Subgroups — C₂×C₁₃×#2432 #15721056

Order 3328.

5502 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₃×#41	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2432	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₁₃×#394	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₃×#391	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#390	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#385	C₂	1	4	yes	maximal, complemented
10	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₁₃×#41	—	2	8	no	—
12	C₂²×C₁₃×#41	—	2	8	no	—
13	C₂²×C₁₃×#41	—	2	8	no	—
14	C₂²×C₁₃×#41	C₂²	1	8	yes	—
15	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
18	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
20	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊Q₈	—	2	8	no	—
22	C₂×C₁₃×C₄⋊Q₈	C₂²	1	8	yes	complemented
23	C₂×C₁₃×#124	—	2	8	no	—
24	C₂×C₁₃×#124	C₂²	1	8	yes	complemented
25	C₂×C₁₃×C₂²⋊Q₈	—	2	8	no	—
26	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	8	yes	complemented
27	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
28	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
29	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
31	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
32	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
33	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
34	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
36	C₁₃×#394	C₂²	1	32	yes	complemented
37	C₁₃×#391	C₂²	1	8	yes	complemented
38	C₁₃×#390	C₂²	1	8	yes	complemented
39	C₁₃×#385	C₂²	1	32	yes	complemented
40	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
41	C₂×C₁₃×#95	C₂²	1	2	yes	—
42	C₂×C₁₃×#95	C₂²	1	4	yes	—
43	C₂⁵×C₁₃	C₂³	1	2	yes	—
44	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
45	C₂×C₁₃×#41	—	2	128	no	—
46	C₂×C₁₃×#41	—	2	32	no	—
47	C₂×C₁₃×#41	—	2	32	no	—
48	C₂×C₁₃×#41	—	2	32	no	—
49	C₂²×Q₈×C₁₃	—	2	4	no	—
50	C₂²×Q₈×C₁₃	—	2	4	no	—
51	C₂²×Q₈×C₁₃	—	2	4	no	—
52	C₂²×Q₈×C₁₃	—	2	4	no	—
53	C₂²×Q₈×C₁₃	—	2	4	no	—
54	C₂²×Q₈×C₁₃	D₄	1	8	yes	—
55	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
56	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
57	C₂²×D₄×C₁₃	—	2	8	no	—
58	C₂²×D₄×C₁₃	—	2	8	no	—
59	C₂²×D₄×C₁₃	—	2	8	no	—
60	C₂²×D₄×C₁₃	—	2	4	no	—
61	C₂²×D₄×C₁₃	—	2	4	no	—
62	C₂²×D₄×C₁₃	D₄	1	8	yes	—
63	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
64	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
65	C₂³×C₄×C₁₃	—	2	8	no	—
66	C₂³×C₄×C₁₃	—	2	8	no	—
67	C₂³×C₄×C₁₃	—	2	8	no	—
68	C₂³×C₄×C₁₃	—	2	4	no	—
69	C₂³×C₄×C₁₃	—	2	4	no	—
70	C₂³×C₄×C₁₃	D₄	1	8	yes	—
71	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
72	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
73	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
74	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
75	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
76	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
78	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
79	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
80	C₁₃×C₄⋊Q₈	—	2	32	no	—
81	C₁₃×#124	—	2	32	no	—
82	C₁₃×C₂²⋊Q₈	—	2	32	no	—
83	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
84	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
85	C₂×C₁₃×C₄⋊C₄	—	2	16	no	—
86	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
89	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
90	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
91	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
92	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
93	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
94	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
95	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
96	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
97	C₂×C₄²×C₁₃	—	2	4	no	—
98	C₂×C₄²×C₁₃	—	2	4	no	—
99	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
100	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
101	C₁₃×#95	C₂³	1	8	yes	—
102	C₁₃×#95	C₂³	1	16	yes	—
103	C₂×#2432	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
104	C₂⁴×C₁₃	—	2	4	no	—
105	C₂⁴×C₁₃	—	2	2	no	—
106	C₂⁴×C₁₃	—	2	4	no	—
107	C₂⁴×C₁₃	—	2	2	no	—
108	C₂⁴×C₁₃	—	2	4	no	—
109	C₂⁴×C₁₃	—	2	8	no	—
110	C₂⁴×C₁₃	—	2	4	no	—
111	C₂⁴×C₁₃	—	2	8	no	—
112	C₂⁴×C₁₃	C₂×D₄	1	8	yes	—
113	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
114	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
115	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
116	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
117	C₁₃×#41	—	2	256	no	—
118	C₂×Q₈×C₁₃	—	2	32	no	—
119	C₂×Q₈×C₁₃	—	2	8	no	—
120	C₂×Q₈×C₁₃	—	2	8	no	—
121	C₂×Q₈×C₁₃	—	2	8	no	—
122	C₂×Q₈×C₁₃	—	2	8	no	—
123	C₂×Q₈×C₁₃	—	2	8	no	—
124	C₂×Q₈×C₁₃	—	4	16	no	—
125	C₂×Q₈×C₁₃	C₂×D₄	1	16	yes	—
126	C₂×D₄×C₁₃	—	2	64	no	—
127	C₂×D₄×C₁₃	—	2	16	no	—
128	C₂×D₄×C₁₃	—	2	16	no	—
129	C₂×D₄×C₁₃	—	2	32	no	—
130	C₂×D₄×C₁₃	—	2	16	no	—
131	C₂×D₄×C₁₃	—	2	8	no	—
132	C₂×D₄×C₁₃	—	2	8	no	—
133	C₂×D₄×C₁₃	C₂×D₄	1	16	yes	—
134	C₂²×C₄×C₁₃	—	2	64	no	—
135	C₂²×C₄×C₁₃	—	2	4	no	—
136	C₂²×C₄×C₁₃	—	2	2	no	—
137	C₂²×C₄×C₁₃	—	2	2	no	—
138	C₂²×C₄×C₁₃	—	2	4	no	—
139	C₂²×C₄×C₁₃	—	2	4	no	—
140	C₂²×C₄×C₁₃	—	2	16	no	—
141	C₂²×C₄×C₁₃	—	2	4	no	—
142	C₂²×C₄×C₁₃	—	2	32	no	—
143	C₂²×C₄×C₁₃	—	2	16	no	—
144	C₂²×C₄×C₁₃	—	2	16	no	—
145	C₂²×C₄×C₁₃	—	2	8	no	—
146	C₂²×C₄×C₁₃	—	2	8	no	—
147	C₂²×C₄×C₁₃	—	2	4	no	—
148	C₂²×C₄×C₁₃	—	2	4	no	—
149	C₂²×C₄×C₁₃	—	2	4	no	—
150	C₂²×C₄×C₁₃	—	2	4	no	—
151	C₂²×C₄×C₁₃	—	2	4	no	—
152	C₂²×C₄×C₁₃	—	2	8	no	—
153	C₂²×C₄×C₁₃	—	2	4	no	—
154	C₂²×C₄×C₁₃	—	2	4	no	—
155	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
156	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
157	C₂²×C₄×C₁₃	C₂×D₄	1	16	yes	—
158	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
159	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
160	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
161	C₂²×C₄×C₁₃	#41	1	8	yes	complemented
162	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
163	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
164	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
165	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
166	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
167	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
168	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
169	C₁₃×C₄⋊C₄	—	2	8	no	—
170	C₁₃×C₄⋊C₄	—	2	16	no	—
171	C₁₃×C₄⋊C₄	—	2	32	no	—
172	C₁₃×C₂²⋊C₄	—	2	16	no	—
173	C₁₃×C₂²⋊C₄	—	2	32	no	—
174	C₁₃×C₂²⋊C₄	—	2	16	no	—
175	C₁₃×C₂²⋊C₄	—	2	32	no	—
176	C₄²×C₁₃	—	2	8	no	—
177	C₄²×C₁₃	—	2	8	no	—
178	C₂³×#41	C₂×C₁₃	1	1	yes	characteristic
179	C₂²×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
180	C₂²×#124	C₂×C₁₃	1	1	yes	characteristic, complemented
181	C₂²×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
182	#2432	C₂×C₁₃	1	16	yes	direct product factor
183	C₂×#394	C₂×C₁₃	1	4	yes	complemented
184	C₂×#391	C₂×C₁₃	1	1	yes	characteristic, complemented
185	C₂×#390	C₂×C₁₃	1	1	yes	characteristic, complemented
186	C₂×#385	C₂×C₁₃	1	4	yes	complemented
187	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
188	C₂³×C₁₃	—	2	16	no	—
189	C₂³×C₁₃	—	2	8	no	—
190	C₂³×C₁₃	—	2	8	no	—
191	C₂³×C₁₃	—	2	8	no	—
192	C₂³×C₁₃	—	2	32	no	—
193	C₂³×C₁₃	—	2	4	no	—
194	C₂³×C₁₃	—	2	2	no	—
195	C₂³×C₁₃	—	2	4	no	—
196	C₂³×C₁₃	—	2	2	no	—
197	C₂³×C₁₃	—	2	4	no	—
198	C₂³×C₁₃	—	2	8	no	—
199	C₂³×C₁₃	—	2	4	no	—
200	C₂³×C₁₃	—	2	8	no	—
201	C₂³×C₁₃	—	4	8	no	—
202	C₂³×C₁₃	—	4	8	no	—
203	C₂³×C₁₃	—	4	8	no	—
204	C₂³×C₁₃	—	4	8	no	—
205	C₂³×C₁₃	—	4	16	no	—
206	C₂³×C₁₃	C₂²×D₄	1	8	yes	—
207	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
208	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
209	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
210	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
211	C₂³×C₁₃	C₂×#41	1	4	yes	—
212	C₂³×C₁₃	2₋¹⁺⁴	1	4	yes	—
213	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
214	Q₈×C₁₃	—	2	32	no	—
215	Q₈×C₁₃	—	4	16	no	—
216	D₄×C₁₃	—	2	64	no	—
217	D₄×C₁₃	—	2	32	no	—
218	C₂×C₄×C₁₃	—	2	64	no	—
219	C₂×C₄×C₁₃	—	2	8	no	—
220	C₂×C₄×C₁₃	—	2	16	no	—
221	C₂×C₄×C₁₃	—	2	16	no	—
222	C₂×C₄×C₁₃	—	2	4	no	—
223	C₂×C₄×C₁₃	—	2	2	no	—
224	C₂×C₄×C₁₃	—	2	2	no	—
225	C₂×C₄×C₁₃	—	2	4	no	—
226	C₂×C₄×C₁₃	—	2	4	no	—
227	C₂×C₄×C₁₃	—	2	4	no	—
228	C₂×C₄×C₁₃	—	2	32	no	—
229	C₂×C₄×C₁₃	—	2	4	no	—
230	C₂×C₄×C₁₃	—	2	4	no	—
231	C₂×C₄×C₁₃	—	2	4	no	—
232	C₂×C₄×C₁₃	—	2	4	no	—
233	C₂×C₄×C₁₃	—	2	4	no	—
234	C₂×C₄×C₁₃	—	2	8	no	—
235	C₂×C₄×C₁₃	—	2	4	no	—
236	C₂×C₄×C₁₃	—	2	4	no	—
237	C₂×C₄×C₁₃	—	4	8	no	—
238	C₂×C₄×C₁₃	—	4	8	no	—
239	C₂×C₄×C₁₃	—	4	8	no	—
240	C₂×C₄×C₁₃	#120	1	16	yes	—
241	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
242	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
243	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
244	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
245	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
246	C₂×C₄×C₁₃	C₂×#41	1	8	yes	complemented
247	C₂²×#41	—	2	8	no	—
248	C₂²×#41	—	2	8	no	—
249	C₂²×#41	—	2	8	no	—
250	C₂²×#41	C₂²×C₁₃	1	8	yes	—
251	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
252	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
253	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
254	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
255	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
256	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
257	C₂×C₄⋊Q₈	—	2	8	no	—
258	C₂×C₄⋊Q₈	C₂²×C₁₃	1	8	yes	complemented
259	C₂×#124	—	2	8	no	—
260	C₂×#124	C₂²×C₁₃	1	8	yes	complemented
261	C₂×C₂²⋊Q₈	—	2	8	no	—
262	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	8	yes	complemented
263	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
264	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
265	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
266	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
267	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
268	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
269	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
270	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
271	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
272	#394	C₂²×C₁₃	1	32	yes	complemented
273	#391	C₂²×C₁₃	1	8	yes	complemented
274	#390	C₂²×C₁₃	1	8	yes	complemented
275	#385	C₂²×C₁₃	1	32	yes	complemented
276	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
277	C₂×#95	C₂²×C₁₃	1	4	yes	—
278	C₂×#95	C₂²×C₁₃	1	2	yes	—
279	C₂²×C₁₃	—	2	8	no	—
280	C₂²×C₁₃	—	2	4	no	—
281	C₂²×C₁₃	—	2	4	no	—
282	C₂²×C₁₃	—	2	4	no	—
283	C₂²×C₁₃	—	2	16	no	—
284	C₂²×C₁₃	—	4	4	no	—
285	C₂²×C₁₃	—	4	4	no	—
286	C₂²×C₁₃	—	4	16	no	—
287	C₂²×C₁₃	—	4	32	no	—
288	C₂²×C₁₃	—	4	4	no	—
289	C₂²×C₁₃	—	4	4	no	—
290	C₂²×C₁₃	—	4	8	no	—
291	C₂²×C₁₃	C₂×#120	1	4	yes	—
292	C₂²×C₁₃	#532	1	4	yes	—
293	C₂²×C₁₃	#536	1	4	yes	—
294	C₂²×C₁₃	#547	1	8	yes	—
295	C₂²×C₁₃	#548	1	8	yes	—
296	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
297	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
298	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
299	C₂²×C₁₃	C₂²×#41	1	2	yes	—
300	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
301	C₄×C₁₃	—	2	4	no	—
302	C₄×C₁₃	—	2	8	no	—
303	C₄×C₁₃	—	2	8	no	—
304	C₄×C₁₃	—	4	4	no	—
305	C₄×C₁₃	—	4	4	no	—
306	C₄×C₁₃	—	4	4	no	—
307	C₄×C₁₃	C₂×#120	1	8	yes	—
308	C₂⁵	C₂³×C₁₃	1	2	yes	—
309	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
310	C₂×#41	—	2	128	no	—
311	C₂×#41	—	2	32	no	—
312	C₂×#41	—	2	32	no	—
313	C₂×#41	—	2	32	no	—
314	C₂²×Q₈	—	2	4	no	—
315	C₂²×Q₈	—	2	4	no	—
316	C₂²×Q₈	—	2	4	no	—
317	C₂²×Q₈	—	2	4	no	—
318	C₂²×Q₈	—	2	4	no	—
319	C₂²×Q₈	D₄×C₁₃	1	8	yes	—
320	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
321	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
322	C₂²×D₄	—	2	8	no	—
323	C₂²×D₄	—	2	8	no	—
324	C₂²×D₄	—	2	8	no	—
325	C₂²×D₄	—	2	4	no	—
326	C₂²×D₄	—	2	4	no	—
327	C₂²×D₄	D₄×C₁₃	1	8	yes	—
328	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
329	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
330	C₂³×C₄	—	2	8	no	—
331	C₂³×C₄	—	2	8	no	—
332	C₂³×C₄	—	2	8	no	—
333	C₂³×C₄	—	2	4	no	—
334	C₂³×C₄	—	2	4	no	—
335	C₂³×C₄	D₄×C₁₃	1	8	yes	—
336	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
337	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
338	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
339	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
340	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
341	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
342	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
343	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
344	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
345	C₄⋊Q₈	—	2	32	no	—
346	#124	—	2	32	no	—
347	C₂²⋊Q₈	—	2	32	no	—
348	C₂×C₄⋊C₄	—	2	4	no	—
349	C₂×C₄⋊C₄	—	2	8	no	—
350	C₂×C₄⋊C₄	—	2	16	no	—
351	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
352	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
353	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
354	C₂×C₂²⋊C₄	—	2	8	no	—
355	C₂×C₂²⋊C₄	—	2	16	no	—
356	C₂×C₂²⋊C₄	—	2	8	no	—
357	C₂×C₂²⋊C₄	—	2	16	no	—
358	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
359	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
360	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
361	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
362	C₂×C₄²	—	2	4	no	—
363	C₂×C₄²	—	2	4	no	—
364	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
365	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
366	#95	C₂³×C₁₃	1	8	yes	—
367	#95	C₂³×C₁₃	1	16	yes	—
368	C₂×C₁₃	—	4	4	no	—
369	C₂×C₁₃	—	4	8	no	—
370	C₂×C₁₃	#2432	1	8	yes	direct product factor
371	C₂×C₁₃	C₂²×#120	1	1	yes	characteristic
372	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
373	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
374	C₂×C₁₃	C₂×#547	1	2	yes	—
375	C₂×C₁₃	C₂×#548	1	2	yes	—
376	C₂⁴	—	2	4	no	—
377	C₂⁴	—	2	2	no	—
378	C₂⁴	—	2	4	no	—
379	C₂⁴	—	2	2	no	—
380	C₂⁴	—	2	4	no	—
381	C₂⁴	—	2	8	no	—
382	C₂⁴	—	2	4	no	—
383	C₂⁴	—	2	8	no	—
384	C₂⁴	C₂×D₄×C₁₃	1	8	yes	—
385	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
386	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
387	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
388	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
389	#41	—	2	256	no	—
390	C₂×Q₈	—	2	32	no	—
391	C₂×Q₈	—	2	8	no	—
392	C₂×Q₈	—	2	8	no	—
393	C₂×Q₈	—	2	8	no	—
394	C₂×Q₈	—	2	8	no	—
395	C₂×Q₈	—	2	8	no	—
396	C₂×Q₈	—	4	16	no	—
397	C₂×Q₈	C₂×D₄×C₁₃	1	16	yes	—
398	C₂×D₄	—	2	64	no	—
399	C₂×D₄	—	2	16	no	—
400	C₂×D₄	—	2	16	no	—
401	C₂×D₄	—	2	32	no	—
402	C₂×D₄	—	2	16	no	—
403	C₂×D₄	—	2	8	no	—
404	C₂×D₄	—	2	8	no	—
405	C₂×D₄	C₂×D₄×C₁₃	1	16	yes	—
406	C₂²×C₄	—	2	64	no	—
407	C₂²×C₄	—	2	4	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	4	no	—
411	C₂²×C₄	—	2	4	no	—
412	C₂²×C₄	—	2	16	no	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	2	32	no	—
415	C₂²×C₄	—	2	16	no	—
416	C₂²×C₄	—	2	16	no	—
417	C₂²×C₄	—	2	8	no	—
418	C₂²×C₄	—	2	8	no	—
419	C₂²×C₄	—	2	4	no	—
420	C₂²×C₄	—	2	4	no	—
421	C₂²×C₄	—	2	4	no	—
422	C₂²×C₄	—	2	4	no	—
423	C₂²×C₄	—	2	4	no	—
424	C₂²×C₄	—	2	8	no	—
425	C₂²×C₄	—	2	4	no	—
426	C₂²×C₄	—	2	4	no	—
427	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
428	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
429	C₂²×C₄	C₂×D₄×C₁₃	1	16	yes	—
430	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
431	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
432	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
433	C₂²×C₄	C₁₃×#41	1	8	yes	complemented
434	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
435	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
436	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
437	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
438	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
439	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
440	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
441	C₄⋊C₄	—	2	8	no	—
442	C₄⋊C₄	—	2	16	no	—
443	C₄⋊C₄	—	2	32	no	—
444	C₂²⋊C₄	—	2	16	no	—
445	C₂²⋊C₄	—	2	32	no	—
446	C₂²⋊C₄	—	2	16	no	—
447	C₂²⋊C₄	—	2	32	no	—
448	C₄²	—	2	8	no	—
449	C₄²	—	2	8	no	—
450	C₁₃	C₂×#2432	1	1	yes	characteristic, direct product factor, Sylow
451	C₂³	—	2	16	no	—
452	C₂³	—	2	8	no	—
453	C₂³	—	2	8	no	—
454	C₂³	—	2	8	no	—
455	C₂³	—	2	32	no	—
456	C₂³	—	2	4	no	—
457	C₂³	—	2	2	no	—
458	C₂³	—	2	4	no	—
459	C₂³	—	2	2	no	—
460	C₂³	—	2	4	no	—
461	C₂³	—	2	8	no	—
462	C₂³	—	2	4	no	—
463	C₂³	—	2	8	no	—
464	C₂³	—	4	8	no	—
465	C₂³	—	4	8	no	—
466	C₂³	—	4	8	no	—
467	C₂³	—	4	8	no	—
468	C₂³	—	4	16	no	—
469	C₂³	C₂²×D₄×C₁₃	1	8	yes	—
470	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
471	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
472	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
473	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
474	C₂³	C₂×C₁₃×#41	1	4	yes	—
475	C₂³	C₁₃×2₋¹⁺⁴	1	4	yes	—
476	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
477	Q₈	—	2	32	no	—
478	Q₈	—	4	16	no	—
479	D₄	—	2	64	no	—
480	D₄	—	2	32	no	—
481	C₂×C₄	—	2	64	no	—
482	C₂×C₄	—	2	8	no	—
483	C₂×C₄	—	2	16	no	—
484	C₂×C₄	—	2	16	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	4	no	—
491	C₂×C₄	—	2	32	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	8	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	4	8	no	—
501	C₂×C₄	—	4	8	no	—
502	C₂×C₄	—	4	8	no	—
503	C₂×C₄	C₁₃×#120	1	16	yes	—
504	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
505	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
506	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
507	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
508	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
509	C₂×C₄	C₂×C₁₃×#41	1	8	yes	complemented
510	C₂²	—	2	8	no	—
511	C₂²	—	2	4	no	—
512	C₂²	—	2	4	no	—
513	C₂²	—	2	4	no	—
514	C₂²	—	2	16	no	—
515	C₂²	—	4	4	no	—
516	C₂²	—	4	4	no	—
517	C₂²	—	4	16	no	—
518	C₂²	—	4	32	no	—
519	C₂²	—	4	4	no	—
520	C₂²	—	4	4	no	—
521	C₂²	—	4	8	no	—
522	C₂²	C₂×C₁₃×#120	1	4	yes	—
523	C₂²	C₁₃×#532	1	4	yes	—
524	C₂²	C₁₃×#536	1	4	yes	—
525	C₂²	C₁₃×#547	1	8	yes	—
526	C₂²	C₁₃×#548	1	8	yes	—
527	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
528	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
529	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
530	C₂²	C₂²×C₁₃×#41	1	2	yes	—
531	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
532	C₄	—	2	4	no	—
533	C₄	—	2	8	no	—
534	C₄	—	2	8	no	—
535	C₄	—	4	4	no	—
536	C₄	—	4	4	no	—
537	C₄	—	4	4	no	—
538	C₄	C₂×C₁₃×#120	1	8	yes	—
539	C₂	—	4	4	no	—
540	C₂	—	4	8	no	—
541	C₂	C₁₃×#2432	1	8	yes	direct product factor
542	C₂	C₂²×C₁₃×#120	1	1	yes	characteristic
543	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
544	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
545	C₂	C₂×C₁₃×#547	1	2	yes	—
546	C₂	C₂×C₁₃×#548	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂³×C₁₃×#41	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₃×C₄⋊Q₈	C₂	semidirect
3. C₂²×C₁₃×#124	C₂	semidirect
4. C₂²×C₁₃×C₂²⋊Q₈	C₂	semidirect
5. C₁₃×#2432	C₂	direct (N × H)
6. C₂×C₁₃×#394	C₂	semidirect
7. C₂×C₁₃×#391	C₂	semidirect
8. C₂×C₁₃×#390	C₂	semidirect
9. C₂×C₁₃×#385	C₂	semidirect
10. C₂×C₄×C₁₃×C₂²⋊C₄	C₂	semidirect
22. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
24. C₂×C₁₃×#124	C₂²	semidirect
26. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
36. C₁₃×#394	C₂²	semidirect
37. C₁₃×#391	C₂²	semidirect
38. C₁₃×#390	C₂²	semidirect
39. C₁₃×#385	C₂²	semidirect
40. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
103. C₂×#2432	C₁₃	direct (N × H)
161. C₂²×C₄×C₁₃	#41	semidirect
179. C₂²×C₄⋊Q₈	C₂×C₁₃	semidirect
180. C₂²×#124	C₂×C₁₃	semidirect
181. C₂²×C₂²⋊Q₈	C₂×C₁₃	semidirect
182. #2432	C₂×C₁₃	direct (N × H)
183. C₂×#394	C₂×C₁₃	semidirect
184. C₂×#391	C₂×C₁₃	semidirect
185. C₂×#390	C₂×C₁₃	semidirect
186. C₂×#385	C₂×C₁₃	semidirect
187. C₂×C₄×C₂²⋊C₄	C₂×C₁₃	semidirect
246. C₂×C₄×C₁₃	C₂×#41	semidirect
258. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
260. C₂×#124	C₂²×C₁₃	semidirect
262. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
272. #394	C₂²×C₁₃	semidirect
273. #391	C₂²×C₁₃	semidirect
274. #390	C₂²×C₁₃	semidirect
275. #385	C₂²×C₁₃	semidirect
276. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
370. C₂×C₁₃	#2432	direct (N × H)
433. C₂²×C₄	C₁₃×#41	semidirect
450. C₁₃	C₂×#2432	direct (N × H)
509. C₂×C₄	C₂×C₁₃×#41	semidirect
541. C₂	C₁₃×#2432	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₁₃×#41	2
C₂²×C₁₃×C₄⋊Q₈	2
C₂²×C₁₃×#124	2
C₂²×C₁₃×C₂²⋊Q₈	2
C₁₃×#2432	2
C₂×C₁₃×#394	2
C₂×C₁₃×#391	2
C₂×C₁₃×#390	2
C₂×C₁₃×#385	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
C₂×#2432	13

Subgroups — C2×C13×#2432 #15721056

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2432 #15721056