Subgroups — C₂×C₁₃×#3384 #15747697

Order 3328.

2082 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3384	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#501	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#498	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#478	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#476	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#474	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#446	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#442	C₂	1	2	yes	maximal
12	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic
13	C₂³×Q₈×C₁₃	—	2	1	no	—
14	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
15	C₁₃×#554	—	2	4	no	—
16	C₁₃×#554	C₂²	1	8	yes	complemented
17	D₄×Q₈×C₁₃	—	2	4	no	—
18	D₄×Q₈×C₁₃	C₂²	1	8	yes	complemented
19	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₁₃×#125	C₂²	1	2	yes	—
23	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
24	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
25	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
26	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
27	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
32	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
33	C₁₃×#501	C₂²	1	16	yes	complemented
34	C₁₃×#498	C₂²	1	8	yes	complemented
35	C₁₃×#478	C₂²	1	16	yes	complemented
36	C₁₃×#476	C₂²	1	16	yes	complemented
37	C₁₃×#476	C₂²	1	8	yes	complemented
38	C₁₃×#474	C₂²	1	8	yes	complemented
39	C₁₃×#446	C₂²	1	8	yes	complemented
40	C₁₃×#442	C₂²	1	16	yes	—
41	C₄×C₁₃×D₈	C₂²	1	8	yes	—
42	C₂×C₁₃×#107	C₂²	1	2	yes	—
43	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#106	C₂²	1	2	yes	—
45	C₂×C₁₃×#106	C₂²	1	2	yes	—
46	C₂×C₁₃×#106	C₂²	1	2	yes	—
47	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
48	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
49	C₂×C₁₃×#102	C₂²	1	2	yes	—
50	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
51	C₂×C₁₃×#102	C₂²	1	2	yes	—
52	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×#97	C₂²	1	2	yes	—
54	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
55	C₂²×Q₈×C₁₃	—	2	8	no	—
56	C₂²×Q₈×C₁₃	—	2	2	no	—
57	C₂²×Q₈×C₁₃	—	2	1	no	—
58	C₂²×Q₈×C₁₃	—	2	1	no	—
59	C₂²×Q₈×C₁₃	—	4	8	no	—
60	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
61	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₃	—	2	1	no	—
64	C₂³×C₄×C₁₃	—	2	2	no	—
65	C₂³×C₄×C₁₃	—	2	1	no	—
66	C₂³×C₄×C₁₃	—	2	2	no	—
67	C₂×C₁₃×D₈	Q₈	1	8	yes	complemented
68	C₂×C₁₃×D₈	C₂³	1	4	yes	—
69	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
71	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
72	C₁₃×C₄⋊Q₈	—	2	4	no	—
73	C₁₃×C₄⋊Q₈	—	2	2	no	—
74	C₁₃×C₄⋊Q₈	—	2	2	no	—
75	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
76	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
77	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
78	C₁₃×#125	—	2	4	no	—
79	C₁₃×#125	C₂³	1	8	yes	—
80	C₁₃×C₂²⋊Q₈	—	2	8	no	—
81	C₁₃×C₂²⋊Q₈	—	2	8	no	—
82	C₁₃×C₂²⋊Q₈	—	2	16	no	—
83	C₁₃×C₂²⋊Q₈	—	2	16	no	—
84	C₄×Q₈×C₁₃	D₄	1	4	yes	—
85	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
86	C₄×D₄×C₁₃	—	2	4	no	—
87	C₄×D₄×C₁₃	—	2	2	no	—
88	C₄×D₄×C₁₃	—	2	4	no	—
89	C₄×D₄×C₁₃	—	2	2	no	—
90	C₄×D₄×C₁₃	C₂³	1	4	yes	—
91	C₄×D₄×C₁₃	C₂³	1	4	yes	—
92	C₄×D₄×C₁₃	C₂³	1	8	yes	—
93	C₄×D₄×C₁₃	C₂³	1	8	yes	—
94	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
95	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
96	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
97	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
98	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
99	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
100	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
101	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
106	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
107	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
108	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
109	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
110	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
112	C₁₃×#107	C₂³	1	4	yes	—
113	C₁₃×#107	C₂³	1	8	yes	—
114	C₁₃×#106	C₂³	1	8	yes	—
115	C₁₃×#106	C₂³	1	8	yes	—
116	C₁₃×#106	C₂³	1	8	yes	—
117	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
118	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
119	C₁₃×#102	C₂³	1	4	yes	—
120	C₁₃×#102	C₂³	1	4	yes	—
121	C₁₃×#102	C₂³	1	8	yes	—
122	C₁₃×#102	C₂³	1	8	yes	—
123	C₁₃×#97	C₂³	1	8	yes	—
124	C₄×C₈×C₁₃	C₂³	1	4	yes	—
125	C₂×#3384	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂⁴×C₁₃	—	2	1	no	—
127	C₂⁴×C₁₃	—	2	1	no	—
128	C₂×Q₈×C₁₃	—	2	4	no	—
129	C₂×Q₈×C₁₃	—	2	8	no	—
130	C₂×Q₈×C₁₃	—	2	4	no	—
131	C₂×Q₈×C₁₃	—	2	4	no	—
132	C₂×Q₈×C₁₃	—	4	8	no	—
133	C₂×Q₈×C₁₃	—	4	32	no	—
134	C₂×Q₈×C₁₃	—	4	4	no	—
135	C₂×Q₈×C₁₃	—	8	2	no	—
136	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
137	C₂×D₄×C₁₃	—	2	1	no	—
138	C₂×D₄×C₁₃	—	2	1	no	—
139	C₂×D₄×C₁₃	—	2	2	no	—
140	C₂×D₄×C₁₃	—	2	2	no	—
141	C₂×D₄×C₁₃	C₂×Q₈	1	4	yes	—
142	C₂×D₄×C₁₃	C₂×Q₈	1	4	yes	complemented
143	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
144	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
145	C₂²×C₄×C₁₃	—	2	1	no	—
146	C₂²×C₄×C₁₃	—	2	2	no	—
147	C₂²×C₄×C₁₃	—	2	2	no	—
148	C₂²×C₄×C₁₃	—	2	1	no	—
149	C₂²×C₄×C₁₃	—	2	4	no	—
150	C₂²×C₄×C₁₃	—	2	8	no	—
151	C₂²×C₄×C₁₃	—	2	4	no	—
152	C₂²×C₄×C₁₃	—	2	8	no	—
153	C₂²×C₄×C₁₃	—	4	8	no	—
154	C₂²×C₄×C₁₃	—	4	4	no	—
155	C₂²×C₄×C₁₃	—	4	4	no	—
156	C₂²×C₄×C₁₃	—	8	4	no	—
157	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
160	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
162	C₁₃×D₈	C₂×Q₈	1	16	yes	complemented
163	C₂×C₈×C₁₃	—	2	2	no	—
164	C₂×C₈×C₁₃	—	2	4	no	—
165	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	complemented
166	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
167	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
168	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
169	C₁₃×C₄⋊C₄	—	2	8	no	—
170	C₁₃×C₄⋊C₄	—	2	4	no	—
171	C₁₃×C₄⋊C₄	—	2	8	no	—
172	C₁₃×C₄⋊C₄	—	2	4	no	—
173	C₁₃×C₄⋊C₄	—	2	8	no	—
174	C₁₃×C₄⋊C₄	—	2	1	no	—
175	C₁₃×C₄⋊C₄	—	2	2	no	—
176	C₁₃×C₄⋊C₄	—	2	2	no	—
177	C₁₃×C₄⋊C₄	—	2	1	no	—
178	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
179	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
180	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
181	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
182	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
183	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
184	C₁₃×C₂²⋊C₄	—	2	4	no	—
185	C₁₃×C₂²⋊C₄	—	2	8	no	—
186	C₁₃×C₂²⋊C₄	—	2	4	no	—
187	C₁₃×C₂²⋊C₄	—	2	8	no	—
188	C₄²×C₁₃	C₂×D₄	1	4	yes	—
189	C₄²×C₁₃	C₂×D₄	1	2	yes	—
190	C₄²×C₁₃	C₂⁴	1	2	yes	—
191	C₄²×C₁₃	C₂⁴	1	4	yes	—
192	C₂×#554	C₂×C₁₃	1	1	yes	characteristic, complemented
193	C₂×D₄×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
194	#3384	C₂×C₁₃	1	16	yes	direct product factor
195	C₂×#501	C₂×C₁₃	1	2	yes	complemented
196	C₂×#498	C₂×C₁₃	1	1	yes	characteristic, complemented
197	C₂×#478	C₂×C₁₃	1	2	yes	complemented
198	C₂×#476	C₂×C₁₃	1	1	yes	characteristic, complemented
199	C₂×#476	C₂×C₁₃	1	2	yes	complemented
200	C₂×#474	C₂×C₁₃	1	1	yes	characteristic, complemented
201	C₂×#446	C₂×C₁₃	1	1	yes	characteristic, complemented
202	C₂×#442	C₂×C₁₃	1	2	yes	—
203	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic
204	C₂³×C₁₃	—	2	4	no	—
205	C₂³×C₁₃	—	2	4	no	—
206	C₂³×C₁₃	—	2	2	no	—
207	C₂³×C₁₃	—	2	2	no	—
208	C₂³×C₁₃	—	4	2	no	—
209	C₂³×C₁₃	—	4	2	no	—
210	C₂³×C₁₃	—	4	2	no	—
211	C₂³×C₁₃	—	4	2	no	—
212	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
213	Q₈×C₁₃	—	2	8	no	—
214	Q₈×C₁₃	—	4	16	no	—
215	Q₈×C₁₃	—	4	8	no	—
216	Q₈×C₁₃	—	8	4	no	—
217	D₄×C₁₃	—	2	4	no	—
218	D₄×C₁₃	—	2	4	no	—
219	D₄×C₁₃	—	2	2	no	—
220	D₄×C₁₃	—	2	2	no	—
221	D₄×C₁₃	C₂²×Q₈	1	4	yes	—
222	D₄×C₁₃	C₂²×Q₈	1	4	yes	complemented
223	C₂×C₄×C₁₃	—	2	4	no	—
224	C₂×C₄×C₁₃	—	2	4	no	—
225	C₂×C₄×C₁₃	—	2	2	no	—
226	C₂×C₄×C₁₃	—	2	2	no	—
227	C₂×C₄×C₁₃	—	2	4	no	—
228	C₂×C₄×C₁₃	—	2	4	no	—
229	C₂×C₄×C₁₃	—	2	2	no	—
230	C₂×C₄×C₁₃	—	4	16	no	—
231	C₂×C₄×C₁₃	—	4	2	no	—
232	C₂×C₄×C₁₃	—	4	4	no	—
233	C₂×C₄×C₁₃	—	4	2	no	—
234	C₂×C₄×C₁₃	—	4	4	no	—
235	C₂×C₄×C₁₃	—	4	8	no	—
236	C₂×C₄×C₁₃	—	4	8	no	—
237	C₂×C₄×C₁₃	—	8	8	no	—
238	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
239	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
240	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
241	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
242	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
244	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
245	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
246	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
247	C₈×C₁₃	—	2	2	no	—
248	C₈×C₁₃	—	2	4	no	—
249	C₈×C₁₃	C₂²×Q₈	1	4	yes	complemented
250	C₂³×Q₈	—	2	1	no	—
251	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
252	#554	—	2	4	no	—
253	#554	C₂²×C₁₃	1	8	yes	complemented
254	D₄×Q₈	—	2	4	no	—
255	D₄×Q₈	C₂²×C₁₃	1	8	yes	complemented
256	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
257	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
258	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
259	C₂×#125	C₂²×C₁₃	1	2	yes	—
260	C₂×C₂²⋊Q₈	—	2	1	no	—
261	C₂×C₂²⋊Q₈	—	2	1	no	—
262	C₂×C₂²⋊Q₈	—	2	2	no	—
263	C₂×C₂²⋊Q₈	—	2	2	no	—
264	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
265	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
266	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
267	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
268	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
269	C₂²×C₄⋊C₄	—	2	1	no	—
270	#501	C₂²×C₁₃	1	16	yes	complemented
271	#498	C₂²×C₁₃	1	8	yes	complemented
272	#478	C₂²×C₁₃	1	16	yes	complemented
273	#476	C₂²×C₁₃	1	16	yes	complemented
274	#476	C₂²×C₁₃	1	8	yes	complemented
275	#474	C₂²×C₁₃	1	8	yes	complemented
276	#446	C₂²×C₁₃	1	8	yes	complemented
277	#442	C₂²×C₁₃	1	16	yes	—
278	C₄×D₈	C₂²×C₁₃	1	8	yes	—
279	C₂×#107	C₂²×C₁₃	1	2	yes	—
280	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
281	C₂×#106	C₂²×C₁₃	1	2	yes	—
282	C₂×#106	C₂²×C₁₃	1	2	yes	—
283	C₂×#106	C₂²×C₁₃	1	2	yes	—
284	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
285	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
286	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
287	C₂×#102	C₂²×C₁₃	1	2	yes	—
288	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
289	C₂×#102	C₂²×C₁₃	1	2	yes	—
290	C₂×#97	C₂²×C₁₃	1	2	yes	—
291	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
292	C₂²×C₁₃	—	2	4	no	—
293	C₂²×C₁₃	—	2	4	no	—
294	C₂²×C₁₃	—	4	8	no	—
295	C₂²×C₁₃	—	4	8	no	—
296	C₂²×C₁₃	—	4	2	no	—
297	C₂²×C₁₃	—	4	2	no	—
298	C₂²×C₁₃	—	4	2	no	—
299	C₂²×C₁₃	—	4	2	no	—
300	C₂²×C₁₃	D₄×Q₈	1	2	yes	—
301	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
302	C₂²×C₁₃	#577	1	2	yes	—
303	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
304	C₄×C₁₃	—	2	4	no	—
305	C₄×C₁₃	—	2	4	no	—
306	C₄×C₁₃	—	2	2	no	—
307	C₄×C₁₃	—	4	2	no	—
308	C₄×C₁₃	—	4	4	no	—
309	C₄×C₁₃	—	4	2	no	—
310	C₄×C₁₃	—	4	4	no	—
311	C₄×C₁₃	D₄×Q₈	1	2	yes	—
312	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
313	C₄×C₁₃	C₂³×Q₈	1	1	yes	characteristic
314	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
315	C₂²×Q₈	—	2	8	no	—
316	C₂²×Q₈	—	2	2	no	—
317	C₂²×Q₈	—	2	1	no	—
318	C₂²×Q₈	—	2	1	no	—
319	C₂²×Q₈	—	4	8	no	—
320	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
321	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
322	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
323	C₂³×C₄	—	2	1	no	—
324	C₂³×C₄	—	2	2	no	—
325	C₂³×C₄	—	2	1	no	—
326	C₂³×C₄	—	2	2	no	—
327	C₂×D₈	Q₈×C₁₃	1	8	yes	complemented
328	C₂×D₈	C₂³×C₁₃	1	4	yes	—
329	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
330	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
331	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
332	C₄⋊Q₈	—	2	4	no	—
333	C₄⋊Q₈	—	2	2	no	—
334	C₄⋊Q₈	—	2	2	no	—
335	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
336	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
337	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
338	#125	—	2	4	no	—
339	#125	C₂³×C₁₃	1	8	yes	—
340	C₂²⋊Q₈	—	2	8	no	—
341	C₂²⋊Q₈	—	2	8	no	—
342	C₂²⋊Q₈	—	2	16	no	—
343	C₂²⋊Q₈	—	2	16	no	—
344	C₄×Q₈	D₄×C₁₃	1	4	yes	—
345	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
346	C₄×D₄	—	2	4	no	—
347	C₄×D₄	—	2	2	no	—
348	C₄×D₄	—	2	4	no	—
349	C₄×D₄	—	2	2	no	—
350	C₄×D₄	C₂³×C₁₃	1	4	yes	—
351	C₄×D₄	C₂³×C₁₃	1	8	yes	—
352	C₄×D₄	C₂³×C₁₃	1	4	yes	—
353	C₄×D₄	C₂³×C₁₃	1	8	yes	—
354	C₂×C₄⋊C₄	—	2	2	no	—
355	C₂×C₄⋊C₄	—	2	1	no	—
356	C₂×C₄⋊C₄	—	2	2	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	2	no	—
359	C₂×C₄⋊C₄	—	2	8	no	—
360	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
361	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
362	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
364	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
365	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
366	C₂×C₂²⋊C₄	—	2	1	no	—
367	C₂×C₂²⋊C₄	—	2	2	no	—
368	C₂×C₂²⋊C₄	—	2	1	no	—
369	C₂×C₂²⋊C₄	—	2	2	no	—
370	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
371	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
372	#107	C₂³×C₁₃	1	4	yes	—
373	#107	C₂³×C₁₃	1	8	yes	—
374	#106	C₂³×C₁₃	1	8	yes	—
375	#106	C₂³×C₁₃	1	8	yes	—
376	#106	C₂³×C₁₃	1	8	yes	—
377	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
378	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
379	#102	C₂³×C₁₃	1	4	yes	—
380	#102	C₂³×C₁₃	1	4	yes	—
381	#102	C₂³×C₁₃	1	8	yes	—
382	#102	C₂³×C₁₃	1	8	yes	—
383	#97	C₂³×C₁₃	1	8	yes	—
384	C₄×C₈	C₂³×C₁₃	1	4	yes	—
385	C₂×C₁₃	—	4	4	no	—
386	C₂×C₁₃	—	4	4	no	—
387	C₂×C₁₃	#3384	1	4	yes	direct product factor
388	C₂×C₁₃	C₂×D₄×Q₈	1	1	yes	characteristic
389	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
390	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
391	C₂⁴	—	2	1	no	—
392	C₂⁴	—	2	1	no	—
393	C₂×Q₈	—	2	4	no	—
394	C₂×Q₈	—	2	8	no	—
395	C₂×Q₈	—	2	4	no	—
396	C₂×Q₈	—	2	4	no	—
397	C₂×Q₈	—	4	8	no	—
398	C₂×Q₈	—	4	32	no	—
399	C₂×Q₈	—	4	4	no	—
400	C₂×Q₈	—	8	2	no	—
401	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
402	C₂×D₄	—	2	1	no	—
403	C₂×D₄	—	2	1	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	C₂×Q₈×C₁₃	1	4	yes	—
407	C₂×D₄	C₂×Q₈×C₁₃	1	4	yes	complemented
408	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
409	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	4	no	—
415	C₂²×C₄	—	2	8	no	—
416	C₂²×C₄	—	2	4	no	—
417	C₂²×C₄	—	2	8	no	—
418	C₂²×C₄	—	4	8	no	—
419	C₂²×C₄	—	4	4	no	—
420	C₂²×C₄	—	4	4	no	—
421	C₂²×C₄	—	8	4	no	—
422	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
423	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
424	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
425	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
426	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
427	D₈	C₂×Q₈×C₁₃	1	16	yes	complemented
428	C₂×C₈	—	2	2	no	—
429	C₂×C₈	—	2	4	no	—
430	C₂×C₈	C₂×Q₈×C₁₃	1	4	yes	complemented
431	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
432	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
433	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
434	C₄⋊C₄	—	2	8	no	—
435	C₄⋊C₄	—	2	4	no	—
436	C₄⋊C₄	—	2	8	no	—
437	C₄⋊C₄	—	2	4	no	—
438	C₄⋊C₄	—	2	8	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
444	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
445	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
446	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
447	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
448	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
449	C₂²⋊C₄	—	2	4	no	—
450	C₂²⋊C₄	—	2	8	no	—
451	C₂²⋊C₄	—	2	4	no	—
452	C₂²⋊C₄	—	2	8	no	—
453	C₄²	C₂×D₄×C₁₃	1	4	yes	—
454	C₄²	C₂×D₄×C₁₃	1	2	yes	—
455	C₄²	C₂⁴×C₁₃	1	2	yes	—
456	C₄²	C₂⁴×C₁₃	1	4	yes	—
457	C₁₃	C₂×#3384	1	1	yes	characteristic, direct product factor, Sylow
458	C₂³	—	2	4	no	—
459	C₂³	—	2	4	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	4	2	no	—
463	C₂³	—	4	2	no	—
464	C₂³	—	4	2	no	—
465	C₂³	—	4	2	no	—
466	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
467	Q₈	—	2	8	no	—
468	Q₈	—	4	16	no	—
469	Q₈	—	4	8	no	—
470	Q₈	—	8	4	no	—
471	D₄	—	2	4	no	—
472	D₄	—	2	4	no	—
473	D₄	—	2	2	no	—
474	D₄	—	2	2	no	—
475	D₄	C₂²×Q₈×C₁₃	1	4	yes	—
476	D₄	C₂²×Q₈×C₁₃	1	4	yes	complemented
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	4	16	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	4	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	4	no	—
489	C₂×C₄	—	4	8	no	—
490	C₂×C₄	—	4	8	no	—
491	C₂×C₄	—	8	8	no	—
492	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
493	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
494	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
495	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
496	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
497	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
498	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
499	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
500	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
501	C₈	—	2	2	no	—
502	C₈	—	2	4	no	—
503	C₈	C₂²×Q₈×C₁₃	1	4	yes	complemented
504	C₂²	—	2	4	no	—
505	C₂²	—	2	4	no	—
506	C₂²	—	4	2	no	—
507	C₂²	—	4	2	no	—
508	C₂²	—	4	2	no	—
509	C₂²	—	4	2	no	—
510	C₂²	—	4	8	no	—
511	C₂²	—	4	8	no	—
512	C₂²	D₄×Q₈×C₁₃	1	2	yes	—
513	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
514	C₂²	C₁₃×#577	1	2	yes	—
515	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
516	C₄	—	2	4	no	—
517	C₄	—	2	4	no	—
518	C₄	—	2	2	no	—
519	C₄	—	4	2	no	—
520	C₄	—	4	4	no	—
521	C₄	—	4	2	no	—
522	C₄	—	4	4	no	—
523	C₄	D₄×Q₈×C₁₃	1	2	yes	—
524	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
525	C₄	C₂³×Q₈×C₁₃	1	1	yes	characteristic
526	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
527	C₂	—	4	4	no	—
528	C₂	—	4	4	no	—
529	C₂	C₁₃×#3384	1	4	yes	direct product factor
530	C₂	C₂×D₄×Q₈×C₁₃	1	1	yes	characteristic
531	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
532	C₂	C₂×C₁₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂²×C₁₃×D₈	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₁₃×#554	C₂	semidirect
2. C₂×D₄×Q₈×C₁₃	C₂	semidirect
3. C₁₃×#3384	C₂	direct (N × H)
4. C₂×C₁₃×#501	C₂	semidirect
5. C₂×C₁₃×#498	C₂	semidirect
6. C₂×C₁₃×#478	C₂	semidirect
7. C₂×C₁₃×#476	C₂	semidirect
8. C₂×C₁₃×#476	C₂	semidirect
9. C₂×C₁₃×#474	C₂	semidirect
10. C₂×C₁₃×#446	C₂	semidirect
16. C₁₃×#554	C₂²	semidirect
18. D₄×Q₈×C₁₃	C₂²	semidirect
33. C₁₃×#501	C₂²	semidirect
34. C₁₃×#498	C₂²	semidirect
35. C₁₃×#478	C₂²	semidirect
36. C₁₃×#476	C₂²	semidirect
37. C₁₃×#476	C₂²	semidirect
38. C₁₃×#474	C₂²	semidirect
39. C₁₃×#446	C₂²	semidirect
67. C₂×C₁₃×D₈	Q₈	semidirect
125. C₂×#3384	C₁₃	direct (N × H)
142. C₂×D₄×C₁₃	C₂×Q₈	semidirect
162. C₁₃×D₈	C₂×Q₈	semidirect
165. C₂×C₈×C₁₃	C₂×Q₈	semidirect
192. C₂×#554	C₂×C₁₃	semidirect
193. C₂×D₄×Q₈	C₂×C₁₃	semidirect
194. #3384	C₂×C₁₃	direct (N × H)
195. C₂×#501	C₂×C₁₃	semidirect
196. C₂×#498	C₂×C₁₃	semidirect
197. C₂×#478	C₂×C₁₃	semidirect
198. C₂×#476	C₂×C₁₃	semidirect
199. C₂×#476	C₂×C₁₃	semidirect
200. C₂×#474	C₂×C₁₃	semidirect
201. C₂×#446	C₂×C₁₃	semidirect
222. D₄×C₁₃	C₂²×Q₈	semidirect
249. C₈×C₁₃	C₂²×Q₈	semidirect
253. #554	C₂²×C₁₃	semidirect
255. D₄×Q₈	C₂²×C₁₃	semidirect
270. #501	C₂²×C₁₃	semidirect
271. #498	C₂²×C₁₃	semidirect
272. #478	C₂²×C₁₃	semidirect
273. #476	C₂²×C₁₃	semidirect
274. #476	C₂²×C₁₃	semidirect
275. #474	C₂²×C₁₃	semidirect
276. #446	C₂²×C₁₃	semidirect
327. C₂×D₈	Q₈×C₁₃	semidirect
387. C₂×C₁₃	#3384	direct (N × H)
407. C₂×D₄	C₂×Q₈×C₁₃	semidirect
427. D₈	C₂×Q₈×C₁₃	semidirect
430. C₂×C₈	C₂×Q₈×C₁₃	semidirect
457. C₁₃	C₂×#3384	direct (N × H)
476. D₄	C₂²×Q₈×C₁₃	semidirect
503. C₈	C₂²×Q₈×C₁₃	semidirect
529. C₂	C₁₃×#3384	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×#554	2
C₂×D₄×Q₈×C₁₃	2
C₁₃×#3384	2
C₂×C₁₃×#501	2
C₂×C₁₃×#498	2
C₂×C₁₃×#478	2
C₂×C₁₃×#476	2
C₂×C₁₃×#474	2
C₂×C₁₃×#446	2
C₂×C₁₃×#442	2
C₂×C₄×C₁₃×D₈	2
C₂×#3384	13

Subgroups — C2×C13×#3384 #15747697

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3384 #15747697