1	2	yes	—
365	C₂×C₄	C₁₃×#131	1	2	yes	—
366	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
367	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
368	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
369	C₂×C₄	C₁₃×#137	1	1	yes	characteristic
370	C₈	—	4	4	no	—
371	C₈	—	4	4	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	2	2	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	8	1	no	—
379	C₂²	—	8	1	no	—
380	C₂²	—	8	1	no	—
381	C₂²	—	8	1	no	—
382	C₂²	—	8	1	no	—
383	C₂²	—	8	1	no	—
384	C₂²	—	8	1	no	—
385	C₂²	C₁₃×#327	1	4	yes	—
386	C₂²	C₁₃×#408	1	1	yes	characteristic
387	C₂²	C₂×C₁₃×#99	1	1	yes	characteristic
388	C₂²	C₁₃×#413	1	1	yes	characteristic
389	C₂²	C₂×C₁₃×#102	1	1	yes	characteristic
390	C₂²	C₁₃×#417	1	1	yes	characteristic
391	C₂²	C₂×C₁₃×#104	1	1	yes	characteristic
392	C₂²	C₂×C₁₃×#104	1	1	yes	characteristic
393	C₄	—	2	1	no	—
394	C₄	—	2	2	no	—
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	2	no	—
398	C₄	—	2	1	no	—
399	C₄	—	2	2	no	—
400	C₄	—	4	1	no	—
401	C₄	—	8	1	no	—
402	C₄	—	8	1	no	—
403	C₄	—	8	1	no	—
404	C₂	—	2	4	no	—
405	C₂	—	16	1	no	—
406	C₂	C₁₃×#1468	1	1	yes	characteristic
407	C₂	C₁₃×#1483	1	1	yes	characteristic
408	C₂	C₁₃×#1492	1	1	yes	characteristic
409	C₂	C₂×C₁₃×#327	1	1	yes	characteristic
410	C₂	C₁₃×#1504	1	1	yes	characteristic
411	C₂	C₁₃×#1524	1	1	yes	characteristic
412	C₂	C₁₃×#1547	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂×C₁₃×#121	C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₁₃×#1728	C₂	semidirect
3. C₂×C₁₃×#336	C₂	semidirect
4. C₁₃×#1271	C₂	semidirect
5. C₁₃×#1270	C₂	semidirect
58. #7678	C₁₃	direct (N × H)
114. #1728	C₂×C₁₃	semidirect
115. C₂×#336	C₂×C₁₃	semidirect
116. #1271	C₂×C₁₃	semidirect
117. #1270	C₂×C₁₃	semidirect
318. C₁₃	#7678	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×#2854	2
C₁₃×#1728	2
C₂×C₁₃×#336	2
C₁₃×#1271	2
C₁₃×#1270	2
#7678	13

Subgroups — C13×#7678 #15694017

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#7678 #15694017