Subgroups — C₁₃×#24319 #15710658

Order 3328.

930 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3502	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3078	C₂	1	2	yes	maximal
3	C₁₃×#2327	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2061	C₂	1	2	yes	maximal
5	C₁₃×#2028	C₂	1	2	yes	maximal
6	C₁₃×#1995	C₂	1	2	yes	maximal
7	C₁₃×#1886	C₂	1	2	yes	maximal
8	C₁₃×#1857	C₂	1	2	yes	maximal
9	C₁₃×#1801	C₂	1	1	yes	maximal, characteristic
10	Q₈²×C₁₃	—	2	2	no	—
11	C₁₃×#557	—	2	2	no	—
12	C₁₃×#557	—	2	4	no	—
13	C₁₃×#544	—	2	2	no	—
14	C₁₃×#544	C₂²	1	2	yes	—
15	C₁₃×#533	—	2	2	no	—
16	C₁₃×#533	C₂²	1	2	yes	—
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₁₃×#519	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₁₃×#479	—	2	4	no	—
22	C₁₃×#477	—	2	2	no	—
23	C₁₃×#475	—	2	2	no	—
24	C₁₃×#428	C₂²	1	4	yes	—
25	C₁₃×#423	C₂²	1	2	yes	—
26	C₁₃×#419	C₂²	1	4	yes	—
27	C₂×C₁₃×#101	C₂²	1	2	yes	—
28	C₁₃×#391	C₂²	1	1	yes	characteristic
29	C₁₃×#391	C₂²	1	1	yes	characteristic
30	C₁₃×#387	—	2	2	no	—
31	C₁₃×#387	—	2	2	no	—
32	C₁₃×#382	C₂²	1	1	yes	characteristic
33	C₁₃×#376	C₂²	1	1	yes	characteristic
34	C₁₃×#343	C₂²	1	2	yes	—
35	C₁₃×#339	C₂²	1	4	yes	—
36	C₁₃×#339	C₂²	1	4	yes	—
37	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
38	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
39	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
40	C₁₃×C₄⋊Q₈	—	2	2	no	—
41	C₁₃×C₄⋊Q₈	—	2	2	no	—
42	C₁₃×C₄⋊Q₈	—	2	8	no	—
43	C₁₃×C₄⋊Q₈	—	2	2	no	—
44	C₁₃×C₄⋊Q₈	—	2	4	no	—
45	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
46	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
47	C₁₃×C₄⋊Q₈	Q₈	1	4	yes	complemented
48	C₁₃×#125	—	2	4	no	—
49	C₁₃×#125	—	2	8	no	—
50	C₁₃×#125	—	2	4	no	—
51	C₁₃×#125	D₄	1	4	yes	—
52	C₁₃×C₂²⋊Q₈	—	2	2	no	—
53	C₁₃×C₂²⋊Q₈	—	2	4	no	—
54	C₁₃×C₂²⋊Q₈	—	2	2	no	—
55	C₄×Q₈×C₁₃	—	2	4	no	—
56	C₄×Q₈×C₁₃	—	2	4	no	—
57	C₄×Q₈×C₁₃	—	2	4	no	—
58	C₄×Q₈×C₁₃	—	2	4	no	—
59	C₄×Q₈×C₁₃	—	2	2	no	—
60	C₄×Q₈×C₁₃	—	2	2	no	—
61	C₄×Q₈×C₁₃	—	2	2	no	—
62	C₄×Q₈×C₁₃	—	2	2	no	—
63	C₄×Q₈×C₁₃	—	2	2	no	—
64	C₄×Q₈×C₁₃	—	2	2	no	—
65	C₁₃×#117	—	2	4	no	—
66	C₁₃×#117	C₂³	1	4	yes	—
67	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
69	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₁₃	—	2	1	no	—
73	C₂×C₄²×C₁₃	D₄	1	2	yes	—
74	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
77	C₁₃×#107	—	2	4	no	—
78	C₁₃×#106	—	2	4	no	—
79	C₁₃×C₄⋊C₈	—	2	2	no	—
80	C₁₃×C₄⋊C₈	—	2	2	no	—
81	C₁₃×#103	—	2	4	no	—
82	C₁₃×#103	—	2	4	no	—
83	C₁₃×#101	—	2	4	no	—
84	C₁₃×#95	—	2	2	no	—
85	C₁₃×#95	—	2	2	no	—
86	C₁₃×#95	—	2	2	no	—
87	C₁₃×#95	—	2	1	no	—
88	C₁₃×#95	—	2	1	no	—
89	#24319	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂×Q₈×C₁₃	—	2	4	no	—
91	C₂×Q₈×C₁₃	—	2	2	no	—
92	C₂×Q₈×C₁₃	—	2	2	no	—
93	C₂×Q₈×C₁₃	—	2	2	no	—
94	C₂×Q₈×C₁₃	—	2	1	no	—
95	C₂×Q₈×C₁₃	—	2	2	no	—
96	C₂×Q₈×C₁₃	—	2	2	no	—
97	C₂×Q₈×C₁₃	—	2	2	no	—
98	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
99	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
100	C₂×Q₈×C₁₃	#41	1	2	yes	—
101	C₂²×C₄×C₁₃	—	2	1	no	—
102	C₂²×C₄×C₁₃	—	2	1	no	—
103	C₂²×C₄×C₁₃	—	2	1	no	—
104	C₂²×C₄×C₁₃	—	2	1	no	—
105	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
110	C₁₃×M₁₆	—	2	4	no	—
111	C₁₃×M₁₆	—	2	4	no	—
112	C₂×C₈×C₁₃	—	2	4	no	—
113	C₁₃×C₄⋊C₄	—	2	4	no	—
114	C₁₃×C₄⋊C₄	—	2	4	no	—
115	C₁₃×C₄⋊C₄	—	2	4	no	—
116	C₁₃×C₄⋊C₄	—	2	8	no	—
117	C₁₃×C₄⋊C₄	—	2	4	no	—
118	C₁₃×C₄⋊C₄	—	2	4	no	—
119	C₁₃×C₄⋊C₄	—	2	2	no	—
120	C₁₃×C₄⋊C₄	—	2	2	no	—
121	C₁₃×C₄⋊C₄	—	2	4	no	—
122	C₁₃×C₄⋊C₄	—	2	8	no	—
123	C₁₃×C₄⋊C₄	—	2	2	no	—
124	C₁₃×C₄⋊C₄	—	2	2	no	—
125	C₁₃×C₄⋊C₄	—	4	1	no	—
126	C₁₃×C₄⋊C₄	—	4	1	no	—
127	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
128	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
129	C₁₃×C₂²⋊C₄	—	2	4	no	—
130	C₄²×C₁₃	—	2	8	no	—
131	C₄²×C₁₃	—	2	2	no	—
132	C₄²×C₁₃	—	2	2	no	—
133	C₄²×C₁₃	—	2	4	no	—
134	C₄²×C₁₃	—	2	1	no	—
135	C₄²×C₁₃	—	2	2	no	—
136	C₄²×C₁₃	—	4	2	no	—
137	C₄²×C₁₃	C₂×D₄	1	2	yes	—
138	C₄²×C₁₃	C₂×D₄	1	2	yes	—
139	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
140	#3502	C₂×C₁₃	1	1	yes	characteristic
141	#3078	C₂×C₁₃	1	2	yes	—
142	#2327	C₂×C₁₃	1	1	yes	characteristic
143	#2061	C₂×C₁₃	1	2	yes	—
144	#2028	C₂×C₁₃	1	2	yes	—
145	#1995	C₂×C₁₃	1	2	yes	—
146	#1886	C₂×C₁₃	1	2	yes	—
147	#1857	C₂×C₁₃	1	2	yes	—
148	#1801	C₂×C₁₃	1	1	yes	characteristic
149	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
150	Q₈×C₁₃	—	2	4	no	—
151	Q₈×C₁₃	—	2	4	no	—
152	Q₈×C₁₃	—	2	4	no	—
153	Q₈×C₁₃	—	4	4	no	—
154	Q₈×C₁₃	—	4	2	no	—
155	Q₈×C₁₃	—	8	2	no	—
156	Q₈×C₁₃	—	8	4	no	—
157	C₂×C₄×C₁₃	—	2	2	no	—
158	C₂×C₄×C₁₃	—	2	2	no	—
159	C₂×C₄×C₁₃	—	2	4	no	—
160	C₂×C₄×C₁₃	—	2	4	no	—
161	C₂×C₄×C₁₃	—	2	2	no	—
162	C₂×C₄×C₁₃	—	2	2	no	—
163	C₂×C₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	—	4	1	no	—
165	C₂×C₄×C₁₃	—	4	1	no	—
166	C₂×C₄×C₁₃	—	4	1	no	—
167	C₂×C₄×C₁₃	—	4	1	no	—
168	C₂×C₄×C₁₃	—	4	1	no	—
169	C₂×C₄×C₁₃	—	4	1	no	—
170	C₂×C₄×C₁₃	—	4	2	no	—
171	C₂×C₄×C₁₃	—	4	1	no	—
172	C₂×C₄×C₁₃	—	4	1	no	—
173	C₂×C₄×C₁₃	—	4	2	no	—
174	C₂×C₄×C₁₃	—	4	1	no	—
175	C₂×C₄×C₁₃	—	4	1	no	—
176	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
177	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
178	C₂×C₄×C₁₃	#120	1	2	yes	—
179	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
180	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
181	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
184	C₈×C₁₃	—	4	4	no	—
185	Q₈²	—	2	2	no	—
186	#557	—	2	2	no	—
187	#557	—	2	4	no	—
188	#544	—	2	2	no	—
189	#544	C₂²×C₁₃	1	2	yes	—
190	#533	—	2	2	no	—
191	#533	C₂²×C₁₃	1	2	yes	—
192	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
193	#519	C₂²×C₁₃	1	2	yes	—
194	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
195	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
196	#479	—	2	4	no	—
197	#477	—	2	2	no	—
198	#475	—	2	2	no	—
199	#428	C₂²×C₁₃	1	4	yes	—
200	#423	C₂²×C₁₃	1	2	yes	—
201	#419	C₂²×C₁₃	1	4	yes	—
202	C₂×#101	C₂²×C₁₃	1	2	yes	—
203	#391	C₂²×C₁₃	1	1	yes	characteristic
204	#391	C₂²×C₁₃	1	1	yes	characteristic
205	#387	—	2	2	no	—
206	#387	—	2	2	no	—
207	#382	C₂²×C₁₃	1	1	yes	characteristic
208	#376	C₂²×C₁₃	1	1	yes	characteristic
209	#343	C₂²×C₁₃	1	2	yes	—
210	#339	C₂²×C₁₃	1	4	yes	—
211	#339	C₂²×C₁₃	1	4	yes	—
212	C₂²×C₁₃	—	2	1	no	—
213	C₂²×C₁₃	—	2	1	no	—
214	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
215	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
216	C₂²×C₁₃	#536	1	1	yes	characteristic
217	C₄×C₁₃	—	2	4	no	—
218	C₄×C₁₃	—	2	1	no	—
219	C₄×C₁₃	—	2	1	no	—
220	C₄×C₁₃	—	2	2	no	—
221	C₄×C₁₃	—	4	2	no	—
222	C₄×C₁₃	—	4	2	no	—
223	C₄×C₁₃	—	4	4	no	—
224	C₄×C₁₃	—	4	2	no	—
225	C₄×C₁₃	—	4	4	no	—
226	C₄×C₁₃	—	8	1	no	—
227	C₄×C₁₃	—	8	1	no	—
228	C₄×C₁₃	#548	1	2	yes	—
229	C₄×C₁₃	D₄×Q₈	1	2	yes	—
230	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
231	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
232	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
233	C₄⋊Q₈	—	2	2	no	—
234	C₄⋊Q₈	—	2	2	no	—
235	C₄⋊Q₈	—	2	8	no	—
236	C₄⋊Q₈	—	2	2	no	—
237	C₄⋊Q₈	—	2	4	no	—
238	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
239	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
240	C₄⋊Q₈	Q₈×C₁₃	1	4	yes	complemented
241	#125	—	2	4	no	—
242	#125	—	2	8	no	—
243	#125	—	2	4	no	—
244	#125	D₄×C₁₃	1	4	yes	—
245	C₂²⋊Q₈	—	2	2	no	—
246	C₂²⋊Q₈	—	2	4	no	—
247	C₂²⋊Q₈	—	2	2	no	—
248	C₄×Q₈	—	2	4	no	—
249	C₄×Q₈	—	2	4	no	—
250	C₄×Q₈	—	2	4	no	—
251	C₄×Q₈	—	2	4	no	—
252	C₄×Q₈	—	2	2	no	—
253	C₄×Q₈	—	2	2	no	—
254	C₄×Q₈	—	2	2	no	—
255	C₄×Q₈	—	2	2	no	—
256	C₄×Q₈	—	2	2	no	—
257	C₄×Q₈	—	2	2	no	—
258	#117	—	2	4	no	—
259	#117	C₂³×C₁₃	1	4	yes	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
263	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
264	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
265	C₂×C₄²	—	2	1	no	—
266	C₂×C₄²	D₄×C₁₃	1	2	yes	—
267	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
268	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
269	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
270	#107	—	2	4	no	—
271	#106	—	2	4	no	—
272	C₄⋊C₈	—	2	2	no	—
273	C₄⋊C₈	—	2	2	no	—
274	#103	—	2	4	no	—
275	#103	—	2	4	no	—
276	#101	—	2	4	no	—
277	#95	—	2	1	no	—
278	#95	—	2	1	no	—
279	#95	—	2	2	no	—
280	#95	—	2	2	no	—
281	#95	—	2	2	no	—
282	C₂×C₁₃	—	2	1	no	—
283	C₂×C₁₃	—	2	1	no	—
284	C₂×C₁₃	#2409	1	1	yes	characteristic
285	C₂×C₁₃	#3020	1	1	yes	characteristic
286	C₂×C₁₃	#3022	1	1	yes	characteristic
287	C₂×Q₈	—	2	4	no	—
288	C₂×Q₈	—	2	2	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	2	1	no	—
292	C₂×Q₈	—	2	2	no	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
296	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
297	C₂×Q₈	C₁₃×#41	1	2	yes	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
303	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
304	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
305	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
306	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
307	M₁₆	—	2	4	no	—
308	M₁₆	—	2	4	no	—
309	C₂×C₈	—	2	4	no	—
310	C₄⋊C₄	—	2	4	no	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	—	2	4	no	—
313	C₄⋊C₄	—	2	8	no	—
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	—	2	4	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	—	2	8	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	C₂×D₄×C₁₃	1	4	yes	—
325	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
326	C₂²⋊C₄	—	2	4	no	—
327	C₄²	—	2	8	no	—
328	C₄²	—	2	2	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	2	4	no	—
331	C₄²	—	2	1	no	—
332	C₄²	—	2	2	no	—
333	C₄²	—	4	2	no	—
334	C₄²	C₂×D₄×C₁₃	1	2	yes	—
335	C₄²	C₂×D₄×C₁₃	1	2	yes	—
336	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
337	C₁₃	#24319	1	1	yes	characteristic, direct product factor, Sylow
338	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
339	Q₈	—	2	4	no	—
340	Q₈	—	2	4	no	—
341	Q₈	—	2	4	no	—
342	Q₈	—	4	4	no	—
343	Q₈	—	4	2	no	—
344	Q₈	—	8	2	no	—
345	Q₈	—	8	4	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	4	1	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	2	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
366	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
367	C₂×C₄	C₁₃×#120	1	2	yes	—
368	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
369	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
370	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
371	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
372	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
373	C₈	—	4	4	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
377	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
378	C₂²	C₁₃×#536	1	1	yes	characteristic
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	2	no	—
382	C₄	—	2	4	no	—
383	C₄	—	4	2	no	—
384	C₄	—	4	4	no	—
385	C₄	—	4	2	no	—
386	C₄	—	4	4	no	—
387	C₄	—	4	2	no	—
388	C₄	—	8	1	no	—
389	C₄	—	8	1	no	—
390	C₄	C₁₃×#548	1	2	yes	—
391	C₄	D₄×Q₈×C₁₃	1	2	yes	—
392	C₂	—	2	1	no	—
393	C₂	—	2	1	no	—
394	C₂	C₁₃×#2409	1	1	yes	characteristic
395	C₂	C₁₃×#3020	1	1	yes	characteristic
396	C₂	C₁₃×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂³×C₁₃	C₂²×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ 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
47. C₁₃×C₄⋊Q₈	Q₈	semidirect
89. #24319	C₁₃	direct (N × H)
240. C₄⋊Q₈	Q₈×C₁₃	semidirect
337. C₁₃	#24319	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×#3502	2
C₁₃×#3078	2
C₁₃×#2327	2
C₁₃×#2061	2
C₁₃×#2028	2
C₁₃×#1995	2
C₁₃×#1886	2
C₁₃×#1857	2
C₁₃×#1801	2
#24319	13

Subgroups — C13×#24319 #15710658

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24319 #15710658