Subgroups — C₁₃×#33613 #15719952

Order 3328.

662 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#504	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3061	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#3059	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2220	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2219	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2217	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2216	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2159	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2138	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#358	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
15	C₁₃×#537	—	2	1	no	—
16	C₁₃×#536	—	2	1	no	—
17	C₁₃×#510	—	2	4	no	—
18	C₂×C₁₃×Q₃₂	C₂²	1	2	yes	—
19	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	—
20	C₁₃×#504	—	2	4	no	—
21	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
22	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
25	C₁₃×#470	—	2	2	no	—
26	C₁₃×#468	—	2	2	no	—
27	C₁₃×#467	C₂²	1	2	yes	—
28	C₁₃×#467	C₂²	1	2	yes	—
29	C₁₃×#467	C₂²	1	2	yes	—
30	C₁₃×#466	C₂²	1	2	yes	—
31	C₁₃×#427	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
33	C₁₃×#419	—	2	1	no	—
34	C₁₃×#417	—	2	1	no	—
35	C₁₃×#367	C₂²	1	2	yes	—
36	C₁₃×#366	C₂²	1	2	yes	—
37	C₁₃×#358	C₂²	1	2	yes	—
38	C₁₃×#358	C₂²	1	2	yes	—
39	C₁₃×#358	C₂²	1	1	yes	characteristic
40	C₁₃×#358	C₂²	1	1	yes	characteristic
41	C₁₃×#357	C₂²	1	1	yes	characteristic
42	C₁₃×#357	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#41	—	2	1	no	—
44	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
45	C₂²×Q₈×C₁₃	—	2	1	no	—
46	C₁₃×#135	—	2	2	no	—
47	C₁₃×#135	—	2	2	no	—
48	C₂×C₁₃×Q₁₆	—	2	2	no	—
49	C₂×C₁₃×Q₁₆	—	2	1	no	—
50	C₂×C₁₃×Q₁₆	—	2	2	no	—
51	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
52	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
53	C₂×C₁₃×SD₁₆	—	2	1	no	—
54	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
55	C₁₃×#131	—	2	2	no	—
56	C₁₃×#131	—	2	2	no	—
57	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
58	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
59	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
60	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
61	C₁₃×C₄⋊Q₈	—	4	1	no	—
62	C₁₃×#124	—	4	1	no	—
63	C₁₃×#123	—	4	2	no	—
64	C₁₃×C₂²⋊Q₈	—	2	2	no	—
65	C₁₃×C₂²⋊Q₈	—	2	2	no	—
66	C₁₃×C₂²⋊Q₈	—	2	2	no	—
67	C₁₃×C₂²⋊Q₈	—	4	1	no	—
68	C₁₃×#121	—	2	2	no	—
69	C₁₃×#121	—	4	1	no	—
70	C₁₃×#121	—	4	2	no	—
71	C₁₃×#117	—	2	1	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
73	C₁₃×Q₃₂	—	2	4	no	—
74	C₁₃×SD₃₂	—	2	4	no	—
75	C₁₃×M₃₂	—	2	4	no	—
76	C₁₃×M₃₂	D₄	1	4	yes	complemented
77	C₂×C₁₃×C₁₆	—	2	2	no	—
78	C₂×C₁₃×C₁₆	—	2	4	no	—
79	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
80	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
81	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
82	C₁₃×#107	—	2	1	no	—
83	C₁₃×#107	C₂³	1	2	yes	—
84	C₁₃×#107	C₂³	1	1	yes	characteristic
85	C₁₃×#107	C₂³	1	1	yes	characteristic
86	C₁₃×#106	—	2	1	no	—
87	C₁₃×#103	—	2	2	no	—
88	C₁₃×#103	—	2	2	no	—
89	C₁₃×#103	—	2	2	no	—
90	C₁₃×#102	—	2	2	no	—
91	#33613	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
92	C₁₃×#41	—	2	2	no	—
93	C₁₃×#41	—	2	2	no	—
94	C₁₃×#41	—	4	2	no	—
95	C₁₃×#41	—	4	2	no	—
96	C₂×Q₈×C₁₃	—	2	1	no	—
97	C₂×Q₈×C₁₃	—	2	2	no	—
98	C₂×Q₈×C₁₃	—	4	1	no	—
99	C₂×Q₈×C₁₃	—	4	2	no	—
100	C₂×Q₈×C₁₃	—	4	2	no	—
101	C₂×Q₈×C₁₃	D₈	1	1	yes	characteristic
102	C₂×D₄×C₁₃	—	2	1	no	—
103	C₂×D₄×C₁₃	—	4	1	no	—
104	C₂×D₄×C₁₃	—	4	2	no	—
105	C₂×D₄×C₁₃	D₈	1	2	yes	—
106	C₂×D₄×C₁₃	D₈	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	—	4	1	no	—
108	C₂²×C₄×C₁₃	—	4	1	no	—
109	C₂²×C₄×C₁₃	—	4	1	no	—
110	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₁₃×Q₁₆	—	2	2	no	—
113	C₁₃×Q₁₆	—	2	1	no	—
114	C₁₃×Q₁₆	—	2	2	no	—
115	C₁₃×Q₁₆	—	2	1	no	—
116	C₁₃×Q₁₆	—	4	2	no	—
117	C₁₃×SD₁₆	—	4	2	no	—
118	C₁₃×D₈	—	2	1	no	—
119	C₁₃×D₈	—	2	1	no	—
120	C₁₃×M₁₆	—	2	2	no	—
121	C₁₃×M₁₆	—	2	4	no	—
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
125	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₁₃	#41	1	2	yes	—
128	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
129	C₁₃×C₄⋊C₄	—	2	2	no	—
130	C₁₃×C₄⋊C₄	—	2	1	no	—
131	C₁₃×C₄⋊C₄	—	2	1	no	—
132	C₁₃×C₄⋊C₄	—	4	1	no	—
133	C₁₃×C₄⋊C₄	—	4	2	no	—
134	C₁₃×C₄⋊C₄	—	4	2	no	—
135	C₁₃×C₄⋊C₄	—	4	2	no	—
136	C₁₃×C₂²⋊C₄	—	4	1	no	—
137	C₁₃×C₂²⋊C₄	—	4	2	no	—
138	C₁₃×C₂²⋊C₄	—	4	2	no	—
139	C₁₃×C₂²⋊C₄	—	4	2	no	—
140	C₁₃×C₂²⋊C₄	—	4	2	no	—
141	C₄²×C₁₃	—	4	1	no	—
142	C₁₃×C₁₆	—	2	1	no	—
143	C₁₃×C₁₆	—	2	1	no	—
144	C₁₃×C₁₆	C₂×D₄	1	4	yes	—
145	C₂×#510	C₂×C₁₃	1	1	yes	characteristic, complemented
146	C₂×#504	C₂×C₁₃	1	1	yes	characteristic, complemented
147	#3061	C₂×C₁₃	1	1	yes	characteristic
148	#3059	C₂×C₁₃	1	1	yes	characteristic, complemented
149	#2220	C₂×C₁₃	1	2	yes	complemented
150	#2219	C₂×C₁₃	1	2	yes	complemented
151	#2217	C₂×C₁₃	1	2	yes	complemented
152	#2216	C₂×C₁₃	1	2	yes	complemented
153	#2159	C₂×C₁₃	1	1	yes	characteristic, complemented
154	#2138	C₂×C₁₃	1	1	yes	characteristic, complemented
155	C₂×#358	C₂×C₁₃	1	1	yes	characteristic, complemented
156	C₂³×C₁₃	—	4	1	no	—
157	C₂³×C₁₃	C₂×D₈	1	2	yes	—
158	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
159	Q₈×C₁₃	—	2	2	no	—
160	Q₈×C₁₃	—	4	1	no	—
161	Q₈×C₁₃	—	4	2	no	—
162	Q₈×C₁₃	—	4	2	no	—
163	Q₈×C₁₃	—	4	1	no	—
164	Q₈×C₁₃	—	8	2	no	—
165	D₄×C₁₃	—	2	4	no	—
166	D₄×C₁₃	—	2	2	no	—
167	D₄×C₁₃	—	4	1	no	—
168	D₄×C₁₃	—	4	1	no	—
169	D₄×C₁₃	—	8	2	no	—
170	D₄×C₁₃	—	16	2	no	—
171	C₂×C₄×C₁₃	—	2	2	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	4	1	no	—
174	C₂×C₄×C₁₃	—	4	1	no	—
175	C₂×C₄×C₁₃	—	4	2	no	—
176	C₂×C₄×C₁₃	—	4	1	no	—
177	C₂×C₄×C₁₃	—	4	2	no	—
178	C₂×C₄×C₁₃	—	8	2	no	—
179	C₂×C₄×C₁₃	—	8	2	no	—
180	C₂×C₄×C₁₃	—	16	1	no	—
181	C₂×C₄×C₁₃	#121	1	2	yes	—
182	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
183	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
184	C₂×C₄×C₁₃	#135	1	2	yes	—
185	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
186	C₈×C₁₃	—	2	2	no	—
187	C₈×C₁₃	#121	1	2	yes	—
188	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
189	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
190	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
191	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
192	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
193	#537	—	2	1	no	—
194	#536	—	2	1	no	—
195	#510	—	2	4	no	—
196	C₂×Q₃₂	C₂²×C₁₃	1	2	yes	—
197	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	—
198	#504	—	2	4	no	—
199	C₂×M₃₂	C₂²×C₁₃	1	2	yes	—
200	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
201	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
202	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	—
203	#470	—	2	2	no	—
204	#468	—	2	2	no	—
205	#467	C₂²×C₁₃	1	2	yes	—
206	#467	C₂²×C₁₃	1	2	yes	—
207	#467	C₂²×C₁₃	1	2	yes	—
208	#466	C₂²×C₁₃	1	2	yes	—
209	#427	C₂²×C₁₃	1	1	yes	characteristic
210	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
211	#419	—	2	1	no	—
212	#417	—	2	1	no	—
213	#367	C₂²×C₁₃	1	2	yes	—
214	#366	C₂²×C₁₃	1	2	yes	—
215	#358	C₂²×C₁₃	1	2	yes	—
216	#358	C₂²×C₁₃	1	2	yes	—
217	#358	C₂²×C₁₃	1	1	yes	characteristic
218	#358	C₂²×C₁₃	1	1	yes	characteristic
219	#357	C₂²×C₁₃	1	1	yes	characteristic
220	#357	C₂²×C₁₃	1	1	yes	characteristic
221	C₂²×C₁₃	—	2	1	no	—
222	C₂²×C₁₃	—	2	1	no	—
223	C₂²×C₁₃	—	2	2	no	—
224	C₂²×C₁₃	—	2	2	no	—
225	C₂²×C₁₃	—	2	2	no	—
226	C₂²×C₁₃	—	8	1	no	—
227	C₂²×C₁₃	—	8	1	no	—
228	C₂²×C₁₃	—	8	1	no	—
229	C₂²×C₁₃	#466	1	2	yes	—
230	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
231	C₄×C₁₃	—	2	2	no	—
232	C₄×C₁₃	—	8	1	no	—
233	C₄×C₁₃	—	8	2	no	—
234	C₄×C₁₃	—	8	1	no	—
235	C₄×C₁₃	—	8	1	no	—
236	C₄×C₁₃	—	8	2	no	—
237	C₄×C₁₃	#466	1	2	yes	—
238	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
239	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
240	C₂×#41	—	2	1	no	—
241	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
242	C₂²×Q₈	—	2	1	no	—
243	#135	—	2	2	no	—
244	#135	—	2	2	no	—
245	C₂×Q₁₆	—	2	2	no	—
246	C₂×Q₁₆	—	2	1	no	—
247	C₂×Q₁₆	—	2	2	no	—
248	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
249	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
250	C₂×SD₁₆	—	2	1	no	—
251	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
252	#131	—	2	2	no	—
253	#131	—	2	2	no	—
254	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
255	C₂×M₁₆	D₄×C₁₃	1	2	yes	—
256	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
257	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
258	C₄⋊Q₈	—	4	1	no	—
259	#124	—	4	1	no	—
260	#123	—	4	2	no	—
261	C₂²⋊Q₈	—	2	2	no	—
262	C₂²⋊Q₈	—	2	2	no	—
263	C₂²⋊Q₈	—	2	2	no	—
264	C₂²⋊Q₈	—	4	1	no	—
265	#121	—	2	2	no	—
266	#121	—	4	1	no	—
267	#121	—	4	2	no	—
268	#117	—	2	1	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	Q₃₂	—	2	4	no	—
271	SD₃₂	—	2	4	no	—
272	M₃₂	—	2	4	no	—
273	M₃₂	D₄×C₁₃	1	4	yes	complemented
274	C₂×C₁₆	—	2	2	no	—
275	C₂×C₁₆	—	2	4	no	—
276	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
277	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
278	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
279	#107	—	2	1	no	—
280	#107	C₂³×C₁₃	1	1	yes	characteristic
281	#107	C₂³×C₁₃	1	1	yes	characteristic
282	#107	C₂³×C₁₃	1	2	yes	—
283	#106	—	2	1	no	—
284	#103	—	2	2	no	—
285	#103	—	2	2	no	—
286	#103	—	2	2	no	—
287	#102	—	2	2	no	—
288	C₂×C₁₃	—	2	2	no	—
289	C₂×C₁₃	—	4	2	no	—
290	C₂×C₁₃	—	16	1	no	—
291	C₂×C₁₃	C₂×#466	1	1	yes	characteristic
292	C₂×C₁₃	#3416	1	1	yes	characteristic
293	C₂×C₁₃	#3417	1	1	yes	characteristic
294	#41	—	2	2	no	—
295	#41	—	2	2	no	—
296	#41	—	4	2	no	—
297	#41	—	4	2	no	—
298	C₂×Q₈	—	2	1	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	4	1	no	—
301	C₂×Q₈	—	4	2	no	—
302	C₂×Q₈	—	4	2	no	—
303	C₂×Q₈	C₁₃×D₈	1	1	yes	characteristic
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	—	4	1	no	—
306	C₂×D₄	—	4	2	no	—
307	C₂×D₄	C₁₃×D₈	1	2	yes	—
308	C₂×D₄	C₁₃×D₈	1	1	yes	characteristic
309	C₂²×C₄	—	4	1	no	—
310	C₂²×C₄	—	4	1	no	—
311	C₂²×C₄	—	4	1	no	—
312	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
313	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
314	Q₁₆	—	2	2	no	—
315	Q₁₆	—	2	1	no	—
316	Q₁₆	—	2	2	no	—
317	Q₁₆	—	2	1	no	—
318	Q₁₆	—	4	2	no	—
319	SD₁₆	—	4	2	no	—
320	D₈	—	2	1	no	—
321	D₈	—	2	1	no	—
322	M₁₆	—	2	2	no	—
323	M₁₆	—	2	4	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
327	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
328	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
329	C₂×C₈	C₁₃×#41	1	2	yes	—
330	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	1	no	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	4	1	no	—
335	C₄⋊C₄	—	4	2	no	—
336	C₄⋊C₄	—	4	2	no	—
337	C₄⋊C₄	—	4	2	no	—
338	C₂²⋊C₄	—	4	1	no	—
339	C₂²⋊C₄	—	4	2	no	—
340	C₂²⋊C₄	—	4	2	no	—
341	C₂²⋊C₄	—	4	2	no	—
342	C₂²⋊C₄	—	4	2	no	—
343	C₄²	—	4	1	no	—
344	C₁₆	—	2	1	no	—
345	C₁₆	—	2	1	no	—
346	C₁₆	C₂×D₄×C₁₃	1	4	yes	—
347	C₁₃	#33613	1	1	yes	characteristic, direct product factor, Sylow
348	C₂³	—	4	1	no	—
349	C₂³	C₂×C₁₃×D₈	1	2	yes	—
350	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
351	Q₈	—	2	2	no	—
352	Q₈	—	4	1	no	—
353	Q₈	—	4	2	no	—
354	Q₈	—	4	2	no	—
355	Q₈	—	4	1	no	—
356	Q₈	—	8	2	no	—
357	D₄	—	2	4	no	—
358	D₄	—	2	2	no	—
359	D₄	—	4	1	no	—
360	D₄	—	4	1	no	—
361	D₄	—	8	2	no	—
362	D₄	—	16	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	8	2	no	—
371	C₂×C₄	—	8	2	no	—
372	C₂×C₄	—	16	1	no	—
373	C₂×C₄	C₁₃×#121	1	2	yes	—
374	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
375	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
376	C₂×C₄	C₁₃×#135	1	2	yes	—
377	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
378	C₈	—	2	2	no	—
379	C₈	C₁₃×#121	1	2	yes	—
380	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
381	C₈	C₂×C₁₃×#41	1	1	yes	characteristic
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	8	1	no	—
388	C₂²	—	8	1	no	—
389	C₂²	—	8	1	no	—
390	C₂²	C₁₃×#466	1	2	yes	—
391	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
392	C₄	—	2	2	no	—
393	C₄	—	8	1	no	—
394	C₄	—	8	2	no	—
395	C₄	—	8	1	no	—
396	C₄	—	8	2	no	—
397	C₄	—	8	1	no	—
398	C₄	C₁₃×#466	1	2	yes	—
399	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
400	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
401	C₂	—	2	2	no	—
402	C₂	—	4	2	no	—
403	C₂	—	16	1	no	—
404	C₂	C₂×C₁₃×#466	1	1	yes	characteristic
405	C₂	C₁₃×#3416	1	1	yes	characteristic
406	C₂	C₁₃×#3417	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
prime radical	C₁₃×#3061	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₁₃×#41 ◁ C₂×C₁₃×#131 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#510	C₂	semidirect
2. C₂×C₁₃×#504	C₂	semidirect
4. C₁₃×#3059	C₂	semidirect
5. C₁₃×#2220	C₂	semidirect
6. C₁₃×#2219	C₂	semidirect
7. C₁₃×#2217	C₂	semidirect
8. C₁₃×#2216	C₂	semidirect
9. C₁₃×#2159	C₂	semidirect
10. C₁₃×#2138	C₂	semidirect
11. C₂×C₁₃×#358	C₂	semidirect
76. C₁₃×M₃₂	D₄	semidirect
91. #33613	C₁₃	direct (N × H)
145. C₂×#510	C₂×C₁₃	semidirect
146. C₂×#504	C₂×C₁₃	semidirect
148. #3059	C₂×C₁₃	semidirect
149. #2220	C₂×C₁₃	semidirect
150. #2219	C₂×C₁₃	semidirect
151. #2217	C₂×C₁₃	semidirect
152. #2216	C₂×C₁₃	semidirect
153. #2159	C₂×C₁₃	semidirect
154. #2138	C₂×C₁₃	semidirect
155. C₂×#358	C₂×C₁₃	semidirect
273. M₃₂	D₄×C₁₃	semidirect
347. C₁₃	#33613	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×#510	2
C₂×C₁₃×#504	2
C₁₃×#3061	2
C₁₃×#3059	2
C₁₃×#2220	2
C₁₃×#2219	2
C₁₃×#2217	2
C₁₃×#2216	2
C₁₃×#2159	2
C₁₃×#2138	2
C₂×C₁₃×#358	2
#33613	13

Subgroups — C13×#33613 #15719952

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33613 #15719952