Subgroups — C₁₃×#62858 #15749197

Order 3328.

7310 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3524	C₂	1	4	yes	maximal, complemented
2	C₁₃×#3519	C₂	1	12	yes	maximal, complemented
3	C₁₃×#3517	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3513	C₂	1	12	yes	maximal, complemented
5	C₁₃×#3512	C₂	1	3	yes	maximal, complemented
6	C₁₃×#3508	C₂	1	3	yes	maximal, complemented
7	C₁₃×#3504	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3498	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3494	C₂	1	6	yes	maximal, complemented
10	C₁₃×#3488	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3460	C₂	1	6	yes	maximal, complemented
12	C₁₃×#3455	C₂	1	3	yes	maximal, complemented
13	C₂×C₁₃×#540	C₂	1	3	yes	maximal, complemented
14	C₄×C₁₃×H(5,𝔽₂)	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3428	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	2	yes	—
17	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
18	C₁₃×#559	C₂²	1	12	yes	complemented
19	C₁₃×#557	C₂²	1	4	yes	complemented
20	C₁₃×#555	C₂²	1	12	yes	complemented
21	C₁₃×#554	C₂²	1	12	yes	complemented
22	C₁₃×#553	C₂²	1	12	yes	complemented
23	C₁₃×#553	C₂²	1	24	yes	complemented
24	C₁₃×#553	C₂²	1	12	yes	complemented
25	C₁₃×#553	C₂²	1	12	yes	complemented
26	C₁₃×#552	C₂²	1	12	yes	complemented
27	C₁₃×#551	C₂²	1	24	yes	complemented
28	C₁₃×#550	C₂²	1	12	yes	complemented
29	C₁₃×#550	C₂²	1	4	yes	complemented
30	C₁₃×#550	C₂²	1	4	yes	complemented
31	C₁₃×#548	C₂²	1	4	yes	complemented
32	C₁₃×#547	C₂²	1	12	yes	complemented
33	C₁₃×#546	C₂²	1	24	yes	complemented
34	C₁₃×#546	C₂²	1	24	yes	complemented
35	C₁₃×#546	C₂²	1	12	yes	complemented
36	D₄²×C₁₃	C₂²	1	12	yes	complemented
37	D₄²×C₁₃	C₂²	1	12	yes	complemented
38	C₁₃×#544	C₂²	1	6	yes	complemented
39	C₁₃×#542	C₂²	1	12	yes	complemented
40	C₁₃×#542	C₂²	1	6	yes	complemented
41	C₁₃×#542	C₂²	1	6	yes	complemented
42	C₁₃×#541	C₂²	1	1	yes	characteristic, complemented
43	C₁₃×#541	C₂²	1	3	yes	complemented
44	C₁₃×#540	C₂²	1	12	yes	complemented
45	C₁₃×#540	C₂²	1	12	yes	complemented
46	C₁₃×#540	C₂²	1	3	yes	complemented
47	C₁₃×#540	C₂²	1	6	yes	complemented
48	C₁₃×#540	C₂²	1	6	yes	complemented
49	C₁₃×#540	C₂²	1	6	yes	complemented
50	C₁₃×#540	C₂²	1	12	yes	complemented
51	C₁₃×#540	C₂²	1	3	yes	complemented
52	C₁₃×#539	C₂²	1	12	yes	complemented
53	C₁₃×#538	C₂²	1	12	yes	complemented
54	C₁₃×#538	C₂²	1	24	yes	complemented
55	C₁₃×#537	C₂²	1	6	yes	complemented
56	C₁₃×#535	C₂²	1	6	yes	complemented
57	C₁₃×#535	C₂²	1	6	yes	complemented
58	C₁₃×#533	C₂²	1	3	yes	complemented
59	C₁₃×#532	C₂²	1	12	yes	complemented
60	C₁₃×#532	C₂²	1	3	yes	complemented
61	C₁₃×#532	C₂²	1	12	yes	complemented
62	C₂×C₁₃×#127	C₂²	1	3	yes	complemented
63	C₁₃×#529	C₂²	1	12	yes	complemented
64	C₁₃×#529	C₂²	1	12	yes	complemented
65	C₁₃×#529	C₂²	1	12	yes	complemented
66	C₁₃×#529	C₂²	1	12	yes	complemented
67	C₂×C₁₃×#125	C₂²	1	3	yes	complemented
68	C₁₃×#525	C₂²	1	24	yes	complemented
69	C₁₃×#525	C₂²	1	6	yes	complemented
70	C₂×C₁₃×#123	C₂²	1	12	yes	complemented
71	C₂×C₁₃×#121	C₂²	1	12	yes	complemented
72	C₂×C₁₃×#121	C₂²	1	6	yes	complemented
73	C₁₃×#520	C₂²	1	2	yes	—
74	C₁₃×#520	C₂²	1	4	yes	complemented
75	C₁₃×#520	C₂²	1	6	yes	complemented
76	C₁₃×#520	C₂²	1	2	yes	complemented
77	C₁₃×#520	C₂²	1	6	yes	complemented
78	C₁₃×#519	C₂²	1	2	yes	complemented
79	C₁₃×#518	C₂²	1	6	yes	complemented
80	C₁₃×#518	C₂²	1	12	yes	complemented
81	C₁₃×#518	C₂²	1	6	yes	complemented
82	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
83	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
84	C₄×C₁₃×#41	C₂²	1	4	yes	complemented
85	C₄×C₁₃×#41	C₂²	1	3	yes	complemented
86	C₄×C₁₃×#41	C₂²	1	3	yes	complemented
87	C₄×C₁₃×#41	C₂²	1	6	yes	complemented
88	C₂×C₄×D₄×C₁₃	C₂²	1	12	yes	complemented
89	C₂×C₄×D₄×C₁₃	C₂²	1	6	yes	complemented
90	C₂×C₁₃×#117	C₂²	1	3	yes	complemented
91	C₂×C₁₃×#117	C₂²	1	3	yes	complemented
92	C₁₃×H(5,𝔽₂)	—	2	16	no	—
93	C₂×C₁₃×#41	—	2	8	no	—
94	C₂×C₁₃×#41	C₂³	1	3	yes	—
95	C₂×C₁₃×#41	C₂³	1	6	yes	—
96	C₂×C₁₃×#41	C₂³	1	4	yes	—
97	C₂×C₁₃×#41	C₂³	1	3	yes	—
98	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
99	C₂×C₁₃×#41	C₂³	1	24	yes	—
100	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
101	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
102	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
103	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
104	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
105	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
106	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
107	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
108	C₂³×C₄×C₁₃	C₂³	1	12	yes	—
109	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
110	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
111	C₁₃×C₄⋊Q₈	C₂³	1	12	yes	—
112	C₁₃×#127	C₂³	1	3	yes	—
113	C₁₃×#127	C₂³	1	6	yes	—
114	C₁₃×#127	C₂³	1	12	yes	—
115	C₁₃×#127	C₂³	1	12	yes	—
116	C₁₃×#126	C₂³	1	4	yes	—
117	C₁₃×#126	C₂³	1	12	yes	—
118	C₁₃×#126	C₂³	1	12	yes	—
119	C₁₃×#126	C₂³	1	24	yes	—
120	C₁₃×#126	C₂³	1	12	yes	—
121	C₁₃×#125	C₂³	1	3	yes	—
122	C₁₃×#125	C₂³	1	6	yes	—
123	C₁₃×#125	C₂³	1	12	yes	—
124	C₁₃×#125	C₂³	1	4	yes	—
125	C₁₃×#125	C₂³	1	12	yes	—
126	C₁₃×#125	C₂³	1	12	yes	—
127	C₁₃×#125	C₂³	1	1	yes	characteristic
128	C₁₃×#124	C₂³	1	6	yes	—
129	C₁₃×#124	C₂³	1	12	yes	—
130	C₁₃×#124	C₂³	1	12	yes	—
131	C₁₃×#124	C₂³	1	12	yes	—
132	C₁₃×#124	C₂³	1	24	yes	—
133	C₁₃×#123	C₂³	1	12	yes	—
134	C₁₃×#123	C₂³	1	24	yes	—
135	C₁₃×#123	C₂³	1	24	yes	—
136	C₁₃×#123	C₂³	1	24	yes	—
137	C₁₃×#123	C₂³	1	12	yes	—
138	C₁₃×#123	C₂³	1	12	yes	—
139	C₁₃×#123	C₂³	1	24	yes	—
140	C₁₃×#123	C₂³	1	12	yes	—
141	C₁₃×#123	C₂³	1	12	yes	—
142	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
143	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
144	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
145	C₁₃×C₂²⋊Q₈	C₂³	1	24	yes	—
146	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
147	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
148	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
149	C₁₃×#121	C₂³	1	6	yes	—
150	C₁₃×#121	C₂³	1	12	yes	—
151	C₁₃×#121	C₂³	1	24	yes	—
152	C₁₃×#121	C₂³	1	12	yes	—
153	C₁₃×#121	C₂³	1	12	yes	—
154	C₁₃×#121	C₂³	1	24	yes	—
155	C₁₃×#121	C₂³	1	12	yes	—
156	C₁₃×#121	C₂³	1	24	yes	—
157	C₁₃×#121	C₂³	1	6	yes	—
158	C₁₃×#121	C₂³	1	24	yes	—
159	C₁₃×#121	C₂³	1	12	yes	—
160	C₁₃×#121	C₂³	1	12	yes	—
161	C₁₃×#121	C₂³	1	12	yes	—
162	C₁₃×#121	C₂³	1	12	yes	—
163	C₁₃×#121	C₂³	1	12	yes	—
164	C₁₃×#121	C₂³	1	24	yes	—
165	C₁₃×#120	C₂³	1	24	yes	—
166	C₁₃×#120	C₂³	1	24	yes	—
167	C₁₃×#120	C₂³	1	12	yes	—
168	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
169	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
170	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
171	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
172	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
173	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
174	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
175	C₄×Q₈×C₁₃	C₂³	1	12	yes	—
176	C₄×D₄×C₁₃	C₂³	1	6	yes	—
177	C₄×D₄×C₁₃	C₂³	1	12	yes	—
178	C₄×D₄×C₁₃	C₂³	1	12	yes	—
179	C₄×D₄×C₁₃	C₂³	1	6	yes	—
180	C₄×D₄×C₁₃	C₂³	1	12	yes	—
181	C₄×D₄×C₁₃	C₂³	1	12	yes	—
182	C₄×D₄×C₁₃	C₂³	1	12	yes	—
183	C₄×D₄×C₁₃	C₂³	1	24	yes	—
184	C₄×D₄×C₁₃	C₂³	1	12	yes	—
185	C₄×D₄×C₁₃	C₂³	1	6	yes	—
186	C₄×D₄×C₁₃	C₂³	1	12	yes	—
187	C₄×D₄×C₁₃	C₂³	1	6	yes	—
188	C₄×D₄×C₁₃	C₂³	1	12	yes	—
189	C₄×D₄×C₁₃	C₂³	1	12	yes	—
190	C₄×D₄×C₁₃	C₂³	1	6	yes	—
191	C₄×D₄×C₁₃	C₂³	1	12	yes	—
192	C₄×D₄×C₁₃	C₂³	1	6	yes	—
193	C₄×D₄×C₁₃	C₂³	1	12	yes	—
194	C₄×D₄×C₁₃	C₂³	1	12	yes	—
195	C₄×D₄×C₁₃	C₂³	1	24	yes	—
196	C₄×D₄×C₁₃	C₂³	1	24	yes	—
197	C₄×D₄×C₁₃	C₂³	1	12	yes	—
198	C₁₃×#117	C₂³	1	1	yes	characteristic
199	C₁₃×#117	C₂³	1	3	yes	—
200	C₁₃×#117	C₂³	1	3	yes	—
201	C₁₃×#117	C₂³	1	3	yes	—
202	C₁₃×#117	C₂³	1	3	yes	—
203	C₁₃×#117	C₂³	1	3	yes	—
204	C₁₃×#117	C₂³	1	6	yes	—
205	C₁₃×#117	C₂³	1	6	yes	—
206	C₁₃×#117	C₂³	1	6	yes	—
207	C₁₃×#117	C₂³	1	6	yes	—
208	C₁₃×#117	C₂³	1	6	yes	—
209	C₁₃×#117	C₂³	1	12	yes	—
210	C₁₃×#117	C₂³	1	12	yes	—
211	C₁₃×#117	C₂³	1	24	yes	—
212	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
213	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
214	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
215	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
216	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
217	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
218	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
219	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
220	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
221	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
222	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
223	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
224	C₂×C₄²×C₁₃	C₂³	1	6	yes	—
225	C₂×C₄²×C₁₃	C₂³	1	12	yes	—
226	#62858	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
227	C₂⁴×C₁₃	C₂⁴	1	3	yes	—
228	C₂⁴×C₁₃	C₂⁴	1	12	yes	—
229	C₁₃×#41	—	2	4	no	—
230	C₁₃×#41	—	2	16	no	—
231	C₁₃×#41	—	2	12	no	—
232	C₁₃×#41	—	2	12	no	—
233	C₁₃×#41	—	2	24	no	—
234	C₁₃×#41	—	8	24	no	—
235	C₁₃×#41	#41	1	8	yes	complemented
236	C₂×Q₈×C₁₃	—	2	4	no	—
237	C₂×Q₈×C₁₃	C₂⁴	1	3	yes	—
238	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
239	C₂×Q₈×C₁₃	C₂⁴	1	12	yes	—
240	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
241	C₂×D₄×C₁₃	—	2	12	no	—
242	C₂×D₄×C₁₃	—	2	48	no	—
243	C₂×D₄×C₁₃	—	2	24	no	—
244	C₂×D₄×C₁₃	—	8	12	no	—
245	C₂×D₄×C₁₃	—	8	12	no	—
246	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
247	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
248	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
249	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
250	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
251	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
252	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
253	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
254	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
255	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
256	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
257	C₂²×C₄×C₁₃	—	2	12	no	—
258	C₂²×C₄×C₁₃	—	8	12	no	—
259	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
260	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
261	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
262	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
263	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
264	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
266	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
267	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
268	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
269	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
270	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
271	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
272	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
273	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
274	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
275	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
276	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
277	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
278	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
279	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
280	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
281	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
282	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
283	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
284	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
285	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
286	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
287	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
288	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
289	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
290	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
291	C₁₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
292	C₁₃×C₂²⋊C₄	C₂⁴	1	2	yes	—
293	C₁₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
294	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
295	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
296	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
297	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
298	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
299	C₁₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
300	C₁₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
301	C₁₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
302	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
303	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
304	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
305	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
306	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
307	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
308	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
309	C₄²×C₁₃	C₂⁴	1	3	yes	—
310	C₄²×C₁₃	C₂⁴	1	6	yes	—
311	C₄²×C₁₃	C₂⁴	1	3	yes	—
312	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
313	C₄²×C₁₃	C₂⁴	1	4	yes	—
314	C₄²×C₁₃	C₂⁴	1	12	yes	—
315	C₄²×C₁₃	C₂⁴	1	12	yes	—
316	C₄²×C₁₃	C₂⁴	1	12	yes	—
317	C₄²×C₁₃	C₂⁴	1	6	yes	—
318	#3524	C₂×C₁₃	1	4	yes	complemented
319	#3519	C₂×C₁₃	1	12	yes	complemented
320	#3517	C₂×C₁₃	1	4	yes	complemented
321	#3513	C₂×C₁₃	1	12	yes	complemented
322	#3512	C₂×C₁₃	1	3	yes	complemented
323	#3508	C₂×C₁₃	1	3	yes	complemented
324	#3504	C₂×C₁₃	1	1	yes	characteristic, complemented
325	#3498	C₂×C₁₃	1	1	yes	characteristic, complemented
326	#3494	C₂×C₁₃	1	6	yes	complemented
327	#3488	C₂×C₁₃	1	2	yes	complemented
328	#3460	C₂×C₁₃	1	6	yes	complemented
329	#3455	C₂×C₁₃	1	3	yes	complemented
330	C₂×#540	C₂×C₁₃	1	3	yes	complemented
331	C₄×H(5,𝔽₂)	C₂×C₁₃	1	2	yes	complemented
332	#3428	C₂×C₁₃	1	1	yes	characteristic, complemented
333	C₂³×C₁₃	—	2	6	no	—
334	C₂³×C₁₃	—	2	24	no	—
335	C₂³×C₁₃	—	4	12	no	—
336	C₂³×C₁₃	—	4	6	no	—
337	C₂³×C₁₃	—	4	12	no	—
338	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
339	C₂³×C₁₃	C₂⁵	1	12	yes	—
340	C₂³×C₁₃	C₂⁵	1	3	yes	—
341	C₂³×C₁₃	C₂⁵	1	3	yes	—
342	Q₈×C₁₃	—	2	6	no	—
343	Q₈×C₁₃	—	2	4	no	—
344	Q₈×C₁₃	—	4	12	no	—
345	Q₈×C₁₃	C₂×#41	1	4	yes	—
346	D₄×C₁₃	—	2	24	no	—
347	D₄×C₁₃	—	2	12	no	—
348	D₄×C₁₃	—	2	24	no	—
349	D₄×C₁₃	—	2	12	no	—
350	D₄×C₁₃	—	2	6	no	—
351	D₄×C₁₃	—	4	12	no	—
352	D₄×C₁₃	—	4	12	no	—
353	D₄×C₁₃	—	4	24	no	—
354	D₄×C₁₃	—	4	24	no	—
355	D₄×C₁₃	—	4	12	no	—
356	D₄×C₁₃	C₂×#41	1	12	yes	—
357	C₂×C₄×C₁₃	—	2	6	no	—
358	C₂×C₄×C₁₃	—	2	2	no	—
359	C₂×C₄×C₁₃	—	2	6	no	—
360	C₂×C₄×C₁₃	—	2	6	no	—
361	C₂×C₄×C₁₃	—	2	6	no	—
362	C₂×C₄×C₁₃	—	2	24	no	—
363	C₂×C₄×C₁₃	—	4	6	no	—
364	C₂×C₄×C₁₃	—	4	12	no	—
365	C₂×C₄×C₁₃	—	4	12	no	—
366	C₂×C₄×C₁₃	—	4	24	no	—
367	C₂×C₄×C₁₃	—	4	6	no	—
368	C₂×C₄×C₁₃	—	4	12	no	—
369	C₂×C₄×C₁₃	—	4	12	no	—
370	C₂×C₄×C₁₃	C₂×#41	1	12	yes	—
371	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
372	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
373	C₂×C₄×C₁₃	C₂⁵	1	3	yes	—
374	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
375	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
376	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
377	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
378	C₂×C₄×C₁₃	C₂⁵	1	12	yes	—
379	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
380	C₂×C₄×C₁₃	C₂⁵	1	3	yes	—
381	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
382	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	—
383	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
384	#559	C₂²×C₁₃	1	12	yes	complemented
385	#557	C₂²×C₁₃	1	4	yes	complemented
386	#555	C₂²×C₁₃	1	12	yes	complemented
387	#554	C₂²×C₁₃	1	12	yes	complemented
388	#553	C₂²×C₁₃	1	12	yes	complemented
389	#553	C₂²×C₁₃	1	12	yes	complemented
390	#553	C₂²×C₁₃	1	24	yes	complemented
391	#553	C₂²×C₁₃	1	12	yes	complemented
392	#552	C₂²×C₁₃	1	12	yes	complemented
393	#551	C₂²×C₁₃	1	24	yes	complemented
394	#550	C₂²×C₁₃	1	4	yes	complemented
395	#550	C₂²×C₁₃	1	4	yes	complemented
396	#550	C₂²×C₁₃	1	12	yes	complemented
397	#548	C₂²×C₁₃	1	4	yes	complemented
398	#547	C₂²×C₁₃	1	12	yes	complemented
399	#546	C₂²×C₁₃	1	12	yes	complemented
400	#546	C₂²×C₁₃	1	24	yes	complemented
401	#546	C₂²×C₁₃	1	24	yes	complemented
402	D₄²	C₂²×C₁₃	1	12	yes	complemented
403	D₄²	C₂²×C₁₃	1	12	yes	complemented
404	#544	C₂²×C₁₃	1	6	yes	complemented
405	#542	C₂²×C₁₃	1	6	yes	complemented
406	#542	C₂²×C₁₃	1	6	yes	complemented
407	#542	C₂²×C₁₃	1	12	yes	complemented
408	#541	C₂²×C₁₃	1	1	yes	characteristic, complemented
409	#541	C₂²×C₁₃	1	3	yes	complemented
410	#540	C₂²×C₁₃	1	3	yes	complemented
411	#540	C₂²×C₁₃	1	6	yes	complemented
412	#540	C₂²×C₁₃	1	6	yes	complemented
413	#540	C₂²×C₁₃	1	6	yes	complemented
414	#540	C₂²×C₁₃	1	12	yes	complemented
415	#540	C₂²×C₁₃	1	12	yes	complemented
416	#540	C₂²×C₁₃	1	3	yes	complemented
417	#540	C₂²×C₁₃	1	12	yes	complemented
418	#539	C₂²×C₁₃	1	12	yes	complemented
419	#538	C₂²×C₁₃	1	12	yes	complemented
420	#538	C₂²×C₁₃	1	24	yes	complemented
421	#537	C₂²×C₁₃	1	6	yes	complemented
422	#535	C₂²×C₁₃	1	6	yes	complemented
423	#535	C₂²×C₁₃	1	6	yes	complemented
424	#533	C₂²×C₁₃	1	3	yes	complemented
425	#532	C₂²×C₁₃	1	3	yes	complemented
426	#532	C₂²×C₁₃	1	12	yes	complemented
427	#532	C₂²×C₁₃	1	12	yes	complemented
428	C₂×#127	C₂²×C₁₃	1	3	yes	complemented
429	#529	C₂²×C₁₃	1	12	yes	complemented
430	#529	C₂²×C₁₃	1	12	yes	complemented
431	#529	C₂²×C₁₃	1	12	yes	complemented
432	#529	C₂²×C₁₃	1	12	yes	complemented
433	C₂×#125	C₂²×C₁₃	1	3	yes	complemented
434	#525	C₂²×C₁₃	1	6	yes	complemented
435	#525	C₂²×C₁₃	1	24	yes	complemented
436	C₂×#123	C₂²×C₁₃	1	12	yes	complemented
437	C₂×#121	C₂²×C₁₃	1	6	yes	complemented
438	C₂×#121	C₂²×C₁₃	1	12	yes	complemented
439	#520	C₂²×C₁₃	1	2	yes	—
440	#520	C₂²×C₁₃	1	6	yes	complemented
441	#520	C₂²×C₁₃	1	2	yes	complemented
442	#520	C₂²×C₁₃	1	6	yes	complemented
443	#520	C₂²×C₁₃	1	4	yes	complemented
444	#519	C₂²×C₁₃	1	2	yes	complemented
445	#518	C₂²×C₁₃	1	6	yes	complemented
446	#518	C₂²×C₁₃	1	6	yes	complemented
447	#518	C₂²×C₁₃	1	12	yes	complemented
448	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
449	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
450	C₄×#41	C₂²×C₁₃	1	3	yes	complemented
451	C₄×#41	C₂²×C₁₃	1	3	yes	complemented
452	C₄×#41	C₂²×C₁₃	1	6	yes	complemented
453	C₄×#41	C₂²×C₁₃	1	4	yes	complemented
454	C₂×C₄×D₄	C₂²×C₁₃	1	6	yes	complemented
455	C₂×C₄×D₄	C₂²×C₁₃	1	12	yes	complemented
456	C₂×#117	C₂²×C₁₃	1	3	yes	complemented
457	C₂×#117	C₂²×C₁₃	1	3	yes	complemented
458	C₂²×C₁₃	—	2	6	no	—
459	C₂²×C₁₃	—	2	1	no	—
460	C₂²×C₁₃	—	2	3	no	—
461	C₂²×C₁₃	—	2	12	no	—
462	C₂²×C₁₃	—	2	12	no	—
463	C₂²×C₁₃	—	2	6	no	—
464	C₂²×C₁₃	—	2	12	no	—
465	C₂²×C₁₃	—	2	2	no	—
466	C₂²×C₁₃	—	8	6	no	—
467	C₂²×C₁₃	—	8	24	no	—
468	C₂²×C₁₃	C₂²×#41	1	6	yes	—
469	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
470	C₄×C₁₃	—	2	1	no	—
471	C₄×C₁₃	—	2	4	no	—
472	C₄×C₁₃	—	2	3	no	—
473	C₄×C₁₃	—	2	2	no	—
474	C₄×C₁₃	—	2	6	no	—
475	C₄×C₁₃	—	2	12	no	—
476	C₄×C₁₃	—	2	2	no	—
477	C₄×C₁₃	—	2	6	no	—
478	C₄×C₁₃	—	2	4	no	—
479	C₄×C₁₃	C₂²×#41	1	6	yes	—
480	C₄×C₁₃	C₂²×#41	1	2	yes	—
481	H(5,𝔽₂)	—	2	16	no	—
482	C₂×#41	—	2	8	no	—
483	C₂×#41	C₂³×C₁₃	1	3	yes	—
484	C₂×#41	C₂³×C₁₃	1	6	yes	—
485	C₂×#41	C₂³×C₁₃	1	4	yes	—
486	C₂×#41	C₂³×C₁₃	1	3	yes	—
487	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
488	C₂×#41	C₂³×C₁₃	1	24	yes	—
489	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
490	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
491	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
492	C₂²×D₄	C₂³×C₁₃	1	12	yes	—
493	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
494	C₂²×D₄	C₂³×C₁₃	1	12	yes	—
495	C₂²×D₄	C₂³×C₁₃	1	12	yes	—
496	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
497	C₂³×C₄	C₂³×C₁₃	1	12	yes	—
498	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
499	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
500	C₄⋊Q₈	C₂³×C₁₃	1	12	yes	—
501	#127	C₂³×C₁₃	1	3	yes	—
502	#127	C₂³×C₁₃	1	6	yes	—
503	#127	C₂³×C₁₃	1	12	yes	—
504	#127	C₂³×C₁₃	1	12	yes	—
505	#126	C₂³×C₁₃	1	4	yes	—
506	#126	C₂³×C₁₃	1	12	yes	—
507	#126	C₂³×C₁₃	1	12	yes	—
508	#126	C₂³×C₁₃	1	24	yes	—
509	#126	C₂³×C₁₃	1	12	yes	—
510	#125	C₂³×C₁₃	1	3	yes	—
511	#125	C₂³×C₁₃	1	6	yes	—
512	#125	C₂³×C₁₃	1	12	yes	—
513	#125	C₂³×C₁₃	1	4	yes	—
514	#125	C₂³×C₁₃	1	12	yes	—
515	#125	C₂³×C₁₃	1	12	yes	—
516	#125	C₂³×C₁₃	1	1	yes	characteristic
517	#124	C₂³×C₁₃	1	6	yes	—
518	#124	C₂³×C₁₃	1	12	yes	—
519	#124	C₂³×C₁₃	1	12	yes	—
520	#124	C₂³×C₁₃	1	12	yes	—
521	#124	C₂³×C₁₃	1	24	yes	—
522	#123	C₂³×C₁₃	1	12	yes	—
523	#123	C₂³×C₁₃	1	24	yes	—
524	#123	C₂³×C₁₃	1	24	yes	—
525	#123	C₂³×C₁₃	1	24	yes	—
526	#123	C₂³×C₁₃	1	12	yes	—
527	#123	C₂³×C₁₃	1	12	yes	—
528	#123	C₂³×C₁₃	1	24	yes	—
529	#123	C₂³×C₁₃	1	12	yes	—
530	#123	C₂³×C₁₃	1	12	yes	—
531	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
532	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
533	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
534	C₂²⋊Q₈	C₂³×C₁₃	1	24	yes	—
535	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
536	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
537	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
538	#121	C₂³×C₁₃	1	6	yes	—
539	#121	C₂³×C₁₃	1	12	yes	—
540	#121	C₂³×C₁₃	1	24	yes	—
541	#121	C₂³×C₁₃	1	12	yes	—
542	#121	C₂³×C₁₃	1	12	yes	—
543	#121	C₂³×C₁₃	1	24	yes	—
544	#121	C₂³×C₁₃	1	12	yes	—
545	#121	C₂³×C₁₃	1	24	yes	—
546	#121	C₂³×C₁₃	1	6	yes	—
547	#121	C₂³×C₁₃	1	24	yes	—
548	#121	C₂³×C₁₃	1	12	yes	—
549	#121	C₂³×C₁₃	1	12	yes	—
550	#121	C₂³×C₁₃	1	12	yes	—
551	#121	C₂³×C₁₃	1	12	yes	—
552	#121	C₂³×C₁₃	1	12	yes	—
553	#121	C₂³×C₁₃	1	24	yes	—
554	#120	C₂³×C₁₃	1	24	yes	—
555	#120	C₂³×C₁₃	1	24	yes	—
556	#120	C₂³×C₁₃	1	12	yes	—
557	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
558	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
559	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
560	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
561	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
562	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
563	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
564	C₄×Q₈	C₂³×C₁₃	1	12	yes	—
565	C₄×D₄	C₂³×C₁₃	1	6	yes	—
566	C₄×D₄	C₂³×C₁₃	1	12	yes	—
567	C₄×D₄	C₂³×C₁₃	1	6	yes	—
568	C₄×D₄	C₂³×C₁₃	1	12	yes	—
569	C₄×D₄	C₂³×C₁₃	1	12	yes	—
570	C₄×D₄	C₂³×C₁₃	1	12	yes	—
571	C₄×D₄	C₂³×C₁₃	1	12	yes	—
572	C₄×D₄	C₂³×C₁₃	1	24	yes	—
573	C₄×D₄	C₂³×C₁₃	1	12	yes	—
574	C₄×D₄	C₂³×C₁₃	1	6	yes	—
575	C₄×D₄	C₂³×C₁₃	1	12	yes	—
576	C₄×D₄	C₂³×C₁₃	1	6	yes	—
577	C₄×D₄	C₂³×C₁₃	1	12	yes	—
578	C₄×D₄	C₂³×C₁₃	1	12	yes	—
579	C₄×D₄	C₂³×C₁₃	1	6	yes	—
580	C₄×D₄	C₂³×C₁₃	1	12	yes	—
581	C₄×D₄	C₂³×C₁₃	1	6	yes	—
582	C₄×D₄	C₂³×C₁₃	1	12	yes	—
583	C₄×D₄	C₂³×C₁₃	1	12	yes	—
584	C₄×D₄	C₂³×C₁₃	1	24	yes	—
585	C₄×D₄	C₂³×C₁₃	1	24	yes	—
586	C₄×D₄	C₂³×C₁₃	1	12	yes	—
587	#117	C₂³×C₁₃	1	1	yes	characteristic
588	#117	C₂³×C₁₃	1	3	yes	—
589	#117	C₂³×C₁₃	1	3	yes	—
590	#117	C₂³×C₁₃	1	3	yes	—
591	#117	C₂³×C₁₃	1	3	yes	—
592	#117	C₂³×C₁₃	1	3	yes	—
593	#117	C₂³×C₁₃	1	6	yes	—
594	#117	C₂³×C₁₃	1	6	yes	—
595	#117	C₂³×C₁₃	1	6	yes	—
596	#117	C₂³×C₁₃	1	6	yes	—
597	#117	C₂³×C₁₃	1	6	yes	—
598	#117	C₂³×C₁₃	1	12	yes	—
599	#117	C₂³×C₁₃	1	12	yes	—
600	#117	C₂³×C₁₃	1	24	yes	—
601	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
602	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
603	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
604	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
605	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₁₃	1	12	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₁₃	1	12	yes	—
611	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
612	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
613	C₂×C₄²	C₂³×C₁₃	1	6	yes	—
614	C₂×C₄²	C₂³×C₁₃	1	12	yes	—
615	C₂×C₁₃	—	2	6	no	—
616	C₂×C₁₃	—	4	3	no	—
617	C₂×C₁₃	—	4	12	no	—
618	C₂×C₁₃	—	4	1	no	—
619	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
620	C₂×C₁₃	H(7,𝔽₂)	1	2	yes	—
621	C₂⁴	C₂⁴×C₁₃	1	3	yes	—
622	C₂⁴	C₂⁴×C₁₃	1	12	yes	—
623	#41	—	2	4	no	—
624	#41	—	2	16	no	—
625	#41	—	2	12	no	—
626	#41	—	2	12	no	—
627	#41	—	2	24	no	—
628	#41	—	8	24	no	—
629	#41	C₁₃×#41	1	8	yes	complemented
630	C₂×Q₈	—	2	4	no	—
631	C₂×Q₈	C₂⁴×C₁₃	1	3	yes	—
632	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
633	C₂×Q₈	C₂⁴×C₁₃	1	12	yes	—
634	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
635	C₂×D₄	—	2	12	no	—
636	C₂×D₄	—	2	48	no	—
637	C₂×D₄	—	2	24	no	—
638	C₂×D₄	—	8	12	no	—
639	C₂×D₄	—	8	12	no	—
640	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
641	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
642	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
643	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
644	C₂×D₄	C₂⁴×C₁₃	1	3	yes	—
645	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
646	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
647	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
648	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
649	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
650	C₂×D₄	C₂⁴×C₁₃	1	3	yes	—
651	C₂²×C₄	—	2	12	no	—
652	C₂²×C₄	—	8	12	no	—
653	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
654	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
655	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
656	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
657	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
658	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
659	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
660	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
661	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
662	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
663	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
664	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
665	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
666	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
667	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
668	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
669	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
670	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
671	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
672	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
673	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
674	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
675	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
676	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
677	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
678	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
679	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
680	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
681	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
682	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
683	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
684	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
685	C₂²⋊C₄	C₂⁴×C₁₃	1	6	yes	—
686	C₂²⋊C₄	C₂⁴×C₁₃	1	2	yes	—
687	C₂²⋊C₄	C₂⁴×C₁₃	1	6	yes	—
688	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
689	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
690	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
691	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
692	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
693	C₂²⋊C₄	C₂⁴×C₁₃	1	6	yes	—
694	C₂²⋊C₄	C₂⁴×C₁₃	1	6	yes	—
695	C₂²⋊C₄	C₂⁴×C₁₃	1	6	yes	—
696	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
697	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
698	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
699	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
700	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
701	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
702	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
703	C₄²	C₂⁴×C₁₃	1	3	yes	—
704	C₄²	C₂⁴×C₁₃	1	6	yes	—
705	C₄²	C₂⁴×C₁₃	1	3	yes	—
706	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
707	C₄²	C₂⁴×C₁₃	1	4	yes	—
708	C₄²	C₂⁴×C₁₃	1	12	yes	—
709	C₄²	C₂⁴×C₁₃	1	12	yes	—
710	C₄²	C₂⁴×C₁₃	1	12	yes	—
711	C₄²	C₂⁴×C₁₃	1	6	yes	—
712	C₁₃	#62858	1	1	yes	characteristic, direct product factor, Sylow
713	C₂³	—	2	6	no	—
714	C₂³	—	2	24	no	—
715	C₂³	—	4	12	no	—
716	C₂³	—	4	6	no	—
717	C₂³	—	4	12	no	—
718	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
719	C₂³	C₂⁵×C₁₃	1	12	yes	—
720	C₂³	C₂⁵×C₁₃	1	3	yes	—
721	C₂³	C₂⁵×C₁₃	1	3	yes	—
722	Q₈	—	2	6	no	—
723	Q₈	—	2	4	no	—
724	Q₈	—	4	12	no	—
725	Q₈	C₂×C₁₃×#41	1	4	yes	—
726	D₄	—	2	24	no	—
727	D₄	—	2	12	no	—
728	D₄	—	2	24	no	—
729	D₄	—	2	12	no	—
730	D₄	—	2	6	no	—
731	D₄	—	4	12	no	—
732	D₄	—	4	12	no	—
733	D₄	—	4	24	no	—
734	D₄	—	4	24	no	—
735	D₄	—	4	12	no	—
736	D₄	C₂×C₁₃×#41	1	12	yes	—
737	C₂×C₄	—	2	6	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	6	no	—
740	C₂×C₄	—	2	6	no	—
741	C₂×C₄	—	2	6	no	—
742	C₂×C₄	—	2	24	no	—
743	C₂×C₄	—	4	6	no	—
744	C₂×C₄	—	4	12	no	—
745	C₂×C₄	—	4	12	no	—
746	C₂×C₄	—	4	24	no	—
747	C₂×C₄	—	4	6	no	—
748	C₂×C₄	—	4	12	no	—
749	C₂×C₄	—	4	12	no	—
750	C₂×C₄	C₂×C₁₃×#41	1	12	yes	—
751	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
752	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
753	C₂×C₄	C₂⁵×C₁₃	1	3	yes	—
754	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
755	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
756	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
757	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
758	C₂×C₄	C₂⁵×C₁₃	1	12	yes	—
759	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
760	C₂×C₄	C₂⁵×C₁₃	1	3	yes	—
761	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
762	C₂²	—	2	6	no	—
763	C₂²	—	2	1	no	—
764	C₂²	—	2	3	no	—
765	C₂²	—	2	12	no	—
766	C₂²	—	2	12	no	—
767	C₂²	—	2	6	no	—
768	C₂²	—	2	12	no	—
769	C₂²	—	2	2	no	—
770	C₂²	—	8	6	no	—
771	C₂²	—	8	24	no	—
772	C₂²	C₂²×C₁₃×#41	1	6	yes	—
773	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
774	C₄	—	2	1	no	—
775	C₄	—	2	4	no	—
776	C₄	—	2	3	no	—
777	C₄	—	2	2	no	—
778	C₄	—	2	6	no	—
779	C₄	—	2	12	no	—
780	C₄	—	2	2	no	—
781	C₄	—	2	6	no	—
782	C₄	—	2	4	no	—
783	C₄	C₂²×C₁₃×#41	1	6	yes	—
784	C₄	C₂²×C₁₃×#41	1	2	yes	—
785	C₂	—	2	6	no	—
786	C₂	—	4	1	no	—
787	C₂	—	4	12	no	—
788	C₂	—	4	3	no	—
789	C₂	C₂³×C₁₃×#41	1	1	yes	characteristic
790	C₂	C₁₃×H(7,𝔽₂)	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3524	C₂	semidirect
2. C₁₃×#3519	C₂	semidirect
3. C₁₃×#3517	C₂	semidirect
4. C₁₃×#3513	C₂	semidirect
5. C₁₃×#3512	C₂	semidirect
6. C₁₃×#3508	C₂	semidirect
7. C₁₃×#3504	C₂	semidirect
8. C₁₃×#3498	C₂	semidirect
9. C₁₃×#3494	C₂	semidirect
10. C₁₃×#3488	C₂	semidirect
11. C₁₃×#3460	C₂	semidirect
12. C₁₃×#3455	C₂	semidirect
13. C₂×C₁₃×#540	C₂	semidirect
14. C₄×C₁₃×H(5,𝔽₂)	C₂	semidirect
15. C₁₃×#3428	C₂	semidirect
18. C₁₃×#559	C₂²	semidirect
19. C₁₃×#557	C₂²	semidirect
20. C₁₃×#555	C₂²	semidirect
21. C₁₃×#554	C₂²	semidirect
22. C₁₃×#553	C₂²	semidirect
23. C₁₃×#553	C₂²	semidirect
24. C₁₃×#553	C₂²	semidirect
25. C₁₃×#553	C₂²	semidirect
26. C₁₃×#552	C₂²	semidirect
27. C₁₃×#551	C₂²	semidirect
28. C₁₃×#550	C₂²	semidirect
29. C₁₃×#550	C₂²	semidirect
30. C₁₃×#550	C₂²	semidirect
31. C₁₃×#548	C₂²	semidirect
32. C₁₃×#547	C₂²	semidirect
33. C₁₃×#546	C₂²	semidirect
34. C₁₃×#546	C₂²	semidirect
35. C₁₃×#546	C₂²	semidirect
36. D₄²×C₁₃	C₂²	semidirect
37. D₄²×C₁₃	C₂²	semidirect
38. C₁₃×#544	C₂²	semidirect
39. C₁₃×#542	C₂²	semidirect
40. C₁₃×#542	C₂²	semidirect
41. C₁₃×#542	C₂²	semidirect
42. C₁₃×#541	C₂²	semidirect
43. C₁₃×#541	C₂²	semidirect
44. C₁₃×#540	C₂²	semidirect
45. C₁₃×#540	C₂²	semidirect
46. C₁₃×#540	C₂²	semidirect
47. C₁₃×#540	C₂²	semidirect
48. C₁₃×#540	C₂²	semidirect
49. C₁₃×#540	C₂²	semidirect
50. C₁₃×#540	C₂²	semidirect
51. C₁₃×#540	C₂²	semidirect
52. C₁₃×#539	C₂²	semidirect
53. C₁₃×#538	C₂²	semidirect
54. C₁₃×#538	C₂²	semidirect
55. C₁₃×#537	C₂²	semidirect
56. C₁₃×#535	C₂²	semidirect
57. C₁₃×#535	C₂²	semidirect
58. C₁₃×#533	C₂²	semidirect
59. C₁₃×#532	C₂²	semidirect
60. C₁₃×#532	C₂²	semidirect
61. C₁₃×#532	C₂²	semidirect
62. C₂×C₁₃×#127	C₂²	semidirect
63. C₁₃×#529	C₂²	semidirect
64. C₁₃×#529	C₂²	semidirect
65. C₁₃×#529	C₂²	semidirect
66. C₁₃×#529	C₂²	semidirect
67. C₂×C₁₃×#125	C₂²	semidirect
68. C₁₃×#525	C₂²	semidirect
69. C₁₃×#525	C₂²	semidirect
70. C₂×C₁₃×#123	C₂²	semidirect
71. C₂×C₁₃×#121	C₂²	semidirect
72. C₂×C₁₃×#121	C₂²	semidirect
74. C₁₃×#520	C₂²	semidirect
75. C₁₃×#520	C₂²	semidirect
76. C₁₃×#520	C₂²	semidirect
77. C₁₃×#520	C₂²	semidirect
78. C₁₃×#519	C₂²	semidirect
79. C₁₃×#518	C₂²	semidirect
80. C₁₃×#518	C₂²	semidirect
81. C₁₃×#518	C₂²	semidirect
84. C₄×C₁₃×#41	C₂²	semidirect
85. C₄×C₁₃×#41	C₂²	semidirect
86. C₄×C₁₃×#41	C₂²	semidirect
87. C₄×C₁₃×#41	C₂²	semidirect
88. C₂×C₄×D₄×C₁₃	C₂²	semidirect
89. C₂×C₄×D₄×C₁₃	C₂²	semidirect
90. C₂×C₁₃×#117	C₂²	semidirect
91. C₂×C₁₃×#117	C₂²	semidirect
226. #62858	C₁₃	direct (N × H)
235. C₁₃×#41	#41	semidirect
318. #3524	C₂×C₁₃	semidirect
319. #3519	C₂×C₁₃	semidirect
320. #3517	C₂×C₁₃	semidirect
321. #3513	C₂×C₁₃	semidirect
322. #3512	C₂×C₁₃	semidirect
323. #3508	C₂×C₁₃	semidirect
324. #3504	C₂×C₁₃	semidirect
325. #3498	C₂×C₁₃	semidirect
326. #3494	C₂×C₁₃	semidirect
327. #3488	C₂×C₁₃	semidirect
328. #3460	C₂×C₁₃	semidirect
329. #3455	C₂×C₁₃	semidirect
330. C₂×#540	C₂×C₁₃	semidirect
331. C₄×H(5,𝔽₂)	C₂×C₁₃	semidirect
332. #3428	C₂×C₁₃	semidirect
384. #559	C₂²×C₁₃	semidirect
385. #557	C₂²×C₁₃	semidirect
386. #555	C₂²×C₁₃	semidirect
387. #554	C₂²×C₁₃	semidirect
388. #553	C₂²×C₁₃	semidirect
389. #553	C₂²×C₁₃	semidirect
390. #553	C₂²×C₁₃	semidirect
391. #553	C₂²×C₁₃	semidirect
392. #552	C₂²×C₁₃	semidirect
393. #551	C₂²×C₁₃	semidirect
394. #550	C₂²×C₁₃	semidirect
395. #550	C₂²×C₁₃	semidirect
396. #550	C₂²×C₁₃	semidirect
397. #548	C₂²×C₁₃	semidirect
398. #547	C₂²×C₁₃	semidirect
399. #546	C₂²×C₁₃	semidirect
400. #546	C₂²×C₁₃	semidirect
401. #546	C₂²×C₁₃	semidirect
402. D₄²	C₂²×C₁₃	semidirect
403. D₄²	C₂²×C₁₃	semidirect
404. #544	C₂²×C₁₃	semidirect
405. #542	C₂²×C₁₃	semidirect
406. #542	C₂²×C₁₃	semidirect
407. #542	C₂²×C₁₃	semidirect
408. #541	C₂²×C₁₃	semidirect
409. #541	C₂²×C₁₃	semidirect
410. #540	C₂²×C₁₃	semidirect
411. #540	C₂²×C₁₃	semidirect
412. #540	C₂²×C₁₃	semidirect
413. #540	C₂²×C₁₃	semidirect
414. #540	C₂²×C₁₃	semidirect
415. #540	C₂²×C₁₃	semidirect
416. #540	C₂²×C₁₃	semidirect
417. #540	C₂²×C₁₃	semidirect
418. #539	C₂²×C₁₃	semidirect
419. #538	C₂²×C₁₃	semidirect
420. #538	C₂²×C₁₃	semidirect
421. #537	C₂²×C₁₃	semidirect
422. #535	C₂²×C₁₃	semidirect
423. #535	C₂²×C₁₃	semidirect
424. #533	C₂²×C₁₃	semidirect
425. #532	C₂²×C₁₃	semidirect
426. #532	C₂²×C₁₃	semidirect
427. #532	C₂²×C₁₃	semidirect
428. C₂×#127	C₂²×C₁₃	semidirect
429. #529	C₂²×C₁₃	semidirect
430. #529	C₂²×C₁₃	semidirect
431. #529	C₂²×C₁₃	semidirect
432. #529	C₂²×C₁₃	semidirect
433. C₂×#125	C₂²×C₁₃	semidirect
434. #525	C₂²×C₁₃	semidirect
435. #525	C₂²×C₁₃	semidirect
436. C₂×#123	C₂²×C₁₃	semidirect
437. C₂×#121	C₂²×C₁₃	semidirect
438. C₂×#121	C₂²×C₁₃	semidirect
440. #520	C₂²×C₁₃	semidirect
441. #520	C₂²×C₁₃	semidirect
442. #520	C₂²×C₁₃	semidirect
443. #520	C₂²×C₁₃	semidirect
444. #519	C₂²×C₁₃	semidirect
445. #518	C₂²×C₁₃	semidirect
446. #518	C₂²×C₁₃	semidirect
447. #518	C₂²×C₁₃	semidirect
450. C₄×#41	C₂²×C₁₃	semidirect
451. C₄×#41	C₂²×C₁₃	semidirect
452. C₄×#41	C₂²×C₁₃	semidirect
453. C₄×#41	C₂²×C₁₃	semidirect
454. C₂×C₄×D₄	C₂²×C₁₃	semidirect
455. C₂×C₄×D₄	C₂²×C₁₃	semidirect
456. C₂×#117	C₂²×C₁₃	semidirect
457. C₂×#117	C₂²×C₁₃	semidirect
629. #41	C₁₃×#41	semidirect
712. C₁₃	#62858	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3524	2
C₁₃×#3519	2
C₁₃×#3517	2
C₁₃×#3513	2
C₁₃×#3512	2
C₁₃×#3508	2
C₁₃×#3504	2
C₁₃×#3498	2
C₁₃×#3494	2
C₁₃×#3488	2
C₁₃×#3460	2
C₁₃×#3455	2
C₂×C₁₃×#540	2
C₄×C₁₃×H(5,𝔽₂)	2
C₁₃×#3428	2
#62858	13

Subgroups — C13×#62858 #15749197

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62858 #15749197