Subgroups — C₂×C₁₃×#3269 #15747366

Order 3328.

2774 conjugacy classes of subgroups.

The subgroup lattice has 888 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	C₂²×C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#548	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3269	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×#462	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#463	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#452	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#452	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×#449	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#451	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	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
20	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#137	—	2	8	no	—
22	C₂×C₁₃×#137	C₂²	1	8	yes	complemented
23	C₂×C₁₃×#135	—	2	8	no	—
24	C₂×C₁₃×#135	C₂²	1	8	yes	complemented
25	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
26	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
27	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
28	C₂²×C₁₃×Q₁₆	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×D₈	C₂²	1	1	yes	characteristic
34	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
35	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
36	C₁₃×#548	—	2	4	no	—
37	C₁₃×#548	C₂²	1	8	yes	complemented
38	C₁₃×#547	—	2	4	no	—
39	C₁₃×#547	C₂²	1	8	yes	complemented
40	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#124	—	2	1	no	—
42	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#123	—	2	1	no	—
44	C₂×C₁₃×#123	—	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
49	C₂×C₁₃×#121	—	2	1	no	—
50	C₂×C₁₃×#121	—	2	1	no	—
51	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
52	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
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×C₄⋊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×#463	C₂²	1	8	yes	complemented
61	C₁₃×#462	C₂²	1	8	yes	complemented
62	C₁₃×#452	C₂²	1	8	yes	complemented
63	C₁₃×#452	C₂²	1	8	yes	complemented
64	C₁₃×#451	C₂²	1	8	yes	complemented
65	C₁₃×#449	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
69	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
70	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
71	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
72	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
73	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
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
78	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
79	C₂×C₁₃×#41	—	2	2	no	—
80	C₂×C₁₃×#41	—	2	2	no	—
81	C₂×C₁₃×#41	—	2	2	no	—
82	C₂×C₁₃×#41	—	2	4	no	—
83	C₂×C₁₃×#41	—	2	4	no	—
84	C₂×C₁₃×#41	—	2	4	no	—
85	C₂×C₁₃×#41	—	4	2	no	—
86	C₂×C₁₃×#41	—	4	2	no	—
87	C₂×C₁₃×#41	—	4	2	no	—
88	C₂×C₁₃×#41	C₂³	1	4	yes	—
89	C₂×C₁₃×#41	C₂³	1	4	yes	—
90	C₂×C₁₃×#41	C₂³	1	4	yes	—
91	C₂²×Q₈×C₁₃	—	2	1	no	—
92	C₂²×Q₈×C₁₃	—	2	2	no	—
93	C₂²×Q₈×C₁₃	—	2	4	no	—
94	C₂²×Q₈×C₁₃	—	4	2	no	—
95	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
99	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
100	C₂²×D₄×C₁₃	—	2	1	no	—
101	C₂²×D₄×C₁₃	—	2	1	no	—
102	C₂²×D₄×C₁₃	—	2	1	no	—
103	C₂²×D₄×C₁₃	—	2	1	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	1	yes	characteristic
107	C₂³×C₄×C₁₃	—	2	1	no	—
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	C₁₃×#135	—	2	32	no	—
116	C₂×C₁₃×Q₁₆	—	2	4	no	—
117	C₂×C₁₃×Q₁₆	—	2	4	no	—
118	C₂×C₁₃×Q₁₆	—	2	4	no	—
119	C₂×C₁₃×Q₁₆	—	4	2	no	—
120	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
121	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
122	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
123	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
124	C₂×C₁₃×SD₁₆	—	2	4	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×D₈	—	2	4	no	—
133	C₂×C₁₃×D₈	C₂³	1	4	yes	—
134	C₂×C₁₃×M₁₆	—	2	4	no	—
135	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
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	2	no	—
143	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
144	C₁₃×#124	—	2	8	no	—
145	C₁₃×#124	—	2	2	no	—
146	C₁₃×#124	C₂³	1	4	yes	—
147	C₁₃×#123	—	2	8	no	—
148	C₁₃×#123	—	2	8	no	—
149	C₁₃×C₂²⋊Q₈	—	2	2	no	—
150	C₁₃×C₂²⋊Q₈	—	2	2	no	—
151	C₁₃×C₂²⋊Q₈	—	2	2	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	—
156	C₁₃×#121	—	2	8	no	—
157	C₁₃×#121	—	2	8	no	—
158	C₁₃×#121	—	2	2	no	—
159	C₁₃×#121	C₂³	1	4	yes	—
160	C₄×Q₈×C₁₃	—	2	2	no	—
161	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
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	—	2	8	no	—
174	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
175	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	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	—
189	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
190	C₁₃×#103	C₂³	1	4	yes	—
191	C₁₃×#103	C₂³	1	4	yes	—
192	C₁₃×#103	C₂³	1	4	yes	—
193	C₁₃×#103	C₂³	1	4	yes	—
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	—
198	C₁₃×#97	C₂³	1	4	yes	—
199	C₂×#3269	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	C₂×D₄	1	1	yes	characteristic
203	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
204	C₁₃×#41	—	2	8	no	—
205	C₁₃×#41	—	2	8	no	—
206	C₁₃×#41	—	2	8	no	—
207	C₁₃×#41	—	4	4	no	—
208	C₁₃×#41	—	4	4	no	—
209	C₁₃×#41	—	4	4	no	—
210	C₁₃×#41	—	4	8	no	—
211	C₁₃×#41	—	4	8	no	—
212	C₁₃×#41	—	4	8	no	—
213	C₂×Q₈×C₁₃	—	2	1	no	—
214	C₂×Q₈×C₁₃	—	2	4	no	—
215	C₂×Q₈×C₁₃	—	2	1	no	—
216	C₂×Q₈×C₁₃	—	2	1	no	—
217	C₂×Q₈×C₁₃	—	2	1	no	—
218	C₂×Q₈×C₁₃	—	2	2	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	8	no	—
229	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
230	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
231	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
232	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
233	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
234	C₂×D₄×C₁₃	—	2	4	no	—
235	C₂×D₄×C₁₃	—	2	4	no	—
236	C₂×D₄×C₁₃	—	2	4	no	—
237	C₂×D₄×C₁₃	—	2	4	no	—
238	C₂×D₄×C₁₃	—	2	1	no	—
239	C₂×D₄×C₁₃	—	2	2	no	—
240	C₂×D₄×C₁₃	—	2	1	no	—
241	C₂×D₄×C₁₃	—	2	2	no	—
242	C₂×D₄×C₁₃	—	2	2	no	—
243	C₂×D₄×C₁₃	—	4	2	no	—
244	C₂×D₄×C₁₃	—	4	4	no	—
245	C₂×D₄×C₁₃	—	4	4	no	—
246	C₂×D₄×C₁₃	—	4	4	no	—
247	C₂×D₄×C₁₃	—	4	4	no	—
248	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
249	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
250	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
251	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₁₃	—	2	1	no	—
253	C₂²×C₄×C₁₃	—	2	2	no	—
254	C₂²×C₄×C₁₃	—	2	2	no	—
255	C₂²×C₄×C₁₃	—	2	2	no	—
256	C₂²×C₄×C₁₃	—	2	2	no	—
257	C₂²×C₄×C₁₃	—	2	4	no	—
258	C₂²×C₄×C₁₃	—	2	1	no	—
259	C₂²×C₄×C₁₃	—	2	1	no	—
260	C₂²×C₄×C₁₃	—	2	1	no	—
261	C₂²×C₄×C₁₃	—	2	1	no	—
262	C₂²×C₄×C₁₃	—	2	1	no	—
263	C₂²×C₄×C₁₃	—	2	4	no	—
264	C₂²×C₄×C₁₃	—	2	4	no	—
265	C₂²×C₄×C₁₃	—	2	4	no	—
266	C₂²×C₄×C₁₃	—	2	4	no	—
267	C₂²×C₄×C₁₃	—	4	4	no	—
268	C₂²×C₄×C₁₃	—	4	4	no	—
269	C₂²×C₄×C₁₃	—	4	4	no	—
270	C₂²×C₄×C₁₃	—	4	4	no	—
271	C₂²×C₄×C₁₃	—	4	4	no	—
272	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
273	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
274	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
277	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
278	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
281	C₁₃×Q₁₆	—	2	8	no	—
282	C₁₃×Q₁₆	—	2	8	no	—
283	C₁₃×Q₁₆	—	2	8	no	—
284	C₁₃×Q₁₆	—	4	4	no	—
285	C₁₃×SD₁₆	—	2	8	no	—
286	C₁₃×SD₁₆	—	2	8	no	—
287	C₁₃×SD₁₆	—	4	4	no	—
288	C₁₃×SD₁₆	C₂×D₄	1	16	yes	complemented
289	C₁₃×D₈	—	2	8	no	—
290	C₁₃×M₁₆	—	2	8	no	—
291	C₂×C₈×C₁₃	—	2	2	no	—
292	C₂×C₈×C₁₃	—	2	2	no	—
293	C₂×C₈×C₁₃	—	2	2	no	—
294	C₂×C₈×C₁₃	—	2	8	no	—
295	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
296	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
297	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
298	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
299	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
300	C₁₃×C₄⋊C₄	—	2	4	no	—
301	C₁₃×C₄⋊C₄	—	2	4	no	—
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	1	no	—
307	C₁₃×C₄⋊C₄	—	2	1	no	—
308	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
309	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
310	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
311	C₁₃×C₂²⋊C₄	—	2	4	no	—
312	C₁₃×C₂²⋊C₄	—	2	4	no	—
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	C₂×D₄	1	4	yes	—
319	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
320	C₄²×C₁₃	—	2	4	no	—
321	C₄²×C₁₃	C₂×D₄	1	2	yes	—
322	C₄²×C₁₃	C₂⁴	1	2	yes	—
323	C₂²×#137	C₂×C₁₃	1	1	yes	characteristic, complemented
324	C₂²×#135	C₂×C₁₃	1	1	yes	characteristic, complemented
325	C₂×#548	C₂×C₁₃	1	1	yes	characteristic, complemented
326	C₂×#547	C₂×C₁₃	1	1	yes	characteristic, complemented
327	#3269	C₂×C₁₃	1	16	yes	direct product factor
328	C₂×#497	C₂×C₁₃	1	1	yes	characteristic, complemented
329	C₂×#468	C₂×C₁₃	1	1	yes	characteristic, complemented
330	C₂×#467	C₂×C₁₃	1	1	yes	characteristic, complemented
331	C₂×#462	C₂×C₁₃	1	1	yes	characteristic, complemented
332	C₂×#463	C₂×C₁₃	1	1	yes	characteristic, complemented
333	C₂×#452	C₂×C₁₃	1	1	yes	characteristic, complemented
334	C₂×#452	C₂×C₁₃	1	1	yes	characteristic, complemented
335	C₂×#449	C₂×C₁₃	1	1	yes	characteristic, complemented
336	C₂×#451	C₂×C₁₃	1	1	yes	characteristic, complemented
337	C₂×#440	C₂×C₁₃	1	1	yes	characteristic, complemented
338	C₂×#435	C₂×C₁₃	1	1	yes	characteristic, complemented
339	C₂³×C₁₃	—	2	2	no	—
340	C₂³×C₁₃	—	2	2	no	—
341	C₂³×C₁₃	—	2	4	no	—
342	C₂³×C₁₃	—	2	2	no	—
343	C₂³×C₁₃	—	2	2	no	—
344	C₂³×C₁₃	—	2	2	no	—
345	C₂³×C₁₃	—	2	2	no	—
346	C₂³×C₁₃	—	2	2	no	—
347	C₂³×C₁₃	—	2	2	no	—
348	C₂³×C₁₃	—	4	2	no	—
349	C₂³×C₁₃	—	4	2	no	—
350	C₂³×C₁₃	—	4	2	no	—
351	C₂³×C₁₃	—	4	2	no	—
352	C₂³×C₁₃	—	4	2	no	—
353	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
354	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
355	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
356	Q₈×C₁₃	—	2	4	no	—
357	Q₈×C₁₃	—	2	2	no	—
358	Q₈×C₁₃	—	2	2	no	—
359	Q₈×C₁₃	—	2	2	no	—
360	Q₈×C₁₃	—	2	2	no	—
361	Q₈×C₁₃	—	2	2	no	—
362	Q₈×C₁₃	—	2	2	no	—
363	Q₈×C₁₃	—	2	2	no	—
364	Q₈×C₁₃	—	4	8	no	—
365	Q₈×C₁₃	—	4	2	no	—
366	Q₈×C₁₃	—	4	2	no	—
367	Q₈×C₁₃	—	4	2	no	—
368	Q₈×C₁₃	C₂²×D₄	1	4	yes	—
369	D₄×C₁₃	—	2	4	no	—
370	D₄×C₁₃	—	2	2	no	—
371	D₄×C₁₃	—	2	2	no	—
372	D₄×C₁₃	—	2	2	no	—
373	D₄×C₁₃	—	4	4	no	—
374	D₄×C₁₃	—	4	8	no	—
375	D₄×C₁₃	—	4	8	no	—
376	D₄×C₁₃	—	4	8	no	—
377	D₄×C₁₃	—	4	8	no	—
378	D₄×C₁₃	—	4	2	no	—
379	D₄×C₁₃	C₂²×D₄	1	4	yes	—
380	C₂×C₄×C₁₃	—	2	2	no	—
381	C₂×C₄×C₁₃	—	2	2	no	—
382	C₂×C₄×C₁₃	—	2	4	no	—
383	C₂×C₄×C₁₃	—	2	2	no	—
384	C₂×C₄×C₁₃	—	2	2	no	—
385	C₂×C₄×C₁₃	—	2	2	no	—
386	C₂×C₄×C₁₃	—	2	4	no	—
387	C₂×C₄×C₁₃	—	2	4	no	—
388	C₂×C₄×C₁₃	—	2	2	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	2	no	—
393	C₂×C₄×C₁₃	—	2	2	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	—	4	8	no	—
398	C₂×C₄×C₁₃	—	4	8	no	—
399	C₂×C₄×C₁₃	—	4	8	no	—
400	C₂×C₄×C₁₃	—	4	8	no	—
401	C₂×C₄×C₁₃	—	4	8	no	—
402	C₂×C₄×C₁₃	—	4	2	no	—
403	C₂×C₄×C₁₃	—	4	2	no	—
404	C₂×C₄×C₁₃	—	4	2	no	—
405	C₂×C₄×C₁₃	—	4	2	no	—
406	C₂×C₄×C₁₃	—	4	2	no	—
407	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
408	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
409	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
410	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
411	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
412	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
413	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
414	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
415	C₈×C₁₃	—	2	2	no	—
416	C₈×C₁₃	—	2	2	no	—
417	C₈×C₁₃	—	2	2	no	—
418	C₈×C₁₃	C₂²×D₄	1	4	yes	—
419	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
420	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
421	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
422	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
423	C₂×#137	—	2	8	no	—
424	C₂×#137	C₂²×C₁₃	1	8	yes	complemented
425	C₂×#135	—	2	8	no	—
426	C₂×#135	C₂²×C₁₃	1	8	yes	complemented
427	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
428	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
429	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
430	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
431	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
432	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
433	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
434	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
435	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
436	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
437	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
438	#548	—	2	4	no	—
439	#548	C₂²×C₁₃	1	8	yes	complemented
440	#547	—	2	4	no	—
441	#547	C₂²×C₁₃	1	8	yes	complemented
442	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
443	C₂×#124	—	2	1	no	—
444	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
445	C₂×#123	—	2	1	no	—
446	C₂×#123	—	2	1	no	—
447	C₂×C₂²⋊Q₈	—	2	1	no	—
448	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
449	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
450	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
451	C₂×#121	—	2	1	no	—
452	C₂×#121	—	2	1	no	—
453	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
454	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
455	C₂×C₄×D₄	—	2	1	no	—
456	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
457	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
458	C₂²×C₄⋊C₄	—	2	1	no	—
459	#497	C₂²×C₁₃	1	8	yes	complemented
460	#468	C₂²×C₁₃	1	8	yes	complemented
461	#467	C₂²×C₁₃	1	8	yes	complemented
462	#463	C₂²×C₁₃	1	8	yes	complemented
463	#462	C₂²×C₁₃	1	8	yes	complemented
464	#452	C₂²×C₁₃	1	8	yes	complemented
465	#452	C₂²×C₁₃	1	8	yes	complemented
466	#451	C₂²×C₁₃	1	8	yes	complemented
467	#449	C₂²×C₁₃	1	8	yes	complemented
468	#440	C₂²×C₁₃	1	8	yes	complemented
469	#435	C₂²×C₁₃	1	8	yes	complemented
470	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
471	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
472	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
473	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
474	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
475	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
476	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
477	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
478	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
479	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
480	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
481	C₂²×C₁₃	—	2	2	no	—
482	C₂²×C₁₃	—	2	2	no	—
483	C₂²×C₁₃	—	2	4	no	—
484	C₂²×C₁₃	—	2	2	no	—
485	C₂²×C₁₃	—	2	2	no	—
486	C₂²×C₁₃	—	2	2	no	—
487	C₂²×C₁₃	—	2	2	no	—
488	C₂²×C₁₃	—	4	4	no	—
489	C₂²×C₁₃	—	4	4	no	—
490	C₂²×C₁₃	—	4	8	no	—
491	C₂²×C₁₃	—	4	2	no	—
492	C₂²×C₁₃	—	4	2	no	—
493	C₂²×C₁₃	—	4	2	no	—
494	C₂²×C₁₃	—	4	2	no	—
495	C₂²×C₁₃	—	4	2	no	—
496	C₂²×C₁₃	—	8	4	no	—
497	C₂²×C₁₃	D₄²	1	2	yes	—
498	C₂²×C₁₃	#575	1	2	yes	—
499	C₂²×C₁₃	#578	1	2	yes	—
500	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
501	C₄×C₁₃	—	2	2	no	—
502	C₄×C₁₃	—	2	2	no	—
503	C₄×C₁₃	—	2	4	no	—
504	C₄×C₁₃	—	2	2	no	—
505	C₄×C₁₃	—	2	2	no	—
506	C₄×C₁₃	—	4	2	no	—
507	C₄×C₁₃	—	4	2	no	—
508	C₄×C₁₃	—	4	2	no	—
509	C₄×C₁₃	—	4	2	no	—
510	C₄×C₁₃	—	4	2	no	—
511	C₄×C₁₃	D₄²	1	2	yes	—
512	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
513	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
514	C₂×#41	—	2	2	no	—
515	C₂×#41	—	2	2	no	—
516	C₂×#41	—	2	2	no	—
517	C₂×#41	—	2	4	no	—
518	C₂×#41	—	2	4	no	—
519	C₂×#41	—	2	4	no	—
520	C₂×#41	—	4	2	no	—
521	C₂×#41	—	4	2	no	—
522	C₂×#41	—	4	2	no	—
523	C₂×#41	C₂³×C₁₃	1	4	yes	—
524	C₂×#41	C₂³×C₁₃	1	4	yes	—
525	C₂×#41	C₂³×C₁₃	1	4	yes	—
526	C₂²×Q₈	—	2	1	no	—
527	C₂²×Q₈	—	2	2	no	—
528	C₂²×Q₈	—	2	4	no	—
529	C₂²×Q₈	—	4	2	no	—
530	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
531	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
532	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
533	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
534	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
535	C₂²×D₄	—	2	1	no	—
536	C₂²×D₄	—	2	1	no	—
537	C₂²×D₄	—	2	1	no	—
538	C₂²×D₄	—	2	1	no	—
539	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
540	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
541	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
542	C₂³×C₄	—	2	1	no	—
543	C₂³×C₄	—	2	1	no	—
544	C₂³×C₄	—	2	1	no	—
545	C₂³×C₄	—	2	1	no	—
546	C₂³×C₄	—	2	1	no	—
547	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
548	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
549	#137	—	2	32	no	—
550	#135	—	2	32	no	—
551	C₂×Q₁₆	—	2	4	no	—
552	C₂×Q₁₆	—	2	4	no	—
553	C₂×Q₁₆	—	2	4	no	—
554	C₂×Q₁₆	—	4	2	no	—
555	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
556	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
557	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
558	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
559	C₂×SD₁₆	—	2	4	no	—
560	C₂×SD₁₆	—	2	4	no	—
561	C₂×SD₁₆	—	4	2	no	—
562	C₂×SD₁₆	D₄×C₁₃	1	8	yes	complemented
563	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
564	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
565	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
566	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
567	C₂×D₈	—	2	4	no	—
568	C₂×D₈	C₂³×C₁₃	1	4	yes	—
569	C₂×M₁₆	—	2	4	no	—
570	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
571	C₂²×C₈	—	2	4	no	—
572	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
573	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
574	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
575	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
576	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
577	C₄⋊Q₈	—	2	2	no	—
578	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
579	#124	—	2	8	no	—
580	#124	—	2	2	no	—
581	#124	C₂³×C₁₃	1	4	yes	—
582	#123	—	2	8	no	—
583	#123	—	2	8	no	—
584	C₂²⋊Q₈	—	2	2	no	—
585	C₂²⋊Q₈	—	2	2	no	—
586	C₂²⋊Q₈	—	2	2	no	—
587	C₂²⋊Q₈	—	2	8	no	—
588	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
589	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
590	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
591	#121	—	2	8	no	—
592	#121	—	2	8	no	—
593	#121	—	2	2	no	—
594	#121	C₂³×C₁₃	1	4	yes	—
595	C₄×Q₈	—	2	2	no	—
596	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
597	C₄×D₄	—	2	8	no	—
598	C₄×D₄	—	2	2	no	—
599	C₄×D₄	D₄×C₁₃	1	4	yes	—
600	C₄×D₄	C₂³×C₁₃	1	4	yes	—
601	C₄×D₄	C₂³×C₁₃	1	4	yes	—
602	C₂×C₄⋊C₄	—	2	1	no	—
603	C₂×C₄⋊C₄	—	2	1	no	—
604	C₂×C₄⋊C₄	—	2	1	no	—
605	C₂×C₄⋊C₄	—	2	1	no	—
606	C₂×C₄⋊C₄	—	2	1	no	—
607	C₂×C₄⋊C₄	—	2	1	no	—
608	C₂×C₄⋊C₄	—	2	8	no	—
609	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
612	C₂×C₂²⋊C₄	—	2	1	no	—
613	C₂×C₂²⋊C₄	—	2	1	no	—
614	C₂×C₂²⋊C₄	—	2	1	no	—
615	C₂×C₂²⋊C₄	—	2	1	no	—
616	C₂×C₂²⋊C₄	—	2	1	no	—
617	C₂×C₂²⋊C₄	—	2	1	no	—
618	C₂×C₂²⋊C₄	—	2	1	no	—
619	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
620	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
621	C₂×C₄²	—	2	1	no	—
622	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
623	#107	C₂³×C₁₃	1	4	yes	—
624	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
625	#103	C₂³×C₁₃	1	4	yes	—
626	#103	C₂³×C₁₃	1	4	yes	—
627	#103	C₂³×C₁₃	1	4	yes	—
628	#103	C₂³×C₁₃	1	4	yes	—
629	#102	C₂³×C₁₃	1	4	yes	—
630	#102	C₂³×C₁₃	1	4	yes	—
631	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
632	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
633	#97	C₂³×C₁₃	1	4	yes	—
634	C₂×C₁₃	—	4	2	no	—
635	C₂×C₁₃	—	4	2	no	—
636	C₂×C₁₃	—	4	4	no	—
637	C₂×C₁₃	—	8	2	no	—
638	C₂×C₁₃	#3269	1	4	yes	direct product factor
639	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
640	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
641	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
642	C₂⁴	—	2	1	no	—
643	C₂⁴	—	2	1	no	—
644	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
645	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
646	#41	—	2	8	no	—
647	#41	—	2	8	no	—
648	#41	—	2	8	no	—
649	#41	—	4	4	no	—
650	#41	—	4	4	no	—
651	#41	—	4	4	no	—
652	#41	—	4	8	no	—
653	#41	—	4	8	no	—
654	#41	—	4	8	no	—
655	C₂×Q₈	—	2	1	no	—
656	C₂×Q₈	—	2	4	no	—
657	C₂×Q₈	—	2	1	no	—
658	C₂×Q₈	—	2	1	no	—
659	C₂×Q₈	—	2	1	no	—
660	C₂×Q₈	—	2	2	no	—
661	C₂×Q₈	—	2	8	no	—
662	C₂×Q₈	—	2	2	no	—
663	C₂×Q₈	—	2	2	no	—
664	C₂×Q₈	—	2	2	no	—
665	C₂×Q₈	—	2	2	no	—
666	C₂×Q₈	—	2	2	no	—
667	C₂×Q₈	—	2	2	no	—
668	C₂×Q₈	—	4	4	no	—
669	C₂×Q₈	—	4	4	no	—
670	C₂×Q₈	—	4	8	no	—
671	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
672	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
673	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
674	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
675	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
676	C₂×D₄	—	2	4	no	—
677	C₂×D₄	—	2	4	no	—
678	C₂×D₄	—	2	4	no	—
679	C₂×D₄	—	2	4	no	—
680	C₂×D₄	—	2	1	no	—
681	C₂×D₄	—	2	2	no	—
682	C₂×D₄	—	2	1	no	—
683	C₂×D₄	—	2	2	no	—
684	C₂×D₄	—	2	2	no	—
685	C₂×D₄	—	4	2	no	—
686	C₂×D₄	—	4	4	no	—
687	C₂×D₄	—	4	4	no	—
688	C₂×D₄	—	4	4	no	—
689	C₂×D₄	—	4	4	no	—
690	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
691	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
692	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
693	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
694	C₂²×C₄	—	2	1	no	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	2	1	no	—
700	C₂²×C₄	—	2	1	no	—
701	C₂²×C₄	—	2	1	no	—
702	C₂²×C₄	—	2	1	no	—
703	C₂²×C₄	—	2	1	no	—
704	C₂²×C₄	—	2	4	no	—
705	C₂²×C₄	—	2	4	no	—
706	C₂²×C₄	—	2	4	no	—
707	C₂²×C₄	—	2	4	no	—
708	C₂²×C₄	—	2	4	no	—
709	C₂²×C₄	—	4	4	no	—
710	C₂²×C₄	—	4	4	no	—
711	C₂²×C₄	—	4	4	no	—
712	C₂²×C₄	—	4	4	no	—
713	C₂²×C₄	—	4	4	no	—
714	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
715	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
716	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
717	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
718	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
719	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
720	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
721	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
722	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
723	Q₁₆	—	2	8	no	—
724	Q₁₆	—	2	8	no	—
725	Q₁₆	—	2	8	no	—
726	Q₁₆	—	4	4	no	—
727	SD₁₆	—	2	8	no	—
728	SD₁₆	—	2	8	no	—
729	SD₁₆	—	4	4	no	—
730	SD₁₆	C₂×D₄×C₁₃	1	16	yes	complemented
731	D₈	—	2	8	no	—
732	M₁₆	—	2	8	no	—
733	C₂×C₈	—	2	2	no	—
734	C₂×C₈	—	2	2	no	—
735	C₂×C₈	—	2	2	no	—
736	C₂×C₈	—	2	8	no	—
737	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
738	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
739	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
740	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
741	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
742	C₄⋊C₄	—	2	4	no	—
743	C₄⋊C₄	—	2	4	no	—
744	C₄⋊C₄	—	2	4	no	—
745	C₄⋊C₄	—	2	4	no	—
746	C₄⋊C₄	—	2	4	no	—
747	C₄⋊C₄	—	2	4	no	—
748	C₄⋊C₄	—	2	1	no	—
749	C₄⋊C₄	—	2	1	no	—
750	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
751	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
752	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
753	C₂²⋊C₄	—	2	4	no	—
754	C₂²⋊C₄	—	2	4	no	—
755	C₂²⋊C₄	—	2	4	no	—
756	C₂²⋊C₄	—	2	4	no	—
757	C₂²⋊C₄	—	2	4	no	—
758	C₂²⋊C₄	—	2	4	no	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
761	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
762	C₄²	—	2	4	no	—
763	C₄²	C₂×D₄×C₁₃	1	2	yes	—
764	C₄²	C₂⁴×C₁₃	1	2	yes	—
765	C₁₃	C₂×#3269	1	1	yes	characteristic, direct product factor, Sylow
766	C₂³	—	2	2	no	—
767	C₂³	—	2	2	no	—
768	C₂³	—	2	4	no	—
769	C₂³	—	2	2	no	—
770	C₂³	—	2	2	no	—
771	C₂³	—	2	2	no	—
772	C₂³	—	2	2	no	—
773	C₂³	—	2	2	no	—
774	C₂³	—	2	2	no	—
775	C₂³	—	4	2	no	—
776	C₂³	—	4	2	no	—
777	C₂³	—	4	2	no	—
778	C₂³	—	4	2	no	—
779	C₂³	—	4	2	no	—
780	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
781	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
782	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
783	Q₈	—	2	4	no	—
784	Q₈	—	2	2	no	—
785	Q₈	—	2	2	no	—
786	Q₈	—	2	2	no	—
787	Q₈	—	2	2	no	—
788	Q₈	—	2	2	no	—
789	Q₈	—	2	2	no	—
790	Q₈	—	2	2	no	—
791	Q₈	—	4	8	no	—
792	Q₈	—	4	2	no	—
793	Q₈	—	4	2	no	—
794	Q₈	—	4	2	no	—
795	Q₈	C₂²×D₄×C₁₃	1	4	yes	—
796	D₄	—	2	4	no	—
797	D₄	—	2	2	no	—
798	D₄	—	2	2	no	—
799	D₄	—	2	2	no	—
800	D₄	—	4	4	no	—
801	D₄	—	4	8	no	—
802	D₄	—	4	8	no	—
803	D₄	—	4	8	no	—
804	D₄	—	4	8	no	—
805	D₄	—	4	2	no	—
806	D₄	C₂²×D₄×C₁₃	1	4	yes	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	4	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	4	no	—
814	C₂×C₄	—	2	4	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	4	8	no	—
825	C₂×C₄	—	4	8	no	—
826	C₂×C₄	—	4	8	no	—
827	C₂×C₄	—	4	8	no	—
828	C₂×C₄	—	4	8	no	—
829	C₂×C₄	—	4	2	no	—
830	C₂×C₄	—	4	2	no	—
831	C₂×C₄	—	4	2	no	—
832	C₂×C₄	—	4	2	no	—
833	C₂×C₄	—	4	2	no	—
834	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
835	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
836	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
837	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
838	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
839	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
840	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
841	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
842	C₈	—	2	2	no	—
843	C₈	—	2	2	no	—
844	C₈	—	2	2	no	—
845	C₈	C₂²×D₄×C₁₃	1	4	yes	—
846	C₂²	—	2	2	no	—
847	C₂²	—	2	2	no	—
848	C₂²	—	2	2	no	—
849	C₂²	—	2	2	no	—
850	C₂²	—	2	2	no	—
851	C₂²	—	2	2	no	—
852	C₂²	—	2	4	no	—
853	C₂²	—	4	4	no	—
854	C₂²	—	4	4	no	—
855	C₂²	—	4	8	no	—
856	C₂²	—	4	2	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	4	2	no	—
859	C₂²	—	4	2	no	—
860	C₂²	—	4	2	no	—
861	C₂²	—	8	4	no	—
862	C₂²	D₄²×C₁₃	1	2	yes	—
863	C₂²	C₁₃×#575	1	2	yes	—
864	C₂²	C₁₃×#578	1	2	yes	—
865	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
866	C₄	—	2	2	no	—
867	C₄	—	2	2	no	—
868	C₄	—	2	2	no	—
869	C₄	—	2	2	no	—
870	C₄	—	2	4	no	—
871	C₄	—	4	2	no	—
872	C₄	—	4	2	no	—
873	C₄	—	4	2	no	—
874	C₄	—	4	2	no	—
875	C₄	—	4	2	no	—
876	C₄	D₄²×C₁₃	1	2	yes	—
877	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
878	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
879	C₂	—	4	2	no	—
880	C₂	—	4	2	no	—
881	C₂	—	4	4	no	—
882	C₂	—	8	2	no	—
883	C₂	C₁₃×#3269	1	4	yes	direct product factor
884	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
885	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
886	C₂	C₂×C₁₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
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. C₂²×C₁₃×#135	C₂	semidirect
3. C₂×C₁₃×#548	C₂	semidirect
4. C₂×C₁₃×#547	C₂	semidirect
5. C₁₃×#3269	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×#462	C₂	semidirect
10. C₂×C₁₃×#463	C₂	semidirect
11. C₂×C₁₃×#452	C₂	semidirect
12. C₂×C₁₃×#452	C₂	semidirect
13. C₂×C₁₃×#449	C₂	semidirect
14. C₂×C₁₃×#451	C₂	semidirect
15. C₂×C₁₃×#440	C₂	semidirect
16. C₂×C₁₃×#435	C₂	semidirect
22. C₂×C₁₃×#137	C₂²	semidirect
24. C₂×C₁₃×#135	C₂²	semidirect
37. C₁₃×#548	C₂²	semidirect
39. C₁₃×#547	C₂²	semidirect
57. C₁₃×#497	C₂²	semidirect
58. C₁₃×#468	C₂²	semidirect
59. C₁₃×#467	C₂²	semidirect
60. C₁₃×#463	C₂²	semidirect
61. C₁₃×#462	C₂²	semidirect
62. C₁₃×#452	C₂²	semidirect
63. C₁₃×#452	C₂²	semidirect
64. C₁₃×#451	C₂²	semidirect
65. C₁₃×#449	C₂²	semidirect
66. C₁₃×#440	C₂²	semidirect
67. C₁₃×#435	C₂²	semidirect
127. C₂×C₁₃×SD₁₆	D₄	semidirect
199. C₂×#3269	C₁₃	direct (N × H)
288. C₁₃×SD₁₆	C₂×D₄	semidirect
323. C₂²×#137	C₂×C₁₃	semidirect
324. C₂²×#135	C₂×C₁₃	semidirect
325. C₂×#548	C₂×C₁₃	semidirect
326. C₂×#547	C₂×C₁₃	semidirect
327. #3269	C₂×C₁₃	direct (N × H)
328. C₂×#497	C₂×C₁₃	semidirect
329. C₂×#468	C₂×C₁₃	semidirect
330. C₂×#467	C₂×C₁₃	semidirect
331. C₂×#462	C₂×C₁₃	semidirect
332. C₂×#463	C₂×C₁₃	semidirect
333. C₂×#452	C₂×C₁₃	semidirect
334. C₂×#452	C₂×C₁₃	semidirect
335. C₂×#449	C₂×C₁₃	semidirect
336. C₂×#451	C₂×C₁₃	semidirect
337. C₂×#440	C₂×C₁₃	semidirect
338. C₂×#435	C₂×C₁₃	semidirect
424. C₂×#137	C₂²×C₁₃	semidirect
426. C₂×#135	C₂²×C₁₃	semidirect
439. #548	C₂²×C₁₃	semidirect
441. #547	C₂²×C₁₃	semidirect
459. #497	C₂²×C₁₃	semidirect
460. #468	C₂²×C₁₃	semidirect
461. #467	C₂²×C₁₃	semidirect
462. #463	C₂²×C₁₃	semidirect
463. #462	C₂²×C₁₃	semidirect
464. #452	C₂²×C₁₃	semidirect
465. #452	C₂²×C₁₃	semidirect
466. #451	C₂²×C₁₃	semidirect
467. #449	C₂²×C₁₃	semidirect
468. #440	C₂²×C₁₃	semidirect
469. #435	C₂²×C₁₃	semidirect
562. C₂×SD₁₆	D₄×C₁₃	semidirect
638. C₂×C₁₃	#3269	direct (N × H)
730. SD₁₆	C₂×D₄×C₁₃	semidirect
765. C₁₃	C₂×#3269	direct (N × H)
883. C₂	C₁₃×#3269	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
C₂²×C₁₃×#135	2
C₂×C₁₃×#548	2
C₂×C₁₃×#547	2
C₁₃×#3269	2
C₂×C₁₃×#497	2
C₂×C₁₃×#468	2
C₂×C₁₃×#467	2
C₂×C₁₃×#462	2
C₂×C₁₃×#463	2
C₂×C₁₃×#452	2
C₂×C₁₃×#449	2
C₂×C₁₃×#451	2
C₂×C₁₃×#440	2
C₂×C₁₃×#435	2
C₂×#3269	13

Subgroups — C2×C13×#3269 #15747366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3269 #15747366