Subgroups — C₂×C₁₃×#3489 #15749140

Order 3328.

11438 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3489	C₂	1	32	yes	maximal, direct product factor
4	C₂×D₄×Q₈×C₁₃	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#548	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#547	C₂	1	6	yes	maximal, complemented
7	C₂×C₁₃×#546	C₂	1	6	yes	maximal, complemented
8	C₂×C₁₃×#537	C₂	1	3	yes	maximal, complemented
9	C₂×C₁₃×#536	C₂	1	3	yes	maximal, complemented
10	C₂×C₁₃×#525	C₂	1	3	yes	maximal, complemented
11	C₂²×C₁₃×C₂²⋊Q₈	C₂	1	3	yes	maximal, complemented
12	C₂×C₁₃×#520	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×2₋¹⁺⁴	—	2	16	no	—
14	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	16	yes	complemented
15	C₂²×C₁₃×#41	—	2	16	no	—
16	C₂²×C₁₃×#41	C₂²	1	3	yes	—
17	C₂²×C₁₃×#41	C₂²	1	3	yes	—
18	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×#41	C₂²	1	16	yes	complemented
21	C₂²×C₁₃×#41	C₂²	1	3	yes	complemented
22	C₂²×C₁₃×#41	C₂²	1	6	yes	complemented
23	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₂³×Q₈×C₁₃	C₂²	1	3	yes	complemented
25	C₂³×Q₈×C₁₃	C₂²	1	2	yes	complemented
26	C₂³×D₄×C₁₃	C₂²	1	3	yes	—
27	C₂⁴×C₄×C₁₃	C₂²	1	3	yes	—
28	D₄×Q₈×C₁₃	C₂²	1	32	yes	complemented
29	C₁₃×#548	C₂²	1	32	yes	complemented
30	C₁₃×#547	C₂²	1	96	yes	complemented
31	C₁₃×#546	C₂²	1	96	yes	complemented
32	C₁₃×#537	C₂²	1	48	yes	complemented
33	C₁₃×#536	C₂²	1	48	yes	complemented
34	C₂×C₁₃×C₄⋊Q₈	C₂²	1	6	yes	complemented
35	C₂×C₁₃×#124	C₂²	1	6	yes	complemented
36	C₁₃×#525	C₂²	1	48	yes	complemented
37	C₂×C₁₃×#123	C₂²	1	6	yes	complemented
38	C₂×C₁₃×#123	C₂²	1	12	yes	complemented
39	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	3	yes	—
40	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	6	yes	—
41	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	6	yes	complemented
42	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	6	yes	complemented
43	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	3	yes	complemented
44	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	6	yes	complemented
45	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	48	yes	complemented
46	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×#121	C₂²	1	3	yes	complemented
48	C₂×C₁₃×#121	C₂²	1	12	yes	complemented
49	C₂×C₁₃×#121	C₂²	1	6	yes	complemented
50	C₂×C₁₃×#120	C₂²	1	6	yes	—
51	C₁₃×#520	C₂²	1	16	yes	complemented
52	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
53	C₂×C₄×D₄×C₁₃	C₂²	1	6	yes	—
54	C₂×C₄×D₄×C₁₃	C₂²	1	6	yes	complemented
55	C₂×C₄×D₄×C₁₃	C₂²	1	6	yes	complemented
56	C₂×C₁₃×#117	C₂²	1	3	yes	complemented
57	C₂²×C₁₃×C₄⋊C₄	C₂²	1	3	yes	complemented
58	C₂²×C₁₃×C₄⋊C₄	C₂²	1	6	yes	complemented
59	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	6	yes	—
60	C₂⁵×C₁₃	C₂³	1	3	yes	—
61	C₁₃×2₋¹⁺⁴	—	2	128	no	—
62	C₂×C₁₃×#41	—	2	128	no	—
63	C₂×C₁₃×#41	—	2	8	no	—
64	C₂×C₁₃×#41	—	2	24	no	—
65	C₂×C₁₃×#41	—	2	48	no	—
66	C₂×C₁₃×#41	—	2	24	no	—
67	C₂×C₁₃×#41	—	2	24	no	—
68	C₂×C₁₃×#41	D₄	1	16	yes	complemented
69	C₂×C₁₃×#41	C₂³	1	24	yes	—
70	C₂×C₁₃×#41	C₂³	1	24	yes	—
71	C₂×C₁₃×#41	C₂³	1	8	yes	—
72	C₂×C₁₃×#41	C₂³	1	8	yes	—
73	C₂×C₁₃×#41	C₂³	1	24	yes	complemented
74	C₂×C₁₃×#41	C₂³	1	48	yes	complemented
75	C₂²×Q₈×C₁₃	—	2	8	no	—
76	C₂²×Q₈×C₁₃	—	2	16	no	—
77	C₂²×Q₈×C₁₃	—	2	24	no	—
78	C₂²×Q₈×C₁₃	C₂³	1	3	yes	—
79	C₂²×Q₈×C₁₃	C₂³	1	6	yes	—
80	C₂²×Q₈×C₁₃	C₂³	1	3	yes	—
81	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
82	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
83	C₂²×Q₈×C₁₃	C₂³	1	24	yes	complemented
84	C₂²×Q₈×C₁₃	C₂³	1	16	yes	complemented
85	C₂²×D₄×C₁₃	—	2	24	no	—
86	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
87	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
88	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
90	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
91	C₂²×D₄×C₁₃	C₂³	1	24	yes	—
92	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
93	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
94	C₂³×C₄×C₁₃	—	2	24	no	—
95	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
96	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
97	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
98	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
99	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
100	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
102	C₂³×C₄×C₁₃	C₂³	1	24	yes	—
103	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
104	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
105	C₁₃×C₄⋊Q₈	C₂³	1	48	yes	complemented
106	C₁₃×#124	C₂³	1	48	yes	complemented
107	C₁₃×#123	C₂³	1	48	yes	complemented
108	C₁₃×#123	C₂³	1	96	yes	complemented
109	C₁₃×C₂²⋊Q₈	C₂³	1	24	yes	—
110	C₁₃×C₂²⋊Q₈	C₂³	1	48	yes	—
111	C₁₃×C₂²⋊Q₈	C₂³	1	48	yes	complemented
112	C₁₃×C₂²⋊Q₈	C₂³	1	48	yes	complemented
113	C₁₃×C₂²⋊Q₈	C₂³	1	24	yes	complemented
114	C₁₃×C₂²⋊Q₈	C₂³	1	48	yes	complemented
115	C₁₃×#121	C₂³	1	8	yes	—
116	C₁₃×#121	C₂³	1	24	yes	complemented
117	C₁₃×#121	C₂³	1	96	yes	complemented
118	C₁₃×#121	C₂³	1	48	yes	complemented
119	C₁₃×#120	C₂³	1	48	yes	—
120	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
121	C₄×D₄×C₁₃	C₂³	1	48	yes	—
122	C₄×D₄×C₁₃	C₂³	1	48	yes	complemented
123	C₄×D₄×C₁₃	C₂³	1	48	yes	complemented
124	C₁₃×#117	C₂³	1	24	yes	complemented
125	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
126	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
127	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
128	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
129	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
130	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
131	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	complemented
132	C₂×C₁₃×C₄⋊C₄	C₂³	1	48	yes	complemented
133	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
134	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
135	C₂×C₁₃×C₂²⋊C₄	C₂³	1	48	yes	—
136	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
137	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
138	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
139	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
140	C₂×C₄²×C₁₃	C₂³	1	6	yes	—
141	C₂×#3489	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
142	C₂⁴×C₁₃	—	2	12	no	—
143	C₂⁴×C₁₃	—	2	12	no	—
144	C₂⁴×C₁₃	—	4	6	no	—
145	C₂⁴×C₁₃	C₂⁴	1	3	yes	—
146	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
147	C₂⁴×C₁₃	C₂⁴	1	12	yes	—
148	C₂⁴×C₁₃	C₂⁴	1	3	yes	—
149	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
150	C₁₃×#41	—	2	32	no	—
151	C₁₃×#41	—	2	96	no	—
152	C₁₃×#41	—	2	192	no	—
153	C₁₃×#41	—	2	96	no	—
154	C₁₃×#41	—	2	96	no	—
155	C₁₃×#41	C₂×D₄	1	64	yes	complemented
156	C₂×Q₈×C₁₃	—	2	32	no	—
157	C₂×Q₈×C₁₃	—	2	64	no	—
158	C₂×Q₈×C₁₃	—	2	12	no	—
159	C₂×Q₈×C₁₃	—	2	24	no	—
160	C₂×Q₈×C₁₃	—	2	12	no	—
161	C₂×Q₈×C₁₃	—	2	96	no	—
162	C₂×Q₈×C₁₃	C₂×D₄	1	8	yes	—
163	C₂×Q₈×C₁₃	C₂⁴	1	12	yes	—
164	C₂×Q₈×C₁₃	C₂⁴	1	24	yes	—
165	C₂×Q₈×C₁₃	C₂⁴	1	12	yes	—
166	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
167	C₂×D₄×C₁₃	—	2	24	no	—
168	C₂×D₄×C₁₃	—	2	24	no	—
169	C₂×D₄×C₁₃	—	2	8	no	—
170	C₂×D₄×C₁₃	—	2	96	no	—
171	C₂×D₄×C₁₃	—	2	12	no	—
172	C₂×D₄×C₁₃	—	2	4	no	—
173	C₂×D₄×C₁₃	—	4	12	no	—
174	C₂×D₄×C₁₃	C₂×D₄	1	24	yes	—
175	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
176	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
177	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
178	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
179	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
180	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
181	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
182	C₂²×C₄×C₁₃	—	2	12	no	—
183	C₂²×C₄×C₁₃	—	2	24	no	—
184	C₂²×C₄×C₁₃	—	2	4	no	—
185	C₂²×C₄×C₁₃	—	2	12	no	—
186	C₂²×C₄×C₁₃	—	2	12	no	—
187	C₂²×C₄×C₁₃	—	2	12	no	—
188	C₂²×C₄×C₁₃	—	2	96	no	—
189	C₂²×C₄×C₁₃	—	2	24	no	—
190	C₂²×C₄×C₁₃	—	4	12	no	—
191	C₂²×C₄×C₁₃	C₂×D₄	1	24	yes	—
192	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
193	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
194	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
195	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
196	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
197	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
198	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
199	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
201	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
202	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
203	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
204	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
205	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
206	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
207	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
208	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
209	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
210	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
211	C₁₃×C₄⋊C₄	C₂⁴	1	48	yes	—
212	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
213	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
214	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
215	C₁₃×C₂²⋊C₄	C₂⁴	1	48	yes	—
216	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
217	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
218	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
219	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
220	C₄²×C₁₃	C₂⁴	1	24	yes	—
221	C₂²×2₋¹⁺⁴	C₂×C₁₃	1	1	yes	characteristic, complemented
222	C₂³×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#3489	C₂×C₁₃	1	32	yes	direct product factor
224	C₂×D₄×Q₈	C₂×C₁₃	1	2	yes	complemented
225	C₂×#548	C₂×C₁₃	1	2	yes	complemented
226	C₂×#547	C₂×C₁₃	1	6	yes	complemented
227	C₂×#546	C₂×C₁₃	1	6	yes	complemented
228	C₂×#537	C₂×C₁₃	1	3	yes	complemented
229	C₂×#536	C₂×C₁₃	1	3	yes	complemented
230	C₂×#525	C₂×C₁₃	1	3	yes	complemented
231	C₂²×C₂²⋊Q₈	C₂×C₁₃	1	3	yes	complemented
232	C₂×#520	C₂×C₁₃	1	1	yes	characteristic, complemented
233	C₂³×C₁₃	—	2	2	no	—
234	C₂³×C₁₃	—	2	6	no	—
235	C₂³×C₁₃	—	2	6	no	—
236	C₂³×C₁₃	—	2	2	no	—
237	C₂³×C₁₃	—	2	4	no	—
238	C₂³×C₁₃	—	2	24	no	—
239	C₂³×C₁₃	—	2	6	no	—
240	C₂³×C₁₃	—	2	4	no	—
241	C₂³×C₁₃	—	2	6	no	—
242	C₂³×C₁₃	—	2	24	no	—
243	C₂³×C₁₃	—	2	4	no	—
244	C₂³×C₁₃	—	2	6	no	—
245	C₂³×C₁₃	—	4	12	no	—
246	C₂³×C₁₃	—	4	48	no	—
247	C₂³×C₁₃	C₂²×D₄	1	12	yes	—
248	C₂³×C₁₃	2₋¹⁺⁴	1	4	yes	complemented
249	C₂³×C₁₃	C₂⁵	1	6	yes	—
250	C₂³×C₁₃	C₂⁵	1	4	yes	—
251	C₂³×C₁₃	C₂⁵	1	6	yes	—
252	C₂³×C₁₃	C₂⁵	1	2	yes	—
253	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
254	Q₈×C₁₃	—	2	24	no	—
255	Q₈×C₁₃	—	2	48	no	—
256	Q₈×C₁₃	—	2	24	no	—
257	Q₈×C₁₃	C₂²×D₄	1	16	yes	—
258	D₄×C₁₃	—	2	48	no	—
259	D₄×C₁₃	—	2	48	no	—
260	D₄×C₁₃	—	2	16	no	—
261	D₄×C₁₃	—	2	24	no	—
262	D₄×C₁₃	—	2	8	no	—
263	D₄×C₁₃	—	4	24	no	—
264	D₄×C₁₃	C₂²×D₄	1	48	yes	—
265	C₂×C₄×C₁₃	—	2	2	no	—
266	C₂×C₄×C₁₃	—	2	6	no	—
267	C₂×C₄×C₁₃	—	2	12	no	—
268	C₂×C₄×C₁₃	—	2	24	no	—
269	C₂×C₄×C₁₃	—	2	48	no	—
270	C₂×C₄×C₁₃	—	2	4	no	—
271	C₂×C₄×C₁₃	—	2	12	no	—
272	C₂×C₄×C₁₃	—	2	8	no	—
273	C₂×C₄×C₁₃	—	2	24	no	—
274	C₂×C₄×C₁₃	—	2	24	no	—
275	C₂×C₄×C₁₃	—	2	24	no	—
276	C₂×C₄×C₁₃	—	2	48	no	—
277	C₂×C₄×C₁₃	—	4	24	no	—
278	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
279	C₂×C₄×C₁₃	C₂²×D₄	1	12	yes	—
280	C₂×C₄×C₁₃	C₂²×D₄	1	48	yes	—
281	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
282	C₂×C₄×C₁₃	C₂⁵	1	12	yes	—
283	C₂×C₄×C₁₃	C₂⁵	1	12	yes	—
284	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
285	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
286	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
287	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
288	C₂×2₋¹⁺⁴	—	2	16	no	—
289	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	16	yes	complemented
290	C₂²×#41	—	2	16	no	—
291	C₂²×#41	C₂²×C₁₃	1	3	yes	—
292	C₂²×#41	C₂²×C₁₃	1	3	yes	—
293	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
294	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
295	C₂²×#41	C₂²×C₁₃	1	16	yes	complemented
296	C₂²×#41	C₂²×C₁₃	1	3	yes	complemented
297	C₂²×#41	C₂²×C₁₃	1	6	yes	complemented
298	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
299	C₂³×Q₈	C₂²×C₁₃	1	3	yes	complemented
300	C₂³×Q₈	C₂²×C₁₃	1	2	yes	complemented
301	C₂³×D₄	C₂²×C₁₃	1	3	yes	—
302	C₂⁴×C₄	C₂²×C₁₃	1	3	yes	—
303	D₄×Q₈	C₂²×C₁₃	1	32	yes	complemented
304	#548	C₂²×C₁₃	1	32	yes	complemented
305	#547	C₂²×C₁₃	1	96	yes	complemented
306	#546	C₂²×C₁₃	1	96	yes	complemented
307	#537	C₂²×C₁₃	1	48	yes	complemented
308	#536	C₂²×C₁₃	1	48	yes	complemented
309	C₂×C₄⋊Q₈	C₂²×C₁₃	1	6	yes	complemented
310	C₂×#124	C₂²×C₁₃	1	6	yes	complemented
311	#525	C₂²×C₁₃	1	48	yes	complemented
312	C₂×#123	C₂²×C₁₃	1	6	yes	complemented
313	C₂×#123	C₂²×C₁₃	1	12	yes	complemented
314	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	3	yes	—
315	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	6	yes	—
316	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	6	yes	complemented
317	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	6	yes	complemented
318	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	3	yes	complemented
319	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	6	yes	complemented
320	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	48	yes	complemented
321	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
322	C₂×#121	C₂²×C₁₃	1	3	yes	complemented
323	C₂×#121	C₂²×C₁₃	1	12	yes	complemented
324	C₂×#121	C₂²×C₁₃	1	6	yes	complemented
325	C₂×#120	C₂²×C₁₃	1	6	yes	—
326	#520	C₂²×C₁₃	1	16	yes	complemented
327	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
328	C₂×C₄×D₄	C₂²×C₁₃	1	6	yes	—
329	C₂×C₄×D₄	C₂²×C₁₃	1	6	yes	complemented
330	C₂×C₄×D₄	C₂²×C₁₃	1	6	yes	complemented
331	C₂×#117	C₂²×C₁₃	1	3	yes	complemented
332	C₂²×C₄⋊C₄	C₂²×C₁₃	1	3	yes	complemented
333	C₂²×C₄⋊C₄	C₂²×C₁₃	1	6	yes	complemented
334	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	6	yes	—
335	C₂²×C₁₃	—	2	2	no	—
336	C₂²×C₁₃	—	2	6	no	—
337	C₂²×C₁₃	—	2	6	no	—
338	C₂²×C₁₃	—	2	2	no	—
339	C₂²×C₁₃	—	2	8	no	—
340	C₂²×C₁₃	—	2	24	no	—
341	C₂²×C₁₃	—	2	4	no	—
342	C₂²×C₁₃	—	2	6	no	—
343	C₂²×C₁₃	—	2	4	no	—
344	C₂²×C₁₃	—	2	6	no	—
345	C₂²×C₁₃	—	2	4	no	—
346	C₂²×C₁₃	—	2	6	no	—
347	C₂²×C₁₃	—	4	48	no	—
348	C₂²×C₁₃	—	4	8	no	—
349	C₂²×C₁₃	—	4	12	no	—
350	C₂²×C₁₃	C₂³×D₄	1	12	yes	—
351	C₂²×C₁₃	C₂³×D₄	1	2	yes	—
352	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
353	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	4	yes	complemented
354	C₂²×C₁₃	#585	1	2	yes	—
355	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
356	C₄×C₁₃	—	2	2	no	—
357	C₄×C₁₃	—	2	6	no	—
358	C₄×C₁₃	—	2	12	no	—
359	C₄×C₁₃	—	2	4	no	—
360	C₄×C₁₃	—	2	12	no	—
361	C₄×C₁₃	C₂³×D₄	1	4	yes	—
362	C₄×C₁₃	C₂³×D₄	1	12	yes	—
363	C₂⁵	C₂³×C₁₃	1	3	yes	—
364	2₋¹⁺⁴	—	2	128	no	—
365	C₂×#41	—	2	128	no	—
366	C₂×#41	—	2	8	no	—
367	C₂×#41	—	2	24	no	—
368	C₂×#41	—	2	48	no	—
369	C₂×#41	—	2	24	no	—
370	C₂×#41	—	2	24	no	—
371	C₂×#41	D₄×C₁₃	1	16	yes	complemented
372	C₂×#41	C₂³×C₁₃	1	24	yes	—
373	C₂×#41	C₂³×C₁₃	1	24	yes	—
374	C₂×#41	C₂³×C₁₃	1	8	yes	—
375	C₂×#41	C₂³×C₁₃	1	8	yes	—
376	C₂×#41	C₂³×C₁₃	1	24	yes	complemented
377	C₂×#41	C₂³×C₁₃	1	48	yes	complemented
378	C₂²×Q₈	—	2	8	no	—
379	C₂²×Q₈	—	2	16	no	—
380	C₂²×Q₈	—	2	24	no	—
381	C₂²×Q₈	C₂³×C₁₃	1	3	yes	—
382	C₂²×Q₈	C₂³×C₁₃	1	6	yes	—
383	C₂²×Q₈	C₂³×C₁₃	1	3	yes	—
384	C₂²×Q₈	C₂³×C₁₃	1	8	yes	—
385	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
386	C₂²×Q₈	C₂³×C₁₃	1	24	yes	complemented
387	C₂²×Q₈	C₂³×C₁₃	1	16	yes	complemented
388	C₂²×D₄	—	2	24	no	—
389	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
390	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
391	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
392	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
393	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
394	C₂²×D₄	C₂³×C₁₃	1	24	yes	—
395	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
396	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
397	C₂³×C₄	—	2	24	no	—
398	C₂³×C₄	C₂³×C₁₃	1	6	yes	—
399	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
400	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
401	C₂³×C₄	C₂³×C₁₃	1	6	yes	—
402	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
403	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
404	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
405	C₂³×C₄	C₂³×C₁₃	1	24	yes	—
406	C₂³×C₄	C₂³×C₁₃	1	6	yes	—
407	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
408	C₄⋊Q₈	C₂³×C₁₃	1	48	yes	complemented
409	#124	C₂³×C₁₃	1	48	yes	complemented
410	#123	C₂³×C₁₃	1	48	yes	complemented
411	#123	C₂³×C₁₃	1	96	yes	complemented
412	C₂²⋊Q₈	C₂³×C₁₃	1	24	yes	—
413	C₂²⋊Q₈	C₂³×C₁₃	1	48	yes	—
414	C₂²⋊Q₈	C₂³×C₁₃	1	48	yes	complemented
415	C₂²⋊Q₈	C₂³×C₁₃	1	48	yes	complemented
416	C₂²⋊Q₈	C₂³×C₁₃	1	24	yes	complemented
417	C₂²⋊Q₈	C₂³×C₁₃	1	48	yes	complemented
418	#121	C₂³×C₁₃	1	8	yes	—
419	#121	C₂³×C₁₃	1	24	yes	complemented
420	#121	C₂³×C₁₃	1	96	yes	complemented
421	#121	C₂³×C₁₃	1	48	yes	complemented
422	#120	C₂³×C₁₃	1	48	yes	—
423	C₄×Q₈	C₂³×C₁₃	1	16	yes	complemented
424	C₄×D₄	C₂³×C₁₃	1	48	yes	—
425	C₄×D₄	C₂³×C₁₃	1	48	yes	complemented
426	C₄×D₄	C₂³×C₁₃	1	48	yes	complemented
427	#117	C₂³×C₁₃	1	24	yes	complemented
428	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
429	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
430	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
431	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
432	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
433	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
434	C₂×C₄⋊C₄	C₂³×C₁₃	1	24	yes	complemented
435	C₂×C₄⋊C₄	C₂³×C₁₃	1	48	yes	complemented
436	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
437	C₂×C₂²⋊C₄	C₂³×C₁₃	1	12	yes	—
438	C₂×C₂²⋊C₄	C₂³×C₁₃	1	48	yes	—
439	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
440	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
441	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
442	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
443	C₂×C₄²	C₂³×C₁₃	1	6	yes	—
444	C₂×C₁₃	—	2	4	no	—
445	C₂×C₁₃	—	2	12	no	—
446	C₂×C₁₃	—	4	4	no	—
447	C₂×C₁₃	—	4	6	no	—
448	C₂×C₁₃	#3489	1	4	yes	direct product factor
449	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
450	C₂×C₁₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
451	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
452	C₂⁴	—	2	12	no	—
453	C₂⁴	—	2	12	no	—
454	C₂⁴	—	4	6	no	—
455	C₂⁴	C₂⁴×C₁₃	1	3	yes	—
456	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
457	C₂⁴	C₂⁴×C₁₃	1	12	yes	—
458	C₂⁴	C₂⁴×C₁₃	1	3	yes	—
459	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
460	#41	—	2	32	no	—
461	#41	—	2	96	no	—
462	#41	—	2	192	no	—
463	#41	—	2	96	no	—
464	#41	—	2	96	no	—
465	#41	C₂×D₄×C₁₃	1	64	yes	complemented
466	C₂×Q₈	—	2	32	no	—
467	C₂×Q₈	—	2	64	no	—
468	C₂×Q₈	—	2	12	no	—
469	C₂×Q₈	—	2	24	no	—
470	C₂×Q₈	—	2	12	no	—
471	C₂×Q₈	—	2	96	no	—
472	C₂×Q₈	C₂×D₄×C₁₃	1	8	yes	—
473	C₂×Q₈	C₂⁴×C₁₃	1	12	yes	—
474	C₂×Q₈	C₂⁴×C₁₃	1	24	yes	—
475	C₂×Q₈	C₂⁴×C₁₃	1	12	yes	—
476	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
477	C₂×D₄	—	2	24	no	—
478	C₂×D₄	—	2	24	no	—
479	C₂×D₄	—	2	8	no	—
480	C₂×D₄	—	2	96	no	—
481	C₂×D₄	—	2	12	no	—
482	C₂×D₄	—	2	4	no	—
483	C₂×D₄	—	4	12	no	—
484	C₂×D₄	C₂×D₄×C₁₃	1	24	yes	—
485	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
486	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
487	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
488	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
489	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
490	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
491	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
492	C₂²×C₄	—	2	12	no	—
493	C₂²×C₄	—	2	24	no	—
494	C₂²×C₄	—	2	4	no	—
495	C₂²×C₄	—	2	12	no	—
496	C₂²×C₄	—	2	12	no	—
497	C₂²×C₄	—	2	12	no	—
498	C₂²×C₄	—	2	96	no	—
499	C₂²×C₄	—	2	24	no	—
500	C₂²×C₄	—	4	12	no	—
501	C₂²×C₄	C₂×D₄×C₁₃	1	24	yes	—
502	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
503	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
504	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
505	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
506	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
507	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
508	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
509	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
510	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
511	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
512	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
513	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
514	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
515	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
516	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
517	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
518	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
519	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
520	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
521	C₄⋊C₄	C₂⁴×C₁₃	1	48	yes	—
522	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
523	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
524	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
525	C₂²⋊C₄	C₂⁴×C₁₃	1	48	yes	—
526	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
527	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
528	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
529	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
530	C₄²	C₂⁴×C₁₃	1	24	yes	—
531	C₁₃	C₂×#3489	1	1	yes	characteristic, direct product factor, Sylow
532	C₂³	—	2	2	no	—
533	C₂³	—	2	6	no	—
534	C₂³	—	2	6	no	—
535	C₂³	—	2	2	no	—
536	C₂³	—	2	4	no	—
537	C₂³	—	2	24	no	—
538	C₂³	—	2	6	no	—
539	C₂³	—	2	4	no	—
540	C₂³	—	2	6	no	—
541	C₂³	—	2	24	no	—
542	C₂³	—	2	4	no	—
543	C₂³	—	2	6	no	—
544	C₂³	—	4	12	no	—
545	C₂³	—	4	48	no	—
546	C₂³	C₂²×D₄×C₁₃	1	12	yes	—
547	C₂³	C₁₃×2₋¹⁺⁴	1	4	yes	complemented
548	C₂³	C₂⁵×C₁₃	1	6	yes	—
549	C₂³	C₂⁵×C₁₃	1	4	yes	—
550	C₂³	C₂⁵×C₁₃	1	6	yes	—
551	C₂³	C₂⁵×C₁₃	1	2	yes	—
552	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
553	Q₈	—	2	24	no	—
554	Q₈	—	2	48	no	—
555	Q₈	—	2	24	no	—
556	Q₈	C₂²×D₄×C₁₃	1	16	yes	—
557	D₄	—	2	48	no	—
558	D₄	—	2	48	no	—
559	D₄	—	2	16	no	—
560	D₄	—	2	24	no	—
561	D₄	—	2	8	no	—
562	D₄	—	4	24	no	—
563	D₄	C₂²×D₄×C₁₃	1	48	yes	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	6	no	—
566	C₂×C₄	—	2	12	no	—
567	C₂×C₄	—	2	24	no	—
568	C₂×C₄	—	2	48	no	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	2	12	no	—
571	C₂×C₄	—	2	8	no	—
572	C₂×C₄	—	2	24	no	—
573	C₂×C₄	—	2	24	no	—
574	C₂×C₄	—	2	24	no	—
575	C₂×C₄	—	2	48	no	—
576	C₂×C₄	—	4	24	no	—
577	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
578	C₂×C₄	C₂²×D₄×C₁₃	1	12	yes	—
579	C₂×C₄	C₂²×D₄×C₁₃	1	48	yes	—
580	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
581	C₂×C₄	C₂⁵×C₁₃	1	12	yes	—
582	C₂×C₄	C₂⁵×C₁₃	1	12	yes	—
583	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
584	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
585	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
586	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
587	C₂²	—	2	2	no	—
588	C₂²	—	2	6	no	—
589	C₂²	—	2	6	no	—
590	C₂²	—	2	2	no	—
591	C₂²	—	2	8	no	—
592	C₂²	—	2	24	no	—
593	C₂²	—	2	4	no	—
594	C₂²	—	2	6	no	—
595	C₂²	—	2	4	no	—
596	C₂²	—	2	6	no	—
597	C₂²	—	2	4	no	—
598	C₂²	—	2	6	no	—
599	C₂²	—	4	48	no	—
600	C₂²	—	4	8	no	—
601	C₂²	—	4	12	no	—
602	C₂²	C₂³×D₄×C₁₃	1	12	yes	—
603	C₂²	C₂³×D₄×C₁₃	1	2	yes	—
604	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
605	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	4	yes	complemented
606	C₂²	C₁₃×#585	1	2	yes	—
607	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
608	C₄	—	2	2	no	—
609	C₄	—	2	6	no	—
610	C₄	—	2	12	no	—
611	C₄	—	2	4	no	—
612	C₄	—	2	12	no	—
613	C₄	C₂³×D₄×C₁₃	1	4	yes	—
614	C₄	C₂³×D₄×C₁₃	1	12	yes	—
615	C₂	—	2	4	no	—
616	C₂	—	2	12	no	—
617	C₂	—	4	6	no	—
618	C₂	—	4	4	no	—
619	C₂	C₁₃×#3489	1	4	yes	direct product factor
620	C₂	C₂⁴×D₄×C₁₃	1	1	yes	characteristic
621	C₂	C₂²×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
622	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. C₂²×C₁₃×2₋¹⁺⁴	C₂	semidirect
2. C₂³×C₁₃×#41	C₂	semidirect
3. C₁₃×#3489	C₂	direct (N × H)
4. C₂×D₄×Q₈×C₁₃	C₂	semidirect
5. C₂×C₁₃×#548	C₂	semidirect
6. C₂×C₁₃×#547	C₂	semidirect
7. C₂×C₁₃×#546	C₂	semidirect
8. C₂×C₁₃×#537	C₂	semidirect
9. C₂×C₁₃×#536	C₂	semidirect
10. C₂×C₁₃×#525	C₂	semidirect
11. C₂²×C₁₃×C₂²⋊Q₈	C₂	semidirect
12. C₂×C₁₃×#520	C₂	semidirect
14. C₂×C₁₃×2₋¹⁺⁴	C₂²	semidirect
20. C₂²×C₁₃×#41	C₂²	semidirect
21. C₂²×C₁₃×#41	C₂²	semidirect
22. C₂²×C₁₃×#41	C₂²	semidirect
24. C₂³×Q₈×C₁₃	C₂²	semidirect
25. C₂³×Q₈×C₁₃	C₂²	semidirect
28. D₄×Q₈×C₁₃	C₂²	semidirect
29. C₁₃×#548	C₂²	semidirect
30. C₁₃×#547	C₂²	semidirect
31. C₁₃×#546	C₂²	semidirect
32. C₁₃×#537	C₂²	semidirect
33. C₁₃×#536	C₂²	semidirect
34. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
35. C₂×C₁₃×#124	C₂²	semidirect
36. C₁₃×#525	C₂²	semidirect
37. C₂×C₁₃×#123	C₂²	semidirect
38. C₂×C₁₃×#123	C₂²	semidirect
41. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
42. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
43. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
44. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
45. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
47. C₂×C₁₃×#121	C₂²	semidirect
48. C₂×C₁₃×#121	C₂²	semidirect
49. C₂×C₁₃×#121	C₂²	semidirect
51. C₁₃×#520	C₂²	semidirect
52. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
54. C₂×C₄×D₄×C₁₃	C₂²	semidirect
55. C₂×C₄×D₄×C₁₃	C₂²	semidirect
56. C₂×C₁₃×#117	C₂²	semidirect
57. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
58. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
68. C₂×C₁₃×#41	D₄	semidirect
73. C₂×C₁₃×#41	C₂³	semidirect
74. C₂×C₁₃×#41	C₂³	semidirect
83. C₂²×Q₈×C₁₃	C₂³	semidirect
84. C₂²×Q₈×C₁₃	C₂³	semidirect
105. C₁₃×C₄⋊Q₈	C₂³	semidirect
106. C₁₃×#124	C₂³	semidirect
107. C₁₃×#123	C₂³	semidirect
108. C₁₃×#123	C₂³	semidirect
111. C₁₃×C₂²⋊Q₈	C₂³	semidirect
112. C₁₃×C₂²⋊Q₈	C₂³	semidirect
113. C₁₃×C₂²⋊Q₈	C₂³	semidirect
114. C₁₃×C₂²⋊Q₈	C₂³	semidirect
116. C₁₃×#121	C₂³	semidirect
117. C₁₃×#121	C₂³	semidirect
118. C₁₃×#121	C₂³	semidirect
120. C₄×Q₈×C₁₃	C₂³	semidirect
122. C₄×D₄×C₁₃	C₂³	semidirect
123. C₄×D₄×C₁₃	C₂³	semidirect
124. C₁₃×#117	C₂³	semidirect
131. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
132. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
141. C₂×#3489	C₁₃	direct (N × H)
155. C₁₃×#41	C₂×D₄	semidirect
221. C₂²×2₋¹⁺⁴	C₂×C₁₃	semidirect
222. C₂³×#41	C₂×C₁₃	semidirect
223. #3489	C₂×C₁₃	direct (N × H)
224. C₂×D₄×Q₈	C₂×C₁₃	semidirect
225. C₂×#548	C₂×C₁₃	semidirect
226. C₂×#547	C₂×C₁₃	semidirect
227. C₂×#546	C₂×C₁₃	semidirect
228. C₂×#537	C₂×C₁₃	semidirect
229. C₂×#536	C₂×C₁₃	semidirect
230. C₂×#525	C₂×C₁₃	semidirect
231. C₂²×C₂²⋊Q₈	C₂×C₁₃	semidirect
232. C₂×#520	C₂×C₁₃	semidirect
248. C₂³×C₁₃	2₋¹⁺⁴	semidirect
289. C₂×2₋¹⁺⁴	C₂²×C₁₃	semidirect
295. C₂²×#41	C₂²×C₁₃	semidirect
296. C₂²×#41	C₂²×C₁₃	semidirect
297. C₂²×#41	C₂²×C₁₃	semidirect
299. C₂³×Q₈	C₂²×C₁₃	semidirect
300. C₂³×Q₈	C₂²×C₁₃	semidirect
303. D₄×Q₈	C₂²×C₁₃	semidirect
304. #548	C₂²×C₁₃	semidirect
305. #547	C₂²×C₁₃	semidirect
306. #546	C₂²×C₁₃	semidirect
307. #537	C₂²×C₁₃	semidirect
308. #536	C₂²×C₁₃	semidirect
309. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
310. C₂×#124	C₂²×C₁₃	semidirect
311. #525	C₂²×C₁₃	semidirect
312. C₂×#123	C₂²×C₁₃	semidirect
313. C₂×#123	C₂²×C₁₃	semidirect
316. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
317. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
318. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
319. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
320. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
322. C₂×#121	C₂²×C₁₃	semidirect
323. C₂×#121	C₂²×C₁₃	semidirect
324. C₂×#121	C₂²×C₁₃	semidirect
326. #520	C₂²×C₁₃	semidirect
327. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
329. C₂×C₄×D₄	C₂²×C₁₃	semidirect
330. C₂×C₄×D₄	C₂²×C₁₃	semidirect
331. C₂×#117	C₂²×C₁₃	semidirect
332. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
333. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
353. C₂²×C₁₃	C₂×2₋¹⁺⁴	semidirect
371. C₂×#41	D₄×C₁₃	semidirect
376. C₂×#41	C₂³×C₁₃	semidirect
377. C₂×#41	C₂³×C₁₃	semidirect
386. C₂²×Q₈	C₂³×C₁₃	semidirect
387. C₂²×Q₈	C₂³×C₁₃	semidirect
408. C₄⋊Q₈	C₂³×C₁₃	semidirect
409. #124	C₂³×C₁₃	semidirect
410. #123	C₂³×C₁₃	semidirect
411. #123	C₂³×C₁₃	semidirect
414. C₂²⋊Q₈	C₂³×C₁₃	semidirect
415. C₂²⋊Q₈	C₂³×C₁₃	semidirect
416. C₂²⋊Q₈	C₂³×C₁₃	semidirect
417. C₂²⋊Q₈	C₂³×C₁₃	semidirect
419. #121	C₂³×C₁₃	semidirect
420. #121	C₂³×C₁₃	semidirect
421. #121	C₂³×C₁₃	semidirect
423. C₄×Q₈	C₂³×C₁₃	semidirect
425. C₄×D₄	C₂³×C₁₃	semidirect
426. C₄×D₄	C₂³×C₁₃	semidirect
427. #117	C₂³×C₁₃	semidirect
434. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
435. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
448. C₂×C₁₃	#3489	direct (N × H)
465. #41	C₂×D₄×C₁₃	semidirect
531. C₁₃	C₂×#3489	direct (N × H)
547. C₂³	C₁₃×2₋¹⁺⁴	semidirect
605. C₂²	C₂×C₁₃×2₋¹⁺⁴	semidirect
619. C₂	C₁₃×#3489	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×2₋¹⁺⁴	2
C₂³×C₁₃×#41	2
C₁₃×#3489	2
C₂×D₄×Q₈×C₁₃	2
C₂×C₁₃×#548	2
C₂×C₁₃×#547	2
C₂×C₁₃×#546	2
C₂×C₁₃×#537	2
C₂×C₁₃×#536	2
C₂×C₁₃×#525	2
C₂²×C₁₃×C₂²⋊Q₈	2
C₂×C₁₃×#520	2
C₂×#3489	13

Subgroups — C2×C13×#3489 #15749140

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3489 #15749140