Subgroups — C₂×C₁₃×#3229 #15747178

Order 3328.

2006 conjugacy classes of subgroups.

The subgroup lattice has 408 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	C₂²×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3229	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#498	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#487	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#483	C₂	1	4	yes	maximal
7	C₂×C₁₃×#475	C₂	1	4	yes	maximal, complemented
8	C₂×C₁₃×#431	C₂	1	1	yes	maximal, characteristic
9	C₂³×Q₈×C₁₃	—	2	1	no	—
10	C₁₃×#533	—	2	4	no	—
11	C₁₃×#533	C₂²	1	8	yes	—
12	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
13	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
14	C₂×C₁₃×C₄⋊Q₈	—	2	4	no	—
15	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₄⋊Q₈	C₂²	1	8	yes	—
20	C₂×C₁₃×#125	—	2	1	no	—
21	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
22	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
24	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
25	C₂×C₁₃×#117	—	2	1	no	—
26	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
27	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
28	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#498	C₂²	1	16	yes	complemented
30	C₁₃×#487	C₂²	1	16	yes	complemented
31	C₁₃×#483	C₂²	1	32	yes	—
32	C₁₃×#475	C₂²	1	32	yes	complemented
33	C₁₃×#431	C₂²	1	8	yes	—
34	C₂×C₁₃×#106	C₂²	1	8	yes	—
35	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
36	C₂×C₁₃×#103	C₂²	1	8	yes	—
37	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
38	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
39	C₂²×Q₈×C₁₃	—	2	1	no	—
40	C₂²×Q₈×C₁₃	—	2	8	no	—
41	C₂²×Q₈×C₁₃	—	2	2	no	—
42	C₂²×Q₈×C₁₃	—	2	2	no	—
43	C₂²×Q₈×C₁₃	—	4	8	no	—
44	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₃	—	2	2	no	—
46	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
50	C₁₃×C₄⋊Q₈	—	2	4	no	—
51	C₁₃×C₄⋊Q₈	—	2	8	no	—
52	C₁₃×C₄⋊Q₈	—	2	8	no	—
53	C₁₃×C₄⋊Q₈	—	2	4	no	—
54	C₁₃×C₄⋊Q₈	—	2	2	no	—
55	C₁₃×C₄⋊Q₈	—	2	2	no	—
56	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
57	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
58	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
59	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
60	C₁₃×#125	—	2	8	no	—
61	C₁₃×C₂²⋊Q₈	—	2	8	no	—
62	C₁₃×C₂²⋊Q₈	—	2	4	no	—
63	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
64	C₄×Q₈×C₁₃	—	2	8	no	—
65	C₄×Q₈×C₁₃	—	2	4	no	—
66	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
67	C₁₃×#117	—	2	8	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
73	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
81	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
82	C₂×C₄²×C₁₃	—	2	2	no	—
83	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
84	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
85	C₂×C₄²×C₁₃	D₄	1	4	yes	—
86	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
89	C₁₃×#106	C₂³	1	32	yes	—
90	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
91	C₁₃×#103	C₂³	1	32	yes	—
92	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
93	C₄×C₈×C₁₃	C₂³	1	8	yes	—
94	C₂×#3229	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
95	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
96	C₂×Q₈×C₁₃	—	2	2	no	—
97	C₂×Q₈×C₁₃	—	2	4	no	—
98	C₂×Q₈×C₁₃	—	2	8	no	—
99	C₂×Q₈×C₁₃	—	2	8	no	—
100	C₂×Q₈×C₁₃	—	2	8	no	—
101	C₂×Q₈×C₁₃	—	4	32	no	—
102	C₂×Q₈×C₁₃	—	4	8	no	—
103	C₂×Q₈×C₁₃	—	4	8	no	—
104	C₂×Q₈×C₁₃	—	4	4	no	—
105	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
106	C₂²×C₄×C₁₃	—	2	4	no	—
107	C₂²×C₄×C₁₃	—	2	4	no	—
108	C₂²×C₄×C₁₃	—	2	8	no	—
109	C₂²×C₄×C₁₃	—	2	2	no	—
110	C₂²×C₄×C₁₃	—	2	2	no	—
111	C₂²×C₄×C₁₃	—	2	4	no	—
112	C₂²×C₄×C₁₃	—	4	8	no	—
113	C₂²×C₄×C₁₃	SD₁₆	1	8	yes	—
114	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
116	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
119	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
123	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
124	C₂×C₈×C₁₃	—	2	8	no	—
125	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
126	C₁₃×C₄⋊C₄	—	2	8	no	—
127	C₁₃×C₄⋊C₄	—	2	8	no	—
128	C₁₃×C₄⋊C₄	—	2	8	no	—
129	C₁₃×C₄⋊C₄	—	2	4	no	—
130	C₁₃×C₄⋊C₄	—	2	4	no	—
131	C₁₃×C₄⋊C₄	—	2	4	no	—
132	C₁₃×C₄⋊C₄	—	2	4	no	—
133	C₁₃×C₄⋊C₄	—	2	8	no	—
134	C₁₃×C₄⋊C₄	—	2	8	no	—
135	C₁₃×C₄⋊C₄	—	2	2	no	—
136	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
137	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
138	C₁₃×C₂²⋊C₄	—	2	8	no	—
139	C₄²×C₁₃	—	2	8	no	—
140	C₄²×C₁₃	C₂×D₄	1	4	yes	—
141	C₄²×C₁₃	C₂×D₄	1	2	yes	—
142	C₄²×C₁₃	C₂×D₄	1	4	yes	—
143	C₄²×C₁₃	C₂×D₄	1	2	yes	—
144	C₄²×C₁₃	C₂⁴	1	2	yes	—
145	C₄²×C₁₃	C₂⁴	1	2	yes	—
146	C₂×#533	C₂×C₁₃	1	1	yes	characteristic
147	C₂²×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic
148	#3229	C₂×C₁₃	1	16	yes	direct product factor
149	C₂×#498	C₂×C₁₃	1	2	yes	complemented
150	C₂×#487	C₂×C₁₃	1	2	yes	complemented
151	C₂×#483	C₂×C₁₃	1	4	yes	—
152	C₂×#475	C₂×C₁₃	1	4	yes	complemented
153	C₂×#431	C₂×C₁₃	1	1	yes	characteristic
154	C₂³×C₁₃	—	2	2	no	—
155	C₂³×C₁₃	—	2	2	no	—
156	C₂³×C₁₃	C₂×SD₁₆	1	4	yes	—
157	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
158	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
159	Q₈×C₁₃	—	2	8	no	—
160	Q₈×C₁₃	—	4	4	no	—
161	Q₈×C₁₃	—	4	16	no	—
162	Q₈×C₁₃	—	4	16	no	—
163	Q₈×C₁₃	—	4	8	no	—
164	C₂×C₄×C₁₃	—	2	2	no	—
165	C₂×C₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	—	2	4	no	—
167	C₂×C₄×C₁₃	—	2	8	no	—
168	C₂×C₄×C₁₃	—	2	4	no	—
169	C₂×C₄×C₁₃	—	2	4	no	—
170	C₂×C₄×C₁₃	—	2	4	no	—
171	C₂×C₄×C₁₃	—	2	8	no	—
172	C₂×C₄×C₁₃	—	4	4	no	—
173	C₂×C₄×C₁₃	—	4	16	no	—
174	C₂×C₄×C₁₃	—	4	8	no	—
175	C₂×C₄×C₁₃	—	4	4	no	—
176	C₂×C₄×C₁₃	C₂×SD₁₆	1	16	yes	—
177	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	—
178	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	—
179	C₂×C₄×C₁₃	#137	1	4	yes	—
180	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
181	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
182	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
184	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
185	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
186	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
187	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
188	C₈×C₁₃	—	2	8	no	—
189	C₂³×Q₈	—	2	1	no	—
190	#533	—	2	4	no	—
191	#533	C₂²×C₁₃	1	8	yes	—
192	C₂×C₄⋊Q₈	—	2	1	no	—
193	C₂×C₄⋊Q₈	—	2	1	no	—
194	C₂×C₄⋊Q₈	—	2	4	no	—
195	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
196	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
197	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
198	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
199	C₂×C₄⋊Q₈	C₂²×C₁₃	1	8	yes	—
200	C₂×#125	—	2	1	no	—
201	C₂×C₂²⋊Q₈	—	2	1	no	—
202	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
203	C₂×C₄×Q₈	—	2	1	no	—
204	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
205	C₂×#117	—	2	1	no	—
206	C₂²×C₄⋊C₄	—	2	1	no	—
207	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
208	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
209	#498	C₂²×C₁₃	1	16	yes	complemented
210	#487	C₂²×C₁₃	1	16	yes	complemented
211	#483	C₂²×C₁₃	1	32	yes	—
212	#475	C₂²×C₁₃	1	32	yes	complemented
213	#431	C₂²×C₁₃	1	8	yes	—
214	C₂×#106	C₂²×C₁₃	1	8	yes	—
215	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
216	C₂×#103	C₂²×C₁₃	1	8	yes	—
217	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
218	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
219	C₂²×C₁₃	—	2	2	no	—
220	C₂²×C₁₃	—	2	8	no	—
221	C₂²×C₁₃	—	2	2	no	—
222	C₂²×C₁₃	#536	1	2	yes	—
223	C₂²×C₁₃	C₂²×SD₁₆	1	4	yes	—
224	C₂²×C₁₃	C₂²×SD₁₆	1	2	yes	—
225	C₂²×C₁₃	C₂×#137	1	2	yes	—
226	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
227	C₄×C₁₃	—	2	2	no	—
228	C₄×C₁₃	—	2	2	no	—
229	C₄×C₁₃	—	4	4	no	—
230	C₄×C₁₃	—	4	8	no	—
231	C₄×C₁₃	—	4	4	no	—
232	C₄×C₁₃	#536	1	2	yes	—
233	C₄×C₁₃	C₂²×SD₁₆	1	4	yes	—
234	C₄×C₁₃	C₂²×SD₁₆	1	4	yes	—
235	C₄×C₁₃	C₂×#137	1	4	yes	—
236	C₄×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
237	C₂²×Q₈	—	2	1	no	—
238	C₂²×Q₈	—	2	2	no	—
239	C₂²×Q₈	—	2	2	no	—
240	C₂²×Q₈	—	2	8	no	—
241	C₂²×Q₈	—	4	8	no	—
242	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
243	C₂³×C₄	—	2	2	no	—
244	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
245	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
246	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
247	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
248	C₄⋊Q₈	—	2	4	no	—
249	C₄⋊Q₈	—	2	8	no	—
250	C₄⋊Q₈	—	2	8	no	—
251	C₄⋊Q₈	—	2	4	no	—
252	C₄⋊Q₈	—	2	2	no	—
253	C₄⋊Q₈	—	2	2	no	—
254	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
255	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
256	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
257	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
258	#125	—	2	8	no	—
259	C₂²⋊Q₈	—	2	8	no	—
260	C₂²⋊Q₈	—	2	4	no	—
261	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
262	C₄×Q₈	—	2	8	no	—
263	C₄×Q₈	—	2	4	no	—
264	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
265	#117	—	2	8	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	8	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	—	2	4	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	—	2	2	no	—
275	C₂×C₄⋊C₄	—	2	2	no	—
276	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
277	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
278	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
279	C₂×C₂²⋊C₄	—	2	2	no	—
280	C₂×C₄²	—	2	2	no	—
281	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
282	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
283	C₂×C₄²	D₄×C₁₃	1	4	yes	—
284	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
285	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
286	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
287	#106	C₂³×C₁₃	1	32	yes	—
288	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
289	#103	C₂³×C₁₃	1	32	yes	—
290	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
291	C₄×C₈	C₂³×C₁₃	1	8	yes	—
292	C₂×C₁₃	—	2	4	no	—
293	C₂×C₁₃	#3229	1	4	yes	direct product factor
294	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
295	C₂×C₁₃	C₂³×SD₁₆	1	1	yes	characteristic
296	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
297	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	—	2	4	no	—
300	C₂×Q₈	—	2	8	no	—
301	C₂×Q₈	—	2	8	no	—
302	C₂×Q₈	—	2	8	no	—
303	C₂×Q₈	—	4	32	no	—
304	C₂×Q₈	—	4	8	no	—
305	C₂×Q₈	—	4	8	no	—
306	C₂×Q₈	—	4	4	no	—
307	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	8	no	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	4	8	no	—
315	C₂²×C₄	C₁₃×SD₁₆	1	8	yes	—
316	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
317	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
318	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
320	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
322	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
323	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
324	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
325	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
326	C₂×C₈	—	2	8	no	—
327	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
328	C₄⋊C₄	—	2	8	no	—
329	C₄⋊C₄	—	2	8	no	—
330	C₄⋊C₄	—	2	8	no	—
331	C₄⋊C₄	—	2	4	no	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	—	2	4	no	—
335	C₄⋊C₄	—	2	8	no	—
336	C₄⋊C₄	—	2	8	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
339	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
340	C₂²⋊C₄	—	2	8	no	—
341	C₄²	—	2	8	no	—
342	C₄²	C₂×D₄×C₁₃	1	4	yes	—
343	C₄²	C₂×D₄×C₁₃	1	2	yes	—
344	C₄²	C₂×D₄×C₁₃	1	4	yes	—
345	C₄²	C₂×D₄×C₁₃	1	2	yes	—
346	C₄²	C₂⁴×C₁₃	1	2	yes	—
347	C₄²	C₂⁴×C₁₃	1	2	yes	—
348	C₁₃	C₂×#3229	1	1	yes	characteristic, direct product factor, Sylow
349	C₂³	—	2	2	no	—
350	C₂³	—	2	2	no	—
351	C₂³	C₂×C₁₃×SD₁₆	1	4	yes	—
352	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
353	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
354	Q₈	—	2	8	no	—
355	Q₈	—	4	4	no	—
356	Q₈	—	4	16	no	—
357	Q₈	—	4	16	no	—
358	Q₈	—	4	8	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	8	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	8	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	4	16	no	—
369	C₂×C₄	—	4	8	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	C₂×C₁₃×SD₁₆	1	16	yes	—
372	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	—
373	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	—
374	C₂×C₄	C₁₃×#137	1	4	yes	—
375	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
376	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
377	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
378	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
379	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
380	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
381	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
382	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
383	C₈	—	2	8	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	8	no	—
387	C₂²	C₁₃×#536	1	2	yes	—
388	C₂²	C₂²×C₁₃×SD₁₆	1	4	yes	—
389	C₂²	C₂²×C₁₃×SD₁₆	1	2	yes	—
390	C₂²	C₂×C₁₃×#137	1	2	yes	—
391	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
392	C₄	—	2	2	no	—
393	C₄	—	2	2	no	—
394	C₄	—	4	8	no	—
395	C₄	—	4	4	no	—
396	C₄	—	4	4	no	—
397	C₄	C₁₃×#536	1	2	yes	—
398	C₄	C₂²×C₁₃×SD₁₆	1	4	yes	—
399	C₄	C₂²×C₁₃×SD₁₆	1	4	yes	—
400	C₄	C₂×C₁₃×#137	1	4	yes	—
401	C₄	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
402	C₂	—	2	4	no	—
403	C₂	C₁₃×#3229	1	4	yes	direct product factor
404	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
405	C₂	C₂³×C₁₃×SD₁₆	1	1	yes	characteristic
406	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂⁴×C₁₃	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ 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
3. C₁₃×#3229	C₂	direct (N × H)
4. C₂×C₁₃×#498	C₂	semidirect
5. C₂×C₁₃×#487	C₂	semidirect
7. C₂×C₁₃×#475	C₂	semidirect
29. C₁₃×#498	C₂²	semidirect
30. C₁₃×#487	C₂²	semidirect
32. C₁₃×#475	C₂²	semidirect
94. C₂×#3229	C₁₃	direct (N × H)
148. #3229	C₂×C₁₃	direct (N × H)
149. C₂×#498	C₂×C₁₃	semidirect
150. C₂×#487	C₂×C₁₃	semidirect
152. C₂×#475	C₂×C₁₃	semidirect
209. #498	C₂²×C₁₃	semidirect
210. #487	C₂²×C₁₃	semidirect
212. #475	C₂²×C₁₃	semidirect
293. C₂×C₁₃	#3229	direct (N × H)
348. C₁₃	C₂×#3229	direct (N × H)
403. C₂	C₁₃×#3229	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
C₂²×C₁₃×C₄⋊Q₈	2
C₁₃×#3229	2
C₂×C₁₃×#498	2
C₂×C₁₃×#487	2
C₂×C₁₃×#483	2
C₂×C₁₃×#475	2
C₂×C₁₃×#431	2
C₂×#3229	13

Subgroups — C2×C13×#3229 #15747178

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3229 #15747178