Subgroups — C₁₃×#10055 #15696394

Order 3328.

702 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	C₂×C₁₃×#492	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#477	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2548	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1987	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#331	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₁₃×SD₁₆	—	2	2	no	—
9	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
10	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#124	—	2	1	no	—
12	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₁₃×#492	—	2	2	no	—
14	C₁₃×#492	—	2	2	no	—
15	C₁₃×#477	—	2	2	no	—
16	C₁₃×#477	—	2	2	no	—
17	C₂×C₁₃×#107	—	2	1	no	—
18	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#103	—	2	1	no	—
21	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#394	—	2	2	no	—
23	C₁₃×#390	—	2	1	no	—
24	C₁₃×#390	—	2	2	no	—
25	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₁₃×#340	—	2	2	no	—
27	C₁₃×#331	—	2	2	no	—
28	C₁₃×Q₈⋊C₈	—	2	2	no	—
29	C₂²×Q₈×C₁₃	—	2	1	no	—
30	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
31	C₂²×D₄×C₁₃	—	2	1	no	—
32	C₂²×D₄×C₁₃	—	2	1	no	—
33	C₂²×D₄×C₁₃	D₄	1	2	yes	—
34	C₂×C₁₃×SD₁₆	—	2	8	no	—
35	C₂×C₁₃×SD₁₆	—	4	8	no	—
36	C₂²×C₈×C₁₃	—	2	1	no	—
37	C₂²×C₈×C₁₃	—	2	1	no	—
38	C₂²×C₈×C₁₃	—	2	1	no	—
39	C₁₃×C₄⋊Q₈	—	2	1	no	—
40	C₁₃×C₄⋊Q₈	—	2	1	no	—
41	C₁₃×C₄⋊Q₈	—	2	1	no	—
42	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
43	C₁₃×#127	—	2	1	no	—
44	C₁₃×#127	—	2	1	no	—
45	C₁₃×#127	—	2	1	no	—
46	C₁₃×#127	—	2	1	no	—
47	C₁₃×#124	—	4	2	no	—
48	C₁₃×#124	—	4	2	no	—
49	C₄×Q₈×C₁₃	—	2	1	no	—
50	C₄×Q₈×C₁₃	—	2	1	no	—
51	C₄×Q₈×C₁₃	—	2	1	no	—
52	C₄×Q₈×C₁₃	—	2	1	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
56	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
57	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
58	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
59	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
60	C₂×C₄²×C₁₃	—	2	1	no	—
61	C₂×C₄²×C₁₃	—	2	1	no	—
62	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
63	C₁₃×#107	—	2	4	no	—
64	C₁₃×C₄⋊C₈	—	2	1	no	—
65	C₁₃×C₄⋊C₈	—	2	1	no	—
66	C₁₃×C₄⋊C₈	—	2	1	no	—
67	C₁₃×C₄⋊C₈	D₄	1	2	yes	—
68	C₁₃×#103	—	2	4	no	—
69	C₄×C₈×C₁₃	—	2	1	no	—
70	C₄×C₈×C₁₃	D₄	1	2	yes	—
71	C₁₃×#95	—	2	1	no	—
72	#10055	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
73	C₂⁴×C₁₃	—	2	2	no	—
74	C₂×Q₈×C₁₃	—	2	1	no	—
75	C₂×Q₈×C₁₃	—	2	1	no	—
76	C₂×Q₈×C₁₃	—	2	2	no	—
77	C₂×Q₈×C₁₃	—	2	1	no	—
78	C₂×Q₈×C₁₃	—	2	1	no	—
79	C₂×Q₈×C₁₃	—	2	1	no	—
80	C₂×Q₈×C₁₃	—	4	4	no	—
81	C₂×Q₈×C₁₃	—	4	1	no	—
82	C₂×Q₈×C₁₃	SD₁₆	1	2	yes	complemented
83	C₂×D₄×C₁₃	—	2	2	no	—
84	C₂×D₄×C₁₃	—	2	2	no	—
85	C₂×D₄×C₁₃	—	4	4	no	—
86	C₂×D₄×C₁₃	—	4	1	no	—
87	C₂×D₄×C₁₃	—	4	1	no	—
88	C₂×D₄×C₁₃	—	4	1	no	—
89	C₂×D₄×C₁₃	—	4	1	no	—
90	C₂×D₄×C₁₃	—	4	1	no	—
91	C₂×D₄×C₁₃	—	4	1	no	—
92	C₂×D₄×C₁₃	—	4	2	no	—
93	C₂×D₄×C₁₃	—	4	1	no	—
94	C₂×D₄×C₁₃	—	4	1	no	—
95	C₂×D₄×C₁₃	—	4	2	no	—
96	C₂²×C₄×C₁₃	—	2	1	no	—
97	C₂²×C₄×C₁₃	—	2	2	no	—
98	C₂²×C₄×C₁₃	—	2	1	no	—
99	C₂²×C₄×C₁₃	—	4	1	no	—
100	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
103	C₁₃×SD₁₆	—	4	16	no	—
104	C₂×C₈×C₁₃	—	2	4	no	—
105	C₂×C₈×C₁₃	—	2	2	no	—
106	C₂×C₈×C₁₃	—	2	2	no	—
107	C₂×C₈×C₁₃	—	4	1	no	—
108	C₂×C₈×C₁₃	—	4	1	no	—
109	C₂×C₈×C₁₃	—	4	1	no	—
110	C₂×C₈×C₁₃	—	4	2	no	—
111	C₁₃×C₄⋊C₄	—	2	2	no	—
112	C₁₃×C₄⋊C₄	—	2	1	no	—
113	C₁₃×C₄⋊C₄	—	2	2	no	—
114	C₁₃×C₄⋊C₄	—	2	1	no	—
115	C₁₃×C₄⋊C₄	—	2	2	no	—
116	C₁₃×C₄⋊C₄	—	2	2	no	—
117	C₁₃×C₄⋊C₄	—	4	1	no	—
118	C₁₃×C₄⋊C₄	—	4	1	no	—
119	C₁₃×C₄⋊C₄	—	4	1	no	—
120	C₁₃×C₄⋊C₄	—	4	1	no	—
121	C₁₃×C₂²⋊C₄	—	4	8	no	—
122	C₁₃×C₂²⋊C₄	—	8	4	no	—
123	C₄²×C₁₃	—	4	1	no	—
124	C₄²×C₁₃	—	4	1	no	—
125	C₄²×C₁₃	—	4	1	no	—
126	C₄²×C₁₃	—	4	1	no	—
127	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₁₃	#41	1	1	yes	characteristic
131	C₂×#492	C₂×C₁₃	1	1	yes	characteristic
132	C₂×#477	C₂×C₁₃	1	1	yes	characteristic, complemented
133	#2548	C₂×C₁₃	1	1	yes	characteristic
134	#1987	C₂×C₁₃	1	1	yes	characteristic, complemented
135	C₂×#331	C₂×C₁₃	1	1	yes	characteristic
136	C₂×Q₈⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
137	#1279	C₂×C₁₃	1	1	yes	characteristic, complemented
138	C₂³×C₁₃	—	4	2	no	—
139	C₂³×C₁₃	—	4	2	no	—
140	C₂³×C₁₃	—	4	2	no	—
141	C₂³×C₁₃	—	4	4	no	—
142	C₂³×C₁₃	—	4	4	no	—
143	C₂³×C₁₃	#120	1	1	yes	characteristic
144	Q₈×C₁₃	—	2	2	no	—
145	Q₈×C₁₃	—	2	2	no	—
146	Q₈×C₁₃	—	4	4	no	—
147	Q₈×C₁₃	—	4	1	no	—
148	Q₈×C₁₃	—	4	1	no	—
149	Q₈×C₁₃	—	8	2	no	—
150	D₄×C₁₃	—	4	4	no	—
151	D₄×C₁₃	—	8	2	no	—
152	D₄×C₁₃	—	8	1	no	—
153	D₄×C₁₃	—	8	1	no	—
154	D₄×C₁₃	—	8	2	no	—
155	D₄×C₁₃	—	8	1	no	—
156	D₄×C₁₃	—	8	1	no	—
157	D₄×C₁₃	—	8	1	no	—
158	D₄×C₁₃	—	8	1	no	—
159	C₂×C₄×C₁₃	—	2	2	no	—
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	—	4	1	no	—
162	C₂×C₄×C₁₃	—	4	1	no	—
163	C₂×C₄×C₁₃	—	4	1	no	—
164	C₂×C₄×C₁₃	—	4	2	no	—
165	C₂×C₄×C₁₃	—	4	2	no	—
166	C₂×C₄×C₁₃	—	4	2	no	—
167	C₂×C₄×C₁₃	—	4	2	no	—
168	C₂×C₄×C₁₃	—	4	2	no	—
169	C₂×C₄×C₁₃	—	8	2	no	—
170	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
171	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
172	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
173	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
174	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
175	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
176	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
177	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
178	C₂×C₄×C₁₃	#135	1	2	yes	—
179	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
180	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
181	C₂×C₄×C₁₃	#137	1	2	yes	—
182	C₈×C₁₃	—	2	4	no	—
183	C₈×C₁₃	—	4	2	no	—
184	C₈×C₁₃	—	8	1	no	—
185	C₂²×SD₁₆	—	2	2	no	—
186	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
187	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
188	C₂×#124	—	2	1	no	—
189	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
190	#492	—	2	2	no	—
191	#492	—	2	2	no	—
192	#477	—	2	2	no	—
193	#477	—	2	2	no	—
194	C₂×#107	—	2	1	no	—
195	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
196	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
197	C₂×#103	—	2	1	no	—
198	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
199	#394	—	2	2	no	—
200	#390	—	2	2	no	—
201	#390	—	2	1	no	—
202	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
203	#340	—	2	2	no	—
204	#331	—	2	2	no	—
205	Q₈⋊C₈	—	2	2	no	—
206	C₂²×C₁₃	—	8	4	no	—
207	C₂²×C₁₃	—	8	4	no	—
208	C₂²×C₁₃	—	8	2	no	—
209	C₂²×C₁₃	—	8	2	no	—
210	C₂²×C₁₃	—	8	2	no	—
211	C₂²×C₁₃	#392	1	1	yes	characteristic
212	C₂²×C₁₃	#450	1	1	yes	characteristic
213	C₂²×C₁₃	#452	1	1	yes	characteristic
214	C₂²×C₁₃	#452	1	2	yes	—
215	C₂²×C₁₃	#453	1	2	yes	—
216	C₄×C₁₃	—	2	1	no	—
217	C₄×C₁₃	—	2	1	no	—
218	C₄×C₁₃	—	4	2	no	—
219	C₄×C₁₃	—	8	2	no	—
220	C₄×C₁₃	—	8	1	no	—
221	C₄×C₁₃	—	8	2	no	—
222	C₄×C₁₃	#448	1	1	yes	characteristic
223	C₄×C₁₃	#449	1	1	yes	characteristic
224	C₄×C₁₃	#464	1	2	yes	—
225	C₄×C₁₃	#465	1	1	yes	characteristic
226	C₄×C₁₃	#468	1	1	yes	characteristic
227	C₄×C₁₃	#495	1	1	yes	characteristic
228	C₄×C₁₃	#497	1	1	yes	characteristic
229	C₂²×Q₈	—	2	1	no	—
230	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
231	C₂²×D₄	—	2	1	no	—
232	C₂²×D₄	—	2	1	no	—
233	C₂²×D₄	D₄×C₁₃	1	2	yes	—
234	C₂×SD₁₆	—	2	8	no	—
235	C₂×SD₁₆	—	4	8	no	—
236	C₂²×C₈	—	2	1	no	—
237	C₂²×C₈	—	2	1	no	—
238	C₂²×C₈	—	2	1	no	—
239	C₄⋊Q₈	—	2	1	no	—
240	C₄⋊Q₈	—	2	1	no	—
241	C₄⋊Q₈	—	2	1	no	—
242	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
243	#127	—	2	1	no	—
244	#127	—	2	1	no	—
245	#127	—	2	1	no	—
246	#127	—	2	1	no	—
247	#124	—	4	2	no	—
248	#124	—	4	2	no	—
249	C₄×Q₈	—	2	1	no	—
250	C₄×Q₈	—	2	1	no	—
251	C₄×Q₈	—	2	1	no	—
252	C₄×Q₈	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
257	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
258	C₂×C₂²⋊C₄	—	2	4	no	—
259	C₂×C₂²⋊C₄	—	2	4	no	—
260	C₂×C₄²	—	2	1	no	—
261	C₂×C₄²	—	2	1	no	—
262	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
263	#107	—	2	4	no	—
264	C₄⋊C₈	—	2	1	no	—
265	C₄⋊C₈	—	2	1	no	—
266	C₄⋊C₈	—	2	1	no	—
267	C₄⋊C₈	D₄×C₁₃	1	2	yes	—
268	#103	—	2	4	no	—
269	C₄×C₈	—	2	1	no	—
270	C₄×C₈	D₄×C₁₃	1	2	yes	—
271	#95	—	2	1	no	—
272	C₂×C₁₃	—	16	2	no	—
273	C₂×C₁₃	#1630	1	2	yes	—
274	C₂×C₁₃	#1631	1	2	yes	—
275	C₂×C₁₃	#2000	1	1	yes	characteristic
276	C₂×C₁₃	#2002	1	1	yes	characteristic
277	C₂×C₁₃	#2015	1	1	yes	characteristic
278	C₂⁴	—	2	2	no	—
279	C₂×Q₈	—	2	1	no	—
280	C₂×Q₈	—	2	1	no	—
281	C₂×Q₈	—	2	2	no	—
282	C₂×Q₈	—	2	1	no	—
283	C₂×Q₈	—	2	1	no	—
284	C₂×Q₈	—	2	1	no	—
285	C₂×Q₈	—	4	4	no	—
286	C₂×Q₈	—	4	1	no	—
287	C₂×Q₈	C₁₃×SD₁₆	1	2	yes	complemented
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	4	4	no	—
291	C₂×D₄	—	4	1	no	—
292	C₂×D₄	—	4	1	no	—
293	C₂×D₄	—	4	1	no	—
294	C₂×D₄	—	4	1	no	—
295	C₂×D₄	—	4	1	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂×D₄	—	4	2	no	—
298	C₂×D₄	—	4	1	no	—
299	C₂×D₄	—	4	1	no	—
300	C₂×D₄	—	4	2	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	4	1	no	—
305	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
306	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
308	SD₁₆	—	4	16	no	—
309	C₂×C₈	—	2	4	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	4	1	no	—
313	C₂×C₈	—	4	1	no	—
314	C₂×C₈	—	4	1	no	—
315	C₂×C₈	—	4	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	1	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	4	1	no	—
323	C₄⋊C₄	—	4	1	no	—
324	C₄⋊C₄	—	4	1	no	—
325	C₄⋊C₄	—	4	1	no	—
326	C₂²⋊C₄	—	4	8	no	—
327	C₂²⋊C₄	—	8	4	no	—
328	C₄²	—	4	1	no	—
329	C₄²	—	4	1	no	—
330	C₄²	—	4	1	no	—
331	C₄²	—	4	1	no	—
332	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
333	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
334	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
335	C₄²	C₁₃×#41	1	1	yes	characteristic
336	C₁₃	#10055	1	1	yes	characteristic, direct product factor, Sylow
337	C₂³	—	4	2	no	—
338	C₂³	—	4	2	no	—
339	C₂³	—	4	2	no	—
340	C₂³	—	4	4	no	—
341	C₂³	—	4	4	no	—
342	C₂³	C₁₃×#120	1	1	yes	characteristic
343	Q₈	—	2	2	no	—
344	Q₈	—	2	2	no	—
345	Q₈	—	4	4	no	—
346	Q₈	—	4	1	no	—
347	Q₈	—	4	1	no	—
348	Q₈	—	8	2	no	—
349	D₄	—	4	4	no	—
350	D₄	—	8	2	no	—
351	D₄	—	8	1	no	—
352	D₄	—	8	1	no	—
353	D₄	—	8	2	no	—
354	D₄	—	8	1	no	—
355	D₄	—	8	1	no	—
356	D₄	—	8	1	no	—
357	D₄	—	8	1	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	8	2	no	—
369	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
370	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
371	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
372	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
373	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
374	C₂×C₄	C₁₃×#127	1	1	yes	characteristic
375	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
376	C₂×C₄	C₁₃×#135	1	1	yes	characteristic
377	C₂×C₄	C₁₃×#135	1	2	yes	—
378	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
379	C₂×C₄	C₁₃×#137	1	1	yes	characteristic
380	C₂×C₄	C₁₃×#137	1	2	yes	—
381	C₈	—	2	4	no	—
382	C₈	—	4	2	no	—
383	C₈	—	8	1	no	—
384	C₂²	—	8	2	no	—
385	C₂²	—	8	2	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	4	no	—
388	C₂²	—	8	4	no	—
389	C₂²	C₁₃×#392	1	1	yes	characteristic
390	C₂²	C₁₃×#450	1	1	yes	characteristic
391	C₂²	C₁₃×#452	1	1	yes	characteristic
392	C₂²	C₁₃×#452	1	2	yes	—
393	C₂²	C₁₃×#453	1	2	yes	—
394	C₄	—	2	1	no	—
395	C₄	—	2	1	no	—
396	C₄	—	4	2	no	—
397	C₄	—	8	1	no	—
398	C₄	—	8	2	no	—
399	C₄	—	8	2	no	—
400	C₄	C₁₃×#448	1	1	yes	characteristic
401	C₄	C₁₃×#449	1	1	yes	characteristic
402	C₄	C₁₃×#464	1	2	yes	—
403	C₄	C₁₃×#465	1	1	yes	characteristic
404	C₄	C₁₃×#468	1	1	yes	characteristic
405	C₄	C₁₃×#495	1	1	yes	characteristic
406	C₄	C₁₃×#497	1	1	yes	characteristic
407	C₂	—	16	2	no	—
408	C₂	C₁₃×#1630	1	2	yes	—
409	C₂	C₁₃×#1631	1	2	yes	—
410	C₂	C₁₃×#2000	1	1	yes	characteristic
411	C₂	C₁₃×#2002	1	1	yes	characteristic
412	C₂	C₁₃×#2015	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂×C₁₃×#127	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#477	C₂	semidirect
4. C₁₃×#1987	C₂	semidirect
6. C₂×C₁₃×Q₈⋊C₈	C₂	semidirect
7. C₁₃×#1279	C₂	semidirect
72. #10055	C₁₃	direct (N × H)
82. C₂×Q₈×C₁₃	SD₁₆	semidirect
132. C₂×#477	C₂×C₁₃	semidirect
134. #1987	C₂×C₁₃	semidirect
136. C₂×Q₈⋊C₈	C₂×C₁₃	semidirect
137. #1279	C₂×C₁₃	semidirect
287. C₂×Q₈	C₁₃×SD₁₆	semidirect
336. C₁₃	#10055	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#492	2
C₂×C₁₃×#477	2
C₁₃×#2548	2
C₁₃×#1987	2
C₂×C₁₃×#331	2
C₂×C₁₃×Q₈⋊C₈	2
C₁₃×#1279	2
#10055	13

Subgroups — C13×#10055 #15696394

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10055 #15696394