Subgroups — C₂×C₁₃×#3314 #15747465

Order 3328.

2298 conjugacy classes of subgroups.

The subgroup lattice has 824 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×#546	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3314	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#489	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#484	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#480	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#474	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#468	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#464	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#452	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#450	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×#417	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#102	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
23	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₁₃×#554	—	2	4	no	—
25	C₁₃×#554	C₂²	1	8	yes	complemented
26	C₁₃×#546	—	2	4	no	—
27	C₁₃×#546	C₂²	1	8	yes	—
28	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₁₃×#125	—	2	1	no	—
30	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#123	—	2	1	no	—
32	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
33	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
34	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₁₃×#121	—	2	1	no	—
38	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#120	—	2	1	no	—
40	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₄×D₄×C₁₃	—	2	1	no	—
42	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
44	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
45	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
46	C₂²×C₁₃×C₂²⋊C₄	—	2	1	no	—
47	C₁₃×#489	C₂²	1	8	yes	complemented
48	C₁₃×#484	C₂²	1	8	yes	complemented
49	C₁₃×#480	C₂²	1	8	yes	complemented
50	C₁₃×#474	C₂²	1	8	yes	complemented
51	C₁₃×#468	C₂²	1	8	yes	complemented
52	C₁₃×#467	C₂²	1	8	yes	complemented
53	C₁₃×#464	C₂²	1	8	yes	complemented
54	C₁₃×#452	C₂²	1	8	yes	complemented
55	C₁₃×#450	C₂²	1	8	yes	complemented
56	C₁₃×#440	C₂²	1	8	yes	complemented
57	C₁₃×#435	C₂²	1	8	yes	complemented
58	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
62	C₁₃×#417	C₂²	1	8	yes	complemented
63	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
66	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
67	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
68	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
69	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
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	8	yes	complemented
74	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
75	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
76	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic, complemented
77	C₂⁵×C₁₃	—	2	1	no	—
78	C₂×C₁₃×#41	—	2	2	no	—
79	C₂×C₁₃×#41	—	2	4	no	—
80	C₂×C₁₃×#41	—	4	2	no	—
81	C₂×C₁₃×#41	C₂³	1	4	yes	—
82	C₂²×Q₈×C₁₃	—	2	1	no	—
83	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
84	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₁₃	—	2	4	no	—
86	C₂²×D₄×C₁₃	—	2	1	no	—
87	C₂²×D₄×C₁₃	—	2	1	no	—
88	C₂²×D₄×C₁₃	—	2	1	no	—
89	C₂²×D₄×C₁₃	—	2	2	no	—
90	C₂²×D₄×C₁₃	—	4	2	no	—
91	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
92	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
93	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
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×Q₁₆	—	4	2	no	—
102	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	complemented
103	C₂×C₁₃×SD₁₆	—	2	4	no	—
104	C₂×C₁₃×SD₁₆	—	4	2	no	—
105	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
106	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
107	C₂×C₁₃×M₁₆	—	4	2	no	—
108	C₂×C₁₃×M₁₆	C₂³	1	4	yes	complemented
109	C₂²×C₈×C₁₃	—	4	2	no	—
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	1	yes	characteristic
114	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
115	C₁₃×C₄⋊Q₈	—	2	2	no	—
116	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	complemented
117	C₁₃×#125	—	2	8	no	—
118	C₁₃×#124	—	2	2	no	—
119	C₁₃×#124	C₂³	1	4	yes	—
120	C₁₃×#123	—	2	8	no	—
121	C₁₃×C₂²⋊Q₈	—	2	2	no	—
122	C₁₃×C₂²⋊Q₈	—	2	2	no	—
123	C₁₃×C₂²⋊Q₈	—	2	2	no	—
124	C₁₃×C₂²⋊Q₈	—	2	8	no	—
125	C₁₃×C₂²⋊Q₈	—	2	8	no	—
126	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
127	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
128	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	complemented
129	C₁₃×#121	—	2	2	no	—
130	C₁₃×#121	—	2	8	no	—
131	C₁₃×#121	C₂³	1	4	yes	—
132	C₁₃×#120	—	2	8	no	—
133	C₄×Q₈×C₁₃	—	2	2	no	—
134	C₄×Q₈×C₁₃	C₂³	1	4	yes	complemented
135	C₄×D₄×C₁₃	—	2	8	no	—
136	C₄×D₄×C₁₃	—	2	2	no	—
137	C₄×D₄×C₁₃	D₄	1	4	yes	—
138	C₄×D₄×C₁₃	C₂³	1	4	yes	—
139	C₄×D₄×C₁₃	C₂³	1	4	yes	—
140	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
141	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
142	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
143	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
144	C₂×C₁₃×C₄⋊C₄	—	2	1	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	4	yes	—
154	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	complemented
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	—	2	8	no	—
164	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
165	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
166	C₂×C₄²×C₁₃	—	2	1	no	—
167	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
168	C₁₃×#107	C₂³	1	4	yes	complemented
169	C₁₃×#107	C₂³	1	4	yes	complemented
170	C₁₃×#107	C₂³	1	4	yes	complemented
171	C₁₃×C₄⋊C₈	C₂³	1	4	yes	complemented
172	C₁₃×#103	C₂³	1	4	yes	complemented
173	C₁₃×#103	C₂³	1	4	yes	complemented
174	C₁₃×#103	C₂³	1	4	yes	complemented
175	C₁₃×#103	C₂³	1	4	yes	complemented
176	C₁₃×#102	C₂³	1	4	yes	—
177	C₁₃×#102	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	complemented
184	C₁₃×#97	C₂³	1	4	yes	complemented
185	C₂×#3314	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	—	2	4	no	—
189	C₂⁴×C₁₃	—	4	4	no	—
190	C₂⁴×C₁₃	—	4	4	no	—
191	C₂⁴×C₁₃	—	8	2	no	—
192	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
193	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
194	C₁₃×#41	—	2	8	no	—
195	C₁₃×#41	—	4	4	no	—
196	C₁₃×#41	—	4	8	no	—
197	C₂×Q₈×C₁₃	—	2	1	no	—
198	C₂×Q₈×C₁₃	—	2	1	no	—
199	C₂×Q₈×C₁₃	—	2	4	no	—
200	C₂×Q₈×C₁₃	—	2	2	no	—
201	C₂×Q₈×C₁₃	—	2	2	no	—
202	C₂×Q₈×C₁₃	—	2	2	no	—
203	C₂×Q₈×C₁₃	—	2	2	no	—
204	C₂×Q₈×C₁₃	—	8	2	no	—
205	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
206	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
207	C₂×D₄×C₁₃	—	2	4	no	—
208	C₂×D₄×C₁₃	—	2	8	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	4	no	—
213	C₂×D₄×C₁₃	—	2	1	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	8	no	—
219	C₂×D₄×C₁₃	—	4	4	no	—
220	C₂×D₄×C₁₃	—	4	4	no	—
221	C₂×D₄×C₁₃	—	8	2	no	—
222	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
223	C₂×D₄×C₁₃	#41	1	4	yes	—
224	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
225	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
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	2	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	1	no	—
236	C₂²×C₄×C₁₃	—	2	4	no	—
237	C₂²×C₄×C₁₃	—	2	4	no	—
238	C₂²×C₄×C₁₃	—	2	4	no	—
239	C₂²×C₄×C₁₃	—	2	4	no	—
240	C₂²×C₄×C₁₃	—	4	4	no	—
241	C₂²×C₄×C₁₃	—	8	2	no	—
242	C₂²×C₄×C₁₃	—	8	2	no	—
243	C₂²×C₄×C₁₃	—	8	2	no	—
244	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
245	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
246	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
253	C₁₃×Q₁₆	—	4	4	no	—
254	C₁₃×SD₁₆	—	2	8	no	—
255	C₁₃×SD₁₆	—	4	4	no	—
256	C₁₃×M₁₆	—	4	4	no	—
257	C₂×C₈×C₁₃	—	2	2	no	—
258	C₂×C₈×C₁₃	—	2	2	no	—
259	C₂×C₈×C₁₃	—	2	2	no	—
260	C₂×C₈×C₁₃	—	2	2	no	—
261	C₂×C₈×C₁₃	—	4	4	no	—
262	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
263	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
264	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
265	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
266	C₁₃×C₄⋊C₄	—	2	1	no	—
267	C₁₃×C₄⋊C₄	—	2	4	no	—
268	C₁₃×C₄⋊C₄	—	2	1	no	—
269	C₁₃×C₄⋊C₄	—	2	1	no	—
270	C₁₃×C₄⋊C₄	—	2	4	no	—
271	C₁₃×C₄⋊C₄	—	2	4	no	—
272	C₁₃×C₄⋊C₄	—	2	4	no	—
273	C₁₃×C₄⋊C₄	—	2	4	no	—
274	C₁₃×C₄⋊C₄	—	2	4	no	—
275	C₁₃×C₄⋊C₄	—	2	4	no	—
276	C₁₃×C₄⋊C₄	—	2	1	no	—
277	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
278	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
279	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
280	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
281	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
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	—	2	4	no	—
287	C₁₃×C₂²⋊C₄	—	2	4	no	—
288	C₁₃×C₂²⋊C₄	—	2	4	no	—
289	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
290	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
291	C₄²×C₁₃	—	2	4	no	—
292	C₄²×C₁₃	C₂×D₄	1	2	yes	—
293	C₄²×C₁₃	C₂⁴	1	2	yes	—
294	C₂×#554	C₂×C₁₃	1	1	yes	characteristic, complemented
295	C₂×#546	C₂×C₁₃	1	1	yes	characteristic
296	#3314	C₂×C₁₃	1	16	yes	direct product factor
297	C₂×#489	C₂×C₁₃	1	1	yes	characteristic, complemented
298	C₂×#484	C₂×C₁₃	1	1	yes	characteristic, complemented
299	C₂×#480	C₂×C₁₃	1	1	yes	characteristic, complemented
300	C₂×#474	C₂×C₁₃	1	1	yes	characteristic, complemented
301	C₂×#468	C₂×C₁₃	1	1	yes	characteristic, complemented
302	C₂×#467	C₂×C₁₃	1	1	yes	characteristic, complemented
303	C₂×#464	C₂×C₁₃	1	1	yes	characteristic, complemented
304	C₂×#452	C₂×C₁₃	1	1	yes	characteristic, complemented
305	C₂×#450	C₂×C₁₃	1	1	yes	characteristic, complemented
306	C₂×#440	C₂×C₁₃	1	1	yes	characteristic, complemented
307	C₂×#435	C₂×C₁₃	1	1	yes	characteristic, complemented
308	C₂×#417	C₂×C₁₃	1	1	yes	characteristic, complemented
309	C₂²×#102	C₂×C₁₃	1	1	yes	characteristic, complemented
310	C₂³×C₁₃	—	2	2	no	—
311	C₂³×C₁₃	—	2	2	no	—
312	C₂³×C₁₃	—	2	2	no	—
313	C₂³×C₁₃	—	2	4	no	—
314	C₂³×C₁₃	—	2	2	no	—
315	C₂³×C₁₃	—	2	2	no	—
316	C₂³×C₁₃	—	2	2	no	—
317	C₂³×C₁₃	—	2	2	no	—
318	C₂³×C₁₃	—	4	8	no	—
319	C₂³×C₁₃	—	4	2	no	—
320	C₂³×C₁₃	—	4	2	no	—
321	C₂³×C₁₃	—	4	2	no	—
322	C₂³×C₁₃	—	4	8	no	—
323	C₂³×C₁₃	—	4	2	no	—
324	C₂³×C₁₃	—	4	2	no	—
325	C₂³×C₁₃	—	8	4	no	—
326	C₂³×C₁₃	—	8	16	no	—
327	C₂³×C₁₃	#137	1	4	yes	—
328	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
329	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
330	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
331	Q₈×C₁₃	—	2	2	no	—
332	Q₈×C₁₃	—	2	2	no	—
333	Q₈×C₁₃	—	2	2	no	—
334	Q₈×C₁₃	—	2	2	no	—
335	Q₈×C₁₃	—	4	2	no	—
336	Q₈×C₁₃	—	4	2	no	—
337	Q₈×C₁₃	—	8	4	no	—
338	D₄×C₁₃	—	2	8	no	—
339	D₄×C₁₃	—	2	4	no	—
340	D₄×C₁₃	—	2	2	no	—
341	D₄×C₁₃	—	2	2	no	—
342	D₄×C₁₃	—	2	2	no	—
343	D₄×C₁₃	—	4	8	no	—
344	D₄×C₁₃	—	4	8	no	—
345	D₄×C₁₃	—	4	2	no	—
346	D₄×C₁₃	—	8	4	no	—
347	D₄×C₁₃	C₂×#41	1	4	yes	—
348	C₂×C₄×C₁₃	—	2	2	no	—
349	C₂×C₄×C₁₃	—	2	2	no	—
350	C₂×C₄×C₁₃	—	2	2	no	—
351	C₂×C₄×C₁₃	—	2	2	no	—
352	C₂×C₄×C₁₃	—	2	4	no	—
353	C₂×C₄×C₁₃	—	2	4	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	—	2	2	no	—
361	C₂×C₄×C₁₃	—	2	2	no	—
362	C₂×C₄×C₁₃	—	2	2	no	—
363	C₂×C₄×C₁₃	—	2	2	no	—
364	C₂×C₄×C₁₃	—	4	8	no	—
365	C₂×C₄×C₁₃	—	4	2	no	—
366	C₂×C₄×C₁₃	—	4	2	no	—
367	C₂×C₄×C₁₃	—	4	2	no	—
368	C₂×C₄×C₁₃	—	4	2	no	—
369	C₂×C₄×C₁₃	—	4	2	no	—
370	C₂×C₄×C₁₃	—	4	2	no	—
371	C₂×C₄×C₁₃	—	8	4	no	—
372	C₂×C₄×C₁₃	—	8	4	no	—
373	C₂×C₄×C₁₃	—	8	4	no	—
374	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
375	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
376	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
377	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
378	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
380	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
381	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
382	C₈×C₁₃	—	2	2	no	—
383	C₈×C₁₃	—	2	2	no	—
384	C₈×C₁₃	—	2	2	no	—
385	C₈×C₁₃	—	2	2	no	—
386	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
387	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
388	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
389	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
390	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
391	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
392	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
393	#554	—	2	4	no	—
394	#554	C₂²×C₁₃	1	8	yes	complemented
395	#546	—	2	4	no	—
396	#546	C₂²×C₁₃	1	8	yes	—
397	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
398	C₂×#125	—	2	1	no	—
399	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
400	C₂×#123	—	2	1	no	—
401	C₂×C₂²⋊Q₈	—	2	1	no	—
402	C₂×C₂²⋊Q₈	—	2	1	no	—
403	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
404	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
405	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
406	C₂×#121	—	2	1	no	—
407	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
408	C₂×#120	—	2	1	no	—
409	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
410	C₂×C₄×D₄	—	2	1	no	—
411	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
412	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
413	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
414	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
415	C₂²×C₂²⋊C₄	—	2	1	no	—
416	#489	C₂²×C₁₃	1	8	yes	complemented
417	#484	C₂²×C₁₃	1	8	yes	complemented
418	#480	C₂²×C₁₃	1	8	yes	complemented
419	#474	C₂²×C₁₃	1	8	yes	complemented
420	#468	C₂²×C₁₃	1	8	yes	complemented
421	#467	C₂²×C₁₃	1	8	yes	complemented
422	#464	C₂²×C₁₃	1	8	yes	complemented
423	#452	C₂²×C₁₃	1	8	yes	complemented
424	#450	C₂²×C₁₃	1	8	yes	complemented
425	#440	C₂²×C₁₃	1	8	yes	complemented
426	#435	C₂²×C₁₃	1	8	yes	complemented
427	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
428	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
429	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
430	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
431	#417	C₂²×C₁₃	1	8	yes	complemented
432	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
433	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
434	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
435	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
436	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
437	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
438	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
439	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
440	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
441	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
442	C₂×#102	C₂²×C₁₃	1	8	yes	complemented
443	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
444	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
445	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic, complemented
446	C₂²×C₁₃	—	2	2	no	—
447	C₂²×C₁₃	—	2	8	no	—
448	C₂²×C₁₃	—	2	2	no	—
449	C₂²×C₁₃	—	2	2	no	—
450	C₂²×C₁₃	—	2	4	no	—
451	C₂²×C₁₃	—	2	2	no	—
452	C₂²×C₁₃	—	2	2	no	—
453	C₂²×C₁₃	—	4	4	no	—
454	C₂²×C₁₃	—	4	8	no	—
455	C₂²×C₁₃	—	4	2	no	—
456	C₂²×C₁₃	—	4	2	no	—
457	C₂²×C₁₃	—	4	2	no	—
458	C₂²×C₁₃	—	4	2	no	—
459	C₂²×C₁₃	—	4	2	no	—
460	C₂²×C₁₃	—	8	16	no	—
461	C₂²×C₁₃	—	8	4	no	—
462	C₂²×C₁₃	#546	1	2	yes	—
463	C₂²×C₁₃	C₂×#137	1	4	yes	—
464	C₂²×C₁₃	C₂×#137	1	2	yes	—
465	C₂²×C₁₃	#576	1	2	yes	—
466	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
467	C₄×C₁₃	—	2	2	no	—
468	C₄×C₁₃	—	2	2	no	—
469	C₄×C₁₃	—	2	2	no	—
470	C₄×C₁₃	—	2	2	no	—
471	C₄×C₁₃	—	4	2	no	—
472	C₄×C₁₃	—	4	2	no	—
473	C₄×C₁₃	—	4	2	no	—
474	C₄×C₁₃	—	4	2	no	—
475	C₄×C₁₃	—	4	2	no	—
476	C₄×C₁₃	—	4	2	no	—
477	C₄×C₁₃	#546	1	2	yes	—
478	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
479	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
480	C₂⁵	—	2	1	no	—
481	C₂×#41	—	2	2	no	—
482	C₂×#41	—	2	4	no	—
483	C₂×#41	—	4	2	no	—
484	C₂×#41	C₂³×C₁₃	1	4	yes	—
485	C₂²×Q₈	—	2	1	no	—
486	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
487	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
488	C₂²×D₄	—	2	4	no	—
489	C₂²×D₄	—	2	1	no	—
490	C₂²×D₄	—	2	1	no	—
491	C₂²×D₄	—	2	1	no	—
492	C₂²×D₄	—	2	2	no	—
493	C₂²×D₄	—	4	2	no	—
494	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
495	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
496	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
497	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
498	C₂³×C₄	—	2	1	no	—
499	C₂³×C₄	—	2	1	no	—
500	C₂³×C₄	—	2	1	no	—
501	C₂³×C₄	—	2	1	no	—
502	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
503	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
504	C₂×Q₁₆	—	4	2	no	—
505	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	complemented
506	C₂×SD₁₆	—	2	4	no	—
507	C₂×SD₁₆	—	4	2	no	—
508	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
509	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
510	C₂×M₁₆	—	4	2	no	—
511	C₂×M₁₆	C₂³×C₁₃	1	4	yes	complemented
512	C₂²×C₈	—	4	2	no	—
513	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
514	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
515	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
516	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
517	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
518	C₄⋊Q₈	—	2	2	no	—
519	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	complemented
520	#125	—	2	8	no	—
521	#124	—	2	2	no	—
522	#124	C₂³×C₁₃	1	4	yes	—
523	#123	—	2	8	no	—
524	C₂²⋊Q₈	—	2	2	no	—
525	C₂²⋊Q₈	—	2	2	no	—
526	C₂²⋊Q₈	—	2	2	no	—
527	C₂²⋊Q₈	—	2	8	no	—
528	C₂²⋊Q₈	—	2	8	no	—
529	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
530	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
531	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	complemented
532	#121	—	2	2	no	—
533	#121	—	2	8	no	—
534	#121	C₂³×C₁₃	1	4	yes	—
535	#120	—	2	8	no	—
536	C₄×Q₈	—	2	2	no	—
537	C₄×Q₈	C₂³×C₁₃	1	4	yes	complemented
538	C₄×D₄	—	2	8	no	—
539	C₄×D₄	—	2	2	no	—
540	C₄×D₄	D₄×C₁₃	1	4	yes	—
541	C₄×D₄	C₂³×C₁₃	1	4	yes	—
542	C₄×D₄	C₂³×C₁₃	1	4	yes	—
543	C₂×C₄⋊C₄	—	2	1	no	—
544	C₂×C₄⋊C₄	—	2	2	no	—
545	C₂×C₄⋊C₄	—	2	1	no	—
546	C₂×C₄⋊C₄	—	2	2	no	—
547	C₂×C₄⋊C₄	—	2	1	no	—
548	C₂×C₄⋊C₄	—	2	1	no	—
549	C₂×C₄⋊C₄	—	2	1	no	—
550	C₂×C₄⋊C₄	—	2	1	no	—
551	C₂×C₄⋊C₄	—	2	1	no	—
552	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
553	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
554	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
555	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
556	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
557	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
558	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	complemented
559	C₂×C₂²⋊C₄	—	2	1	no	—
560	C₂×C₂²⋊C₄	—	2	1	no	—
561	C₂×C₂²⋊C₄	—	2	1	no	—
562	C₂×C₂²⋊C₄	—	2	1	no	—
563	C₂×C₂²⋊C₄	—	2	1	no	—
564	C₂×C₂²⋊C₄	—	2	1	no	—
565	C₂×C₂²⋊C₄	—	2	1	no	—
566	C₂×C₂²⋊C₄	—	2	8	no	—
567	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
568	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
569	C₂×C₄²	—	2	1	no	—
570	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
571	#107	C₂³×C₁₃	1	4	yes	complemented
572	#107	C₂³×C₁₃	1	4	yes	complemented
573	#107	C₂³×C₁₃	1	4	yes	complemented
574	C₄⋊C₈	C₂³×C₁₃	1	4	yes	complemented
575	#103	C₂³×C₁₃	1	4	yes	complemented
576	#103	C₂³×C₁₃	1	4	yes	complemented
577	#103	C₂³×C₁₃	1	4	yes	complemented
578	#103	C₂³×C₁₃	1	4	yes	complemented
579	#102	C₂³×C₁₃	1	4	yes	—
580	#102	C₂³×C₁₃	1	4	yes	—
581	#102	C₂³×C₁₃	1	4	yes	—
582	#102	C₂³×C₁₃	1	4	yes	—
583	#102	C₂³×C₁₃	1	4	yes	—
584	#102	C₂³×C₁₃	1	4	yes	—
585	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
586	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	complemented
587	#97	C₂³×C₁₃	1	4	yes	complemented
588	C₂×C₁₃	—	2	4	no	—
589	C₂×C₁₃	—	4	2	no	—
590	C₂×C₁₃	—	4	4	no	—
591	C₂×C₁₃	—	8	2	no	—
592	C₂×C₁₃	#3314	1	4	yes	direct product factor
593	C₂×C₁₃	C₂×#546	1	1	yes	characteristic
594	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
595	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
596	C₂⁴	—	2	1	no	—
597	C₂⁴	—	2	1	no	—
598	C₂⁴	—	2	4	no	—
599	C₂⁴	—	4	4	no	—
600	C₂⁴	—	4	4	no	—
601	C₂⁴	—	8	2	no	—
602	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
603	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
604	#41	—	2	8	no	—
605	#41	—	4	4	no	—
606	#41	—	4	8	no	—
607	C₂×Q₈	—	2	1	no	—
608	C₂×Q₈	—	2	1	no	—
609	C₂×Q₈	—	2	4	no	—
610	C₂×Q₈	—	2	2	no	—
611	C₂×Q₈	—	2	2	no	—
612	C₂×Q₈	—	2	2	no	—
613	C₂×Q₈	—	2	2	no	—
614	C₂×Q₈	—	8	2	no	—
615	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
616	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
617	C₂×D₄	—	2	4	no	—
618	C₂×D₄	—	2	8	no	—
619	C₂×D₄	—	2	4	no	—
620	C₂×D₄	—	2	4	no	—
621	C₂×D₄	—	2	1	no	—
622	C₂×D₄	—	2	4	no	—
623	C₂×D₄	—	2	1	no	—
624	C₂×D₄	—	2	2	no	—
625	C₂×D₄	—	2	2	no	—
626	C₂×D₄	—	2	2	no	—
627	C₂×D₄	—	4	4	no	—
628	C₂×D₄	—	4	8	no	—
629	C₂×D₄	—	4	4	no	—
630	C₂×D₄	—	4	4	no	—
631	C₂×D₄	—	8	2	no	—
632	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
633	C₂×D₄	C₁₃×#41	1	4	yes	—
634	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
635	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
636	C₂²×C₄	—	2	2	no	—
637	C₂²×C₄	—	2	2	no	—
638	C₂²×C₄	—	2	2	no	—
639	C₂²×C₄	—	2	2	no	—
640	C₂²×C₄	—	2	1	no	—
641	C₂²×C₄	—	2	1	no	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	1	no	—
645	C₂²×C₄	—	2	1	no	—
646	C₂²×C₄	—	2	4	no	—
647	C₂²×C₄	—	2	4	no	—
648	C₂²×C₄	—	2	4	no	—
649	C₂²×C₄	—	2	4	no	—
650	C₂²×C₄	—	4	4	no	—
651	C₂²×C₄	—	8	2	no	—
652	C₂²×C₄	—	8	2	no	—
653	C₂²×C₄	—	8	2	no	—
654	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
655	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
656	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
657	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
658	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
659	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
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	Q₁₆	—	4	4	no	—
664	SD₁₆	—	2	8	no	—
665	SD₁₆	—	4	4	no	—
666	M₁₆	—	4	4	no	—
667	C₂×C₈	—	2	2	no	—
668	C₂×C₈	—	2	2	no	—
669	C₂×C₈	—	2	2	no	—
670	C₂×C₈	—	2	2	no	—
671	C₂×C₈	—	4	4	no	—
672	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
673	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
674	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
675	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
676	C₄⋊C₄	—	2	1	no	—
677	C₄⋊C₄	—	2	4	no	—
678	C₄⋊C₄	—	2	1	no	—
679	C₄⋊C₄	—	2	1	no	—
680	C₄⋊C₄	—	2	4	no	—
681	C₄⋊C₄	—	2	4	no	—
682	C₄⋊C₄	—	2	4	no	—
683	C₄⋊C₄	—	2	4	no	—
684	C₄⋊C₄	—	2	4	no	—
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	2	1	no	—
687	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
688	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
689	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
690	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
691	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	4	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	4	no	—
698	C₂²⋊C₄	—	2	4	no	—
699	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
700	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
701	C₄²	—	2	4	no	—
702	C₄²	C₂×D₄×C₁₃	1	2	yes	—
703	C₄²	C₂⁴×C₁₃	1	2	yes	—
704	C₁₃	C₂×#3314	1	1	yes	characteristic, direct product factor, Sylow
705	C₂³	—	2	2	no	—
706	C₂³	—	2	2	no	—
707	C₂³	—	2	2	no	—
708	C₂³	—	2	4	no	—
709	C₂³	—	2	2	no	—
710	C₂³	—	2	2	no	—
711	C₂³	—	2	2	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	4	8	no	—
714	C₂³	—	4	2	no	—
715	C₂³	—	4	2	no	—
716	C₂³	—	4	2	no	—
717	C₂³	—	4	8	no	—
718	C₂³	—	4	2	no	—
719	C₂³	—	4	2	no	—
720	C₂³	—	8	4	no	—
721	C₂³	—	8	16	no	—
722	C₂³	C₁₃×#137	1	4	yes	—
723	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
724	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
725	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
726	Q₈	—	2	2	no	—
727	Q₈	—	2	2	no	—
728	Q₈	—	2	2	no	—
729	Q₈	—	2	2	no	—
730	Q₈	—	4	2	no	—
731	Q₈	—	4	2	no	—
732	Q₈	—	8	4	no	—
733	D₄	—	2	8	no	—
734	D₄	—	2	4	no	—
735	D₄	—	2	2	no	—
736	D₄	—	2	2	no	—
737	D₄	—	2	2	no	—
738	D₄	—	4	8	no	—
739	D₄	—	4	8	no	—
740	D₄	—	4	2	no	—
741	D₄	—	8	4	no	—
742	D₄	C₂×C₁₃×#41	1	4	yes	—
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	4	no	—
748	C₂×C₄	—	2	4	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	4	8	no	—
760	C₂×C₄	—	4	2	no	—
761	C₂×C₄	—	4	2	no	—
762	C₂×C₄	—	4	2	no	—
763	C₂×C₄	—	4	2	no	—
764	C₂×C₄	—	4	2	no	—
765	C₂×C₄	—	4	2	no	—
766	C₂×C₄	—	8	4	no	—
767	C₂×C₄	—	8	4	no	—
768	C₂×C₄	—	8	4	no	—
769	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
770	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
771	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
772	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
773	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
774	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
775	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
776	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
777	C₈	—	2	2	no	—
778	C₈	—	2	2	no	—
779	C₈	—	2	2	no	—
780	C₈	—	2	2	no	—
781	C₂²	—	2	8	no	—
782	C₂²	—	2	2	no	—
783	C₂²	—	2	2	no	—
784	C₂²	—	2	2	no	—
785	C₂²	—	2	2	no	—
786	C₂²	—	2	2	no	—
787	C₂²	—	2	4	no	—
788	C₂²	—	4	4	no	—
789	C₂²	—	4	8	no	—
790	C₂²	—	4	2	no	—
791	C₂²	—	4	2	no	—
792	C₂²	—	4	2	no	—
793	C₂²	—	4	2	no	—
794	C₂²	—	4	2	no	—
795	C₂²	—	8	16	no	—
796	C₂²	—	8	4	no	—
797	C₂²	C₁₃×#546	1	2	yes	—
798	C₂²	C₂×C₁₃×#137	1	4	yes	—
799	C₂²	C₂×C₁₃×#137	1	2	yes	—
800	C₂²	C₁₃×#576	1	2	yes	—
801	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
802	C₄	—	2	2	no	—
803	C₄	—	2	2	no	—
804	C₄	—	2	2	no	—
805	C₄	—	2	2	no	—
806	C₄	—	4	2	no	—
807	C₄	—	4	2	no	—
808	C₄	—	4	2	no	—
809	C₄	—	4	2	no	—
810	C₄	—	4	2	no	—
811	C₄	—	4	2	no	—
812	C₄	C₁₃×#546	1	2	yes	—
813	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
814	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
815	C₂	—	2	4	no	—
816	C₂	—	4	2	no	—
817	C₂	—	4	4	no	—
818	C₂	—	8	2	no	—
819	C₂	C₁₃×#3314	1	4	yes	direct product factor
820	C₂	C₂×C₁₃×#546	1	1	yes	characteristic
821	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
822	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×#546	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×#3314	C₂	direct (N × H)
4. C₂×C₁₃×#489	C₂	semidirect
5. C₂×C₁₃×#484	C₂	semidirect
6. C₂×C₁₃×#480	C₂	semidirect
7. C₂×C₁₃×#474	C₂	semidirect
8. C₂×C₁₃×#468	C₂	semidirect
9. C₂×C₁₃×#467	C₂	semidirect
10. C₂×C₁₃×#464	C₂	semidirect
11. C₂×C₁₃×#452	C₂	semidirect
12. C₂×C₁₃×#450	C₂	semidirect
13. C₂×C₁₃×#440	C₂	semidirect
14. C₂×C₁₃×#435	C₂	semidirect
15. C₂×C₁₃×#417	C₂	semidirect
16. C₂²×C₁₃×#102	C₂	semidirect
19. C₂²×C₁₃×Q₁₆	C₂²	semidirect
22. C₂²×C₁₃×M₁₆	C₂²	semidirect
25. C₁₃×#554	C₂²	semidirect
28. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
36. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
40. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
45. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
47. C₁₃×#489	C₂²	semidirect
48. C₁₃×#484	C₂²	semidirect
49. C₁₃×#480	C₂²	semidirect
50. C₁₃×#474	C₂²	semidirect
51. C₁₃×#468	C₂²	semidirect
52. C₁₃×#467	C₂²	semidirect
53. C₁₃×#464	C₂²	semidirect
54. C₁₃×#452	C₂²	semidirect
55. C₁₃×#450	C₂²	semidirect
56. C₁₃×#440	C₂²	semidirect
57. C₁₃×#435	C₂²	semidirect
58. C₂×C₁₃×#107	C₂²	semidirect
59. C₂×C₁₃×#107	C₂²	semidirect
60. C₂×C₁₃×#107	C₂²	semidirect
61. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
62. C₁₃×#417	C₂²	semidirect
63. C₂×C₁₃×#103	C₂²	semidirect
64. C₂×C₁₃×#103	C₂²	semidirect
65. C₂×C₁₃×#103	C₂²	semidirect
66. C₂×C₁₃×#103	C₂²	semidirect
73. C₂×C₁₃×#102	C₂²	semidirect
75. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
76. C₂×C₁₃×#97	C₂²	semidirect
102. C₂×C₁₃×Q₁₆	C₂³	semidirect
108. C₂×C₁₃×M₁₆	C₂³	semidirect
116. C₁₃×C₄⋊Q₈	C₂³	semidirect
128. C₁₃×C₂²⋊Q₈	C₂³	semidirect
134. C₄×Q₈×C₁₃	C₂³	semidirect
155. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
168. C₁₃×#107	C₂³	semidirect
169. C₁₃×#107	C₂³	semidirect
170. C₁₃×#107	C₂³	semidirect
171. C₁₃×C₄⋊C₈	C₂³	semidirect
172. C₁₃×#103	C₂³	semidirect
173. C₁₃×#103	C₂³	semidirect
174. C₁₃×#103	C₂³	semidirect
175. C₁₃×#103	C₂³	semidirect
183. C₁₃×C₂²⋊C₈	C₂³	semidirect
184. C₁₃×#97	C₂³	semidirect
185. C₂×#3314	C₁₃	direct (N × H)
294. C₂×#554	C₂×C₁₃	semidirect
296. #3314	C₂×C₁₃	direct (N × H)
297. C₂×#489	C₂×C₁₃	semidirect
298. C₂×#484	C₂×C₁₃	semidirect
299. C₂×#480	C₂×C₁₃	semidirect
300. C₂×#474	C₂×C₁₃	semidirect
301. C₂×#468	C₂×C₁₃	semidirect
302. C₂×#467	C₂×C₁₃	semidirect
303. C₂×#464	C₂×C₁₃	semidirect
304. C₂×#452	C₂×C₁₃	semidirect
305. C₂×#450	C₂×C₁₃	semidirect
306. C₂×#440	C₂×C₁₃	semidirect
307. C₂×#435	C₂×C₁₃	semidirect
308. C₂×#417	C₂×C₁₃	semidirect
309. C₂²×#102	C₂×C₁₃	semidirect
388. C₂²×Q₁₆	C₂²×C₁₃	semidirect
391. C₂²×M₁₆	C₂²×C₁₃	semidirect
394. #554	C₂²×C₁₃	semidirect
397. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
405. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
409. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
414. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
416. #489	C₂²×C₁₃	semidirect
417. #484	C₂²×C₁₃	semidirect
418. #480	C₂²×C₁₃	semidirect
419. #474	C₂²×C₁₃	semidirect
420. #468	C₂²×C₁₃	semidirect
421. #467	C₂²×C₁₃	semidirect
422. #464	C₂²×C₁₃	semidirect
423. #452	C₂²×C₁₃	semidirect
424. #450	C₂²×C₁₃	semidirect
425. #440	C₂²×C₁₃	semidirect
426. #435	C₂²×C₁₃	semidirect
427. C₂×#107	C₂²×C₁₃	semidirect
428. C₂×#107	C₂²×C₁₃	semidirect
429. C₂×#107	C₂²×C₁₃	semidirect
430. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
431. #417	C₂²×C₁₃	semidirect
432. C₂×#103	C₂²×C₁₃	semidirect
433. C₂×#103	C₂²×C₁₃	semidirect
434. C₂×#103	C₂²×C₁₃	semidirect
435. C₂×#103	C₂²×C₁₃	semidirect
442. C₂×#102	C₂²×C₁₃	semidirect
444. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
445. C₂×#97	C₂²×C₁₃	semidirect
505. C₂×Q₁₆	C₂³×C₁₃	semidirect
511. C₂×M₁₆	C₂³×C₁₃	semidirect
519. C₄⋊Q₈	C₂³×C₁₃	semidirect
531. C₂²⋊Q₈	C₂³×C₁₃	semidirect
537. C₄×Q₈	C₂³×C₁₃	semidirect
558. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
571. #107	C₂³×C₁₃	semidirect
572. #107	C₂³×C₁₃	semidirect
573. #107	C₂³×C₁₃	semidirect
574. C₄⋊C₈	C₂³×C₁₃	semidirect
575. #103	C₂³×C₁₃	semidirect
576. #103	C₂³×C₁₃	semidirect
577. #103	C₂³×C₁₃	semidirect
578. #103	C₂³×C₁₃	semidirect
586. C₂²⋊C₈	C₂³×C₁₃	semidirect
587. #97	C₂³×C₁₃	semidirect
592. C₂×C₁₃	#3314	direct (N × H)
704. C₁₃	C₂×#3314	direct (N × H)
819. C₂	C₁₃×#3314	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×#546	2
C₁₃×#3314	2
C₂×C₁₃×#489	2
C₂×C₁₃×#484	2
C₂×C₁₃×#480	2
C₂×C₁₃×#474	2
C₂×C₁₃×#468	2
C₂×C₁₃×#467	2
C₂×C₁₃×#464	2
C₂×C₁₃×#452	2
C₂×C₁₃×#450	2
C₂×C₁₃×#440	2
C₂×C₁₃×#435	2
C₂×C₁₃×#417	2
C₂²×C₁₃×#102	2
C₂×#3314	13

Subgroups — C2×C13×#3314 #15747465

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3314 #15747465