Subgroups — C₂×C₁₃×#3346 #15747577

Order 3328.

1942 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#553	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3346	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#501	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#484	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#481	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#485	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#480	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#479	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#474	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#468	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#465	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×#440	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#428	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#554	—	2	4	no	—
21	C₁₃×#554	C₂²	1	8	yes	complemented
22	C₁₃×#553	—	2	4	no	—
23	C₁₃×#553	C₂²	1	8	yes	—
24	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#126	—	2	1	no	—
26	C₂×C₁₃×#125	—	2	1	no	—
27	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#123	—	2	1	no	—
29	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
30	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
31	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#121	—	2	1	no	—
34	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₁₃	—	2	1	no	—
38	C₂×C₄×D₄×C₁₃	—	2	1	no	—
39	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
42	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
43	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
44	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
45	C₁₃×#501	C₂²	1	8	yes	complemented
46	C₁₃×#485	C₂²	1	8	yes	complemented
47	C₁₃×#484	C₂²	1	8	yes	complemented
48	C₁₃×#481	C₂²	1	8	yes	complemented
49	C₁₃×#480	C₂²	1	8	yes	complemented
50	C₁₃×#479	C₂²	1	8	yes	complemented
51	C₁₃×#474	C₂²	1	8	yes	complemented
52	C₁₃×#468	C₂²	1	8	yes	complemented
53	C₁₃×#465	C₂²	1	8	yes	complemented
54	C₁₃×#440	C₂²	1	8	yes	complemented
55	C₁₃×#435	C₂²	1	8	yes	complemented
56	C₁₃×#428	C₂²	1	8	yes	complemented
57	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
58	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
59	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
60	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
61	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
62	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
63	C₂×C₁₃×#107	C₂²	1	8	yes	complemented
64	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
65	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
66	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
68	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
69	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
70	C₂×C₁₃×#103	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×C₁₃×#97	C₂²	1	1	yes	characteristic
77	C₂²×Q₈×C₁₃	—	2	1	no	—
78	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
79	C₂²×D₄×C₁₃	—	2	1	no	—
80	C₂²×D₄×C₁₃	—	2	1	no	—
81	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
82	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₁₃	—	2	1	no	—
84	C₂³×C₄×C₁₃	—	2	1	no	—
85	C₂³×C₄×C₁₃	—	2	1	no	—
86	C₂³×C₄×C₁₃	—	2	1	no	—
87	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
89	C₂×C₁₃×SD₁₆	—	2	4	no	—
90	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
91	C₂×C₁₃×M₁₆	—	2	4	no	—
92	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
93	C₂²×C₈×C₁₃	—	2	4	no	—
94	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
98	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
99	C₁₃×C₄⋊Q₈	—	2	2	no	—
100	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
101	C₁₃×#126	—	2	8	no	—
102	C₁₃×#125	—	2	8	no	—
103	C₁₃×#125	—	2	2	no	—
104	C₁₃×#125	C₂³	1	4	yes	—
105	C₁₃×#123	—	2	8	no	—
106	C₁₃×C₂²⋊Q₈	—	2	2	no	—
107	C₁₃×C₂²⋊Q₈	—	2	2	no	—
108	C₁₃×C₂²⋊Q₈	—	2	8	no	—
109	C₁₃×C₂²⋊Q₈	—	2	8	no	—
110	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
111	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
112	C₁₃×#121	—	2	8	no	—
113	C₁₃×#121	—	2	2	no	—
114	C₁₃×#121	—	2	2	no	—
115	C₁₃×#121	C₂³	1	4	yes	—
116	C₁₃×#121	C₂³	1	4	yes	—
117	C₄×Q₈×C₁₃	—	2	2	no	—
118	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
119	C₄×D₄×C₁₃	—	2	8	no	—
120	C₄×D₄×C₁₃	—	2	8	no	—
121	C₄×D₄×C₁₃	—	2	2	no	—
122	C₄×D₄×C₁₃	D₄	1	4	yes	—
123	C₄×D₄×C₁₃	C₂³	1	4	yes	—
124	C₄×D₄×C₁₃	C₂³	1	4	yes	—
125	C₁₃×#117	—	2	2	no	—
126	C₁₃×#117	C₂³	1	4	yes	—
127	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
128	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
129	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
130	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
132	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
133	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
134	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
135	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
136	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
137	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
138	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
139	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
140	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
141	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
142	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
143	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
144	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
145	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
146	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
147	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
148	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
149	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
150	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
151	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
152	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
153	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
154	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
155	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
156	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
157	C₂×C₄²×C₁₃	—	2	1	no	—
158	C₂×C₄²×C₁₃	—	2	1	no	—
159	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
160	C₁₃×#107	C₂³	1	4	yes	—
161	C₁₃×#107	C₂³	1	4	yes	—
162	C₁₃×#107	C₂³	1	4	yes	—
163	C₁₃×#107	C₂³	1	4	yes	—
164	C₁₃×#107	C₂³	1	4	yes	—
165	C₁₃×#107	C₂³	1	4	yes	—
166	C₁₃×#106	C₂³	1	4	yes	—
167	C₁₃×#106	C₂³	1	4	yes	—
168	C₁₃×#106	C₂³	1	4	yes	—
169	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
170	C₁₃×#103	C₂³	1	4	yes	—
171	C₁₃×#103	C₂³	1	4	yes	—
172	C₁₃×#103	C₂³	1	4	yes	—
173	C₁₃×#102	C₂³	1	4	yes	—
174	C₁₃×#102	C₂³	1	4	yes	—
175	C₁₃×#102	C₂³	1	4	yes	—
176	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
177	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
178	C₁₃×#97	C₂³	1	4	yes	—
179	C₂×#3346	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₂⁴×C₁₃	—	2	1	no	—
181	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
182	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
183	C₂×Q₈×C₁₃	—	2	1	no	—
184	C₂×Q₈×C₁₃	—	2	4	no	—
185	C₂×Q₈×C₁₃	—	2	2	no	—
186	C₂×Q₈×C₁₃	—	2	2	no	—
187	C₂×Q₈×C₁₃	—	8	2	no	—
188	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
189	C₂×D₄×C₁₃	—	2	4	no	—
190	C₂×D₄×C₁₃	—	2	4	no	—
191	C₂×D₄×C₁₃	—	2	4	no	—
192	C₂×D₄×C₁₃	—	2	1	no	—
193	C₂×D₄×C₁₃	—	2	2	no	—
194	C₂×D₄×C₁₃	—	2	2	no	—
195	C₂×D₄×C₁₃	—	4	4	no	—
196	C₂×D₄×C₁₃	—	8	2	no	—
197	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
198	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₁₃	—	2	2	no	—
200	C₂²×C₄×C₁₃	—	2	2	no	—
201	C₂²×C₄×C₁₃	—	2	2	no	—
202	C₂²×C₄×C₁₃	—	2	2	no	—
203	C₂²×C₄×C₁₃	—	2	1	no	—
204	C₂²×C₄×C₁₃	—	2	1	no	—
205	C₂²×C₄×C₁₃	—	2	1	no	—
206	C₂²×C₄×C₁₃	—	2	1	no	—
207	C₂²×C₄×C₁₃	—	2	1	no	—
208	C₂²×C₄×C₁₃	—	2	1	no	—
209	C₂²×C₄×C₁₃	—	2	1	no	—
210	C₂²×C₄×C₁₃	—	2	4	no	—
211	C₂²×C₄×C₁₃	—	2	4	no	—
212	C₂²×C₄×C₁₃	—	2	4	no	—
213	C₂²×C₄×C₁₃	—	2	4	no	—
214	C₂²×C₄×C₁₃	—	8	2	no	—
215	C₂²×C₄×C₁₃	—	8	2	no	—
216	C₂²×C₄×C₁₃	—	8	2	no	—
217	C₂²×C₄×C₁₃	—	8	2	no	—
218	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
219	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
220	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
227	C₁₃×SD₁₆	—	2	8	no	—
228	C₁₃×M₁₆	—	2	8	no	—
229	C₂×C₈×C₁₃	—	2	2	no	—
230	C₂×C₈×C₁₃	—	2	2	no	—
231	C₂×C₈×C₁₃	—	2	2	no	—
232	C₂×C₈×C₁₃	—	2	8	no	—
233	C₂×C₈×C₁₃	#41	1	4	yes	—
234	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
235	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
236	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
237	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
238	C₁₃×C₄⋊C₄	—	2	1	no	—
239	C₁₃×C₄⋊C₄	—	2	1	no	—
240	C₁₃×C₄⋊C₄	—	2	1	no	—
241	C₁₃×C₄⋊C₄	—	2	4	no	—
242	C₁₃×C₄⋊C₄	—	2	4	no	—
243	C₁₃×C₄⋊C₄	—	2	1	no	—
244	C₁₃×C₄⋊C₄	—	2	1	no	—
245	C₁₃×C₄⋊C₄	—	2	4	no	—
246	C₁₃×C₄⋊C₄	—	2	4	no	—
247	C₁₃×C₄⋊C₄	—	2	4	no	—
248	C₁₃×C₄⋊C₄	—	2	4	no	—
249	C₁₃×C₄⋊C₄	—	2	4	no	—
250	C₁₃×C₄⋊C₄	—	2	4	no	—
251	C₁₃×C₄⋊C₄	—	2	4	no	—
252	C₁₃×C₄⋊C₄	—	2	1	no	—
253	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
254	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
255	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
256	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
257	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
258	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
259	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
260	C₁₃×C₂²⋊C₄	—	2	4	no	—
261	C₁₃×C₂²⋊C₄	—	2	4	no	—
262	C₁₃×C₂²⋊C₄	—	2	4	no	—
263	C₁₃×C₂²⋊C₄	—	2	4	no	—
264	C₁₃×C₂²⋊C₄	—	2	4	no	—
265	C₁₃×C₂²⋊C₄	—	2	4	no	—
266	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
267	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
268	C₄²×C₁₃	—	2	4	no	—
269	C₄²×C₁₃	—	2	4	no	—
270	C₄²×C₁₃	C₂×D₄	1	2	yes	—
271	C₄²×C₁₃	C₂⁴	1	2	yes	—
272	C₂×#554	C₂×C₁₃	1	1	yes	characteristic, complemented
273	C₂×#553	C₂×C₁₃	1	1	yes	characteristic
274	#3346	C₂×C₁₃	1	16	yes	direct product factor
275	C₂×#501	C₂×C₁₃	1	1	yes	characteristic, complemented
276	C₂×#484	C₂×C₁₃	1	1	yes	characteristic, complemented
277	C₂×#481	C₂×C₁₃	1	1	yes	characteristic, complemented
278	C₂×#485	C₂×C₁₃	1	1	yes	characteristic, complemented
279	C₂×#480	C₂×C₁₃	1	1	yes	characteristic, complemented
280	C₂×#479	C₂×C₁₃	1	1	yes	characteristic, complemented
281	C₂×#474	C₂×C₁₃	1	1	yes	characteristic, complemented
282	C₂×#468	C₂×C₁₃	1	1	yes	characteristic, complemented
283	C₂×#465	C₂×C₁₃	1	1	yes	characteristic, complemented
284	C₂×#440	C₂×C₁₃	1	1	yes	characteristic, complemented
285	C₂×#435	C₂×C₁₃	1	1	yes	characteristic, complemented
286	C₂×#428	C₂×C₁₃	1	1	yes	characteristic, complemented
287	C₂²×#107	C₂×C₁₃	1	1	yes	characteristic, complemented
288	C₂³×C₁₃	—	2	2	no	—
289	C₂³×C₁₃	—	2	2	no	—
290	C₂³×C₁₃	—	2	2	no	—
291	C₂³×C₁₃	—	2	2	no	—
292	C₂³×C₁₃	—	2	2	no	—
293	C₂³×C₁₃	—	2	2	no	—
294	C₂³×C₁₃	—	4	2	no	—
295	C₂³×C₁₃	—	4	2	no	—
296	C₂³×C₁₃	—	4	2	no	—
297	C₂³×C₁₃	#137	1	4	yes	—
298	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
299	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
300	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
301	Q₈×C₁₃	—	2	2	no	—
302	Q₈×C₁₃	—	2	2	no	—
303	Q₈×C₁₃	—	4	2	no	—
304	Q₈×C₁₃	—	8	4	no	—
305	D₄×C₁₃	—	2	8	no	—
306	D₄×C₁₃	—	2	2	no	—
307	D₄×C₁₃	—	2	2	no	—
308	D₄×C₁₃	—	4	8	no	—
309	D₄×C₁₃	—	4	2	no	—
310	D₄×C₁₃	—	8	4	no	—
311	C₂×C₄×C₁₃	—	2	2	no	—
312	C₂×C₄×C₁₃	—	2	2	no	—
313	C₂×C₄×C₁₃	—	2	2	no	—
314	C₂×C₄×C₁₃	—	2	2	no	—
315	C₂×C₄×C₁₃	—	2	4	no	—
316	C₂×C₄×C₁₃	—	2	4	no	—
317	C₂×C₄×C₁₃	—	2	2	no	—
318	C₂×C₄×C₁₃	—	2	2	no	—
319	C₂×C₄×C₁₃	—	2	2	no	—
320	C₂×C₄×C₁₃	—	2	2	no	—
321	C₂×C₄×C₁₃	—	2	2	no	—
322	C₂×C₄×C₁₃	—	2	2	no	—
323	C₂×C₄×C₁₃	—	2	2	no	—
324	C₂×C₄×C₁₃	—	2	2	no	—
325	C₂×C₄×C₁₃	—	2	2	no	—
326	C₂×C₄×C₁₃	—	2	2	no	—
327	C₂×C₄×C₁₃	—	2	2	no	—
328	C₂×C₄×C₁₃	—	4	2	no	—
329	C₂×C₄×C₁₃	—	4	2	no	—
330	C₂×C₄×C₁₃	—	4	2	no	—
331	C₂×C₄×C₁₃	—	4	2	no	—
332	C₂×C₄×C₁₃	—	4	2	no	—
333	C₂×C₄×C₁₃	—	4	2	no	—
334	C₂×C₄×C₁₃	—	4	2	no	—
335	C₂×C₄×C₁₃	—	8	4	no	—
336	C₂×C₄×C₁₃	—	8	4	no	—
337	C₂×C₄×C₁₃	—	8	4	no	—
338	C₂×C₄×C₁₃	—	8	4	no	—
339	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
340	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
341	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
342	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
343	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
344	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
345	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
346	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
347	C₈×C₁₃	—	2	2	no	—
348	C₈×C₁₃	—	2	2	no	—
349	C₈×C₁₃	—	2	2	no	—
350	C₈×C₁₃	C₂×#41	1	4	yes	—
351	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
352	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
353	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
354	#554	—	2	4	no	—
355	#554	C₂²×C₁₃	1	8	yes	complemented
356	#553	—	2	4	no	—
357	#553	C₂²×C₁₃	1	8	yes	—
358	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
359	C₂×#126	—	2	1	no	—
360	C₂×#125	—	2	1	no	—
361	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
362	C₂×#123	—	2	1	no	—
363	C₂×C₂²⋊Q₈	—	2	1	no	—
364	C₂×C₂²⋊Q₈	—	2	1	no	—
365	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
366	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
367	C₂×#121	—	2	1	no	—
368	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
369	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
370	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
371	C₂×C₄×D₄	—	2	1	no	—
372	C₂×C₄×D₄	—	2	1	no	—
373	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
374	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
375	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
376	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
377	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
378	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
379	#501	C₂²×C₁₃	1	8	yes	complemented
380	#485	C₂²×C₁₃	1	8	yes	complemented
381	#484	C₂²×C₁₃	1	8	yes	complemented
382	#481	C₂²×C₁₃	1	8	yes	complemented
383	#480	C₂²×C₁₃	1	8	yes	complemented
384	#479	C₂²×C₁₃	1	8	yes	complemented
385	#474	C₂²×C₁₃	1	8	yes	complemented
386	#468	C₂²×C₁₃	1	8	yes	complemented
387	#465	C₂²×C₁₃	1	8	yes	complemented
388	#440	C₂²×C₁₃	1	8	yes	complemented
389	#435	C₂²×C₁₃	1	8	yes	complemented
390	#428	C₂²×C₁₃	1	8	yes	complemented
391	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
392	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
393	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
394	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
395	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
396	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
397	C₂×#107	C₂²×C₁₃	1	8	yes	complemented
398	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
399	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
400	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
401	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
402	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
403	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
404	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
405	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
406	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
407	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
408	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
409	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
410	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
411	C₂²×C₁₃	—	2	8	no	—
412	C₂²×C₁₃	—	2	2	no	—
413	C₂²×C₁₃	—	2	2	no	—
414	C₂²×C₁₃	—	2	2	no	—
415	C₂²×C₁₃	—	2	2	no	—
416	C₂²×C₁₃	—	2	2	no	—
417	C₂²×C₁₃	—	4	4	no	—
418	C₂²×C₁₃	—	4	2	no	—
419	C₂²×C₁₃	—	4	2	no	—
420	C₂²×C₁₃	—	4	2	no	—
421	C₂²×C₁₃	—	8	4	no	—
422	C₂²×C₁₃	#547	1	2	yes	—
423	C₂²×C₁₃	C₂×#137	1	4	yes	—
424	C₂²×C₁₃	C₂×#137	1	2	yes	—
425	C₂²×C₁₃	#576	1	2	yes	—
426	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
427	C₄×C₁₃	—	2	2	no	—
428	C₄×C₁₃	—	2	2	no	—
429	C₄×C₁₃	—	2	2	no	—
430	C₄×C₁₃	—	2	2	no	—
431	C₄×C₁₃	—	4	2	no	—
432	C₄×C₁₃	—	4	2	no	—
433	C₄×C₁₃	—	4	2	no	—
434	C₄×C₁₃	—	4	2	no	—
435	C₄×C₁₃	—	4	2	no	—
436	C₄×C₁₃	—	4	2	no	—
437	C₄×C₁₃	—	4	2	no	—
438	C₄×C₁₃	#547	1	2	yes	—
439	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
440	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
441	C₂²×Q₈	—	2	1	no	—
442	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
443	C₂²×D₄	—	2	1	no	—
444	C₂²×D₄	—	2	1	no	—
445	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
446	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
447	C₂³×C₄	—	2	1	no	—
448	C₂³×C₄	—	2	1	no	—
449	C₂³×C₄	—	2	1	no	—
450	C₂³×C₄	—	2	1	no	—
451	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
452	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
453	C₂×SD₁₆	—	2	4	no	—
454	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
455	C₂×M₁₆	—	2	4	no	—
456	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
457	C₂²×C₈	—	2	4	no	—
458	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
459	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
460	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
461	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
462	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
463	C₄⋊Q₈	—	2	2	no	—
464	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
465	#126	—	2	8	no	—
466	#125	—	2	8	no	—
467	#125	—	2	2	no	—
468	#125	C₂³×C₁₃	1	4	yes	—
469	#123	—	2	8	no	—
470	C₂²⋊Q₈	—	2	2	no	—
471	C₂²⋊Q₈	—	2	2	no	—
472	C₂²⋊Q₈	—	2	8	no	—
473	C₂²⋊Q₈	—	2	8	no	—
474	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
475	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
476	#121	—	2	8	no	—
477	#121	—	2	2	no	—
478	#121	—	2	2	no	—
479	#121	C₂³×C₁₃	1	4	yes	—
480	#121	C₂³×C₁₃	1	4	yes	—
481	C₄×Q₈	—	2	2	no	—
482	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
483	C₄×D₄	—	2	8	no	—
484	C₄×D₄	—	2	8	no	—
485	C₄×D₄	—	2	2	no	—
486	C₄×D₄	D₄×C₁₃	1	4	yes	—
487	C₄×D₄	C₂³×C₁₃	1	4	yes	—
488	C₄×D₄	C₂³×C₁₃	1	4	yes	—
489	#117	—	2	2	no	—
490	#117	C₂³×C₁₃	1	4	yes	—
491	C₂×C₄⋊C₄	—	2	1	no	—
492	C₂×C₄⋊C₄	—	2	1	no	—
493	C₂×C₄⋊C₄	—	2	1	no	—
494	C₂×C₄⋊C₄	—	2	2	no	—
495	C₂×C₄⋊C₄	—	2	2	no	—
496	C₂×C₄⋊C₄	—	2	2	no	—
497	C₂×C₄⋊C₄	—	2	1	no	—
498	C₂×C₄⋊C₄	—	2	1	no	—
499	C₂×C₄⋊C₄	—	2	1	no	—
500	C₂×C₄⋊C₄	—	2	1	no	—
501	C₂×C₄⋊C₄	—	2	1	no	—
502	C₂×C₄⋊C₄	—	2	1	no	—
503	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
504	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
506	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
507	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
508	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
509	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
510	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
511	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
512	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
513	C₂×C₂²⋊C₄	—	2	1	no	—
514	C₂×C₂²⋊C₄	—	2	1	no	—
515	C₂×C₂²⋊C₄	—	2	1	no	—
516	C₂×C₂²⋊C₄	—	2	1	no	—
517	C₂×C₂²⋊C₄	—	2	1	no	—
518	C₂×C₂²⋊C₄	—	2	1	no	—
519	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
520	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
521	C₂×C₄²	—	2	1	no	—
522	C₂×C₄²	—	2	1	no	—
523	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
524	#107	C₂³×C₁₃	1	4	yes	—
525	#107	C₂³×C₁₃	1	4	yes	—
526	#107	C₂³×C₁₃	1	4	yes	—
527	#107	C₂³×C₁₃	1	4	yes	—
528	#107	C₂³×C₁₃	1	4	yes	—
529	#107	C₂³×C₁₃	1	4	yes	—
530	#106	C₂³×C₁₃	1	4	yes	—
531	#106	C₂³×C₁₃	1	4	yes	—
532	#106	C₂³×C₁₃	1	4	yes	—
533	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
534	#103	C₂³×C₁₃	1	4	yes	—
535	#103	C₂³×C₁₃	1	4	yes	—
536	#103	C₂³×C₁₃	1	4	yes	—
537	#102	C₂³×C₁₃	1	4	yes	—
538	#102	C₂³×C₁₃	1	4	yes	—
539	#102	C₂³×C₁₃	1	4	yes	—
540	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
541	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
542	#97	C₂³×C₁₃	1	4	yes	—
543	C₂×C₁₃	—	2	4	no	—
544	C₂×C₁₃	—	4	2	no	—
545	C₂×C₁₃	—	8	2	no	—
546	C₂×C₁₃	#3346	1	4	yes	direct product factor
547	C₂×C₁₃	C₂×#547	1	1	yes	characteristic
548	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
549	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
550	C₂⁴	—	2	1	no	—
551	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
552	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
553	C₂×Q₈	—	2	1	no	—
554	C₂×Q₈	—	2	4	no	—
555	C₂×Q₈	—	2	2	no	—
556	C₂×Q₈	—	2	2	no	—
557	C₂×Q₈	—	8	2	no	—
558	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
559	C₂×D₄	—	2	4	no	—
560	C₂×D₄	—	2	4	no	—
561	C₂×D₄	—	2	4	no	—
562	C₂×D₄	—	2	1	no	—
563	C₂×D₄	—	2	2	no	—
564	C₂×D₄	—	2	2	no	—
565	C₂×D₄	—	4	4	no	—
566	C₂×D₄	—	8	2	no	—
567	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
568	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
569	C₂²×C₄	—	2	2	no	—
570	C₂²×C₄	—	2	2	no	—
571	C₂²×C₄	—	2	2	no	—
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	—	2	4	no	—
583	C₂²×C₄	—	2	4	no	—
584	C₂²×C₄	—	8	2	no	—
585	C₂²×C₄	—	8	2	no	—
586	C₂²×C₄	—	8	2	no	—
587	C₂²×C₄	—	8	2	no	—
588	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
589	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
590	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
591	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
592	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
593	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
594	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
595	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
596	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
597	SD₁₆	—	2	8	no	—
598	M₁₆	—	2	8	no	—
599	C₂×C₈	—	2	2	no	—
600	C₂×C₈	—	2	2	no	—
601	C₂×C₈	—	2	2	no	—
602	C₂×C₈	—	2	8	no	—
603	C₂×C₈	C₁₃×#41	1	4	yes	—
604	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
605	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
606	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
607	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	1	no	—
614	C₄⋊C₄	—	2	1	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	4	no	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	1	no	—
623	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
624	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
625	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
626	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
627	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
628	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
629	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
637	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
638	C₄²	—	2	4	no	—
639	C₄²	—	2	4	no	—
640	C₄²	C₂×D₄×C₁₃	1	2	yes	—
641	C₄²	C₂⁴×C₁₃	1	2	yes	—
642	C₁₃	C₂×#3346	1	1	yes	characteristic, direct product factor, Sylow
643	C₂³	—	2	2	no	—
644	C₂³	—	2	2	no	—
645	C₂³	—	2	2	no	—
646	C₂³	—	2	2	no	—
647	C₂³	—	2	2	no	—
648	C₂³	—	2	2	no	—
649	C₂³	—	4	2	no	—
650	C₂³	—	4	2	no	—
651	C₂³	—	4	2	no	—
652	C₂³	C₁₃×#137	1	4	yes	—
653	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
654	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
655	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
656	Q₈	—	2	2	no	—
657	Q₈	—	2	2	no	—
658	Q₈	—	4	2	no	—
659	Q₈	—	8	4	no	—
660	D₄	—	2	8	no	—
661	D₄	—	2	2	no	—
662	D₄	—	2	2	no	—
663	D₄	—	4	8	no	—
664	D₄	—	4	2	no	—
665	D₄	—	8	4	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	4	no	—
671	C₂×C₄	—	2	4	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	4	2	no	—
684	C₂×C₄	—	4	2	no	—
685	C₂×C₄	—	4	2	no	—
686	C₂×C₄	—	4	2	no	—
687	C₂×C₄	—	4	2	no	—
688	C₂×C₄	—	4	2	no	—
689	C₂×C₄	—	4	2	no	—
690	C₂×C₄	—	8	4	no	—
691	C₂×C₄	—	8	4	no	—
692	C₂×C₄	—	8	4	no	—
693	C₂×C₄	—	8	4	no	—
694	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
695	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
696	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
697	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
698	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
699	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
700	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
701	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
702	C₈	—	2	2	no	—
703	C₈	—	2	2	no	—
704	C₈	—	2	2	no	—
705	C₈	C₂×C₁₃×#41	1	4	yes	—
706	C₂²	—	2	2	no	—
707	C₂²	—	2	8	no	—
708	C₂²	—	2	2	no	—
709	C₂²	—	2	2	no	—
710	C₂²	—	2	2	no	—
711	C₂²	—	2	2	no	—
712	C₂²	—	4	4	no	—
713	C₂²	—	4	2	no	—
714	C₂²	—	4	2	no	—
715	C₂²	—	4	2	no	—
716	C₂²	—	8	4	no	—
717	C₂²	C₁₃×#547	1	2	yes	—
718	C₂²	C₂×C₁₃×#137	1	4	yes	—
719	C₂²	C₂×C₁₃×#137	1	2	yes	—
720	C₂²	C₁₃×#576	1	2	yes	—
721	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
722	C₄	—	2	2	no	—
723	C₄	—	2	2	no	—
724	C₄	—	2	2	no	—
725	C₄	—	2	2	no	—
726	C₄	—	4	2	no	—
727	C₄	—	4	2	no	—
728	C₄	—	4	2	no	—
729	C₄	—	4	2	no	—
730	C₄	—	4	2	no	—
731	C₄	—	4	2	no	—
732	C₄	—	4	2	no	—
733	C₄	C₁₃×#547	1	2	yes	—
734	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
735	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
736	C₂	—	2	4	no	—
737	C₂	—	4	2	no	—
738	C₂	—	8	2	no	—
739	C₂	C₁₃×#3346	1	4	yes	direct product factor
740	C₂	C₂×C₁₃×#547	1	1	yes	characteristic
741	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
742	C₂	C₂×C₁₃×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#553	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. C₂×C₁₃×#554	C₂	semidirect
3. C₁₃×#3346	C₂	direct (N × H)
4. C₂×C₁₃×#501	C₂	semidirect
5. C₂×C₁₃×#484	C₂	semidirect
6. C₂×C₁₃×#481	C₂	semidirect
7. C₂×C₁₃×#485	C₂	semidirect
8. C₂×C₁₃×#480	C₂	semidirect
9. C₂×C₁₃×#479	C₂	semidirect
10. C₂×C₁₃×#474	C₂	semidirect
11. C₂×C₁₃×#468	C₂	semidirect
12. C₂×C₁₃×#465	C₂	semidirect
13. C₂×C₁₃×#440	C₂	semidirect
14. C₂×C₁₃×#435	C₂	semidirect
15. C₂×C₁₃×#428	C₂	semidirect
16. C₂²×C₁₃×#107	C₂	semidirect
21. C₁₃×#554	C₂²	semidirect
45. C₁₃×#501	C₂²	semidirect
46. C₁₃×#485	C₂²	semidirect
47. C₁₃×#484	C₂²	semidirect
48. C₁₃×#481	C₂²	semidirect
49. C₁₃×#480	C₂²	semidirect
50. C₁₃×#479	C₂²	semidirect
51. C₁₃×#474	C₂²	semidirect
52. C₁₃×#468	C₂²	semidirect
53. C₁₃×#465	C₂²	semidirect
54. C₁₃×#440	C₂²	semidirect
55. C₁₃×#435	C₂²	semidirect
56. C₁₃×#428	C₂²	semidirect
63. C₂×C₁₃×#107	C₂²	semidirect
179. C₂×#3346	C₁₃	direct (N × H)
272. C₂×#554	C₂×C₁₃	semidirect
274. #3346	C₂×C₁₃	direct (N × H)
275. C₂×#501	C₂×C₁₃	semidirect
276. C₂×#484	C₂×C₁₃	semidirect
277. C₂×#481	C₂×C₁₃	semidirect
278. C₂×#485	C₂×C₁₃	semidirect
279. C₂×#480	C₂×C₁₃	semidirect
280. C₂×#479	C₂×C₁₃	semidirect
281. C₂×#474	C₂×C₁₃	semidirect
282. C₂×#468	C₂×C₁₃	semidirect
283. C₂×#465	C₂×C₁₃	semidirect
284. C₂×#440	C₂×C₁₃	semidirect
285. C₂×#435	C₂×C₁₃	semidirect
286. C₂×#428	C₂×C₁₃	semidirect
287. C₂²×#107	C₂×C₁₃	semidirect
355. #554	C₂²×C₁₃	semidirect
379. #501	C₂²×C₁₃	semidirect
380. #485	C₂²×C₁₃	semidirect
381. #484	C₂²×C₁₃	semidirect
382. #481	C₂²×C₁₃	semidirect
383. #480	C₂²×C₁₃	semidirect
384. #479	C₂²×C₁₃	semidirect
385. #474	C₂²×C₁₃	semidirect
386. #468	C₂²×C₁₃	semidirect
387. #465	C₂²×C₁₃	semidirect
388. #440	C₂²×C₁₃	semidirect
389. #435	C₂²×C₁₃	semidirect
390. #428	C₂²×C₁₃	semidirect
397. C₂×#107	C₂²×C₁₃	semidirect
546. C₂×C₁₃	#3346	direct (N × H)
642. C₁₃	C₂×#3346	direct (N × H)
739. C₂	C₁₃×#3346	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×#554	2
C₂×C₁₃×#553	2
C₁₃×#3346	2
C₂×C₁₃×#501	2
C₂×C₁₃×#484	2
C₂×C₁₃×#481	2
C₂×C₁₃×#485	2
C₂×C₁₃×#480	2
C₂×C₁₃×#479	2
C₂×C₁₃×#474	2
C₂×C₁₃×#468	2
C₂×C₁₃×#465	2
C₂×C₁₃×#440	2
C₂×C₁₃×#435	2
C₂×C₁₃×#428	2
C₂²×C₁₃×#107	2
C₂×#3346	13

Subgroups — C2×C13×#3346 #15747577

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3346 #15747577