Subgroups — C₁₃×#62834 #15749173

Order 3328.

7900 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3558	C₂	1	8	yes	maximal, complemented
2	C₁₃×#3549	C₂	1	2	yes	maximal, complemented
3	C₁₃×#3548	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3546	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3537	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3519	C₂	1	8	yes	maximal, complemented
7	C₁₃×#3511	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3508	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3506	C₂	1	4	yes	maximal, complemented
10	C₁₃×#3498	C₂	1	4	yes	maximal, complemented
11	C₁₃×#3496	C₂	1	4	yes	maximal, complemented
12	C₁₃×#3488	C₂	1	8	yes	maximal, complemented
13	C₁₃×#3444	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#532	C₂	1	2	yes	maximal, complemented
15	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	8	yes	complemented
16	C₂²×C₁₃×#41	C₂²	1	4	yes	complemented
17	C₁₃×#562	C₂²	1	8	yes	complemented
18	C₁₃×H(3,𝔽₄)	C₂²	1	8	yes	complemented
19	C₁₃×#560	C₂²	1	16	yes	complemented
20	C₁₃×#559	C₂²	1	16	yes	complemented
21	C₁₃×#556	C₂²	1	8	yes	complemented
22	C₁₃×#555	C₂²	1	8	yes	complemented
23	C₁₃×#555	C₂²	1	4	yes	complemented
24	C₁₃×#554	C₂²	1	8	yes	complemented
25	C₁₃×#553	C₂²	1	16	yes	complemented
26	C₁₃×#553	C₂²	1	16	yes	complemented
27	C₁₃×#550	C₂²	1	8	yes	complemented
28	C₁₃×#550	C₂²	1	16	yes	complemented
29	C₁₃×#550	C₂²	1	8	yes	complemented
30	C₁₃×#548	C₂²	1	16	yes	complemented
31	C₁₃×#547	C₂²	1	8	yes	complemented
32	C₁₃×#547	C₂²	1	8	yes	complemented
33	C₁₃×#546	C₂²	1	16	yes	complemented
34	C₁₃×#546	C₂²	1	32	yes	complemented
35	C₁₃×#546	C₂²	1	16	yes	complemented
36	C₁₃×#546	C₂²	1	16	yes	complemented
37	D₄²×C₁₃	C₂²	1	16	yes	complemented
38	D₄²×C₁₃	C₂²	1	8	yes	complemented
39	D₄²×C₁₃	C₂²	1	16	yes	complemented
40	D₄²×C₁₃	C₂²	1	8	yes	complemented
41	D₄²×C₁₃	C₂²	1	4	yes	complemented
42	D₄²×C₁₃	C₂²	1	16	yes	complemented
43	C₁₃×#542	C₂²	1	16	yes	complemented
44	C₁₃×#540	C₂²	1	8	yes	complemented
45	C₁₃×#540	C₂²	1	8	yes	complemented
46	C₁₃×#538	C₂²	1	32	yes	complemented
47	C₁₃×#538	C₂²	1	16	yes	complemented
48	C₁₃×#537	C₂²	1	16	yes	complemented
49	C₁₃×#537	C₂²	1	8	yes	complemented
50	C₁₃×#535	C₂²	1	8	yes	complemented
51	C₁₃×#535	C₂²	1	16	yes	complemented
52	C₁₃×#535	C₂²	1	16	yes	complemented
53	C₁₃×#535	C₂²	1	8	yes	complemented
54	C₁₃×#534	C₂²	1	16	yes	complemented
55	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
56	C₁₃×#533	C₂²	1	2	yes	complemented
57	C₁₃×#533	C₂²	1	4	yes	complemented
58	C₁₃×#532	C₂²	1	4	yes	complemented
59	C₁₃×#532	C₂²	1	4	yes	complemented
60	C₁₃×#532	C₂²	1	4	yes	complemented
61	C₁₃×#532	C₂²	1	4	yes	complemented
62	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#532	C₂²	1	4	yes	complemented
64	C₁₃×#532	C₂²	1	4	yes	complemented
65	C₁₃×#532	C₂²	1	4	yes	complemented
66	C₁₃×#532	C₂²	1	4	yes	complemented
67	C₁₃×#532	C₂²	1	2	yes	complemented
68	C₁₃×#532	C₂²	1	8	yes	complemented
69	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
70	C₂×C₁₃×#127	C₂²	1	2	yes	complemented
71	C₂×C₁₃×#127	C₂²	1	4	yes	complemented
72	C₁₃×#529	C₂²	1	4	yes	complemented
73	C₁₃×#529	C₂²	1	4	yes	complemented
74	C₁₃×#529	C₂²	1	4	yes	complemented
75	C₂×C₁₃×#124	C₂²	1	4	yes	complemented
76	C₁₃×#525	C₂²	1	16	yes	complemented
77	C₁₃×#525	C₂²	1	2	yes	complemented
78	C₁₃×#525	C₂²	1	4	yes	complemented
79	C₂×C₁₃×#121	C₂²	1	16	yes	complemented
80	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
81	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
82	C₁₃×#520	C₂²	1	8	yes	complemented
83	C₁₃×#518	C₂²	1	8	yes	complemented
84	C₄×C₁₃×#41	C₂²	1	4	yes	complemented
85	C₄×C₁₃×#41	C₂²	1	2	yes	complemented
86	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
87	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
88	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
89	C₁₃×H(5,𝔽₂)	—	4	32	no	—
90	C₂×C₁₃×#41	—	4	16	no	—
91	C₂×C₁₃×#41	C₂³	1	4	yes	—
92	C₂×C₁₃×#41	C₂³	1	8	yes	—
93	C₂×C₁₃×#41	C₂³	1	2	yes	—
94	C₂×C₁₃×#41	C₂³	1	16	yes	—
95	C₂×C₁₃×#41	C₂³	1	8	yes	—
96	C₂×C₁₃×#41	C₂³	1	8	yes	—
97	C₂×C₁₃×#41	C₂³	1	8	yes	—
98	C₂×C₁₃×#41	C₂³	1	16	yes	—
99	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
100	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
101	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
102	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
103	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
104	C₂²×D₄×C₁₃	C₂³	1	32	yes	—
105	C₂²×D₄×C₁₃	C₂³	1	16	yes	—
106	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
107	C₂²×D₄×C₁₃	C₂³	1	16	yes	—
108	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
109	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
111	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
112	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
113	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
114	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
115	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
116	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₁₃×#127	C₂³	1	4	yes	—
118	C₁₃×#127	C₂³	1	4	yes	—
119	C₁₃×#127	C₂³	1	4	yes	—
120	C₁₃×#127	C₂³	1	4	yes	—
121	C₁₃×#127	C₂³	1	16	yes	—
122	C₁₃×#127	C₂³	1	8	yes	—
123	C₁₃×#127	C₂³	1	1	yes	characteristic
124	C₁₃×#127	C₂³	1	16	yes	—
125	C₁₃×#126	C₂³	1	8	yes	—
126	C₁₃×#126	C₂³	1	32	yes	—
127	C₁₃×#125	C₂³	1	4	yes	—
128	C₁₃×#125	C₂³	1	2	yes	—
129	C₁₃×#125	C₂³	1	8	yes	—
130	C₁₃×#124	C₂³	1	8	yes	—
131	C₁₃×#124	C₂³	1	8	yes	—
132	C₁₃×#124	C₂³	1	8	yes	—
133	C₁₃×#124	C₂³	1	8	yes	—
134	C₁₃×#124	C₂³	1	4	yes	—
135	C₁₃×#124	C₂³	1	2	yes	—
136	C₁₃×#124	C₂³	1	16	yes	—
137	C₁₃×#124	C₂³	1	16	yes	—
138	C₁₃×#124	C₂³	1	32	yes	—
139	C₁₃×#123	C₂³	1	8	yes	—
140	C₁₃×#123	C₂³	1	4	yes	—
141	C₁₃×#123	C₂³	1	32	yes	—
142	C₁₃×#123	C₂³	1	32	yes	—
143	C₁₃×#123	C₂³	1	32	yes	—
144	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
145	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
146	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
147	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
148	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
149	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
150	C₁₃×#121	C₂³	1	4	yes	—
151	C₁₃×#121	C₂³	1	8	yes	—
152	C₁₃×#121	C₂³	1	8	yes	—
153	C₁₃×#121	C₂³	1	8	yes	—
154	C₁₃×#121	C₂³	1	8	yes	—
155	C₁₃×#121	C₂³	1	8	yes	—
156	C₁₃×#121	C₂³	1	8	yes	—
157	C₁₃×#121	C₂³	1	8	yes	—
158	C₁₃×#121	C₂³	1	8	yes	—
159	C₁₃×#121	C₂³	1	32	yes	—
160	C₁₃×#121	C₂³	1	16	yes	—
161	C₁₃×#121	C₂³	1	16	yes	—
162	C₁₃×#121	C₂³	1	32	yes	—
163	C₁₃×#121	C₂³	1	4	yes	—
164	C₁₃×#121	C₂³	1	4	yes	—
165	C₁₃×#121	C₂³	1	16	yes	—
166	C₁₃×#121	C₂³	1	16	yes	—
167	C₁₃×#121	C₂³	1	16	yes	—
168	C₁₃×#121	C₂³	1	32	yes	—
169	C₁₃×#121	C₂³	1	32	yes	—
170	C₁₃×#121	C₂³	1	32	yes	—
171	C₁₃×#120	C₂³	1	4	yes	—
172	C₁₃×#120	C₂³	1	32	yes	—
173	C₁₃×#120	C₂³	1	16	yes	—
174	C₁₃×#120	C₂³	1	32	yes	—
175	C₁₃×#120	C₂³	1	16	yes	—
176	C₁₃×#120	C₂³	1	32	yes	—
177	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
178	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
179	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
180	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
181	C₄×D₄×C₁₃	C₂³	1	8	yes	—
182	C₄×D₄×C₁₃	C₂³	1	8	yes	—
183	C₄×D₄×C₁₃	C₂³	1	8	yes	—
184	C₄×D₄×C₁₃	C₂³	1	8	yes	—
185	C₄×D₄×C₁₃	C₂³	1	8	yes	—
186	C₄×D₄×C₁₃	C₂³	1	8	yes	—
187	C₄×D₄×C₁₃	C₂³	1	8	yes	—
188	C₄×D₄×C₁₃	C₂³	1	8	yes	—
189	C₄×D₄×C₁₃	C₂³	1	8	yes	—
190	C₄×D₄×C₁₃	C₂³	1	8	yes	—
191	C₄×D₄×C₁₃	C₂³	1	8	yes	—
192	C₄×D₄×C₁₃	C₂³	1	4	yes	—
193	C₄×D₄×C₁₃	C₂³	1	4	yes	—
194	C₄×D₄×C₁₃	C₂³	1	4	yes	—
195	C₄×D₄×C₁₃	C₂³	1	32	yes	—
196	C₄×D₄×C₁₃	C₂³	1	16	yes	—
197	C₄×D₄×C₁₃	C₂³	1	32	yes	—
198	C₄×D₄×C₁₃	C₂³	1	16	yes	—
199	C₁₃×#117	C₂³	1	4	yes	—
200	C₁₃×#117	C₂³	1	4	yes	—
201	C₁₃×#117	C₂³	1	2	yes	—
202	C₁₃×#117	C₂³	1	8	yes	—
203	C₁₃×#117	C₂³	1	8	yes	—
204	C₁₃×#117	C₂³	1	16	yes	—
205	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
206	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
207	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
208	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
209	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
210	C₂×C₁₃×C₂²⋊C₄	C₂³	1	32	yes	—
211	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
212	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
213	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
214	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
216	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
217	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
218	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
219	#62834	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
220	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
221	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
222	C₂⁴×C₁₃	C₂⁴	1	16	yes	—
223	C₁₃×#41	—	2	32	no	—
224	C₁₃×#41	—	2	16	no	—
225	C₁₃×#41	—	4	16	no	—
226	C₁₃×#41	—	4	4	no	—
227	C₁₃×#41	—	4	16	no	—
228	C₁₃×#41	—	4	16	no	—
229	C₁₃×#41	—	4	32	no	—
230	C₁₃×#41	—	4	32	no	—
231	C₂×Q₈×C₁₃	—	4	8	no	—
232	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
233	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
234	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
235	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
236	C₂×D₄×C₁₃	—	2	16	no	—
237	C₂×D₄×C₁₃	—	4	8	no	—
238	C₂×D₄×C₁₃	—	4	16	no	—
239	C₂×D₄×C₁₃	—	4	8	no	—
240	C₂×D₄×C₁₃	—	4	32	no	—
241	C₂×D₄×C₁₃	—	4	32	no	—
242	C₂×D₄×C₁₃	—	4	16	no	—
243	C₂×D₄×C₁₃	—	4	64	no	—
244	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
245	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
246	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
247	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
248	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
249	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
250	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
251	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
252	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
253	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
254	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
255	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
256	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
257	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
258	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
259	C₂²×C₄×C₁₃	—	2	8	no	—
260	C₂²×C₄×C₁₃	—	4	2	no	—
261	C₂²×C₄×C₁₃	—	4	16	no	—
262	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
270	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
271	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
272	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
275	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
276	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	—
277	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
278	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
279	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
280	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
281	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
282	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
283	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
284	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
285	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
286	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
287	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
288	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
289	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
290	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
291	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
292	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
293	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
294	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
295	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
296	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
297	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
298	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
299	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
300	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
301	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
302	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
303	C₄²×C₁₃	C₂⁴	1	2	yes	—
304	C₄²×C₁₃	C₂⁴	1	2	yes	—
305	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
306	C₄²×C₁₃	C₂⁴	1	2	yes	—
307	C₄²×C₁₃	C₂⁴	1	2	yes	—
308	C₄²×C₁₃	C₂⁴	1	2	yes	—
309	C₄²×C₁₃	C₂⁴	1	2	yes	—
310	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
311	C₄²×C₁₃	C₂⁴	1	4	yes	—
312	C₄²×C₁₃	C₂⁴	1	8	yes	—
313	C₄²×C₁₃	C₂⁴	1	16	yes	—
314	#3558	C₂×C₁₃	1	8	yes	complemented
315	#3549	C₂×C₁₃	1	2	yes	complemented
316	#3548	C₂×C₁₃	1	2	yes	complemented
317	#3546	C₂×C₁₃	1	8	yes	complemented
318	#3537	C₂×C₁₃	1	4	yes	complemented
319	#3519	C₂×C₁₃	1	8	yes	complemented
320	#3511	C₂×C₁₃	1	4	yes	complemented
321	#3508	C₂×C₁₃	1	4	yes	complemented
322	#3506	C₂×C₁₃	1	4	yes	complemented
323	#3498	C₂×C₁₃	1	4	yes	complemented
324	#3496	C₂×C₁₃	1	4	yes	complemented
325	#3488	C₂×C₁₃	1	8	yes	complemented
326	#3444	C₂×C₁₃	1	1	yes	characteristic, complemented
327	C₂×#532	C₂×C₁₃	1	2	yes	complemented
328	C₂³×C₁₃	—	2	4	no	—
329	C₂³×C₁₃	—	2	16	no	—
330	C₂³×C₁₃	—	4	1	no	—
331	C₂³×C₁₃	—	4	8	no	—
332	C₂³×C₁₃	—	4	8	no	—
333	C₂³×C₁₃	—	4	32	no	—
334	C₂³×C₁₃	—	4	16	no	—
335	C₂³×C₁₃	C₂⁵	1	4	yes	—
336	C₂³×C₁₃	C₂⁵	1	16	yes	—
337	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
338	C₂³×C₁₃	C₂⁵	1	2	yes	—
339	Q₈×C₁₃	—	2	16	no	—
340	Q₈×C₁₃	—	2	8	no	—
341	Q₈×C₁₃	—	4	8	no	—
342	Q₈×C₁₃	—	4	2	no	—
343	D₄×C₁₃	—	2	16	no	—
344	D₄×C₁₃	—	2	32	no	—
345	D₄×C₁₃	—	2	16	no	—
346	D₄×C₁₃	—	2	16	no	—
347	D₄×C₁₃	—	2	8	no	—
348	D₄×C₁₃	—	2	16	no	—
349	D₄×C₁₃	—	2	16	no	—
350	D₄×C₁₃	—	4	32	no	—
351	D₄×C₁₃	—	4	32	no	—
352	D₄×C₁₃	—	4	8	no	—
353	D₄×C₁₃	—	4	16	no	—
354	D₄×C₁₃	—	4	8	no	—
355	D₄×C₁₃	—	4	16	no	—
356	D₄×C₁₃	—	4	2	no	—
357	D₄×C₁₃	—	4	4	no	—
358	C₂×C₄×C₁₃	—	2	4	no	—
359	C₂×C₄×C₁₃	—	2	4	no	—
360	C₂×C₄×C₁₃	—	2	4	no	—
361	C₂×C₄×C₁₃	—	2	4	no	—
362	C₂×C₄×C₁₃	—	2	4	no	—
363	C₂×C₄×C₁₃	—	2	32	no	—
364	C₂×C₄×C₁₃	—	2	16	no	—
365	C₂×C₄×C₁₃	—	2	4	no	—
366	C₂×C₄×C₁₃	—	2	2	no	—
367	C₂×C₄×C₁₃	—	2	8	no	—
368	C₂×C₄×C₁₃	—	4	1	no	—
369	C₂×C₄×C₁₃	—	4	2	no	—
370	C₂×C₄×C₁₃	—	4	8	no	—
371	C₂×C₄×C₁₃	—	4	16	no	—
372	C₂×C₄×C₁₃	—	4	32	no	—
373	C₂×C₄×C₁₃	H(5,𝔽₂)	1	8	yes	complemented
374	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
375	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
376	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
377	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
378	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
379	C₂×C₄×C₁₃	C₂⁵	1	16	yes	—
380	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
381	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
382	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
383	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
384	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	8	yes	complemented
385	C₂²×#41	C₂²×C₁₃	1	4	yes	complemented
386	#562	C₂²×C₁₃	1	8	yes	complemented
387	H(3,𝔽₄)	C₂²×C₁₃	1	8	yes	complemented
388	#560	C₂²×C₁₃	1	16	yes	complemented
389	#559	C₂²×C₁₃	1	16	yes	complemented
390	#556	C₂²×C₁₃	1	8	yes	complemented
391	#555	C₂²×C₁₃	1	4	yes	complemented
392	#555	C₂²×C₁₃	1	8	yes	complemented
393	#554	C₂²×C₁₃	1	8	yes	complemented
394	#553	C₂²×C₁₃	1	16	yes	complemented
395	#553	C₂²×C₁₃	1	16	yes	complemented
396	#550	C₂²×C₁₃	1	16	yes	complemented
397	#550	C₂²×C₁₃	1	8	yes	complemented
398	#550	C₂²×C₁₃	1	8	yes	complemented
399	#548	C₂²×C₁₃	1	16	yes	complemented
400	#547	C₂²×C₁₃	1	8	yes	complemented
401	#547	C₂²×C₁₃	1	8	yes	complemented
402	#546	C₂²×C₁₃	1	16	yes	complemented
403	#546	C₂²×C₁₃	1	32	yes	complemented
404	#546	C₂²×C₁₃	1	16	yes	complemented
405	#546	C₂²×C₁₃	1	16	yes	complemented
406	D₄²	C₂²×C₁₃	1	16	yes	complemented
407	D₄²	C₂²×C₁₃	1	16	yes	complemented
408	D₄²	C₂²×C₁₃	1	4	yes	complemented
409	D₄²	C₂²×C₁₃	1	8	yes	complemented
410	D₄²	C₂²×C₁₃	1	16	yes	complemented
411	D₄²	C₂²×C₁₃	1	8	yes	complemented
412	#542	C₂²×C₁₃	1	16	yes	complemented
413	#540	C₂²×C₁₃	1	8	yes	complemented
414	#540	C₂²×C₁₃	1	8	yes	complemented
415	#538	C₂²×C₁₃	1	16	yes	complemented
416	#538	C₂²×C₁₃	1	32	yes	complemented
417	#537	C₂²×C₁₃	1	8	yes	complemented
418	#537	C₂²×C₁₃	1	16	yes	complemented
419	#535	C₂²×C₁₃	1	8	yes	complemented
420	#535	C₂²×C₁₃	1	16	yes	complemented
421	#535	C₂²×C₁₃	1	16	yes	complemented
422	#535	C₂²×C₁₃	1	8	yes	complemented
423	#534	C₂²×C₁₃	1	16	yes	complemented
424	#533	C₂²×C₁₃	1	2	yes	complemented
425	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
426	#533	C₂²×C₁₃	1	4	yes	complemented
427	#532	C₂²×C₁₃	1	4	yes	complemented
428	#532	C₂²×C₁₃	1	4	yes	complemented
429	#532	C₂²×C₁₃	1	4	yes	complemented
430	#532	C₂²×C₁₃	1	4	yes	complemented
431	#532	C₂²×C₁₃	1	4	yes	complemented
432	#532	C₂²×C₁₃	1	4	yes	complemented
433	#532	C₂²×C₁₃	1	4	yes	complemented
434	#532	C₂²×C₁₃	1	4	yes	complemented
435	#532	C₂²×C₁₃	1	2	yes	complemented
436	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
437	#532	C₂²×C₁₃	1	8	yes	complemented
438	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
439	C₂×#127	C₂²×C₁₃	1	2	yes	complemented
440	C₂×#127	C₂²×C₁₃	1	4	yes	complemented
441	#529	C₂²×C₁₃	1	4	yes	complemented
442	#529	C₂²×C₁₃	1	4	yes	complemented
443	#529	C₂²×C₁₃	1	4	yes	complemented
444	C₂×#124	C₂²×C₁₃	1	4	yes	complemented
445	#525	C₂²×C₁₃	1	4	yes	complemented
446	#525	C₂²×C₁₃	1	2	yes	complemented
447	#525	C₂²×C₁₃	1	16	yes	complemented
448	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
449	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
450	C₂×#121	C₂²×C₁₃	1	16	yes	complemented
451	#520	C₂²×C₁₃	1	8	yes	complemented
452	#518	C₂²×C₁₃	1	8	yes	complemented
453	C₄×#41	C₂²×C₁₃	1	4	yes	complemented
454	C₄×#41	C₂²×C₁₃	1	2	yes	complemented
455	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
456	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
457	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
458	C₂²×C₁₃	—	2	2	no	—
459	C₂²×C₁₃	—	2	2	no	—
460	C₂²×C₁₃	—	2	2	no	—
461	C₂²×C₁₃	—	2	16	no	—
462	C₂²×C₁₃	—	2	8	no	—
463	C₂²×C₁₃	—	2	16	no	—
464	C₂²×C₁₃	—	2	1	no	—
465	C₂²×C₁₃	—	2	4	no	—
466	C₂²×C₁₃	—	2	16	no	—
467	C₂²×C₁₃	—	4	4	no	—
468	C₂²×C₁₃	—	8	16	no	—
469	C₂²×C₁₃	—	16	16	no	—
470	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
471	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
472	C₄×C₁₃	—	2	2	no	—
473	C₄×C₁₃	—	2	2	no	—
474	C₄×C₁₃	—	2	8	no	—
475	C₄×C₁₃	—	2	16	no	—
476	C₄×C₁₃	—	2	2	no	—
477	C₄×C₁₃	—	2	1	no	—
478	C₄×C₁₃	—	2	4	no	—
479	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
480	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
481	C₄×C₁₃	#585	1	2	yes	—
482	H(5,𝔽₂)	—	4	32	no	—
483	C₂×#41	—	4	16	no	—
484	C₂×#41	C₂³×C₁₃	1	4	yes	—
485	C₂×#41	C₂³×C₁₃	1	8	yes	—
486	C₂×#41	C₂³×C₁₃	1	2	yes	—
487	C₂×#41	C₂³×C₁₃	1	16	yes	—
488	C₂×#41	C₂³×C₁₃	1	8	yes	—
489	C₂×#41	C₂³×C₁₃	1	8	yes	—
490	C₂×#41	C₂³×C₁₃	1	8	yes	—
491	C₂×#41	C₂³×C₁₃	1	16	yes	—
492	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
493	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
494	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
495	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
496	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
497	C₂²×D₄	C₂³×C₁₃	1	32	yes	—
498	C₂²×D₄	C₂³×C₁₃	1	16	yes	—
499	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
500	C₂²×D₄	C₂³×C₁₃	1	16	yes	—
501	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
502	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
503	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
504	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
505	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
506	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
507	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
508	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
509	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
510	#127	C₂³×C₁₃	1	4	yes	—
511	#127	C₂³×C₁₃	1	4	yes	—
512	#127	C₂³×C₁₃	1	4	yes	—
513	#127	C₂³×C₁₃	1	4	yes	—
514	#127	C₂³×C₁₃	1	16	yes	—
515	#127	C₂³×C₁₃	1	8	yes	—
516	#127	C₂³×C₁₃	1	1	yes	characteristic
517	#127	C₂³×C₁₃	1	16	yes	—
518	#126	C₂³×C₁₃	1	8	yes	—
519	#126	C₂³×C₁₃	1	32	yes	—
520	#125	C₂³×C₁₃	1	4	yes	—
521	#125	C₂³×C₁₃	1	2	yes	—
522	#125	C₂³×C₁₃	1	8	yes	—
523	#124	C₂³×C₁₃	1	8	yes	—
524	#124	C₂³×C₁₃	1	8	yes	—
525	#124	C₂³×C₁₃	1	8	yes	—
526	#124	C₂³×C₁₃	1	8	yes	—
527	#124	C₂³×C₁₃	1	4	yes	—
528	#124	C₂³×C₁₃	1	2	yes	—
529	#124	C₂³×C₁₃	1	16	yes	—
530	#124	C₂³×C₁₃	1	16	yes	—
531	#124	C₂³×C₁₃	1	32	yes	—
532	#123	C₂³×C₁₃	1	8	yes	—
533	#123	C₂³×C₁₃	1	4	yes	—
534	#123	C₂³×C₁₃	1	32	yes	—
535	#123	C₂³×C₁₃	1	32	yes	—
536	#123	C₂³×C₁₃	1	32	yes	—
537	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
538	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
539	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
540	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
541	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
542	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
543	#121	C₂³×C₁₃	1	4	yes	—
544	#121	C₂³×C₁₃	1	8	yes	—
545	#121	C₂³×C₁₃	1	8	yes	—
546	#121	C₂³×C₁₃	1	8	yes	—
547	#121	C₂³×C₁₃	1	8	yes	—
548	#121	C₂³×C₁₃	1	8	yes	—
549	#121	C₂³×C₁₃	1	8	yes	—
550	#121	C₂³×C₁₃	1	8	yes	—
551	#121	C₂³×C₁₃	1	8	yes	—
552	#121	C₂³×C₁₃	1	32	yes	—
553	#121	C₂³×C₁₃	1	16	yes	—
554	#121	C₂³×C₁₃	1	16	yes	—
555	#121	C₂³×C₁₃	1	32	yes	—
556	#121	C₂³×C₁₃	1	4	yes	—
557	#121	C₂³×C₁₃	1	4	yes	—
558	#121	C₂³×C₁₃	1	16	yes	—
559	#121	C₂³×C₁₃	1	16	yes	—
560	#121	C₂³×C₁₃	1	16	yes	—
561	#121	C₂³×C₁₃	1	32	yes	—
562	#121	C₂³×C₁₃	1	32	yes	—
563	#121	C₂³×C₁₃	1	32	yes	—
564	#120	C₂³×C₁₃	1	4	yes	—
565	#120	C₂³×C₁₃	1	32	yes	—
566	#120	C₂³×C₁₃	1	16	yes	—
567	#120	C₂³×C₁₃	1	32	yes	—
568	#120	C₂³×C₁₃	1	16	yes	—
569	#120	C₂³×C₁₃	1	32	yes	—
570	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
571	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
572	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
573	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
574	C₄×D₄	C₂³×C₁₃	1	8	yes	—
575	C₄×D₄	C₂³×C₁₃	1	8	yes	—
576	C₄×D₄	C₂³×C₁₃	1	8	yes	—
577	C₄×D₄	C₂³×C₁₃	1	8	yes	—
578	C₄×D₄	C₂³×C₁₃	1	8	yes	—
579	C₄×D₄	C₂³×C₁₃	1	8	yes	—
580	C₄×D₄	C₂³×C₁₃	1	8	yes	—
581	C₄×D₄	C₂³×C₁₃	1	8	yes	—
582	C₄×D₄	C₂³×C₁₃	1	8	yes	—
583	C₄×D₄	C₂³×C₁₃	1	8	yes	—
584	C₄×D₄	C₂³×C₁₃	1	8	yes	—
585	C₄×D₄	C₂³×C₁₃	1	4	yes	—
586	C₄×D₄	C₂³×C₁₃	1	4	yes	—
587	C₄×D₄	C₂³×C₁₃	1	4	yes	—
588	C₄×D₄	C₂³×C₁₃	1	32	yes	—
589	C₄×D₄	C₂³×C₁₃	1	16	yes	—
590	C₄×D₄	C₂³×C₁₃	1	32	yes	—
591	C₄×D₄	C₂³×C₁₃	1	16	yes	—
592	#117	C₂³×C₁₃	1	4	yes	—
593	#117	C₂³×C₁₃	1	4	yes	—
594	#117	C₂³×C₁₃	1	2	yes	—
595	#117	C₂³×C₁₃	1	8	yes	—
596	#117	C₂³×C₁₃	1	8	yes	—
597	#117	C₂³×C₁₃	1	16	yes	—
598	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
599	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
600	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₁₃	1	32	yes	—
604	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
605	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
606	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
607	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
608	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
609	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
610	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
611	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
612	C₂×C₁₃	—	2	4	no	—
613	C₂×C₁₃	—	4	1	no	—
614	C₂×C₁₃	—	4	16	no	—
615	C₂×C₁₃	—	4	4	no	—
616	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	2	yes	—
617	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
618	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
619	C₂⁴	C₂⁴×C₁₃	1	8	yes	—
620	C₂⁴	C₂⁴×C₁₃	1	16	yes	—
621	#41	—	2	32	no	—
622	#41	—	2	16	no	—
623	#41	—	4	16	no	—
624	#41	—	4	4	no	—
625	#41	—	4	16	no	—
626	#41	—	4	16	no	—
627	#41	—	4	32	no	—
628	#41	—	4	32	no	—
629	C₂×Q₈	—	4	8	no	—
630	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
631	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
632	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
633	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
634	C₂×D₄	—	2	16	no	—
635	C₂×D₄	—	4	8	no	—
636	C₂×D₄	—	4	32	no	—
637	C₂×D₄	—	4	32	no	—
638	C₂×D₄	—	4	8	no	—
639	C₂×D₄	—	4	16	no	—
640	C₂×D₄	—	4	16	no	—
641	C₂×D₄	—	4	64	no	—
642	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
643	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
644	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
645	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
646	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
647	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
648	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
649	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
650	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
651	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
652	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
653	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
654	C₂×D₄	C₂⁴×C₁₃	1	32	yes	—
655	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
656	C₂×D₄	C₂⁴×C₁₃	1	32	yes	—
657	C₂²×C₄	—	2	8	no	—
658	C₂²×C₄	—	4	16	no	—
659	C₂²×C₄	—	4	2	no	—
660	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
661	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
662	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
663	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
664	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
665	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
666	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
667	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
668	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
669	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
670	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
671	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
672	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
673	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
674	C₂²×C₄	C₂⁴×C₁₃	1	32	yes	—
675	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
676	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
677	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
678	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
679	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
680	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
681	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
682	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
683	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
684	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
685	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
686	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
687	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
688	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
689	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
690	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
691	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
692	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
693	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
694	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
695	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
696	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
697	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
698	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
699	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
700	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
701	C₄²	C₂⁴×C₁₃	1	2	yes	—
702	C₄²	C₂⁴×C₁₃	1	2	yes	—
703	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
704	C₄²	C₂⁴×C₁₃	1	2	yes	—
705	C₄²	C₂⁴×C₁₃	1	2	yes	—
706	C₄²	C₂⁴×C₁₃	1	2	yes	—
707	C₄²	C₂⁴×C₁₃	1	2	yes	—
708	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
709	C₄²	C₂⁴×C₁₃	1	4	yes	—
710	C₄²	C₂⁴×C₁₃	1	8	yes	—
711	C₄²	C₂⁴×C₁₃	1	16	yes	—
712	C₁₃	#62834	1	1	yes	characteristic, direct product factor, Sylow
713	C₂³	—	2	4	no	—
714	C₂³	—	2	16	no	—
715	C₂³	—	4	1	no	—
716	C₂³	—	4	8	no	—
717	C₂³	—	4	8	no	—
718	C₂³	—	4	32	no	—
719	C₂³	—	4	16	no	—
720	C₂³	C₂⁵×C₁₃	1	4	yes	—
721	C₂³	C₂⁵×C₁₃	1	16	yes	—
722	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
723	C₂³	C₂⁵×C₁₃	1	2	yes	—
724	Q₈	—	2	16	no	—
725	Q₈	—	2	8	no	—
726	Q₈	—	4	8	no	—
727	Q₈	—	4	2	no	—
728	D₄	—	2	16	no	—
729	D₄	—	2	32	no	—
730	D₄	—	2	16	no	—
731	D₄	—	2	16	no	—
732	D₄	—	2	8	no	—
733	D₄	—	2	16	no	—
734	D₄	—	2	16	no	—
735	D₄	—	4	32	no	—
736	D₄	—	4	32	no	—
737	D₄	—	4	8	no	—
738	D₄	—	4	16	no	—
739	D₄	—	4	8	no	—
740	D₄	—	4	16	no	—
741	D₄	—	4	2	no	—
742	D₄	—	4	4	no	—
743	C₂×C₄	—	2	4	no	—
744	C₂×C₄	—	2	4	no	—
745	C₂×C₄	—	2	4	no	—
746	C₂×C₄	—	2	4	no	—
747	C₂×C₄	—	2	4	no	—
748	C₂×C₄	—	2	32	no	—
749	C₂×C₄	—	2	16	no	—
750	C₂×C₄	—	2	4	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	8	no	—
753	C₂×C₄	—	4	8	no	—
754	C₂×C₄	—	4	1	no	—
755	C₂×C₄	—	4	2	no	—
756	C₂×C₄	—	4	16	no	—
757	C₂×C₄	—	4	32	no	—
758	C₂×C₄	C₁₃×H(5,𝔽₂)	1	8	yes	complemented
759	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
760	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
761	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
762	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
763	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
764	C₂×C₄	C₂⁵×C₁₃	1	16	yes	—
765	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
766	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
767	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
768	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
769	C₂²	—	2	2	no	—
770	C₂²	—	2	2	no	—
771	C₂²	—	2	2	no	—
772	C₂²	—	2	16	no	—
773	C₂²	—	2	8	no	—
774	C₂²	—	2	16	no	—
775	C₂²	—	2	1	no	—
776	C₂²	—	2	4	no	—
777	C₂²	—	2	16	no	—
778	C₂²	—	4	4	no	—
779	C₂²	—	8	16	no	—
780	C₂²	—	16	16	no	—
781	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
782	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
783	C₄	—	2	2	no	—
784	C₄	—	2	2	no	—
785	C₄	—	2	8	no	—
786	C₄	—	2	16	no	—
787	C₄	—	2	2	no	—
788	C₄	—	2	1	no	—
789	C₄	—	2	4	no	—
790	C₄	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
791	C₄	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
792	C₄	C₁₃×#585	1	2	yes	—
793	C₂	—	2	4	no	—
794	C₂	—	4	1	no	—
795	C₂	—	4	16	no	—
796	C₂	—	4	4	no	—
797	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	2	yes	—
798	C₂	C₂×C₁₃×#585	1	1	yes	characteristic

	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×#3558	C₂	semidirect
2. C₁₃×#3549	C₂	semidirect
3. C₁₃×#3548	C₂	semidirect
4. C₁₃×#3546	C₂	semidirect
5. C₁₃×#3537	C₂	semidirect
6. C₁₃×#3519	C₂	semidirect
7. C₁₃×#3511	C₂	semidirect
8. C₁₃×#3508	C₂	semidirect
9. C₁₃×#3506	C₂	semidirect
10. C₁₃×#3498	C₂	semidirect
11. C₁₃×#3496	C₂	semidirect
12. C₁₃×#3488	C₂	semidirect
13. C₁₃×#3444	C₂	semidirect
14. C₂×C₁₃×#532	C₂	semidirect
15. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
16. C₂²×C₁₃×#41	C₂²	semidirect
17. C₁₃×#562	C₂²	semidirect
18. C₁₃×H(3,𝔽₄)	C₂²	semidirect
19. C₁₃×#560	C₂²	semidirect
20. C₁₃×#559	C₂²	semidirect
21. C₁₃×#556	C₂²	semidirect
22. C₁₃×#555	C₂²	semidirect
23. C₁₃×#555	C₂²	semidirect
24. C₁₃×#554	C₂²	semidirect
25. C₁₃×#553	C₂²	semidirect
26. C₁₃×#553	C₂²	semidirect
27. C₁₃×#550	C₂²	semidirect
28. C₁₃×#550	C₂²	semidirect
29. C₁₃×#550	C₂²	semidirect
30. C₁₃×#548	C₂²	semidirect
31. C₁₃×#547	C₂²	semidirect
32. C₁₃×#547	C₂²	semidirect
33. C₁₃×#546	C₂²	semidirect
34. C₁₃×#546	C₂²	semidirect
35. C₁₃×#546	C₂²	semidirect
36. C₁₃×#546	C₂²	semidirect
37. D₄²×C₁₃	C₂²	semidirect
38. D₄²×C₁₃	C₂²	semidirect
39. D₄²×C₁₃	C₂²	semidirect
40. D₄²×C₁₃	C₂²	semidirect
41. D₄²×C₁₃	C₂²	semidirect
42. D₄²×C₁₃	C₂²	semidirect
43. C₁₃×#542	C₂²	semidirect
44. C₁₃×#540	C₂²	semidirect
45. C₁₃×#540	C₂²	semidirect
46. C₁₃×#538	C₂²	semidirect
47. C₁₃×#538	C₂²	semidirect
48. C₁₃×#537	C₂²	semidirect
49. C₁₃×#537	C₂²	semidirect
50. C₁₃×#535	C₂²	semidirect
51. C₁₃×#535	C₂²	semidirect
52. C₁₃×#535	C₂²	semidirect
53. C₁₃×#535	C₂²	semidirect
54. C₁₃×#534	C₂²	semidirect
55. C₁₃×#533	C₂²	semidirect
56. C₁₃×#533	C₂²	semidirect
57. C₁₃×#533	C₂²	semidirect
58. C₁₃×#532	C₂²	semidirect
59. C₁₃×#532	C₂²	semidirect
60. C₁₃×#532	C₂²	semidirect
61. C₁₃×#532	C₂²	semidirect
62. C₁₃×#532	C₂²	semidirect
63. C₁₃×#532	C₂²	semidirect
64. C₁₃×#532	C₂²	semidirect
65. C₁₃×#532	C₂²	semidirect
66. C₁₃×#532	C₂²	semidirect
67. C₁₃×#532	C₂²	semidirect
68. C₁₃×#532	C₂²	semidirect
69. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
70. C₂×C₁₃×#127	C₂²	semidirect
71. C₂×C₁₃×#127	C₂²	semidirect
72. C₁₃×#529	C₂²	semidirect
73. C₁₃×#529	C₂²	semidirect
74. C₁₃×#529	C₂²	semidirect
75. C₂×C₁₃×#124	C₂²	semidirect
76. C₁₃×#525	C₂²	semidirect
77. C₁₃×#525	C₂²	semidirect
78. C₁₃×#525	C₂²	semidirect
79. C₂×C₁₃×#121	C₂²	semidirect
80. C₂×C₁₃×#121	C₂²	semidirect
81. C₂×C₁₃×#121	C₂²	semidirect
82. C₁₃×#520	C₂²	semidirect
83. C₁₃×#518	C₂²	semidirect
84. C₄×C₁₃×#41	C₂²	semidirect
85. C₄×C₁₃×#41	C₂²	semidirect
86. C₂×C₄×D₄×C₁₃	C₂²	semidirect
87. C₂×C₄×D₄×C₁₃	C₂²	semidirect
88. C₂²×C₄²×C₁₃	C₂²	semidirect
219. #62834	C₁₃	direct (N × H)
314. #3558	C₂×C₁₃	semidirect
315. #3549	C₂×C₁₃	semidirect
316. #3548	C₂×C₁₃	semidirect
317. #3546	C₂×C₁₃	semidirect
318. #3537	C₂×C₁₃	semidirect
319. #3519	C₂×C₁₃	semidirect
320. #3511	C₂×C₁₃	semidirect
321. #3508	C₂×C₁₃	semidirect
322. #3506	C₂×C₁₃	semidirect
323. #3498	C₂×C₁₃	semidirect
324. #3496	C₂×C₁₃	semidirect
325. #3488	C₂×C₁₃	semidirect
326. #3444	C₂×C₁₃	semidirect
327. C₂×#532	C₂×C₁₃	semidirect
373. C₂×C₄×C₁₃	H(5,𝔽₂)	semidirect
384. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
385. C₂²×#41	C₂²×C₁₃	semidirect
386. #562	C₂²×C₁₃	semidirect
387. H(3,𝔽₄)	C₂²×C₁₃	semidirect
388. #560	C₂²×C₁₃	semidirect
389. #559	C₂²×C₁₃	semidirect
390. #556	C₂²×C₁₃	semidirect
391. #555	C₂²×C₁₃	semidirect
392. #555	C₂²×C₁₃	semidirect
393. #554	C₂²×C₁₃	semidirect
394. #553	C₂²×C₁₃	semidirect
395. #553	C₂²×C₁₃	semidirect
396. #550	C₂²×C₁₃	semidirect
397. #550	C₂²×C₁₃	semidirect
398. #550	C₂²×C₁₃	semidirect
399. #548	C₂²×C₁₃	semidirect
400. #547	C₂²×C₁₃	semidirect
401. #547	C₂²×C₁₃	semidirect
402. #546	C₂²×C₁₃	semidirect
403. #546	C₂²×C₁₃	semidirect
404. #546	C₂²×C₁₃	semidirect
405. #546	C₂²×C₁₃	semidirect
406. D₄²	C₂²×C₁₃	semidirect
407. D₄²	C₂²×C₁₃	semidirect
408. D₄²	C₂²×C₁₃	semidirect
409. D₄²	C₂²×C₁₃	semidirect
410. D₄²	C₂²×C₁₃	semidirect
411. D₄²	C₂²×C₁₃	semidirect
412. #542	C₂²×C₁₃	semidirect
413. #540	C₂²×C₁₃	semidirect
414. #540	C₂²×C₁₃	semidirect
415. #538	C₂²×C₁₃	semidirect
416. #538	C₂²×C₁₃	semidirect
417. #537	C₂²×C₁₃	semidirect
418. #537	C₂²×C₁₃	semidirect
419. #535	C₂²×C₁₃	semidirect
420. #535	C₂²×C₁₃	semidirect
421. #535	C₂²×C₁₃	semidirect
422. #535	C₂²×C₁₃	semidirect
423. #534	C₂²×C₁₃	semidirect
424. #533	C₂²×C₁₃	semidirect
425. #533	C₂²×C₁₃	semidirect
426. #533	C₂²×C₁₃	semidirect
427. #532	C₂²×C₁₃	semidirect
428. #532	C₂²×C₁₃	semidirect
429. #532	C₂²×C₁₃	semidirect
430. #532	C₂²×C₁₃	semidirect
431. #532	C₂²×C₁₃	semidirect
432. #532	C₂²×C₁₃	semidirect
433. #532	C₂²×C₁₃	semidirect
434. #532	C₂²×C₁₃	semidirect
435. #532	C₂²×C₁₃	semidirect
436. #532	C₂²×C₁₃	semidirect
437. #532	C₂²×C₁₃	semidirect
438. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
439. C₂×#127	C₂²×C₁₃	semidirect
440. C₂×#127	C₂²×C₁₃	semidirect
441. #529	C₂²×C₁₃	semidirect
442. #529	C₂²×C₁₃	semidirect
443. #529	C₂²×C₁₃	semidirect
444. C₂×#124	C₂²×C₁₃	semidirect
445. #525	C₂²×C₁₃	semidirect
446. #525	C₂²×C₁₃	semidirect
447. #525	C₂²×C₁₃	semidirect
448. C₂×#121	C₂²×C₁₃	semidirect
449. C₂×#121	C₂²×C₁₃	semidirect
450. C₂×#121	C₂²×C₁₃	semidirect
451. #520	C₂²×C₁₃	semidirect
452. #518	C₂²×C₁₃	semidirect
453. C₄×#41	C₂²×C₁₃	semidirect
454. C₄×#41	C₂²×C₁₃	semidirect
455. C₂×C₄×D₄	C₂²×C₁₃	semidirect
456. C₂×C₄×D₄	C₂²×C₁₃	semidirect
457. C₂²×C₄²	C₂²×C₁₃	semidirect
712. C₁₃	#62834	direct (N × H)
758. C₂×C₄	C₁₃×H(5,𝔽₂)	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3558	2
C₁₃×#3549	2
C₁₃×#3548	2
C₁₃×#3546	2
C₁₃×#3537	2
C₁₃×#3519	2
C₁₃×#3511	2
C₁₃×#3508	2
C₁₃×#3506	2
C₁₃×#3498	2
C₁₃×#3496	2
C₁₃×#3488	2
C₁₃×#3444	2
C₂×C₁₃×#532	2
#62834	13

Subgroups — C13×#62834 #15749173

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62834 #15749173