Subgroups — C₂×C₁₃×#3518 #15749130

Order 3328.

7118 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3518	C₂	1	32	yes	maximal, direct product factor
2	C₂×Q₈²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#556	C₂	1	6	yes	maximal, complemented
4	C₂×C₁₃×#556	C₂	1	3	yes	maximal, complemented
5	C₂×C₁₃×#555	C₂	1	3	yes	maximal, complemented
6	C₂×D₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#548	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#542	C₂	1	6	yes	maximal, complemented
9	C₂×C₁₃×#533	C₂	1	3	yes	maximal, complemented
10	C₂×C₁₃×#529	C₂	1	3	yes	maximal, complemented
11	C₂×C₁₃×#519	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
14	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
15	Q₈²×C₁₃	C₂²	1	16	yes	complemented
16	C₁₃×#556	C₂²	1	96	yes	complemented
17	C₁₃×#556	C₂²	1	48	yes	complemented
18	C₁₃×#555	C₂²	1	48	yes	complemented
19	D₄×Q₈×C₁₃	C₂²	1	16	yes	complemented
20	C₁₃×#548	C₂²	1	32	yes	complemented
21	C₁₃×#542	C₂²	1	96	yes	complemented
22	C₁₃×#533	C₂²	1	48	yes	complemented
23	C₂×C₁₃×C₄⋊Q₈	C₂²	1	3	yes	—
24	C₂×C₁₃×C₄⋊Q₈	C₂²	1	3	yes	—
25	C₂×C₁₃×C₄⋊Q₈	C₂²	1	6	yes	—
26	C₁₃×#529	C₂²	1	48	yes	complemented
27	C₂×C₁₃×#126	C₂²	1	6	yes	—
28	C₂×C₁₃×#126	C₂²	1	12	yes	—
29	C₂×C₁₃×#125	C₂²	1	3	yes	—
30	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#124	C₂²	1	6	yes	—
32	C₂×C₁₃×#124	C₂²	1	12	yes	—
33	C₂×C₁₃×#123	C₂²	1	6	yes	—
34	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	3	yes	—
35	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	6	yes	—
36	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	6	yes	—
37	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	6	yes	—
38	C₂×C₁₃×#121	C₂²	1	3	yes	—
39	C₂×C₁₃×#121	C₂²	1	6	yes	—
40	C₁₃×#519	C₂²	1	32	yes	complemented
41	C₄×C₁₃×#41	C₂²	1	16	yes	complemented
42	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
43	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×Q₈×C₁₃	C₂²	1	6	yes	—
45	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
46	C₂×C₄×Q₈×C₁₃	C₂²	1	6	yes	—
47	C₂×C₄×Q₈×C₁₃	C₂²	1	3	yes	—
48	C₂×C₄×Q₈×C₁₃	C₂²	1	6	yes	—
49	C₂×C₄×D₄×C₁₃	C₂²	1	3	yes	—
50	C₂×C₄×D₄×C₁₃	C₂²	1	3	yes	—
51	C₂×C₄×D₄×C₁₃	C₂²	1	6	yes	—
52	C₂×C₄×D₄×C₁₃	C₂²	1	3	yes	—
53	C₂×C₁₃×#117	C₂²	1	3	yes	—
54	C₂×C₁₃×#117	C₂²	1	6	yes	—
55	C₂×C₁₃×#117	C₂²	1	6	yes	—
56	C₂×C₁₃×#117	C₂²	1	6	yes	—
57	C₂²×C₄²×C₁₃	C₂²	1	3	yes	—
58	C₂×C₁₃×#41	—	2	8	no	—
59	C₂×C₁₃×#41	C₂³	1	8	yes	—
60	C₂²×Q₈×C₁₃	—	2	16	no	—
61	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×Q₈×C₁₃	C₂³	1	6	yes	—
63	C₂²×Q₈×C₁₃	C₂³	1	16	yes	—
64	C₂²×Q₈×C₁₃	C₂³	1	6	yes	—
65	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
67	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
68	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
69	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
70	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
71	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
72	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
73	C₁₃×C₄⋊Q₈	C₂³	1	24	yes	—
74	C₁₃×C₄⋊Q₈	C₂³	1	24	yes	—
75	C₁₃×C₄⋊Q₈	C₂³	1	48	yes	—
76	C₁₃×#126	C₂³	1	48	yes	—
77	C₁₃×#126	C₂³	1	96	yes	—
78	C₁₃×#125	C₂³	1	24	yes	—
79	C₁₃×#124	C₂³	1	8	yes	—
80	C₁₃×#124	C₂³	1	48	yes	—
81	C₁₃×#124	C₂³	1	96	yes	—
82	C₁₃×#123	C₂³	1	48	yes	—
83	C₁₃×C₂²⋊Q₈	C₂³	1	24	yes	—
84	C₁₃×C₂²⋊Q₈	C₂³	1	48	yes	—
85	C₁₃×C₂²⋊Q₈	C₂³	1	48	yes	—
86	C₁₃×C₂²⋊Q₈	C₂³	1	48	yes	—
87	C₁₃×#121	C₂³	1	24	yes	—
88	C₁₃×#121	C₂³	1	48	yes	—
89	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
90	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
91	C₄×Q₈×C₁₃	C₂³	1	48	yes	—
92	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
93	C₄×Q₈×C₁₃	C₂³	1	48	yes	—
94	C₄×Q₈×C₁₃	C₂³	1	24	yes	—
95	C₄×Q₈×C₁₃	C₂³	1	48	yes	—
96	C₄×D₄×C₁₃	C₂³	1	24	yes	—
97	C₄×D₄×C₁₃	C₂³	1	24	yes	—
98	C₄×D₄×C₁₃	C₂³	1	48	yes	—
99	C₄×D₄×C₁₃	C₂³	1	24	yes	—
100	C₁₃×#117	C₂³	1	24	yes	—
101	C₁₃×#117	C₂³	1	48	yes	—
102	C₁₃×#117	C₂³	1	48	yes	—
103	C₁₃×#117	C₂³	1	48	yes	—
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
105	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
106	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
114	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
115	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
116	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
117	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
118	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
119	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
120	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
121	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
123	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
124	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
125	C₂×C₄²×C₁₃	C₂³	1	24	yes	—
126	C₂×C₄²×C₁₃	C₂³	1	12	yes	—
127	C₂×C₄²×C₁₃	C₂³	1	6	yes	—
128	C₂×#3518	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
129	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
130	C₂⁴×C₁₃	C₂⁴	1	3	yes	—
131	C₁₃×#41	—	2	32	no	—
132	C₂×Q₈×C₁₃	—	2	64	no	—
133	C₂×Q₈×C₁₃	—	2	24	no	—
134	C₂×Q₈×C₁₃	—	2	4	no	—
135	C₂×Q₈×C₁₃	—	4	12	no	—
136	C₂×Q₈×C₁₃	#41	1	8	yes	—
137	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
138	C₂×Q₈×C₁₃	C₂⁴	1	24	yes	—
139	C₂×Q₈×C₁₃	C₂⁴	1	24	yes	—
140	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
141	C₂×D₄×C₁₃	—	2	12	no	—
142	C₂×D₄×C₁₃	—	2	4	no	—
143	C₂×D₄×C₁₃	—	4	12	no	—
144	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
145	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
146	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
147	C₂²×C₄×C₁₃	—	2	24	no	—
148	C₂²×C₄×C₁₃	—	2	12	no	—
149	C₂²×C₄×C₁₃	—	2	12	no	—
150	C₂²×C₄×C₁₃	—	4	6	no	—
151	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
152	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
153	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
154	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
155	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
157	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
158	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
159	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
160	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
161	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
162	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
163	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
164	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
165	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
166	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
167	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
168	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
169	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
170	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
171	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
172	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
173	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
174	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
175	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
176	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
177	C₁₃×C₂²⋊C₄	C₂⁴	1	48	yes	—
178	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
179	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
180	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
181	C₄²×C₁₃	C₂⁴	1	4	yes	—
182	C₄²×C₁₃	C₂⁴	1	12	yes	—
183	C₄²×C₁₃	C₂⁴	1	12	yes	—
184	C₄²×C₁₃	C₂⁴	1	12	yes	—
185	C₄²×C₁₃	C₂⁴	1	48	yes	—
186	C₄²×C₁₃	C₂⁴	1	24	yes	—
187	#3518	C₂×C₁₃	1	32	yes	direct product factor
188	C₂×Q₈²	C₂×C₁₃	1	1	yes	characteristic, complemented
189	C₂×#556	C₂×C₁₃	1	6	yes	complemented
190	C₂×#556	C₂×C₁₃	1	3	yes	complemented
191	C₂×#555	C₂×C₁₃	1	3	yes	complemented
192	C₂×D₄×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
193	C₂×#548	C₂×C₁₃	1	2	yes	complemented
194	C₂×#542	C₂×C₁₃	1	6	yes	complemented
195	C₂×#533	C₂×C₁₃	1	3	yes	complemented
196	C₂×#529	C₂×C₁₃	1	3	yes	complemented
197	C₂×#519	C₂×C₁₃	1	2	yes	complemented
198	C₂×C₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
199	C₂³×C₁₃	—	2	4	no	—
200	C₂³×C₁₃	—	2	6	no	—
201	C₂³×C₁₃	—	2	6	no	—
202	C₂³×C₁₃	—	2	4	no	—
203	C₂³×C₁₃	—	2	6	no	—
204	C₂³×C₁₃	—	2	4	no	—
205	C₂³×C₁₃	C₂⁵	1	4	yes	—
206	C₂³×C₁₃	C₂⁵	1	6	yes	—
207	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
208	Q₈×C₁₃	—	2	48	no	—
209	Q₈×C₁₃	—	2	8	no	—
210	Q₈×C₁₃	—	4	24	no	—
211	Q₈×C₁₃	C₂×#41	1	16	yes	—
212	D₄×C₁₃	—	2	24	no	—
213	D₄×C₁₃	—	2	8	no	—
214	D₄×C₁₃	—	4	24	no	—
215	C₂×C₄×C₁₃	—	2	2	no	—
216	C₂×C₄×C₁₃	—	2	12	no	—
217	C₂×C₄×C₁₃	—	2	6	no	—
218	C₂×C₄×C₁₃	—	2	4	no	—
219	C₂×C₄×C₁₃	—	2	2	no	—
220	C₂×C₄×C₁₃	—	2	6	no	—
221	C₂×C₄×C₁₃	—	2	12	no	—
222	C₂×C₄×C₁₃	—	2	48	no	—
223	C₂×C₄×C₁₃	—	2	24	no	—
224	C₂×C₄×C₁₃	—	2	24	no	—
225	C₂×C₄×C₁₃	—	4	12	no	—
226	C₂×C₄×C₁₃	C₂×#41	1	12	yes	—
227	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
228	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
229	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
230	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
231	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
232	C₂×C₄×C₁₃	C₂⁵	1	12	yes	—
233	C₂×C₄×C₁₃	C₂⁵	1	12	yes	—
234	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
235	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
236	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
237	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
238	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
239	Q₈²	C₂²×C₁₃	1	16	yes	complemented
240	#556	C₂²×C₁₃	1	96	yes	complemented
241	#556	C₂²×C₁₃	1	48	yes	complemented
242	#555	C₂²×C₁₃	1	48	yes	complemented
243	D₄×Q₈	C₂²×C₁₃	1	16	yes	complemented
244	#548	C₂²×C₁₃	1	32	yes	complemented
245	#542	C₂²×C₁₃	1	96	yes	complemented
246	#533	C₂²×C₁₃	1	48	yes	complemented
247	C₂×C₄⋊Q₈	C₂²×C₁₃	1	3	yes	—
248	C₂×C₄⋊Q₈	C₂²×C₁₃	1	3	yes	—
249	C₂×C₄⋊Q₈	C₂²×C₁₃	1	6	yes	—
250	#529	C₂²×C₁₃	1	48	yes	complemented
251	C₂×#126	C₂²×C₁₃	1	6	yes	—
252	C₂×#126	C₂²×C₁₃	1	12	yes	—
253	C₂×#125	C₂²×C₁₃	1	3	yes	—
254	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
255	C₂×#124	C₂²×C₁₃	1	6	yes	—
256	C₂×#124	C₂²×C₁₃	1	12	yes	—
257	C₂×#123	C₂²×C₁₃	1	6	yes	—
258	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	3	yes	—
259	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	6	yes	—
260	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	6	yes	—
261	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	6	yes	—
262	C₂×#121	C₂²×C₁₃	1	3	yes	—
263	C₂×#121	C₂²×C₁₃	1	6	yes	—
264	#519	C₂²×C₁₃	1	32	yes	complemented
265	C₄×#41	C₂²×C₁₃	1	16	yes	complemented
266	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
267	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
268	C₂×C₄×Q₈	C₂²×C₁₃	1	6	yes	—
269	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
270	C₂×C₄×Q₈	C₂²×C₁₃	1	6	yes	—
271	C₂×C₄×Q₈	C₂²×C₁₃	1	3	yes	—
272	C₂×C₄×Q₈	C₂²×C₁₃	1	6	yes	—
273	C₂×C₄×D₄	C₂²×C₁₃	1	3	yes	—
274	C₂×C₄×D₄	C₂²×C₁₃	1	3	yes	—
275	C₂×C₄×D₄	C₂²×C₁₃	1	6	yes	—
276	C₂×C₄×D₄	C₂²×C₁₃	1	3	yes	—
277	C₂×#117	C₂²×C₁₃	1	3	yes	—
278	C₂×#117	C₂²×C₁₃	1	6	yes	—
279	C₂×#117	C₂²×C₁₃	1	6	yes	—
280	C₂×#117	C₂²×C₁₃	1	6	yes	—
281	C₂²×C₄²	C₂²×C₁₃	1	3	yes	—
282	C₂²×C₁₃	—	2	4	no	—
283	C₂²×C₁₃	—	2	6	no	—
284	C₂²×C₁₃	—	2	6	no	—
285	C₂²×C₁₃	—	2	4	no	—
286	C₂²×C₁₃	—	2	6	no	—
287	C₂²×C₁₃	—	2	4	no	—
288	C₂²×C₁₃	—	4	8	no	—
289	C₂²×C₁₃	—	4	12	no	—
290	C₂²×C₁₃	C₂²×#41	1	2	yes	—
291	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
292	C₂²×C₁₃	#585	1	2	yes	—
293	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
294	C₄×C₁₃	—	2	2	no	—
295	C₄×C₁₃	—	2	12	no	—
296	C₄×C₁₃	—	2	6	no	—
297	C₄×C₁₃	—	2	4	no	—
298	C₄×C₁₃	—	2	2	no	—
299	C₄×C₁₃	—	2	6	no	—
300	C₄×C₁₃	—	2	12	no	—
301	C₄×C₁₃	C₂²×#41	1	12	yes	—
302	C₄×C₁₃	C₂×2₋¹⁺⁴	1	4	yes	—
303	C₂×#41	—	2	8	no	—
304	C₂×#41	C₂³×C₁₃	1	8	yes	—
305	C₂²×Q₈	—	2	16	no	—
306	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
307	C₂²×Q₈	C₂³×C₁₃	1	6	yes	—
308	C₂²×Q₈	C₂³×C₁₃	1	16	yes	—
309	C₂²×Q₈	C₂³×C₁₃	1	6	yes	—
310	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
311	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
312	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
313	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
314	C₂³×C₄	C₂³×C₁₃	1	6	yes	—
315	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
316	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
317	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
318	C₄⋊Q₈	C₂³×C₁₃	1	24	yes	—
319	C₄⋊Q₈	C₂³×C₁₃	1	24	yes	—
320	C₄⋊Q₈	C₂³×C₁₃	1	48	yes	—
321	#126	C₂³×C₁₃	1	48	yes	—
322	#126	C₂³×C₁₃	1	96	yes	—
323	#125	C₂³×C₁₃	1	24	yes	—
324	#124	C₂³×C₁₃	1	8	yes	—
325	#124	C₂³×C₁₃	1	48	yes	—
326	#124	C₂³×C₁₃	1	96	yes	—
327	#123	C₂³×C₁₃	1	48	yes	—
328	C₂²⋊Q₈	C₂³×C₁₃	1	24	yes	—
329	C₂²⋊Q₈	C₂³×C₁₃	1	48	yes	—
330	C₂²⋊Q₈	C₂³×C₁₃	1	48	yes	—
331	C₂²⋊Q₈	C₂³×C₁₃	1	48	yes	—
332	#121	C₂³×C₁₃	1	24	yes	—
333	#121	C₂³×C₁₃	1	48	yes	—
334	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
335	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
336	C₄×Q₈	C₂³×C₁₃	1	48	yes	—
337	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
338	C₄×Q₈	C₂³×C₁₃	1	48	yes	—
339	C₄×Q₈	C₂³×C₁₃	1	24	yes	—
340	C₄×Q₈	C₂³×C₁₃	1	48	yes	—
341	C₄×D₄	C₂³×C₁₃	1	24	yes	—
342	C₄×D₄	C₂³×C₁₃	1	24	yes	—
343	C₄×D₄	C₂³×C₁₃	1	48	yes	—
344	C₄×D₄	C₂³×C₁₃	1	24	yes	—
345	#117	C₂³×C₁₃	1	24	yes	—
346	#117	C₂³×C₁₃	1	48	yes	—
347	#117	C₂³×C₁₃	1	48	yes	—
348	#117	C₂³×C₁₃	1	48	yes	—
349	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
350	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
351	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
352	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
353	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
354	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
355	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
356	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
357	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
358	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
359	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
360	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
361	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
362	C₂×C₂²⋊C₄	C₂³×C₁₃	1	12	yes	—
363	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
364	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
365	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
366	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
367	C₂×C₄²	C₂³×C₁₃	1	12	yes	—
368	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
369	C₂×C₄²	C₂³×C₁₃	1	6	yes	—
370	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
371	C₂×C₄²	C₂³×C₁₃	1	24	yes	—
372	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
373	C₂×C₁₃	—	4	4	no	—
374	C₂×C₁₃	—	4	6	no	—
375	C₂×C₁₃	#3518	1	4	yes	direct product factor
376	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
377	C₂×C₁₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
378	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
379	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
380	C₂⁴	C₂⁴×C₁₃	1	3	yes	—
381	#41	—	2	32	no	—
382	C₂×Q₈	—	2	64	no	—
383	C₂×Q₈	—	2	24	no	—
384	C₂×Q₈	—	2	4	no	—
385	C₂×Q₈	—	4	12	no	—
386	C₂×Q₈	C₁₃×#41	1	8	yes	—
387	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
388	C₂×Q₈	C₂⁴×C₁₃	1	24	yes	—
389	C₂×Q₈	C₂⁴×C₁₃	1	24	yes	—
390	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
391	C₂×D₄	—	2	12	no	—
392	C₂×D₄	—	2	4	no	—
393	C₂×D₄	—	4	12	no	—
394	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
395	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
396	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
397	C₂²×C₄	—	2	24	no	—
398	C₂²×C₄	—	2	12	no	—
399	C₂²×C₄	—	2	12	no	—
400	C₂²×C₄	—	4	6	no	—
401	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
402	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
403	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
404	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
405	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
406	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
407	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
408	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
409	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
410	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
411	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
412	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
413	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
414	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
415	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
416	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
417	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
418	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
419	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
420	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
421	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
422	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
423	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
424	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
425	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
426	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
427	C₂²⋊C₄	C₂⁴×C₁₃	1	48	yes	—
428	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
429	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
430	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
431	C₄²	C₂⁴×C₁₃	1	4	yes	—
432	C₄²	C₂⁴×C₁₃	1	12	yes	—
433	C₄²	C₂⁴×C₁₃	1	12	yes	—
434	C₄²	C₂⁴×C₁₃	1	12	yes	—
435	C₄²	C₂⁴×C₁₃	1	48	yes	—
436	C₄²	C₂⁴×C₁₃	1	24	yes	—
437	C₁₃	C₂×#3518	1	1	yes	characteristic, direct product factor, Sylow
438	C₂³	—	2	4	no	—
439	C₂³	—	2	6	no	—
440	C₂³	—	2	6	no	—
441	C₂³	—	2	4	no	—
442	C₂³	—	2	6	no	—
443	C₂³	—	2	4	no	—
444	C₂³	C₂⁵×C₁₃	1	4	yes	—
445	C₂³	C₂⁵×C₁₃	1	6	yes	—
446	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
447	Q₈	—	2	48	no	—
448	Q₈	—	2	8	no	—
449	Q₈	—	4	24	no	—
450	Q₈	C₂×C₁₃×#41	1	16	yes	—
451	D₄	—	2	24	no	—
452	D₄	—	2	8	no	—
453	D₄	—	4	24	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	12	no	—
456	C₂×C₄	—	2	6	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	6	no	—
460	C₂×C₄	—	2	12	no	—
461	C₂×C₄	—	2	48	no	—
462	C₂×C₄	—	2	24	no	—
463	C₂×C₄	—	2	24	no	—
464	C₂×C₄	—	4	12	no	—
465	C₂×C₄	C₂×C₁₃×#41	1	12	yes	—
466	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
467	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
468	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
469	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
470	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
471	C₂×C₄	C₂⁵×C₁₃	1	12	yes	—
472	C₂×C₄	C₂⁵×C₁₃	1	12	yes	—
473	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
474	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
475	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
476	C₂²	—	2	4	no	—
477	C₂²	—	2	6	no	—
478	C₂²	—	2	6	no	—
479	C₂²	—	2	4	no	—
480	C₂²	—	2	6	no	—
481	C₂²	—	2	4	no	—
482	C₂²	—	4	8	no	—
483	C₂²	—	4	12	no	—
484	C₂²	C₂²×C₁₃×#41	1	2	yes	—
485	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
486	C₂²	C₁₃×#585	1	2	yes	—
487	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
488	C₄	—	2	2	no	—
489	C₄	—	2	12	no	—
490	C₄	—	2	6	no	—
491	C₄	—	2	4	no	—
492	C₄	—	2	2	no	—
493	C₄	—	2	6	no	—
494	C₄	—	2	12	no	—
495	C₄	C₂²×C₁₃×#41	1	12	yes	—
496	C₄	C₂×C₁₃×2₋¹⁺⁴	1	4	yes	—
497	C₂	—	4	4	no	—
498	C₂	—	4	6	no	—
499	C₂	C₁₃×#3518	1	4	yes	direct product factor
500	C₂	C₂³×C₁₃×#41	1	1	yes	characteristic
501	C₂	C₂²×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
502	C₂	C₂×C₁₃×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3518	C₂	direct (N × H)
2. C₂×Q₈²×C₁₃	C₂	semidirect
3. C₂×C₁₃×#556	C₂	semidirect
4. C₂×C₁₃×#556	C₂	semidirect
5. C₂×C₁₃×#555	C₂	semidirect
6. C₂×D₄×Q₈×C₁₃	C₂	semidirect
7. C₂×C₁₃×#548	C₂	semidirect
8. C₂×C₁₃×#542	C₂	semidirect
9. C₂×C₁₃×#533	C₂	semidirect
10. C₂×C₁₃×#529	C₂	semidirect
11. C₂×C₁₃×#519	C₂	semidirect
12. C₂×C₄×C₁₃×#41	C₂	semidirect
15. Q₈²×C₁₃	C₂²	semidirect
16. C₁₃×#556	C₂²	semidirect
17. C₁₃×#556	C₂²	semidirect
18. C₁₃×#555	C₂²	semidirect
19. D₄×Q₈×C₁₃	C₂²	semidirect
20. C₁₃×#548	C₂²	semidirect
21. C₁₃×#542	C₂²	semidirect
22. C₁₃×#533	C₂²	semidirect
26. C₁₃×#529	C₂²	semidirect
40. C₁₃×#519	C₂²	semidirect
41. C₄×C₁₃×#41	C₂²	semidirect
128. C₂×#3518	C₁₃	direct (N × H)
187. #3518	C₂×C₁₃	direct (N × H)
188. C₂×Q₈²	C₂×C₁₃	semidirect
189. C₂×#556	C₂×C₁₃	semidirect
190. C₂×#556	C₂×C₁₃	semidirect
191. C₂×#555	C₂×C₁₃	semidirect
192. C₂×D₄×Q₈	C₂×C₁₃	semidirect
193. C₂×#548	C₂×C₁₃	semidirect
194. C₂×#542	C₂×C₁₃	semidirect
195. C₂×#533	C₂×C₁₃	semidirect
196. C₂×#529	C₂×C₁₃	semidirect
197. C₂×#519	C₂×C₁₃	semidirect
198. C₂×C₄×#41	C₂×C₁₃	semidirect
239. Q₈²	C₂²×C₁₃	semidirect
240. #556	C₂²×C₁₃	semidirect
241. #556	C₂²×C₁₃	semidirect
242. #555	C₂²×C₁₃	semidirect
243. D₄×Q₈	C₂²×C₁₃	semidirect
244. #548	C₂²×C₁₃	semidirect
245. #542	C₂²×C₁₃	semidirect
246. #533	C₂²×C₁₃	semidirect
250. #529	C₂²×C₁₃	semidirect
264. #519	C₂²×C₁₃	semidirect
265. C₄×#41	C₂²×C₁₃	semidirect
375. C₂×C₁₃	#3518	direct (N × H)
437. C₁₃	C₂×#3518	direct (N × H)
499. C₂	C₁₃×#3518	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#3518	2
C₂×Q₈²×C₁₃	2
C₂×C₁₃×#556	2
C₂×C₁₃×#555	2
C₂×D₄×Q₈×C₁₃	2
C₂×C₁₃×#548	2
C₂×C₁₃×#542	2
C₂×C₁₃×#533	2
C₂×C₁₃×#529	2
C₂×C₁₃×#519	2
C₂×C₄×C₁₃×#41	2
C₂×#3518	13

Subgroups — C2×C13×#3518 #15749130

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3518 #15749130