Subgroups — C₂×C₄×C₁₃×#120 #15720366

Order 3328.

8582 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×#120	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×D₄×C₁₃	C₂	1	3	yes	maximal, complemented
4	C₄×C₁₃×#120	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₁₃×#386	C₂	1	3	yes	maximal, complemented
6	C₂×C₁₃×#385	C₂	1	3	yes	maximal, complemented
7	C₂×C₁₃×#379	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	3	yes	maximal, complemented
9	C₂⁶×C₁₃	C₂²	1	1	yes	characteristic
10	C₂³×D₄×C₁₃	C₂²	1	3	yes	—
11	C₂⁴×C₄×C₁₃	—	2	24	no	—
12	C₂⁴×C₄×C₁₃	C₂²	1	3	yes	—
13	C₂⁴×C₄×C₁₃	C₂²	1	3	yes	—
14	C₂⁴×C₄×C₁₃	C₂²	1	8	yes	complemented
15	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₁₃×#120	C₄	1	16	yes	direct product factor
17	C₂×C₁₃×#120	C₂²	1	8	yes	—
18	C₂×C₄×D₄×C₁₃	—	2	24	no	—
19	C₂×C₄×D₄×C₁₃	C₂²	1	24	yes	complemented
20	C₂²×C₁₃×C₄⋊C₄	C₂²	1	3	yes	complemented
21	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	3	yes	—
22	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	3	yes	—
23	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	3	yes	—
24	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	3	yes	complemented
25	C₂²×C₄²×C₁₃	C₂²	1	3	yes	complemented
26	C₁₃×#386	C₂²	1	24	yes	complemented
27	C₁₃×#385	C₂²	1	24	yes	complemented
28	C₁₃×#379	C₂²	1	8	yes	complemented
29	C₄×C₁₃×C₂²⋊C₄	C₂²	1	24	yes	complemented
30	C₂×C₁₃×#95	C₂²	1	6	yes	complemented
31	C₂⁵×C₁₃	—	2	12	no	—
32	C₂⁵×C₁₃	—	2	12	no	—
33	C₂⁵×C₁₃	C₂×C₄	1	8	yes	complemented
34	C₂⁵×C₁₃	C₂³	1	4	yes	—
35	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
36	C₂⁵×C₁₃	C₂³	1	3	yes	—
37	C₂²×D₄×C₁₃	—	2	12	no	—
38	C₂²×D₄×C₁₃	—	2	12	no	—
39	C₂²×D₄×C₁₃	C₂×C₄	1	24	yes	complemented
40	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
41	C₂³×C₄×C₁₃	—	2	128	no	—
42	C₂³×C₄×C₁₃	—	2	12	no	—
43	C₂³×C₄×C₁₃	—	2	24	no	—
44	C₂³×C₄×C₁₃	—	2	24	no	—
45	C₂³×C₄×C₁₃	—	2	96	no	—
46	C₂³×C₄×C₁₃	—	2	12	no	—
47	C₂³×C₄×C₁₃	D₄	1	24	yes	complemented
48	C₂³×C₄×C₁₃	C₂³	1	12	yes	—
49	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
50	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
52	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
53	C₂³×C₄×C₁₃	C₂³	1	12	yes	—
54	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₁₃	C₂³	1	4	yes	complemented
56	C₁₃×#120	C₂×C₄	1	64	yes	direct product factor
57	C₄×D₄×C₁₃	—	2	96	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	12	no	—
59	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	complemented
60	C₂×C₁₃×C₂²⋊C₄	—	2	12	no	—
61	C₂×C₁₃×C₂²⋊C₄	—	2	12	no	—
62	C₂×C₁₃×C₂²⋊C₄	—	2	12	no	—
63	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	24	yes	complemented
64	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
65	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
66	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
67	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	complemented
68	C₂×C₄²×C₁₃	—	2	12	no	—
69	C₂×C₄²×C₁₃	C₂³	1	12	yes	complemented
70	C₁₃×#95	C₂³	1	24	yes	complemented
71	C₂×C₄×#120	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
72	C₂⁴×C₁₃	—	2	32	no	—
73	C₂⁴×C₁₃	—	2	96	no	—
74	C₂⁴×C₁₃	—	2	96	no	—
75	C₂⁴×C₁₃	—	2	24	no	—
76	C₂⁴×C₁₃	—	2	12	no	—
77	C₂⁴×C₁₃	—	2	24	no	—
78	C₂⁴×C₁₃	—	2	12	no	—
79	C₂⁴×C₁₃	—	2	6	no	—
80	C₂⁴×C₁₃	—	2	6	no	—
81	C₂⁴×C₁₃	C₂²×C₄	1	12	yes	—
82	C₂⁴×C₁₃	C₂²×C₄	1	16	yes	complemented
83	C₂⁴×C₁₃	C₂²×C₄	1	4	yes	complemented
84	C₂⁴×C₁₃	C₂×D₄	1	12	yes	—
85	C₂⁴×C₁₃	#41	1	12	yes	—
86	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
87	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
88	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
89	C₂×D₄×C₁₃	—	2	96	no	—
90	C₂×D₄×C₁₃	—	2	24	no	—
91	C₂×D₄×C₁₃	—	2	24	no	—
92	C₂×D₄×C₁₃	C₂²×C₄	1	48	yes	complemented
93	C₂²×C₄×C₁₃	—	2	96	no	—
94	C₂²×C₄×C₁₃	—	2	256	no	—
95	C₂²×C₄×C₁₃	—	2	6	no	—
96	C₂²×C₄×C₁₃	—	2	24	no	—
97	C₂²×C₄×C₁₃	—	2	12	no	—
98	C₂²×C₄×C₁₃	—	2	6	no	—
99	C₂²×C₄×C₁₃	—	2	96	no	—
100	C₂²×C₄×C₁₃	—	2	48	no	—
101	C₂²×C₄×C₁₃	—	2	48	no	—
102	C₂²×C₄×C₁₃	—	2	6	no	—
103	C₂²×C₄×C₁₃	—	2	6	no	—
104	C₂²×C₄×C₁₃	—	2	12	no	—
105	C₂²×C₄×C₁₃	—	2	24	no	—
106	C₂²×C₄×C₁₃	—	4	16	no	—
107	C₂²×C₄×C₁₃	C₂²×C₄	1	12	yes	complemented
108	C₂²×C₄×C₁₃	C₂×D₄	1	12	yes	—
109	C₂²×C₄×C₁₃	C₂×D₄	1	12	yes	—
110	C₂²×C₄×C₁₃	C₂×D₄	1	48	yes	complemented
111	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
112	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
113	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
114	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
115	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
116	C₁₃×C₄⋊C₄	—	2	24	no	—
117	C₁₃×C₂²⋊C₄	—	2	24	no	—
118	C₁₃×C₂²⋊C₄	—	2	24	no	—
119	C₁₃×C₂²⋊C₄	—	2	24	no	—
120	C₁₃×C₂²⋊C₄	C₂²×C₄	1	48	yes	complemented
121	C₄²×C₁₃	—	2	24	no	—
122	C₂⁵×C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
123	C₂²×#120	C₂×C₁₃	1	1	yes	characteristic
124	C₂²×C₄×D₄	C₂×C₁₃	1	3	yes	complemented
125	C₄×#120	C₂×C₁₃	1	16	yes	direct product factor
126	C₂×#386	C₂×C₁₃	1	3	yes	complemented
127	C₂×#385	C₂×C₁₃	1	3	yes	complemented
128	C₂×#379	C₂×C₁₃	1	1	yes	characteristic, complemented
129	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	3	yes	complemented
130	C₂³×C₁₃	—	2	32	no	—
131	C₂³×C₁₃	—	2	96	no	—
132	C₂³×C₁₃	—	2	256	no	—
133	C₂³×C₁₃	—	2	48	no	—
134	C₂³×C₁₃	—	2	96	no	—
135	C₂³×C₁₃	—	2	24	no	—
136	C₂³×C₁₃	—	2	24	no	—
137	C₂³×C₁₃	—	2	48	no	—
138	C₂³×C₁₃	—	2	12	no	—
139	C₂³×C₁₃	—	2	12	no	—
140	C₂³×C₁₃	—	2	24	no	—
141	C₂³×C₁₃	—	2	6	no	—
142	C₂³×C₁₃	—	2	6	no	—
143	C₂³×C₁₃	—	4	4	no	—
144	C₂³×C₁₃	—	4	12	no	—
145	C₂³×C₁₃	C₄×D₄	1	48	yes	complemented
146	C₂³×C₁₃	C₂³×C₄	1	12	yes	—
147	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
148	C₂³×C₁₃	C₂³×C₄	1	4	yes	complemented
149	C₂³×C₁₃	C₂²×D₄	1	12	yes	—
150	C₂³×C₁₃	C₂²×D₄	1	6	yes	—
151	C₂³×C₁₃	C₂×#41	1	12	yes	—
152	C₂³×C₁₃	C₂×#41	1	6	yes	—
153	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
154	D₄×C₁₃	—	2	96	no	—
155	C₂×C₄×C₁₃	—	2	96	no	—
156	C₂×C₄×C₁₃	—	2	24	no	—
157	C₂×C₄×C₁₃	—	2	24	no	—
158	C₂×C₄×C₁₃	—	2	6	no	—
159	C₂×C₄×C₁₃	—	2	12	no	—
160	C₂×C₄×C₁₃	—	2	6	no	—
161	C₂×C₄×C₁₃	—	2	96	no	—
162	C₂×C₄×C₁₃	—	2	6	no	—
163	C₂×C₄×C₁₃	—	2	6	no	—
164	C₂×C₄×C₁₃	—	2	12	no	—
165	C₂×C₄×C₁₃	—	4	4	no	—
166	C₂×C₄×C₁₃	—	4	12	no	—
167	C₂×C₄×C₁₃	—	4	16	no	—
168	C₂×C₄×C₁₃	#120	1	16	yes	direct product factor
169	C₂×C₄×C₁₃	C₂³×C₄	1	12	yes	complemented
170	C₂×C₄×C₁₃	C₂²×D₄	1	12	yes	—
171	C₂×C₄×C₁₃	C₂²×D₄	1	12	yes	—
172	C₂⁶	C₂²×C₁₃	1	1	yes	characteristic
173	C₂³×D₄	C₂²×C₁₃	1	3	yes	—
174	C₂⁴×C₄	—	2	24	no	—
175	C₂⁴×C₄	C₂²×C₁₃	1	3	yes	—
176	C₂⁴×C₄	C₂²×C₁₃	1	3	yes	—
177	C₂⁴×C₄	C₂²×C₁₃	1	8	yes	complemented
178	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
179	C₂×#120	C₄×C₁₃	1	16	yes	direct product factor
180	C₂×#120	C₂²×C₁₃	1	8	yes	—
181	C₂×C₄×D₄	—	2	24	no	—
182	C₂×C₄×D₄	C₂²×C₁₃	1	24	yes	complemented
183	C₂²×C₄⋊C₄	C₂²×C₁₃	1	3	yes	complemented
184	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	3	yes	—
185	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	3	yes	—
186	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	3	yes	—
187	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	3	yes	complemented
188	C₂²×C₄²	C₂²×C₁₃	1	3	yes	complemented
189	#386	C₂²×C₁₃	1	24	yes	complemented
190	#385	C₂²×C₁₃	1	24	yes	complemented
191	#379	C₂²×C₁₃	1	8	yes	complemented
192	C₄×C₂²⋊C₄	C₂²×C₁₃	1	24	yes	complemented
193	C₂×#95	C₂²×C₁₃	1	6	yes	complemented
194	C₂²×C₁₃	—	2	128	no	—
195	C₂²×C₁₃	—	2	24	no	—
196	C₂²×C₁₃	—	2	12	no	—
197	C₂²×C₁₃	—	2	12	no	—
198	C₂²×C₁₃	—	2	24	no	—
199	C₂²×C₁₃	—	2	96	no	—
200	C₂²×C₁₃	—	2	12	no	—
201	C₂²×C₁₃	—	4	2	no	—
202	C₂²×C₁₃	—	4	6	no	—
203	C₂²×C₁₃	—	4	16	no	—
204	C₂²×C₁₃	C₂×C₄×D₄	1	12	yes	—
205	C₂²×C₁₃	C₂×C₄×D₄	1	24	yes	complemented
206	C₂²×C₁₃	C₂×#120	1	4	yes	—
207	C₂²×C₁₃	#525	1	12	yes	—
208	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
209	C₂²×C₁₃	C₂³×D₄	1	3	yes	—
210	C₂²×C₁₃	C₂²×#41	1	3	yes	—
211	C₄×C₁₃	—	2	12	no	—
212	C₄×C₁₃	—	2	12	no	—
213	C₄×C₁₃	—	4	2	no	—
214	C₄×C₁₃	—	4	6	no	—
215	C₄×C₁₃	C₂×#120	1	8	yes	direct product factor
216	C₂⁵	—	2	12	no	—
217	C₂⁵	—	2	12	no	—
218	C₂⁵	C₂×C₄×C₁₃	1	8	yes	complemented
219	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
220	C₂⁵	C₂³×C₁₃	1	4	yes	—
221	C₂⁵	C₂³×C₁₃	1	3	yes	—
222	C₂²×D₄	—	2	12	no	—
223	C₂²×D₄	—	2	12	no	—
224	C₂²×D₄	C₂×C₄×C₁₃	1	24	yes	complemented
225	C₂²×D₄	C₂³×C₁₃	1	12	yes	—
226	C₂³×C₄	—	2	128	no	—
227	C₂³×C₄	—	2	12	no	—
228	C₂³×C₄	—	2	24	no	—
229	C₂³×C₄	—	2	24	no	—
230	C₂³×C₄	—	2	96	no	—
231	C₂³×C₄	—	2	12	no	—
232	C₂³×C₄	D₄×C₁₃	1	24	yes	complemented
233	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
234	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
235	C₂³×C₄	C₂³×C₁₃	1	12	yes	—
236	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
237	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
238	C₂³×C₄	C₂³×C₁₃	1	12	yes	—
239	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
240	C₂³×C₄	C₂³×C₁₃	1	4	yes	complemented
241	#120	C₂×C₄×C₁₃	1	64	yes	direct product factor
242	C₄×D₄	—	2	96	no	—
243	C₂×C₄⋊C₄	—	2	12	no	—
244	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	complemented
245	C₂×C₂²⋊C₄	—	2	12	no	—
246	C₂×C₂²⋊C₄	—	2	12	no	—
247	C₂×C₂²⋊C₄	—	2	12	no	—
248	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	24	yes	complemented
249	C₂×C₂²⋊C₄	C₂³×C₁₃	1	12	yes	—
250	C₂×C₂²⋊C₄	C₂³×C₁₃	1	12	yes	—
251	C₂×C₂²⋊C₄	C₂³×C₁₃	1	12	yes	—
252	C₂×C₂²⋊C₄	C₂³×C₁₃	1	12	yes	complemented
253	C₂×C₄²	—	2	12	no	—
254	C₂×C₄²	C₂³×C₁₃	1	12	yes	complemented
255	#95	C₂³×C₁₃	1	24	yes	complemented
256	C₂×C₁₃	—	2	24	no	—
257	C₂×C₁₃	—	4	4	no	—
258	C₂×C₁₃	C₄×#120	1	8	yes	direct product factor
259	C₂×C₁₃	C₂²×C₄×D₄	1	3	yes	—
260	C₂×C₁₃	C₂²×#120	1	1	yes	characteristic
261	C₂×C₁₃	C₂×#525	1	3	yes	—
262	C₂⁴	—	2	32	no	—
263	C₂⁴	—	2	96	no	—
264	C₂⁴	—	2	96	no	—
265	C₂⁴	—	2	24	no	—
266	C₂⁴	—	2	12	no	—
267	C₂⁴	—	2	24	no	—
268	C₂⁴	—	2	12	no	—
269	C₂⁴	—	2	6	no	—
270	C₂⁴	—	2	6	no	—
271	C₂⁴	C₂²×C₄×C₁₃	1	12	yes	—
272	C₂⁴	C₂²×C₄×C₁₃	1	16	yes	complemented
273	C₂⁴	C₂²×C₄×C₁₃	1	4	yes	complemented
274	C₂⁴	C₂×D₄×C₁₃	1	12	yes	—
275	C₂⁴	C₁₃×#41	1	12	yes	—
276	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
277	C₂⁴	C₂⁴×C₁₃	1	6	yes	—
278	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
279	C₂×D₄	—	2	96	no	—
280	C₂×D₄	—	2	24	no	—
281	C₂×D₄	—	2	24	no	—
282	C₂×D₄	C₂²×C₄×C₁₃	1	48	yes	complemented
283	C₂²×C₄	—	2	96	no	—
284	C₂²×C₄	—	2	256	no	—
285	C₂²×C₄	—	2	6	no	—
286	C₂²×C₄	—	2	24	no	—
287	C₂²×C₄	—	2	12	no	—
288	C₂²×C₄	—	2	6	no	—
289	C₂²×C₄	—	2	96	no	—
290	C₂²×C₄	—	2	48	no	—
291	C₂²×C₄	—	2	48	no	—
292	C₂²×C₄	—	2	6	no	—
293	C₂²×C₄	—	2	6	no	—
294	C₂²×C₄	—	2	12	no	—
295	C₂²×C₄	—	2	24	no	—
296	C₂²×C₄	—	4	16	no	—
297	C₂²×C₄	C₂²×C₄×C₁₃	1	12	yes	complemented
298	C₂²×C₄	C₂×D₄×C₁₃	1	12	yes	—
299	C₂²×C₄	C₂×D₄×C₁₃	1	12	yes	—
300	C₂²×C₄	C₂×D₄×C₁₃	1	48	yes	complemented
301	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
302	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
303	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
304	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
305	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
306	C₄⋊C₄	—	2	24	no	—
307	C₂²⋊C₄	—	2	24	no	—
308	C₂²⋊C₄	—	2	24	no	—
309	C₂²⋊C₄	—	2	24	no	—
310	C₂²⋊C₄	C₂²×C₄×C₁₃	1	48	yes	complemented
311	C₄²	—	2	24	no	—
312	C₁₃	C₂×C₄×#120	1	1	yes	characteristic, direct product factor, Sylow
313	C₂³	—	2	32	no	—
314	C₂³	—	2	256	no	—
315	C₂³	—	2	96	no	—
316	C₂³	—	2	48	no	—
317	C₂³	—	2	96	no	—
318	C₂³	—	2	24	no	—
319	C₂³	—	2	24	no	—
320	C₂³	—	2	48	no	—
321	C₂³	—	2	12	no	—
322	C₂³	—	2	12	no	—
323	C₂³	—	2	24	no	—
324	C₂³	—	2	6	no	—
325	C₂³	—	2	6	no	—
326	C₂³	—	4	4	no	—
327	C₂³	—	4	12	no	—
328	C₂³	C₄×D₄×C₁₃	1	48	yes	complemented
329	C₂³	C₂³×C₄×C₁₃	1	12	yes	—
330	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
331	C₂³	C₂³×C₄×C₁₃	1	4	yes	complemented
332	C₂³	C₂²×D₄×C₁₃	1	12	yes	—
333	C₂³	C₂²×D₄×C₁₃	1	6	yes	—
334	C₂³	C₂×C₁₃×#41	1	12	yes	—
335	C₂³	C₂×C₁₃×#41	1	6	yes	—
336	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
337	D₄	—	2	96	no	—
338	C₂×C₄	—	2	96	no	—
339	C₂×C₄	—	2	24	no	—
340	C₂×C₄	—	2	24	no	—
341	C₂×C₄	—	2	6	no	—
342	C₂×C₄	—	2	12	no	—
343	C₂×C₄	—	2	6	no	—
344	C₂×C₄	—	2	96	no	—
345	C₂×C₄	—	2	6	no	—
346	C₂×C₄	—	2	6	no	—
347	C₂×C₄	—	2	12	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	—	4	12	no	—
350	C₂×C₄	—	4	16	no	—
351	C₂×C₄	C₁₃×#120	1	16	yes	direct product factor
352	C₂×C₄	C₂³×C₄×C₁₃	1	12	yes	complemented
353	C₂×C₄	C₂²×D₄×C₁₃	1	12	yes	—
354	C₂×C₄	C₂²×D₄×C₁₃	1	12	yes	—
355	C₂²	—	2	128	no	—
356	C₂²	—	2	96	no	—
357	C₂²	—	2	24	no	—
358	C₂²	—	2	12	no	—
359	C₂²	—	2	12	no	—
360	C₂²	—	2	24	no	—
361	C₂²	—	2	12	no	—
362	C₂²	—	4	16	no	—
363	C₂²	—	4	2	no	—
364	C₂²	—	4	6	no	—
365	C₂²	C₂×C₄×D₄×C₁₃	1	12	yes	—
366	C₂²	C₂×C₄×D₄×C₁₃	1	24	yes	complemented
367	C₂²	C₂×C₁₃×#120	1	4	yes	—
368	C₂²	C₁₃×#525	1	12	yes	—
369	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
370	C₂²	C₂³×D₄×C₁₃	1	3	yes	—
371	C₂²	C₂²×C₁₃×#41	1	3	yes	—
372	C₄	—	2	12	no	—
373	C₄	—	2	12	no	—
374	C₄	—	4	2	no	—
375	C₄	—	4	6	no	—
376	C₄	C₂×C₁₃×#120	1	8	yes	direct product factor
377	C₂	—	2	24	no	—
378	C₂	—	4	4	no	—
379	C₂	C₄×C₁₃×#120	1	8	yes	direct product factor
380	C₂	C₂²×C₄×D₄×C₁₃	1	3	yes	—
381	C₂	C₂²×C₁₃×#120	1	1	yes	characteristic
382	C₂	C₂×C₁₃×#525	1	3	yes	—

	subgroup	G/H
center	C₂³×C₄×C₁₃	C₂³
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂⁴×C₁₃	C₂⁴
prime radical	C₂²×C₁₃×#120	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂⁵×C₄×C₁₃	C₂	semidirect
3. C₂²×C₄×D₄×C₁₃	C₂	semidirect
4. C₄×C₁₃×#120	C₂	direct (N × H)
5. C₂×C₁₃×#386	C₂	semidirect
6. C₂×C₁₃×#385	C₂	semidirect
7. C₂×C₁₃×#379	C₂	semidirect
8. C₂×C₄×C₁₃×C₂²⋊C₄	C₂	semidirect
14. C₂⁴×C₄×C₁₃	C₂²	semidirect
15. C₂⁴×C₄×C₁₃	C₂²	semidirect
16. C₂×C₁₃×#120	C₄	direct (N × H)
19. C₂×C₄×D₄×C₁₃	C₂²	semidirect
20. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
24. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
25. C₂²×C₄²×C₁₃	C₂²	semidirect
26. C₁₃×#386	C₂²	semidirect
27. C₁₃×#385	C₂²	semidirect
28. C₁₃×#379	C₂²	semidirect
29. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
30. C₂×C₁₃×#95	C₂²	semidirect
33. C₂⁵×C₁₃	C₂×C₄	semidirect
39. C₂²×D₄×C₁₃	C₂×C₄	semidirect
47. C₂³×C₄×C₁₃	D₄	semidirect
55. C₂³×C₄×C₁₃	C₂³	semidirect
56. C₁₃×#120	C₂×C₄	direct (N × H)
59. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
63. C₂×C₁₃×C₂²⋊C₄	C₂×C₄	semidirect
67. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
69. C₂×C₄²×C₁₃	C₂³	semidirect
70. C₁₃×#95	C₂³	semidirect
71. C₂×C₄×#120	C₁₃	direct (N × H)
82. C₂⁴×C₁₃	C₂²×C₄	semidirect
83. C₂⁴×C₁₃	C₂²×C₄	semidirect
92. C₂×D₄×C₁₃	C₂²×C₄	semidirect
107. C₂²×C₄×C₁₃	C₂²×C₄	semidirect
110. C₂²×C₄×C₁₃	C₂×D₄	semidirect
120. C₁₃×C₂²⋊C₄	C₂²×C₄	semidirect
122. C₂⁵×C₄	C₂×C₁₃	semidirect
124. C₂²×C₄×D₄	C₂×C₁₃	semidirect
125. C₄×#120	C₂×C₁₃	direct (N × H)
126. C₂×#386	C₂×C₁₃	semidirect
127. C₂×#385	C₂×C₁₃	semidirect
128. C₂×#379	C₂×C₁₃	semidirect
129. C₂×C₄×C₂²⋊C₄	C₂×C₁₃	semidirect
145. C₂³×C₁₃	C₄×D₄	semidirect
148. C₂³×C₁₃	C₂³×C₄	semidirect
168. C₂×C₄×C₁₃	#120	direct (N × H)
169. C₂×C₄×C₁₃	C₂³×C₄	semidirect
177. C₂⁴×C₄	C₂²×C₁₃	semidirect
178. C₂⁴×C₄	C₂²×C₁₃	semidirect
179. C₂×#120	C₄×C₁₃	direct (N × H)
182. C₂×C₄×D₄	C₂²×C₁₃	semidirect
183. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
187. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
188. C₂²×C₄²	C₂²×C₁₃	semidirect
189. #386	C₂²×C₁₃	semidirect
190. #385	C₂²×C₁₃	semidirect
191. #379	C₂²×C₁₃	semidirect
192. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
193. C₂×#95	C₂²×C₁₃	semidirect
205. C₂²×C₁₃	C₂×C₄×D₄	semidirect
215. C₄×C₁₃	C₂×#120	direct (N × H)
218. C₂⁵	C₂×C₄×C₁₃	semidirect
224. C₂²×D₄	C₂×C₄×C₁₃	semidirect
232. C₂³×C₄	D₄×C₁₃	semidirect
240. C₂³×C₄	C₂³×C₁₃	semidirect
241. #120	C₂×C₄×C₁₃	direct (N × H)
244. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
248. C₂×C₂²⋊C₄	C₂×C₄×C₁₃	semidirect
252. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
254. C₂×C₄²	C₂³×C₁₃	semidirect
255. #95	C₂³×C₁₃	semidirect
258. C₂×C₁₃	C₄×#120	direct (N × H)
272. C₂⁴	C₂²×C₄×C₁₃	semidirect
273. C₂⁴	C₂²×C₄×C₁₃	semidirect
282. C₂×D₄	C₂²×C₄×C₁₃	semidirect
297. C₂²×C₄	C₂²×C₄×C₁₃	semidirect
300. C₂²×C₄	C₂×D₄×C₁₃	semidirect
310. C₂²⋊C₄	C₂²×C₄×C₁₃	semidirect
312. C₁₃	C₂×C₄×#120	direct (N × H)
328. C₂³	C₄×D₄×C₁₃	semidirect
331. C₂³	C₂³×C₄×C₁₃	semidirect
351. C₂×C₄	C₁₃×#120	direct (N × H)
352. C₂×C₄	C₂³×C₄×C₁₃	semidirect
366. C₂²	C₂×C₄×D₄×C₁₃	semidirect
376. C₄	C₂×C₁₃×#120	direct (N × H)
379. C₂	C₄×C₁₃×#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
C₂⁵×C₄×C₁₃	2
C₂²×C₁₃×#120	2
C₂²×C₄×D₄×C₁₃	2
C₄×C₁₃×#120	2
C₂×C₁₃×#386	2
C₂×C₁₃×#385	2
C₂×C₁₃×#379	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
C₂×C₄×#120	13

Subgroups — C2×C4×C13×#120 #15720366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₁₃×#120 #15720366