Subgroups — C₂×C₁₃×#3266 #15747363

Order 3328.

2882 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#546	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#3266	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₁₃×#497	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#468	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#464	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#452	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#451	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×#448	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#450	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#440	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
18	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
20	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#137	—	2	8	no	—
22	C₂×C₁₃×#137	C₂²	1	8	yes	complemented
23	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
24	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₁₃×SD₁₆	—	2	8	no	—
27	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
28	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
29	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
30	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
31	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
32	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
33	C₂²×C₁₃×SD₁₆	C₂²	1	8	yes	complemented
34	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
35	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
36	D₄×Q₈×C₁₃	—	2	4	no	—
37	D₄×Q₈×C₁₃	C₂²	1	8	yes	complemented
38	C₁₃×#546	—	2	4	no	—
39	C₁₃×#546	C₂²	1	8	yes	—
40	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
41	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#123	—	2	1	no	—
44	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
45	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
46	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
48	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₁₃×#121	—	2	1	no	—
50	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
51	C₂×C₁₃×#120	—	2	1	no	—
52	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₄×D₄×C₁₃	—	2	1	no	—
54	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
55	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
56	C₂²×C₁₃×C₂²⋊C₄	—	2	1	no	—
57	C₁₃×#497	C₂²	1	8	yes	complemented
58	C₁₃×#468	C₂²	1	8	yes	complemented
59	C₁₃×#467	C₂²	1	8	yes	complemented
60	C₁₃×#464	C₂²	1	8	yes	complemented
61	C₁₃×#461	C₂²	1	8	yes	complemented
62	C₁₃×#452	C₂²	1	8	yes	complemented
63	C₁₃×#451	C₂²	1	8	yes	complemented
64	C₁₃×#450	C₂²	1	8	yes	complemented
65	C₁₃×#448	C₂²	1	8	yes	complemented
66	C₁₃×#440	C₂²	1	8	yes	complemented
67	C₁₃×#435	C₂²	1	8	yes	complemented
68	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
69	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
70	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
71	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
72	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
73	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
74	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
75	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
76	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
77	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
78	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic, complemented
79	C₂⁵×C₁₃	—	2	1	no	—
80	C₂×C₁₃×#41	—	2	2	no	—
81	C₂×C₁₃×#41	—	2	4	no	—
82	C₂×C₁₃×#41	—	4	2	no	—
83	C₂×C₁₃×#41	C₂³	1	4	yes	—
84	C₂²×Q₈×C₁₃	—	2	1	no	—
85	C₂²×Q₈×C₁₃	—	2	1	no	—
86	C₂²×Q₈×C₁₃	—	2	2	no	—
87	C₂²×Q₈×C₁₃	—	2	2	no	—
88	C₂²×Q₈×C₁₃	—	2	4	no	—
89	C₂²×Q₈×C₁₃	—	2	4	no	—
90	C₂²×Q₈×C₁₃	—	4	2	no	—
91	C₂²×Q₈×C₁₃	—	4	2	no	—
92	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
93	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
94	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
95	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
96	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₁₃	C₂³	1	4	yes	complemented
98	C₂²×D₄×C₁₃	—	2	4	no	—
99	C₂²×D₄×C₁₃	—	2	1	no	—
100	C₂²×D₄×C₁₃	—	2	1	no	—
101	C₂²×D₄×C₁₃	—	2	1	no	—
102	C₂²×D₄×C₁₃	—	2	2	no	—
103	C₂²×D₄×C₁₃	—	4	2	no	—
104	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
105	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
106	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
107	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₁₃	—	2	1	no	—
109	C₂³×C₄×C₁₃	—	2	1	no	—
110	C₂³×C₄×C₁₃	—	2	1	no	—
111	C₂³×C₄×C₁₃	—	2	1	no	—
112	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
114	C₁₃×#137	—	2	32	no	—
115	C₂×C₁₃×Q₁₆	—	2	4	no	—
116	C₂×C₁₃×Q₁₆	—	2	4	no	—
117	C₂×C₁₃×Q₁₆	—	4	2	no	—
118	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	complemented
119	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	complemented
120	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	complemented
121	C₂×C₁₃×SD₁₆	—	2	4	no	—
122	C₂×C₁₃×SD₁₆	—	2	4	no	—
123	C₂×C₁₃×SD₁₆	—	2	4	no	—
124	C₂×C₁₃×SD₁₆	—	2	32	no	—
125	C₂×C₁₃×SD₁₆	—	2	4	no	—
126	C₂×C₁₃×SD₁₆	—	4	2	no	—
127	C₂×C₁₃×SD₁₆	D₄	1	8	yes	complemented
128	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
129	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
130	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
131	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
132	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
133	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
134	C₂×C₁₃×M₁₆	—	2	4	no	—
135	C₂×C₁₃×M₁₆	C₂³	1	4	yes	complemented
136	C₂²×C₈×C₁₃	—	2	4	no	—
137	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
138	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
139	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
140	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
141	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
142	C₁₃×C₄⋊Q₈	—	2	8	no	—
143	C₁₃×C₄⋊Q₈	—	2	2	no	—
144	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	complemented
145	C₁₃×#124	—	2	2	no	—
146	C₁₃×#124	C₂³	1	4	yes	—
147	C₁₃×#123	—	2	8	no	—
148	C₁₃×C₂²⋊Q₈	—	2	2	no	—
149	C₁₃×C₂²⋊Q₈	—	2	2	no	—
150	C₁₃×C₂²⋊Q₈	—	2	2	no	—
151	C₁₃×C₂²⋊Q₈	—	2	8	no	—
152	C₁₃×C₂²⋊Q₈	—	2	8	no	—
153	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
154	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
155	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	complemented
156	C₁₃×#121	—	2	2	no	—
157	C₁₃×#121	—	2	8	no	—
158	C₁₃×#121	C₂³	1	4	yes	—
159	C₁₃×#120	—	2	8	no	—
160	C₄×Q₈×C₁₃	—	2	2	no	—
161	C₄×Q₈×C₁₃	C₂³	1	4	yes	complemented
162	C₄×D₄×C₁₃	—	2	8	no	—
163	C₄×D₄×C₁₃	—	2	2	no	—
164	C₄×D₄×C₁₃	D₄	1	4	yes	—
165	C₄×D₄×C₁₃	C₂³	1	4	yes	—
166	C₄×D₄×C₁₃	C₂³	1	4	yes	—
167	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
168	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
169	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
170	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
171	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
172	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
173	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
174	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
177	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
178	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
179	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
180	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
181	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
182	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
183	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
184	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
185	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
186	C₂×C₄²×C₁₃	—	2	1	no	—
187	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
188	C₁₃×#107	C₂³	1	4	yes	complemented
189	C₁₃×C₄⋊C₈	C₂³	1	4	yes	complemented
190	C₁₃×#103	C₂³	1	4	yes	complemented
191	C₁₃×#103	C₂³	1	4	yes	complemented
192	C₁₃×#103	C₂³	1	4	yes	complemented
193	C₁₃×#103	C₂³	1	4	yes	complemented
194	C₁₃×#102	C₂³	1	4	yes	—
195	C₁₃×#102	C₂³	1	4	yes	—
196	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
197	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	complemented
198	C₁₃×#97	C₂³	1	4	yes	complemented
199	C₂×#3266	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₂⁴×C₁₃	—	2	1	no	—
201	C₂⁴×C₁₃	—	2	1	no	—
202	C₂⁴×C₁₃	—	2	4	no	—
203	C₂⁴×C₁₃	—	4	4	no	—
204	C₂⁴×C₁₃	—	4	4	no	—
205	C₂⁴×C₁₃	—	8	2	no	—
206	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
207	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
208	C₁₃×#41	—	2	8	no	—
209	C₁₃×#41	—	4	4	no	—
210	C₁₃×#41	—	4	8	no	—
211	C₂×Q₈×C₁₃	—	2	1	no	—
212	C₂×Q₈×C₁₃	—	2	1	no	—
213	C₂×Q₈×C₁₃	—	2	4	no	—
214	C₂×Q₈×C₁₃	—	2	1	no	—
215	C₂×Q₈×C₁₃	—	2	1	no	—
216	C₂×Q₈×C₁₃	—	2	4	no	—
217	C₂×Q₈×C₁₃	—	2	2	no	—
218	C₂×Q₈×C₁₃	—	2	8	no	—
219	C₂×Q₈×C₁₃	—	2	8	no	—
220	C₂×Q₈×C₁₃	—	2	2	no	—
221	C₂×Q₈×C₁₃	—	2	2	no	—
222	C₂×Q₈×C₁₃	—	2	2	no	—
223	C₂×Q₈×C₁₃	—	2	2	no	—
224	C₂×Q₈×C₁₃	—	2	2	no	—
225	C₂×Q₈×C₁₃	—	2	2	no	—
226	C₂×Q₈×C₁₃	—	4	4	no	—
227	C₂×Q₈×C₁₃	—	4	4	no	—
228	C₂×Q₈×C₁₃	—	4	4	no	—
229	C₂×Q₈×C₁₃	—	4	4	no	—
230	C₂×Q₈×C₁₃	—	4	8	no	—
231	C₂×Q₈×C₁₃	—	4	8	no	—
232	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
233	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
234	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
235	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
236	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
237	C₂×D₄×C₁₃	—	2	4	no	—
238	C₂×D₄×C₁₃	—	2	8	no	—
239	C₂×D₄×C₁₃	—	2	4	no	—
240	C₂×D₄×C₁₃	—	2	4	no	—
241	C₂×D₄×C₁₃	—	2	1	no	—
242	C₂×D₄×C₁₃	—	2	2	no	—
243	C₂×D₄×C₁₃	—	2	4	no	—
244	C₂×D₄×C₁₃	—	2	1	no	—
245	C₂×D₄×C₁₃	—	2	2	no	—
246	C₂×D₄×C₁₃	—	2	2	no	—
247	C₂×D₄×C₁₃	—	4	4	no	—
248	C₂×D₄×C₁₃	—	4	8	no	—
249	C₂×D₄×C₁₃	—	4	4	no	—
250	C₂×D₄×C₁₃	—	4	4	no	—
251	C₂×D₄×C₁₃	—	8	2	no	—
252	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
253	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
254	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
255	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₁₃	—	2	1	no	—
257	C₂²×C₄×C₁₃	—	2	2	no	—
258	C₂²×C₄×C₁₃	—	2	2	no	—
259	C₂²×C₄×C₁₃	—	2	2	no	—
260	C₂²×C₄×C₁₃	—	2	2	no	—
261	C₂²×C₄×C₁₃	—	2	4	no	—
262	C₂²×C₄×C₁₃	—	2	4	no	—
263	C₂²×C₄×C₁₃	—	2	1	no	—
264	C₂²×C₄×C₁₃	—	2	1	no	—
265	C₂²×C₄×C₁₃	—	2	1	no	—
266	C₂²×C₄×C₁₃	—	2	1	no	—
267	C₂²×C₄×C₁₃	—	2	1	no	—
268	C₂²×C₄×C₁₃	—	2	4	no	—
269	C₂²×C₄×C₁₃	—	2	4	no	—
270	C₂²×C₄×C₁₃	—	4	4	no	—
271	C₂²×C₄×C₁₃	—	4	4	no	—
272	C₂²×C₄×C₁₃	—	4	4	no	—
273	C₂²×C₄×C₁₃	—	8	2	no	—
274	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
275	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
276	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
277	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
278	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
279	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
280	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
283	C₁₃×Q₁₆	—	2	8	no	—
284	C₁₃×Q₁₆	—	2	8	no	—
285	C₁₃×Q₁₆	—	4	4	no	—
286	C₁₃×SD₁₆	—	2	8	no	—
287	C₁₃×SD₁₆	—	2	8	no	—
288	C₁₃×SD₁₆	—	2	8	no	—
289	C₁₃×SD₁₆	—	2	8	no	—
290	C₁₃×SD₁₆	—	4	4	no	—
291	C₁₃×SD₁₆	C₂×D₄	1	16	yes	complemented
292	C₁₃×M₁₆	—	2	8	no	—
293	C₂×C₈×C₁₃	—	2	2	no	—
294	C₂×C₈×C₁₃	—	2	2	no	—
295	C₂×C₈×C₁₃	—	2	2	no	—
296	C₂×C₈×C₁₃	—	2	8	no	—
297	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
298	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
299	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
300	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
301	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
302	C₁₃×C₄⋊C₄	—	2	4	no	—
303	C₁₃×C₄⋊C₄	—	2	4	no	—
304	C₁₃×C₄⋊C₄	—	2	4	no	—
305	C₁₃×C₄⋊C₄	—	2	4	no	—
306	C₁₃×C₄⋊C₄	—	2	4	no	—
307	C₁₃×C₄⋊C₄	—	2	4	no	—
308	C₁₃×C₄⋊C₄	—	2	1	no	—
309	C₁₃×C₄⋊C₄	—	2	1	no	—
310	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
311	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
312	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
313	C₁₃×C₂²⋊C₄	—	2	4	no	—
314	C₁₃×C₂²⋊C₄	—	2	4	no	—
315	C₁₃×C₂²⋊C₄	—	2	4	no	—
316	C₁₃×C₂²⋊C₄	—	2	4	no	—
317	C₁₃×C₂²⋊C₄	—	2	4	no	—
318	C₁₃×C₂²⋊C₄	—	2	4	no	—
319	C₁₃×C₂²⋊C₄	—	2	4	no	—
320	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
321	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
322	C₄²×C₁₃	—	2	4	no	—
323	C₄²×C₁₃	C₂×D₄	1	2	yes	—
324	C₄²×C₁₃	C₂⁴	1	2	yes	—
325	C₂²×#137	C₂×C₁₃	1	1	yes	characteristic, complemented
326	C₂³×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
327	C₂×D₄×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
328	C₂×#546	C₂×C₁₃	1	1	yes	characteristic
329	#3266	C₂×C₁₃	1	16	yes	direct product factor
330	C₂×#497	C₂×C₁₃	1	1	yes	characteristic, complemented
331	C₂×#468	C₂×C₁₃	1	1	yes	characteristic, complemented
332	C₂×#467	C₂×C₁₃	1	1	yes	characteristic, complemented
333	C₂×#464	C₂×C₁₃	1	1	yes	characteristic, complemented
334	C₂×#461	C₂×C₁₃	1	1	yes	characteristic, complemented
335	C₂×#452	C₂×C₁₃	1	1	yes	characteristic, complemented
336	C₂×#451	C₂×C₁₃	1	1	yes	characteristic, complemented
337	C₂×#448	C₂×C₁₃	1	1	yes	characteristic, complemented
338	C₂×#450	C₂×C₁₃	1	1	yes	characteristic, complemented
339	C₂×#440	C₂×C₁₃	1	1	yes	characteristic, complemented
340	C₂×#435	C₂×C₁₃	1	1	yes	characteristic, complemented
341	C₂³×C₁₃	—	2	2	no	—
342	C₂³×C₁₃	—	2	2	no	—
343	C₂³×C₁₃	—	2	2	no	—
344	C₂³×C₁₃	—	2	4	no	—
345	C₂³×C₁₃	—	2	2	no	—
346	C₂³×C₁₃	—	2	2	no	—
347	C₂³×C₁₃	—	2	2	no	—
348	C₂³×C₁₃	—	2	2	no	—
349	C₂³×C₁₃	—	4	8	no	—
350	C₂³×C₁₃	—	4	2	no	—
351	C₂³×C₁₃	—	4	2	no	—
352	C₂³×C₁₃	—	4	2	no	—
353	C₂³×C₁₃	—	4	2	no	—
354	C₂³×C₁₃	—	4	8	no	—
355	C₂³×C₁₃	—	4	2	no	—
356	C₂³×C₁₃	—	8	4	no	—
357	C₂³×C₁₃	—	8	16	no	—
358	C₂³×C₁₃	#137	1	4	yes	complemented
359	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
360	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
361	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
362	Q₈×C₁₃	—	2	4	no	—
363	Q₈×C₁₃	—	2	2	no	—
364	Q₈×C₁₃	—	2	2	no	—
365	Q₈×C₁₃	—	2	2	no	—
366	Q₈×C₁₃	—	2	2	no	—
367	Q₈×C₁₃	—	2	2	no	—
368	Q₈×C₁₃	—	2	2	no	—
369	Q₈×C₁₃	—	2	2	no	—
370	Q₈×C₁₃	—	4	8	no	—
371	Q₈×C₁₃	—	4	8	no	—
372	Q₈×C₁₃	—	4	2	no	—
373	Q₈×C₁₃	—	4	2	no	—
374	Q₈×C₁₃	—	4	2	no	—
375	Q₈×C₁₃	C₂²×D₄	1	4	yes	—
376	D₄×C₁₃	—	2	8	no	—
377	D₄×C₁₃	—	2	4	no	—
378	D₄×C₁₃	—	2	2	no	—
379	D₄×C₁₃	—	2	2	no	—
380	D₄×C₁₃	—	2	2	no	—
381	D₄×C₁₃	—	4	8	no	—
382	D₄×C₁₃	—	4	8	no	—
383	D₄×C₁₃	—	4	2	no	—
384	D₄×C₁₃	—	8	4	no	—
385	D₄×C₁₃	C₂²×D₄	1	4	yes	—
386	C₂×C₄×C₁₃	—	2	2	no	—
387	C₂×C₄×C₁₃	—	2	2	no	—
388	C₂×C₄×C₁₃	—	2	4	no	—
389	C₂×C₄×C₁₃	—	2	2	no	—
390	C₂×C₄×C₁₃	—	2	2	no	—
391	C₂×C₄×C₁₃	—	2	2	no	—
392	C₂×C₄×C₁₃	—	2	4	no	—
393	C₂×C₄×C₁₃	—	2	4	no	—
394	C₂×C₄×C₁₃	—	2	2	no	—
395	C₂×C₄×C₁₃	—	2	2	no	—
396	C₂×C₄×C₁₃	—	2	2	no	—
397	C₂×C₄×C₁₃	—	2	2	no	—
398	C₂×C₄×C₁₃	—	2	2	no	—
399	C₂×C₄×C₁₃	—	2	2	no	—
400	C₂×C₄×C₁₃	—	2	2	no	—
401	C₂×C₄×C₁₃	—	2	2	no	—
402	C₂×C₄×C₁₃	—	2	2	no	—
403	C₂×C₄×C₁₃	—	4	8	no	—
404	C₂×C₄×C₁₃	—	4	8	no	—
405	C₂×C₄×C₁₃	—	4	8	no	—
406	C₂×C₄×C₁₃	—	4	2	no	—
407	C₂×C₄×C₁₃	—	4	2	no	—
408	C₂×C₄×C₁₃	—	4	2	no	—
409	C₂×C₄×C₁₃	—	4	2	no	—
410	C₂×C₄×C₁₃	—	4	2	no	—
411	C₂×C₄×C₁₃	—	8	4	no	—
412	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
413	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
414	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
415	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
416	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
417	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
418	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
419	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
420	C₈×C₁₃	—	2	2	no	—
421	C₈×C₁₃	—	2	2	no	—
422	C₈×C₁₃	—	2	2	no	—
423	C₈×C₁₃	C₂²×D₄	1	4	yes	—
424	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
425	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
426	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
427	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
428	C₂×#137	—	2	8	no	—
429	C₂×#137	C₂²×C₁₃	1	8	yes	complemented
430	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
431	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
432	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
433	C₂²×SD₁₆	—	2	8	no	—
434	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
435	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
436	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
437	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
438	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
439	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
440	C₂²×SD₁₆	C₂²×C₁₃	1	8	yes	complemented
441	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
442	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
443	D₄×Q₈	—	2	4	no	—
444	D₄×Q₈	C₂²×C₁₃	1	8	yes	complemented
445	#546	—	2	4	no	—
446	#546	C₂²×C₁₃	1	8	yes	—
447	C₂×C₄⋊Q₈	—	2	1	no	—
448	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
449	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
450	C₂×#123	—	2	1	no	—
451	C₂×C₂²⋊Q₈	—	2	1	no	—
452	C₂×C₂²⋊Q₈	—	2	1	no	—
453	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
454	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
455	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
456	C₂×#121	—	2	1	no	—
457	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
458	C₂×#120	—	2	1	no	—
459	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
460	C₂×C₄×D₄	—	2	1	no	—
461	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
462	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
463	C₂²×C₂²⋊C₄	—	2	1	no	—
464	#497	C₂²×C₁₃	1	8	yes	complemented
465	#468	C₂²×C₁₃	1	8	yes	complemented
466	#467	C₂²×C₁₃	1	8	yes	complemented
467	#464	C₂²×C₁₃	1	8	yes	complemented
468	#461	C₂²×C₁₃	1	8	yes	complemented
469	#452	C₂²×C₁₃	1	8	yes	complemented
470	#451	C₂²×C₁₃	1	8	yes	complemented
471	#450	C₂²×C₁₃	1	8	yes	complemented
472	#448	C₂²×C₁₃	1	8	yes	complemented
473	#440	C₂²×C₁₃	1	8	yes	complemented
474	#435	C₂²×C₁₃	1	8	yes	complemented
475	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
476	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
477	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
478	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
479	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
480	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
481	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
482	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
483	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
484	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
485	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic, complemented
486	C₂²×C₁₃	—	2	2	no	—
487	C₂²×C₁₃	—	2	8	no	—
488	C₂²×C₁₃	—	2	2	no	—
489	C₂²×C₁₃	—	2	2	no	—
490	C₂²×C₁₃	—	2	4	no	—
491	C₂²×C₁₃	—	2	2	no	—
492	C₂²×C₁₃	—	2	2	no	—
493	C₂²×C₁₃	—	4	4	no	—
494	C₂²×C₁₃	—	4	8	no	—
495	C₂²×C₁₃	—	4	2	no	—
496	C₂²×C₁₃	—	4	2	no	—
497	C₂²×C₁₃	—	4	2	no	—
498	C₂²×C₁₃	—	4	2	no	—
499	C₂²×C₁₃	—	4	2	no	—
500	C₂²×C₁₃	—	8	16	no	—
501	C₂²×C₁₃	—	8	4	no	—
502	C₂²×C₁₃	D₄²	1	2	yes	—
503	C₂²×C₁₃	C₂×#137	1	2	yes	—
504	C₂²×C₁₃	C₂×#137	1	4	yes	complemented
505	C₂²×C₁₃	#577	1	2	yes	—
506	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
507	C₄×C₁₃	—	2	2	no	—
508	C₄×C₁₃	—	2	2	no	—
509	C₄×C₁₃	—	2	4	no	—
510	C₄×C₁₃	—	2	2	no	—
511	C₄×C₁₃	—	2	2	no	—
512	C₄×C₁₃	—	4	2	no	—
513	C₄×C₁₃	—	4	2	no	—
514	C₄×C₁₃	—	4	2	no	—
515	C₄×C₁₃	—	4	2	no	—
516	C₄×C₁₃	—	4	2	no	—
517	C₄×C₁₃	D₄²	1	2	yes	—
518	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
519	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
520	C₂⁵	—	2	1	no	—
521	C₂×#41	—	2	2	no	—
522	C₂×#41	—	2	4	no	—
523	C₂×#41	—	4	2	no	—
524	C₂×#41	C₂³×C₁₃	1	4	yes	—
525	C₂²×Q₈	—	2	1	no	—
526	C₂²×Q₈	—	2	1	no	—
527	C₂²×Q₈	—	2	2	no	—
528	C₂²×Q₈	—	2	2	no	—
529	C₂²×Q₈	—	2	4	no	—
530	C₂²×Q₈	—	2	4	no	—
531	C₂²×Q₈	—	4	2	no	—
532	C₂²×Q₈	—	4	2	no	—
533	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
534	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
535	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
536	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
537	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
538	C₂²×Q₈	C₂³×C₁₃	1	4	yes	complemented
539	C₂²×D₄	—	2	4	no	—
540	C₂²×D₄	—	2	1	no	—
541	C₂²×D₄	—	2	1	no	—
542	C₂²×D₄	—	2	1	no	—
543	C₂²×D₄	—	2	2	no	—
544	C₂²×D₄	—	4	2	no	—
545	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
546	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
547	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
548	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
549	C₂³×C₄	—	2	1	no	—
550	C₂³×C₄	—	2	1	no	—
551	C₂³×C₄	—	2	1	no	—
552	C₂³×C₄	—	2	1	no	—
553	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
554	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
555	#137	—	2	32	no	—
556	C₂×Q₁₆	—	2	4	no	—
557	C₂×Q₁₆	—	2	4	no	—
558	C₂×Q₁₆	—	4	2	no	—
559	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	complemented
560	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	complemented
561	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	complemented
562	C₂×SD₁₆	—	2	4	no	—
563	C₂×SD₁₆	—	2	4	no	—
564	C₂×SD₁₆	—	2	4	no	—
565	C₂×SD₁₆	—	2	32	no	—
566	C₂×SD₁₆	—	2	4	no	—
567	C₂×SD₁₆	—	4	2	no	—
568	C₂×SD₁₆	D₄×C₁₃	1	8	yes	complemented
569	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
570	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
571	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
572	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
573	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
574	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
575	C₂×M₁₆	—	2	4	no	—
576	C₂×M₁₆	C₂³×C₁₃	1	4	yes	complemented
577	C₂²×C₈	—	2	4	no	—
578	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
579	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
580	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
581	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
582	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
583	C₄⋊Q₈	—	2	8	no	—
584	C₄⋊Q₈	—	2	2	no	—
585	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	complemented
586	#124	—	2	2	no	—
587	#124	C₂³×C₁₃	1	4	yes	—
588	#123	—	2	8	no	—
589	C₂²⋊Q₈	—	2	2	no	—
590	C₂²⋊Q₈	—	2	2	no	—
591	C₂²⋊Q₈	—	2	2	no	—
592	C₂²⋊Q₈	—	2	8	no	—
593	C₂²⋊Q₈	—	2	8	no	—
594	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
595	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
596	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	complemented
597	#121	—	2	2	no	—
598	#121	—	2	8	no	—
599	#121	C₂³×C₁₃	1	4	yes	—
600	#120	—	2	8	no	—
601	C₄×Q₈	—	2	2	no	—
602	C₄×Q₈	C₂³×C₁₃	1	4	yes	complemented
603	C₄×D₄	—	2	8	no	—
604	C₄×D₄	—	2	2	no	—
605	C₄×D₄	D₄×C₁₃	1	4	yes	—
606	C₄×D₄	C₂³×C₁₃	1	4	yes	—
607	C₄×D₄	C₂³×C₁₃	1	4	yes	—
608	C₂×C₄⋊C₄	—	2	1	no	—
609	C₂×C₄⋊C₄	—	2	1	no	—
610	C₂×C₄⋊C₄	—	2	1	no	—
611	C₂×C₄⋊C₄	—	2	1	no	—
612	C₂×C₄⋊C₄	—	2	1	no	—
613	C₂×C₄⋊C₄	—	2	1	no	—
614	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
617	C₂×C₂²⋊C₄	—	2	1	no	—
618	C₂×C₂²⋊C₄	—	2	1	no	—
619	C₂×C₂²⋊C₄	—	2	1	no	—
620	C₂×C₂²⋊C₄	—	2	1	no	—
621	C₂×C₂²⋊C₄	—	2	1	no	—
622	C₂×C₂²⋊C₄	—	2	1	no	—
623	C₂×C₂²⋊C₄	—	2	1	no	—
624	C₂×C₂²⋊C₄	—	2	8	no	—
625	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
626	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
627	C₂×C₄²	—	2	1	no	—
628	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
629	#107	C₂³×C₁₃	1	4	yes	complemented
630	C₄⋊C₈	C₂³×C₁₃	1	4	yes	complemented
631	#103	C₂³×C₁₃	1	4	yes	complemented
632	#103	C₂³×C₁₃	1	4	yes	complemented
633	#103	C₂³×C₁₃	1	4	yes	complemented
634	#103	C₂³×C₁₃	1	4	yes	complemented
635	#102	C₂³×C₁₃	1	4	yes	—
636	#102	C₂³×C₁₃	1	4	yes	—
637	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
638	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	complemented
639	#97	C₂³×C₁₃	1	4	yes	complemented
640	C₂×C₁₃	—	2	4	no	—
641	C₂×C₁₃	—	4	2	no	—
642	C₂×C₁₃	—	4	4	no	—
643	C₂×C₁₃	—	8	2	no	—
644	C₂×C₁₃	#3266	1	4	yes	direct product factor
645	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
646	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
647	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
648	C₂⁴	—	2	1	no	—
649	C₂⁴	—	2	1	no	—
650	C₂⁴	—	2	4	no	—
651	C₂⁴	—	4	4	no	—
652	C₂⁴	—	4	4	no	—
653	C₂⁴	—	8	2	no	—
654	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
655	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
656	#41	—	2	8	no	—
657	#41	—	4	4	no	—
658	#41	—	4	8	no	—
659	C₂×Q₈	—	2	1	no	—
660	C₂×Q₈	—	2	1	no	—
661	C₂×Q₈	—	2	4	no	—
662	C₂×Q₈	—	2	1	no	—
663	C₂×Q₈	—	2	1	no	—
664	C₂×Q₈	—	2	4	no	—
665	C₂×Q₈	—	2	2	no	—
666	C₂×Q₈	—	2	8	no	—
667	C₂×Q₈	—	2	8	no	—
668	C₂×Q₈	—	2	2	no	—
669	C₂×Q₈	—	2	2	no	—
670	C₂×Q₈	—	2	2	no	—
671	C₂×Q₈	—	2	2	no	—
672	C₂×Q₈	—	2	2	no	—
673	C₂×Q₈	—	2	2	no	—
674	C₂×Q₈	—	4	4	no	—
675	C₂×Q₈	—	4	4	no	—
676	C₂×Q₈	—	4	4	no	—
677	C₂×Q₈	—	4	4	no	—
678	C₂×Q₈	—	4	8	no	—
679	C₂×Q₈	—	4	8	no	—
680	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
681	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
682	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
683	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
684	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
685	C₂×D₄	—	2	4	no	—
686	C₂×D₄	—	2	8	no	—
687	C₂×D₄	—	2	4	no	—
688	C₂×D₄	—	2	4	no	—
689	C₂×D₄	—	2	1	no	—
690	C₂×D₄	—	2	2	no	—
691	C₂×D₄	—	2	4	no	—
692	C₂×D₄	—	2	1	no	—
693	C₂×D₄	—	2	2	no	—
694	C₂×D₄	—	2	2	no	—
695	C₂×D₄	—	4	4	no	—
696	C₂×D₄	—	4	8	no	—
697	C₂×D₄	—	4	4	no	—
698	C₂×D₄	—	4	4	no	—
699	C₂×D₄	—	8	2	no	—
700	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
701	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
702	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
703	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
704	C₂²×C₄	—	2	1	no	—
705	C₂²×C₄	—	2	2	no	—
706	C₂²×C₄	—	2	2	no	—
707	C₂²×C₄	—	2	2	no	—
708	C₂²×C₄	—	2	2	no	—
709	C₂²×C₄	—	2	1	no	—
710	C₂²×C₄	—	2	1	no	—
711	C₂²×C₄	—	2	1	no	—
712	C₂²×C₄	—	2	1	no	—
713	C₂²×C₄	—	2	1	no	—
714	C₂²×C₄	—	2	4	no	—
715	C₂²×C₄	—	2	4	no	—
716	C₂²×C₄	—	2	4	no	—
717	C₂²×C₄	—	2	4	no	—
718	C₂²×C₄	—	4	4	no	—
719	C₂²×C₄	—	4	4	no	—
720	C₂²×C₄	—	4	4	no	—
721	C₂²×C₄	—	8	2	no	—
722	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
723	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
724	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
725	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
726	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
727	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
728	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
730	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
731	Q₁₆	—	2	8	no	—
732	Q₁₆	—	2	8	no	—
733	Q₁₆	—	4	4	no	—
734	SD₁₆	—	2	8	no	—
735	SD₁₆	—	2	8	no	—
736	SD₁₆	—	2	8	no	—
737	SD₁₆	—	2	8	no	—
738	SD₁₆	—	4	4	no	—
739	SD₁₆	C₂×D₄×C₁₃	1	16	yes	complemented
740	M₁₆	—	2	8	no	—
741	C₂×C₈	—	2	2	no	—
742	C₂×C₈	—	2	2	no	—
743	C₂×C₈	—	2	2	no	—
744	C₂×C₈	—	2	8	no	—
745	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
746	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
747	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
748	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
749	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
750	C₄⋊C₄	—	2	4	no	—
751	C₄⋊C₄	—	2	4	no	—
752	C₄⋊C₄	—	2	4	no	—
753	C₄⋊C₄	—	2	4	no	—
754	C₄⋊C₄	—	2	4	no	—
755	C₄⋊C₄	—	2	4	no	—
756	C₄⋊C₄	—	2	1	no	—
757	C₄⋊C₄	—	2	1	no	—
758	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
759	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
760	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
761	C₂²⋊C₄	—	2	4	no	—
762	C₂²⋊C₄	—	2	4	no	—
763	C₂²⋊C₄	—	2	4	no	—
764	C₂²⋊C₄	—	2	4	no	—
765	C₂²⋊C₄	—	2	4	no	—
766	C₂²⋊C₄	—	2	4	no	—
767	C₂²⋊C₄	—	2	4	no	—
768	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
769	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
770	C₄²	—	2	4	no	—
771	C₄²	C₂×D₄×C₁₃	1	2	yes	—
772	C₄²	C₂⁴×C₁₃	1	2	yes	—
773	C₁₃	C₂×#3266	1	1	yes	characteristic, direct product factor, Sylow
774	C₂³	—	2	2	no	—
775	C₂³	—	2	2	no	—
776	C₂³	—	2	2	no	—
777	C₂³	—	2	4	no	—
778	C₂³	—	2	2	no	—
779	C₂³	—	2	2	no	—
780	C₂³	—	2	2	no	—
781	C₂³	—	2	2	no	—
782	C₂³	—	4	8	no	—
783	C₂³	—	4	2	no	—
784	C₂³	—	4	2	no	—
785	C₂³	—	4	2	no	—
786	C₂³	—	4	2	no	—
787	C₂³	—	4	8	no	—
788	C₂³	—	4	2	no	—
789	C₂³	—	8	4	no	—
790	C₂³	—	8	16	no	—
791	C₂³	C₁₃×#137	1	4	yes	complemented
792	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
793	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
794	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
795	Q₈	—	2	4	no	—
796	Q₈	—	2	2	no	—
797	Q₈	—	2	2	no	—
798	Q₈	—	2	2	no	—
799	Q₈	—	2	2	no	—
800	Q₈	—	2	2	no	—
801	Q₈	—	2	2	no	—
802	Q₈	—	2	2	no	—
803	Q₈	—	4	8	no	—
804	Q₈	—	4	8	no	—
805	Q₈	—	4	2	no	—
806	Q₈	—	4	2	no	—
807	Q₈	—	4	2	no	—
808	Q₈	C₂²×D₄×C₁₃	1	4	yes	—
809	D₄	—	2	8	no	—
810	D₄	—	2	4	no	—
811	D₄	—	2	2	no	—
812	D₄	—	2	2	no	—
813	D₄	—	2	2	no	—
814	D₄	—	4	8	no	—
815	D₄	—	4	8	no	—
816	D₄	—	4	2	no	—
817	D₄	—	8	4	no	—
818	D₄	C₂²×D₄×C₁₃	1	4	yes	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	4	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	4	no	—
826	C₂×C₄	—	2	4	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	4	8	no	—
837	C₂×C₄	—	4	8	no	—
838	C₂×C₄	—	4	8	no	—
839	C₂×C₄	—	4	2	no	—
840	C₂×C₄	—	4	2	no	—
841	C₂×C₄	—	4	2	no	—
842	C₂×C₄	—	4	2	no	—
843	C₂×C₄	—	4	2	no	—
844	C₂×C₄	—	8	4	no	—
845	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
846	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
847	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
848	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
849	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
850	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
851	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
852	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
853	C₈	—	2	2	no	—
854	C₈	—	2	2	no	—
855	C₈	—	2	2	no	—
856	C₈	C₂²×D₄×C₁₃	1	4	yes	—
857	C₂²	—	2	8	no	—
858	C₂²	—	2	2	no	—
859	C₂²	—	2	2	no	—
860	C₂²	—	2	2	no	—
861	C₂²	—	2	2	no	—
862	C₂²	—	2	2	no	—
863	C₂²	—	2	4	no	—
864	C₂²	—	4	4	no	—
865	C₂²	—	4	8	no	—
866	C₂²	—	4	2	no	—
867	C₂²	—	4	2	no	—
868	C₂²	—	4	2	no	—
869	C₂²	—	4	2	no	—
870	C₂²	—	4	2	no	—
871	C₂²	—	8	16	no	—
872	C₂²	—	8	4	no	—
873	C₂²	D₄²×C₁₃	1	2	yes	—
874	C₂²	C₂×C₁₃×#137	1	2	yes	—
875	C₂²	C₂×C₁₃×#137	1	4	yes	complemented
876	C₂²	C₁₃×#577	1	2	yes	—
877	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
878	C₄	—	2	2	no	—
879	C₄	—	2	2	no	—
880	C₄	—	2	2	no	—
881	C₄	—	2	2	no	—
882	C₄	—	2	4	no	—
883	C₄	—	4	2	no	—
884	C₄	—	4	2	no	—
885	C₄	—	4	2	no	—
886	C₄	—	4	2	no	—
887	C₄	—	4	2	no	—
888	C₄	D₄²×C₁₃	1	2	yes	—
889	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
890	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
891	C₂	—	2	4	no	—
892	C₂	—	4	2	no	—
893	C₂	—	4	4	no	—
894	C₂	—	8	2	no	—
895	C₂	C₁₃×#3266	1	4	yes	direct product factor
896	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
897	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
898	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	C₂×C₁₃×#546	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×#137	C₂	semidirect
2. C₂³×C₁₃×SD₁₆	C₂	semidirect
3. C₂×D₄×Q₈×C₁₃	C₂	semidirect
5. C₁₃×#3266	C₂	direct (N × H)
6. C₂×C₁₃×#497	C₂	semidirect
7. C₂×C₁₃×#468	C₂	semidirect
8. C₂×C₁₃×#467	C₂	semidirect
9. C₂×C₁₃×#464	C₂	semidirect
10. C₂×C₁₃×#461	C₂	semidirect
11. C₂×C₁₃×#452	C₂	semidirect
12. C₂×C₁₃×#451	C₂	semidirect
13. C₂×C₁₃×#448	C₂	semidirect
14. C₂×C₁₃×#450	C₂	semidirect
15. C₂×C₁₃×#440	C₂	semidirect
16. C₂×C₁₃×#435	C₂	semidirect
19. C₂³×Q₈×C₁₃	C₂²	semidirect
22. C₂×C₁₃×#137	C₂²	semidirect
23. C₂²×C₁₃×Q₁₆	C₂²	semidirect
24. C₂²×C₁₃×Q₁₆	C₂²	semidirect
25. C₂²×C₁₃×Q₁₆	C₂²	semidirect
33. C₂²×C₁₃×SD₁₆	C₂²	semidirect
34. C₂²×C₁₃×M₁₆	C₂²	semidirect
37. D₄×Q₈×C₁₃	C₂²	semidirect
41. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
48. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
52. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
57. C₁₃×#497	C₂²	semidirect
58. C₁₃×#468	C₂²	semidirect
59. C₁₃×#467	C₂²	semidirect
60. C₁₃×#464	C₂²	semidirect
61. C₁₃×#461	C₂²	semidirect
62. C₁₃×#452	C₂²	semidirect
63. C₁₃×#451	C₂²	semidirect
64. C₁₃×#450	C₂²	semidirect
65. C₁₃×#448	C₂²	semidirect
66. C₁₃×#440	C₂²	semidirect
67. C₁₃×#435	C₂²	semidirect
68. C₂×C₁₃×#107	C₂²	semidirect
69. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
70. C₂×C₁₃×#103	C₂²	semidirect
71. C₂×C₁₃×#103	C₂²	semidirect
72. C₂×C₁₃×#103	C₂²	semidirect
73. C₂×C₁₃×#103	C₂²	semidirect
77. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
78. C₂×C₁₃×#97	C₂²	semidirect
97. C₂²×Q₈×C₁₃	C₂³	semidirect
118. C₂×C₁₃×Q₁₆	C₂³	semidirect
119. C₂×C₁₃×Q₁₆	C₂³	semidirect
120. C₂×C₁₃×Q₁₆	C₂³	semidirect
127. C₂×C₁₃×SD₁₆	D₄	semidirect
135. C₂×C₁₃×M₁₆	C₂³	semidirect
144. C₁₃×C₄⋊Q₈	C₂³	semidirect
155. C₁₃×C₂²⋊Q₈	C₂³	semidirect
161. C₄×Q₈×C₁₃	C₂³	semidirect
188. C₁₃×#107	C₂³	semidirect
189. C₁₃×C₄⋊C₈	C₂³	semidirect
190. C₁₃×#103	C₂³	semidirect
191. C₁₃×#103	C₂³	semidirect
192. C₁₃×#103	C₂³	semidirect
193. C₁₃×#103	C₂³	semidirect
197. C₁₃×C₂²⋊C₈	C₂³	semidirect
198. C₁₃×#97	C₂³	semidirect
199. C₂×#3266	C₁₃	direct (N × H)
291. C₁₃×SD₁₆	C₂×D₄	semidirect
325. C₂²×#137	C₂×C₁₃	semidirect
326. C₂³×SD₁₆	C₂×C₁₃	semidirect
327. C₂×D₄×Q₈	C₂×C₁₃	semidirect
329. #3266	C₂×C₁₃	direct (N × H)
330. C₂×#497	C₂×C₁₃	semidirect
331. C₂×#468	C₂×C₁₃	semidirect
332. C₂×#467	C₂×C₁₃	semidirect
333. C₂×#464	C₂×C₁₃	semidirect
334. C₂×#461	C₂×C₁₃	semidirect
335. C₂×#452	C₂×C₁₃	semidirect
336. C₂×#451	C₂×C₁₃	semidirect
337. C₂×#448	C₂×C₁₃	semidirect
338. C₂×#450	C₂×C₁₃	semidirect
339. C₂×#440	C₂×C₁₃	semidirect
340. C₂×#435	C₂×C₁₃	semidirect
358. C₂³×C₁₃	#137	semidirect
426. C₂³×Q₈	C₂²×C₁₃	semidirect
429. C₂×#137	C₂²×C₁₃	semidirect
430. C₂²×Q₁₆	C₂²×C₁₃	semidirect
431. C₂²×Q₁₆	C₂²×C₁₃	semidirect
432. C₂²×Q₁₆	C₂²×C₁₃	semidirect
440. C₂²×SD₁₆	C₂²×C₁₃	semidirect
441. C₂²×M₁₆	C₂²×C₁₃	semidirect
444. D₄×Q₈	C₂²×C₁₃	semidirect
448. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
455. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
459. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
464. #497	C₂²×C₁₃	semidirect
465. #468	C₂²×C₁₃	semidirect
466. #467	C₂²×C₁₃	semidirect
467. #464	C₂²×C₁₃	semidirect
468. #461	C₂²×C₁₃	semidirect
469. #452	C₂²×C₁₃	semidirect
470. #451	C₂²×C₁₃	semidirect
471. #450	C₂²×C₁₃	semidirect
472. #448	C₂²×C₁₃	semidirect
473. #440	C₂²×C₁₃	semidirect
474. #435	C₂²×C₁₃	semidirect
475. C₂×#107	C₂²×C₁₃	semidirect
476. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
477. C₂×#103	C₂²×C₁₃	semidirect
478. C₂×#103	C₂²×C₁₃	semidirect
479. C₂×#103	C₂²×C₁₃	semidirect
480. C₂×#103	C₂²×C₁₃	semidirect
484. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
485. C₂×#97	C₂²×C₁₃	semidirect
504. C₂²×C₁₃	C₂×#137	semidirect
538. C₂²×Q₈	C₂³×C₁₃	semidirect
559. C₂×Q₁₆	C₂³×C₁₃	semidirect
560. C₂×Q₁₆	C₂³×C₁₃	semidirect
561. C₂×Q₁₆	C₂³×C₁₃	semidirect
568. C₂×SD₁₆	D₄×C₁₃	semidirect
576. C₂×M₁₆	C₂³×C₁₃	semidirect
585. C₄⋊Q₈	C₂³×C₁₃	semidirect
596. C₂²⋊Q₈	C₂³×C₁₃	semidirect
602. C₄×Q₈	C₂³×C₁₃	semidirect
629. #107	C₂³×C₁₃	semidirect
630. C₄⋊C₈	C₂³×C₁₃	semidirect
631. #103	C₂³×C₁₃	semidirect
632. #103	C₂³×C₁₃	semidirect
633. #103	C₂³×C₁₃	semidirect
634. #103	C₂³×C₁₃	semidirect
638. C₂²⋊C₈	C₂³×C₁₃	semidirect
639. #97	C₂³×C₁₃	semidirect
644. C₂×C₁₃	#3266	direct (N × H)
739. SD₁₆	C₂×D₄×C₁₃	semidirect
773. C₁₃	C₂×#3266	direct (N × H)
791. C₂³	C₁₃×#137	semidirect
875. C₂²	C₂×C₁₃×#137	semidirect
895. C₂	C₁₃×#3266	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×#137	2
C₂³×C₁₃×SD₁₆	2
C₂×D₄×Q₈×C₁₃	2
C₂×C₁₃×#546	2
C₁₃×#3266	2
C₂×C₁₃×#497	2
C₂×C₁₃×#468	2
C₂×C₁₃×#467	2
C₂×C₁₃×#464	2
C₂×C₁₃×#461	2
C₂×C₁₃×#452	2
C₂×C₁₃×#451	2
C₂×C₁₃×#448	2
C₂×C₁₃×#450	2
C₂×C₁₃×#440	2
C₂×C₁₃×#435	2
C₂×#3266	13

Subgroups — C2×C13×#3266 #15747363

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3266 #15747363