Subgroups — C₂×C₁₃×#1527 #15703978

Order 3328.

1394 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#124	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#432	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1527	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₁₃×#329	C₂	1	4	yes	maximal, complemented
6	C₂³×Q₈×C₁₃	C₄	1	1	yes	characteristic
7	C₂³×D₄×C₁₃	C₄	1	1	yes	characteristic
8	C₂²×C₁₃×M₁₆	—	2	1	no	—
9	C₂×C₁₃×#124	—	2	1	no	—
10	C₂×C₁₃×#124	—	2	2	no	—
11	C₂×C₁₃×#124	—	2	1	no	—
12	C₂×C₁₃×#124	—	2	2	no	—
13	C₂×C₁₃×#124	C₄	1	4	yes	—
14	C₂×C₁₃×#124	C₄	1	2	yes	—
15	C₂×C₁₃×#124	C₂²	1	2	yes	—
16	C₂×C₁₃×#124	C₂²	1	4	yes	—
17	C₂²×C₁₃×C₂²⋊C₄	—	2	1	no	—
18	C₂²×C₁₃×C₂²⋊C₄	—	2	1	no	—
19	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#432	—	2	2	no	—
21	C₁₃×#432	C₂²	1	4	yes	complemented
22	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
23	C₂×C₁₃×C₂²⋊C₈	—	2	1	no	—
24	C₄×C₁₃×M₁₆	—	2	2	no	—
25	C₄×C₁₃×M₁₆	C₂²	1	4	yes	complemented
26	C₂×C₁₃×#97	C₂²	1	2	yes	complemented
27	C₂×C₁₃×#97	C₂²	1	2	yes	complemented
28	C₂×C₄×C₈×C₁₃	—	2	1	no	—
29	C₁₃×#329	C₂²	1	16	yes	complemented
30	C₂⁵×C₁₃	—	2	1	no	—
31	C₂²×Q₈×C₁₃	—	2	2	no	—
32	C₂²×Q₈×C₁₃	—	2	1	no	—
33	C₂²×Q₈×C₁₃	—	4	4	no	—
34	C₂²×Q₈×C₁₃	C₂×C₄	1	4	yes	—
35	C₂²×Q₈×C₁₃	C₂×C₄	1	2	yes	—
36	C₂²×D₄×C₁₃	—	2	2	no	—
37	C₂²×D₄×C₁₃	—	2	1	no	—
38	C₂²×D₄×C₁₃	—	4	4	no	—
39	C₂²×D₄×C₁₃	C₂×C₄	1	4	yes	—
40	C₂²×D₄×C₁₃	C₂×C₄	1	2	yes	—
41	C₂³×C₄×C₁₃	—	2	1	no	—
42	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
45	C₂×C₁₃×M₁₆	—	2	8	no	—
46	C₂×C₁₃×M₁₆	—	2	4	no	—
47	C₂²×C₈×C₁₃	—	2	2	no	—
48	C₂²×C₈×C₁₃	—	2	2	no	—
49	C₁₃×#124	—	2	4	no	—
50	C₁₃×#124	—	2	4	no	—
51	C₁₃×#124	—	2	4	no	—
52	C₁₃×#124	—	2	4	no	—
53	C₁₃×#124	—	2	2	no	—
54	C₁₃×#124	—	2	2	no	—
55	C₁₃×#124	—	2	4	no	—
56	C₁₃×#124	C₂×C₄	1	4	yes	—
57	C₁₃×#124	C₂×C₄	1	8	yes	—
58	C₁₃×#124	C₂³	1	4	yes	—
59	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
60	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
61	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
62	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
63	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
64	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
65	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
66	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
67	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
68	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₁₃	D₄	1	2	yes	—
71	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₁₃	D₄	1	2	yes	—
73	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
75	C₁₃×C₄⋊C₈	—	2	4	no	—
76	C₁₃×C₂²⋊C₈	—	2	4	no	—
77	C₁₃×#97	—	2	2	no	—
78	C₁₃×#97	—	2	2	no	—
79	C₁₃×#97	C₂³	1	4	yes	complemented
80	C₁₃×#97	C₂³	1	4	yes	complemented
81	C₄×C₈×C₁₃	—	2	4	no	—
82	C₂×#1527	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
83	C₂⁴×C₁₃	—	2	4	no	—
84	C₂⁴×C₁₃	—	2	2	no	—
85	C₂⁴×C₁₃	—	4	4	no	—
86	C₂⁴×C₁₃	—	4	4	no	—
87	C₂⁴×C₁₃	—	4	4	no	—
88	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
89	C₂×Q₈×C₁₃	—	2	2	no	—
90	C₂×Q₈×C₁₃	—	2	4	no	—
91	C₂×Q₈×C₁₃	—	4	8	no	—
92	C₂×Q₈×C₁₃	—	4	8	no	—
93	C₂×Q₈×C₁₃	—	4	4	no	—
94	C₂×Q₈×C₁₃	—	4	4	no	—
95	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
96	C₂×D₄×C₁₃	—	2	2	no	—
97	C₂×D₄×C₁₃	—	2	4	no	—
98	C₂×D₄×C₁₃	—	4	4	no	—
99	C₂×D₄×C₁₃	—	4	8	no	—
100	C₂×D₄×C₁₃	—	4	8	no	—
101	C₂×D₄×C₁₃	—	4	4	no	—
102	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
103	C₂²×C₄×C₁₃	—	2	4	no	—
104	C₂²×C₄×C₁₃	—	2	4	no	—
105	C₂²×C₄×C₁₃	—	2	4	no	—
106	C₂²×C₄×C₁₃	—	2	2	no	—
107	C₂²×C₄×C₁₃	—	4	2	no	—
108	C₂²×C₄×C₁₃	—	4	4	no	—
109	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
110	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
111	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
114	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
121	C₁₃×M₁₆	—	2	16	no	—
122	C₂×C₈×C₁₃	—	2	8	no	—
123	C₂×C₈×C₁₃	—	2	4	no	—
124	C₂×C₈×C₁₃	—	2	4	no	—
125	C₂×C₈×C₁₃	—	4	4	no	—
126	C₁₃×C₂²⋊C₄	—	2	4	no	—
127	C₁₃×C₂²⋊C₄	—	2	8	no	—
128	C₁₃×C₂²⋊C₄	—	2	8	no	—
129	C₁₃×C₂²⋊C₄	—	2	4	no	—
130	C₁₃×C₂²⋊C₄	—	2	4	no	—
131	C₁₃×C₂²⋊C₄	—	2	4	no	—
132	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
133	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
134	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
135	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
136	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
137	C₄²×C₁₃	C₂×D₄	1	2	yes	—
138	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₁₃	C₂×D₄	1	2	yes	—
141	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
142	C₂²×#124	C₂×C₁₃	1	1	yes	characteristic
143	C₂×#432	C₂×C₁₃	1	1	yes	characteristic, complemented
144	C₂×C₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
145	#1527	C₂×C₁₃	1	8	yes	direct product factor
146	C₂×#329	C₂×C₁₃	1	4	yes	complemented
147	C₂³×C₁₃	—	2	2	no	—
148	C₂³×C₁₃	—	2	2	no	—
149	C₂³×C₁₃	—	2	4	no	—
150	C₂³×C₁₃	—	4	8	no	—
151	C₂³×C₁₃	—	4	8	no	—
152	C₂³×C₁₃	—	4	4	no	—
153	C₂³×C₁₃	—	4	8	no	—
154	C₂³×C₁₃	—	4	4	no	—
155	C₂³×C₁₃	—	4	4	no	—
156	C₂³×C₁₃	—	8	16	no	—
157	C₂³×C₁₃	#104	1	4	yes	—
158	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
159	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	Q₈×C₁₃	—	4	4	no	—
161	Q₈×C₁₃	—	4	4	no	—
162	Q₈×C₁₃	—	4	8	no	—
163	D₄×C₁₃	—	4	4	no	—
164	D₄×C₁₃	—	4	4	no	—
165	D₄×C₁₃	—	4	8	no	—
166	C₂×C₄×C₁₃	—	2	2	no	—
167	C₂×C₄×C₁₃	—	2	2	no	—
168	C₂×C₄×C₁₃	—	2	4	no	—
169	C₂×C₄×C₁₃	—	2	4	no	—
170	C₂×C₄×C₁₃	—	2	2	no	—
171	C₂×C₄×C₁₃	—	2	2	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	2	4	no	—
174	C₂×C₄×C₁₃	—	2	4	no	—
175	C₂×C₄×C₁₃	—	2	4	no	—
176	C₂×C₄×C₁₃	—	4	2	no	—
177	C₂×C₄×C₁₃	—	4	2	no	—
178	C₂×C₄×C₁₃	—	4	8	no	—
179	C₂×C₄×C₁₃	—	4	4	no	—
180	C₂×C₄×C₁₃	#100	1	4	yes	—
181	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
183	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
184	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
187	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
188	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
190	C₈×C₁₃	—	2	8	no	—
191	C₈×C₁₃	—	4	4	no	—
192	C₂³×Q₈	C₄×C₁₃	1	1	yes	characteristic
193	C₂³×D₄	C₄×C₁₃	1	1	yes	characteristic
194	C₂²×M₁₆	—	2	1	no	—
195	C₂×#124	—	2	1	no	—
196	C₂×#124	—	2	2	no	—
197	C₂×#124	—	2	1	no	—
198	C₂×#124	—	2	2	no	—
199	C₂×#124	C₄×C₁₃	1	2	yes	—
200	C₂×#124	C₄×C₁₃	1	4	yes	—
201	C₂×#124	C₂²×C₁₃	1	2	yes	—
202	C₂×#124	C₂²×C₁₃	1	4	yes	—
203	C₂²×C₂²⋊C₄	—	2	1	no	—
204	C₂²×C₂²⋊C₄	—	2	1	no	—
205	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
206	#432	—	2	2	no	—
207	#432	C₂²×C₁₃	1	4	yes	complemented
208	C₂×C₄⋊C₈	—	2	1	no	—
209	C₂×C₂²⋊C₈	—	2	1	no	—
210	C₄×M₁₆	—	2	2	no	—
211	C₄×M₁₆	C₂²×C₁₃	1	4	yes	complemented
212	C₂×#97	C₂²×C₁₃	1	2	yes	complemented
213	C₂×#97	C₂²×C₁₃	1	2	yes	complemented
214	C₂×C₄×C₈	—	2	1	no	—
215	#329	C₂²×C₁₃	1	16	yes	complemented
216	C₂²×C₁₃	—	2	2	no	—
217	C₂²×C₁₃	—	2	2	no	—
218	C₂²×C₁₃	—	2	8	no	—
219	C₂²×C₁₃	—	4	4	no	—
220	C₂²×C₁₃	—	4	4	no	—
221	C₂²×C₁₃	—	4	4	no	—
222	C₂²×C₁₃	—	8	16	no	—
223	C₂²×C₁₃	—	8	8	no	—
224	C₂²×C₁₃	C₂×#100	1	2	yes	—
225	C₂²×C₁₃	C₂×#104	1	4	yes	—
226	C₂²×C₁₃	C₂×#104	1	2	yes	—
227	C₂²×C₁₃	#421	1	2	yes	—
228	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
229	C₄×C₁₃	—	2	1	no	—
230	C₄×C₁₃	—	2	1	no	—
231	C₄×C₁₃	—	2	1	no	—
232	C₄×C₁₃	—	2	1	no	—
233	C₄×C₁₃	—	2	2	no	—
234	C₄×C₁₃	—	2	1	no	—
235	C₄×C₁₃	—	2	1	no	—
236	C₄×C₁₃	—	2	2	no	—
237	C₄×C₁₃	—	4	4	no	—
238	C₄×C₁₃	C₂×#100	1	4	yes	—
239	C₂⁵	—	2	1	no	—
240	C₂²×Q₈	—	2	2	no	—
241	C₂²×Q₈	—	2	1	no	—
242	C₂²×Q₈	—	4	4	no	—
243	C₂²×Q₈	C₂×C₄×C₁₃	1	4	yes	—
244	C₂²×Q₈	C₂×C₄×C₁₃	1	2	yes	—
245	C₂²×D₄	—	2	2	no	—
246	C₂²×D₄	—	2	1	no	—
247	C₂²×D₄	—	4	4	no	—
248	C₂²×D₄	C₂×C₄×C₁₃	1	2	yes	—
249	C₂²×D₄	C₂×C₄×C₁₃	1	4	yes	—
250	C₂³×C₄	—	2	1	no	—
251	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
252	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
253	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
254	C₂×M₁₆	—	2	8	no	—
255	C₂×M₁₆	—	2	4	no	—
256	C₂²×C₈	—	2	2	no	—
257	C₂²×C₈	—	2	2	no	—
258	#124	—	2	4	no	—
259	#124	—	2	4	no	—
260	#124	—	2	4	no	—
261	#124	—	2	4	no	—
262	#124	—	2	2	no	—
263	#124	—	2	2	no	—
264	#124	—	2	4	no	—
265	#124	C₂×C₄×C₁₃	1	4	yes	—
266	#124	C₂×C₄×C₁₃	1	8	yes	—
267	#124	C₂³×C₁₃	1	4	yes	—
268	C₂×C₂²⋊C₄	—	2	4	no	—
269	C₂×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₂²⋊C₄	—	2	2	no	—
271	C₂×C₂²⋊C₄	—	2	4	no	—
272	C₂×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₂²⋊C₄	—	2	2	no	—
274	C₂×C₂²⋊C₄	—	2	4	no	—
275	C₂×C₂²⋊C₄	—	2	4	no	—
276	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
277	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
278	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
279	C₂×C₄²	D₄×C₁₃	1	2	yes	—
280	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
281	C₂×C₄²	D₄×C₁₃	1	2	yes	—
282	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
283	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
284	C₄⋊C₈	—	2	4	no	—
285	C₂²⋊C₈	—	2	4	no	—
286	#97	—	2	2	no	—
287	#97	—	2	2	no	—
288	#97	C₂³×C₁₃	1	4	yes	complemented
289	#97	C₂³×C₁₃	1	4	yes	complemented
290	C₄×C₈	—	2	4	no	—
291	C₂×C₁₃	—	2	4	no	—
292	C₂×C₁₃	—	8	4	no	—
293	C₂×C₁₃	#1527	1	4	yes	direct product factor
294	C₂×C₁₃	C₂²×#100	1	1	yes	characteristic
295	C₂×C₁₃	C₂²×#104	1	1	yes	characteristic
296	C₂×C₁₃	C₂×#421	1	1	yes	characteristic
297	C₂⁴	—	2	4	no	—
298	C₂⁴	—	2	2	no	—
299	C₂⁴	—	4	4	no	—
300	C₂⁴	—	4	4	no	—
301	C₂⁴	—	4	4	no	—
302	C₂⁴	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	—	2	4	no	—
305	C₂×Q₈	—	4	8	no	—
306	C₂×Q₈	—	4	8	no	—
307	C₂×Q₈	—	4	4	no	—
308	C₂×Q₈	—	4	4	no	—
309	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	4	no	—
312	C₂×D₄	—	4	4	no	—
313	C₂×D₄	—	4	8	no	—
314	C₂×D₄	—	4	8	no	—
315	C₂×D₄	—	4	4	no	—
316	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	4	2	no	—
322	C₂²×C₄	—	4	4	no	—
323	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
324	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
325	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
326	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
327	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
328	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
329	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
330	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
331	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
334	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
335	M₁₆	—	2	16	no	—
336	C₂×C₈	—	2	8	no	—
337	C₂×C₈	—	2	4	no	—
338	C₂×C₈	—	2	4	no	—
339	C₂×C₈	—	4	4	no	—
340	C₂²⋊C₄	—	2	4	no	—
341	C₂²⋊C₄	—	2	8	no	—
342	C₂²⋊C₄	—	2	8	no	—
343	C₂²⋊C₄	—	2	4	no	—
344	C₂²⋊C₄	—	2	4	no	—
345	C₂²⋊C₄	—	2	4	no	—
346	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
347	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
348	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
349	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
350	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
351	C₄²	C₂×D₄×C₁₃	1	2	yes	—
352	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
353	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
354	C₄²	C₂×D₄×C₁₃	1	2	yes	—
355	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
356	C₁₃	C₂×#1527	1	1	yes	characteristic, direct product factor, Sylow
357	C₂³	—	2	2	no	—
358	C₂³	—	2	2	no	—
359	C₂³	—	2	4	no	—
360	C₂³	—	4	8	no	—
361	C₂³	—	4	8	no	—
362	C₂³	—	4	4	no	—
363	C₂³	—	4	8	no	—
364	C₂³	—	4	4	no	—
365	C₂³	—	4	4	no	—
366	C₂³	—	8	16	no	—
367	C₂³	C₁₃×#104	1	4	yes	—
368	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
369	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
370	Q₈	—	4	4	no	—
371	Q₈	—	4	4	no	—
372	Q₈	—	4	8	no	—
373	D₄	—	4	4	no	—
374	D₄	—	4	4	no	—
375	D₄	—	4	8	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	8	no	—
389	C₂×C₄	—	4	4	no	—
390	C₂×C₄	C₁₃×#100	1	4	yes	—
391	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
392	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
393	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
394	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
395	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
396	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
397	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
398	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
399	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
400	C₈	—	2	8	no	—
401	C₈	—	4	4	no	—
402	C₂²	—	2	8	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	2	2	no	—
405	C₂²	—	4	4	no	—
406	C₂²	—	4	4	no	—
407	C₂²	—	4	4	no	—
408	C₂²	—	8	16	no	—
409	C₂²	—	8	8	no	—
410	C₂²	C₂×C₁₃×#100	1	2	yes	—
411	C₂²	C₂×C₁₃×#104	1	4	yes	—
412	C₂²	C₂×C₁₃×#104	1	2	yes	—
413	C₂²	C₁₃×#421	1	2	yes	—
414	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
415	C₄	—	2	1	no	—
416	C₄	—	2	1	no	—
417	C₄	—	2	1	no	—
418	C₄	—	2	1	no	—
419	C₄	—	2	2	no	—
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	2	no	—
423	C₄	—	4	4	no	—
424	C₄	C₂×C₁₃×#100	1	4	yes	—
425	C₂	—	2	4	no	—
426	C₂	—	8	4	no	—
427	C₂	C₁₃×#1527	1	4	yes	direct product factor
428	C₂	C₂²×C₁₃×#100	1	1	yes	characteristic
429	C₂	C₂²×C₁₃×#104	1	1	yes	characteristic
430	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	C₂³×D₄×C₁₃	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. C₂×C₄×C₁₃×M₁₆	C₂	semidirect
4. C₁₃×#1527	C₂	direct (N × H)
5. C₂×C₁₃×#329	C₂	semidirect
21. C₁₃×#432	C₂²	semidirect
25. C₄×C₁₃×M₁₆	C₂²	semidirect
26. C₂×C₁₃×#97	C₂²	semidirect
27. C₂×C₁₃×#97	C₂²	semidirect
29. C₁₃×#329	C₂²	semidirect
79. C₁₃×#97	C₂³	semidirect
80. C₁₃×#97	C₂³	semidirect
82. C₂×#1527	C₁₃	direct (N × H)
143. C₂×#432	C₂×C₁₃	semidirect
144. C₂×C₄×M₁₆	C₂×C₁₃	semidirect
145. #1527	C₂×C₁₃	direct (N × H)
146. C₂×#329	C₂×C₁₃	semidirect
207. #432	C₂²×C₁₃	semidirect
211. C₄×M₁₆	C₂²×C₁₃	semidirect
212. C₂×#97	C₂²×C₁₃	semidirect
213. C₂×#97	C₂²×C₁₃	semidirect
215. #329	C₂²×C₁₃	semidirect
288. #97	C₂³×C₁₃	semidirect
289. #97	C₂³×C₁₃	semidirect
293. C₂×C₁₃	#1527	direct (N × H)
356. C₁₃	C₂×#1527	direct (N × H)
427. C₂	C₁₃×#1527	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×#124	2
C₂×C₁₃×#432	2
C₂×C₄×C₁₃×M₁₆	2
C₁₃×#1527	2
C₂×C₁₃×#329	2
C₂×#1527	13

Subgroups — C2×C13×#1527 #15703978

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#1527 #15703978