Subgroups — C₂×C₁₃×#3227 #15747180

Order 3328.

2286 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3227	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#498	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#486	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#481	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₃×#476	C₂	1	4	yes	maximal, complemented
8	C₂×C₁₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₃×#41	—	2	1	no	—
10	C₂³×Q₈×C₁₃	—	2	1	no	—
11	C₁₃×#532	—	2	4	no	—
12	C₁₃×#532	C₂²	1	8	yes	—
13	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
14	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
15	C₂×C₁₃×C₄⋊Q₈	—	2	4	no	—
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	complemented
20	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#124	—	2	1	no	—
22	C₂×C₁₃×#121	—	2	1	no	—
23	C₂×C₁₃×#121	C₂²	1	2	yes	—
24	C₂×C₄×D₄×C₁₃	—	2	1	no	—
25	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
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×#486	C₂²	1	16	yes	complemented
31	C₁₃×#481	C₂²	1	32	yes	complemented
32	C₁₃×#476	C₂²	1	32	yes	complemented
33	C₁₃×#431	C₂²	1	8	yes	complemented
34	C₂×C₁₃×#106	C₂²	1	8	yes	—
35	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
36	C₂×C₁₃×#102	C₂²	1	8	yes	—
37	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
38	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
39	C₂×C₁₃×#41	—	2	8	no	—
40	C₂×C₁₃×#41	—	4	8	no	—
41	C₂²×Q₈×C₁₃	—	2	1	no	—
42	C₂²×Q₈×C₁₃	—	2	2	no	—
43	C₂²×Q₈×C₁₃	—	2	2	no	—
44	C₂²×Q₈×C₁₃	—	2	8	no	—
45	C₂²×Q₈×C₁₃	—	4	8	no	—
46	C₂²×D₄×C₁₃	—	2	2	no	—
47	C₂²×D₄×C₁₃	—	2	1	no	—
48	C₂²×D₄×C₁₃	—	2	1	no	—
49	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
50	C₂³×C₄×C₁₃	—	2	2	no	—
51	C₂³×C₄×C₁₃	—	2	2	no	—
52	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
53	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
54	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
56	C₁₃×C₄⋊Q₈	—	2	4	no	—
57	C₁₃×C₄⋊Q₈	—	2	4	no	—
58	C₁₃×C₄⋊Q₈	—	2	8	no	—
59	C₁₃×C₄⋊Q₈	—	2	8	no	—
60	C₁₃×C₄⋊Q₈	—	2	2	no	—
61	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
62	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
63	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
64	C₁₃×#127	—	2	2	no	—
65	C₁₃×#127	C₂³	1	4	yes	—
66	C₁₃×#124	—	2	8	no	—
67	C₁₃×#121	—	2	8	no	—
68	C₁₃×#121	—	2	4	no	—
69	C₁₃×#121	C₂³	1	8	yes	—
70	C₄×D₄×C₁₃	—	2	8	no	—
71	C₄×D₄×C₁₃	—	2	4	no	—
72	C₄×D₄×C₁₃	C₂³	1	8	yes	—
73	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
78	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
82	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
83	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
84	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
85	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₁₃	D₄	1	4	yes	—
87	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
90	C₁₃×#106	C₂³	1	32	yes	—
91	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
92	C₁₃×#102	C₂³	1	32	yes	—
93	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
94	C₄×C₈×C₁₃	C₂³	1	8	yes	—
95	C₂×#3227	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₂⁴×C₁₃	—	2	2	no	—
97	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
98	C₁₃×#41	—	4	32	no	—
99	C₂×Q₈×C₁₃	—	2	4	no	—
100	C₂×Q₈×C₁₃	—	2	8	no	—
101	C₂×Q₈×C₁₃	—	2	8	no	—
102	C₂×Q₈×C₁₃	—	4	8	no	—
103	C₂×Q₈×C₁₃	—	4	32	no	—
104	C₂×Q₈×C₁₃	—	4	4	no	—
105	C₂×Q₈×C₁₃	—	4	8	no	—
106	C₂×D₄×C₁₃	—	2	8	no	—
107	C₂×D₄×C₁₃	—	2	2	no	—
108	C₂×D₄×C₁₃	—	2	4	no	—
109	C₂×D₄×C₁₃	—	2	4	no	—
110	C₂×D₄×C₁₃	—	2	8	no	—
111	C₂×D₄×C₁₃	—	4	8	no	—
112	C₂×D₄×C₁₃	—	4	4	no	—
113	C₂×D₄×C₁₃	—	4	4	no	—
114	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
115	C₂²×C₄×C₁₃	—	2	4	no	—
116	C₂²×C₄×C₁₃	—	2	4	no	—
117	C₂²×C₄×C₁₃	—	2	8	no	—
118	C₂²×C₄×C₁₃	—	2	2	no	—
119	C₂²×C₄×C₁₃	—	2	4	no	—
120	C₂²×C₄×C₁₃	—	2	8	no	—
121	C₂²×C₄×C₁₃	—	4	8	no	—
122	C₂²×C₄×C₁₃	—	4	8	no	—
123	C₂²×C₄×C₁₃	SD₁₆	1	8	yes	—
124	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
126	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
129	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
133	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
134	C₂×C₈×C₁₃	—	2	8	no	—
135	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
136	C₁₃×C₄⋊C₄	—	2	8	no	—
137	C₁₃×C₄⋊C₄	—	2	8	no	—
138	C₁₃×C₄⋊C₄	—	2	8	no	—
139	C₁₃×C₄⋊C₄	—	2	4	no	—
140	C₁₃×C₄⋊C₄	—	2	4	no	—
141	C₁₃×C₄⋊C₄	—	2	2	no	—
142	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
143	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
144	C₁₃×C₂²⋊C₄	—	2	8	no	—
145	C₁₃×C₂²⋊C₄	—	2	8	no	—
146	C₄²×C₁₃	C₂×D₄	1	4	yes	—
147	C₄²×C₁₃	C₂×D₄	1	2	yes	—
148	C₄²×C₁₃	C₂×D₄	1	4	yes	—
149	C₄²×C₁₃	C₂×D₄	1	2	yes	—
150	C₄²×C₁₃	C₂⁴	1	2	yes	—
151	C₄²×C₁₃	C₂⁴	1	2	yes	—
152	C₂×#532	C₂×C₁₃	1	1	yes	characteristic
153	C₂²×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
154	#3227	C₂×C₁₃	1	16	yes	direct product factor
155	C₂×#498	C₂×C₁₃	1	2	yes	complemented
156	C₂×#486	C₂×C₁₃	1	2	yes	complemented
157	C₂×#481	C₂×C₁₃	1	4	yes	complemented
158	C₂×#476	C₂×C₁₃	1	4	yes	complemented
159	C₂×#431	C₂×C₁₃	1	1	yes	characteristic, complemented
160	C₂³×C₁₃	—	2	2	no	—
161	C₂³×C₁₃	—	2	2	no	—
162	C₂³×C₁₃	—	2	4	no	—
163	C₂³×C₁₃	—	4	4	no	—
164	C₂³×C₁₃	—	4	4	no	—
165	C₂³×C₁₃	—	4	4	no	—
166	C₂³×C₁₃	C₂×SD₁₆	1	4	yes	—
167	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
168	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
169	Q₈×C₁₃	—	4	16	no	—
170	Q₈×C₁₃	—	4	8	no	—
171	Q₈×C₁₃	—	4	16	no	—
172	D₄×C₁₃	—	2	8	no	—
173	D₄×C₁₃	—	4	16	no	—
174	D₄×C₁₃	—	4	4	no	—
175	D₄×C₁₃	—	4	8	no	—
176	D₄×C₁₃	—	4	8	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	4	no	—
180	C₂×C₄×C₁₃	—	2	8	no	—
181	C₂×C₄×C₁₃	—	2	4	no	—
182	C₂×C₄×C₁₃	—	2	4	no	—
183	C₂×C₄×C₁₃	—	2	8	no	—
184	C₂×C₄×C₁₃	—	4	16	no	—
185	C₂×C₄×C₁₃	—	4	4	no	—
186	C₂×C₄×C₁₃	—	4	8	no	—
187	C₂×C₄×C₁₃	—	4	16	no	—
188	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	—
189	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	—
190	C₂×C₄×C₁₃	C₂×SD₁₆	1	16	yes	—
191	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
192	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
193	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
194	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
196	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
197	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
198	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
199	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
200	C₈×C₁₃	—	2	8	no	—
201	C₂²×#41	—	2	1	no	—
202	C₂³×Q₈	—	2	1	no	—
203	#532	—	2	4	no	—
204	#532	C₂²×C₁₃	1	8	yes	—
205	C₂×C₄⋊Q₈	—	2	1	no	—
206	C₂×C₄⋊Q₈	—	2	1	no	—
207	C₂×C₄⋊Q₈	—	2	4	no	—
208	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
209	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
210	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
211	C₂×C₄⋊Q₈	C₂²×C₁₃	1	8	yes	complemented
212	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
213	C₂×#124	—	2	1	no	—
214	C₂×#121	—	2	1	no	—
215	C₂×#121	C₂²×C₁₃	1	2	yes	—
216	C₂×C₄×D₄	—	2	1	no	—
217	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
218	C₂²×C₄⋊C₄	—	2	1	no	—
219	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
220	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
221	#498	C₂²×C₁₃	1	16	yes	complemented
222	#486	C₂²×C₁₃	1	16	yes	complemented
223	#481	C₂²×C₁₃	1	32	yes	complemented
224	#476	C₂²×C₁₃	1	32	yes	complemented
225	#431	C₂²×C₁₃	1	8	yes	complemented
226	C₂×#106	C₂²×C₁₃	1	8	yes	—
227	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
228	C₂×#102	C₂²×C₁₃	1	8	yes	—
229	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
230	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
231	C₂²×C₁₃	—	2	2	no	—
232	C₂²×C₁₃	—	2	8	no	—
233	C₂²×C₁₃	—	2	2	no	—
234	C₂²×C₁₃	—	4	4	no	—
235	C₂²×C₁₃	—	4	4	no	—
236	C₂²×C₁₃	—	4	4	no	—
237	C₂²×C₁₃	—	8	8	no	—
238	C₂²×C₁₃	#536	1	2	yes	—
239	C₂²×C₁₃	C₂²×SD₁₆	1	4	yes	—
240	C₂²×C₁₃	C₂²×SD₁₆	1	2	yes	—
241	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
242	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
243	C₄×C₁₃	—	2	2	no	—
244	C₄×C₁₃	—	2	2	no	—
245	C₄×C₁₃	—	4	4	no	—
246	C₄×C₁₃	—	4	8	no	—
247	C₄×C₁₃	#536	1	2	yes	—
248	C₄×C₁₃	C₂²×SD₁₆	1	4	yes	—
249	C₄×C₁₃	C₂²×SD₁₆	1	4	yes	—
250	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
251	C₄×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
252	C₂×#41	—	2	8	no	—
253	C₂×#41	—	4	8	no	—
254	C₂²×Q₈	—	2	1	no	—
255	C₂²×Q₈	—	2	2	no	—
256	C₂²×Q₈	—	2	2	no	—
257	C₂²×Q₈	—	2	8	no	—
258	C₂²×Q₈	—	4	8	no	—
259	C₂²×D₄	—	2	2	no	—
260	C₂²×D₄	—	2	1	no	—
261	C₂²×D₄	—	2	1	no	—
262	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
263	C₂³×C₄	—	2	2	no	—
264	C₂³×C₄	—	2	2	no	—
265	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
266	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
267	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
268	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
269	C₄⋊Q₈	—	2	4	no	—
270	C₄⋊Q₈	—	2	4	no	—
271	C₄⋊Q₈	—	2	8	no	—
272	C₄⋊Q₈	—	2	8	no	—
273	C₄⋊Q₈	—	2	2	no	—
274	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
275	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
276	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
277	#127	—	2	2	no	—
278	#127	C₂³×C₁₃	1	4	yes	—
279	#124	—	2	8	no	—
280	#121	—	2	8	no	—
281	#121	—	2	4	no	—
282	#121	C₂³×C₁₃	1	8	yes	—
283	C₄×D₄	—	2	8	no	—
284	C₄×D₄	—	2	4	no	—
285	C₄×D₄	C₂³×C₁₃	1	8	yes	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	8	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	4	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
293	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
294	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
295	C₂×C₂²⋊C₄	—	2	2	no	—
296	C₂×C₂²⋊C₄	—	2	2	no	—
297	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
298	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
299	C₂×C₄²	D₄×C₁₃	1	4	yes	—
300	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
301	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
302	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
303	#106	C₂³×C₁₃	1	32	yes	—
304	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
305	#102	C₂³×C₁₃	1	32	yes	—
306	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
307	C₄×C₈	C₂³×C₁₃	1	8	yes	—
308	C₂×C₁₃	—	2	4	no	—
309	C₂×C₁₃	—	8	4	no	—
310	C₂×C₁₃	#3227	1	4	yes	direct product factor
311	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
312	C₂×C₁₃	C₂³×SD₁₆	1	1	yes	characteristic
313	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
314	C₂⁴	—	2	2	no	—
315	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
316	#41	—	4	32	no	—
317	C₂×Q₈	—	2	4	no	—
318	C₂×Q₈	—	2	8	no	—
319	C₂×Q₈	—	2	8	no	—
320	C₂×Q₈	—	4	8	no	—
321	C₂×Q₈	—	4	32	no	—
322	C₂×Q₈	—	4	4	no	—
323	C₂×Q₈	—	4	8	no	—
324	C₂×D₄	—	2	8	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	4	no	—
327	C₂×D₄	—	2	4	no	—
328	C₂×D₄	—	2	8	no	—
329	C₂×D₄	—	4	8	no	—
330	C₂×D₄	—	4	4	no	—
331	C₂×D₄	—	4	4	no	—
332	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	8	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	2	8	no	—
339	C₂²×C₄	—	4	8	no	—
340	C₂²×C₄	—	4	8	no	—
341	C₂²×C₄	C₁₃×SD₁₆	1	8	yes	—
342	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
344	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
345	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
346	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
347	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
348	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
349	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
350	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
351	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
352	C₂×C₈	—	2	8	no	—
353	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
354	C₄⋊C₄	—	2	8	no	—
355	C₄⋊C₄	—	2	8	no	—
356	C₄⋊C₄	—	2	8	no	—
357	C₄⋊C₄	—	2	4	no	—
358	C₄⋊C₄	—	2	4	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
361	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
362	C₂²⋊C₄	—	2	8	no	—
363	C₂²⋊C₄	—	2	8	no	—
364	C₄²	C₂×D₄×C₁₃	1	4	yes	—
365	C₄²	C₂×D₄×C₁₃	1	2	yes	—
366	C₄²	C₂×D₄×C₁₃	1	4	yes	—
367	C₄²	C₂×D₄×C₁₃	1	2	yes	—
368	C₄²	C₂⁴×C₁₃	1	2	yes	—
369	C₄²	C₂⁴×C₁₃	1	2	yes	—
370	C₁₃	C₂×#3227	1	1	yes	characteristic, direct product factor, Sylow
371	C₂³	—	2	2	no	—
372	C₂³	—	2	2	no	—
373	C₂³	—	2	4	no	—
374	C₂³	—	4	4	no	—
375	C₂³	—	4	4	no	—
376	C₂³	—	4	4	no	—
377	C₂³	C₂×C₁₃×SD₁₆	1	4	yes	—
378	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
379	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
380	Q₈	—	4	16	no	—
381	Q₈	—	4	8	no	—
382	Q₈	—	4	16	no	—
383	D₄	—	2	8	no	—
384	D₄	—	4	16	no	—
385	D₄	—	4	4	no	—
386	D₄	—	4	8	no	—
387	D₄	—	4	8	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	8	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	8	no	—
395	C₂×C₄	—	4	16	no	—
396	C₂×C₄	—	4	4	no	—
397	C₂×C₄	—	4	8	no	—
398	C₂×C₄	—	4	16	no	—
399	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	—
400	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	—
401	C₂×C₄	C₂×C₁₃×SD₁₆	1	16	yes	—
402	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
403	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
404	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
405	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
406	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
407	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
408	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
409	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
410	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
411	C₈	—	2	8	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	2	2	no	—
414	C₂²	—	2	8	no	—
415	C₂²	—	4	4	no	—
416	C₂²	—	4	4	no	—
417	C₂²	—	4	4	no	—
418	C₂²	—	8	8	no	—
419	C₂²	C₁₃×#536	1	2	yes	—
420	C₂²	C₂²×C₁₃×SD₁₆	1	4	yes	—
421	C₂²	C₂²×C₁₃×SD₁₆	1	2	yes	—
422	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
423	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
424	C₄	—	2	2	no	—
425	C₄	—	2	2	no	—
426	C₄	—	4	4	no	—
427	C₄	—	4	8	no	—
428	C₄	C₁₃×#536	1	2	yes	—
429	C₄	C₂²×C₁₃×SD₁₆	1	4	yes	—
430	C₄	C₂²×C₁₃×SD₁₆	1	4	yes	—
431	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
432	C₄	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
433	C₂	—	2	4	no	—
434	C₂	—	8	4	no	—
435	C₂	C₁₃×#3227	1	4	yes	direct product factor
436	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
437	C₂	C₂³×C₁₃×SD₁₆	1	1	yes	characteristic
438	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#532	C₂
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
2. C₂²×C₁₃×C₄⋊Q₈	C₂	semidirect
3. C₁₃×#3227	C₂	direct (N × H)
4. C₂×C₁₃×#498	C₂	semidirect
5. C₂×C₁₃×#486	C₂	semidirect
6. C₂×C₁₃×#481	C₂	semidirect
7. C₂×C₁₃×#476	C₂	semidirect
8. C₂×C₁₃×#431	C₂	semidirect
19. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
29. C₁₃×#498	C₂²	semidirect
30. C₁₃×#486	C₂²	semidirect
31. C₁₃×#481	C₂²	semidirect
32. C₁₃×#476	C₂²	semidirect
33. C₁₃×#431	C₂²	semidirect
95. C₂×#3227	C₁₃	direct (N × H)
153. C₂²×C₄⋊Q₈	C₂×C₁₃	semidirect
154. #3227	C₂×C₁₃	direct (N × H)
155. C₂×#498	C₂×C₁₃	semidirect
156. C₂×#486	C₂×C₁₃	semidirect
157. C₂×#481	C₂×C₁₃	semidirect
158. C₂×#476	C₂×C₁₃	semidirect
159. C₂×#431	C₂×C₁₃	semidirect
211. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
221. #498	C₂²×C₁₃	semidirect
222. #486	C₂²×C₁₃	semidirect
223. #481	C₂²×C₁₃	semidirect
224. #476	C₂²×C₁₃	semidirect
225. #431	C₂²×C₁₃	semidirect
310. C₂×C₁₃	#3227	direct (N × H)
370. C₁₃	C₂×#3227	direct (N × H)
435. C₂	C₁₃×#3227	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×#532	2
C₂²×C₁₃×C₄⋊Q₈	2
C₁₃×#3227	2
C₂×C₁₃×#498	2
C₂×C₁₃×#486	2
C₂×C₁₃×#481	2
C₂×C₁₃×#476	2
C₂×C₁₃×#431	2
C₂×#3227	13

Subgroups — C2×C13×#3227 #15747180

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3227 #15747180