Subgroups — D₄×C₁₃×#107 #15708994

Order 3328.

1126 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₃×#107	C₂	1	2	yes	maximal, complemented
3	D₄×C₁₃×C₄⋊C₄	C₂	1	2	yes	maximal
4	C₁₃×#1947	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1852	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1845	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1808	C₂	1	2	yes	maximal, complemented
8	C₄×C₁₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
10	C₂×C₄×D₄×C₁₃	—	2	2	no	—
11	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
12	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
13	C₈×D₄×C₁₃	C₄	1	8	yes	complemented
14	C₂×C₁₃×#107	—	2	8	no	—
15	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#107	C₂²	1	2	yes	—
17	C₂×C₁₃×#107	C₂²	1	4	yes	—
18	C₂×C₁₃×#107	C₂²	1	2	yes	—
19	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₁₃×#389	—	2	2	no	—
24	C₁₃×#385	—	2	4	no	—
25	C₁₃×#384	C₂²	1	2	yes	—
26	C₁₃×#380	C₂²	1	4	yes	—
27	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
28	C₁₃×#340	C₂²	1	2	yes	—
29	C₁₃×#340	C₂²	1	4	yes	—
30	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
31	C₂³×C₄×C₁₃	—	2	4	no	—
32	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
33	C₂²×C₈×C₁₃	—	2	4	no	—
34	C₂²×C₈×C₁₃	—	2	4	no	—
35	C₂²×C₈×C₁₃	C₂×C₄	1	8	yes	complemented
36	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
37	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
38	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
39	C₄×D₄×C₁₃	—	4	8	no	—
40	C₄×D₄×C₁₃	C₂×C₄	1	4	yes	—
41	C₄×D₄×C₁₃	Q₈	1	4	yes	—
42	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
43	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
44	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
45	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
46	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
47	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
48	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
49	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
50	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
51	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
52	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
53	C₂×C₄²×C₁₃	—	2	2	no	—
54	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
55	C₁₃×#107	—	2	4	no	—
56	C₁₃×#107	—	2	2	no	—
57	C₁₃×#107	—	2	8	no	—
58	C₁₃×#107	—	4	2	no	—
59	C₁₃×#107	D₄	1	4	yes	direct product factor
60	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
61	C₁₃×C₂²⋊C₈	C₂×C₄	1	8	yes	complemented
62	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	complemented
63	C₁₃×#95	—	2	2	no	—
64	C₁₃×#95	—	2	4	no	—
65	D₄×#107	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
66	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
67	C₂×D₄×C₁₃	C₄⋊C₄	1	4	yes	—
68	C₂×D₄×C₁₃	D₈	1	4	yes	—
69	C₂×D₄×C₁₃	Q₁₆	1	4	yes	—
70	C₂²×C₄×C₁₃	—	2	2	no	—
71	C₂²×C₄×C₁₃	—	2	2	no	—
72	C₂²×C₄×C₁₃	—	2	2	no	—
73	C₂²×C₄×C₁₃	—	2	2	no	—
74	C₂²×C₄×C₁₃	—	2	2	no	—
75	C₂²×C₄×C₁₃	—	2	2	no	—
76	C₂²×C₄×C₁₃	—	2	4	no	—
77	C₂²×C₄×C₁₃	—	4	8	no	—
78	C₂²×C₄×C₁₃	—	4	8	no	—
79	C₂²×C₄×C₁₃	—	8	4	no	—
80	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
81	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
83	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
85	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
86	C₂×C₈×C₁₃	—	2	2	no	—
87	C₂×C₈×C₁₃	—	2	2	no	—
88	C₂×C₈×C₁₃	—	2	1	no	—
89	C₂×C₈×C₁₃	—	2	1	no	—
90	C₂×C₈×C₁₃	—	2	16	no	—
91	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
92	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
93	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
94	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
95	C₂×C₈×C₁₃	#41	1	2	yes	—
96	C₁₃×C₄⋊C₄	—	2	2	no	—
97	C₁₃×C₄⋊C₄	—	2	4	no	—
98	C₁₃×C₄⋊C₄	—	2	2	no	—
99	C₁₃×C₄⋊C₄	—	2	4	no	—
100	C₁₃×C₄⋊C₄	—	2	2	no	—
101	C₁₃×C₄⋊C₄	—	4	8	no	—
102	C₁₃×C₄⋊C₄	—	4	4	no	—
103	C₁₃×C₄⋊C₄	—	8	2	no	—
104	C₁₃×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
105	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
106	C₁₃×C₂²⋊C₄	—	4	8	no	—
107	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	8	yes	—
108	C₄²×C₁₃	—	4	4	no	—
109	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
110	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
111	C₂×C₈×D₄	C₂×C₁₃	1	1	yes	characteristic
112	C₂²×#107	C₂×C₁₃	1	2	yes	complemented
113	D₄×C₄⋊C₄	C₂×C₁₃	1	2	yes	—
114	#1947	C₂×C₁₃	1	2	yes	complemented
115	#1852	C₂×C₁₃	1	4	yes	complemented
116	#1845	C₂×C₁₃	1	1	yes	characteristic, complemented
117	#1808	C₂×C₁₃	1	2	yes	complemented
118	C₄×#107	C₂×C₁₃	1	1	yes	characteristic, complemented
119	C₂³×C₁₃	—	2	2	no	—
120	C₂³×C₁₃	—	2	2	no	—
121	C₂³×C₁₃	—	2	2	no	—
122	C₂³×C₁₃	—	2	2	no	—
123	C₂³×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
124	C₂³×C₁₃	C₂×D₈	1	4	yes	—
125	C₂³×C₁₃	C₂×Q₁₆	1	4	yes	—
126	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
127	D₄×C₁₃	#107	1	16	yes	direct product factor
128	C₂×C₄×C₁₃	—	2	2	no	—
129	C₂×C₄×C₁₃	—	2	2	no	—
130	C₂×C₄×C₁₃	—	2	1	no	—
131	C₂×C₄×C₁₃	—	2	1	no	—
132	C₂×C₄×C₁₃	—	2	4	no	—
133	C₂×C₄×C₁₃	—	2	4	no	—
134	C₂×C₄×C₁₃	—	2	4	no	—
135	C₂×C₄×C₁₃	—	2	4	no	—
136	C₂×C₄×C₁₃	—	2	4	no	—
137	C₂×C₄×C₁₃	—	4	2	no	—
138	C₂×C₄×C₁₃	—	4	2	no	—
139	C₂×C₄×C₁₃	—	4	4	no	—
140	C₂×C₄×C₁₃	—	4	2	no	—
141	C₂×C₄×C₁₃	—	4	2	no	—
142	C₂×C₄×C₁₃	—	4	4	no	—
143	C₂×C₄×C₁₃	—	4	4	no	—
144	C₂×C₄×C₁₃	—	4	2	no	—
145	C₂×C₄×C₁₃	—	8	16	no	—
146	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
147	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
148	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
149	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
150	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
151	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
152	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
154	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
155	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
156	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
157	C₈×C₁₃	—	2	4	no	—
158	C₈×C₁₃	—	2	2	no	—
159	C₈×C₁₃	C₄×D₄	1	4	yes	complemented
160	C₂³×C₈	C₂²×C₁₃	1	2	yes	—
161	C₂×C₄×D₄	—	2	2	no	—
162	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
163	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
164	C₈×D₄	C₄×C₁₃	1	8	yes	complemented
165	C₂×#107	—	2	8	no	—
166	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
167	C₂×#107	C₂²×C₁₃	1	2	yes	—
168	C₂×#107	C₂²×C₁₃	1	4	yes	—
169	C₂×#107	C₂²×C₁₃	1	2	yes	—
170	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
171	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
172	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
173	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
174	#389	—	2	2	no	—
175	#385	—	2	4	no	—
176	#384	C₂²×C₁₃	1	2	yes	—
177	#380	C₂²×C₁₃	1	4	yes	—
178	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
179	#340	C₂²×C₁₃	1	4	yes	—
180	#340	C₂²×C₁₃	1	2	yes	—
181	C₂²×C₁₃	—	2	4	no	—
182	C₂²×C₁₃	—	2	4	no	—
183	C₂²×C₁₃	—	2	4	no	—
184	C₂²×C₁₃	—	2	4	no	—
185	C₂²×C₁₃	—	2	4	no	—
186	C₂²×C₁₃	—	2	4	no	—
187	C₂²×C₁₃	C₂×#107	1	8	yes	complemented
188	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
189	C₂²×C₁₃	D₄²	1	1	yes	characteristic
190	C₂²×C₁₃	#547	1	1	yes	characteristic
191	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
192	C₂²×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
193	C₂²×C₁₃	#576	1	1	yes	characteristic
194	C₂²×C₁₃	#578	1	1	yes	characteristic
195	C₄×C₁₃	—	2	4	no	—
196	C₄×C₁₃	—	2	2	no	—
197	C₄×C₁₃	—	4	4	no	—
198	C₄×C₁₃	—	8	2	no	—
199	C₄×C₁₃	—	8	4	no	—
200	C₄×C₁₃	C₂×#107	1	4	yes	complemented
201	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
202	C₄×C₁₃	#520	1	1	yes	characteristic
203	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
204	C₄×C₁₃	#554	1	1	yes	characteristic
205	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
206	C₂³×C₄	—	2	4	no	—
207	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
208	C₂²×C₈	—	2	4	no	—
209	C₂²×C₈	—	2	4	no	—
210	C₂²×C₈	C₂×C₄×C₁₃	1	8	yes	complemented
211	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
212	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
213	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
214	C₄×D₄	—	4	8	no	—
215	C₄×D₄	C₂×C₄×C₁₃	1	4	yes	—
216	C₄×D₄	Q₈×C₁₃	1	4	yes	—
217	C₂×C₄⋊C₄	—	2	8	no	—
218	C₂×C₄⋊C₄	—	2	4	no	—
219	C₂×C₄⋊C₄	—	2	2	no	—
220	C₂×C₄⋊C₄	—	2	2	no	—
221	C₂×C₄⋊C₄	—	4	4	no	—
222	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
223	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
224	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
225	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
226	C₂×C₂²⋊C₄	—	2	4	no	—
227	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
228	C₂×C₄²	—	2	2	no	—
229	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
230	#107	—	2	4	no	—
231	#107	—	2	2	no	—
232	#107	—	2	8	no	—
233	#107	—	4	2	no	—
234	#107	D₄×C₁₃	1	4	yes	direct product factor
235	C₄⋊C₈	C₂×C₄×C₁₃	1	4	yes	complemented
236	C₂²⋊C₈	C₂×C₄×C₁₃	1	8	yes	complemented
237	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	complemented
238	#95	—	2	2	no	—
239	#95	—	2	4	no	—
240	C₂×C₁₃	—	2	8	no	—
241	C₂×C₁₃	D₄×C₄⋊C₄	1	1	yes	characteristic
242	C₂×C₁₃	C₂²×#107	1	1	yes	characteristic
243	C₂×C₁₃	#2913	1	1	yes	characteristic
244	C₂×C₁₃	D₄×D₈	1	1	yes	characteristic
245	C₂×C₁₃	D₄×Q₁₆	1	1	yes	characteristic
246	C₂×C₁₃	#3334	1	1	yes	characteristic
247	C₂×C₁₃	#3338	1	1	yes	characteristic
248	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
249	C₂×D₄	C₁₃×C₄⋊C₄	1	4	yes	—
250	C₂×D₄	C₁₃×D₈	1	4	yes	—
251	C₂×D₄	C₁₃×Q₁₆	1	4	yes	—
252	C₂²×C₄	—	2	2	no	—
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	2	4	no	—
259	C₂²×C₄	—	4	8	no	—
260	C₂²×C₄	—	4	8	no	—
261	C₂²×C₄	—	8	4	no	—
262	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
263	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
264	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
265	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
266	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
267	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
268	C₂×C₈	—	2	2	no	—
269	C₂×C₈	—	2	2	no	—
270	C₂×C₈	—	2	1	no	—
271	C₂×C₈	—	2	1	no	—
272	C₂×C₈	—	2	16	no	—
273	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
274	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
275	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
276	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
277	C₂×C₈	C₁₃×#41	1	2	yes	—
278	C₄⋊C₄	—	2	2	no	—
279	C₄⋊C₄	—	2	4	no	—
280	C₄⋊C₄	—	2	2	no	—
281	C₄⋊C₄	—	2	4	no	—
282	C₄⋊C₄	—	2	2	no	—
283	C₄⋊C₄	—	4	8	no	—
284	C₄⋊C₄	—	4	4	no	—
285	C₄⋊C₄	—	8	2	no	—
286	C₄⋊C₄	C₁₃×C₄⋊C₄	1	4	yes	—
287	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
288	C₂²⋊C₄	—	4	8	no	—
289	C₂²⋊C₄	C₁₃×C₄⋊C₄	1	8	yes	—
290	C₄²	—	4	4	no	—
291	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
292	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
293	C₁₃	D₄×#107	1	1	yes	characteristic, direct product factor, Sylow
294	C₂³	—	2	2	no	—
295	C₂³	—	2	2	no	—
296	C₂³	—	2	2	no	—
297	C₂³	—	2	2	no	—
298	C₂³	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
299	C₂³	C₂×C₁₃×D₈	1	4	yes	—
300	C₂³	C₂×C₁₃×Q₁₆	1	4	yes	—
301	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
302	D₄	C₁₃×#107	1	16	yes	direct product factor
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	4	no	—
308	C₂×C₄	—	2	4	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	4	2	no	—
313	C₂×C₄	—	4	2	no	—
314	C₂×C₄	—	4	4	no	—
315	C₂×C₄	—	4	2	no	—
316	C₂×C₄	—	4	2	no	—
317	C₂×C₄	—	4	4	no	—
318	C₂×C₄	—	4	4	no	—
319	C₂×C₄	—	4	2	no	—
320	C₂×C₄	—	8	16	no	—
321	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
322	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
323	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
324	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
325	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
326	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
327	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
328	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
329	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
330	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
331	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
332	C₈	—	2	4	no	—
333	C₈	—	2	2	no	—
334	C₈	C₄×D₄×C₁₃	1	4	yes	complemented
335	C₂²	—	2	4	no	—
336	C₂²	—	2	4	no	—
337	C₂²	—	2	4	no	—
338	C₂²	—	2	4	no	—
339	C₂²	—	2	4	no	—
340	C₂²	—	2	4	no	—
341	C₂²	C₂×C₁₃×#107	1	8	yes	complemented
342	C₂²	C₂²×C₁₃×C₄⋊C₄	1	1	yes	characteristic
343	C₂²	D₄²×C₁₃	1	1	yes	characteristic
344	C₂²	C₁₃×#547	1	1	yes	characteristic
345	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
346	C₂²	C₂²×C₁₃×Q₁₆	1	1	yes	characteristic
347	C₂²	C₁₃×#576	1	1	yes	characteristic
348	C₂²	C₁₃×#578	1	1	yes	characteristic
349	C₄	—	2	4	no	—
350	C₄	—	2	2	no	—
351	C₄	—	4	4	no	—
352	C₄	—	8	4	no	—
353	C₄	—	8	2	no	—
354	C₄	C₂×C₁₃×#107	1	4	yes	complemented
355	C₄	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
356	C₄	C₁₃×#520	1	1	yes	characteristic
357	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
358	C₄	C₁₃×#554	1	1	yes	characteristic
359	C₂	—	2	8	no	—
360	C₂	D₄×C₁₃×C₄⋊C₄	1	1	yes	characteristic
361	C₂	C₂²×C₁₃×#107	1	1	yes	characteristic
362	C₂	C₁₃×#2913	1	1	yes	characteristic
363	C₂	D₄×C₁₃×D₈	1	1	yes	characteristic
364	C₂	D₄×C₁₃×Q₁₆	1	1	yes	characteristic
365	C₂	C₁₃×#3334	1	1	yes	characteristic
366	C₂	C₁₃×#3338	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₃×#107	C₂	semidirect
4. C₁₃×#1947	C₂	semidirect
5. C₁₃×#1852	C₂	semidirect
6. C₁₃×#1845	C₂	semidirect
7. C₁₃×#1808	C₂	semidirect
8. C₄×C₁₃×#107	C₂	semidirect
13. C₈×D₄×C₁₃	C₄	semidirect
35. C₂²×C₈×C₁₃	C₂×C₄	semidirect
59. C₁₃×#107	D₄	direct (N × H)
60. C₁₃×C₄⋊C₈	C₂×C₄	semidirect
61. C₁₃×C₂²⋊C₈	C₂×C₄	semidirect
62. C₄×C₈×C₁₃	C₂×C₄	semidirect
65. D₄×#107	C₁₃	direct (N × H)
112. C₂²×#107	C₂×C₁₃	semidirect
114. #1947	C₂×C₁₃	semidirect
115. #1852	C₂×C₁₃	semidirect
116. #1845	C₂×C₁₃	semidirect
117. #1808	C₂×C₁₃	semidirect
118. C₄×#107	C₂×C₁₃	semidirect
127. D₄×C₁₃	#107	direct (N × H)
159. C₈×C₁₃	C₄×D₄	semidirect
164. C₈×D₄	C₄×C₁₃	semidirect
187. C₂²×C₁₃	C₂×#107	semidirect
200. C₄×C₁₃	C₂×#107	semidirect
210. C₂²×C₈	C₂×C₄×C₁₃	semidirect
234. #107	D₄×C₁₃	direct (N × H)
235. C₄⋊C₈	C₂×C₄×C₁₃	semidirect
236. C₂²⋊C₈	C₂×C₄×C₁₃	semidirect
237. C₄×C₈	C₂×C₄×C₁₃	semidirect
293. C₁₃	D₄×#107	direct (N × H)
302. D₄	C₁₃×#107	direct (N × H)
334. C₈	C₄×D₄×C₁₃	semidirect
341. C₂²	C₂×C₁₃×#107	semidirect
354. C₄	C₂×C₁₃×#107	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×D₄×C₁₃	2
C₂²×C₁₃×#107	2
D₄×C₁₃×C₄⋊C₄	2
C₁₃×#1947	2
C₁₃×#1852	2
C₁₃×#1845	2
C₁₃×#1808	2
C₄×C₁₃×#107	2
D₄×#107	13

Subgroups — D4×C13×#107 #15708994

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×C₁₃×#107 #15708994