Subgroups — C₄×D₁₃×#107 #15860961

Order 3328.

1358 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₃×#107	C₂	1	2	yes	maximal
2	C₂×C₄×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
3	C₄×C₄⋊C₄×D₁₃	C₂	1	2	yes	maximal
4	#107×Dic₁₃	C₂	1	2	yes	maximal, complemented
5	C₄×#88047	C₂	1	2	yes	maximal, complemented
6	C₄×#88058	C₂	1	1	yes	maximal, characteristic, complemented
7	#13114728	C₂	1	2	yes	maximal, complemented
8	D₁₃×#340	C₂	1	2	yes	maximal
9	C₄×C₁₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
11	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊C₄×D₁₃	C₂²	1	4	yes	—
13	C₂×C₄²×D₁₃	—	2	2	no	—
14	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#107	C₂²	1	2	yes	—
16	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂×#88058	C₂²	1	2	yes	—
19	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
21	C₄⋊C₄×Dic₁₃	C₂²	1	4	yes	—
22	C₂×#88047	C₂²	1	4	yes	—
23	C₄×C₄⋊Dic₁₃	C₂²	1	2	yes	—
24	C₄×#6101	—	2	2	no	—
25	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
26	D₁₃×#107	C₄	1	16	yes	direct product factor
27	C₄×C₈×D₁₃	C₄	1	8	yes	complemented
28	D₁₃×#95	—	2	2	no	—
29	#11718310	—	2	2	no	—
30	C₁₃×#340	C₂²	1	2	yes	—
31	#11718143	C₂²	1	2	yes	—
32	#11718121	C₂²	1	4	yes	—
33	C₂²×C₄×D₁₃	—	2	4	no	—
34	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
35	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
36	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
37	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
38	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
39	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
40	C₂×C₄²×C₁₃	—	2	2	no	—
41	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
42	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	—
43	C₂×#6101	—	2	4	no	—
44	C₂×C₄×Dic₁₃	—	2	2	no	—
45	C₂×C₄×Dic₁₃	—	2	4	no	—
46	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
47	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
48	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
49	C₂²×#1055	C₂³	1	1	yes	characteristic
50	C₂²×#1055	C₂³	1	1	yes	characteristic
51	C₂×C₈×D₁₃	—	2	4	no	—
52	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
53	C₂×C₈×D₁₃	C₂×C₄	1	8	yes	—
54	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
55	C₄⋊C₄×D₁₃	—	2	8	no	—
56	C₄⋊C₄×D₁₃	C₂×C₄	1	16	yes	—
57	C₄²×D₁₃	—	4	8	no	—
58	C₄²×D₁₃	C₂×C₄	1	4	yes	—
59	C₄²×D₁₃	Q₈	1	4	yes	—
60	C₁₃×#107	C₂×C₄	1	8	yes	complemented
61	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	complemented
62	C₁₃×#95	—	2	2	no	—
63	#88071	—	2	2	no	—
64	#88071	—	2	4	no	—
65	#88058	C₂×C₄	1	8	yes	complemented
66	C₈×Dic₁₃	C₂×C₄	1	4	yes	complemented
67	C₈×Dic₁₃	C₂×C₄	1	4	yes	complemented
68	#88047	C₂×C₄	1	16	yes	complemented
69	C₄×#1055	C₂×C₄	1	4	yes	complemented
70	C₂×C₄×#107	—	13	1	no	maximal, Sylow
71	C₂³×D₁₃	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₃	—	2	4	no	—
73	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
76	C₂²×Dic₁₃	—	2	4	no	—
77	C₂²×Dic₁₃	C₂×D₄	1	1	yes	characteristic
78	C₂²×Dic₁₃	C₂×D₄	1	1	yes	characteristic
79	C₂²×Dic₁₃	C₂×D₄	1	1	yes	characteristic
80	C₂×C₄×D₁₃	—	2	4	no	—
81	C₂×C₄×D₁₃	—	2	16	no	—
82	C₂×C₄×D₁₃	—	4	8	no	—
83	C₂×C₄×D₁₃	—	4	8	no	—
84	C₂×C₄×D₁₃	C₄⋊C₄	1	4	yes	—
85	C₂×C₄×D₁₃	C₄⋊C₄	1	4	yes	—
86	C₂×C₄×D₁₃	D₈	1	4	yes	—
87	C₂×C₄×D₁₃	Q₁₆	1	4	yes	—
88	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
89	C₂×C₄×D₁₃	C₂²×C₄	1	4	yes	—
90	C₂×C₄×D₁₃	C₂×Q₈	1	2	yes	—
91	C₂×C₄×D₁₃	#41	1	4	yes	—
92	C₂×C₈×C₁₃	—	2	2	no	—
93	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
94	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
95	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
96	C₁₃×C₄⋊C₄	—	2	4	no	—
97	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
98	C₄²×C₁₃	—	4	4	no	—
99	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
100	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
101	C₄⋊Dic₁₃	—	2	4	no	—
102	C₄⋊Dic₁₃	C₂²×C₄	1	8	yes	—
103	#6101	—	2	16	no	—
104	C₄×Dic₁₃	—	4	4	no	—
105	C₄×Dic₁₃	—	4	8	no	—
106	C₄×Dic₁₃	C₄⋊C₄	1	4	yes	—
107	C₄×Dic₁₃	C₄⋊C₄	1	4	yes	—
108	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
109	C₄×Dic₁₃	C₂×Q₈	1	2	yes	—
110	C₂×#1055	—	2	2	no	—
111	C₂×#1055	C₂²×C₄	1	2	yes	—
112	C₂×#1055	C₂²×C₄	1	2	yes	—
113	C₂×#1055	C₂²×C₄	1	4	yes	—
114	C₈×D₁₃	—	2	8	no	—
115	C₈×D₁₃	C₄²	1	16	yes	complemented
116	C₂²×#107	—	13	2	no	—
117	C₂²×C₄×C₈	—	13	1	no	—
118	C₂×C₄×C₄⋊C₄	—	13	2	no	—
119	C₄×#107	—	13	2	no	—
120	C₄×#107	—	13	1	no	—
121	C₄×#107	—	13	2	no	—
122	C₄×#107	—	13	2	no	—
123	C₄×#107	D₁₃	1	1	yes	characteristic, direct product factor
124	C₂×#340	—	13	2	no	—
125	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
126	C₂²×D₁₃	C₂×C₄⋊C₄	1	2	yes	—
127	C₂²×D₁₃	C₄×D₄	1	4	yes	—
128	C₂²×D₁₃	C₂×D₈	1	2	yes	—
129	C₂²×D₁₃	C₂×Q₁₆	1	2	yes	—
130	C₂²×D₁₃	#135	1	4	yes	—
131	C₂×C₄×C₁₃	—	2	2	no	—
132	C₂×C₄×C₁₃	—	2	8	no	—
133	C₂×C₄×C₁₃	—	4	4	no	—
134	C₂×C₄×C₁₃	—	4	4	no	—
135	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
136	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
137	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
138	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
139	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
140	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
141	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
142	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
143	C₂×Dic₁₃	—	2	2	no	—
144	C₂×Dic₁₃	—	2	8	no	—
145	C₂×Dic₁₃	—	4	4	no	—
146	C₂×Dic₁₃	—	4	4	no	—
147	C₂×Dic₁₃	C₂×C₄⋊C₄	1	2	yes	—
148	C₂×Dic₁₃	C₂×C₄⋊C₄	1	2	yes	—
149	C₂×Dic₁₃	C₂×C₄⋊C₄	1	2	yes	—
150	C₂×Dic₁₃	C₄×D₄	1	4	yes	—
151	C₂×Dic₁₃	C₂×D₈	1	2	yes	—
152	C₂×Dic₁₃	C₂×Q₁₆	1	2	yes	—
153	C₄×D₁₃	—	2	8	no	—
154	C₄×D₁₃	—	4	32	no	—
155	C₄×D₁₃	#107	1	16	yes	direct product factor
156	C₄×D₁₃	C₂×C₄²	1	4	yes	—
157	C₄×D₁₃	#117	1	4	yes	—
158	C₄×D₁₃	C₄×Q₈	1	8	yes	—
159	C₈×C₁₃	—	2	2	no	—
160	C₈×C₁₃	C₂×C₄²	1	4	yes	complemented
161	#1055	—	2	2	no	—
162	#1055	C₂×C₄²	1	4	yes	complemented
163	C₂³×C₈	—	13	1	no	—
164	C₂³×C₈	—	13	1	no	—
165	C₂²×C₄⋊C₄	—	13	4	no	—
166	C₂²×C₄²	—	13	1	no	—
167	C₂²×C₄²	—	26	2	no	—
168	C₂×#107	—	13	2	no	—
169	C₂×#107	—	13	4	no	—
170	C₂×#107	—	13	16	no	—
171	C₂×#107	C₂×D₁₃	1	2	yes	—
172	C₂×C₄×C₈	—	13	1	no	—
173	C₂×C₄×C₈	—	13	1	no	—
174	C₂×C₄×C₈	—	13	1	no	—
175	C₂×C₄×C₈	—	13	8	no	—
176	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
177	C₄×C₄⋊C₄	—	13	4	no	—
178	C₄×C₄⋊C₄	—	13	2	no	—
179	C₄×C₄⋊C₄	—	26	2	no	—
180	C₄×C₄⋊C₄	—	26	2	no	—
181	C₄×C₄⋊C₄	C₂×D₁₃	1	2	yes	—
182	C₂×#95	—	26	2	no	—
183	#340	—	13	2	no	—
184	#340	—	13	4	no	—
185	#340	C₂×D₁₃	1	2	yes	—
186	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
187	C₂²×C₁₃	C₂×C₄×D₄	1	2	yes	—
188	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
189	C₂²×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
190	C₂²×C₁₃	C₂×#135	1	2	yes	—
191	C₂×D₁₃	C₄×C₄⋊C₄	1	4	yes	—
192	C₂×D₁₃	C₂×#107	1	4	yes	—
193	C₂×D₁₃	#427	1	4	yes	—
194	C₂×D₁₃	C₄×D₈	1	8	yes	—
195	C₂×D₁₃	C₄×Q₁₆	1	8	yes	—
196	C₄×C₁₃	—	2	2	no	—
197	C₄×C₁₃	—	4	8	no	—
198	C₄×C₁₃	C₂×#107	1	4	yes	complemented
199	C₄×C₁₃	C₂²×C₄²	1	1	yes	characteristic
200	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
201	C₄×C₁₃	C₂×C₄×Q₈	1	2	yes	—
202	Dic₁₃	—	2	2	no	—
203	Dic₁₃	—	4	8	no	—
204	Dic₁₃	C₄×C₄⋊C₄	1	4	yes	—
205	Dic₁₃	C₂×#107	1	4	yes	complemented
206	C₂³×C₄	—	13	1	no	—
207	C₂³×C₄	—	13	1	no	—
208	C₂³×C₄	—	13	1	no	—
209	C₂³×C₄	—	26	4	no	—
210	C₂²×C₈	—	13	1	no	—
211	C₂²×C₈	—	13	4	no	—
212	C₂²×C₈	—	13	8	no	—
213	C₂²×C₈	—	13	1	no	—
214	C₂²×C₈	—	13	4	no	—
215	C₂²×C₈	—	26	4	no	—
216	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
217	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
218	C₂×C₄⋊C₄	—	13	4	no	—
219	C₂×C₄⋊C₄	—	13	16	no	—
220	C₂×C₄⋊C₄	—	26	8	no	—
221	C₂×C₄⋊C₄	—	26	4	no	—
222	C₂×C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
223	C₂×C₄²	—	2	2	no	—
224	C₂×C₄²	—	13	1	no	—
225	C₂×C₄²	—	13	1	no	—
226	C₂×C₄²	—	13	1	no	—
227	C₂×C₄²	—	13	4	no	—
228	C₂×C₄²	—	13	4	no	—
229	C₂×C₄²	—	26	4	no	—
230	C₂×C₄²	—	26	2	no	—
231	C₂×C₄²	—	52	8	no	—
232	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
233	#107	—	13	8	no	—
234	#107	—	13	16	no	—
235	#107	C₄×D₁₃	1	8	yes	direct product factor
236	C₄×C₈	—	13	4	no	—
237	C₄×C₈	—	13	4	no	—
238	C₄×C₈	—	13	4	no	—
239	C₄×C₈	C₄×D₁₃	1	4	yes	complemented
240	#95	—	2	2	no	—
241	#95	—	26	4	no	—
242	#95	—	26	2	no	—
243	C₂×C₁₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
244	C₂×C₁₃	C₂²×#107	1	1	yes	characteristic
245	C₂×C₁₃	C₂×#427	1	1	yes	characteristic
246	C₂×C₁₃	C₂×C₄×D₈	1	2	yes	—
247	C₂×C₁₃	C₂×C₄×Q₁₆	1	2	yes	—
248	D₁₃	C₄×#107	1	8	yes	direct product factor
249	C₂⁴	—	13	1	no	—
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	13	1	no	—
252	C₂²×C₄	—	13	1	no	—
253	C₂²×C₄	—	13	4	no	—
254	C₂²×C₄	—	13	4	no	—
255	C₂²×C₄	—	13	4	no	—
256	C₂²×C₄	—	13	2	no	—
257	C₂²×C₄	—	13	4	no	—
258	C₂²×C₄	—	13	2	no	—
259	C₂²×C₄	—	13	4	no	—
260	C₂²×C₄	—	13	1	no	—
261	C₂²×C₄	—	13	4	no	—
262	C₂²×C₄	—	26	4	no	—
263	C₂²×C₄	—	26	16	no	—
264	C₂²×C₄	—	26	4	no	—
265	C₂²×C₄	—	52	8	no	—
266	C₂²×C₄	—	52	8	no	—
267	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
268	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
269	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
270	C₂×C₈	—	2	2	no	—
271	C₂×C₈	—	13	2	no	—
272	C₂×C₈	—	13	4	no	—
273	C₂×C₈	—	13	16	no	—
274	C₂×C₈	—	13	2	no	—
275	C₂×C₈	—	26	8	no	—
276	C₂×C₈	—	26	2	no	—
277	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
278	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
279	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
280	C₄⋊C₄	—	2	4	no	—
281	C₄⋊C₄	—	13	8	no	—
282	C₄⋊C₄	—	26	16	no	—
283	C₄⋊C₄	—	26	4	no	—
284	C₄⋊C₄	C₂×C₄×D₁₃	1	8	yes	—
285	C₄²	—	4	4	no	—
286	C₄²	—	13	4	no	—
287	C₄²	—	13	4	no	—
288	C₄²	—	13	2	no	—
289	C₄²	—	13	2	no	—
290	C₄²	—	52	8	no	—
291	C₄²	—	52	4	no	—
292	C₄²	C₂×C₄×D₁₃	1	2	yes	—
293	C₄²	Q₈×D₁₃	1	2	yes	—
294	C₁₃	C₂×C₄×#107	1	1	yes	characteristic, complemented, Sylow
295	C₂³	—	13	2	no	—
296	C₂³	—	13	2	no	—
297	C₂³	—	13	2	no	—
298	C₂³	—	13	4	no	—
299	C₂³	—	13	4	no	—
300	C₂³	C₂×D₄×D₁₃	1	1	yes	characteristic
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	8	no	—
303	C₂×C₄	—	4	4	no	—
304	C₂×C₄	—	4	4	no	—
305	C₂×C₄	—	13	2	no	—
306	C₂×C₄	—	13	2	no	—
307	C₂×C₄	—	13	2	no	—
308	C₂×C₄	—	13	2	no	—
309	C₂×C₄	—	13	4	no	—
310	C₂×C₄	—	13	4	no	—
311	C₂×C₄	—	13	4	no	—
312	C₂×C₄	—	13	8	no	—
313	C₂×C₄	—	13	16	no	—
314	C₂×C₄	—	13	2	no	—
315	C₂×C₄	—	26	8	no	—
316	C₂×C₄	—	26	2	no	—
317	C₂×C₄	—	26	8	no	—
318	C₂×C₄	—	52	32	no	—
319	C₂×C₄	—	52	4	no	—
320	C₂×C₄	—	52	4	no	—
321	C₂×C₄	C₄⋊C₄×D₁₃	1	2	yes	—
322	C₂×C₄	C₄⋊C₄×D₁₃	1	2	yes	—
323	C₂×C₄	D₈×D₁₃	1	2	yes	—
324	C₂×C₄	Q₁₆×D₁₃	1	2	yes	—
325	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
326	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
327	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
328	C₂×C₄	#41×D₁₃	1	2	yes	—
329	C₈	—	2	2	no	—
330	C₈	—	13	4	no	—
331	C₈	—	26	2	no	—
332	C₈	C₄²×D₁₃	1	4	yes	complemented
333	C₂²	—	13	8	no	—
334	C₂²	—	13	4	no	—
335	C₂²	—	13	4	no	—
336	C₂²	—	13	4	no	—
337	C₂²	—	13	8	no	—
338	C₂²	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
339	C₂²	C₄×D₄×D₁₃	1	2	yes	—
340	C₂²	C₂×D₈×D₁₃	1	1	yes	characteristic
341	C₂²	C₂×Q₁₆×D₁₃	1	1	yes	characteristic
342	C₂²	D₁₃×#135	1	2	yes	—
343	C₄	—	2	2	no	—
344	C₄	—	4	8	no	—
345	C₄	—	13	4	no	—
346	C₄	—	13	4	no	—
347	C₄	—	26	2	no	—
348	C₄	—	52	8	no	—
349	C₄	D₁₃×#107	1	4	yes	direct product factor
350	C₄	C₂×C₄²×D₁₃	1	1	yes	characteristic
351	C₄	D₁₃×#117	1	1	yes	characteristic
352	C₄	C₄×Q₈×D₁₃	1	2	yes	—
353	C₂	—	13	8	no	—
354	C₂	C₄×C₄⋊C₄×D₁₃	1	1	yes	characteristic
355	C₂	C₂×D₁₃×#107	1	1	yes	characteristic
356	C₂	D₁₃×#427	1	1	yes	characteristic
357	C₂	C₄×D₈×D₁₃	1	2	yes	—
358	C₂	C₄×Q₁₆×D₁₃	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₃
commutator	C₄×C₁₃	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₄×C₁₃×#107	C₂
socle	C₂³×C₁₃	C₂²×D₄
prime radical	C₂³×D₁₃	C₂×D₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₄×#107	D₁₃
hypocenter	C₁₃	C₂×C₄×#107
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₄×#107

Complements

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

N	H ≅ G/N	type
4. #107×Dic₁₃	C₂	semidirect
5. C₄×#88047	C₂	semidirect
6. C₄×#88058	C₂	semidirect
7. #13114728	C₂	semidirect
9. C₄×C₁₃×#107	C₂	semidirect
26. D₁₃×#107	C₄	direct (N × H)
27. C₄×C₈×D₁₃	C₄	semidirect
60. C₁₃×#107	C₂×C₄	semidirect
61. C₄×C₈×C₁₃	C₂×C₄	semidirect
65. #88058	C₂×C₄	semidirect
66. C₈×Dic₁₃	C₂×C₄	semidirect
67. C₈×Dic₁₃	C₂×C₄	semidirect
68. #88047	C₂×C₄	semidirect
69. C₄×#1055	C₂×C₄	semidirect
115. C₈×D₁₃	C₄²	semidirect
123. C₄×#107	D₁₃	direct (N × H)
155. C₄×D₁₃	#107	direct (N × H)
160. C₈×C₁₃	C₂×C₄²	semidirect
162. #1055	C₂×C₄²	semidirect
198. C₄×C₁₃	C₂×#107	semidirect
205. Dic₁₃	C₂×#107	semidirect
235. #107	C₄×D₁₃	direct (N × H)
239. C₄×C₈	C₄×D₁₃	semidirect
248. D₁₃	C₄×#107	direct (N × H)
294. C₁₃	C₂×C₄×#107	semidirect
332. C₈	C₄²×D₁₃	semidirect
349. C₄	D₁₃×#107	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×D₁₃×#107	2
C₂×C₄×C₈×D₁₃	2
C₄×C₄⋊C₄×D₁₃	2
#107×Dic₁₃	2
C₄×#88047	2
C₄×#88058	2
#13114728	2
D₁₃×#340	2
C₄×C₁₃×#107	2
C₂×C₄×#107	13

Subgroups — C4×D13×#107 #15860961

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×D₁₃×#107 #15860961