Subgroups — C₂×#13128734 #16771411

Order 3328.

7302 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13128734	C₂	1	32	yes	maximal, direct product factor
2	C₂×#11719290	C₂	1	4	yes	maximal, complemented
3	C₂×#11719289	C₂	1	4	yes	maximal, complemented
4	C₂×#11719342	C₂	1	8	yes	maximal, complemented
5	C₂×#11719438	C₂	1	4	yes	maximal, complemented
6	C₂×#11719231	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#11719230	C₂	1	1	yes	maximal, characteristic
8	C₂×#11719396	C₂	1	4	yes	maximal, complemented
9	C₂²×#88129	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#11719221	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#11719226	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×#6127	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#6127	C₂²	1	1	yes	characteristic
15	C₂³×D₅₂	C₂²	1	1	yes	characteristic
16	C₂³×Dic₂₆	C₂²	1	1	yes	characteristic
17	C₁₃×#533	C₂²	1	16	yes	complemented
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
19	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
20	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
21	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
22	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
25	C₂×#88201	C₂²	1	8	yes	complemented
26	C₂×#88200	C₂²	1	8	yes	complemented
27	C₂×C₄×C₂²⋊D₁₃	C₂²	1	4	yes	—
28	C₂²×#6103	C₂²	1	4	yes	—
29	C₂×#88180	C₂²	1	1	yes	characteristic
30	#11719438	C₂²	1	64	yes	complemented
31	#11719396	C₂²	1	64	yes	complemented
32	#11719342	C₂²	1	128	yes	complemented
33	#11719290	C₂²	1	64	yes	complemented
34	#11719289	C₂²	1	64	yes	complemented
35	#11719231	C₂²	1	16	yes	complemented
36	#11719230	C₂²	1	16	yes	—
37	#11719226	C₂²	1	16	yes	complemented
38	#11719221	C₂²	1	16	yes	complemented
39	C₂×#88152	C₂²	1	8	yes	complemented
40	C₂×#88152	C₂²	1	8	yes	complemented
41	C₂×#88151	C₂²	1	4	yes	complemented
42	C₂×#88149	C₂²	1	4	yes	—
43	C₂×#88148	C₂²	1	8	yes	complemented
44	C₂×#88148	C₂²	1	8	yes	complemented
45	C₂×#88147	C₂²	1	4	yes	—
46	C₂×#88147	C₂²	1	8	yes	complemented
47	C₂×#88146	C₂²	1	8	yes	complemented
48	C₂×#88141	C₂²	1	4	yes	complemented
49	C₂×#88140	C₂²	1	4	yes	—
50	C₂×#88136	C₂²	1	4	yes	—
51	C₂×C₂²⋊C₄×D₁₃	C₂²	1	4	yes	—
52	C₂×#88131	C₂²	1	4	yes	—
53	C₂×#88129	C₂²	1	2	yes	—
54	C₂×#88129	C₂²	1	2	yes	—
55	C₂×#88129	C₂²	1	4	yes	—
56	C₂×#88129	C₂²	1	2	yes	—
57	C₂×#88129	C₂²	1	16	yes	complemented
58	C₂×#88129	C₂²	1	2	yes	complemented
59	C₂×#88128	C₂²	1	2	yes	—
60	C₄×#6127	C₂²	1	16	yes	complemented
61	C₂×C₄×D₅₂	C₂²	1	4	yes	—
62	C₂×C₄×D₅₂	C₂²	1	2	yes	complemented
63	C₂×#88126	C₂²	1	2	yes	complemented
64	C₂×C₄²×D₁₃	C₂²	1	2	yes	complemented
65	C₂×#88123	C₂²	1	2	yes	complemented
66	C₂×C₄×Dic₂₆	C₂²	1	2	yes	complemented
67	C₂×C₄×Dic₂₆	C₂²	1	4	yes	complemented
68	C₂⁴×D₁₃	C₂³	1	2	yes	—
69	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
70	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
71	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
72	C₂²×C₂²⋊D₁₃	C₂³	1	2	yes	—
73	C₂³×Dic₁₃	C₂³	1	2	yes	—
74	C₂×#6127	—	2	8	no	—
75	C₂×#6127	C₂³	1	8	yes	—
76	C₂²×D₅₂	—	2	8	no	—
77	C₂²×D₅₂	C₂³	1	2	yes	—
78	C₂²×D₅₂	C₂³	1	1	yes	characteristic
79	C₂²×D₅₂	C₂³	1	2	yes	—
80	C₂²×D₅₂	C₂³	1	8	yes	—
81	C₂²×D₅₂	C₂³	1	8	yes	—
82	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
83	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
84	C₂²×C₄×D₁₃	C₂³	1	8	yes	—
85	C₂²×Dic₂₆	—	2	8	no	—
86	C₂²×Dic₂₆	C₂³	1	1	yes	characteristic
87	C₂²×Dic₂₆	C₂³	1	2	yes	—
88	C₂²×Dic₂₆	C₂³	1	2	yes	—
89	C₂²×Dic₂₆	C₂³	1	8	yes	—
90	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	complemented
91	C₁₃×#125	C₂³	1	16	yes	complemented
92	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
93	C₄×Q₈×C₁₃	C₂³	1	32	yes	complemented
94	C₁₃×#117	C₂³	1	8	yes	—
95	C₁₃×#117	C₂³	1	8	yes	—
96	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
97	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
98	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
101	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
102	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
103	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
104	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
105	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
106	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
109	C₂×C₂²⋊Dic₁₃	C₂³	1	2	yes	—
110	#88201	C₂³	1	64	yes	complemented
111	#88200	C₂³	1	64	yes	complemented
112	C₄×C₂²⋊D₁₃	C₂³	1	32	yes	—
113	C₂×#6103	C₂³	1	4	yes	—
114	C₂×#6103	C₂³	1	8	yes	—
115	C₂×#6103	C₂³	1	8	yes	—
116	C₂×#6103	C₂³	1	8	yes	—
117	C₂×#6103	C₂³	1	8	yes	—
118	C₂×#6103	C₂³	1	32	yes	—
119	C₂×#6103	C₂³	1	8	yes	—
120	#88180	C₂³	1	8	yes	—
121	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
122	C₂×C₄⋊Dic₁₃	C₂³	1	8	yes	—
123	C₂×#6101	C₂³	1	4	yes	—
124	C₂×#6101	C₂³	1	8	yes	—
125	C₂×C₄×Dic₁₃	C₂³	1	4	yes	—
126	C₂×C₄×Dic₁₃	C₂³	1	8	yes	—
127	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
128	#88152	C₂³	1	64	yes	complemented
129	#88152	C₂³	1	64	yes	complemented
130	#88151	C₂³	1	32	yes	complemented
131	#88149	C₂³	1	32	yes	—
132	#88148	C₂³	1	64	yes	complemented
133	#88148	C₂³	1	64	yes	complemented
134	#88147	C₂³	1	32	yes	—
135	#88147	C₂³	1	64	yes	complemented
136	#88146	C₂³	1	64	yes	complemented
137	#88141	C₂³	1	32	yes	complemented
138	#88140	C₂³	1	32	yes	—
139	#88136	C₂³	1	32	yes	—
140	C₂²⋊C₄×D₁₃	C₂³	1	32	yes	—
141	#88131	C₂³	1	32	yes	—
142	#88129	C₂³	1	16	yes	—
143	#88129	C₂³	1	32	yes	—
144	#88129	C₂³	1	16	yes	—
145	#88129	C₂³	1	16	yes	—
146	#88129	C₂³	1	16	yes	complemented
147	#88128	C₂³	1	16	yes	—
148	C₄×D₅₂	C₂³	1	32	yes	—
149	C₄×D₅₂	C₂³	1	16	yes	complemented
150	#88126	C₂³	1	16	yes	complemented
151	C₄²×D₁₃	C₂³	1	16	yes	complemented
152	#88123	C₂³	1	16	yes	complemented
153	C₄×Dic₂₆	C₂³	1	16	yes	complemented
154	C₄×Dic₂₆	C₂³	1	32	yes	complemented
155	C₂×#3510	—	13	1	no	maximal, Sylow
156	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
157	C₂³×D₁₃	—	2	8	no	—
158	C₂³×D₁₃	—	4	8	no	—
159	C₂³×D₁₃	C₂⁴	1	4	yes	—
160	C₂³×D₁₃	C₂⁴	1	2	yes	—
161	C₂³×D₁₃	C₂⁴	1	8	yes	—
162	C₂×Q₈×C₁₃	—	4	8	no	—
163	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	—
164	C₂²×C₄×C₁₃	—	4	4	no	—
165	C₂²×C₄×C₁₃	#41	1	8	yes	—
166	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
167	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
168	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
169	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
170	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
171	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
172	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
173	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
174	C₂×C₂²⋊D₁₃	—	2	8	no	—
175	C₂×C₂²⋊D₁₃	C₂⁴	1	8	yes	—
176	C₂²×Dic₁₃	—	2	8	no	—
177	C₂²×Dic₁₃	C₂⁴	1	8	yes	—
178	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
179	C₂²×Dic₁₃	C₂⁴	1	2	yes	—
180	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
181	#6127	—	2	32	no	—
182	C₂×D₅₂	—	2	8	no	—
183	C₂×D₅₂	—	2	8	no	—
184	C₂×D₅₂	—	2	32	no	—
185	C₂×D₅₂	—	2	4	no	—
186	C₂×D₅₂	—	4	16	no	—
187	C₂×D₅₂	C₂⁴	1	8	yes	—
188	C₂×D₅₂	C₂⁴	1	4	yes	—
189	C₂×D₅₂	C₂⁴	1	8	yes	—
190	C₂×D₅₂	C₂⁴	1	32	yes	—
191	C₂×C₄×D₁₃	—	2	8	no	—
192	C₂×C₄×D₁₃	—	4	8	no	—
193	C₂×C₄×D₁₃	—	4	16	no	—
194	C₂×C₄×D₁₃	C₂⁴	1	8	yes	—
195	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
196	C₂×C₄×D₁₃	C₂⁴	1	32	yes	—
197	C₂×Dic₂₆	—	2	8	no	—
198	C₂×Dic₂₆	—	2	8	no	—
199	C₂×Dic₂₆	—	2	32	no	—
200	C₂×Dic₂₆	—	2	4	no	—
201	C₂×Dic₂₆	C₂⁴	1	4	yes	—
202	C₂×Dic₂₆	C₂⁴	1	8	yes	—
203	C₂×Dic₂₆	C₂⁴	1	8	yes	—
204	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
205	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
206	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
207	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
208	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
209	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
210	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
211	C₄²×C₁₃	C₂⁴	1	8	yes	—
212	C₄²×C₁₃	C₂⁴	1	8	yes	—
213	C₄²×C₁₃	C₂⁴	1	8	yes	—
214	C₄²×C₁₃	C₂⁴	1	4	yes	—
215	C₄²×C₁₃	C₂⁴	1	4	yes	—
216	C₂²⋊Dic₁₃	C₂⁴	1	8	yes	—
217	#6103	C₂⁴	1	16	yes	—
218	#6103	C₂⁴	1	32	yes	—
219	#6103	C₂⁴	1	32	yes	—
220	#6103	C₂⁴	1	32	yes	—
221	#6103	C₂⁴	1	32	yes	—
222	#6103	C₂⁴	1	32	yes	—
223	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
224	C₄⋊Dic₁₃	C₂⁴	1	32	yes	—
225	#6101	C₂⁴	1	16	yes	—
226	#6101	C₂⁴	1	32	yes	—
227	C₄×Dic₁₃	C₂⁴	1	16	yes	—
228	C₄×Dic₁₃	C₂⁴	1	32	yes	—
229	C₄×Dic₁₃	C₂⁴	1	8	yes	—
230	#3510	—	13	32	no	—
231	C₂×#559	—	13	4	no	—
232	C₂×#556	—	13	4	no	—
233	C₂×#551	—	13	8	no	—
234	C₂×#542	—	13	4	no	—
235	C₂×#536	—	13	1	no	—
236	C₂×#535	—	13	1	no	—
237	C₂×#533	D₁₃	1	1	yes	characteristic, complemented
238	C₂×#529	—	13	4	no	—
239	C₂²×#124	—	13	1	no	—
240	C₂×#519	—	13	1	no	—
241	C₂×#518	—	13	1	no	—
242	C₂×C₄×#41	—	13	1	no	—
243	C₂³×C₁₃	—	2	4	no	—
244	C₂³×C₁₃	C₂×#41	1	4	yes	—
245	C₂³×C₁₃	C₂⁵	1	2	yes	—
246	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
247	C₂²×D₁₃	—	2	4	no	—
248	C₂²×D₁₃	—	2	8	no	—
249	C₂²×D₁₃	—	2	8	no	—
250	C₂²×D₁₃	—	2	16	no	—
251	C₂²×D₁₃	—	2	16	no	—
252	C₂²×D₁₃	—	4	16	no	—
253	C₂²×D₁₃	—	8	16	no	—
254	C₂²×D₁₃	C₂⁵	1	8	yes	—
255	C₂²×D₁₃	C₂⁵	1	4	yes	—
256	Q₈×C₁₃	—	4	16	no	—
257	C₂×C₄×C₁₃	—	2	4	no	—
258	C₂×C₄×C₁₃	—	2	8	no	—
259	C₂×C₄×C₁₃	—	2	8	no	—
260	C₂×C₄×C₁₃	—	2	4	no	—
261	C₂×C₄×C₁₃	—	4	8	no	—
262	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
263	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
264	C₂×C₄×C₁₃	C₂×#41	1	16	yes	—
265	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
266	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
267	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
268	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
269	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
270	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
271	C₂²⋊D₁₃	—	2	16	no	—
272	C₂×Dic₁₃	—	2	16	no	—
273	C₂×Dic₁₃	—	2	8	no	—
274	C₂×Dic₁₃	—	2	4	no	—
275	C₂×Dic₁₃	—	2	8	no	—
276	C₂×Dic₁₃	C₂⁵	1	8	yes	—
277	C₂×Dic₁₃	C₂⁵	1	4	yes	—
278	C₂×Dic₁₃	C₂⁵	1	8	yes	—
279	D₅₂	—	2	16	no	—
280	D₅₂	—	2	16	no	—
281	D₅₂	—	2	8	no	—
282	D₅₂	—	4	32	no	—
283	C₄×D₁₃	—	2	16	no	—
284	C₄×D₁₃	—	4	16	no	—
285	C₄×D₁₃	—	4	32	no	—
286	Dic₂₆	—	2	16	no	—
287	Dic₂₆	—	2	16	no	—
288	Dic₂₆	—	2	8	no	—
289	C₂²×#41	—	13	1	no	—
290	C₂³×Q₈	—	13	1	no	—
291	C₂³×D₄	—	13	1	no	—
292	#559	—	13	64	no	—
293	#556	—	13	64	no	—
294	#551	—	13	128	no	—
295	#542	—	13	64	no	—
296	#536	—	13	16	no	—
297	#535	—	13	16	no	—
298	#533	C₂×D₁₃	1	16	yes	complemented
299	C₂×C₄⋊Q₈	—	13	2	no	—
300	C₂×C₄⋊Q₈	C₂×D₁₃	1	2	yes	complemented
301	C₂×#127	—	13	2	no	—
302	#529	—	13	64	no	—
303	C₂×#126	—	13	8	no	—
304	C₂×#126	—	13	8	no	—
305	C₂×#125	C₂×D₁₃	1	2	yes	complemented
306	C₂×#124	—	13	8	no	—
307	C₂×#124	—	13	2	no	—
308	C₂×#124	—	13	2	no	—
309	C₂×#124	—	13	4	no	—
310	C₂×#124	—	13	2	no	—
311	C₂×#124	—	13	16	no	—
312	C₂×#124	—	13	2	no	—
313	C₂×#123	—	13	8	no	—
314	C₂×#123	—	13	8	no	—
315	C₂×#123	—	13	4	no	—
316	C₂×C₂²⋊Q₈	—	13	8	no	—
317	C₂×C₂²⋊Q₈	—	13	4	no	—
318	C₂×C₂²⋊Q₈	C₂×D₁₃	1	4	yes	—
319	C₂×#121	—	13	4	no	—
320	C₂×#120	—	13	4	no	—
321	#519	—	13	16	no	—
322	#518	—	13	16	no	—
323	C₄×#41	—	13	16	no	—
324	C₂×C₄×Q₈	—	13	4	no	—
325	C₂×C₄×Q₈	—	13	2	no	—
326	C₂×C₄×Q₈	—	13	4	no	—
327	C₂×C₄×Q₈	C₂×D₁₃	1	4	yes	complemented
328	C₂×C₄×D₄	—	13	4	no	—
329	C₂×C₄×D₄	—	13	4	no	—
330	C₂×C₄×D₄	—	13	8	no	—
331	C₂×C₄×D₄	—	13	4	no	—
332	C₂×C₄×D₄	—	13	2	no	—
333	C₂×#117	—	13	1	no	—
334	C₂×#117	—	13	8	no	—
335	C₂×#117	—	13	4	no	—
336	C₂×#117	—	13	2	no	—
337	C₂×#117	C₂×D₁₃	1	1	yes	characteristic
338	C₂×#117	C₂×D₁₃	1	1	yes	characteristic
339	C₂²×C₂²⋊C₄	—	13	4	no	—
340	C₂²×C₂²⋊C₄	—	13	4	no	—
341	C₂²×C₄²	—	13	2	no	—
342	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
343	C₂²×C₁₃	—	2	4	no	—
344	C₂²×C₁₃	—	2	8	no	—
345	C₂²×C₁₃	C₂²×#41	1	4	yes	—
346	C₂²×C₁₃	C₂²×#41	1	2	yes	—
347	C₂²×C₁₃	#585	1	4	yes	—
348	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
349	C₂×D₁₃	—	2	4	no	—
350	C₂×D₁₃	—	2	8	no	—
351	C₂×D₁₃	—	2	8	no	—
352	C₂×D₁₃	—	2	16	no	—
353	C₂×D₁₃	—	4	8	no	—
354	C₂×D₁₃	—	4	16	no	—
355	C₂×D₁₃	—	8	16	no	—
356	C₄×C₁₃	—	2	4	no	—
357	C₄×C₁₃	—	2	8	no	—
358	C₄×C₁₃	—	2	8	no	—
359	C₄×C₁₃	—	2	4	no	—
360	C₄×C₁₃	C₂²×#41	1	4	yes	—
361	C₄×C₁₃	C₂²×#41	1	4	yes	—
362	Dic₁₃	—	2	8	no	—
363	Dic₁₃	—	2	4	no	—
364	Dic₁₃	—	2	8	no	—
365	C₂⁵	—	13	2	no	—
366	C₂×#41	—	13	8	no	—
367	C₂×#41	—	26	8	no	—
368	C₂²×Q₈	—	13	2	no	—
369	C₂²×Q₈	—	13	2	no	—
370	C₂²×Q₈	—	13	1	no	—
371	C₂²×Q₈	—	13	8	no	—
372	C₂²×Q₈	—	26	8	no	—
373	C₂²×Q₈	C₂²×D₁₃	1	4	yes	—
374	C₂²×D₄	—	13	2	no	—
375	C₂²×D₄	—	13	2	no	—
376	C₂²×D₄	—	13	2	no	—
377	C₂²×D₄	—	13	1	no	—
378	C₂²×D₄	—	13	8	no	—
379	C₂²×D₄	—	13	8	no	—
380	C₂²×D₄	—	26	8	no	—
381	C₂³×C₄	—	13	2	no	—
382	C₂³×C₄	—	13	2	no	—
383	C₂³×C₄	—	13	8	no	—
384	C₂³×C₄	—	13	4	no	—
385	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
386	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
387	C₄⋊Q₈	—	13	16	no	—
388	C₄⋊Q₈	C₂²×D₁₃	1	16	yes	complemented
389	#127	—	13	16	no	—
390	#126	—	13	64	no	—
391	#126	—	13	64	no	—
392	#125	C₂²×D₁₃	1	16	yes	complemented
393	#124	—	13	64	no	—
394	#124	—	13	16	no	—
395	#124	—	13	16	no	—
396	#124	—	13	32	no	—
397	#124	—	13	16	no	—
398	#124	—	13	16	no	—
399	#123	—	13	64	no	—
400	#123	—	13	64	no	—
401	#123	—	13	32	no	—
402	C₂²⋊Q₈	—	13	64	no	—
403	C₂²⋊Q₈	—	13	32	no	—
404	C₂²⋊Q₈	C₂²×D₁₃	1	32	yes	—
405	#121	—	13	32	no	—
406	#120	—	13	32	no	—
407	C₄×Q₈	—	13	32	no	—
408	C₄×Q₈	—	13	16	no	—
409	C₄×Q₈	—	13	32	no	—
410	C₄×Q₈	C₂²×D₁₃	1	32	yes	complemented
411	C₄×D₄	—	13	32	no	—
412	C₄×D₄	—	13	32	no	—
413	C₄×D₄	—	13	64	no	—
414	C₄×D₄	—	13	16	no	—
415	C₄×D₄	—	13	32	no	—
416	#117	—	13	8	no	—
417	#117	—	13	64	no	—
418	#117	—	13	32	no	—
419	#117	—	13	16	no	—
420	#117	C₂²×D₁₃	1	8	yes	—
421	#117	C₂²×D₁₃	1	8	yes	—
422	C₂×C₄⋊C₄	—	13	2	no	—
423	C₂×C₄⋊C₄	—	13	4	no	—
424	C₂×C₄⋊C₄	—	13	8	no	—
425	C₂×C₄⋊C₄	—	13	8	no	—
426	C₂×C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
427	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
428	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
429	C₂×C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
430	C₂×C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
431	C₂×C₂²⋊C₄	—	13	2	no	—
432	C₂×C₂²⋊C₄	—	13	8	no	—
433	C₂×C₂²⋊C₄	—	13	8	no	—
434	C₂×C₂²⋊C₄	—	13	8	no	—
435	C₂×C₂²⋊C₄	—	13	32	no	—
436	C₂×C₂²⋊C₄	—	13	4	no	—
437	C₂×C₂²⋊C₄	—	13	8	no	—
438	C₂×C₂²⋊C₄	—	13	8	no	—
439	C₂×C₂²⋊C₄	—	13	32	no	—
440	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
441	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
442	C₂×C₄²	—	13	2	no	—
443	C₂×C₄²	—	13	8	no	—
444	C₂×C₄²	—	13	4	no	—
445	C₂×C₄²	—	13	16	no	—
446	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
447	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
448	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
449	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
450	C₂×C₄²	C₂²×D₁₃	1	8	yes	—
451	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
452	C₂×C₁₃	—	2	4	no	—
453	C₂×C₁₃	#3510	1	4	yes	complemented
454	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
455	C₂×C₁₃	C₂×#585	1	2	yes	—
456	D₁₃	—	4	4	no	—
457	D₁₃	—	4	8	no	—
458	C₂⁴	—	13	4	no	—
459	C₂⁴	—	13	2	no	—
460	C₂⁴	—	13	8	no	—
461	C₂⁴	—	26	8	no	—
462	C₂⁴	—	52	8	no	—
463	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
464	#41	—	26	32	no	—
465	C₂×Q₈	—	4	8	no	—
466	C₂×Q₈	—	13	8	no	—
467	C₂×Q₈	—	13	8	no	—
468	C₂×Q₈	—	13	4	no	—
469	C₂×Q₈	—	26	8	no	—
470	C₂×Q₈	—	26	8	no	—
471	C₂×Q₈	—	26	32	no	—
472	C₂×Q₈	—	26	4	no	—
473	C₂×Q₈	C₂³×D₁₃	1	16	yes	—
474	C₂×D₄	—	13	8	no	—
475	C₂×D₄	—	13	8	no	—
476	C₂×D₄	—	13	8	no	—
477	C₂×D₄	—	13	4	no	—
478	C₂×D₄	—	13	32	no	—
479	C₂×D₄	—	26	8	no	—
480	C₂×D₄	—	26	8	no	—
481	C₂×D₄	—	26	8	no	—
482	C₂×D₄	—	26	32	no	—
483	C₂×D₄	—	26	4	no	—
484	C₂×D₄	—	52	16	no	—
485	C₂²×C₄	—	4	4	no	—
486	C₂²×C₄	—	13	8	no	—
487	C₂²×C₄	—	13	4	no	—
488	C₂²×C₄	—	13	4	no	—
489	C₂²×C₄	—	13	2	no	—
490	C₂²×C₄	—	13	8	no	—
491	C₂²×C₄	—	13	16	no	—
492	C₂²×C₄	—	13	32	no	—
493	C₂²×C₄	—	26	8	no	—
494	C₂²×C₄	—	26	8	no	—
495	C₂²×C₄	—	52	8	no	—
496	C₂²×C₄	—	52	16	no	—
497	C₂²×C₄	#6131	1	8	yes	—
498	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
499	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
500	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
501	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
502	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
503	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
504	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
505	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
506	C₄⋊C₄	—	13	8	no	—
507	C₄⋊C₄	—	13	16	no	—
508	C₄⋊C₄	—	13	32	no	—
509	C₄⋊C₄	—	13	32	no	—
510	C₄⋊C₄	C₂³×D₁₃	1	16	yes	—
511	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
512	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
513	C₄⋊C₄	C₂³×D₁₃	1	16	yes	—
514	C₄⋊C₄	C₂³×D₁₃	1	16	yes	—
515	C₂²⋊C₄	—	13	8	no	—
516	C₂²⋊C₄	—	13	32	no	—
517	C₂²⋊C₄	—	13	32	no	—
518	C₂²⋊C₄	—	13	32	no	—
519	C₂²⋊C₄	—	13	16	no	—
520	C₂²⋊C₄	—	13	32	no	—
521	C₂²⋊C₄	—	13	32	no	—
522	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
523	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
524	C₄²	—	13	8	no	—
525	C₄²	—	13	16	no	—
526	C₄²	—	13	32	no	—
527	C₄²	C₂³×D₁₃	1	4	yes	—
528	C₄²	C₂³×D₁₃	1	4	yes	—
529	C₄²	C₂³×D₁₃	1	8	yes	—
530	C₄²	C₂³×D₁₃	1	8	yes	—
531	C₄²	C₂³×D₁₃	1	8	yes	—
532	C₁₃	C₂×#3510	1	1	yes	characteristic, complemented, Sylow
533	C₂³	—	2	4	no	—
534	C₂³	—	13	8	no	—
535	C₂³	—	13	4	no	—
536	C₂³	—	26	4	no	—
537	C₂³	—	26	8	no	—
538	C₂³	—	26	8	no	—
539	C₂³	—	26	16	no	—
540	C₂³	—	26	16	no	—
541	C₂³	—	52	16	no	—
542	C₂³	—	104	16	no	—
543	C₂³	C₂×#6131	1	4	yes	—
544	C₂³	C₂⁴×D₁₃	1	2	yes	—
545	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
546	Q₈	—	4	16	no	—
547	Q₈	—	26	16	no	—
548	Q₈	—	26	16	no	—
549	Q₈	—	26	8	no	—
550	D₄	—	26	16	no	—
551	D₄	—	26	16	no	—
552	D₄	—	26	16	no	—
553	D₄	—	26	8	no	—
554	D₄	—	52	32	no	—
555	C₂×C₄	—	2	4	no	—
556	C₂×C₄	—	2	4	no	—
557	C₂×C₄	—	2	8	no	—
558	C₂×C₄	—	2	8	no	—
559	C₂×C₄	—	4	8	no	—
560	C₂×C₄	—	13	8	no	—
561	C₂×C₄	—	13	8	no	—
562	C₂×C₄	—	13	4	no	—
563	C₂×C₄	—	26	4	no	—
564	C₂×C₄	—	26	16	no	—
565	C₂×C₄	—	26	8	no	—
566	C₂×C₄	—	26	8	no	—
567	C₂×C₄	—	26	16	no	—
568	C₂×C₄	—	52	16	no	—
569	C₂×C₄	—	52	32	no	—
570	C₂×C₄	C₂×#6131	1	4	yes	—
571	C₂×C₄	C₂×#6131	1	4	yes	—
572	C₂×C₄	C₂×#6131	1	16	yes	—
573	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
574	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
575	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
576	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
577	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
578	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
579	C₂²	—	2	8	no	—
580	C₂²	—	2	4	no	—
581	C₂²	—	26	4	no	—
582	C₂²	—	26	8	no	—
583	C₂²	—	26	8	no	—
584	C₂²	—	26	16	no	—
585	C₂²	—	52	8	no	—
586	C₂²	—	52	16	no	—
587	C₂²	—	104	16	no	—
588	C₂²	C₂²×#6131	1	4	yes	—
589	C₂²	C₂²×#6131	1	2	yes	—
590	C₂²	#11719648	1	4	yes	—
591	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
592	C₄	—	2	4	no	—
593	C₄	—	2	4	no	—
594	C₄	—	2	8	no	—
595	C₄	—	2	8	no	—
596	C₄	—	26	4	no	—
597	C₄	—	26	8	no	—
598	C₄	—	26	8	no	—
599	C₄	C₂²×#6131	1	4	yes	—
600	C₄	C₂²×#6131	1	4	yes	—
601	C₂	—	2	4	no	—
602	C₂	—	52	8	no	—
603	C₂	—	52	4	no	—
604	C₂	#13128734	1	4	yes	direct product factor
605	C₂	C₂³×#6131	1	1	yes	characteristic
606	C₂	C₂×#11719648	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂×C₁₃×#533	C₂
socle	C₂³×C₁₃	C₂⁵
prime radical	C₂×#11719230	C₂
hypercenter	C₂×#533	D₁₃
hypocenter	C₁₃	C₂×#3510
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×#533

Complements

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

N	H ≅ G/N	type
1. #13128734	C₂	direct (N × H)
2. C₂×#11719290	C₂	semidirect
3. C₂×#11719289	C₂	semidirect
4. C₂×#11719342	C₂	semidirect
5. C₂×#11719438	C₂	semidirect
6. C₂×#11719231	C₂	semidirect
8. C₂×#11719396	C₂	semidirect
9. C₂²×#88129	C₂	semidirect
10. C₂×#11719221	C₂	semidirect
11. C₂×#11719226	C₂	semidirect
12. C₂×C₄×#6127	C₂	semidirect
13. C₂×C₁₃×#533	C₂	semidirect
17. C₁₃×#533	C₂²	semidirect
18. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
19. C₂×C₁₃×#125	C₂²	semidirect
21. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
25. C₂×#88201	C₂²	semidirect
26. C₂×#88200	C₂²	semidirect
30. #11719438	C₂²	semidirect
31. #11719396	C₂²	semidirect
32. #11719342	C₂²	semidirect
33. #11719290	C₂²	semidirect
34. #11719289	C₂²	semidirect
35. #11719231	C₂²	semidirect
37. #11719226	C₂²	semidirect
38. #11719221	C₂²	semidirect
39. C₂×#88152	C₂²	semidirect
40. C₂×#88152	C₂²	semidirect
41. C₂×#88151	C₂²	semidirect
43. C₂×#88148	C₂²	semidirect
44. C₂×#88148	C₂²	semidirect
46. C₂×#88147	C₂²	semidirect
47. C₂×#88146	C₂²	semidirect
48. C₂×#88141	C₂²	semidirect
57. C₂×#88129	C₂²	semidirect
58. C₂×#88129	C₂²	semidirect
60. C₄×#6127	C₂²	semidirect
62. C₂×C₄×D₅₂	C₂²	semidirect
63. C₂×#88126	C₂²	semidirect
64. C₂×C₄²×D₁₃	C₂²	semidirect
65. C₂×#88123	C₂²	semidirect
66. C₂×C₄×Dic₂₆	C₂²	semidirect
67. C₂×C₄×Dic₂₆	C₂²	semidirect
90. C₁₃×C₄⋊Q₈	C₂³	semidirect
91. C₁₃×#125	C₂³	semidirect
93. C₄×Q₈×C₁₃	C₂³	semidirect
110. #88201	C₂³	semidirect
111. #88200	C₂³	semidirect
128. #88152	C₂³	semidirect
129. #88152	C₂³	semidirect
130. #88151	C₂³	semidirect
132. #88148	C₂³	semidirect
133. #88148	C₂³	semidirect
135. #88147	C₂³	semidirect
136. #88146	C₂³	semidirect
137. #88141	C₂³	semidirect
146. #88129	C₂³	semidirect
149. C₄×D₅₂	C₂³	semidirect
150. #88126	C₂³	semidirect
151. C₄²×D₁₃	C₂³	semidirect
152. #88123	C₂³	semidirect
153. C₄×Dic₂₆	C₂³	semidirect
154. C₄×Dic₂₆	C₂³	semidirect
237. C₂×#533	D₁₃	semidirect
298. #533	C₂×D₁₃	semidirect
300. C₂×C₄⋊Q₈	C₂×D₁₃	semidirect
305. C₂×#125	C₂×D₁₃	semidirect
327. C₂×C₄×Q₈	C₂×D₁₃	semidirect
388. C₄⋊Q₈	C₂²×D₁₃	semidirect
392. #125	C₂²×D₁₃	semidirect
410. C₄×Q₈	C₂²×D₁₃	semidirect
453. C₂×C₁₃	#3510	semidirect
532. C₁₃	C₂×#3510	semidirect
604. C₂	#13128734	direct (N × H)

Maximal subgroups

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

subgroup	index
#13128734	2
C₂×#11719290	2
C₂×#11719289	2
C₂×#11719342	2
C₂×#11719438	2
C₂×#11719231	2
C₂×#11719230	2
C₂×#11719396	2
C₂²×#88129	2
C₂×#11719221	2
C₂×#11719226	2
C₂×C₄×#6127	2
C₂×C₁₃×#533	2
C₂×#3510	13

Subgroups — C2×#13128734 #16771411

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13128734 #16771411