Subgroups — C₂×C₁₃×#1506 #15703879

Order 3328.

1130 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#432	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#376	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1506	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₁₃×#328	C₂	1	4	yes	maximal
6	C₁₃×#533	—	2	2	no	—
7	C₁₃×#533	—	2	2	no	—
8	C₁₃×#533	C₄	1	4	yes	complemented
9	C₁₃×#533	C₂²	1	4	yes	—
10	C₂×C₁₃×C₄⋊Q₈	C₄	1	1	yes	characteristic, complemented
11	C₂×C₁₃×C₄⋊Q₈	C₄	1	1	yes	characteristic, complemented
12	C₂×C₁₃×#125	—	2	1	no	—
13	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
14	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
16	C₂×C₄×Q₈×C₁₃	C₄	1	2	yes	complemented
17	C₂×C₁₃×#117	—	2	1	no	—
18	C₂²×C₄²×C₁₃	—	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	—
22	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
23	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
24	C₂×C₁₃×#97	—	2	1	no	—
25	C₁₃×#376	—	2	2	no	—
26	C₁₃×#376	C₂²	1	4	yes	—
27	C₂×C₁₃×#95	—	2	1	no	—
28	C₂×C₁₃×#95	C₂²	1	2	yes	—
29	C₁₃×#328	C₂²	1	16	yes	—
30	C₂²×Q₈×C₁₃	—	2	1	no	—
31	C₂²×Q₈×C₁₃	C₂×C₄	1	2	yes	—
32	C₂³×C₄×C₁₃	—	2	2	no	—
33	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
36	C₂²×C₈×C₁₃	—	2	2	no	—
37	C₁₃×C₄⋊Q₈	—	2	2	no	—
38	C₁₃×C₄⋊Q₈	—	2	2	no	—
39	C₁₃×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
40	C₁₃×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
41	C₁₃×#125	—	2	4	no	—
42	C₁₃×#125	—	2	4	no	—
43	C₁₃×C₂²⋊Q₈	—	2	4	no	—
44	C₁₃×C₂²⋊Q₈	—	2	4	no	—
45	C₁₃×C₂²⋊Q₈	—	2	2	no	—
46	C₁₃×C₂²⋊Q₈	—	2	2	no	—
47	C₁₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
48	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
49	C₄×Q₈×C₁₃	—	2	4	no	—
50	C₄×Q₈×C₁₃	—	2	4	no	—
51	C₄×Q₈×C₁₃	—	2	4	no	—
52	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	complemented
53	C₁₃×#117	—	2	4	no	—
54	C₁₃×#117	—	2	4	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
60	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
61	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
62	C₂×C₄²×C₁₃	—	2	8	no	—
63	C₂×C₄²×C₁₃	—	2	2	no	—
64	C₂×C₄²×C₁₃	—	2	4	no	—
65	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
68	C₂×C₄²×C₁₃	D₄	1	2	yes	—
69	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₁₃	D₄	1	2	yes	—
72	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
73	C₁₃×C₄⋊C₈	—	2	4	no	—
74	C₁₃×C₂²⋊C₈	—	2	2	no	—
75	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
76	C₁₃×#97	—	2	4	no	—
77	C₁₃×#95	—	2	4	no	—
78	C₁₃×#95	—	2	2	no	—
79	C₁₃×#95	C₂³	1	4	yes	—
80	C₂×#1506	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
81	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
82	C₂×Q₈×C₁₃	—	2	2	no	—
83	C₂×Q₈×C₁₃	—	2	4	no	—
84	C₂×Q₈×C₁₃	—	4	4	no	—
85	C₂×Q₈×C₁₃	—	4	4	no	—
86	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
87	C₂²×C₄×C₁₃	—	2	4	no	—
88	C₂²×C₄×C₁₃	—	2	4	no	—
89	C₂²×C₄×C₁₃	—	2	8	no	—
90	C₂²×C₄×C₁₃	—	2	2	no	—
91	C₂²×C₄×C₁₃	—	2	2	no	—
92	C₂²×C₄×C₁₃	—	2	4	no	—
93	C₂²×C₄×C₁₃	—	4	2	no	—
94	C₂²×C₄×C₁₃	—	4	4	no	—
95	C₂²×C₄×C₁₃	—	4	4	no	—
96	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
97	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
98	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
110	C₂×C₈×C₁₃	—	2	4	no	—
111	C₂×C₈×C₁₃	—	4	4	no	—
112	C₁₃×C₄⋊C₄	—	2	4	no	—
113	C₁₃×C₄⋊C₄	—	2	4	no	—
114	C₁₃×C₄⋊C₄	—	2	4	no	—
115	C₁₃×C₄⋊C₄	—	2	4	no	—
116	C₁₃×C₄⋊C₄	—	2	8	no	—
117	C₁₃×C₄⋊C₄	—	2	2	no	—
118	C₁₃×C₄⋊C₄	—	2	4	no	—
119	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
120	C₁₃×C₂²⋊C₄	—	2	4	no	—
121	C₁₃×C₂²⋊C₄	—	2	4	no	—
122	C₄²×C₁₃	—	2	16	no	—
123	C₄²×C₁₃	—	2	8	no	—
124	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
125	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
126	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
127	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
128	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
129	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
130	C₄²×C₁₃	C₂×D₄	1	2	yes	—
131	C₄²×C₁₃	C₂×D₄	1	2	yes	—
132	C₂×#533	C₂×C₁₃	1	1	yes	characteristic
133	C₂×#432	C₂×C₁₃	1	1	yes	characteristic
134	C₂×#376	C₂×C₁₃	1	1	yes	characteristic
135	#1506	C₂×C₁₃	1	8	yes	direct product factor
136	C₂×#328	C₂×C₁₃	1	4	yes	—
137	C₂³×C₁₃	—	2	2	no	—
138	C₂³×C₁₃	—	2	2	no	—
139	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
140	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
141	C₂³×C₁₃	#137	1	4	yes	—
142	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
143	Q₈×C₁₃	—	4	4	no	—
144	Q₈×C₁₃	—	4	4	no	—
145	Q₈×C₁₃	—	4	8	no	—
146	C₂×C₄×C₁₃	—	2	4	no	—
147	C₂×C₄×C₁₃	—	2	2	no	—
148	C₂×C₄×C₁₃	—	2	2	no	—
149	C₂×C₄×C₁₃	—	2	4	no	—
150	C₂×C₄×C₁₃	—	2	2	no	—
151	C₂×C₄×C₁₃	—	2	2	no	—
152	C₂×C₄×C₁₃	—	2	2	no	—
153	C₂×C₄×C₁₃	—	2	4	no	—
154	C₂×C₄×C₁₃	—	2	4	no	—
155	C₂×C₄×C₁₃	—	2	8	no	—
156	C₂×C₄×C₁₃	—	2	4	no	—
157	C₂×C₄×C₁₃	—	2	4	no	—
158	C₂×C₄×C₁₃	—	4	1	no	—
159	C₂×C₄×C₁₃	—	4	1	no	—
160	C₂×C₄×C₁₃	—	4	1	no	—
161	C₂×C₄×C₁₃	—	4	1	no	—
162	C₂×C₄×C₁₃	—	4	4	no	—
163	C₂×C₄×C₁₃	—	4	16	no	—
164	C₂×C₄×C₁₃	—	4	4	no	—
165	C₂×C₄×C₁₃	—	4	4	no	—
166	C₂×C₄×C₁₃	—	4	4	no	—
167	C₂×C₄×C₁₃	#104	1	4	yes	—
168	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
169	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
172	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
173	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
174	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
176	C₈×C₁₃	—	4	4	no	—
177	#533	—	2	2	no	—
178	#533	—	2	2	no	—
179	#533	C₄×C₁₃	1	4	yes	complemented
180	#533	C₂²×C₁₃	1	4	yes	—
181	C₂×C₄⋊Q₈	C₄×C₁₃	1	1	yes	characteristic, complemented
182	C₂×C₄⋊Q₈	C₄×C₁₃	1	1	yes	characteristic, complemented
183	C₂×#125	—	2	1	no	—
184	C₂×C₂²⋊Q₈	—	2	1	no	—
185	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
186	C₂×C₄×Q₈	—	2	1	no	—
187	C₂×C₄×Q₈	C₄×C₁₃	1	2	yes	complemented
188	C₂×#117	—	2	1	no	—
189	C₂²×C₄²	—	2	1	no	—
190	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
191	#432	—	2	2	no	—
192	#432	C₂²×C₁₃	1	4	yes	—
193	C₂×C₄⋊C₈	—	2	1	no	—
194	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
195	C₂×#97	—	2	1	no	—
196	#376	—	2	2	no	—
197	#376	C₂²×C₁₃	1	4	yes	—
198	C₂×#95	—	2	1	no	—
199	C₂×#95	C₂²×C₁₃	1	2	yes	—
200	#328	C₂²×C₁₃	1	16	yes	—
201	C₂²×C₁₃	—	2	1	no	—
202	C₂²×C₁₃	—	2	1	no	—
203	C₂²×C₁₃	—	2	1	no	—
204	C₂²×C₁₃	—	2	1	no	—
205	C₂²×C₁₃	—	2	8	no	—
206	C₂²×C₁₃	#410	1	2	yes	—
207	C₂²×C₁₃	#419	1	2	yes	—
208	C₂²×C₁₃	#419	1	2	yes	—
209	C₂²×C₁₃	C₂×#104	1	2	yes	—
210	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
211	C₂²×C₁₃	C₂×#137	1	2	yes	—
212	C₄×C₁₃	—	2	1	no	—
213	C₄×C₁₃	—	2	1	no	—
214	C₄×C₁₃	—	2	1	no	—
215	C₄×C₁₃	—	2	1	no	—
216	C₄×C₁₃	—	2	2	no	—
217	C₄×C₁₃	—	2	2	no	—
218	C₄×C₁₃	—	2	2	no	—
219	C₄×C₁₃	—	4	8	no	—
220	C₄×C₁₃	—	4	4	no	—
221	C₄×C₁₃	—	4	4	no	—
222	C₄×C₁₃	C₂×#104	1	4	yes	—
223	C₂²×Q₈	—	2	1	no	—
224	C₂²×Q₈	C₂×C₄×C₁₃	1	2	yes	—
225	C₂³×C₄	—	2	2	no	—
226	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
227	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
228	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
229	C₂²×C₈	—	2	2	no	—
230	C₄⋊Q₈	—	2	2	no	—
231	C₄⋊Q₈	—	2	2	no	—
232	C₄⋊Q₈	C₂×C₄×C₁₃	1	4	yes	complemented
233	C₄⋊Q₈	C₂×C₄×C₁₃	1	4	yes	complemented
234	#125	—	2	4	no	—
235	#125	—	2	4	no	—
236	C₂²⋊Q₈	—	2	4	no	—
237	C₂²⋊Q₈	—	2	4	no	—
238	C₂²⋊Q₈	—	2	2	no	—
239	C₂²⋊Q₈	—	2	2	no	—
240	C₂²⋊Q₈	C₂×C₄×C₁₃	1	4	yes	—
241	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
242	C₄×Q₈	—	2	4	no	—
243	C₄×Q₈	—	2	4	no	—
244	C₄×Q₈	—	2	4	no	—
245	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
246	#117	—	2	4	no	—
247	#117	—	2	4	no	—
248	C₂×C₄⋊C₄	—	2	1	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	—	2	1	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
254	C₂×C₂²⋊C₄	—	2	2	no	—
255	C₂×C₄²	—	2	8	no	—
256	C₂×C₄²	—	2	2	no	—
257	C₂×C₄²	—	2	4	no	—
258	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
259	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
260	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
261	C₂×C₄²	D₄×C₁₃	1	2	yes	—
262	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
263	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
264	C₂×C₄²	D₄×C₁₃	1	2	yes	—
265	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
266	C₄⋊C₈	—	2	4	no	—
267	C₂²⋊C₈	—	2	2	no	—
268	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
269	#97	—	2	4	no	—
270	#95	—	2	4	no	—
271	#95	—	2	2	no	—
272	#95	C₂³×C₁₃	1	4	yes	—
273	C₂×C₁₃	—	2	2	no	—
274	C₂×C₁₃	—	2	2	no	—
275	C₂×C₁₃	#1506	1	4	yes	direct product factor
276	C₂×C₁₃	C₂×#410	1	1	yes	characteristic
277	C₂×C₁₃	C₂×#419	1	1	yes	characteristic
278	C₂×C₁₃	C₂²×#104	1	1	yes	characteristic
279	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
280	C₂×Q₈	—	2	2	no	—
281	C₂×Q₈	—	2	4	no	—
282	C₂×Q₈	—	4	4	no	—
283	C₂×Q₈	—	4	4	no	—
284	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	8	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	4	no	—
291	C₂²×C₄	—	4	2	no	—
292	C₂²×C₄	—	4	4	no	—
293	C₂²×C₄	—	4	4	no	—
294	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
295	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
296	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
297	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
298	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
299	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
300	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
301	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
302	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
303	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
304	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
305	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
306	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
307	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
308	C₂×C₈	—	2	4	no	—
309	C₂×C₈	—	4	4	no	—
310	C₄⋊C₄	—	2	4	no	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	—	2	4	no	—
313	C₄⋊C₄	—	2	4	no	—
314	C₄⋊C₄	—	2	8	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
318	C₂²⋊C₄	—	2	4	no	—
319	C₂²⋊C₄	—	2	4	no	—
320	C₄²	—	2	16	no	—
321	C₄²	—	2	8	no	—
322	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
323	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
324	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
325	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
326	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
327	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
328	C₄²	C₂×D₄×C₁₃	1	2	yes	—
329	C₄²	C₂×D₄×C₁₃	1	2	yes	—
330	C₁₃	C₂×#1506	1	1	yes	characteristic, direct product factor, Sylow
331	C₂³	—	2	2	no	—
332	C₂³	—	2	2	no	—
333	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
334	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
335	C₂³	C₁₃×#137	1	4	yes	—
336	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
337	Q₈	—	4	4	no	—
338	Q₈	—	4	4	no	—
339	Q₈	—	4	8	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	8	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	16	no	—
357	C₂×C₄	—	4	4	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	—	4	4	no	—
360	C₂×C₄	—	4	4	no	—
361	C₂×C₄	C₁₃×#104	1	4	yes	—
362	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
363	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
364	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
365	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
366	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
367	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
368	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
369	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
370	C₈	—	4	4	no	—
371	C₂²	—	2	8	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	C₁₃×#410	1	2	yes	—
377	C₂²	C₁₃×#419	1	2	yes	—
378	C₂²	C₁₃×#419	1	2	yes	—
379	C₂²	C₂×C₁₃×#104	1	2	yes	—
380	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
381	C₂²	C₂×C₁₃×#137	1	2	yes	—
382	C₄	—	2	1	no	—
383	C₄	—	2	1	no	—
384	C₄	—	2	1	no	—
385	C₄	—	2	1	no	—
386	C₄	—	2	2	no	—
387	C₄	—	2	2	no	—
388	C₄	—	2	2	no	—
389	C₄	—	4	8	no	—
390	C₄	—	4	4	no	—
391	C₄	—	4	4	no	—
392	C₄	C₂×C₁₃×#104	1	4	yes	—
393	C₂	—	2	2	no	—
394	C₂	—	2	2	no	—
395	C₂	C₁₃×#1506	1	4	yes	direct product factor
396	C₂	C₂×C₁₃×#410	1	1	yes	characteristic
397	C₂	C₂×C₁₃×#419	1	1	yes	characteristic
398	C₂	C₂²×C₁₃×#104	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂⁴×C₁₃	C₂×D₄
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
4. C₁₃×#1506	C₂	direct (N × H)
8. C₁₃×#533	C₄	semidirect
10. C₂×C₁₃×C₄⋊Q₈	C₄	semidirect
11. C₂×C₁₃×C₄⋊Q₈	C₄	semidirect
16. C₂×C₄×Q₈×C₁₃	C₄	semidirect
39. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
40. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
52. C₄×Q₈×C₁₃	C₂×C₄	semidirect
80. C₂×#1506	C₁₃	direct (N × H)
135. #1506	C₂×C₁₃	direct (N × H)
179. #533	C₄×C₁₃	semidirect
181. C₂×C₄⋊Q₈	C₄×C₁₃	semidirect
182. C₂×C₄⋊Q₈	C₄×C₁₃	semidirect
187. C₂×C₄×Q₈	C₄×C₁₃	semidirect
232. C₄⋊Q₈	C₂×C₄×C₁₃	semidirect
233. C₄⋊Q₈	C₂×C₄×C₁₃	semidirect
245. C₄×Q₈	C₂×C₄×C₁₃	semidirect
275. C₂×C₁₃	#1506	direct (N × H)
330. C₁₃	C₂×#1506	direct (N × H)
395. C₂	C₁₃×#1506	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×#533	2
C₂×C₁₃×#432	2
C₂×C₁₃×#376	2
C₁₃×#1506	2
C₂×C₁₃×#328	2
C₂×#1506	13

Subgroups — C2×C13×#1506 #15703879

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#1506 #15703879