Subgroups — C₂²×D₁₃×#120 #16769548

Order 3328.

42862 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁶×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×D₄×D₁₃	C₂	1	3	yes	maximal, complemented
3	C₂²×#88136	C₂	1	3	yes	maximal, complemented
4	C₂²×#88207	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#88191	C₂	1	3	yes	maximal, complemented
6	C₂×D₁₃×#120	C₂	1	48	yes	maximal, direct product factor
7	C₂²×C₂²⋊C₄×D₁₃	C₂	1	3	yes	maximal, complemented
8	C₂²×C₁₃×#120	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂⁶×C₁₃	C₂²	1	1	yes	characteristic, complemented
10	C₂⁵×D₁₃	—	2	48	no	—
11	C₂⁵×D₁₃	C₂²	1	3	yes	—
12	C₂⁵×D₁₃	C₂²	1	24	yes	complemented
13	C₂⁵×D₁₃	C₂²	1	3	yes	complemented
14	C₂⁵×D₁₃	C₂²	1	1	yes	characteristic, complemented
15	C₂³×D₄×C₁₃	C₂²	1	3	yes	complemented
16	C₂³×C₂²⋊D₁₃	C₂²	1	3	yes	complemented
17	C₂³×C₂²⋊D₁₃	C₂²	1	3	yes	complemented
18	C₂²×D₄×D₁₃	—	2	48	no	—
19	C₂²×D₄×D₁₃	C₂²	1	72	yes	complemented
20	C₂³×D₅₂	C₂²	1	3	yes	complemented
21	C₂³×C₄×D₁₃	C₂²	1	3	yes	complemented
22	C₂×C₁₃×#120	C₂²	1	24	yes	complemented
23	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	3	yes	complemented
24	C₂×#88207	C₂²	1	24	yes	complemented
25	C₂²×C₂²⋊Dic₁₃	C₂²	1	3	yes	complemented
26	C₂×#88191	C₂²	1	72	yes	complemented
27	C₂²×#6103	C₂²	1	6	yes	complemented
28	D₁₃×#120	C₂²	1	256	yes	direct product factor
29	C₂×#88136	C₂²	1	72	yes	complemented
30	C₂×C₂²⋊C₄×D₁₃	C₂²	1	72	yes	complemented
31	C₂⁵×C₁₃	—	2	24	no	—
32	C₂⁵×C₁₃	C₂³	1	3	yes	—
33	C₂⁵×C₁₃	C₂³	1	12	yes	complemented
34	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic, complemented
35	C₂⁴×D₁₃	—	2	512	no	—
36	C₂⁴×D₁₃	—	2	24	no	—
37	C₂⁴×D₁₃	—	2	48	no	—
38	C₂⁴×D₁₃	—	2	48	no	—
39	C₂⁴×D₁₃	—	2	576	no	—
40	C₂⁴×D₁₃	—	2	24	no	—
41	C₂⁴×D₁₃	D₄	1	48	yes	complemented
42	C₂⁴×D₁₃	C₂³	1	36	yes	—
43	C₂⁴×D₁₃	C₂³	1	3	yes	—
44	C₂⁴×D₁₃	C₂³	1	1	yes	characteristic
45	C₂⁴×D₁₃	C₂³	1	64	yes	complemented
46	C₂⁴×D₁₃	C₂³	1	36	yes	complemented
47	C₂⁴×D₁₃	C₂³	1	12	yes	complemented
48	C₂⁴×D₁₃	C₂³	1	1	yes	characteristic, complemented
49	C₂²×D₄×C₁₃	—	2	24	no	—
50	C₂²×D₄×C₁₃	C₂³	1	36	yes	complemented
51	C₂³×C₄×C₁₃	C₂³	1	3	yes	complemented
52	C₂²×C₂²⋊D₁₃	—	2	24	no	—
53	C₂²×C₂²⋊D₁₃	—	2	24	no	—
54	C₂²×C₂²⋊D₁₃	C₂³	1	36	yes	complemented
55	C₂²×C₂²⋊D₁₃	C₂³	1	36	yes	complemented
56	C₂³×Dic₁₃	C₂³	1	3	yes	complemented
57	C₂×D₄×D₁₃	—	2	576	no	—
58	C₂×D₄×D₁₃	C₂³	1	192	yes	complemented
59	C₂²×D₅₂	—	2	24	no	—
60	C₂²×D₅₂	C₂³	1	36	yes	complemented
61	C₂²×C₄×D₁₃	—	2	24	no	—
62	C₂²×C₄×D₁₃	C₂³	1	36	yes	complemented
63	C₁₃×#120	C₂³	1	64	yes	complemented
64	C₂×C₁₃×C₂²⋊C₄	C₂³	1	36	yes	complemented
65	#88207	C₂³	1	64	yes	complemented
66	C₂×C₂²⋊Dic₁₃	C₂³	1	36	yes	complemented
67	#88191	C₂³	1	192	yes	complemented
68	C₂×#6103	C₂³	1	72	yes	complemented
69	#88136	C₂³	1	192	yes	complemented
70	C₂²⋊C₄×D₁₃	C₂³	1	192	yes	complemented
71	C₂³×#120	—	13	1	no	maximal, Sylow
72	C₂⁴×C₁₃	—	2	128	no	—
73	C₂⁴×C₁₃	—	2	24	no	—
74	C₂⁴×C₁₃	—	2	144	no	—
75	C₂⁴×C₁₃	—	2	12	no	—
76	C₂⁴×C₁₃	C₂×D₄	1	24	yes	complemented
77	C₂⁴×C₁₃	C₂⁴	1	18	yes	—
78	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
79	C₂⁴×C₁₃	C₂⁴	1	16	yes	complemented
80	C₂⁴×C₁₃	C₂⁴	1	6	yes	complemented
81	C₂³×D₁₃	—	2	384	no	—
82	C₂³×D₁₃	—	2	3072	no	—
83	C₂³×D₁₃	—	2	24	no	—
84	C₂³×D₁₃	—	2	144	no	—
85	C₂³×D₁₃	—	2	384	no	—
86	C₂³×D₁₃	—	2	288	no	—
87	C₂³×D₁₃	—	2	288	no	—
88	C₂³×D₁₃	—	2	768	no	—
89	C₂³×D₁₃	—	2	12	no	—
90	C₂³×D₁₃	—	2	144	no	—
91	C₂³×D₁₃	—	4	64	no	—
92	C₂³×D₁₃	C₂×D₄	1	24	yes	—
93	C₂³×D₁₃	C₂×D₄	1	288	yes	complemented
94	C₂³×D₁₃	C₂×D₄	1	24	yes	complemented
95	C₂³×D₁₃	C₂⁴	1	48	yes	—
96	C₂³×D₁₃	C₂⁴	1	18	yes	—
97	C₂³×D₁₃	C₂⁴	1	6	yes	—
98	C₂³×D₁₃	C₂⁴	1	48	yes	complemented
99	C₂³×D₁₃	C₂⁴	1	16	yes	complemented
100	C₂³×D₁₃	C₂⁴	1	6	yes	complemented
101	C₂×D₄×C₁₃	—	2	144	no	—
102	C₂×D₄×C₁₃	C₂⁴	1	48	yes	complemented
103	C₂²×C₄×C₁₃	—	2	12	no	—
104	C₂²×C₄×C₁₃	C₂⁴	1	18	yes	complemented
105	C₂×C₂²⋊D₁₃	—	2	144	no	—
106	C₂×C₂²⋊D₁₃	—	2	144	no	—
107	C₂×C₂²⋊D₁₃	C₂⁴	1	48	yes	complemented
108	C₂×C₂²⋊D₁₃	C₂⁴	1	48	yes	complemented
109	C₂²×Dic₁₃	—	2	12	no	—
110	C₂²×Dic₁₃	C₂⁴	1	18	yes	complemented
111	D₄×D₁₃	—	2	768	no	—
112	C₂×D₅₂	—	2	144	no	—
113	C₂×D₅₂	C₂⁴	1	48	yes	complemented
114	C₂×C₄×D₁₃	—	2	144	no	—
115	C₂×C₄×D₁₃	C₂⁴	1	48	yes	complemented
116	C₁₃×C₂²⋊C₄	C₂⁴	1	48	yes	complemented
117	C₂²⋊Dic₁₃	C₂⁴	1	48	yes	complemented
118	#6103	C₂⁴	1	96	yes	complemented
119	C₂⁷	—	13	1	no	—
120	C₂⁴×D₄	—	13	3	no	—
121	C₂²×#120	—	13	1	no	—
122	C₂²×#120	—	13	3	no	—
123	C₂²×#120	—	13	48	no	—
124	C₂²×#120	—	13	3	no	—
125	C₂²×#120	D₁₃	1	1	yes	characteristic, direct product factor
126	C₂³×C₂²⋊C₄	—	13	3	no	—
127	C₂³×C₁₃	—	2	384	no	—
128	C₂³×C₁₃	—	2	96	no	—
129	C₂³×C₁₃	—	2	72	no	—
130	C₂³×C₁₃	—	2	96	no	—
131	C₂³×C₁₃	—	2	36	no	—
132	C₂³×C₁₃	—	4	16	no	—
133	C₂³×C₁₃	C₂²×D₄	1	12	yes	—
134	C₂³×C₁₃	C₂²×D₄	1	72	yes	complemented
135	C₂³×C₁₃	C₂⁵	1	12	yes	—
136	C₂³×C₁₃	C₂⁵	1	3	yes	—
137	C₂³×C₁₃	C₂⁵	1	4	yes	complemented
138	C₂²×D₁₃	—	2	1152	no	—
139	C₂²×D₁₃	—	2	2048	no	—
140	C₂²×D₁₃	—	2	96	no	—
141	C₂²×D₁₃	—	2	72	no	—
142	C₂²×D₁₃	—	2	96	no	—
143	C₂²×D₁₃	—	2	1152	no	—
144	C₂²×D₁₃	—	2	192	no	—
145	C₂²×D₁₃	—	2	192	no	—
146	C₂²×D₁₃	—	2	36	no	—
147	C₂²×D₁₃	—	2	96	no	—
148	C₂²×D₁₃	—	4	16	no	—
149	C₂²×D₁₃	—	4	192	no	—
150	C₂²×D₁₃	#120	1	64	yes	direct product factor
151	C₂²×D₁₃	C₂²×D₄	1	72	yes	—
152	C₂²×D₁₃	C₂²×D₄	1	192	yes	complemented
153	C₂²×D₁₃	C₂²×D₄	1	72	yes	complemented
154	C₂²×D₁₃	C₂⁵	1	12	yes	—
155	C₂²×D₁₃	C₂⁵	1	4	yes	—
156	C₂²×D₁₃	C₂⁵	1	4	yes	complemented
157	D₄×C₁₃	—	2	96	no	—
158	C₂×C₄×C₁₃	—	2	36	no	—
159	C₂×C₄×C₁₃	C₂⁵	1	12	yes	complemented
160	C₂²⋊D₁₃	—	2	96	no	—
161	C₂²⋊D₁₃	—	2	96	no	—
162	C₂×Dic₁₃	—	2	36	no	—
163	C₂×Dic₁₃	C₂⁵	1	12	yes	complemented
164	D₅₂	—	2	96	no	—
165	C₄×D₁₃	—	2	96	no	—
166	C₂⁶	—	13	3	no	—
167	C₂⁶	—	13	3	no	—
168	C₂⁶	—	13	1	no	—
169	C₂⁶	—	13	24	no	—
170	C₂⁶	—	26	48	no	—
171	C₂⁶	C₂×D₁₃	1	1	yes	characteristic, complemented
172	C₂³×D₄	—	13	3	no	—
173	C₂³×D₄	—	13	3	no	—
174	C₂³×D₄	—	13	72	no	—
175	C₂³×D₄	—	13	3	no	—
176	C₂³×D₄	—	26	48	no	—
177	C₂³×D₄	C₂×D₁₃	1	3	yes	complemented
178	C₂⁴×C₄	—	13	3	no	—
179	C₂×#120	—	13	24	no	—
180	C₂×#120	—	13	72	no	—
181	C₂×#120	—	13	256	no	—
182	C₂×#120	—	13	72	no	—
183	C₂×#120	C₂×D₁₃	1	24	yes	direct product factor
184	C₂²×C₂²⋊C₄	—	13	3	no	—
185	C₂²×C₂²⋊C₄	—	13	6	no	—
186	C₂²×C₂²⋊C₄	—	13	72	no	—
187	C₂²×C₂²⋊C₄	C₂×D₁₃	1	3	yes	complemented
188	C₂²×C₁₃	—	2	128	no	—
189	C₂²×C₁₃	—	2	24	no	—
190	C₂²×C₁₃	—	2	144	no	—
191	C₂²×C₁₃	—	2	12	no	—
192	C₂²×C₁₃	—	4	24	no	—
193	C₂²×C₁₃	C₂×#120	1	16	yes	complemented
194	C₂²×C₁₃	C₂³×D₄	1	18	yes	—
195	C₂²×C₁₃	C₂³×D₄	1	24	yes	complemented
196	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
197	C₂×D₁₃	—	2	384	no	—
198	C₂×D₁₃	—	2	24	no	—
199	C₂×D₁₃	—	2	144	no	—
200	C₂×D₁₃	—	2	384	no	—
201	C₂×D₁₃	—	2	12	no	—
202	C₂×D₁₃	—	4	24	no	—
203	C₂×D₁₃	—	4	64	no	—
204	C₂×D₁₃	C₂×#120	1	96	yes	direct product factor
205	C₂×D₁₃	C₂³×D₄	1	24	yes	—
206	C₂×D₁₃	C₂³×D₄	1	24	yes	complemented
207	C₄×C₁₃	—	2	12	no	—
208	Dic₁₃	—	2	12	no	—
209	C₂⁵	—	2	24	no	—
210	C₂⁵	—	13	1	no	—
211	C₂⁵	—	13	48	no	—
212	C₂⁵	—	13	36	no	—
213	C₂⁵	—	13	3	no	—
214	C₂⁵	—	13	36	no	—
215	C₂⁵	—	13	1	no	—
216	C₂⁵	—	13	64	no	—
217	C₂⁵	—	13	12	no	—
218	C₂⁵	—	26	48	no	—
219	C₂⁵	—	26	48	no	—
220	C₂⁵	—	26	576	no	—
221	C₂⁵	—	26	24	no	—
222	C₂⁵	—	26	512	no	—
223	C₂⁵	—	26	24	no	—
224	C₂⁵	C₂²×D₁₃	1	3	yes	—
225	C₂⁵	C₂²×D₁₃	1	12	yes	complemented
226	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic, complemented
227	C₂²×D₄	—	2	24	no	—
228	C₂²×D₄	—	13	36	no	—
229	C₂²×D₄	—	13	36	no	—
230	C₂²×D₄	—	13	192	no	—
231	C₂²×D₄	—	13	36	no	—
232	C₂²×D₄	—	26	24	no	—
233	C₂²×D₄	—	26	576	no	—
234	C₂²×D₄	—	26	24	no	—
235	C₂²×D₄	—	26	24	no	—
236	C₂²×D₄	C₂²×D₁₃	1	36	yes	complemented
237	C₂³×C₄	—	13	3	no	—
238	C₂³×C₄	—	13	36	no	—
239	C₂³×C₄	—	26	24	no	—
240	C₂³×C₄	C₂²×D₁₃	1	3	yes	complemented
241	#120	—	13	64	no	—
242	#120	—	13	192	no	—
243	#120	—	13	192	no	—
244	#120	C₂²×D₁₃	1	64	yes	direct product factor
245	C₂×C₂²⋊C₄	—	13	36	no	—
246	C₂×C₂²⋊C₄	—	13	72	no	—
247	C₂×C₂²⋊C₄	—	13	192	no	—
248	C₂×C₂²⋊C₄	C₂²×D₁₃	1	36	yes	complemented
249	C₂×C₁₃	—	2	24	no	—
250	C₂×C₁₃	—	4	4	no	—
251	C₂×C₁₃	C₂²×#120	1	12	yes	complemented
252	C₂×C₁₃	C₂⁴×D₄	1	3	yes	—
253	D₁₃	—	2	24	no	—
254	D₁₃	—	4	4	no	—
255	D₁₃	C₂²×#120	1	16	yes	direct product factor
256	C₂⁴	—	2	128	no	—
257	C₂⁴	—	2	24	no	—
258	C₂⁴	—	2	144	no	—
259	C₂⁴	—	2	12	no	—
260	C₂⁴	—	13	24	no	—
261	C₂⁴	—	13	6	no	—
262	C₂⁴	—	13	24	no	—
263	C₂⁴	—	13	288	no	—
264	C₂⁴	—	13	48	no	—
265	C₂⁴	—	13	18	no	—
266	C₂⁴	—	13	48	no	—
267	C₂⁴	—	13	6	no	—
268	C₂⁴	—	13	16	no	—
269	C₂⁴	—	26	384	no	—
270	C₂⁴	—	26	288	no	—
271	C₂⁴	—	26	288	no	—
272	C₂⁴	—	26	768	no	—
273	C₂⁴	—	26	144	no	—
274	C₂⁴	—	26	3072	no	—
275	C₂⁴	—	26	384	no	—
276	C₂⁴	—	26	24	no	—
277	C₂⁴	—	26	144	no	—
278	C₂⁴	—	26	12	no	—
279	C₂⁴	—	52	64	no	—
280	C₂⁴	D₄×D₁₃	1	24	yes	complemented
281	C₂⁴	C₂³×D₁₃	1	18	yes	—
282	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
283	C₂⁴	C₂³×D₁₃	1	16	yes	complemented
284	C₂⁴	C₂³×D₁₃	1	6	yes	complemented
285	C₂×D₄	—	2	144	no	—
286	C₂×D₄	—	13	48	no	—
287	C₂×D₄	—	13	48	no	—
288	C₂×D₄	—	13	48	no	—
289	C₂×D₄	—	26	144	no	—
290	C₂×D₄	—	26	768	no	—
291	C₂×D₄	—	26	144	no	—
292	C₂×D₄	—	26	144	no	—
293	C₂×D₄	C₂³×D₁₃	1	48	yes	complemented
294	C₂²×C₄	—	2	12	no	—
295	C₂²×C₄	—	13	18	no	—
296	C₂²×C₄	—	13	48	no	—
297	C₂²×C₄	—	26	144	no	—
298	C₂²×C₄	—	26	12	no	—
299	C₂²×C₄	C₂³×D₁₃	1	18	yes	complemented
300	C₂²⋊C₄	—	13	48	no	—
301	C₂²⋊C₄	—	13	96	no	—
302	C₂²⋊C₄	C₂³×D₁₃	1	48	yes	complemented
303	C₁₃	C₂³×#120	1	1	yes	characteristic, complemented, Sylow
304	C₂³	—	2	384	no	—
305	C₂³	—	2	96	no	—
306	C₂³	—	2	72	no	—
307	C₂³	—	2	96	no	—
308	C₂³	—	2	36	no	—
309	C₂³	—	4	16	no	—
310	C₂³	—	13	64	no	—
311	C₂³	—	13	72	no	—
312	C₂³	—	13	4	no	—
313	C₂³	—	13	72	no	—
314	C₂³	—	13	192	no	—
315	C₂³	—	13	12	no	—
316	C₂³	—	13	4	no	—
317	C₂³	—	26	1152	no	—
318	C₂³	—	26	192	no	—
319	C₂³	—	26	192	no	—
320	C₂³	—	26	96	no	—
321	C₂³	—	26	2048	no	—
322	C₂³	—	26	1152	no	—
323	C₂³	—	26	96	no	—
324	C₂³	—	26	72	no	—
325	C₂³	—	26	96	no	—
326	C₂³	—	26	36	no	—
327	C₂³	—	52	192	no	—
328	C₂³	—	52	16	no	—
329	C₂³	C₂×D₄×D₁₃	1	12	yes	—
330	C₂³	C₂×D₄×D₁₃	1	72	yes	complemented
331	C₂³	C₂⁴×D₁₃	1	12	yes	—
332	C₂³	C₂⁴×D₁₃	1	3	yes	—
333	C₂³	C₂⁴×D₁₃	1	4	yes	complemented
334	D₄	—	2	96	no	—
335	D₄	—	26	96	no	—
336	D₄	—	26	96	no	—
337	D₄	—	26	96	no	—
338	C₂×C₄	—	2	36	no	—
339	C₂×C₄	—	13	12	no	—
340	C₂×C₄	—	26	96	no	—
341	C₂×C₄	—	26	36	no	—
342	C₂×C₄	C₂⁴×D₁₃	1	12	yes	complemented
343	C₂²	—	2	128	no	—
344	C₂²	—	2	144	no	—
345	C₂²	—	2	24	no	—
346	C₂²	—	2	12	no	—
347	C₂²	—	4	24	no	—
348	C₂²	—	13	96	no	—
349	C₂²	—	13	24	no	—
350	C₂²	—	13	24	no	—
351	C₂²	—	26	384	no	—
352	C₂²	—	26	384	no	—
353	C₂²	—	26	144	no	—
354	C₂²	—	26	24	no	—
355	C₂²	—	26	12	no	—
356	C₂²	—	52	64	no	—
357	C₂²	—	52	24	no	—
358	C₂²	D₁₃×#120	1	16	yes	direct product factor
359	C₂²	C₂²×D₄×D₁₃	1	18	yes	—
360	C₂²	C₂²×D₄×D₁₃	1	24	yes	complemented
361	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
362	C₄	—	2	12	no	—
363	C₄	—	26	12	no	—
364	C₂	—	2	24	no	—
365	C₂	—	4	4	no	—
366	C₂	—	13	16	no	—
367	C₂	—	26	24	no	—
368	C₂	—	52	4	no	—
369	C₂	C₂×D₁₃×#120	1	12	yes	direct product factor
370	C₂	C₂³×D₄×D₁₃	1	3	yes	—

	subgroup	G/H
center	C₂⁴	C₂³×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂²×C₁₃×#120	C₂
socle	C₂⁴×C₁₃	C₂⁴
hypercenter	C₂²×#120	D₁₃
hypocenter	C₁₃	C₂³×#120
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×#120

Complements

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

N	H ≅ G/N	type
1. C₂⁶×D₁₃	C₂	semidirect
2. C₂³×D₄×D₁₃	C₂	semidirect
3. C₂²×#88136	C₂	semidirect
4. C₂²×#88207	C₂	semidirect
5. C₂²×#88191	C₂	semidirect
6. C₂×D₁₃×#120	C₂	direct (N × H)
7. C₂²×C₂²⋊C₄×D₁₃	C₂	semidirect
8. C₂²×C₁₃×#120	C₂	semidirect
9. C₂⁶×C₁₃	C₂²	semidirect
12. C₂⁵×D₁₃	C₂²	semidirect
13. C₂⁵×D₁₃	C₂²	semidirect
14. C₂⁵×D₁₃	C₂²	semidirect
15. C₂³×D₄×C₁₃	C₂²	semidirect
16. C₂³×C₂²⋊D₁₃	C₂²	semidirect
17. C₂³×C₂²⋊D₁₃	C₂²	semidirect
19. C₂²×D₄×D₁₃	C₂²	semidirect
20. C₂³×D₅₂	C₂²	semidirect
21. C₂³×C₄×D₁₃	C₂²	semidirect
22. C₂×C₁₃×#120	C₂²	semidirect
23. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
24. C₂×#88207	C₂²	semidirect
25. C₂²×C₂²⋊Dic₁₃	C₂²	semidirect
26. C₂×#88191	C₂²	semidirect
27. C₂²×#6103	C₂²	semidirect
28. D₁₃×#120	C₂²	direct (N × H)
29. C₂×#88136	C₂²	semidirect
30. C₂×C₂²⋊C₄×D₁₃	C₂²	semidirect
33. C₂⁵×C₁₃	C₂³	semidirect
34. C₂⁵×C₁₃	C₂³	semidirect
41. C₂⁴×D₁₃	D₄	semidirect
45. C₂⁴×D₁₃	C₂³	semidirect
46. C₂⁴×D₁₃	C₂³	semidirect
47. C₂⁴×D₁₃	C₂³	semidirect
48. C₂⁴×D₁₃	C₂³	semidirect
50. C₂²×D₄×C₁₃	C₂³	semidirect
51. C₂³×C₄×C₁₃	C₂³	semidirect
54. C₂²×C₂²⋊D₁₃	C₂³	semidirect
55. C₂²×C₂²⋊D₁₃	C₂³	semidirect
56. C₂³×Dic₁₃	C₂³	semidirect
58. C₂×D₄×D₁₃	C₂³	semidirect
60. C₂²×D₅₂	C₂³	semidirect
62. C₂²×C₄×D₁₃	C₂³	semidirect
63. C₁₃×#120	C₂³	semidirect
64. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
65. #88207	C₂³	semidirect
66. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
67. #88191	C₂³	semidirect
68. C₂×#6103	C₂³	semidirect
69. #88136	C₂³	semidirect
70. C₂²⋊C₄×D₁₃	C₂³	semidirect
76. C₂⁴×C₁₃	C₂×D₄	semidirect
79. C₂⁴×C₁₃	C₂⁴	semidirect
80. C₂⁴×C₁₃	C₂⁴	semidirect
93. C₂³×D₁₃	C₂×D₄	semidirect
94. C₂³×D₁₃	C₂×D₄	semidirect
98. C₂³×D₁₃	C₂⁴	semidirect
99. C₂³×D₁₃	C₂⁴	semidirect
100. C₂³×D₁₃	C₂⁴	semidirect
102. C₂×D₄×C₁₃	C₂⁴	semidirect
104. C₂²×C₄×C₁₃	C₂⁴	semidirect
107. C₂×C₂²⋊D₁₃	C₂⁴	semidirect
108. C₂×C₂²⋊D₁₃	C₂⁴	semidirect
110. C₂²×Dic₁₃	C₂⁴	semidirect
113. C₂×D₅₂	C₂⁴	semidirect
115. C₂×C₄×D₁₃	C₂⁴	semidirect
116. C₁₃×C₂²⋊C₄	C₂⁴	semidirect
117. C₂²⋊Dic₁₃	C₂⁴	semidirect
118. #6103	C₂⁴	semidirect
125. C₂²×#120	D₁₃	direct (N × H)
134. C₂³×C₁₃	C₂²×D₄	semidirect
137. C₂³×C₁₃	C₂⁵	semidirect
150. C₂²×D₁₃	#120	direct (N × H)
152. C₂²×D₁₃	C₂²×D₄	semidirect
153. C₂²×D₁₃	C₂²×D₄	semidirect
156. C₂²×D₁₃	C₂⁵	semidirect
159. C₂×C₄×C₁₃	C₂⁵	semidirect
163. C₂×Dic₁₃	C₂⁵	semidirect
171. C₂⁶	C₂×D₁₃	semidirect
177. C₂³×D₄	C₂×D₁₃	semidirect
183. C₂×#120	C₂×D₁₃	direct (N × H)
187. C₂²×C₂²⋊C₄	C₂×D₁₃	semidirect
193. C₂²×C₁₃	C₂×#120	semidirect
195. C₂²×C₁₃	C₂³×D₄	semidirect
204. C₂×D₁₃	C₂×#120	direct (N × H)
206. C₂×D₁₃	C₂³×D₄	semidirect
225. C₂⁵	C₂²×D₁₃	semidirect
226. C₂⁵	C₂²×D₁₃	semidirect
236. C₂²×D₄	C₂²×D₁₃	semidirect
240. C₂³×C₄	C₂²×D₁₃	semidirect
244. #120	C₂²×D₁₃	direct (N × H)
248. C₂×C₂²⋊C₄	C₂²×D₁₃	semidirect
251. C₂×C₁₃	C₂²×#120	semidirect
255. D₁₃	C₂²×#120	direct (N × H)
280. C₂⁴	D₄×D₁₃	semidirect
283. C₂⁴	C₂³×D₁₃	semidirect
284. C₂⁴	C₂³×D₁₃	semidirect
293. C₂×D₄	C₂³×D₁₃	semidirect
299. C₂²×C₄	C₂³×D₁₃	semidirect
302. C₂²⋊C₄	C₂³×D₁₃	semidirect
303. C₁₃	C₂³×#120	semidirect
330. C₂³	C₂×D₄×D₁₃	semidirect
333. C₂³	C₂⁴×D₁₃	semidirect
342. C₂×C₄	C₂⁴×D₁₃	semidirect
358. C₂²	D₁₃×#120	direct (N × H)
360. C₂²	C₂²×D₄×D₁₃	semidirect
369. C₂	C₂×D₁₃×#120	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁶×D₁₃	2
C₂³×D₄×D₁₃	2
C₂²×#88136	2
C₂²×#88207	2
C₂²×#88191	2
C₂×D₁₃×#120	2
C₂²×C₂²⋊C₄×D₁₃	2
C₂²×C₁₃×#120	2
C₂³×#120	13

Subgroups — C22×D13×#120 #16769548

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×D₁₃×#120 #16769548