Subgroups — C₂×C₁₃×#3506 #15749108

Order 3328.

7994 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3506	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₁₃×#559	C₂	1	4	yes	maximal, complemented
3	C₂×C₁₃×#556	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₃×#555	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#553	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₃×#550	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#547	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#538	C₂	1	4	yes	maximal, complemented
9	C₂×C₁₃×#535	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#525	C₂	1	4	yes	maximal, complemented
13	C₂×C₁₃×#520	C₂	1	2	yes	maximal, complemented
14	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₁₃×#41	C₂²	1	2	yes	—
16	C₂²×C₁₃×#41	C₂²	1	4	yes	complemented
17	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
19	C₁₃×#559	C₂²	1	64	yes	complemented
20	C₁₃×#556	C₂²	1	32	yes	complemented
21	C₁₃×#555	C₂²	1	32	yes	complemented
22	C₁₃×#553	C₂²	1	64	yes	complemented
23	C₁₃×#550	C₂²	1	32	yes	complemented
24	C₁₃×#547	C₂²	1	32	yes	complemented
25	C₁₃×#538	C₂²	1	64	yes	complemented
26	C₁₃×#535	C₂²	1	32	yes	complemented
27	C₁₃×#533	C₂²	1	16	yes	complemented
28	C₁₃×#532	C₂²	1	16	yes	complemented
29	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₁₃×#127	C₂²	1	4	yes	—
33	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₁₃×#126	C₂²	1	8	yes	complemented
35	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
36	C₂×C₁₃×#124	C₂²	1	4	yes	—
37	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
38	C₂×C₁₃×#124	C₂²	1	8	yes	complemented
39	C₁₃×#525	C₂²	1	64	yes	complemented
40	C₂×C₁₃×#123	C₂²	1	8	yes	complemented
41	C₂×C₁₃×#123	C₂²	1	8	yes	complemented
42	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
43	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
44	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
45	C₂×C₁₃×#121	C₂²	1	2	yes	—
46	C₂×C₁₃×#121	C₂²	1	2	yes	—
47	C₂×C₁₃×#121	C₂²	1	4	yes	—
48	C₂×C₁₃×#121	C₂²	1	4	yes	—
49	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
50	C₂×C₁₃×#121	C₂²	1	8	yes	complemented
51	C₂×C₁₃×#120	C₂²	1	8	yes	—
52	C₁₃×#520	C₂²	1	32	yes	complemented
53	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
54	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
55	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
56	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
57	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
58	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
59	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
60	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	—
61	C₂×C₄×D₄×C₁₃	C₂²	1	16	yes	complemented
62	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
63	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	complemented
64	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
65	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
66	C₂×C₁₃×#117	C₂²	1	2	yes	—
67	C₂×C₁₃×#117	C₂²	1	4	yes	complemented
68	C₂×C₁₃×#117	C₂²	1	4	yes	complemented
69	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
70	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
71	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
72	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
73	C₂⁵×C₁₃	C₂³	1	2	yes	—
74	C₂×C₁₃×#41	—	2	16	no	—
75	C₂×C₁₃×#41	—	4	16	no	—
76	C₂×C₁₃×#41	C₂³	1	16	yes	—
77	C₂×C₁₃×#41	C₂³	1	32	yes	complemented
78	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
79	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
80	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
81	C₂²×D₄×C₁₃	—	2	8	no	—
82	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
83	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
84	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
85	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
86	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
87	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
88	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
89	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
90	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
91	C₂³×C₄×C₁₃	—	4	8	no	—
92	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
94	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
95	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
97	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
98	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
99	C₂³×C₄×C₁₃	C₂³	1	16	yes	—
100	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
101	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
102	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
103	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
104	C₁₃×#127	C₂³	1	32	yes	—
105	C₁₃×#127	C₂³	1	8	yes	complemented
106	C₁₃×#126	C₂³	1	64	yes	complemented
107	C₁₃×#125	C₂³	1	16	yes	complemented
108	C₁₃×#124	C₂³	1	32	yes	—
109	C₁₃×#124	C₂³	1	16	yes	complemented
110	C₁₃×#124	C₂³	1	64	yes	complemented
111	C₁₃×#123	C₂³	1	64	yes	complemented
112	C₁₃×#123	C₂³	1	64	yes	complemented
113	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
114	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
115	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	complemented
116	C₁₃×#121	C₂³	1	16	yes	—
117	C₁₃×#121	C₂³	1	16	yes	—
118	C₁₃×#121	C₂³	1	32	yes	—
119	C₁₃×#121	C₂³	1	32	yes	—
120	C₁₃×#121	C₂³	1	32	yes	complemented
121	C₁₃×#121	C₂³	1	64	yes	complemented
122	C₁₃×#120	C₂³	1	64	yes	—
123	C₄×Q₈×C₁₃	C₂³	1	32	yes	complemented
124	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
125	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
126	C₄×D₄×C₁₃	C₂³	1	16	yes	—
127	C₄×D₄×C₁₃	C₂³	1	16	yes	—
128	C₄×D₄×C₁₃	C₂³	1	16	yes	—
129	C₄×D₄×C₁₃	C₂³	1	16	yes	—
130	C₄×D₄×C₁₃	C₂³	1	64	yes	—
131	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
132	C₄×D₄×C₁₃	C₂³	1	64	yes	complemented
133	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
134	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
135	C₁₃×#117	C₂³	1	16	yes	—
136	C₁₃×#117	C₂³	1	32	yes	complemented
137	C₁₃×#117	C₂³	1	32	yes	complemented
138	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
139	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
140	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
141	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
142	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
143	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
144	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
145	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
146	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
147	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
148	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
149	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₁₃×C₄⋊C₄	C₂³	1	32	yes	complemented
151	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
152	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
153	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
154	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
155	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
156	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
157	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
158	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
159	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
160	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
165	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
166	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
167	C₂×#3506	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
168	C₂⁴×C₁₃	—	2	8	no	—
169	C₂⁴×C₁₃	—	4	4	no	—
170	C₂⁴×C₁₃	—	4	4	no	—
171	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
172	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
173	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
174	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
175	C₁₃×#41	—	2	64	no	—
176	C₁₃×#41	—	4	64	no	—
177	C₂×Q₈×C₁₃	—	2	8	no	—
178	C₂×Q₈×C₁₃	—	2	8	no	—
179	C₂×Q₈×C₁₃	—	4	4	no	—
180	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
181	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
182	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
183	C₂×D₄×C₁₃	—	2	16	no	—
184	C₂×D₄×C₁₃	—	2	8	no	—
185	C₂×D₄×C₁₃	—	2	8	no	—
186	C₂×D₄×C₁₃	—	2	8	no	—
187	C₂×D₄×C₁₃	—	2	32	no	—
188	C₂×D₄×C₁₃	—	2	8	no	—
189	C₂×D₄×C₁₃	—	4	4	no	—
190	C₂×D₄×C₁₃	—	4	16	no	—
191	C₂×D₄×C₁₃	—	4	16	no	—
192	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
193	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
194	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
195	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
196	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
197	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
198	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
199	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
200	C₂²×C₄×C₁₃	—	2	16	no	—
201	C₂²×C₄×C₁₃	—	2	4	no	—
202	C₂²×C₄×C₁₃	—	2	16	no	—
203	C₂²×C₄×C₁₃	—	4	32	no	—
204	C₂²×C₄×C₁₃	—	4	4	no	—
205	C₂²×C₄×C₁₃	—	4	8	no	—
206	C₂²×C₄×C₁₃	—	4	2	no	—
207	C₂²×C₄×C₁₃	—	4	16	no	—
208	C₂²×C₄×C₁₃	#41	1	8	yes	complemented
209	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
210	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
211	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
212	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
213	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
214	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
215	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
216	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
217	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
218	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
219	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
220	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
221	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	—
222	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
223	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
226	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
227	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
228	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
229	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
230	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
231	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
232	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
233	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
234	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
235	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
236	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
237	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
238	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
239	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
240	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
241	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
242	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
243	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
244	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
245	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
246	C₄²×C₁₃	C₂⁴	1	4	yes	—
247	C₄²×C₁₃	C₂⁴	1	4	yes	—
248	C₄²×C₁₃	C₂⁴	1	4	yes	—
249	C₄²×C₁₃	C₂⁴	1	4	yes	—
250	C₄²×C₁₃	C₂⁴	1	16	yes	—
251	C₄²×C₁₃	C₂⁴	1	32	yes	—
252	#3506	C₂×C₁₃	1	32	yes	direct product factor
253	C₂×#559	C₂×C₁₃	1	4	yes	complemented
254	C₂×#556	C₂×C₁₃	1	2	yes	complemented
255	C₂×#555	C₂×C₁₃	1	2	yes	complemented
256	C₂×#553	C₂×C₁₃	1	4	yes	complemented
257	C₂×#550	C₂×C₁₃	1	2	yes	complemented
258	C₂×#547	C₂×C₁₃	1	2	yes	complemented
259	C₂×#538	C₂×C₁₃	1	4	yes	complemented
260	C₂×#535	C₂×C₁₃	1	2	yes	complemented
261	C₂×#533	C₂×C₁₃	1	1	yes	characteristic, complemented
262	C₂×#532	C₂×C₁₃	1	1	yes	characteristic, complemented
263	C₂×#525	C₂×C₁₃	1	4	yes	complemented
264	C₂×#520	C₂×C₁₃	1	2	yes	complemented
265	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
266	C₂³×C₁₃	—	2	2	no	—
267	C₂³×C₁₃	—	2	2	no	—
268	C₂³×C₁₃	—	2	8	no	—
269	C₂³×C₁₃	—	2	16	no	—
270	C₂³×C₁₃	—	2	8	no	—
271	C₂³×C₁₃	—	2	8	no	—
272	C₂³×C₁₃	—	2	8	no	—
273	C₂³×C₁₃	—	2	8	no	—
274	C₂³×C₁₃	—	2	8	no	—
275	C₂³×C₁₃	—	4	8	no	—
276	C₂³×C₁₃	—	4	8	no	—
277	C₂³×C₁₃	—	4	32	no	—
278	C₂³×C₁₃	C₂×#41	1	4	yes	—
279	C₂³×C₁₃	C₂⁵	1	8	yes	—
280	C₂³×C₁₃	C₂⁵	1	8	yes	—
281	C₂³×C₁₃	C₂⁵	1	2	yes	—
282	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
283	Q₈×C₁₃	—	2	16	no	—
284	Q₈×C₁₃	—	2	16	no	—
285	Q₈×C₁₃	—	4	8	no	—
286	D₄×C₁₃	—	2	32	no	—
287	D₄×C₁₃	—	2	16	no	—
288	D₄×C₁₃	—	2	16	no	—
289	D₄×C₁₃	—	2	16	no	—
290	D₄×C₁₃	—	2	16	no	—
291	D₄×C₁₃	—	4	8	no	—
292	D₄×C₁₃	—	4	32	no	—
293	D₄×C₁₃	—	4	32	no	—
294	C₂×C₄×C₁₃	—	2	8	no	—
295	C₂×C₄×C₁₃	—	2	2	no	—
296	C₂×C₄×C₁₃	—	2	8	no	—
297	C₂×C₄×C₁₃	—	2	8	no	—
298	C₂×C₄×C₁₃	—	2	2	no	—
299	C₂×C₄×C₁₃	—	2	2	no	—
300	C₂×C₄×C₁₃	—	2	8	no	—
301	C₂×C₄×C₁₃	—	2	32	no	—
302	C₂×C₄×C₁₃	—	2	8	no	—
303	C₂×C₄×C₁₃	—	2	32	no	—
304	C₂×C₄×C₁₃	—	4	8	no	—
305	C₂×C₄×C₁₃	—	4	16	no	—
306	C₂×C₄×C₁₃	—	4	4	no	—
307	C₂×C₄×C₁₃	—	4	32	no	—
308	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
309	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
310	C₂×C₄×C₁₃	C₂×#41	1	16	yes	complemented
311	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
312	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
313	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
314	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
315	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
316	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
317	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
318	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
319	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
320	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
321	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
322	C₂²×#41	C₂²×C₁₃	1	2	yes	—
323	C₂²×#41	C₂²×C₁₃	1	4	yes	complemented
324	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
325	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
326	#559	C₂²×C₁₃	1	64	yes	complemented
327	#556	C₂²×C₁₃	1	32	yes	complemented
328	#555	C₂²×C₁₃	1	32	yes	complemented
329	#553	C₂²×C₁₃	1	64	yes	complemented
330	#550	C₂²×C₁₃	1	32	yes	complemented
331	#547	C₂²×C₁₃	1	32	yes	complemented
332	#538	C₂²×C₁₃	1	64	yes	complemented
333	#535	C₂²×C₁₃	1	32	yes	complemented
334	#533	C₂²×C₁₃	1	16	yes	complemented
335	#532	C₂²×C₁₃	1	16	yes	complemented
336	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
337	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
338	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
339	C₂×#127	C₂²×C₁₃	1	4	yes	—
340	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic, complemented
341	C₂×#126	C₂²×C₁₃	1	8	yes	complemented
342	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
343	C₂×#124	C₂²×C₁₃	1	4	yes	—
344	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
345	C₂×#124	C₂²×C₁₃	1	8	yes	complemented
346	#525	C₂²×C₁₃	1	64	yes	complemented
347	C₂×#123	C₂²×C₁₃	1	8	yes	complemented
348	C₂×#123	C₂²×C₁₃	1	8	yes	complemented
349	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
350	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
351	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
352	C₂×#121	C₂²×C₁₃	1	2	yes	—
353	C₂×#121	C₂²×C₁₃	1	2	yes	—
354	C₂×#121	C₂²×C₁₃	1	4	yes	—
355	C₂×#121	C₂²×C₁₃	1	4	yes	—
356	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
357	C₂×#121	C₂²×C₁₃	1	8	yes	complemented
358	C₂×#120	C₂²×C₁₃	1	8	yes	—
359	#520	C₂²×C₁₃	1	32	yes	complemented
360	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
361	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
362	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
363	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
364	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
365	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
366	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
367	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	—
368	C₂×C₄×D₄	C₂²×C₁₃	1	16	yes	complemented
369	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
370	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	complemented
371	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
372	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
373	C₂×#117	C₂²×C₁₃	1	2	yes	—
374	C₂×#117	C₂²×C₁₃	1	4	yes	complemented
375	C₂×#117	C₂²×C₁₃	1	4	yes	complemented
376	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
377	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
378	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
379	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
380	C₂²×C₁₃	—	2	2	no	—
381	C₂²×C₁₃	—	2	2	no	—
382	C₂²×C₁₃	—	2	8	no	—
383	C₂²×C₁₃	—	2	8	no	—
384	C₂²×C₁₃	—	2	8	no	—
385	C₂²×C₁₃	—	2	8	no	—
386	C₂²×C₁₃	—	2	8	no	—
387	C₂²×C₁₃	—	2	8	no	—
388	C₂²×C₁₃	—	2	8	no	—
389	C₂²×C₁₃	—	4	32	no	—
390	C₂²×C₁₃	—	4	16	no	—
391	C₂²×C₁₃	—	4	16	no	—
392	C₂²×C₁₃	C₂²×#41	1	4	yes	—
393	C₂²×C₁₃	C₂²×#41	1	2	yes	—
394	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
395	C₂²×C₁₃	#585	1	2	yes	—
396	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
397	C₄×C₁₃	—	2	8	no	—
398	C₄×C₁₃	—	2	2	no	—
399	C₄×C₁₃	—	2	8	no	—
400	C₄×C₁₃	—	2	8	no	—
401	C₄×C₁₃	—	2	2	no	—
402	C₄×C₁₃	—	2	2	no	—
403	C₄×C₁₃	—	2	8	no	—
404	C₄×C₁₃	C₂²×#41	1	4	yes	—
405	C₄×C₁₃	C₂²×#41	1	4	yes	—
406	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
407	C₂⁵	C₂³×C₁₃	1	2	yes	—
408	C₂×#41	—	2	16	no	—
409	C₂×#41	—	4	16	no	—
410	C₂×#41	C₂³×C₁₃	1	16	yes	—
411	C₂×#41	C₂³×C₁₃	1	32	yes	complemented
412	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
413	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
414	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
415	C₂²×D₄	—	2	8	no	—
416	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
417	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
418	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
419	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
420	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
421	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
422	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
423	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
424	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
425	C₂³×C₄	—	4	8	no	—
426	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
427	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
428	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
429	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
430	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
431	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
432	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
433	C₂³×C₄	C₂³×C₁₃	1	16	yes	—
434	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
435	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
436	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
437	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
438	#127	C₂³×C₁₃	1	32	yes	—
439	#127	C₂³×C₁₃	1	8	yes	complemented
440	#126	C₂³×C₁₃	1	64	yes	complemented
441	#125	C₂³×C₁₃	1	16	yes	complemented
442	#124	C₂³×C₁₃	1	32	yes	—
443	#124	C₂³×C₁₃	1	16	yes	complemented
444	#124	C₂³×C₁₃	1	64	yes	complemented
445	#123	C₂³×C₁₃	1	64	yes	complemented
446	#123	C₂³×C₁₃	1	64	yes	complemented
447	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
448	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
449	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	complemented
450	#121	C₂³×C₁₃	1	16	yes	—
451	#121	C₂³×C₁₃	1	16	yes	—
452	#121	C₂³×C₁₃	1	32	yes	—
453	#121	C₂³×C₁₃	1	32	yes	—
454	#121	C₂³×C₁₃	1	32	yes	complemented
455	#121	C₂³×C₁₃	1	64	yes	complemented
456	#120	C₂³×C₁₃	1	64	yes	—
457	C₄×Q₈	C₂³×C₁₃	1	32	yes	complemented
458	C₄×Q₈	C₂³×C₁₃	1	16	yes	complemented
459	C₄×Q₈	C₂³×C₁₃	1	16	yes	complemented
460	C₄×D₄	C₂³×C₁₃	1	16	yes	—
461	C₄×D₄	C₂³×C₁₃	1	16	yes	—
462	C₄×D₄	C₂³×C₁₃	1	16	yes	—
463	C₄×D₄	C₂³×C₁₃	1	16	yes	—
464	C₄×D₄	C₂³×C₁₃	1	64	yes	—
465	C₄×D₄	C₂³×C₁₃	1	32	yes	complemented
466	C₄×D₄	C₂³×C₁₃	1	64	yes	complemented
467	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
468	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
469	#117	C₂³×C₁₃	1	16	yes	—
470	#117	C₂³×C₁₃	1	32	yes	complemented
471	#117	C₂³×C₁₃	1	32	yes	complemented
472	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
473	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
474	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
475	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
476	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
477	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
478	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
479	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
480	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
481	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
482	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
483	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
484	C₂×C₄⋊C₄	C₂³×C₁₃	1	32	yes	complemented
485	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
486	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
487	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
488	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
489	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
490	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
491	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
492	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
493	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
494	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
495	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
496	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
497	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
498	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
499	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
500	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
501	C₂×C₁₃	—	2	4	no	—
502	C₂×C₁₃	—	4	8	no	—
503	C₂×C₁₃	—	4	8	no	—
504	C₂×C₁₃	#3506	1	4	yes	direct product factor
505	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
506	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
507	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
508	C₂⁴	—	2	8	no	—
509	C₂⁴	—	4	4	no	—
510	C₂⁴	—	4	4	no	—
511	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
512	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
513	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
514	C₂⁴	C₂⁴×C₁₃	1	8	yes	—
515	#41	—	2	64	no	—
516	#41	—	4	64	no	—
517	C₂×Q₈	—	2	8	no	—
518	C₂×Q₈	—	2	8	no	—
519	C₂×Q₈	—	4	4	no	—
520	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
521	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
522	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
523	C₂×D₄	—	2	16	no	—
524	C₂×D₄	—	2	8	no	—
525	C₂×D₄	—	2	8	no	—
526	C₂×D₄	—	2	8	no	—
527	C₂×D₄	—	2	32	no	—
528	C₂×D₄	—	2	8	no	—
529	C₂×D₄	—	4	16	no	—
530	C₂×D₄	—	4	4	no	—
531	C₂×D₄	—	4	16	no	—
532	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
533	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
534	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
535	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
536	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
537	C₂×D₄	C₂⁴×C₁₃	1	32	yes	—
538	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
539	C₂×D₄	C₂⁴×C₁₃	1	32	yes	—
540	C₂²×C₄	—	2	16	no	—
541	C₂²×C₄	—	2	4	no	—
542	C₂²×C₄	—	2	16	no	—
543	C₂²×C₄	—	4	32	no	—
544	C₂²×C₄	—	4	4	no	—
545	C₂²×C₄	—	4	8	no	—
546	C₂²×C₄	—	4	16	no	—
547	C₂²×C₄	—	4	2	no	—
548	C₂²×C₄	C₁₃×#41	1	8	yes	complemented
549	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
550	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
551	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
552	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
553	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
554	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
555	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
556	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
557	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
558	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
559	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
560	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
561	C₂²×C₄	C₂⁴×C₁₃	1	32	yes	—
562	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
563	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
564	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
565	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
566	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
567	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
568	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
569	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
570	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
571	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
572	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
573	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
574	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
575	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
576	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
577	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
578	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
579	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
580	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
581	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
582	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
583	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
584	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
585	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
586	C₄²	C₂⁴×C₁₃	1	4	yes	—
587	C₄²	C₂⁴×C₁₃	1	4	yes	—
588	C₄²	C₂⁴×C₁₃	1	4	yes	—
589	C₄²	C₂⁴×C₁₃	1	4	yes	—
590	C₄²	C₂⁴×C₁₃	1	16	yes	—
591	C₄²	C₂⁴×C₁₃	1	32	yes	—
592	C₁₃	C₂×#3506	1	1	yes	characteristic, direct product factor, Sylow
593	C₂³	—	2	2	no	—
594	C₂³	—	2	2	no	—
595	C₂³	—	2	8	no	—
596	C₂³	—	2	16	no	—
597	C₂³	—	2	8	no	—
598	C₂³	—	2	8	no	—
599	C₂³	—	2	8	no	—
600	C₂³	—	2	8	no	—
601	C₂³	—	2	8	no	—
602	C₂³	—	4	8	no	—
603	C₂³	—	4	8	no	—
604	C₂³	—	4	32	no	—
605	C₂³	C₂×C₁₃×#41	1	4	yes	—
606	C₂³	C₂⁵×C₁₃	1	8	yes	—
607	C₂³	C₂⁵×C₁₃	1	8	yes	—
608	C₂³	C₂⁵×C₁₃	1	2	yes	—
609	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
610	Q₈	—	2	16	no	—
611	Q₈	—	2	16	no	—
612	Q₈	—	4	8	no	—
613	D₄	—	2	32	no	—
614	D₄	—	2	16	no	—
615	D₄	—	2	16	no	—
616	D₄	—	2	16	no	—
617	D₄	—	2	16	no	—
618	D₄	—	4	8	no	—
619	D₄	—	4	32	no	—
620	D₄	—	4	32	no	—
621	C₂×C₄	—	2	8	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	8	no	—
624	C₂×C₄	—	2	8	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	8	no	—
628	C₂×C₄	—	2	32	no	—
629	C₂×C₄	—	2	8	no	—
630	C₂×C₄	—	2	32	no	—
631	C₂×C₄	—	4	8	no	—
632	C₂×C₄	—	4	16	no	—
633	C₂×C₄	—	4	4	no	—
634	C₂×C₄	—	4	32	no	—
635	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
636	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
637	C₂×C₄	C₂×C₁₃×#41	1	16	yes	complemented
638	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
639	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
640	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
641	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
642	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
643	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
644	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
645	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
646	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
647	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
648	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
649	C₂²	—	2	2	no	—
650	C₂²	—	2	2	no	—
651	C₂²	—	2	8	no	—
652	C₂²	—	2	8	no	—
653	C₂²	—	2	8	no	—
654	C₂²	—	2	8	no	—
655	C₂²	—	2	8	no	—
656	C₂²	—	2	8	no	—
657	C₂²	—	2	8	no	—
658	C₂²	—	4	32	no	—
659	C₂²	—	4	16	no	—
660	C₂²	—	4	16	no	—
661	C₂²	C₂²×C₁₃×#41	1	4	yes	—
662	C₂²	C₂²×C₁₃×#41	1	2	yes	—
663	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
664	C₂²	C₁₃×#585	1	2	yes	—
665	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
666	C₄	—	2	8	no	—
667	C₄	—	2	2	no	—
668	C₄	—	2	8	no	—
669	C₄	—	2	8	no	—
670	C₄	—	2	2	no	—
671	C₄	—	2	2	no	—
672	C₄	—	2	8	no	—
673	C₄	C₂²×C₁₃×#41	1	4	yes	—
674	C₄	C₂²×C₁₃×#41	1	4	yes	—
675	C₄	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
676	C₂	—	2	4	no	—
677	C₂	—	4	8	no	—
678	C₂	—	4	8	no	—
679	C₂	C₁₃×#3506	1	4	yes	direct product factor
680	C₂	C₂³×C₁₃×#41	1	1	yes	characteristic
681	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
682	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×#3506	C₂	direct (N × H)
2. C₂×C₁₃×#559	C₂	semidirect
3. C₂×C₁₃×#556	C₂	semidirect
4. C₂×C₁₃×#555	C₂	semidirect
5. C₂×C₁₃×#553	C₂	semidirect
6. C₂×C₁₃×#550	C₂	semidirect
7. C₂×C₁₃×#547	C₂	semidirect
8. C₂×C₁₃×#538	C₂	semidirect
9. C₂×C₁₃×#535	C₂	semidirect
10. C₂×C₁₃×#533	C₂	semidirect
11. C₂×C₁₃×#532	C₂	semidirect
12. C₂×C₁₃×#525	C₂	semidirect
13. C₂×C₁₃×#520	C₂	semidirect
14. C₂²×C₄×D₄×C₁₃	C₂	semidirect
16. C₂²×C₁₃×#41	C₂²	semidirect
19. C₁₃×#559	C₂²	semidirect
20. C₁₃×#556	C₂²	semidirect
21. C₁₃×#555	C₂²	semidirect
22. C₁₃×#553	C₂²	semidirect
23. C₁₃×#550	C₂²	semidirect
24. C₁₃×#547	C₂²	semidirect
25. C₁₃×#538	C₂²	semidirect
26. C₁₃×#535	C₂²	semidirect
27. C₁₃×#533	C₂²	semidirect
28. C₁₃×#532	C₂²	semidirect
29. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
30. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
31. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
33. C₂×C₁₃×#127	C₂²	semidirect
34. C₂×C₁₃×#126	C₂²	semidirect
35. C₂×C₁₃×#125	C₂²	semidirect
37. C₂×C₁₃×#124	C₂²	semidirect
38. C₂×C₁₃×#124	C₂²	semidirect
39. C₁₃×#525	C₂²	semidirect
40. C₂×C₁₃×#123	C₂²	semidirect
41. C₂×C₁₃×#123	C₂²	semidirect
44. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
49. C₂×C₁₃×#121	C₂²	semidirect
50. C₂×C₁₃×#121	C₂²	semidirect
52. C₁₃×#520	C₂²	semidirect
53. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
54. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
55. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
61. C₂×C₄×D₄×C₁₃	C₂²	semidirect
62. C₂×C₄×D₄×C₁₃	C₂²	semidirect
63. C₂×C₄×D₄×C₁₃	C₂²	semidirect
64. C₂×C₄×D₄×C₁₃	C₂²	semidirect
65. C₂×C₄×D₄×C₁₃	C₂²	semidirect
67. C₂×C₁₃×#117	C₂²	semidirect
68. C₂×C₁₃×#117	C₂²	semidirect
70. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
77. C₂×C₁₃×#41	C₂³	semidirect
101. C₁₃×C₄⋊Q₈	C₂³	semidirect
102. C₁₃×C₄⋊Q₈	C₂³	semidirect
103. C₁₃×C₄⋊Q₈	C₂³	semidirect
105. C₁₃×#127	C₂³	semidirect
106. C₁₃×#126	C₂³	semidirect
107. C₁₃×#125	C₂³	semidirect
109. C₁₃×#124	C₂³	semidirect
110. C₁₃×#124	C₂³	semidirect
111. C₁₃×#123	C₂³	semidirect
112. C₁₃×#123	C₂³	semidirect
115. C₁₃×C₂²⋊Q₈	C₂³	semidirect
120. C₁₃×#121	C₂³	semidirect
121. C₁₃×#121	C₂³	semidirect
123. C₄×Q₈×C₁₃	C₂³	semidirect
124. C₄×Q₈×C₁₃	C₂³	semidirect
125. C₄×Q₈×C₁₃	C₂³	semidirect
131. C₄×D₄×C₁₃	C₂³	semidirect
132. C₄×D₄×C₁₃	C₂³	semidirect
133. C₄×D₄×C₁₃	C₂³	semidirect
134. C₄×D₄×C₁₃	C₂³	semidirect
136. C₁₃×#117	C₂³	semidirect
137. C₁₃×#117	C₂³	semidirect
150. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
167. C₂×#3506	C₁₃	direct (N × H)
208. C₂²×C₄×C₁₃	#41	semidirect
252. #3506	C₂×C₁₃	direct (N × H)
253. C₂×#559	C₂×C₁₃	semidirect
254. C₂×#556	C₂×C₁₃	semidirect
255. C₂×#555	C₂×C₁₃	semidirect
256. C₂×#553	C₂×C₁₃	semidirect
257. C₂×#550	C₂×C₁₃	semidirect
258. C₂×#547	C₂×C₁₃	semidirect
259. C₂×#538	C₂×C₁₃	semidirect
260. C₂×#535	C₂×C₁₃	semidirect
261. C₂×#533	C₂×C₁₃	semidirect
262. C₂×#532	C₂×C₁₃	semidirect
263. C₂×#525	C₂×C₁₃	semidirect
264. C₂×#520	C₂×C₁₃	semidirect
265. C₂²×C₄×D₄	C₂×C₁₃	semidirect
310. C₂×C₄×C₁₃	C₂×#41	semidirect
323. C₂²×#41	C₂²×C₁₃	semidirect
326. #559	C₂²×C₁₃	semidirect
327. #556	C₂²×C₁₃	semidirect
328. #555	C₂²×C₁₃	semidirect
329. #553	C₂²×C₁₃	semidirect
330. #550	C₂²×C₁₃	semidirect
331. #547	C₂²×C₁₃	semidirect
332. #538	C₂²×C₁₃	semidirect
333. #535	C₂²×C₁₃	semidirect
334. #533	C₂²×C₁₃	semidirect
335. #532	C₂²×C₁₃	semidirect
336. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
337. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
338. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
340. C₂×#127	C₂²×C₁₃	semidirect
341. C₂×#126	C₂²×C₁₃	semidirect
342. C₂×#125	C₂²×C₁₃	semidirect
344. C₂×#124	C₂²×C₁₃	semidirect
345. C₂×#124	C₂²×C₁₃	semidirect
346. #525	C₂²×C₁₃	semidirect
347. C₂×#123	C₂²×C₁₃	semidirect
348. C₂×#123	C₂²×C₁₃	semidirect
351. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
356. C₂×#121	C₂²×C₁₃	semidirect
357. C₂×#121	C₂²×C₁₃	semidirect
359. #520	C₂²×C₁₃	semidirect
360. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
361. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
362. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
368. C₂×C₄×D₄	C₂²×C₁₃	semidirect
369. C₂×C₄×D₄	C₂²×C₁₃	semidirect
370. C₂×C₄×D₄	C₂²×C₁₃	semidirect
371. C₂×C₄×D₄	C₂²×C₁₃	semidirect
372. C₂×C₄×D₄	C₂²×C₁₃	semidirect
374. C₂×#117	C₂²×C₁₃	semidirect
375. C₂×#117	C₂²×C₁₃	semidirect
377. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
411. C₂×#41	C₂³×C₁₃	semidirect
435. C₄⋊Q₈	C₂³×C₁₃	semidirect
436. C₄⋊Q₈	C₂³×C₁₃	semidirect
437. C₄⋊Q₈	C₂³×C₁₃	semidirect
439. #127	C₂³×C₁₃	semidirect
440. #126	C₂³×C₁₃	semidirect
441. #125	C₂³×C₁₃	semidirect
443. #124	C₂³×C₁₃	semidirect
444. #124	C₂³×C₁₃	semidirect
445. #123	C₂³×C₁₃	semidirect
446. #123	C₂³×C₁₃	semidirect
449. C₂²⋊Q₈	C₂³×C₁₃	semidirect
454. #121	C₂³×C₁₃	semidirect
455. #121	C₂³×C₁₃	semidirect
457. C₄×Q₈	C₂³×C₁₃	semidirect
458. C₄×Q₈	C₂³×C₁₃	semidirect
459. C₄×Q₈	C₂³×C₁₃	semidirect
465. C₄×D₄	C₂³×C₁₃	semidirect
466. C₄×D₄	C₂³×C₁₃	semidirect
467. C₄×D₄	C₂³×C₁₃	semidirect
468. C₄×D₄	C₂³×C₁₃	semidirect
470. #117	C₂³×C₁₃	semidirect
471. #117	C₂³×C₁₃	semidirect
484. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
504. C₂×C₁₃	#3506	direct (N × H)
548. C₂²×C₄	C₁₃×#41	semidirect
592. C₁₃	C₂×#3506	direct (N × H)
637. C₂×C₄	C₂×C₁₃×#41	semidirect
679. C₂	C₁₃×#3506	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×#3506	2
C₂×C₁₃×#559	2
C₂×C₁₃×#556	2
C₂×C₁₃×#555	2
C₂×C₁₃×#553	2
C₂×C₁₃×#550	2
C₂×C₁₃×#547	2
C₂×C₁₃×#538	2
C₂×C₁₃×#535	2
C₂×C₁₃×#533	2
C₂×C₁₃×#532	2
C₂×C₁₃×#525	2
C₂×C₁₃×#520	2
C₂²×C₄×D₄×C₁₃	2
C₂×#3506	13

Subgroups — C2×C13×#3506 #15749108

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3506 #15749108