Subgroups — C₂×C₁₃×#3301 #15747458

Order 3328.

2210 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#548	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3301	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#488	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#481	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#485	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#479	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#465	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#463	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#449	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#448	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₈×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#416	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#103	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	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
22	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₁₃×#553	—	2	4	no	—
25	C₁₃×#553	C₂²	1	8	yes	complemented
26	C₁₃×#548	—	2	4	no	—
27	C₁₃×#548	C₂²	1	8	yes	complemented
28	C₂×C₁₃×#126	—	2	1	no	—
29	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#124	—	2	1	no	—
31	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#123	—	2	1	no	—
33	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
34	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#121	—	2	1	no	—
36	C₂×C₁₃×#121	—	2	1	no	—
37	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
40	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₁₃	—	2	1	no	—
42	C₂×C₄×D₄×C₁₃	—	2	1	no	—
43	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
46	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	C₁₃×#488	C₂²	1	8	yes	complemented
48	C₁₃×#485	C₂²	1	8	yes	complemented
49	C₁₃×#481	C₂²	1	8	yes	complemented
50	C₁₃×#479	C₂²	1	8	yes	complemented
51	C₁₃×#466	C₂²	1	8	yes	complemented
52	C₁₃×#465	C₂²	1	8	yes	complemented
53	C₁₃×#463	C₂²	1	8	yes	complemented
54	C₁₃×#449	C₂²	1	8	yes	complemented
55	C₁₃×#448	C₂²	1	8	yes	complemented
56	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	complemented
57	C₈×D₄×C₁₃	C₂²	1	8	yes	complemented
58	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
59	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
60	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
61	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
62	C₁₃×#416	C₂²	1	8	yes	complemented
63	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
64	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
65	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
66	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
68	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
69	C₂×C₁₃×#103	C₂²	1	8	yes	complemented
70	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
71	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
72	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
73	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
74	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
75	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
76	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
77	C₂×C₁₃×#41	—	2	2	no	—
78	C₂×C₁₃×#41	—	2	4	no	—
79	C₂×C₁₃×#41	—	4	2	no	—
80	C₂×C₁₃×#41	C₂³	1	4	yes	—
81	C₂²×Q₈×C₁₃	—	2	1	no	—
82	C₂²×Q₈×C₁₃	—	2	2	no	—
83	C₂²×Q₈×C₁₃	—	2	4	no	—
84	C₂²×Q₈×C₁₃	—	4	2	no	—
85	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
87	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₁₃	—	2	1	no	—
89	C₂²×D₄×C₁₃	—	2	1	no	—
90	C₂²×D₄×C₁₃	—	2	1	no	—
91	C₂²×D₄×C₁₃	—	2	1	no	—
92	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
93	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₁₃	—	2	1	no	—
96	C₂³×C₄×C₁₃	—	2	1	no	—
97	C₂³×C₄×C₁₃	—	2	1	no	—
98	C₂³×C₄×C₁₃	—	2	1	no	—
99	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
101	C₂×C₁₃×SD₁₆	—	2	4	no	—
102	C₂×C₁₃×SD₁₆	—	4	2	no	—
103	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
104	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
105	C₂×C₁₃×D₈	—	4	2	no	—
106	C₂×C₁₃×D₈	C₂³	1	4	yes	—
107	C₂²×C₈×C₁₃	—	4	2	no	—
108	C₂²×C₈×C₁₃	—	4	2	no	—
109	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
113	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
114	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
115	C₁₃×#126	—	2	8	no	—
116	C₁₃×#125	—	2	2	no	—
117	C₁₃×#125	C₂³	1	4	yes	—
118	C₁₃×#124	—	2	8	no	—
119	C₁₃×#124	—	2	2	no	—
120	C₁₃×#124	C₂³	1	4	yes	—
121	C₁₃×#123	—	2	8	no	—
122	C₁₃×C₂²⋊Q₈	—	2	2	no	—
123	C₁₃×C₂²⋊Q₈	—	2	8	no	—
124	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
125	C₁₃×#121	—	2	8	no	—
126	C₁₃×#121	—	2	8	no	—
127	C₁₃×#121	—	2	2	no	—
128	C₁₃×#121	—	2	2	no	—
129	C₁₃×#121	—	2	2	no	—
130	C₁₃×#121	C₂³	1	4	yes	—
131	C₁₃×#121	C₂³	1	4	yes	—
132	C₁₃×#121	C₂³	1	4	yes	—
133	C₄×Q₈×C₁₃	—	2	2	no	—
134	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
135	C₄×D₄×C₁₃	—	2	8	no	—
136	C₄×D₄×C₁₃	—	2	8	no	—
137	C₄×D₄×C₁₃	—	2	2	no	—
138	C₄×D₄×C₁₃	D₄	1	4	yes	—
139	C₄×D₄×C₁₃	C₂³	1	4	yes	—
140	C₄×D₄×C₁₃	C₂³	1	4	yes	—
141	C₁₃×#117	—	2	2	no	—
142	C₁₃×#117	C₂³	1	4	yes	—
143	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
144	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
145	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
146	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
147	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
148	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
149	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
150	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
152	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
154	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
155	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
156	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
157	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
158	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
159	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
160	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
161	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
162	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
163	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
164	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
165	C₂×C₄²×C₁₃	—	2	1	no	—
166	C₂×C₄²×C₁₃	—	2	1	no	—
167	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
168	C₁₃×#107	C₂³	1	4	yes	—
169	C₁₃×#106	C₂³	1	4	yes	—
170	C₁₃×#106	C₂³	1	4	yes	—
171	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
172	C₁₃×#103	C₂³	1	4	yes	—
173	C₁₃×#103	C₂³	1	4	yes	—
174	C₁₃×#103	C₂³	1	4	yes	—
175	C₁₃×#103	C₂³	1	4	yes	—
176	C₁₃×#103	C₂³	1	4	yes	—
177	C₁₃×#103	C₂³	1	4	yes	—
178	C₁₃×#102	C₂³	1	4	yes	—
179	C₁₃×#102	C₂³	1	4	yes	—
180	C₁₃×#102	C₂³	1	4	yes	—
181	C₁₃×#102	C₂³	1	4	yes	—
182	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
183	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
184	C₄×C₈×C₁₃	C₂³	1	4	yes	—
185	C₂×#3301	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₂⁴×C₁₃	—	2	1	no	—
187	C₂⁴×C₁₃	—	2	1	no	—
188	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
189	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
190	C₁₃×#41	—	2	8	no	—
191	C₁₃×#41	—	4	4	no	—
192	C₁₃×#41	—	4	8	no	—
193	C₂×Q₈×C₁₃	—	2	1	no	—
194	C₂×Q₈×C₁₃	—	2	4	no	—
195	C₂×Q₈×C₁₃	—	2	1	no	—
196	C₂×Q₈×C₁₃	—	2	2	no	—
197	C₂×Q₈×C₁₃	—	2	8	no	—
198	C₂×Q₈×C₁₃	—	2	2	no	—
199	C₂×Q₈×C₁₃	—	2	2	no	—
200	C₂×Q₈×C₁₃	—	4	4	no	—
201	C₂×Q₈×C₁₃	—	4	4	no	—
202	C₂×Q₈×C₁₃	—	4	8	no	—
203	C₂×Q₈×C₁₃	#41	1	4	yes	—
204	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
205	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
206	C₂×D₄×C₁₃	—	2	4	no	—
207	C₂×D₄×C₁₃	—	2	4	no	—
208	C₂×D₄×C₁₃	—	2	4	no	—
209	C₂×D₄×C₁₃	—	2	4	no	—
210	C₂×D₄×C₁₃	—	2	4	no	—
211	C₂×D₄×C₁₃	—	2	1	no	—
212	C₂×D₄×C₁₃	—	2	1	no	—
213	C₂×D₄×C₁₃	—	2	2	no	—
214	C₂×D₄×C₁₃	—	2	2	no	—
215	C₂×D₄×C₁₃	—	2	2	no	—
216	C₂×D₄×C₁₃	—	2	2	no	—
217	C₂×D₄×C₁₃	—	4	4	no	—
218	C₂×D₄×C₁₃	—	4	4	no	—
219	C₂×D₄×C₁₃	—	4	4	no	—
220	C₂×D₄×C₁₃	—	8	2	no	—
221	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
222	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
223	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₁₃	—	2	1	no	—
225	C₂²×C₄×C₁₃	—	2	2	no	—
226	C₂²×C₄×C₁₃	—	2	2	no	—
227	C₂²×C₄×C₁₃	—	2	2	no	—
228	C₂²×C₄×C₁₃	—	2	2	no	—
229	C₂²×C₄×C₁₃	—	2	4	no	—
230	C₂²×C₄×C₁₃	—	2	1	no	—
231	C₂²×C₄×C₁₃	—	2	1	no	—
232	C₂²×C₄×C₁₃	—	2	1	no	—
233	C₂²×C₄×C₁₃	—	2	1	no	—
234	C₂²×C₄×C₁₃	—	2	1	no	—
235	C₂²×C₄×C₁₃	—	2	4	no	—
236	C₂²×C₄×C₁₃	—	2	4	no	—
237	C₂²×C₄×C₁₃	—	2	4	no	—
238	C₂²×C₄×C₁₃	—	4	4	no	—
239	C₂²×C₄×C₁₃	—	4	4	no	—
240	C₂²×C₄×C₁₃	—	8	2	no	—
241	C₂²×C₄×C₁₃	—	8	2	no	—
242	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
243	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
244	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
251	C₁₃×SD₁₆	—	2	8	no	—
252	C₁₃×SD₁₆	—	4	4	no	—
253	C₁₃×D₈	—	4	4	no	—
254	C₂×C₈×C₁₃	—	2	2	no	—
255	C₂×C₈×C₁₃	—	2	2	no	—
256	C₂×C₈×C₁₃	—	2	2	no	—
257	C₂×C₈×C₁₃	—	2	2	no	—
258	C₂×C₈×C₁₃	—	4	4	no	—
259	C₂×C₈×C₁₃	—	4	4	no	—
260	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
261	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
262	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
263	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
264	C₁₃×C₄⋊C₄	—	2	1	no	—
265	C₁₃×C₄⋊C₄	—	2	1	no	—
266	C₁₃×C₄⋊C₄	—	2	4	no	—
267	C₁₃×C₄⋊C₄	—	2	4	no	—
268	C₁₃×C₄⋊C₄	—	2	4	no	—
269	C₁₃×C₄⋊C₄	—	2	4	no	—
270	C₁₃×C₄⋊C₄	—	2	4	no	—
271	C₁₃×C₄⋊C₄	—	2	1	no	—
272	C₁₃×C₄⋊C₄	—	2	1	no	—
273	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
274	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
275	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
276	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
277	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
278	C₁₃×C₂²⋊C₄	—	2	4	no	—
279	C₁₃×C₂²⋊C₄	—	2	4	no	—
280	C₁₃×C₂²⋊C₄	—	2	4	no	—
281	C₁₃×C₂²⋊C₄	—	2	4	no	—
282	C₁₃×C₂²⋊C₄	—	2	4	no	—
283	C₁₃×C₂²⋊C₄	—	2	4	no	—
284	C₁₃×C₂²⋊C₄	—	2	4	no	—
285	C₁₃×C₂²⋊C₄	—	2	4	no	—
286	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
287	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
288	C₄²×C₁₃	—	2	4	no	—
289	C₄²×C₁₃	—	2	4	no	—
290	C₄²×C₁₃	C₂×D₄	1	2	yes	—
291	C₄²×C₁₃	C₂⁴	1	2	yes	—
292	C₂×#553	C₂×C₁₃	1	1	yes	characteristic, complemented
293	C₂×#548	C₂×C₁₃	1	1	yes	characteristic, complemented
294	#3301	C₂×C₁₃	1	16	yes	direct product factor
295	C₂×#488	C₂×C₁₃	1	1	yes	characteristic, complemented
296	C₂×#481	C₂×C₁₃	1	1	yes	characteristic, complemented
297	C₂×#485	C₂×C₁₃	1	1	yes	characteristic, complemented
298	C₂×#479	C₂×C₁₃	1	1	yes	characteristic, complemented
299	C₂×#466	C₂×C₁₃	1	1	yes	characteristic, complemented
300	C₂×#465	C₂×C₁₃	1	1	yes	characteristic, complemented
301	C₂×#463	C₂×C₁₃	1	1	yes	characteristic, complemented
302	C₂×#449	C₂×C₁₃	1	1	yes	characteristic, complemented
303	C₂×#448	C₂×C₁₃	1	1	yes	characteristic, complemented
304	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
305	C₂×C₈×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
306	C₂×#416	C₂×C₁₃	1	1	yes	characteristic, complemented
307	C₂²×#103	C₂×C₁₃	1	1	yes	characteristic, complemented
308	C₂³×C₁₃	—	2	2	no	—
309	C₂³×C₁₃	—	2	2	no	—
310	C₂³×C₁₃	—	2	2	no	—
311	C₂³×C₁₃	—	2	2	no	—
312	C₂³×C₁₃	—	2	2	no	—
313	C₂³×C₁₃	—	2	2	no	—
314	C₂³×C₁₃	—	2	2	no	—
315	C₂³×C₁₃	—	4	2	no	—
316	C₂³×C₁₃	—	4	2	no	—
317	C₂³×C₁₃	—	4	2	no	—
318	C₂³×C₁₃	—	4	2	no	—
319	C₂³×C₁₃	—	4	2	no	—
320	C₂³×C₁₃	—	4	2	no	—
321	C₂³×C₁₃	#135	1	4	yes	—
322	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
323	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
324	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
325	Q₈×C₁₃	—	2	4	no	—
326	Q₈×C₁₃	—	2	2	no	—
327	Q₈×C₁₃	—	2	2	no	—
328	Q₈×C₁₃	—	2	2	no	—
329	Q₈×C₁₃	—	4	8	no	—
330	Q₈×C₁₃	—	4	2	no	—
331	Q₈×C₁₃	C₂×#41	1	4	yes	—
332	D₄×C₁₃	—	2	8	no	—
333	D₄×C₁₃	—	2	2	no	—
334	D₄×C₁₃	—	2	2	no	—
335	D₄×C₁₃	—	2	2	no	—
336	D₄×C₁₃	—	2	2	no	—
337	D₄×C₁₃	—	4	8	no	—
338	D₄×C₁₃	—	4	8	no	—
339	D₄×C₁₃	—	4	8	no	—
340	D₄×C₁₃	—	4	2	no	—
341	D₄×C₁₃	—	4	2	no	—
342	D₄×C₁₃	—	8	4	no	—
343	C₂×C₄×C₁₃	—	2	2	no	—
344	C₂×C₄×C₁₃	—	2	2	no	—
345	C₂×C₄×C₁₃	—	2	4	no	—
346	C₂×C₄×C₁₃	—	2	2	no	—
347	C₂×C₄×C₁₃	—	2	2	no	—
348	C₂×C₄×C₁₃	—	2	2	no	—
349	C₂×C₄×C₁₃	—	2	4	no	—
350	C₂×C₄×C₁₃	—	2	4	no	—
351	C₂×C₄×C₁₃	—	2	2	no	—
352	C₂×C₄×C₁₃	—	2	2	no	—
353	C₂×C₄×C₁₃	—	2	2	no	—
354	C₂×C₄×C₁₃	—	2	2	no	—
355	C₂×C₄×C₁₃	—	2	2	no	—
356	C₂×C₄×C₁₃	—	2	2	no	—
357	C₂×C₄×C₁₃	—	2	2	no	—
358	C₂×C₄×C₁₃	—	2	2	no	—
359	C₂×C₄×C₁₃	—	2	2	no	—
360	C₂×C₄×C₁₃	—	4	8	no	—
361	C₂×C₄×C₁₃	—	4	8	no	—
362	C₂×C₄×C₁₃	—	4	2	no	—
363	C₂×C₄×C₁₃	—	4	2	no	—
364	C₂×C₄×C₁₃	—	4	2	no	—
365	C₂×C₄×C₁₃	—	4	2	no	—
366	C₂×C₄×C₁₃	—	4	2	no	—
367	C₂×C₄×C₁₃	—	8	4	no	—
368	C₂×C₄×C₁₃	—	8	4	no	—
369	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
370	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
371	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
372	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
373	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
374	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
375	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
376	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
377	C₈×C₁₃	—	2	2	no	—
378	C₈×C₁₃	—	2	2	no	—
379	C₈×C₁₃	—	2	2	no	—
380	C₈×C₁₃	—	2	2	no	—
381	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
382	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
383	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
384	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
385	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
386	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
387	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
388	#553	—	2	4	no	—
389	#553	C₂²×C₁₃	1	8	yes	complemented
390	#548	—	2	4	no	—
391	#548	C₂²×C₁₃	1	8	yes	complemented
392	C₂×#126	—	2	1	no	—
393	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
394	C₂×#124	—	2	1	no	—
395	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
396	C₂×#123	—	2	1	no	—
397	C₂×C₂²⋊Q₈	—	2	1	no	—
398	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
399	C₂×#121	—	2	1	no	—
400	C₂×#121	—	2	1	no	—
401	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
402	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
403	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
404	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
405	C₂×C₄×D₄	—	2	1	no	—
406	C₂×C₄×D₄	—	2	1	no	—
407	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
408	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
409	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
410	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
411	#488	C₂²×C₁₃	1	8	yes	complemented
412	#485	C₂²×C₁₃	1	8	yes	complemented
413	#481	C₂²×C₁₃	1	8	yes	complemented
414	#479	C₂²×C₁₃	1	8	yes	complemented
415	#466	C₂²×C₁₃	1	8	yes	complemented
416	#465	C₂²×C₁₃	1	8	yes	complemented
417	#463	C₂²×C₁₃	1	8	yes	complemented
418	#449	C₂²×C₁₃	1	8	yes	complemented
419	#448	C₂²×C₁₃	1	8	yes	complemented
420	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	complemented
421	C₈×D₄	C₂²×C₁₃	1	8	yes	complemented
422	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
423	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
424	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
425	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
426	#416	C₂²×C₁₃	1	8	yes	complemented
427	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
428	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
429	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
430	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
431	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
432	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
433	C₂×#103	C₂²×C₁₃	1	8	yes	complemented
434	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
435	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
436	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
437	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
438	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
439	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
440	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
441	C₂²×C₁₃	—	2	2	no	—
442	C₂²×C₁₃	—	2	8	no	—
443	C₂²×C₁₃	—	2	2	no	—
444	C₂²×C₁₃	—	2	2	no	—
445	C₂²×C₁₃	—	2	2	no	—
446	C₂²×C₁₃	—	2	2	no	—
447	C₂²×C₁₃	—	4	4	no	—
448	C₂²×C₁₃	—	4	2	no	—
449	C₂²×C₁₃	—	4	2	no	—
450	C₂²×C₁₃	—	4	2	no	—
451	C₂²×C₁₃	—	4	2	no	—
452	C₂²×C₁₃	—	4	2	no	—
453	C₂²×C₁₃	—	4	2	no	—
454	C₂²×C₁₃	—	8	4	no	—
455	C₂²×C₁₃	—	8	4	no	—
456	C₂²×C₁₃	#546	1	2	yes	—
457	C₂²×C₁₃	C₂×#135	1	4	yes	—
458	C₂²×C₁₃	C₂×#135	1	2	yes	—
459	C₂²×C₁₃	#577	1	2	yes	—
460	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
461	C₄×C₁₃	—	2	2	no	—
462	C₄×C₁₃	—	2	2	no	—
463	C₄×C₁₃	—	2	4	no	—
464	C₄×C₁₃	—	2	2	no	—
465	C₄×C₁₃	—	2	2	no	—
466	C₄×C₁₃	—	4	2	no	—
467	C₄×C₁₃	—	4	2	no	—
468	C₄×C₁₃	—	4	2	no	—
469	C₄×C₁₃	—	4	2	no	—
470	C₄×C₁₃	—	4	2	no	—
471	C₄×C₁₃	#546	1	2	yes	—
472	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
473	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
474	C₂×#41	—	2	2	no	—
475	C₂×#41	—	2	4	no	—
476	C₂×#41	—	4	2	no	—
477	C₂×#41	C₂³×C₁₃	1	4	yes	—
478	C₂²×Q₈	—	2	1	no	—
479	C₂²×Q₈	—	2	2	no	—
480	C₂²×Q₈	—	2	4	no	—
481	C₂²×Q₈	—	4	2	no	—
482	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
483	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
484	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
485	C₂²×D₄	—	2	1	no	—
486	C₂²×D₄	—	2	1	no	—
487	C₂²×D₄	—	2	1	no	—
488	C₂²×D₄	—	2	1	no	—
489	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
490	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
491	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
492	C₂³×C₄	—	2	1	no	—
493	C₂³×C₄	—	2	1	no	—
494	C₂³×C₄	—	2	1	no	—
495	C₂³×C₄	—	2	1	no	—
496	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
497	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
498	C₂×SD₁₆	—	2	4	no	—
499	C₂×SD₁₆	—	4	2	no	—
500	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
501	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
502	C₂×D₈	—	4	2	no	—
503	C₂×D₈	C₂³×C₁₃	1	4	yes	—
504	C₂²×C₈	—	4	2	no	—
505	C₂²×C₈	—	4	2	no	—
506	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
507	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
508	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
509	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
510	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
511	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
512	#126	—	2	8	no	—
513	#125	—	2	2	no	—
514	#125	C₂³×C₁₃	1	4	yes	—
515	#124	—	2	8	no	—
516	#124	—	2	2	no	—
517	#124	C₂³×C₁₃	1	4	yes	—
518	#123	—	2	8	no	—
519	C₂²⋊Q₈	—	2	2	no	—
520	C₂²⋊Q₈	—	2	8	no	—
521	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
522	#121	—	2	8	no	—
523	#121	—	2	8	no	—
524	#121	—	2	2	no	—
525	#121	—	2	2	no	—
526	#121	—	2	2	no	—
527	#121	C₂³×C₁₃	1	4	yes	—
528	#121	C₂³×C₁₃	1	4	yes	—
529	#121	C₂³×C₁₃	1	4	yes	—
530	C₄×Q₈	—	2	2	no	—
531	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
532	C₄×D₄	—	2	8	no	—
533	C₄×D₄	—	2	8	no	—
534	C₄×D₄	—	2	2	no	—
535	C₄×D₄	D₄×C₁₃	1	4	yes	—
536	C₄×D₄	C₂³×C₁₃	1	4	yes	—
537	C₄×D₄	C₂³×C₁₃	1	4	yes	—
538	#117	—	2	2	no	—
539	#117	C₂³×C₁₃	1	4	yes	—
540	C₂×C₄⋊C₄	—	2	1	no	—
541	C₂×C₄⋊C₄	—	2	2	no	—
542	C₂×C₄⋊C₄	—	2	1	no	—
543	C₂×C₄⋊C₄	—	2	1	no	—
544	C₂×C₄⋊C₄	—	2	1	no	—
545	C₂×C₄⋊C₄	—	2	1	no	—
546	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
547	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
548	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
549	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
550	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
551	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
552	C₂×C₂²⋊C₄	—	2	1	no	—
553	C₂×C₂²⋊C₄	—	2	1	no	—
554	C₂×C₂²⋊C₄	—	2	1	no	—
555	C₂×C₂²⋊C₄	—	2	1	no	—
556	C₂×C₂²⋊C₄	—	2	1	no	—
557	C₂×C₂²⋊C₄	—	2	1	no	—
558	C₂×C₂²⋊C₄	—	2	1	no	—
559	C₂×C₂²⋊C₄	—	2	1	no	—
560	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
561	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
562	C₂×C₄²	—	2	1	no	—
563	C₂×C₄²	—	2	1	no	—
564	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
565	#107	C₂³×C₁₃	1	4	yes	—
566	#106	C₂³×C₁₃	1	4	yes	—
567	#106	C₂³×C₁₃	1	4	yes	—
568	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
569	#103	C₂³×C₁₃	1	4	yes	—
570	#103	C₂³×C₁₃	1	4	yes	—
571	#103	C₂³×C₁₃	1	4	yes	—
572	#103	C₂³×C₁₃	1	4	yes	—
573	#103	C₂³×C₁₃	1	4	yes	—
574	#103	C₂³×C₁₃	1	4	yes	—
575	#102	C₂³×C₁₃	1	4	yes	—
576	#102	C₂³×C₁₃	1	4	yes	—
577	#102	C₂³×C₁₃	1	4	yes	—
578	#102	C₂³×C₁₃	1	4	yes	—
579	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
580	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
581	C₄×C₈	C₂³×C₁₃	1	4	yes	—
582	C₂×C₁₃	—	2	4	no	—
583	C₂×C₁₃	—	4	2	no	—
584	C₂×C₁₃	—	8	2	no	—
585	C₂×C₁₃	—	8	2	no	—
586	C₂×C₁₃	#3301	1	4	yes	direct product factor
587	C₂×C₁₃	C₂×#546	1	1	yes	characteristic
588	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
589	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
590	C₂⁴	—	2	1	no	—
591	C₂⁴	—	2	1	no	—
592	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
593	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
594	#41	—	2	8	no	—
595	#41	—	4	4	no	—
596	#41	—	4	8	no	—
597	C₂×Q₈	—	2	1	no	—
598	C₂×Q₈	—	2	4	no	—
599	C₂×Q₈	—	2	1	no	—
600	C₂×Q₈	—	2	2	no	—
601	C₂×Q₈	—	2	8	no	—
602	C₂×Q₈	—	2	2	no	—
603	C₂×Q₈	—	2	2	no	—
604	C₂×Q₈	—	4	4	no	—
605	C₂×Q₈	—	4	4	no	—
606	C₂×Q₈	—	4	8	no	—
607	C₂×Q₈	C₁₃×#41	1	4	yes	—
608	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
609	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
610	C₂×D₄	—	2	4	no	—
611	C₂×D₄	—	2	4	no	—
612	C₂×D₄	—	2	4	no	—
613	C₂×D₄	—	2	4	no	—
614	C₂×D₄	—	2	4	no	—
615	C₂×D₄	—	2	1	no	—
616	C₂×D₄	—	2	1	no	—
617	C₂×D₄	—	2	2	no	—
618	C₂×D₄	—	2	2	no	—
619	C₂×D₄	—	2	2	no	—
620	C₂×D₄	—	2	2	no	—
621	C₂×D₄	—	4	4	no	—
622	C₂×D₄	—	4	4	no	—
623	C₂×D₄	—	4	4	no	—
624	C₂×D₄	—	8	2	no	—
625	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
626	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
627	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
628	C₂²×C₄	—	2	1	no	—
629	C₂²×C₄	—	2	2	no	—
630	C₂²×C₄	—	2	2	no	—
631	C₂²×C₄	—	2	2	no	—
632	C₂²×C₄	—	2	2	no	—
633	C₂²×C₄	—	2	1	no	—
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	2	1	no	—
636	C₂²×C₄	—	2	1	no	—
637	C₂²×C₄	—	2	1	no	—
638	C₂²×C₄	—	2	4	no	—
639	C₂²×C₄	—	2	4	no	—
640	C₂²×C₄	—	2	4	no	—
641	C₂²×C₄	—	2	4	no	—
642	C₂²×C₄	—	4	4	no	—
643	C₂²×C₄	—	4	4	no	—
644	C₂²×C₄	—	8	2	no	—
645	C₂²×C₄	—	8	2	no	—
646	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
647	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
648	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
649	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
650	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
651	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
652	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
653	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
654	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
655	SD₁₆	—	2	8	no	—
656	SD₁₆	—	4	4	no	—
657	D₈	—	4	4	no	—
658	C₂×C₈	—	2	2	no	—
659	C₂×C₈	—	2	2	no	—
660	C₂×C₈	—	2	2	no	—
661	C₂×C₈	—	2	2	no	—
662	C₂×C₈	—	4	4	no	—
663	C₂×C₈	—	4	4	no	—
664	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
665	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
666	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
667	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
668	C₄⋊C₄	—	2	1	no	—
669	C₄⋊C₄	—	2	1	no	—
670	C₄⋊C₄	—	2	4	no	—
671	C₄⋊C₄	—	2	4	no	—
672	C₄⋊C₄	—	2	4	no	—
673	C₄⋊C₄	—	2	4	no	—
674	C₄⋊C₄	—	2	4	no	—
675	C₄⋊C₄	—	2	1	no	—
676	C₄⋊C₄	—	2	1	no	—
677	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
678	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
679	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
680	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
681	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
682	C₂²⋊C₄	—	2	4	no	—
683	C₂²⋊C₄	—	2	4	no	—
684	C₂²⋊C₄	—	2	4	no	—
685	C₂²⋊C₄	—	2	4	no	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	4	no	—
690	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
691	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
692	C₄²	—	2	4	no	—
693	C₄²	—	2	4	no	—
694	C₄²	C₂×D₄×C₁₃	1	2	yes	—
695	C₄²	C₂⁴×C₁₃	1	2	yes	—
696	C₁₃	C₂×#3301	1	1	yes	characteristic, direct product factor, Sylow
697	C₂³	—	2	2	no	—
698	C₂³	—	2	2	no	—
699	C₂³	—	2	2	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	4	2	no	—
705	C₂³	—	4	2	no	—
706	C₂³	—	4	2	no	—
707	C₂³	—	4	2	no	—
708	C₂³	—	4	2	no	—
709	C₂³	—	4	2	no	—
710	C₂³	C₁₃×#135	1	4	yes	—
711	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
712	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
713	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
714	Q₈	—	2	4	no	—
715	Q₈	—	2	2	no	—
716	Q₈	—	2	2	no	—
717	Q₈	—	2	2	no	—
718	Q₈	—	4	8	no	—
719	Q₈	—	4	2	no	—
720	Q₈	C₂×C₁₃×#41	1	4	yes	—
721	D₄	—	2	8	no	—
722	D₄	—	2	2	no	—
723	D₄	—	2	2	no	—
724	D₄	—	2	2	no	—
725	D₄	—	2	2	no	—
726	D₄	—	4	8	no	—
727	D₄	—	4	8	no	—
728	D₄	—	4	8	no	—
729	D₄	—	4	2	no	—
730	D₄	—	4	2	no	—
731	D₄	—	8	4	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	4	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	4	no	—
739	C₂×C₄	—	2	4	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	4	8	no	—
750	C₂×C₄	—	4	8	no	—
751	C₂×C₄	—	4	2	no	—
752	C₂×C₄	—	4	2	no	—
753	C₂×C₄	—	4	2	no	—
754	C₂×C₄	—	4	2	no	—
755	C₂×C₄	—	4	2	no	—
756	C₂×C₄	—	8	4	no	—
757	C₂×C₄	—	8	4	no	—
758	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
759	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
760	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
761	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
762	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
763	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
764	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
765	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
766	C₈	—	2	2	no	—
767	C₈	—	2	2	no	—
768	C₈	—	2	2	no	—
769	C₈	—	2	2	no	—
770	C₂²	—	2	8	no	—
771	C₂²	—	2	2	no	—
772	C₂²	—	2	2	no	—
773	C₂²	—	2	2	no	—
774	C₂²	—	2	2	no	—
775	C₂²	—	2	2	no	—
776	C₂²	—	4	4	no	—
777	C₂²	—	4	2	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	4	2	no	—
780	C₂²	—	4	2	no	—
781	C₂²	—	4	2	no	—
782	C₂²	—	4	2	no	—
783	C₂²	—	8	4	no	—
784	C₂²	—	8	4	no	—
785	C₂²	C₁₃×#546	1	2	yes	—
786	C₂²	C₂×C₁₃×#135	1	4	yes	—
787	C₂²	C₂×C₁₃×#135	1	2	yes	—
788	C₂²	C₁₃×#577	1	2	yes	—
789	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
790	C₄	—	2	2	no	—
791	C₄	—	2	2	no	—
792	C₄	—	2	2	no	—
793	C₄	—	2	2	no	—
794	C₄	—	2	4	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	2	no	—
797	C₄	—	4	2	no	—
798	C₄	—	4	2	no	—
799	C₄	—	4	2	no	—
800	C₄	C₁₃×#546	1	2	yes	—
801	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
802	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
803	C₂	—	2	4	no	—
804	C₂	—	4	2	no	—
805	C₂	—	8	2	no	—
806	C₂	—	8	2	no	—
807	C₂	C₁₃×#3301	1	4	yes	direct product factor
808	C₂	C₂×C₁₃×#546	1	1	yes	characteristic
809	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
810	C₂	C₂×C₁₃×#577	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. C₂×C₁₃×#553	C₂	semidirect
2. C₂×C₁₃×#548	C₂	semidirect
3. C₁₃×#3301	C₂	direct (N × H)
4. C₂×C₁₃×#488	C₂	semidirect
5. C₂×C₁₃×#481	C₂	semidirect
6. C₂×C₁₃×#485	C₂	semidirect
7. C₂×C₁₃×#479	C₂	semidirect
8. C₂×C₁₃×#466	C₂	semidirect
9. C₂×C₁₃×#465	C₂	semidirect
10. C₂×C₁₃×#463	C₂	semidirect
11. C₂×C₁₃×#449	C₂	semidirect
12. C₂×C₁₃×#448	C₂	semidirect
13. C₂×C₄×C₁₃×SD₁₆	C₂	semidirect
14. C₂×C₈×D₄×C₁₃	C₂	semidirect
15. C₂×C₁₃×#416	C₂	semidirect
16. C₂²×C₁₃×#103	C₂	semidirect
25. C₁₃×#553	C₂²	semidirect
27. C₁₃×#548	C₂²	semidirect
47. C₁₃×#488	C₂²	semidirect
48. C₁₃×#485	C₂²	semidirect
49. C₁₃×#481	C₂²	semidirect
50. C₁₃×#479	C₂²	semidirect
51. C₁₃×#466	C₂²	semidirect
52. C₁₃×#465	C₂²	semidirect
53. C₁₃×#463	C₂²	semidirect
54. C₁₃×#449	C₂²	semidirect
55. C₁₃×#448	C₂²	semidirect
56. C₄×C₁₃×SD₁₆	C₂²	semidirect
57. C₈×D₄×C₁₃	C₂²	semidirect
62. C₁₃×#416	C₂²	semidirect
69. C₂×C₁₃×#103	C₂²	semidirect
185. C₂×#3301	C₁₃	direct (N × H)
292. C₂×#553	C₂×C₁₃	semidirect
293. C₂×#548	C₂×C₁₃	semidirect
294. #3301	C₂×C₁₃	direct (N × H)
295. C₂×#488	C₂×C₁₃	semidirect
296. C₂×#481	C₂×C₁₃	semidirect
297. C₂×#485	C₂×C₁₃	semidirect
298. C₂×#479	C₂×C₁₃	semidirect
299. C₂×#466	C₂×C₁₃	semidirect
300. C₂×#465	C₂×C₁₃	semidirect
301. C₂×#463	C₂×C₁₃	semidirect
302. C₂×#449	C₂×C₁₃	semidirect
303. C₂×#448	C₂×C₁₃	semidirect
304. C₂×C₄×SD₁₆	C₂×C₁₃	semidirect
305. C₂×C₈×D₄	C₂×C₁₃	semidirect
306. C₂×#416	C₂×C₁₃	semidirect
307. C₂²×#103	C₂×C₁₃	semidirect
389. #553	C₂²×C₁₃	semidirect
391. #548	C₂²×C₁₃	semidirect
411. #488	C₂²×C₁₃	semidirect
412. #485	C₂²×C₁₃	semidirect
413. #481	C₂²×C₁₃	semidirect
414. #479	C₂²×C₁₃	semidirect
415. #466	C₂²×C₁₃	semidirect
416. #465	C₂²×C₁₃	semidirect
417. #463	C₂²×C₁₃	semidirect
418. #449	C₂²×C₁₃	semidirect
419. #448	C₂²×C₁₃	semidirect
420. C₄×SD₁₆	C₂²×C₁₃	semidirect
421. C₈×D₄	C₂²×C₁₃	semidirect
426. #416	C₂²×C₁₃	semidirect
433. C₂×#103	C₂²×C₁₃	semidirect
586. C₂×C₁₃	#3301	direct (N × H)
696. C₁₃	C₂×#3301	direct (N × H)
807. C₂	C₁₃×#3301	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#553	2
C₂×C₁₃×#548	2
C₁₃×#3301	2
C₂×C₁₃×#488	2
C₂×C₁₃×#481	2
C₂×C₁₃×#485	2
C₂×C₁₃×#479	2
C₂×C₁₃×#466	2
C₂×C₁₃×#465	2
C₂×C₁₃×#463	2
C₂×C₁₃×#449	2
C₂×C₁₃×#448	2
C₂×C₄×C₁₃×SD₁₆	2
C₂×C₈×D₄×C₁₃	2
C₂×C₁₃×#416	2
C₂²×C₁₃×#103	2
C₂×#3301	13

Subgroups — C2×C13×#3301 #15747458

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3301 #15747458