Subgroups — C₂×C₁₃×#1554 #15704051

Order 3328.

974 conjugacy classes of subgroups.

The subgroup lattice has 388 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×#431	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1554	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₁₃×#333	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#332	C₂	1	2	yes	maximal, complemented
7	C₁₃×#533	—	2	2	no	—
8	C₁₃×#533	—	2	2	no	—
9	C₁₃×#533	C₄	1	4	yes	—
10	C₁₃×#533	C₂²	1	4	yes	—
11	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#125	—	2	1	no	—
14	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
15	C₂×C₁₃×C₂²⋊Q₈	C₄	1	2	yes	—
16	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
17	C₂×C₄×Q₈×C₁₃	C₄	1	2	yes	—
18	C₂×C₁₃×#117	—	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	C₁₃×#431	—	2	2	no	—
23	C₁₃×#431	C₂²	1	4	yes	—
24	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
25	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
26	C₂×C₁₃×C₂²⋊C₈	—	2	1	no	—
27	C₂×C₁₃×C₂²⋊C₈	—	2	1	no	—
28	C₂×C₁₃×#97	—	2	1	no	—
29	C₂×C₄×C₈×C₁₃	—	2	1	no	—
30	C₁₃×#333	C₂²	1	8	yes	complemented
31	C₁₃×#332	C₂²	1	8	yes	complemented
32	C₂²×Q₈×C₁₃	—	2	1	no	—
33	C₂²×Q₈×C₁₃	C₂×C₄	1	2	yes	—
34	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
37	C₂²×C₈×C₁₃	—	2	2	no	—
38	C₂²×C₈×C₁₃	—	2	2	no	—
39	C₁₃×C₄⋊Q₈	—	2	1	no	—
40	C₁₃×C₄⋊Q₈	—	2	1	no	—
41	C₁₃×C₄⋊Q₈	—	2	1	no	—
42	C₁₃×C₄⋊Q₈	—	2	1	no	—
43	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
44	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
45	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
46	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
47	C₁₃×#125	—	2	4	no	—
48	C₁₃×#125	—	2	4	no	—
49	C₁₃×C₂²⋊Q₈	—	2	4	no	—
50	C₁₃×C₂²⋊Q₈	—	2	4	no	—
51	C₁₃×C₂²⋊Q₈	—	2	4	no	—
52	C₁₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
53	C₄×Q₈×C₁₃	—	2	4	no	—
54	C₄×Q₈×C₁₃	—	2	4	no	—
55	C₄×Q₈×C₁₃	—	2	4	no	—
56	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	—
57	C₁₃×#117	—	2	4	no	—
58	C₁₃×#117	—	2	4	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
64	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
65	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
66	C₂×C₄²×C₁₃	—	2	2	no	—
67	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₃	C₂×C₄	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	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	2	no	—
76	C₁₃×C₄⋊C₈	—	2	2	no	—
77	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
78	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
79	C₁₃×C₂²⋊C₈	—	2	4	no	—
80	C₁₃×C₂²⋊C₈	—	2	4	no	—
81	C₁₃×#97	—	2	4	no	—
82	C₄×C₈×C₁₃	—	2	4	no	—
83	C₂×#1554	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
84	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
85	C₂×Q₈×C₁₃	—	2	2	no	—
86	C₂×Q₈×C₁₃	—	2	2	no	—
87	C₂×Q₈×C₁₃	—	2	2	no	—
88	C₂×Q₈×C₁₃	—	4	4	no	—
89	C₂×Q₈×C₁₃	—	4	4	no	—
90	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
91	C₂²×C₄×C₁₃	—	2	4	no	—
92	C₂²×C₄×C₁₃	—	2	4	no	—
93	C₂²×C₄×C₁₃	—	2	2	no	—
94	C₂²×C₄×C₁₃	—	2	2	no	—
95	C₂²×C₄×C₁₃	—	4	2	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	2	yes	—
102	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
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	C₂×C₈×C₁₃	—	2	4	no	—
109	C₂×C₈×C₁₃	—	2	4	no	—
110	C₂×C₈×C₁₃	—	4	4	no	—
111	C₂×C₈×C₁₃	—	4	4	no	—
112	C₁₃×C₄⋊C₄	—	2	2	no	—
113	C₁₃×C₄⋊C₄	—	2	2	no	—
114	C₁₃×C₄⋊C₄	—	2	2	no	—
115	C₁₃×C₄⋊C₄	—	2	8	no	—
116	C₁₃×C₄⋊C₄	—	2	8	no	—
117	C₁₃×C₄⋊C₄	—	2	2	no	—
118	C₁₃×C₄⋊C₄	—	2	2	no	—
119	C₁₃×C₄⋊C₄	—	2	2	no	—
120	C₁₃×C₄⋊C₄	—	2	2	no	—
121	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
122	C₁₃×C₂²⋊C₄	—	2	8	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	1	yes	characteristic
129	C₄²×C₁₃	C₂×D₄	1	2	yes	—
130	C₄²×C₁₃	C₂×D₄	1	2	yes	—
131	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
134	C₂×#533	C₂×C₁₃	1	1	yes	characteristic
135	C₂×#432	C₂×C₁₃	1	1	yes	characteristic
136	C₂×#431	C₂×C₁₃	1	1	yes	characteristic
137	#1554	C₂×C₁₃	1	8	yes	direct product factor
138	C₂×#333	C₂×C₁₃	1	2	yes	complemented
139	C₂×#332	C₂×C₁₃	1	2	yes	complemented
140	C₂³×C₁₃	—	2	2	no	—
141	C₂³×C₁₃	—	2	2	no	—
142	C₂³×C₁₃	—	2	2	no	—
143	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
144	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
145	Q₈×C₁₃	—	4	4	no	—
146	Q₈×C₁₃	—	4	4	no	—
147	Q₈×C₁₃	—	4	4	no	—
148	Q₈×C₁₃	—	4	4	no	—
149	C₂×C₄×C₁₃	—	2	2	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	4	no	—
156	C₂×C₄×C₁₃	—	2	4	no	—
157	C₂×C₄×C₁₃	—	2	4	no	—
158	C₂×C₄×C₁₃	—	2	4	no	—
159	C₂×C₄×C₁₃	—	4	2	no	—
160	C₂×C₄×C₁₃	—	4	2	no	—
161	C₂×C₄×C₁₃	—	4	4	no	—
162	C₂×C₄×C₁₃	—	4	4	no	—
163	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
164	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
165	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
166	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₁₃	#135	1	4	yes	—
170	C₂×C₄×C₁₃	#137	1	4	yes	—
171	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
174	C₈×C₁₃	—	4	4	no	—
175	C₈×C₁₃	—	4	4	no	—
176	#533	—	2	2	no	—
177	#533	—	2	2	no	—
178	#533	C₄×C₁₃	1	4	yes	—
179	#533	C₂²×C₁₃	1	4	yes	—
180	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
181	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
182	C₂×#125	—	2	1	no	—
183	C₂×C₂²⋊Q₈	—	2	1	no	—
184	C₂×C₂²⋊Q₈	C₄×C₁₃	1	2	yes	—
185	C₂×C₄×Q₈	—	2	1	no	—
186	C₂×C₄×Q₈	C₄×C₁₃	1	2	yes	—
187	C₂×#117	—	2	1	no	—
188	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
189	#432	—	2	2	no	—
190	#432	C₂²×C₁₃	1	4	yes	—
191	#431	—	2	2	no	—
192	#431	C₂²×C₁₃	1	4	yes	—
193	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
194	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
195	C₂×C₂²⋊C₈	—	2	1	no	—
196	C₂×C₂²⋊C₈	—	2	1	no	—
197	C₂×#97	—	2	1	no	—
198	C₂×C₄×C₈	—	2	1	no	—
199	#333	C₂²×C₁₃	1	8	yes	complemented
200	#332	C₂²×C₁₃	1	8	yes	complemented
201	C₂²×C₁₃	—	2	2	no	—
202	C₂²×C₁₃	—	2	2	no	—
203	C₂²×C₁₃	—	2	2	no	—
204	C₂²×C₁₃	—	4	4	no	—
205	C₂²×C₁₃	#413	1	2	yes	—
206	C₂²×C₁₃	#416	1	2	yes	—
207	C₂²×C₁₃	#419	1	2	yes	—
208	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
209	C₄×C₁₃	—	2	2	no	—
210	C₄×C₁₃	—	2	1	no	—
211	C₄×C₁₃	—	2	1	no	—
212	C₄×C₁₃	—	2	2	no	—
213	C₄×C₁₃	—	2	2	no	—
214	C₄×C₁₃	—	4	4	no	—
215	C₄×C₁₃	—	4	4	no	—
216	C₄×C₁₃	#416	1	2	yes	—
217	C₄×C₁₃	#419	1	2	yes	—
218	C₄×C₁₃	C₂×#135	1	2	yes	—
219	C₄×C₁₃	C₂×#137	1	2	yes	—
220	C₂²×Q₈	—	2	1	no	—
221	C₂²×Q₈	C₂×C₄×C₁₃	1	2	yes	—
222	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
223	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
224	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
225	C₂²×C₈	—	2	2	no	—
226	C₂²×C₈	—	2	2	no	—
227	C₄⋊Q₈	—	2	1	no	—
228	C₄⋊Q₈	—	2	1	no	—
229	C₄⋊Q₈	—	2	1	no	—
230	C₄⋊Q₈	—	2	1	no	—
231	C₄⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
232	C₄⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
233	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
234	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
235	#125	—	2	4	no	—
236	#125	—	2	4	no	—
237	C₂²⋊Q₈	—	2	4	no	—
238	C₂²⋊Q₈	—	2	4	no	—
239	C₂²⋊Q₈	—	2	4	no	—
240	C₂²⋊Q₈	C₂×C₄×C₁₃	1	8	yes	—
241	C₄×Q₈	—	2	4	no	—
242	C₄×Q₈	—	2	4	no	—
243	C₄×Q₈	—	2	4	no	—
244	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	—
245	#117	—	2	4	no	—
246	#117	—	2	4	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	—	2	1	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
253	C₂×C₂²⋊C₄	—	2	2	no	—
254	C₂×C₄²	—	2	2	no	—
255	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
256	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
257	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
258	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
259	C₂×C₄²	D₄×C₁₃	1	2	yes	—
260	C₂×C₄²	D₄×C₁₃	1	2	yes	—
261	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
262	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
263	C₄⋊C₈	—	2	2	no	—
264	C₄⋊C₈	—	2	2	no	—
265	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
266	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
267	C₂²⋊C₈	—	2	4	no	—
268	C₂²⋊C₈	—	2	4	no	—
269	#97	—	2	4	no	—
270	C₄×C₈	—	2	4	no	—
271	C₂×C₁₃	—	4	2	no	—
272	C₂×C₁₃	#1554	1	4	yes	direct product factor
273	C₂×C₁₃	C₂×#413	1	1	yes	characteristic
274	C₂×C₁₃	C₂×#416	1	1	yes	characteristic
275	C₂×C₁₃	C₂×#419	1	1	yes	characteristic
276	C₂⁴	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
277	C₂×Q₈	—	2	2	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	—	4	4	no	—
281	C₂×Q₈	—	4	4	no	—
282	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	4	2	no	—
288	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
289	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
290	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
291	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
292	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
293	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
294	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
295	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
296	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
297	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
298	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
299	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
300	C₂×C₈	—	2	4	no	—
301	C₂×C₈	—	2	4	no	—
302	C₂×C₈	—	4	4	no	—
303	C₂×C₈	—	4	4	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	8	no	—
308	C₄⋊C₄	—	2	8	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
314	C₂²⋊C₄	—	2	8	no	—
315	C₄²	—	2	8	no	—
316	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
317	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
318	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
319	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
320	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
321	C₄²	C₂×D₄×C₁₃	1	2	yes	—
322	C₄²	C₂×D₄×C₁₃	1	2	yes	—
323	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
324	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
325	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
326	C₁₃	C₂×#1554	1	1	yes	characteristic, direct product factor, Sylow
327	C₂³	—	2	2	no	—
328	C₂³	—	2	2	no	—
329	C₂³	—	2	2	no	—
330	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
331	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
332	Q₈	—	4	4	no	—
333	Q₈	—	4	4	no	—
334	Q₈	—	4	4	no	—
335	Q₈	—	4	4	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	—	4	4	no	—
350	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
351	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
352	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
353	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
354	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
355	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
356	C₂×C₄	C₁₃×#135	1	4	yes	—
357	C₂×C₄	C₁₃×#137	1	4	yes	—
358	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
359	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
360	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
361	C₈	—	4	4	no	—
362	C₈	—	4	4	no	—
363	C₂²	—	2	2	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	4	4	no	—
367	C₂²	C₁₃×#413	1	2	yes	—
368	C₂²	C₁₃×#416	1	2	yes	—
369	C₂²	C₁₃×#419	1	2	yes	—
370	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
371	C₄	—	2	2	no	—
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	2	no	—
375	C₄	—	2	2	no	—
376	C₄	—	4	4	no	—
377	C₄	—	4	4	no	—
378	C₄	C₁₃×#416	1	2	yes	—
379	C₄	C₁₃×#419	1	2	yes	—
380	C₄	C₂×C₁₃×#135	1	2	yes	—
381	C₄	C₂×C₁₃×#137	1	2	yes	—
382	C₂	—	4	2	no	—
383	C₂	C₁₃×#1554	1	4	yes	direct product factor
384	C₂	C₂×C₁₃×#413	1	1	yes	characteristic
385	C₂	C₂×C₁₃×#416	1	1	yes	characteristic
386	C₂	C₂×C₁₃×#419	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	C₂⁴×C₁₃	C₂²⋊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
4. C₁₃×#1554	C₂	direct (N × H)
5. C₂×C₁₃×#333	C₂	semidirect
6. C₂×C₁₃×#332	C₂	semidirect
30. C₁₃×#333	C₂²	semidirect
31. C₁₃×#332	C₂²	semidirect
83. C₂×#1554	C₁₃	direct (N × H)
137. #1554	C₂×C₁₃	direct (N × H)
138. C₂×#333	C₂×C₁₃	semidirect
139. C₂×#332	C₂×C₁₃	semidirect
199. #333	C₂²×C₁₃	semidirect
200. #332	C₂²×C₁₃	semidirect
272. C₂×C₁₃	#1554	direct (N × H)
326. C₁₃	C₂×#1554	direct (N × H)
383. C₂	C₁₃×#1554	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×#431	2
C₁₃×#1554	2
C₂×C₁₃×#333	2
C₂×C₁₃×#332	2
C₂×#1554	13

Subgroups — C2×C13×#1554 #15704051

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#1554 #15704051