Subgroups — C₂×C₁₃×#1532 #15703984

Order 3328.

1082 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#432	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₃×#97	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1532	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₁₃×#330	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#329	C₂	1	2	yes	maximal, complemented
7	C₂³×C₈×C₁₃	—	2	1	no	—
8	C₁₃×#529	—	2	2	no	—
9	C₁₃×#529	—	2	2	no	—
10	C₁₃×#529	C₄	1	4	yes	—
11	C₁₃×#529	C₂²	1	4	yes	—
12	C₂×C₁₃×#126	—	2	1	no	—
13	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#123	—	2	1	no	—
16	C₂×C₁₃×C₂²⋊Q₈	C₄	1	1	yes	characteristic
17	C₂×C₁₃×#121	C₄	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₁₃	C₄	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₃	—	2	1	no	—
20	C₂×C₄×D₄×C₁₃	C₄	1	1	yes	characteristic
21	C₂×C₁₃×#117	—	2	1	no	—
22	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
23	C₁₃×#432	—	2	2	no	—
24	C₁₃×#432	C₂²	1	4	yes	complemented
25	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
26	C₂×C₁₃×C₂²⋊C₈	—	2	1	no	—
27	C₂×C₁₃×#97	—	2	2	no	—
28	C₂×C₁₃×#97	—	2	1	no	—
29	C₂×C₁₃×#97	C₂²	1	2	yes	—
30	C₂×C₁₃×#97	C₂²	1	2	yes	—
31	C₂×C₁₃×#97	C₂²	1	4	yes	complemented
32	C₁₃×#330	C₂²	1	8	yes	complemented
33	C₁₃×#329	C₂²	1	8	yes	complemented
34	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
35	C₂²×D₄×C₁₃	—	2	1	no	—
36	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₃	—	2	1	no	—
38	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
41	C₂²×C₈×C₁₃	—	2	8	no	—
42	C₂²×C₈×C₁₃	—	2	2	no	—
43	C₂²×C₈×C₁₃	—	2	4	no	—
44	C₂²×C₈×C₁₃	—	2	2	no	—
45	C₁₃×#126	—	2	4	no	—
46	C₁₃×#126	—	2	4	no	—
47	C₁₃×#125	—	2	1	no	—
48	C₁₃×#125	—	2	1	no	—
49	C₁₃×#125	C₂×C₄	1	2	yes	—
50	C₁₃×#125	C₂³	1	2	yes	—
51	C₁₃×#124	—	2	1	no	—
52	C₁₃×#124	—	2	1	no	—
53	C₁₃×#124	C₂×C₄	1	2	yes	—
54	C₁₃×#124	C₂³	1	2	yes	—
55	C₁₃×#123	—	2	4	no	—
56	C₁₃×#123	—	2	4	no	—
57	C₁₃×C₂²⋊Q₈	—	2	2	no	—
58	C₁₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
59	C₁₃×#121	—	2	2	no	—
60	C₁₃×#121	C₂×C₄	1	4	yes	—
61	C₄×Q₈×C₁₃	—	2	2	no	—
62	C₄×Q₈×C₁₃	C₂×C₄	1	4	yes	—
63	C₄×D₄×C₁₃	—	2	4	no	—
64	C₄×D₄×C₁₃	—	2	4	no	—
65	C₄×D₄×C₁₃	—	2	2	no	—
66	C₄×D₄×C₁₃	C₂×C₄	1	4	yes	—
67	C₁₃×#117	—	2	4	no	—
68	C₁₃×#117	—	2	4	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
73	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
75	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
76	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
77	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
78	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
79	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
80	C₂×C₄²×C₁₃	—	2	1	no	—
81	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
83	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
84	C₂×C₄²×C₁₃	D₄	1	2	yes	—
85	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₁₃	D₄	1	2	yes	—
87	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
89	C₁₃×C₄⋊C₈	—	2	4	no	—
90	C₁₃×C₂²⋊C₈	—	2	4	no	—
91	C₁₃×#97	—	2	2	no	—
92	C₁₃×#97	—	2	4	no	—
93	C₁₃×#97	—	2	2	no	—
94	C₁₃×#97	C₂³	1	4	yes	—
95	C₁₃×#97	C₂³	1	4	yes	—
96	C₂×#1532	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
97	C₂⁴×C₁₃	—	2	1	no	—
98	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
99	C₂×Q₈×C₁₃	—	2	1	no	—
100	C₂×Q₈×C₁₃	—	4	2	no	—
101	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
102	C₂×D₄×C₁₃	—	2	4	no	—
103	C₂×D₄×C₁₃	—	2	1	no	—
104	C₂×D₄×C₁₃	—	4	2	no	—
105	C₂×D₄×C₁₃	—	4	4	no	—
106	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₁₃	—	2	4	no	—
108	C₂²×C₄×C₁₃	—	2	1	no	—
109	C₂²×C₄×C₁₃	—	2	1	no	—
110	C₂²×C₄×C₁₃	—	2	1	no	—
111	C₂²×C₄×C₁₃	—	2	4	no	—
112	C₂²×C₄×C₁₃	—	4	2	no	—
113	C₂²×C₄×C₁₃	—	4	2	no	—
114	C₂²×C₄×C₁₃	—	4	4	no	—
115	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
116	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
120	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
121	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
123	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₁₃	—	2	8	no	—
128	C₂×C₈×C₁₃	—	2	16	no	—
129	C₂×C₈×C₁₃	—	2	4	no	—
130	C₂×C₈×C₁₃	—	2	4	no	—
131	C₂×C₈×C₁₃	—	4	4	no	—
132	C₁₃×C₄⋊C₄	—	2	4	no	—
133	C₁₃×C₄⋊C₄	—	2	2	no	—
134	C₁₃×C₄⋊C₄	—	2	2	no	—
135	C₁₃×C₄⋊C₄	—	2	4	no	—
136	C₁₃×C₄⋊C₄	—	2	1	no	—
137	C₁₃×C₄⋊C₄	—	2	1	no	—
138	C₁₃×C₄⋊C₄	—	2	2	no	—
139	C₁₃×C₄⋊C₄	—	2	2	no	—
140	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
141	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
142	C₁₃×C₂²⋊C₄	—	2	4	no	—
143	C₁₃×C₂²⋊C₄	—	2	4	no	—
144	C₁₃×C₂²⋊C₄	—	2	2	no	—
145	C₁₃×C₂²⋊C₄	—	2	2	no	—
146	C₁₃×C₂²⋊C₄	—	2	4	no	—
147	C₁₃×C₂²⋊C₄	—	2	2	no	—
148	C₁₃×C₂²⋊C₄	—	2	2	no	—
149	C₄²×C₁₃	—	2	4	no	—
150	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
151	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
152	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
153	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
154	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
155	C₄²×C₁₃	C₂×D₄	1	2	yes	—
156	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₁₃	C₂×D₄	1	2	yes	—
159	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
160	C₂×#529	C₂×C₁₃	1	1	yes	characteristic
161	C₂×#432	C₂×C₁₃	1	1	yes	characteristic, complemented
162	C₂²×#97	C₂×C₁₃	1	1	yes	characteristic, complemented
163	#1532	C₂×C₁₃	1	8	yes	direct product factor
164	C₂×#330	C₂×C₁₃	1	2	yes	complemented
165	C₂×#329	C₂×C₁₃	1	2	yes	complemented
166	C₂³×C₁₃	—	2	2	no	—
167	C₂³×C₁₃	—	2	2	no	—
168	C₂³×C₁₃	—	2	2	no	—
169	C₂³×C₁₃	—	4	2	no	—
170	C₂³×C₁₃	—	4	2	no	—
171	C₂³×C₁₃	—	4	2	no	—
172	C₂³×C₁₃	#104	1	4	yes	—
173	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
174	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
175	Q₈×C₁₃	—	4	2	no	—
176	Q₈×C₁₃	—	4	2	no	—
177	D₄×C₁₃	—	4	2	no	—
178	D₄×C₁₃	—	4	2	no	—
179	D₄×C₁₃	—	4	8	no	—
180	C₂×C₄×C₁₃	—	2	2	no	—
181	C₂×C₄×C₁₃	—	2	2	no	—
182	C₂×C₄×C₁₃	—	2	4	no	—
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	2	4	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	2	no	—
187	C₂×C₄×C₁₃	—	2	2	no	—
188	C₂×C₄×C₁₃	—	2	2	no	—
189	C₂×C₄×C₁₃	—	2	2	no	—
190	C₂×C₄×C₁₃	—	2	2	no	—
191	C₂×C₄×C₁₃	—	4	2	no	—
192	C₂×C₄×C₁₃	—	4	2	no	—
193	C₂×C₄×C₁₃	—	4	2	no	—
194	C₂×C₄×C₁₃	—	4	2	no	—
195	C₂×C₄×C₁₃	—	4	8	no	—
196	C₂×C₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	—	4	2	no	—
198	C₂×C₄×C₁₃	—	4	2	no	—
199	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
200	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
201	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
202	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
203	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
204	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
206	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
208	C₈×C₁₃	—	2	8	no	—
209	C₈×C₁₃	—	4	4	no	—
210	C₂³×C₈	—	2	1	no	—
211	#529	—	2	2	no	—
212	#529	—	2	2	no	—
213	#529	C₄×C₁₃	1	4	yes	—
214	#529	C₂²×C₁₃	1	4	yes	—
215	C₂×#126	—	2	1	no	—
216	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
217	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
218	C₂×#123	—	2	1	no	—
219	C₂×C₂²⋊Q₈	C₄×C₁₃	1	1	yes	characteristic
220	C₂×#121	C₄×C₁₃	1	1	yes	characteristic
221	C₂×C₄×Q₈	C₄×C₁₃	1	1	yes	characteristic
222	C₂×C₄×D₄	—	2	1	no	—
223	C₂×C₄×D₄	C₄×C₁₃	1	1	yes	characteristic
224	C₂×#117	—	2	1	no	—
225	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
226	#432	—	2	2	no	—
227	#432	C₂²×C₁₃	1	4	yes	complemented
228	C₂×C₄⋊C₈	—	2	1	no	—
229	C₂×C₂²⋊C₈	—	2	1	no	—
230	C₂×#97	—	2	2	no	—
231	C₂×#97	—	2	1	no	—
232	C₂×#97	C₂²×C₁₃	1	2	yes	—
233	C₂×#97	C₂²×C₁₃	1	2	yes	—
234	C₂×#97	C₂²×C₁₃	1	4	yes	complemented
235	#330	C₂²×C₁₃	1	8	yes	complemented
236	#329	C₂²×C₁₃	1	8	yes	complemented
237	C₂²×C₁₃	—	2	2	no	—
238	C₂²×C₁₃	—	2	2	no	—
239	C₂²×C₁₃	—	2	8	no	—
240	C₂²×C₁₃	—	4	2	no	—
241	C₂²×C₁₃	—	4	2	no	—
242	C₂²×C₁₃	—	4	2	no	—
243	C₂²×C₁₃	—	8	4	no	—
244	C₂²×C₁₃	#413	1	2	yes	—
245	C₂²×C₁₃	C₂×#104	1	4	yes	—
246	C₂²×C₁₃	C₂×#104	1	2	yes	—
247	C₂²×C₁₃	#421	1	2	yes	—
248	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
249	C₄×C₁₃	—	2	2	no	—
250	C₄×C₁₃	—	2	1	no	—
251	C₄×C₁₃	—	2	1	no	—
252	C₄×C₁₃	—	2	1	no	—
253	C₄×C₁₃	—	2	2	no	—
254	C₄×C₁₃	—	2	1	no	—
255	C₄×C₁₃	—	2	1	no	—
256	C₄×C₁₃	—	2	2	no	—
257	C₄×C₁₃	—	2	1	no	—
258	C₄×C₁₃	—	4	2	no	—
259	C₄×C₁₃	—	4	2	no	—
260	C₄×C₁₃	—	4	2	no	—
261	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
262	C₂²×D₄	—	2	1	no	—
263	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
264	C₂³×C₄	—	2	1	no	—
265	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
266	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
267	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
268	C₂²×C₈	—	2	8	no	—
269	C₂²×C₈	—	2	2	no	—
270	C₂²×C₈	—	2	4	no	—
271	C₂²×C₈	—	2	2	no	—
272	#126	—	2	4	no	—
273	#126	—	2	4	no	—
274	#125	—	2	1	no	—
275	#125	—	2	1	no	—
276	#125	C₂×C₄×C₁₃	1	2	yes	—
277	#125	C₂³×C₁₃	1	2	yes	—
278	#124	—	2	1	no	—
279	#124	—	2	1	no	—
280	#124	C₂×C₄×C₁₃	1	2	yes	—
281	#124	C₂³×C₁₃	1	2	yes	—
282	#123	—	2	4	no	—
283	#123	—	2	4	no	—
284	C₂²⋊Q₈	—	2	2	no	—
285	C₂²⋊Q₈	C₂×C₄×C₁₃	1	4	yes	—
286	#121	—	2	2	no	—
287	#121	C₂×C₄×C₁₃	1	4	yes	—
288	C₄×Q₈	—	2	2	no	—
289	C₄×Q₈	C₂×C₄×C₁₃	1	4	yes	—
290	C₄×D₄	—	2	4	no	—
291	C₄×D₄	—	2	4	no	—
292	C₄×D₄	—	2	2	no	—
293	C₄×D₄	C₂×C₄×C₁₃	1	4	yes	—
294	#117	—	2	4	no	—
295	#117	—	2	4	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
301	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
302	C₂×C₂²⋊C₄	—	2	1	no	—
303	C₂×C₂²⋊C₄	—	2	1	no	—
304	C₂×C₂²⋊C₄	—	2	1	no	—
305	C₂×C₂²⋊C₄	—	2	1	no	—
306	C₂×C₂²⋊C₄	—	2	1	no	—
307	C₂×C₄²	—	2	1	no	—
308	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
309	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
310	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
311	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
312	C₂×C₄²	D₄×C₁₃	1	2	yes	—
313	C₂×C₄²	D₄×C₁₃	1	2	yes	—
314	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
315	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
316	C₄⋊C₈	—	2	4	no	—
317	C₂²⋊C₈	—	2	4	no	—
318	#97	—	2	2	no	—
319	#97	—	2	4	no	—
320	#97	—	2	2	no	—
321	#97	C₂³×C₁₃	1	4	yes	—
322	#97	C₂³×C₁₃	1	4	yes	—
323	C₂×C₁₃	—	2	4	no	—
324	C₂×C₁₃	—	8	2	no	—
325	C₂×C₁₃	#1532	1	4	yes	direct product factor
326	C₂×C₁₃	C₂×#413	1	1	yes	characteristic
327	C₂×C₁₃	C₂²×#104	1	1	yes	characteristic
328	C₂×C₁₃	C₂×#421	1	1	yes	characteristic
329	C₂⁴	—	2	1	no	—
330	C₂⁴	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
331	C₂×Q₈	—	2	1	no	—
332	C₂×Q₈	—	4	2	no	—
333	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	4	2	no	—
337	C₂×D₄	—	4	4	no	—
338	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
339	C₂²×C₄	—	2	4	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	4	2	no	—
345	C₂²×C₄	—	4	2	no	—
346	C₂²×C₄	—	4	4	no	—
347	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
348	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
349	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
350	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
351	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
352	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
353	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
354	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
355	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
356	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
357	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
358	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
359	C₂×C₈	—	2	8	no	—
360	C₂×C₈	—	2	16	no	—
361	C₂×C₈	—	2	4	no	—
362	C₂×C₈	—	2	4	no	—
363	C₂×C₈	—	4	4	no	—
364	C₄⋊C₄	—	2	4	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	4	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
373	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
374	C₂²⋊C₄	—	2	4	no	—
375	C₂²⋊C₄	—	2	4	no	—
376	C₂²⋊C₄	—	2	2	no	—
377	C₂²⋊C₄	—	2	2	no	—
378	C₂²⋊C₄	—	2	4	no	—
379	C₂²⋊C₄	—	2	2	no	—
380	C₂²⋊C₄	—	2	2	no	—
381	C₄²	—	2	4	no	—
382	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
383	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
384	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
385	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
386	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
387	C₄²	C₂×D₄×C₁₃	1	2	yes	—
388	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
389	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
390	C₄²	C₂×D₄×C₁₃	1	2	yes	—
391	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
392	C₁₃	C₂×#1532	1	1	yes	characteristic, direct product factor, Sylow
393	C₂³	—	2	2	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	2	2	no	—
396	C₂³	—	4	2	no	—
397	C₂³	—	4	2	no	—
398	C₂³	—	4	2	no	—
399	C₂³	C₁₃×#104	1	4	yes	—
400	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
401	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
402	Q₈	—	4	2	no	—
403	Q₈	—	4	2	no	—
404	D₄	—	4	2	no	—
405	D₄	—	4	2	no	—
406	D₄	—	4	8	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	8	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
427	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
428	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
429	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
430	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
431	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
432	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
433	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
434	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
435	C₈	—	2	8	no	—
436	C₈	—	4	4	no	—
437	C₂²	—	2	8	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	8	4	no	—
444	C₂²	C₁₃×#413	1	2	yes	—
445	C₂²	C₂×C₁₃×#104	1	4	yes	—
446	C₂²	C₂×C₁₃×#104	1	2	yes	—
447	C₂²	C₁₃×#421	1	2	yes	—
448	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
449	C₄	—	2	2	no	—
450	C₄	—	2	1	no	—
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	2	no	—
454	C₄	—	2	1	no	—
455	C₄	—	2	1	no	—
456	C₄	—	2	2	no	—
457	C₄	—	2	1	no	—
458	C₄	—	4	2	no	—
459	C₄	—	4	2	no	—
460	C₄	—	4	2	no	—
461	C₂	—	2	4	no	—
462	C₂	—	8	2	no	—
463	C₂	C₁₃×#1532	1	4	yes	direct product factor
464	C₂	C₂×C₁₃×#413	1	1	yes	characteristic
465	C₂	C₂²×C₁₃×#104	1	1	yes	characteristic
466	C₂	C₂×C₁₃×#421	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#121	C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#432	C₂	semidirect
3. C₂²×C₁₃×#97	C₂	semidirect
4. C₁₃×#1532	C₂	direct (N × H)
5. C₂×C₁₃×#330	C₂	semidirect
6. C₂×C₁₃×#329	C₂	semidirect
24. C₁₃×#432	C₂²	semidirect
31. C₂×C₁₃×#97	C₂²	semidirect
32. C₁₃×#330	C₂²	semidirect
33. C₁₃×#329	C₂²	semidirect
96. C₂×#1532	C₁₃	direct (N × H)
161. C₂×#432	C₂×C₁₃	semidirect
162. C₂²×#97	C₂×C₁₃	semidirect
163. #1532	C₂×C₁₃	direct (N × H)
164. C₂×#330	C₂×C₁₃	semidirect
165. C₂×#329	C₂×C₁₃	semidirect
227. #432	C₂²×C₁₃	semidirect
234. C₂×#97	C₂²×C₁₃	semidirect
235. #330	C₂²×C₁₃	semidirect
236. #329	C₂²×C₁₃	semidirect
325. C₂×C₁₃	#1532	direct (N × H)
392. C₁₃	C₂×#1532	direct (N × H)
463. C₂	C₁₃×#1532	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×C₁₃×#529	2
C₂×C₁₃×#432	2
C₂²×C₁₃×#97	2
C₁₃×#1532	2
C₂×C₁₃×#330	2
C₂×C₁₃×#329	2
C₂×#1532	13

Subgroups — C2×C13×#1532 #15703984

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#1532 #15703984