Subgroups — C₁₃×#23731 #15710070

Order 3328.

1314 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#428	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₃×#418	C₂	1	2	yes	maximal
3	C₂×C₁₃×#390	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2285	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2094	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2093	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2092	C₂	1	4	yes	maximal, complemented
8	C₁₃×#1728	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
10	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
11	C₂×C₁₃×#117	C₂²	1	2	yes	—
12	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×C₂²⋊C₄	—	2	2	no	—
14	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
15	C₁₃×#428	—	2	8	no	—
16	C₂×C₁₃×#107	C₂²	1	4	yes	complemented
17	C₂×C₁₃×#106	C₂²	1	4	yes	complemented
18	C₁₃×#418	—	2	8	no	—
19	C₂×C₁₃×#102	C₂²	1	4	yes	—
20	C₂×C₁₃×#102	C₂²	1	4	yes	—
21	C₁₃×#390	—	2	2	no	—
22	C₁₃×#390	C₂²	1	2	yes	—
23	C₁₃×#390	C₂²	1	2	yes	—
24	C₁₃×#384	C₂²	1	1	yes	characteristic, complemented
25	C₁₃×#384	C₂²	1	1	yes	characteristic, complemented
26	C₁₃×#382	C₂²	1	2	yes	complemented
27	C₁₃×#380	—	2	2	no	—
28	C₄×C₁₃×C₄⋊C₄	—	2	2	no	—
29	C₁₃×#336	C₂²	1	2	yes	complemented
30	C₁₃×#336	C₂²	1	2	yes	complemented
31	C₂⁵×C₁₃	—	2	1	no	—
32	C₂²×D₄×C₁₃	—	2	4	no	—
33	C₂²×D₄×C₁₃	—	2	1	no	—
34	C₂²×D₄×C₁₃	—	2	4	no	—
35	C₂²×D₄×C₁₃	—	2	2	no	—
36	C₂²×D₄×C₁₃	Q₈	1	4	yes	—
37	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
38	C₂³×C₄×C₁₃	—	2	1	no	—
39	C₂³×C₄×C₁₃	D₄	1	2	yes	—
40	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
41	C₂×C₁₃×M₁₆	—	2	4	no	—
42	C₂×C₁₃×M₁₆	—	2	4	no	—
43	C₂×C₁₃×M₁₆	D₄	1	8	yes	—
44	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
45	C₁₃×#117	—	2	4	no	—
46	C₁₃×#117	—	2	4	no	—
47	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
48	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
49	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
50	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
51	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
52	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
53	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
54	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
55	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
56	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
57	C₂×C₁₃×C₂²⋊C₄	—	4	8	no	—
58	C₂×C₄²×C₁₃	—	2	4	no	—
59	C₂×C₄²×C₁₃	—	2	2	no	—
60	C₂×C₄²×C₁₃	D₄	1	2	yes	—
61	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
63	C₁₃×#107	—	2	8	no	—
64	C₁₃×#106	—	2	8	no	—
65	C₁₃×#102	—	2	8	no	—
66	C₁₃×#102	—	2	8	no	—
67	C₁₃×#95	—	2	4	no	—
68	#23731	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
69	C₂⁴×C₁₃	—	2	4	no	—
70	C₂⁴×C₁₃	—	2	2	no	—
71	C₂⁴×C₁₃	—	4	4	no	—
72	C₂⁴×C₁₃	—	4	4	no	—
73	C₂⁴×C₁₃	—	4	2	no	—
74	C₂⁴×C₁₃	—	4	2	no	—
75	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
76	C₂×D₄×C₁₃	—	2	16	no	—
77	C₂×D₄×C₁₃	—	2	4	no	—
78	C₂×D₄×C₁₃	—	2	4	no	—
79	C₂×D₄×C₁₃	—	2	4	no	—
80	C₂×D₄×C₁₃	—	2	2	no	—
81	C₂×D₄×C₁₃	—	4	8	no	—
82	C₂×D₄×C₁₃	—	4	2	no	—
83	C₂×D₄×C₁₃	—	4	2	no	—
84	C₂×D₄×C₁₃	C₂×Q₈	1	4	yes	—
85	C₂²×C₄×C₁₃	—	2	4	no	—
86	C₂²×C₄×C₁₃	—	2	4	no	—
87	C₂²×C₄×C₁₃	—	2	2	no	—
88	C₂²×C₄×C₁₃	—	2	2	no	—
89	C₂²×C₄×C₁₃	—	2	2	no	—
90	C₂²×C₄×C₁₃	—	4	2	no	—
91	C₂²×C₄×C₁₃	—	4	4	no	—
92	C₂²×C₄×C₁₃	—	4	2	no	—
93	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
97	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
98	C₂²×C₄×C₁₃	#41	1	4	yes	—
99	C₂²×C₄×C₁₃	#41	1	2	yes	—
100	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
101	C₁₃×M₁₆	—	2	16	no	—
102	C₂×C₈×C₁₃	—	2	4	no	—
103	C₂×C₈×C₁₃	—	2	4	no	—
104	C₂×C₈×C₁₃	C₂×D₄	1	8	yes	—
105	C₁₃×C₄⋊C₄	—	2	2	no	—
106	C₁₃×C₄⋊C₄	—	2	2	no	—
107	C₁₃×C₄⋊C₄	—	2	2	no	—
108	C₁₃×C₄⋊C₄	—	2	4	no	—
109	C₁₃×C₄⋊C₄	—	2	2	no	—
110	C₁₃×C₄⋊C₄	—	4	4	no	—
111	C₁₃×C₄⋊C₄	—	4	2	no	—
112	C₁₃×C₄⋊C₄	—	4	4	no	—
113	C₁₃×C₂²⋊C₄	—	4	8	no	—
114	C₁₃×C₂²⋊C₄	—	4	4	no	—
115	C₁₃×C₂²⋊C₄	—	4	8	no	—
116	C₄²×C₁₃	—	2	4	no	—
117	C₄²×C₁₃	—	2	2	no	—
118	C₄²×C₁₃	—	2	2	no	—
119	C₄²×C₁₃	—	4	4	no	—
120	C₂×#428	C₂×C₁₃	1	2	yes	complemented
121	C₂×#418	C₂×C₁₃	1	2	yes	—
122	C₂×#390	C₂×C₁₃	1	1	yes	characteristic
123	#2285	C₂×C₁₃	1	1	yes	characteristic, complemented
124	#2094	C₂×C₁₃	1	2	yes	complemented
125	#2093	C₂×C₁₃	1	2	yes	complemented
126	#2092	C₂×C₁₃	1	4	yes	complemented
127	#1728	C₂×C₁₃	1	1	yes	characteristic, complemented
128	C₂³×C₁₃	—	2	2	no	—
129	C₂³×C₁₃	—	2	2	no	—
130	C₂³×C₁₃	—	2	4	no	—
131	C₂³×C₁₃	—	4	16	no	—
132	C₂³×C₁₃	—	4	2	no	—
133	C₂³×C₁₃	—	4	2	no	—
134	C₂³×C₁₃	—	4	4	no	—
135	C₂³×C₁₃	—	4	4	no	—
136	C₂³×C₁₃	—	4	8	no	—
137	C₂³×C₁₃	—	8	8	no	—
138	C₂³×C₁₃	—	8	4	no	—
139	C₂³×C₁₃	—	8	4	no	—
140	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
141	C₂³×C₁₃	#123	1	2	yes	—
142	C₂³×C₁₃	#127	1	2	yes	—
143	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
144	D₄×C₁₃	—	2	8	no	—
145	D₄×C₁₃	—	4	4	no	—
146	D₄×C₁₃	—	4	8	no	—
147	C₂×C₄×C₁₃	—	2	2	no	—
148	C₂×C₄×C₁₃	—	2	2	no	—
149	C₂×C₄×C₁₃	—	2	2	no	—
150	C₂×C₄×C₁₃	—	2	2	no	—
151	C₂×C₄×C₁₃	—	2	2	no	—
152	C₂×C₄×C₁₃	—	4	8	no	—
153	C₂×C₄×C₁₃	—	4	2	no	—
154	C₂×C₄×C₁₃	—	4	2	no	—
155	C₂×C₄×C₁₃	—	4	2	no	—
156	C₂×C₄×C₁₃	—	4	4	no	—
157	C₂×C₄×C₁₃	—	4	4	no	—
158	C₂×C₄×C₁₃	—	4	4	no	—
159	C₂×C₄×C₁₃	—	8	4	no	—
160	C₂×C₄×C₁₃	C₂²⋊Q₈	1	8	yes	—
161	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
162	C₂×C₄×C₁₃	#123	1	8	yes	—
163	C₂×C₄×C₁₃	#123	1	2	yes	—
164	C₂×C₄×C₁₃	#127	1	2	yes	—
165	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
166	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
167	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
168	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
169	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
170	C₈×C₁₃	—	2	8	no	—
171	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
172	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
173	C₂×#117	C₂²×C₁₃	1	2	yes	—
174	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
175	C₂²×C₂²⋊C₄	—	2	2	no	—
176	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
177	#428	—	2	8	no	—
178	C₂×#107	C₂²×C₁₃	1	4	yes	complemented
179	C₂×#106	C₂²×C₁₃	1	4	yes	complemented
180	#418	—	2	8	no	—
181	C₂×#102	C₂²×C₁₃	1	4	yes	—
182	C₂×#102	C₂²×C₁₃	1	4	yes	—
183	#390	—	2	2	no	—
184	#390	C₂²×C₁₃	1	2	yes	—
185	#390	C₂²×C₁₃	1	2	yes	—
186	#384	C₂²×C₁₃	1	1	yes	characteristic, complemented
187	#384	C₂²×C₁₃	1	1	yes	characteristic, complemented
188	#382	C₂²×C₁₃	1	2	yes	complemented
189	#380	—	2	2	no	—
190	C₄×C₄⋊C₄	—	2	2	no	—
191	#336	C₂²×C₁₃	1	2	yes	complemented
192	#336	C₂²×C₁₃	1	2	yes	complemented
193	C₂²×C₁₃	—	2	4	no	—
194	C₂²×C₁₃	—	2	4	no	—
195	C₂²×C₁₃	—	2	2	no	—
196	C₂²×C₁₃	—	2	2	no	—
197	C₂²×C₁₃	—	4	8	no	—
198	C₂²×C₁₃	—	4	4	no	—
199	C₂²×C₁₃	—	8	16	no	—
200	C₂²×C₁₃	—	8	4	no	—
201	C₂²×C₁₃	—	8	2	no	—
202	C₂²×C₁₃	—	8	2	no	—
203	C₂²×C₁₃	#399	1	4	yes	—
204	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
205	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
206	C₂²×C₁₃	C₂×#127	1	1	yes	characteristic
207	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
208	C₂²×C₁₃	#575	1	2	yes	—
209	C₄×C₁₃	—	2	4	no	—
210	C₄×C₁₃	—	4	2	no	—
211	C₄×C₁₃	—	8	2	no	—
212	C₄×C₁₃	—	8	2	no	—
213	C₄×C₁₃	—	8	2	no	—
214	C₄×C₁₃	#399	1	4	yes	—
215	C₄×C₁₃	C₂×C₂²⋊Q₈	1	2	yes	—
216	C₄×C₁₃	C₂×#123	1	2	yes	—
217	C₂⁵	—	2	1	no	—
218	C₂²×D₄	—	2	4	no	—
219	C₂²×D₄	—	2	1	no	—
220	C₂²×D₄	—	2	4	no	—
221	C₂²×D₄	—	2	2	no	—
222	C₂²×D₄	Q₈×C₁₃	1	4	yes	—
223	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
224	C₂³×C₄	—	2	1	no	—
225	C₂³×C₄	D₄×C₁₃	1	2	yes	—
226	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
227	C₂×M₁₆	—	2	4	no	—
228	C₂×M₁₆	—	2	4	no	—
229	C₂×M₁₆	D₄×C₁₃	1	8	yes	—
230	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
231	#117	—	2	4	no	—
232	#117	—	2	4	no	—
233	C₂×C₄⋊C₄	—	2	4	no	—
234	C₂×C₄⋊C₄	—	2	1	no	—
235	C₂×C₄⋊C₄	—	2	2	no	—
236	C₂×C₄⋊C₄	—	2	2	no	—
237	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
238	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
239	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
240	C₂×C₂²⋊C₄	—	2	2	no	—
241	C₂×C₂²⋊C₄	—	2	4	no	—
242	C₂×C₂²⋊C₄	—	2	4	no	—
243	C₂×C₂²⋊C₄	—	4	8	no	—
244	C₂×C₄²	—	2	4	no	—
245	C₂×C₄²	—	2	2	no	—
246	C₂×C₄²	D₄×C₁₃	1	2	yes	—
247	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
248	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
249	#107	—	2	8	no	—
250	#106	—	2	8	no	—
251	#102	—	2	8	no	—
252	#102	—	2	8	no	—
253	#95	—	2	4	no	—
254	C₂×C₁₃	—	2	4	no	—
255	C₂×C₁₃	—	8	4	no	—
256	C₂×C₁₃	C₂×#399	1	1	yes	characteristic
257	C₂×C₁₃	#3077	1	2	yes	—
258	C₂×C₁₃	#3094	1	2	yes	—
259	C₂×C₁₃	#3151	1	1	yes	characteristic
260	C₂×C₁₃	#3153	1	1	yes	characteristic
261	C₂⁴	—	2	4	no	—
262	C₂⁴	—	2	2	no	—
263	C₂⁴	—	4	4	no	—
264	C₂⁴	—	4	4	no	—
265	C₂⁴	—	4	2	no	—
266	C₂⁴	—	4	2	no	—
267	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
268	C₂×D₄	—	2	16	no	—
269	C₂×D₄	—	2	4	no	—
270	C₂×D₄	—	2	4	no	—
271	C₂×D₄	—	2	4	no	—
272	C₂×D₄	—	2	2	no	—
273	C₂×D₄	—	4	2	no	—
274	C₂×D₄	—	4	8	no	—
275	C₂×D₄	—	4	2	no	—
276	C₂×D₄	C₂×Q₈×C₁₃	1	4	yes	—
277	C₂²×C₄	—	2	4	no	—
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	4	2	no	—
283	C₂²×C₄	—	4	4	no	—
284	C₂²×C₄	—	4	2	no	—
285	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
286	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
287	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
288	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
289	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
290	C₂²×C₄	C₁₃×#41	1	4	yes	—
291	C₂²×C₄	C₁₃×#41	1	2	yes	—
292	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
293	M₁₆	—	2	16	no	—
294	C₂×C₈	—	2	4	no	—
295	C₂×C₈	—	2	4	no	—
296	C₂×C₈	C₂×D₄×C₁₃	1	8	yes	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	4	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	4	4	no	—
303	C₄⋊C₄	—	4	2	no	—
304	C₄⋊C₄	—	4	4	no	—
305	C₂²⋊C₄	—	4	8	no	—
306	C₂²⋊C₄	—	4	4	no	—
307	C₂²⋊C₄	—	4	8	no	—
308	C₄²	—	2	4	no	—
309	C₄²	—	2	2	no	—
310	C₄²	—	2	2	no	—
311	C₄²	—	4	4	no	—
312	C₁₃	#23731	1	1	yes	characteristic, direct product factor, Sylow
313	C₂³	—	2	2	no	—
314	C₂³	—	2	2	no	—
315	C₂³	—	2	4	no	—
316	C₂³	—	4	16	no	—
317	C₂³	—	4	8	no	—
318	C₂³	—	4	2	no	—
319	C₂³	—	4	2	no	—
320	C₂³	—	4	4	no	—
321	C₂³	—	4	4	no	—
322	C₂³	—	8	8	no	—
323	C₂³	—	8	4	no	—
324	C₂³	—	8	4	no	—
325	C₂³	C₁₃×C₂²⋊Q₈	1	2	yes	—
326	C₂³	C₁₃×#123	1	2	yes	—
327	C₂³	C₁₃×#127	1	2	yes	—
328	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
329	D₄	—	2	8	no	—
330	D₄	—	4	8	no	—
331	D₄	—	4	4	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	4	8	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	8	4	no	—
345	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
346	C₂×C₄	C₁₃×C₂²⋊Q₈	1	8	yes	—
347	C₂×C₄	C₁₃×#123	1	2	yes	—
348	C₂×C₄	C₁₃×#123	1	8	yes	—
349	C₂×C₄	C₁₃×#127	1	2	yes	—
350	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
351	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
352	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
353	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
354	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
355	C₈	—	2	8	no	—
356	C₂²	—	2	4	no	—
357	C₂²	—	2	4	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	2	2	no	—
360	C₂²	—	4	8	no	—
361	C₂²	—	4	4	no	—
362	C₂²	—	8	16	no	—
363	C₂²	—	8	4	no	—
364	C₂²	—	8	2	no	—
365	C₂²	—	8	2	no	—
366	C₂²	C₁₃×#399	1	4	yes	—
367	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
368	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
369	C₂²	C₂×C₁₃×#127	1	1	yes	characteristic
370	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
371	C₂²	C₁₃×#575	1	2	yes	—
372	C₄	—	2	4	no	—
373	C₄	—	4	2	no	—
374	C₄	—	8	2	no	—
375	C₄	—	8	2	no	—
376	C₄	—	8	2	no	—
377	C₄	C₁₃×#399	1	4	yes	—
378	C₄	C₂×C₁₃×C₂²⋊Q₈	1	2	yes	—
379	C₄	C₂×C₁₃×#123	1	2	yes	—
380	C₂	—	2	4	no	—
381	C₂	—	8	4	no	—
382	C₂	C₂×C₁₃×#399	1	1	yes	characteristic
383	C₂	C₁₃×#3077	1	2	yes	—
384	C₂	C₁₃×#3094	1	2	yes	—
385	C₂	C₁₃×#3151	1	1	yes	characteristic
386	C₂	C₁₃×#3153	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂³×D₄×C₁₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ 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
1. C₂×C₁₃×#428	C₂	semidirect
4. C₁₃×#2285	C₂	semidirect
5. C₁₃×#2094	C₂	semidirect
6. C₁₃×#2093	C₂	semidirect
7. C₁₃×#2092	C₂	semidirect
8. C₁₃×#1728	C₂	semidirect
16. C₂×C₁₃×#107	C₂²	semidirect
17. C₂×C₁₃×#106	C₂²	semidirect
24. C₁₃×#384	C₂²	semidirect
25. C₁₃×#384	C₂²	semidirect
26. C₁₃×#382	C₂²	semidirect
29. C₁₃×#336	C₂²	semidirect
30. C₁₃×#336	C₂²	semidirect
68. #23731	C₁₃	direct (N × H)
120. C₂×#428	C₂×C₁₃	semidirect
123. #2285	C₂×C₁₃	semidirect
124. #2094	C₂×C₁₃	semidirect
125. #2093	C₂×C₁₃	semidirect
126. #2092	C₂×C₁₃	semidirect
127. #1728	C₂×C₁₃	semidirect
178. C₂×#107	C₂²×C₁₃	semidirect
179. C₂×#106	C₂²×C₁₃	semidirect
186. #384	C₂²×C₁₃	semidirect
187. #384	C₂²×C₁₃	semidirect
188. #382	C₂²×C₁₃	semidirect
191. #336	C₂²×C₁₃	semidirect
192. #336	C₂²×C₁₃	semidirect
312. C₁₃	#23731	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×#428	2
C₂×C₁₃×#418	2
C₂×C₁₃×#390	2
C₁₃×#2285	2
C₁₃×#2094	2
C₁₃×#2093	2
C₁₃×#2092	2
C₁₃×#1728	2
#23731	13

Subgroups — C13×#23731 #15710070

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23731 #15710070