Subgroups — C₂×#13128631 #16770815

Order 3328.

7738 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13128631	C₂	1	32	yes	maximal, direct product factor
2	C₂×#11719435	C₂	1	2	yes	maximal, complemented
3	C₂×#11719284	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11719244	C₂	1	2	yes	maximal, complemented
5	C₂×#11719340	C₂	1	2	yes	maximal, complemented
6	C₂×#11719248	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#11719341	C₂	1	4	yes	maximal, complemented
8	C₂×#11719432	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×Q₈×C₂²⋊D₁₃	C₂	1	2	yes	maximal, complemented
10	C₂×#11719434	C₂	1	2	yes	maximal, complemented
11	C₂×#11719339	C₂	1	4	yes	maximal, complemented
12	C₂×#11719433	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#11719283	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#88200	C₂	1	2	yes	maximal, complemented
15	C₂×D₁₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
16	C₂×#11719250	C₂	1	2	yes	maximal
17	C₂×C₄×D₄×D₁₃	C₂	1	1	yes	maximal, characteristic
18	C₂×D₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂³×Q₈×C₁₃	C₂²	1	2	yes	complemented
20	C₂²×Q₈×D₁₃	C₂²	1	2	yes	complemented
21	C₂²×D₄×D₁₃	C₂²	1	1	yes	characteristic
22	C₂³×C₄×D₁₃	C₂²	1	2	yes	—
23	D₄×Q₈×C₁₃	C₂²	1	16	yes	complemented
24	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
25	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
27	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
28	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
31	Q₈×C₂²⋊D₁₃	C₂²	1	32	yes	complemented
32	C₂×#88200	C₂²	1	4	yes	—
33	C₂×#88200	C₂²	1	2	yes	—
34	C₂×#88200	C₂²	1	1	yes	characteristic
35	C₂×#88200	C₂²	1	4	yes	complemented
36	C₂×#88200	C₂²	1	2	yes	complemented
37	C₂×#88200	C₂²	1	2	yes	complemented
38	C₂×#88200	C₂²	1	4	yes	complemented
39	C₂×#88200	C₂²	1	32	yes	complemented
40	C₂×Q₈×Dic₁₃	C₂²	1	2	yes	complemented
41	C₂×#88198	C₂²	1	4	yes	complemented
42	C₂×#88198	C₂²	1	1	yes	characteristic, complemented
43	C₂×D₄×Dic₁₃	C₂²	1	1	yes	characteristic
44	C₂×D₄×Dic₁₃	C₂²	1	2	yes	—
45	C₂×C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
46	C₂×C₄×C₂²⋊D₁₃	C₂²	1	4	yes	—
47	C₂²×#6103	C₂²	1	4	yes	—
48	C₂²×C₄⋊Dic₁₃	C₂²	1	2	yes	complemented
49	C₂×#88178	C₂²	1	4	yes	complemented
50	C₂×#88178	C₂²	1	2	yes	complemented
51	C₂²×#6101	C₂²	1	4	yes	complemented
52	#11719435	C₂²	1	32	yes	complemented
53	#11719434	C₂²	1	32	yes	complemented
54	#11719433	C₂²	1	16	yes	complemented
55	#11719432	C₂²	1	16	yes	complemented
56	#11719341	C₂²	1	64	yes	complemented
57	#11719340	C₂²	1	32	yes	complemented
58	#11719339	C₂²	1	64	yes	complemented
59	D₁₃×C₂²⋊Q₈	C₂²	1	32	yes	complemented
60	#11719284	C₂²	1	16	yes	complemented
61	#11719283	C₂²	1	16	yes	complemented
62	#11719250	C₂²	1	32	yes	—
63	C₄×D₄×D₁₃	C₂²	1	16	yes	—
64	#11719248	C₂²	1	16	yes	complemented
65	#11719244	C₂²	1	32	yes	complemented
66	C₂×#88151	C₂²	1	2	yes	—
67	C₂×#88151	C₂²	1	1	yes	characteristic
68	C₂×#88151	C₂²	1	4	yes	complemented
69	C₂×#88150	C₂²	1	2	yes	—
70	C₂×#88150	C₂²	1	4	yes	—
71	C₂×#88150	C₂²	1	4	yes	complemented
72	C₂×#88150	C₂²	1	4	yes	complemented
73	C₂×#88147	C₂²	1	1	yes	characteristic
74	C₂×#88147	C₂²	1	2	yes	—
75	C₂×#88146	C₂²	1	2	yes	—
76	C₂×C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
77	C₂×C₄⋊C₄×D₁₃	C₂²	1	4	yes	complemented
78	C₂×C₄⋊C₄×D₁₃	C₂²	1	2	yes	complemented
79	C₂×#88144	C₂²	1	2	yes	complemented
80	C₂×#88144	C₂²	1	2	yes	complemented
81	C₂×#88143	C₂²	1	4	yes	complemented
82	C₂×#88143	C₂²	1	2	yes	complemented
83	C₂×#88142	C₂²	1	2	yes	complemented
84	C₂×#88142	C₂²	1	1	yes	characteristic, complemented
85	C₂×#88141	C₂²	1	2	yes	complemented
86	C₂×#88135	C₂²	1	2	yes	—
87	C₂×#88135	C₂²	1	4	yes	—
88	C₂×C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
89	C₂×C₂²⋊C₄×D₁₃	C₂²	1	4	yes	—
90	C₂×#88132	C₂²	1	4	yes	complemented
91	C₂×#88132	C₂²	1	4	yes	complemented
92	C₂×#88132	C₂²	1	4	yes	complemented
93	C₂×C₄×D₅₂	C₂²	1	1	yes	characteristic
94	C₂×C₄×D₅₂	C₂²	1	2	yes	—
95	C₂×#88126	C₂²	1	2	yes	—
96	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
97	C₂×#88124	C₂²	1	2	yes	complemented
98	C₂×#88123	C₂²	1	1	yes	characteristic, complemented
99	C₂×C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
100	C₂×C₄×Dic₂₆	C₂²	1	2	yes	complemented
101	C₂⁴×D₁₃	C₂³	1	2	yes	—
102	C₂²×Q₈×C₁₃	—	4	8	no	—
103	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
104	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
105	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
106	C₂²×Q₈×C₁₃	C₂³	1	16	yes	complemented
107	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
109	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
110	C₂²×C₂²⋊D₁₃	C₂³	1	2	yes	—
111	C₂³×Dic₁₃	C₂³	1	2	yes	—
112	C₂³×Dic₁₃	C₂³	1	4	yes	—
113	C₂×Q₈×D₁₃	—	4	8	no	—
114	C₂×Q₈×D₁₃	C₂³	1	16	yes	complemented
115	C₂×D₄×D₁₃	Q₈	1	16	yes	complemented
116	C₂×D₄×D₁₃	C₂³	1	8	yes	—
117	C₂²×D₅₂	C₂³	1	1	yes	characteristic
118	C₂²×C₄×D₁₃	—	4	8	no	—
119	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
120	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
121	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
122	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
123	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
124	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
125	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
126	C₂²×C₄×D₁₃	C₂³	1	16	yes	—
127	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
128	C₂²×Dic₂₆	C₂³	1	1	yes	characteristic
129	C₂²×Dic₂₆	C₂³	1	2	yes	—
130	C₂²×Dic₂₆	C₂³	1	2	yes	—
131	C₂²×Dic₂₆	C₂³	1	4	yes	—
132	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
133	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	complemented
134	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
135	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	complemented
136	C₄×Q₈×C₁₃	C₂³	1	8	yes	complemented
137	C₄×D₄×C₁₃	C₂³	1	16	yes	—
138	C₄×D₄×C₁₃	C₂³	1	8	yes	—
139	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
140	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
141	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
142	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
143	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
144	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
145	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
146	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
147	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
148	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
149	C₂×C₂²⋊Dic₁₃	C₂³	1	2	yes	—
150	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
151	#88200	C₂³	1	16	yes	—
152	#88200	C₂³	1	32	yes	—
153	#88200	C₂³	1	8	yes	—
154	#88200	C₂³	1	16	yes	complemented
155	#88200	C₂³	1	32	yes	complemented
156	#88200	C₂³	1	32	yes	complemented
157	#88200	C₂³	1	16	yes	complemented
158	Q₈×Dic₁₃	C₂³	1	16	yes	complemented
159	#88198	C₂³	1	32	yes	complemented
160	#88198	C₂³	1	8	yes	complemented
161	D₄×Dic₁₃	C₂³	1	8	yes	—
162	D₄×Dic₁₃	C₂³	1	16	yes	—
163	C₄×C₂²⋊D₁₃	C₂³	1	16	yes	—
164	C₄×C₂²⋊D₁₃	C₂³	1	32	yes	—
165	C₂×#6103	C₂³	1	2	yes	—
166	C₂×#6103	C₂³	1	2	yes	—
167	C₂×#6103	C₂³	1	2	yes	—
168	C₂×#6103	C₂³	1	4	yes	—
169	C₂×#6103	C₂³	1	4	yes	—
170	C₂×#6103	C₂³	1	2	yes	—
171	C₂×#6103	C₂³	1	4	yes	—
172	C₂×#6103	C₂³	1	32	yes	—
173	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
174	C₂×C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
176	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
177	C₂×C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	—
179	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	—
180	C₂×C₄⋊Dic₁₃	C₂³	1	16	yes	complemented
181	#88178	C₂³	1	32	yes	complemented
182	#88178	C₂³	1	16	yes	complemented
183	C₂×#6101	C₂³	1	2	yes	—
184	C₂×#6101	C₂³	1	2	yes	—
185	C₂×#6101	C₂³	1	2	yes	—
186	C₂×#6101	C₂³	1	4	yes	—
187	C₂×#6101	C₂³	1	4	yes	—
188	C₂×#6101	C₂³	1	2	yes	—
189	C₂×#6101	C₂³	1	2	yes	—
190	C₂×#6101	C₂³	1	4	yes	—
191	C₂×#6101	C₂³	1	4	yes	—
192	C₂×#6101	C₂³	1	4	yes	—
193	C₂×#6101	C₂³	1	2	yes	—
194	C₂×#6101	C₂³	1	32	yes	complemented
195	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
196	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
197	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
198	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
199	C₂×C₄×Dic₁₃	C₂³	1	4	yes	—
200	#88151	C₂³	1	16	yes	—
201	#88151	C₂³	1	8	yes	—
202	#88151	C₂³	1	32	yes	complemented
203	#88150	C₂³	1	32	yes	—
204	#88150	C₂³	1	16	yes	—
205	#88150	C₂³	1	32	yes	complemented
206	#88150	C₂³	1	32	yes	complemented
207	#88147	C₂³	1	16	yes	—
208	#88147	C₂³	1	8	yes	—
209	#88146	C₂³	1	16	yes	—
210	C₄⋊C₄×D₁₃	C₂³	1	8	yes	—
211	C₄⋊C₄×D₁₃	C₂³	1	32	yes	complemented
212	C₄⋊C₄×D₁₃	C₂³	1	16	yes	complemented
213	#88144	C₂³	1	16	yes	complemented
214	#88144	C₂³	1	16	yes	complemented
215	#88143	C₂³	1	32	yes	complemented
216	#88143	C₂³	1	16	yes	complemented
217	#88142	C₂³	1	16	yes	complemented
218	#88142	C₂³	1	8	yes	complemented
219	#88141	C₂³	1	16	yes	complemented
220	#88135	C₂³	1	16	yes	—
221	#88135	C₂³	1	32	yes	—
222	C₂²⋊C₄×D₁₃	C₂³	1	16	yes	—
223	C₂²⋊C₄×D₁₃	C₂³	1	32	yes	—
224	#88132	C₂³	1	32	yes	complemented
225	#88132	C₂³	1	32	yes	complemented
226	#88132	C₂³	1	32	yes	complemented
227	C₄×D₅₂	C₂³	1	8	yes	—
228	C₄×D₅₂	C₂³	1	16	yes	—
229	#88126	C₂³	1	16	yes	—
230	C₄²×D₁₃	C₂³	1	8	yes	—
231	#88124	C₂³	1	16	yes	complemented
232	#88123	C₂³	1	8	yes	complemented
233	C₄×Dic₂₆	C₂³	1	8	yes	complemented
234	C₄×Dic₂₆	C₂³	1	16	yes	complemented
235	C₂×#3501	—	13	1	no	maximal, Sylow
236	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
237	C₂³×D₁₃	—	4	4	no	—
238	C₂³×D₁₃	—	4	4	no	—
239	C₂³×D₁₃	C₂×Q₈	1	16	yes	complemented
240	C₂³×D₁₃	C₂⁴	1	1	yes	characteristic
241	C₂³×D₁₃	C₂⁴	1	2	yes	—
242	C₂³×D₁₃	C₂⁴	1	8	yes	—
243	C₂×Q₈×C₁₃	—	2	8	no	—
244	C₂×Q₈×C₁₃	—	2	4	no	—
245	C₂×Q₈×C₁₃	—	4	8	no	—
246	C₂×Q₈×C₁₃	—	4	32	no	—
247	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
248	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
249	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	—
250	C₂×D₄×C₁₃	C₂×Q₈	1	8	yes	complemented
251	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
252	C₂²×C₄×C₁₃	—	2	8	no	—
253	C₂²×C₄×C₁₃	—	4	8	no	—
254	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
255	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
260	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
261	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
263	C₂×C₂²⋊D₁₃	C₂×Q₈	1	16	yes	complemented
264	C₂×C₂²⋊D₁₃	C₂⁴	1	8	yes	—
265	C₂²×Dic₁₃	—	4	4	no	—
266	C₂²×Dic₁₃	—	4	8	no	—
267	C₂²×Dic₁₃	C₂⁴	1	1	yes	characteristic
268	C₂²×Dic₁₃	C₂⁴	1	1	yes	characteristic
269	C₂²×Dic₁₃	C₂⁴	1	2	yes	—
270	C₂²×Dic₁₃	C₂⁴	1	2	yes	—
271	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
272	C₂²×Dic₁₃	C₂⁴	1	2	yes	—
273	C₂²×Dic₁₃	C₂⁴	1	8	yes	—
274	C₂²×Dic₁₃	C₂⁴	1	16	yes	—
275	C₂²×Dic₁₃	C₂⁴	1	1	yes	characteristic
276	Q₈×D₁₃	—	4	32	no	—
277	D₄×D₁₃	C₂×Q₈	1	64	yes	complemented
278	C₂×D₅₂	C₂×Q₈	1	8	yes	complemented
279	C₂×D₅₂	C₂⁴	1	4	yes	—
280	C₂×C₄×D₁₃	—	2	4	no	—
281	C₂×C₄×D₁₃	—	2	8	no	—
282	C₂×C₄×D₁₃	—	4	32	no	—
283	C₂×C₄×D₁₃	—	4	4	no	—
284	C₂×C₄×D₁₃	—	4	4	no	—
285	C₂×C₄×D₁₃	—	4	2	no	—
286	C₂×C₄×D₁₃	—	4	8	no	—
287	C₂×C₄×D₁₃	—	4	8	no	—
288	C₂×C₄×D₁₃	C₂×Q₈	1	8	yes	complemented
289	C₂×C₄×D₁₃	C₂⁴	1	4	yes	—
290	C₂×C₄×D₁₃	C₂⁴	1	8	yes	—
291	C₂×C₄×D₁₃	C₂⁴	1	4	yes	—
292	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
293	C₂×C₄×D₁₃	C₂⁴	1	8	yes	—
294	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
295	C₂×C₄×D₁₃	C₂⁴	1	8	yes	—
296	C₂×C₄×D₁₃	C₂⁴	1	4	yes	—
297	C₂×Dic₂₆	—	2	4	no	—
298	C₂×Dic₂₆	—	4	4	no	—
299	C₂×Dic₂₆	—	4	4	no	—
300	C₂×Dic₂₆	—	4	8	no	—
301	C₂×Dic₂₆	C₂⁴	1	4	yes	—
302	C₂×Dic₂₆	C₂⁴	1	8	yes	—
303	C₂×Dic₂₆	C₂⁴	1	8	yes	—
304	C₂×Dic₂₆	C₂⁴	1	16	yes	—
305	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
306	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
307	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
308	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
309	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
310	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
311	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
312	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
313	C₄²×C₁₃	C₂⁴	1	4	yes	—
314	C₄²×C₁₃	C₂⁴	1	8	yes	—
315	C₂²⋊Dic₁₃	C₂⁴	1	8	yes	—
316	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
317	#6103	C₂⁴	1	8	yes	—
318	#6103	C₂⁴	1	8	yes	—
319	#6103	C₂⁴	1	8	yes	—
320	#6103	C₂⁴	1	16	yes	—
321	#6103	C₂⁴	1	16	yes	—
322	#6103	C₂⁴	1	8	yes	—
323	#6103	C₂⁴	1	16	yes	—
324	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
325	C₄⋊Dic₁₃	C₂⁴	1	4	yes	—
326	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
327	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
328	C₄⋊Dic₁₃	C₂⁴	1	4	yes	—
329	C₄⋊Dic₁₃	C₂⁴	1	16	yes	—
330	C₄⋊Dic₁₃	C₂⁴	1	16	yes	—
331	#6101	C₂⁴	1	8	yes	—
332	#6101	C₂⁴	1	8	yes	—
333	#6101	C₂⁴	1	8	yes	—
334	#6101	C₂⁴	1	16	yes	—
335	#6101	C₂⁴	1	16	yes	—
336	#6101	C₂⁴	1	8	yes	—
337	#6101	C₂⁴	1	8	yes	—
338	#6101	C₂⁴	1	16	yes	—
339	#6101	C₂⁴	1	16	yes	—
340	#6101	C₂⁴	1	16	yes	—
341	#6101	C₂⁴	1	8	yes	—
342	C₄×Dic₁₃	C₂⁴	1	4	yes	—
343	C₄×Dic₁₃	C₂⁴	1	8	yes	—
344	C₄×Dic₁₃	C₂⁴	1	4	yes	—
345	C₄×Dic₁₃	C₂⁴	1	4	yes	—
346	C₄×Dic₁₃	C₂⁴	1	16	yes	—
347	#3501	—	13	32	no	—
348	C₂×#554	—	13	2	no	—
349	C₂×#554	—	13	4	no	—
350	C₂×#554	—	13	2	no	—
351	C₂×#554	—	13	1	no	—
352	C₂×#554	—	13	1	no	—
353	C₂×#554	—	13	2	no	—
354	C₂×D₄×Q₈	—	13	2	no	—
355	C₂×D₄×Q₈	—	13	1	no	—
356	C₂×D₄×Q₈	D₁₃	1	1	yes	characteristic, complemented
357	C₂×#544	—	13	2	no	—
358	C₂×#543	—	13	4	no	—
359	C₂×#533	—	13	1	no	—
360	C₂×#533	—	13	1	no	—
361	C₂²×C₂²⋊Q₈	—	13	2	no	—
362	C₂²×C₂²⋊Q₈	—	13	2	no	—
363	C₂×#518	—	13	2	no	—
364	C₂²×C₄×D₄	—	13	1	no	—
365	C₂³×C₁₃	—	2	4	no	—
366	C₂³×C₁₃	—	2	4	no	—
367	C₂³×C₁₃	C₂²×Q₈	1	8	yes	—
368	C₂³×C₁₃	C₂⁵	1	4	yes	—
369	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
370	C₂²×D₁₃	—	2	4	no	—
371	C₂²×D₁₃	—	2	2	no	—
372	C₂²×D₁₃	—	2	4	no	—
373	C₂²×D₁₃	—	2	2	no	—
374	C₂²×D₁₃	—	4	8	no	—
375	C₂²×D₁₃	—	4	32	no	—
376	C₂²×D₁₃	—	4	8	no	—
377	C₂²×D₁₃	C₂²×Q₈	1	4	yes	—
378	C₂²×D₁₃	C₂²×Q₈	1	8	yes	—
379	C₂²×D₁₃	C₂²×Q₈	1	32	yes	complemented
380	C₂²×D₁₃	C₂⁵	1	2	yes	—
381	C₂²×D₁₃	C₂⁵	1	4	yes	—
382	Q₈×C₁₃	—	2	16	no	—
383	Q₈×C₁₃	—	2	8	no	—
384	Q₈×C₁₃	—	4	16	no	—
385	D₄×C₁₃	C₂²×Q₈	1	16	yes	complemented
386	C₂×C₄×C₁₃	—	2	8	no	—
387	C₂×C₄×C₁₃	—	2	4	no	—
388	C₂×C₄×C₁₃	—	2	4	no	—
389	C₂×C₄×C₁₃	—	2	2	no	—
390	C₂×C₄×C₁₃	—	2	4	no	—
391	C₂×C₄×C₁₃	—	2	16	no	—
392	C₂×C₄×C₁₃	—	4	16	no	—
393	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
394	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
395	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
396	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
397	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
398	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
399	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
400	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
401	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
402	C₂²⋊D₁₃	C₂²×Q₈	1	32	yes	complemented
403	C₂×Dic₁₃	—	2	4	no	—
404	C₂×Dic₁₃	—	2	4	no	—
405	C₂×Dic₁₃	—	2	2	no	—
406	C₂×Dic₁₃	—	2	2	no	—
407	C₂×Dic₁₃	—	2	8	no	—
408	C₂×Dic₁₃	—	2	4	no	—
409	C₂×Dic₁₃	—	4	8	no	—
410	C₂×Dic₁₃	—	4	16	no	—
411	C₂×Dic₁₃	C₂²×Q₈	1	4	yes	—
412	C₂×Dic₁₃	C₂⁵	1	2	yes	—
413	C₂×Dic₁₃	C₂⁵	1	2	yes	—
414	C₂×Dic₁₃	C₂⁵	1	4	yes	—
415	C₂×Dic₁₃	C₂⁵	1	4	yes	—
416	C₂×Dic₁₃	C₂⁵	1	8	yes	—
417	C₂×Dic₁₃	C₂⁵	1	4	yes	—
418	C₂×Dic₁₃	C₂⁵	1	2	yes	—
419	D₅₂	C₂²×Q₈	1	16	yes	complemented
420	C₄×D₁₃	—	2	8	no	—
421	C₄×D₁₃	—	2	16	no	—
422	C₄×D₁₃	—	4	8	no	—
423	C₄×D₁₃	—	4	8	no	—
424	C₄×D₁₃	—	4	4	no	—
425	C₄×D₁₃	—	4	16	no	—
426	C₄×D₁₃	—	4	16	no	—
427	C₄×D₁₃	C₂²×Q₈	1	16	yes	complemented
428	Dic₂₆	—	2	8	no	—
429	Dic₂₆	—	4	8	no	—
430	Dic₂₆	—	4	8	no	—
431	Dic₂₆	—	4	16	no	—
432	C₂³×Q₈	—	13	2	no	—
433	C₂³×Q₈	C₂×D₁₃	1	2	yes	complemented
434	C₂³×D₄	—	13	1	no	—
435	C₂⁴×C₄	—	13	2	no	—
436	#554	—	13	32	no	—
437	#554	—	13	32	no	—
438	#554	—	13	64	no	—
439	#554	—	13	16	no	—
440	#554	—	13	32	no	—
441	#554	—	13	16	no	—
442	D₄×Q₈	—	13	32	no	—
443	D₄×Q₈	—	13	16	no	—
444	D₄×Q₈	C₂×D₁₃	1	16	yes	complemented
445	#544	—	13	32	no	—
446	#543	—	13	64	no	—
447	#533	—	13	16	no	—
448	#533	—	13	16	no	—
449	C₂×C₄⋊Q₈	—	13	1	no	—
450	C₂×C₄⋊Q₈	—	13	4	no	—
451	C₂×C₄⋊Q₈	—	13	1	no	—
452	C₂×C₄⋊Q₈	—	13	2	no	—
453	C₂×C₄⋊Q₈	—	13	1	no	—
454	C₂×C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
455	C₂×C₄⋊Q₈	C₂×D₁₃	1	2	yes	complemented
456	C₂×#125	—	13	2	no	—
457	C₂×#125	—	13	4	no	—
458	C₂×#125	—	13	2	no	—
459	C₂×#125	—	13	2	no	—
460	C₂×#125	—	13	2	no	—
461	C₂×C₂²⋊Q₈	—	13	2	no	—
462	C₂×C₂²⋊Q₈	—	13	1	no	—
463	C₂×C₂²⋊Q₈	—	13	4	no	—
464	C₂×C₂²⋊Q₈	—	13	2	no	—
465	C₂×C₂²⋊Q₈	—	13	2	no	—
466	C₂×C₂²⋊Q₈	—	13	4	no	—
467	C₂×C₂²⋊Q₈	—	13	4	no	—
468	C₂×C₂²⋊Q₈	—	13	32	no	—
469	C₂×C₂²⋊Q₈	—	13	2	no	—
470	C₂×C₂²⋊Q₈	—	13	4	no	—
471	C₂×C₂²⋊Q₈	—	13	32	no	—
472	C₂×C₂²⋊Q₈	—	13	4	no	—
473	C₂×C₂²⋊Q₈	—	13	2	no	—
474	C₂×C₂²⋊Q₈	—	13	4	no	—
475	C₂×C₂²⋊Q₈	—	13	4	no	—
476	C₂×C₂²⋊Q₈	—	13	1	no	—
477	C₂×C₂²⋊Q₈	—	13	2	no	—
478	C₂×C₂²⋊Q₈	—	13	4	no	—
479	C₂×C₂²⋊Q₈	—	13	4	no	—
480	C₂×C₂²⋊Q₈	—	13	4	no	—
481	C₂×C₂²⋊Q₈	—	13	4	no	—
482	C₂×C₂²⋊Q₈	C₂×D₁₃	1	2	yes	complemented
483	C₂×C₂²⋊Q₈	C₂×D₁₃	1	4	yes	complemented
484	#518	—	13	32	no	—
485	C₂×C₄×Q₈	—	13	2	no	—
486	C₂×C₄×Q₈	—	13	2	no	—
487	C₂×C₄×Q₈	—	13	1	no	—
488	C₂×C₄×Q₈	—	13	2	no	—
489	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
490	C₂×C₄×D₄	—	13	1	no	—
491	C₂×C₄×D₄	—	13	2	no	—
492	C₂×C₄×D₄	—	13	2	no	—
493	C₂×C₄×D₄	—	13	4	no	—
494	C₂×C₄×D₄	—	13	16	no	—
495	C₂×C₄×D₄	—	13	1	no	—
496	C₂×C₄×D₄	—	13	2	no	—
497	C₂×C₄×D₄	—	13	2	no	—
498	C₂×C₄×D₄	—	13	4	no	—
499	C₂×C₄×D₄	—	13	1	no	—
500	C₂×C₄×D₄	—	13	2	no	—
501	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
502	C₂×C₄×D₄	C₂×D₁₃	1	2	yes	—
503	C₂×#117	—	13	2	no	—
504	C₂×#117	—	13	2	no	—
505	C₂²×C₄⋊C₄	—	13	4	no	—
506	C₂²×C₄⋊C₄	—	13	2	no	—
507	C₂²×C₄⋊C₄	—	13	1	no	—
508	C₂²×C₄⋊C₄	—	13	4	no	—
509	C₂²×C₄⋊C₄	—	13	2	no	—
510	C₂²×C₂²⋊C₄	—	13	4	no	—
511	C₂²×C₂²⋊C₄	—	13	2	no	—
512	C₂²×C₂²⋊C₄	—	13	4	no	—
513	C₂²×C₄²	—	13	1	no	—
514	C₂²×C₁₃	—	2	4	no	—
515	C₂²×C₁₃	—	2	4	no	—
516	C₂²×C₁₃	—	2	16	no	—
517	C₂²×C₁₃	C₂³×Q₈	1	8	yes	—
518	C₂²×C₁₃	C₂³×Q₈	1	2	yes	—
519	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
520	C₂²×C₁₃	#585	1	2	yes	—
521	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
522	C₂×D₁₃	—	2	4	no	—
523	C₂×D₁₃	—	2	2	no	—
524	C₂×D₁₃	—	2	4	no	—
525	C₂×D₁₃	—	2	2	no	—
526	C₂×D₁₃	—	2	8	no	—
527	C₂×D₁₃	—	2	16	no	—
528	C₂×D₁₃	—	4	32	no	—
529	C₂×D₁₃	C₂³×Q₈	1	4	yes	—
530	C₂×D₁₃	C₂³×Q₈	1	8	yes	—
531	C₄×C₁₃	—	2	8	no	—
532	C₄×C₁₃	—	2	4	no	—
533	C₄×C₁₃	—	2	4	no	—
534	C₄×C₁₃	—	2	2	no	—
535	C₄×C₁₃	—	2	4	no	—
536	C₄×C₁₃	C₂³×Q₈	1	4	yes	—
537	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
538	Dic₁₃	—	2	4	no	—
539	Dic₁₃	—	2	4	no	—
540	Dic₁₃	—	2	2	no	—
541	Dic₁₃	—	2	2	no	—
542	Dic₁₃	—	2	8	no	—
543	Dic₁₃	—	2	4	no	—
544	Dic₁₃	C₂³×Q₈	1	4	yes	—
545	C₂⁵	—	13	2	no	—
546	C₂²×Q₈	—	4	8	no	—
547	C₂²×Q₈	—	13	16	no	—
548	C₂²×Q₈	—	13	1	no	—
549	C₂²×Q₈	—	13	2	no	—
550	C₂²×Q₈	—	13	2	no	—
551	C₂²×Q₈	—	13	4	no	—
552	C₂²×Q₈	—	52	8	no	—
553	C₂²×Q₈	C₂²×D₁₃	1	2	yes	—
554	C₂²×Q₈	C₂²×D₁₃	1	1	yes	characteristic
555	C₂²×Q₈	C₂²×D₁₃	1	4	yes	—
556	C₂²×Q₈	C₂²×D₁₃	1	16	yes	complemented
557	C₂²×D₄	—	13	2	no	—
558	C₂²×D₄	—	13	16	no	—
559	C₂²×D₄	—	13	8	no	—
560	C₂²×D₄	—	13	1	no	—
561	C₂²×D₄	C₂²×D₁₃	1	1	yes	characteristic
562	C₂³×C₄	—	13	1	no	—
563	C₂³×C₄	—	13	4	no	—
564	C₂³×C₄	—	13	2	no	—
565	C₂³×C₄	—	13	2	no	—
566	C₂³×C₄	—	13	1	no	—
567	C₂³×C₄	—	13	1	no	—
568	C₂³×C₄	—	13	4	no	—
569	C₂³×C₄	—	13	4	no	—
570	C₂³×C₄	—	13	2	no	—
571	C₂³×C₄	—	13	2	no	—
572	C₂³×C₄	—	13	16	no	—
573	C₂³×C₄	—	52	8	no	—
574	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
575	C₂³×C₄	C₂²×D₁₃	1	4	yes	—
576	C₄⋊Q₈	—	13	8	no	—
577	C₄⋊Q₈	—	13	32	no	—
578	C₄⋊Q₈	—	13	8	no	—
579	C₄⋊Q₈	—	13	16	no	—
580	C₄⋊Q₈	—	13	8	no	—
581	C₄⋊Q₈	C₂²×D₁₃	1	8	yes	complemented
582	C₄⋊Q₈	C₂²×D₁₃	1	16	yes	complemented
583	#125	—	13	16	no	—
584	#125	—	13	16	no	—
585	#125	—	13	32	no	—
586	#125	—	13	16	no	—
587	#125	—	13	16	no	—
588	C₂²⋊Q₈	—	13	16	no	—
589	C₂²⋊Q₈	—	13	8	no	—
590	C₂²⋊Q₈	—	13	32	no	—
591	C₂²⋊Q₈	—	13	16	no	—
592	C₂²⋊Q₈	—	13	16	no	—
593	C₂²⋊Q₈	—	13	32	no	—
594	C₂²⋊Q₈	—	13	32	no	—
595	C₂²⋊Q₈	—	13	16	no	—
596	C₂²⋊Q₈	—	13	32	no	—
597	C₂²⋊Q₈	—	13	8	no	—
598	C₂²⋊Q₈	—	13	32	no	—
599	C₂²⋊Q₈	—	13	16	no	—
600	C₂²⋊Q₈	—	13	16	no	—
601	C₂²⋊Q₈	—	13	32	no	—
602	C₂²⋊Q₈	—	13	32	no	—
603	C₂²⋊Q₈	—	13	32	no	—
604	C₂²⋊Q₈	—	13	32	no	—
605	C₂²⋊Q₈	—	13	32	no	—
606	C₂²⋊Q₈	—	13	32	no	—
607	C₂²⋊Q₈	C₂²×D₁₃	1	16	yes	complemented
608	C₂²⋊Q₈	C₂²×D₁₃	1	32	yes	complemented
609	C₄×Q₈	—	13	16	no	—
610	C₄×Q₈	—	13	16	no	—
611	C₄×Q₈	—	13	8	no	—
612	C₄×Q₈	—	13	16	no	—
613	C₄×Q₈	C₂²×D₁₃	1	8	yes	complemented
614	C₄×D₄	—	13	8	no	—
615	C₄×D₄	—	13	16	no	—
616	C₄×D₄	—	13	16	no	—
617	C₄×D₄	—	13	32	no	—
618	C₄×D₄	—	13	8	no	—
619	C₄×D₄	—	13	16	no	—
620	C₄×D₄	—	13	16	no	—
621	C₄×D₄	—	13	32	no	—
622	C₄×D₄	—	13	8	no	—
623	C₄×D₄	—	13	16	no	—
624	C₄×D₄	C₂²×D₁₃	1	8	yes	—
625	C₄×D₄	C₂²×D₁₃	1	16	yes	—
626	#117	—	13	16	no	—
627	#117	—	13	16	no	—
628	C₂×C₄⋊C₄	—	13	4	no	—
629	C₂×C₄⋊C₄	—	13	2	no	—
630	C₂×C₄⋊C₄	—	13	2	no	—
631	C₂×C₄⋊C₄	—	13	1	no	—
632	C₂×C₄⋊C₄	—	13	2	no	—
633	C₂×C₄⋊C₄	—	13	2	no	—
634	C₂×C₄⋊C₄	—	13	1	no	—
635	C₂×C₄⋊C₄	—	13	4	no	—
636	C₂×C₄⋊C₄	—	13	4	no	—
637	C₂×C₄⋊C₄	—	13	4	no	—
638	C₂×C₄⋊C₄	—	13	4	no	—
639	C₂×C₄⋊C₄	—	13	4	no	—
640	C₂×C₄⋊C₄	—	13	32	no	—
641	C₂×C₄⋊C₄	—	13	16	no	—
642	C₂×C₄⋊C₄	—	13	2	no	—
643	C₂×C₄⋊C₄	—	13	2	no	—
644	C₂×C₄⋊C₄	—	13	2	no	—
645	C₂×C₄⋊C₄	—	13	2	no	—
646	C₂×C₄⋊C₄	—	13	4	no	—
647	C₂×C₄⋊C₄	—	13	2	no	—
648	C₂×C₄⋊C₄	—	13	8	no	—
649	C₂×C₄⋊C₄	—	13	32	no	—
650	C₂×C₄⋊C₄	—	13	16	no	—
651	C₂×C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
652	C₂×C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
653	C₂×C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
654	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
655	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
656	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
657	C₂×C₂²⋊C₄	—	13	2	no	—
658	C₂×C₂²⋊C₄	—	13	4	no	—
659	C₂×C₂²⋊C₄	—	13	4	no	—
660	C₂×C₂²⋊C₄	—	13	2	no	—
661	C₂×C₂²⋊C₄	—	13	2	no	—
662	C₂×C₂²⋊C₄	—	13	2	no	—
663	C₂×C₂²⋊C₄	—	13	4	no	—
664	C₂×C₂²⋊C₄	—	13	4	no	—
665	C₂×C₂²⋊C₄	—	13	2	no	—
666	C₂×C₂²⋊C₄	—	13	32	no	—
667	C₂×C₂²⋊C₄	—	13	16	no	—
668	C₂×C₂²⋊C₄	—	13	32	no	—
669	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
670	C₂×C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
671	C₂×C₄²	—	13	4	no	—
672	C₂×C₄²	—	13	2	no	—
673	C₂×C₄²	—	13	1	no	—
674	C₂×C₄²	—	13	1	no	—
675	C₂×C₄²	—	13	1	no	—
676	C₂×C₄²	—	13	8	no	—
677	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
678	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
679	C₂×C₁₃	—	2	8	no	—
680	C₂×C₁₃	#3501	1	4	yes	complemented
681	C₂×C₁₃	C₂⁴×Q₈	1	1	yes	characteristic
682	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
683	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
684	D₁₃	—	2	4	no	—
685	D₁₃	—	2	8	no	—
686	C₂⁴	—	13	1	no	—
687	C₂⁴	—	13	2	no	—
688	C₂⁴	—	13	16	no	—
689	C₂⁴	—	13	8	no	—
690	C₂⁴	—	52	4	no	—
691	C₂⁴	—	52	4	no	—
692	C₂⁴	C₂³×D₁₃	1	2	yes	—
693	C₂×Q₈	—	2	4	no	—
694	C₂×Q₈	—	2	8	no	—
695	C₂×Q₈	—	4	8	no	—
696	C₂×Q₈	—	4	32	no	—
697	C₂×Q₈	—	13	4	no	—
698	C₂×Q₈	—	13	8	no	—
699	C₂×Q₈	—	13	8	no	—
700	C₂×Q₈	—	13	16	no	—
701	C₂×Q₈	—	26	4	no	—
702	C₂×Q₈	—	52	8	no	—
703	C₂×Q₈	—	52	4	no	—
704	C₂×Q₈	—	52	4	no	—
705	C₂×Q₈	—	52	32	no	—
706	C₂×Q₈	C₂³×D₁₃	1	8	yes	—
707	C₂×Q₈	C₂³×D₁₃	1	4	yes	—
708	C₂×Q₈	C₂³×D₁₃	1	16	yes	—
709	C₂×D₄	—	13	16	no	—
710	C₂×D₄	—	13	8	no	—
711	C₂×D₄	—	13	64	no	—
712	C₂×D₄	—	13	8	no	—
713	C₂×D₄	—	13	4	no	—
714	C₂×D₄	Q₈×D₁₃	1	8	yes	complemented
715	C₂×D₄	C₂³×D₁₃	1	4	yes	—
716	C₂²×C₄	—	2	8	no	—
717	C₂²×C₄	—	4	8	no	—
718	C₂²×C₄	—	13	1	no	—
719	C₂²×C₄	—	13	8	no	—
720	C₂²×C₄	—	13	4	no	—
721	C₂²×C₄	—	13	1	no	—
722	C₂²×C₄	—	13	1	no	—
723	C₂²×C₄	—	13	4	no	—
724	C₂²×C₄	—	13	2	no	—
725	C₂²×C₄	—	13	2	no	—
726	C₂²×C₄	—	13	2	no	—
727	C₂²×C₄	—	13	16	no	—
728	C₂²×C₄	—	13	8	no	—
729	C₂²×C₄	—	13	4	no	—
730	C₂²×C₄	—	13	8	no	—
731	C₂²×C₄	—	13	4	no	—
732	C₂²×C₄	—	13	16	no	—
733	C₂²×C₄	—	13	16	no	—
734	C₂²×C₄	—	13	8	no	—
735	C₂²×C₄	—	13	8	no	—
736	C₂²×C₄	—	26	4	no	—
737	C₂²×C₄	—	26	8	no	—
738	C₂²×C₄	—	52	32	no	—
739	C₂²×C₄	—	52	4	no	—
740	C₂²×C₄	—	52	4	no	—
741	C₂²×C₄	—	52	8	no	—
742	C₂²×C₄	—	52	8	no	—
743	C₂²×C₄	—	52	2	no	—
744	C₂²×C₄	—	52	4	no	—
745	C₂²×C₄	—	52	8	no	—
746	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
747	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
748	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
749	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
750	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
751	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
752	C₂²×C₄	C₂³×D₁₃	1	16	yes	—
753	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
754	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
755	C₄⋊C₄	—	13	16	no	—
756	C₄⋊C₄	—	13	8	no	—
757	C₄⋊C₄	—	13	8	no	—
758	C₄⋊C₄	—	13	4	no	—
759	C₄⋊C₄	—	13	8	no	—
760	C₄⋊C₄	—	13	8	no	—
761	C₄⋊C₄	—	13	4	no	—
762	C₄⋊C₄	—	13	16	no	—
763	C₄⋊C₄	—	13	16	no	—
764	C₄⋊C₄	—	13	16	no	—
765	C₄⋊C₄	—	13	16	no	—
766	C₄⋊C₄	—	13	16	no	—
767	C₄⋊C₄	—	13	8	no	—
768	C₄⋊C₄	—	13	8	no	—
769	C₄⋊C₄	—	13	8	no	—
770	C₄⋊C₄	—	13	8	no	—
771	C₄⋊C₄	—	13	16	no	—
772	C₄⋊C₄	—	13	8	no	—
773	C₄⋊C₄	C₂³×D₁₃	1	4	yes	—
774	C₄⋊C₄	C₂³×D₁₃	1	4	yes	—
775	C₄⋊C₄	C₂³×D₁₃	1	16	yes	—
776	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
777	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
778	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
779	C₂²⋊C₄	—	13	8	no	—
780	C₂²⋊C₄	—	13	16	no	—
781	C₂²⋊C₄	—	13	16	no	—
782	C₂²⋊C₄	—	13	8	no	—
783	C₂²⋊C₄	—	13	8	no	—
784	C₂²⋊C₄	—	13	8	no	—
785	C₂²⋊C₄	—	13	16	no	—
786	C₂²⋊C₄	—	13	16	no	—
787	C₂²⋊C₄	—	13	8	no	—
788	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
789	C₂²⋊C₄	C₂³×D₁₃	1	16	yes	—
790	C₄²	—	13	4	no	—
791	C₄²	—	13	4	no	—
792	C₄²	—	13	4	no	—
793	C₄²	—	13	16	no	—
794	C₄²	—	13	8	no	—
795	C₄²	C₂³×D₁₃	1	4	yes	—
796	C₄²	C₂³×D₁₃	1	8	yes	—
797	C₁₃	C₂×#3501	1	1	yes	characteristic, complemented, Sylow
798	C₂³	—	2	4	no	—
799	C₂³	—	2	4	no	—
800	C₂³	—	13	4	no	—
801	C₂³	—	13	8	no	—
802	C₂³	—	13	2	no	—
803	C₂³	—	13	4	no	—
804	C₂³	—	13	32	no	—
805	C₂³	—	26	4	no	—
806	C₂³	—	26	2	no	—
807	C₂³	—	26	4	no	—
808	C₂³	—	26	2	no	—
809	C₂³	—	52	8	no	—
810	C₂³	—	52	8	no	—
811	C₂³	—	52	32	no	—
812	C₂³	C₂×Q₈×D₁₃	1	8	yes	—
813	C₂³	C₂⁴×D₁₃	1	4	yes	—
814	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
815	Q₈	—	2	8	no	—
816	Q₈	—	2	16	no	—
817	Q₈	—	4	16	no	—
818	Q₈	—	26	8	no	—
819	Q₈	—	52	8	no	—
820	Q₈	—	52	8	no	—
821	Q₈	—	52	16	no	—
822	D₄	—	13	32	no	—
823	D₄	—	13	16	no	—
824	D₄	C₂×Q₈×D₁₃	1	16	yes	complemented
825	C₂×C₄	—	2	4	no	—
826	C₂×C₄	—	2	4	no	—
827	C₂×C₄	—	2	8	no	—
828	C₂×C₄	—	2	4	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	16	no	—
831	C₂×C₄	—	4	16	no	—
832	C₂×C₄	—	13	4	no	—
833	C₂×C₄	—	13	2	no	—
834	C₂×C₄	—	13	16	no	—
835	C₂×C₄	—	13	2	no	—
836	C₂×C₄	—	13	2	no	—
837	C₂×C₄	—	13	8	no	—
838	C₂×C₄	—	13	4	no	—
839	C₂×C₄	—	13	4	no	—
840	C₂×C₄	—	13	4	no	—
841	C₂×C₄	—	26	2	no	—
842	C₂×C₄	—	26	4	no	—
843	C₂×C₄	—	26	4	no	—
844	C₂×C₄	—	26	8	no	—
845	C₂×C₄	—	26	4	no	—
846	C₂×C₄	—	26	2	no	—
847	C₂×C₄	—	26	8	no	—
848	C₂×C₄	—	26	16	no	—
849	C₂×C₄	—	52	16	no	—
850	C₂×C₄	—	52	4	no	—
851	C₂×C₄	—	52	8	no	—
852	C₂×C₄	—	52	8	no	—
853	C₂×C₄	—	52	16	no	—
854	C₂×C₄	—	52	16	no	—
855	C₂×C₄	—	52	8	no	—
856	C₂×C₄	#88251	1	4	yes	—
857	C₂×C₄	C₂×Q₈×D₁₃	1	4	yes	—
858	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
859	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
860	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
861	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
862	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
863	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
864	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
865	C₂²	—	2	4	no	—
866	C₂²	—	2	4	no	—
867	C₂²	—	2	16	no	—
868	C₂²	—	13	4	no	—
869	C₂²	—	13	8	no	—
870	C₂²	—	26	4	no	—
871	C₂²	—	26	2	no	—
872	C₂²	—	26	4	no	—
873	C₂²	—	26	2	no	—
874	C₂²	—	26	16	no	—
875	C₂²	—	26	8	no	—
876	C₂²	—	52	32	no	—
877	C₂²	C₂×#88251	1	2	yes	—
878	C₂²	C₂²×Q₈×D₁₃	1	8	yes	—
879	C₂²	C₂²×Q₈×D₁₃	1	2	yes	—
880	C₂²	#11719652	1	2	yes	—
881	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
882	C₄	—	2	4	no	—
883	C₄	—	2	4	no	—
884	C₄	—	2	8	no	—
885	C₄	—	2	4	no	—
886	C₄	—	2	2	no	—
887	C₄	—	13	4	no	—
888	C₄	—	26	2	no	—
889	C₄	—	26	4	no	—
890	C₄	—	26	4	no	—
891	C₄	—	26	8	no	—
892	C₄	—	26	4	no	—
893	C₄	—	26	2	no	—
894	C₄	C₂×#88251	1	4	yes	—
895	C₄	C₂²×Q₈×D₁₃	1	4	yes	—
896	C₂	—	2	8	no	—
897	C₂	—	26	4	no	—
898	C₂	—	26	8	no	—
899	C₂	#13128631	1	4	yes	direct product factor
900	C₂	C₂³×Q₈×D₁₃	1	1	yes	characteristic
901	C₂	C₂²×#88251	1	1	yes	characteristic
902	C₂	C₂×#11719652	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂×D₄×Q₈×C₁₃	C₂
socle	C₂³×C₁₃	C₂⁵
prime radical	C₂²×D₄×D₁₃	C₂²
hypercenter	C₂×D₄×Q₈	D₁₃
hypocenter	C₁₃	C₂×#3501
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×D₄×Q₈

Complements

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

N	H ≅ G/N	type
1. #13128631	C₂	direct (N × H)
2. C₂×#11719435	C₂	semidirect
3. C₂×#11719284	C₂	semidirect
4. C₂×#11719244	C₂	semidirect
5. C₂×#11719340	C₂	semidirect
6. C₂×#11719248	C₂	semidirect
7. C₂×#11719341	C₂	semidirect
8. C₂×#11719432	C₂	semidirect
9. C₂×Q₈×C₂²⋊D₁₃	C₂	semidirect
10. C₂×#11719434	C₂	semidirect
11. C₂×#11719339	C₂	semidirect
12. C₂×#11719433	C₂	semidirect
13. C₂×#11719283	C₂	semidirect
14. C₂²×#88200	C₂	semidirect
15. C₂×D₁₃×C₂²⋊Q₈	C₂	semidirect
18. C₂×D₄×Q₈×C₁₃	C₂	semidirect
19. C₂³×Q₈×C₁₃	C₂²	semidirect
20. C₂²×Q₈×D₁₃	C₂²	semidirect
23. D₄×Q₈×C₁₃	C₂²	semidirect
24. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
25. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
26. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
27. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
28. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
31. Q₈×C₂²⋊D₁₃	C₂²	semidirect
35. C₂×#88200	C₂²	semidirect
36. C₂×#88200	C₂²	semidirect
37. C₂×#88200	C₂²	semidirect
38. C₂×#88200	C₂²	semidirect
39. C₂×#88200	C₂²	semidirect
40. C₂×Q₈×Dic₁₃	C₂²	semidirect
41. C₂×#88198	C₂²	semidirect
42. C₂×#88198	C₂²	semidirect
48. C₂²×C₄⋊Dic₁₃	C₂²	semidirect
49. C₂×#88178	C₂²	semidirect
50. C₂×#88178	C₂²	semidirect
51. C₂²×#6101	C₂²	semidirect
52. #11719435	C₂²	semidirect
53. #11719434	C₂²	semidirect
54. #11719433	C₂²	semidirect
55. #11719432	C₂²	semidirect
56. #11719341	C₂²	semidirect
57. #11719340	C₂²	semidirect
58. #11719339	C₂²	semidirect
59. D₁₃×C₂²⋊Q₈	C₂²	semidirect
60. #11719284	C₂²	semidirect
61. #11719283	C₂²	semidirect
64. #11719248	C₂²	semidirect
65. #11719244	C₂²	semidirect
68. C₂×#88151	C₂²	semidirect
71. C₂×#88150	C₂²	semidirect
72. C₂×#88150	C₂²	semidirect
77. C₂×C₄⋊C₄×D₁₃	C₂²	semidirect
78. C₂×C₄⋊C₄×D₁₃	C₂²	semidirect
79. C₂×#88144	C₂²	semidirect
80. C₂×#88144	C₂²	semidirect
81. C₂×#88143	C₂²	semidirect
82. C₂×#88143	C₂²	semidirect
83. C₂×#88142	C₂²	semidirect
84. C₂×#88142	C₂²	semidirect
85. C₂×#88141	C₂²	semidirect
90. C₂×#88132	C₂²	semidirect
91. C₂×#88132	C₂²	semidirect
92. C₂×#88132	C₂²	semidirect
97. C₂×#88124	C₂²	semidirect
98. C₂×#88123	C₂²	semidirect
99. C₂×C₄×Dic₂₆	C₂²	semidirect
100. C₂×C₄×Dic₂₆	C₂²	semidirect
106. C₂²×Q₈×C₁₃	C₂³	semidirect
114. C₂×Q₈×D₁₃	C₂³	semidirect
115. C₂×D₄×D₁₃	Q₈	semidirect
132. C₁₃×C₄⋊Q₈	C₂³	semidirect
133. C₁₃×C₄⋊Q₈	C₂³	semidirect
134. C₁₃×C₂²⋊Q₈	C₂³	semidirect
135. C₁₃×C₂²⋊Q₈	C₂³	semidirect
136. C₄×Q₈×C₁₃	C₂³	semidirect
154. #88200	C₂³	semidirect
155. #88200	C₂³	semidirect
156. #88200	C₂³	semidirect
157. #88200	C₂³	semidirect
158. Q₈×Dic₁₃	C₂³	semidirect
159. #88198	C₂³	semidirect
160. #88198	C₂³	semidirect
180. C₂×C₄⋊Dic₁₃	C₂³	semidirect
181. #88178	C₂³	semidirect
182. #88178	C₂³	semidirect
194. C₂×#6101	C₂³	semidirect
202. #88151	C₂³	semidirect
205. #88150	C₂³	semidirect
206. #88150	C₂³	semidirect
211. C₄⋊C₄×D₁₃	C₂³	semidirect
212. C₄⋊C₄×D₁₃	C₂³	semidirect
213. #88144	C₂³	semidirect
214. #88144	C₂³	semidirect
215. #88143	C₂³	semidirect
216. #88143	C₂³	semidirect
217. #88142	C₂³	semidirect
218. #88142	C₂³	semidirect
219. #88141	C₂³	semidirect
224. #88132	C₂³	semidirect
225. #88132	C₂³	semidirect
226. #88132	C₂³	semidirect
231. #88124	C₂³	semidirect
232. #88123	C₂³	semidirect
233. C₄×Dic₂₆	C₂³	semidirect
234. C₄×Dic₂₆	C₂³	semidirect
239. C₂³×D₁₃	C₂×Q₈	semidirect
250. C₂×D₄×C₁₃	C₂×Q₈	semidirect
263. C₂×C₂²⋊D₁₃	C₂×Q₈	semidirect
277. D₄×D₁₃	C₂×Q₈	semidirect
278. C₂×D₅₂	C₂×Q₈	semidirect
288. C₂×C₄×D₁₃	C₂×Q₈	semidirect
356. C₂×D₄×Q₈	D₁₃	semidirect
379. C₂²×D₁₃	C₂²×Q₈	semidirect
385. D₄×C₁₃	C₂²×Q₈	semidirect
402. C₂²⋊D₁₃	C₂²×Q₈	semidirect
419. D₅₂	C₂²×Q₈	semidirect
427. C₄×D₁₃	C₂²×Q₈	semidirect
433. C₂³×Q₈	C₂×D₁₃	semidirect
444. D₄×Q₈	C₂×D₁₃	semidirect
454. C₂×C₄⋊Q₈	C₂×D₁₃	semidirect
455. C₂×C₄⋊Q₈	C₂×D₁₃	semidirect
482. C₂×C₂²⋊Q₈	C₂×D₁₃	semidirect
483. C₂×C₂²⋊Q₈	C₂×D₁₃	semidirect
489. C₂×C₄×Q₈	C₂×D₁₃	semidirect
556. C₂²×Q₈	C₂²×D₁₃	semidirect
581. C₄⋊Q₈	C₂²×D₁₃	semidirect
582. C₄⋊Q₈	C₂²×D₁₃	semidirect
607. C₂²⋊Q₈	C₂²×D₁₃	semidirect
608. C₂²⋊Q₈	C₂²×D₁₃	semidirect
613. C₄×Q₈	C₂²×D₁₃	semidirect
680. C₂×C₁₃	#3501	semidirect
714. C₂×D₄	Q₈×D₁₃	semidirect
797. C₁₃	C₂×#3501	semidirect
824. D₄	C₂×Q₈×D₁₃	semidirect
899. C₂	#13128631	direct (N × H)

Maximal subgroups

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

subgroup	index
#13128631	2
C₂×#11719435	2
C₂×#11719284	2
C₂×#11719244	2
C₂×#11719340	2
C₂×#11719248	2
C₂×#11719341	2
C₂×#11719432	2
C₂×Q₈×C₂²⋊D₁₃	2
C₂×#11719434	2
C₂×#11719339	2
C₂×#11719433	2
C₂×#11719283	2
C₂²×#88200	2
C₂×D₁₃×C₂²⋊Q₈	2
C₂×#11719250	2
C₂×C₄×D₄×D₁₃	2
C₂×D₄×Q₈×C₁₃	2
C₂×#3501	13

Subgroups — C2×#13128631 #16770815

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13128631 #16770815