Subgroups — C₂×#13115735 #15866894

Order 3328.

1474 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718767	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11718897	C₂	1	2	yes	maximal, complemented
3	C₂×#11718901	C₂	1	2	yes	maximal, complemented
4	C₂×#11718762	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115735	C₂	1	8	yes	maximal, direct product factor
6	C₂²×C₁₃×#135	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₁₃×#41	C₂²	1	2	yes	—
8	C₂×C₁₃×#135	—	2	1	no	—
9	C₂×C₁₃×#135	—	2	1	no	—
10	C₂×C₁₃×#135	—	2	2	no	—
11	C₂×C₁₃×#135	—	2	1	no	—
12	C₂×C₁₃×#135	—	2	1	no	—
13	C₂×C₁₃×#135	—	2	2	no	—
14	C₂×C₁₃×#135	C₄	1	4	yes	complemented
15	C₂×C₁₃×#135	C₂²	1	4	yes	—
16	C₂²×C₁₃×Q₁₆	C₄	1	1	yes	characteristic, complemented
17	C₂²×C₁₃×SD₁₆	C₄	1	2	yes	complemented
18	C₂²×C₁₃×D₈	C₄	1	1	yes	characteristic, complemented
19	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×#88180	C₂²	1	2	yes	—
21	C₂×#88180	C₂²	1	1	yes	characteristic
22	C₂²×#6099	C₂²	1	1	yes	characteristic
23	#11718901	—	2	4	no	—
24	#11718901	C₂²	1	8	yes	complemented
25	#11718897	—	2	4	no	—
26	#11718897	C₂²	1	8	yes	complemented
27	C₂×#88077	—	2	4	no	—
28	C₂×#88074	—	2	4	no	—
29	#11718767	—	2	2	no	—
30	#11718767	C₂²	1	4	yes	complemented
31	C₂×#88058	—	2	1	no	—
32	C₂×#88057	—	2	1	no	—
33	#11718762	—	2	2	no	—
34	#11718762	C₂²	1	4	yes	complemented
35	C₂×#88055	—	2	1	no	—
36	C₂×C₈×Dic₁₃	—	2	1	no	—
37	C₂×C₁₃×#41	—	2	2	no	—
38	C₂×C₁₃×#41	—	2	2	no	—
39	C₂×C₁₃×#41	—	2	2	no	—
40	C₂×C₁₃×#41	—	2	2	no	—
41	C₂×C₁₃×#41	—	2	2	no	—
42	C₂×C₁₃×#41	—	2	2	no	—
43	C₂×C₁₃×#41	—	2	2	no	—
44	C₂×C₁₃×#41	—	2	2	no	—
45	C₂×C₁₃×#41	—	2	2	no	—
46	C₂×C₁₃×#41	—	2	2	no	—
47	C₂×C₁₃×#41	C₂×C₄	1	4	yes	—
48	C₂×C₁₃×#41	C₂³	1	4	yes	—
49	C₂²×Q₈×C₁₃	C₂×C₄	1	2	yes	—
50	C₂²×D₄×C₁₃	—	2	2	no	—
51	C₂²×D₄×C₁₃	C₂×C₄	1	2	yes	—
52	C₂³×C₄×C₁₃	—	2	2	no	—
53	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
54	C₁₃×#135	—	2	4	no	—
55	C₁₃×#135	—	2	4	no	—
56	C₁₃×#135	—	2	4	no	—
57	C₁₃×#135	—	2	4	no	—
58	C₁₃×#135	—	2	4	no	—
59	C₁₃×#135	—	2	4	no	—
60	C₁₃×#135	—	2	4	no	—
61	C₁₃×#135	—	2	4	no	—
62	C₂×C₁₃×Q₁₆	—	2	1	no	—
63	C₂×C₁₃×Q₁₆	—	2	1	no	—
64	C₂×C₁₃×Q₁₆	—	2	2	no	—
65	C₂×C₁₃×Q₁₆	C₂×C₄	1	4	yes	complemented
66	C₂×C₁₃×SD₁₆	—	2	2	no	—
67	C₂×C₁₃×SD₁₆	—	2	2	no	—
68	C₂×C₁₃×SD₁₆	—	2	4	no	—
69	C₂×C₁₃×SD₁₆	C₂×C₄	1	8	yes	complemented
70	C₂×C₁₃×D₈	—	2	1	no	—
71	C₂×C₁₃×D₈	—	2	1	no	—
72	C₂×C₁₃×D₈	—	2	2	no	—
73	C₂×C₁₃×D₈	C₂×C₄	1	4	yes	complemented
74	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
75	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
76	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
77	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
78	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
79	C₂²×C₈×C₁₃	D₄	1	2	yes	—
80	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
81	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
82	C₂²×C₈×C₁₃	D₄	1	2	yes	—
83	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
84	C₂×C₂²⋊Dic₁₃	—	2	2	no	—
85	C₂×C₂²⋊Dic₁₃	D₄	1	2	yes	—
86	#88180	—	2	1	no	—
87	#88180	—	2	1	no	—
88	#88180	—	2	2	no	—
89	#88180	—	2	2	no	—
90	#88180	—	2	2	no	—
91	#88180	D₄	1	2	yes	—
92	#88180	C₂³	1	4	yes	—
93	#88180	C₂³	1	2	yes	—
94	C₂×C₄⋊Dic₁₃	—	2	1	no	—
95	C₂×C₄⋊Dic₁₃	—	2	2	no	—
96	C₂×C₄×Dic₁₃	—	2	1	no	—
97	C₂×C₄×Dic₁₃	—	2	2	no	—
98	C₂×#6099	—	2	1	no	—
99	C₂×#6099	—	2	1	no	—
100	C₂×#6099	—	2	1	no	—
101	C₂×#6099	D₄	1	2	yes	—
102	C₂×#6099	D₄	1	2	yes	—
103	C₂×#6099	C₂³	1	2	yes	—
104	C₂²×#1055	—	2	1	no	—
105	#88077	—	2	16	no	—
106	#88074	—	2	16	no	—
107	#88058	—	2	4	no	—
108	#88057	—	2	4	no	—
109	#88055	—	2	4	no	—
110	C₈×Dic₁₃	—	2	4	no	—
111	C₂×#1976	—	13	1	no	maximal, Sylow
112	C₂⁴×C₁₃	—	2	2	no	—
113	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₁₃×#41	—	2	4	no	—
115	C₁₃×#41	—	2	4	no	—
116	C₁₃×#41	—	2	4	no	—
117	C₁₃×#41	—	2	4	no	—
118	C₁₃×#41	—	2	4	no	—
119	C₁₃×#41	—	2	4	no	—
120	C₁₃×#41	—	2	4	no	—
121	C₁₃×#41	—	2	4	no	—
122	C₁₃×#41	—	4	2	no	—
123	C₁₃×#41	—	4	2	no	—
124	C₁₃×#41	—	4	2	no	—
125	C₁₃×#41	—	4	2	no	—
126	C₁₃×#41	—	4	2	no	—
127	C₁₃×#41	—	4	2	no	—
128	C₁₃×#41	—	4	2	no	—
129	C₁₃×#41	—	4	2	no	—
130	C₂×Q₈×C₁₃	—	2	2	no	—
131	C₂×Q₈×C₁₃	—	2	2	no	—
132	C₂×Q₈×C₁₃	—	2	2	no	—
133	C₂×Q₈×C₁₃	—	2	2	no	—
134	C₂×Q₈×C₁₃	—	2	2	no	—
135	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
136	C₂×D₄×C₁₃	—	2	4	no	—
137	C₂×D₄×C₁₃	—	2	4	no	—
138	C₂×D₄×C₁₃	—	2	2	no	—
139	C₂×D₄×C₁₃	—	2	2	no	—
140	C₂×D₄×C₁₃	—	2	2	no	—
141	C₂×D₄×C₁₃	—	2	2	no	—
142	C₂×D₄×C₁₃	—	2	2	no	—
143	C₂×D₄×C₁₃	—	4	2	no	—
144	C₂×D₄×C₁₃	—	4	2	no	—
145	C₂×D₄×C₁₃	—	4	2	no	—
146	C₂×D₄×C₁₃	—	4	2	no	—
147	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
148	C₂²×C₄×C₁₃	—	2	2	no	—
149	C₂²×C₄×C₁₃	—	2	4	no	—
150	C₂²×C₄×C₁₃	—	2	4	no	—
151	C₂²×C₄×C₁₃	—	4	2	no	—
152	C₂²×C₄×C₁₃	—	4	2	no	—
153	C₂²×C₄×C₁₃	—	4	2	no	—
154	C₂²×C₄×C₁₃	—	4	2	no	—
155	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
165	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
166	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
167	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
168	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
169	C₂²×Dic₁₃	—	2	2	no	—
170	C₂²×Dic₁₃	—	4	2	no	—
171	C₁₃×Q₁₆	—	2	4	no	—
172	C₁₃×Q₁₆	—	2	4	no	—
173	C₁₃×SD₁₆	—	2	8	no	—
174	C₁₃×SD₁₆	—	2	8	no	—
175	C₁₃×D₈	—	2	4	no	—
176	C₁₃×D₈	—	2	4	no	—
177	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
178	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
179	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
180	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
181	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
182	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
183	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
184	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
185	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
186	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
187	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
188	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
189	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
190	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
191	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
192	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
193	C₂²⋊Dic₁₃	—	2	2	no	—
194	C₂²⋊Dic₁₃	—	2	4	no	—
195	C₂²⋊Dic₁₃	—	4	2	no	—
196	C₂²⋊Dic₁₃	C₂×D₄	1	4	yes	—
197	C₄⋊Dic₁₃	—	2	2	no	—
198	C₄⋊Dic₁₃	—	2	2	no	—
199	C₄⋊Dic₁₃	—	2	4	no	—
200	C₄⋊Dic₁₃	—	4	2	no	—
201	C₄×Dic₁₃	—	2	2	no	—
202	C₄×Dic₁₃	—	2	2	no	—
203	C₄×Dic₁₃	—	2	4	no	—
204	C₄×Dic₁₃	—	4	2	no	—
205	#6099	—	2	2	no	—
206	#6099	—	2	2	no	—
207	#6099	—	2	2	no	—
208	#6099	C₂×D₄	1	4	yes	—
209	C₂×#1055	—	2	2	no	—
210	C₂×#1055	—	2	2	no	—
211	C₂×#1055	—	2	2	no	—
212	C₂²×#135	D₁₃	1	1	yes	characteristic
213	C₂×#427	—	13	1	no	—
214	C₂×#421	—	13	2	no	—
215	C₂×#410	—	13	2	no	—
216	C₂×#405	—	13	1	no	—
217	#1976	—	13	8	no	—
218	C₂³×C₁₃	—	2	4	no	—
219	C₂³×C₁₃	—	4	2	no	—
220	C₂³×C₁₃	—	4	2	no	—
221	C₂³×C₁₃	—	4	2	no	—
222	C₂³×C₁₃	—	8	4	no	—
223	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
224	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
225	C₂³×C₁₃	#121	1	1	yes	characteristic
226	C₂³×C₁₃	#121	1	1	yes	characteristic
227	C₂³×C₁₃	#127	1	1	yes	characteristic
228	C₂³×C₁₃	#127	1	1	yes	characteristic
229	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
230	Q₈×C₁₃	—	2	4	no	—
231	Q₈×C₁₃	—	2	4	no	—
232	Q₈×C₁₃	—	4	2	no	—
233	Q₈×C₁₃	—	4	2	no	—
234	D₄×C₁₃	—	2	4	no	—
235	D₄×C₁₃	—	2	4	no	—
236	D₄×C₁₃	—	4	4	no	—
237	D₄×C₁₃	—	4	4	no	—
238	D₄×C₁₃	—	4	4	no	—
239	D₄×C₁₃	—	4	4	no	—
240	D₄×C₁₃	—	4	2	no	—
241	D₄×C₁₃	—	4	2	no	—
242	C₂×C₄×C₁₃	—	2	4	no	—
243	C₂×C₄×C₁₃	—	4	2	no	—
244	C₂×C₄×C₁₃	—	4	2	no	—
245	C₂×C₄×C₁₃	—	4	4	no	—
246	C₂×C₄×C₁₃	—	4	4	no	—
247	C₂×C₄×C₁₃	—	4	4	no	—
248	C₂×C₄×C₁₃	—	4	4	no	—
249	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
250	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
251	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
252	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
253	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
254	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
255	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
256	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
257	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
258	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
259	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
260	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
261	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
262	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
263	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
264	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
265	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
266	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
267	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
268	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
269	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
270	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
271	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
272	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
275	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
276	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
277	C₂×Dic₁₃	—	2	4	no	—
278	C₂×Dic₁₃	—	4	4	no	—
279	C₂×Dic₁₃	—	4	4	no	—
280	C₂×Dic₁₃	—	8	4	no	—
281	C₈×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
282	C₈×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
283	C₈×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
284	C₈×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
285	#1055	—	2	4	no	—
286	C₂²×#41	C₂×D₁₃	1	2	yes	—
287	C₂×#135	—	2	1	no	—
288	C₂×#135	—	2	1	no	—
289	C₂×#135	—	2	2	no	—
290	C₂×#135	—	2	1	no	—
291	C₂×#135	—	2	1	no	—
292	C₂×#135	—	2	2	no	—
293	C₂×#135	Dic₁₃	1	4	yes	complemented
294	C₂×#135	C₂×D₁₃	1	4	yes	—
295	C₂²×Q₁₆	Dic₁₃	1	1	yes	characteristic, complemented
296	C₂²×SD₁₆	Dic₁₃	1	2	yes	complemented
297	C₂²×D₈	Dic₁₃	1	1	yes	characteristic, complemented
298	C₂²×M₁₆	—	13	1	no	—
299	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
300	C₂×#117	—	13	1	no	—
301	C₂×#117	—	13	2	no	—
302	#427	—	13	4	no	—
303	#427	—	26	2	no	—
304	C₂×#107	—	26	1	no	—
305	C₂×#106	—	26	1	no	—
306	#421	—	13	8	no	—
307	#421	—	26	4	no	—
308	C₂×#104	—	26	4	no	—
309	#410	—	13	8	no	—
310	#410	—	26	4	no	—
311	C₂×#99	—	26	4	no	—
312	#405	—	13	4	no	—
313	#405	—	26	2	no	—
314	C₂×#97	—	26	1	no	—
315	C₂×C₄×C₈	—	26	1	no	—
316	C₂²×C₁₃	—	2	2	no	—
317	C₂²×C₁₃	—	2	2	no	—
318	C₂²×C₁₃	—	2	2	no	—
319	C₂²×C₁₃	—	4	1	no	—
320	C₂²×C₁₃	—	4	1	no	—
321	C₂²×C₁₃	—	4	1	no	—
322	C₂²×C₁₃	—	4	1	no	—
323	C₂²×C₁₃	—	4	4	no	—
324	C₂²×C₁₃	—	8	4	no	—
325	C₂²×C₁₃	—	8	4	no	—
326	C₂²×C₁₃	—	8	4	no	—
327	C₂²×C₁₃	#390	1	1	yes	characteristic
328	C₂²×C₁₃	#390	1	1	yes	characteristic
329	C₂²×C₁₃	#390	1	1	yes	characteristic
330	C₂²×C₁₃	#390	1	1	yes	characteristic
331	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
332	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
333	C₂²×C₁₃	C₂×#127	1	1	yes	characteristic
334	C₄×C₁₃	—	4	4	no	—
335	C₄×C₁₃	#390	1	1	yes	characteristic
336	C₄×C₁₃	#390	1	1	yes	characteristic
337	C₄×C₁₃	#390	1	1	yes	characteristic
338	C₄×C₁₃	#390	1	1	yes	characteristic
339	C₄×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
340	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
341	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
342	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
343	Dic₁₃	—	4	4	no	—
344	Dic₁₃	—	8	4	no	—
345	C₂×#41	—	2	2	no	—
346	C₂×#41	—	2	2	no	—
347	C₂×#41	—	2	2	no	—
348	C₂×#41	—	2	2	no	—
349	C₂×#41	—	2	2	no	—
350	C₂×#41	—	2	2	no	—
351	C₂×#41	—	2	2	no	—
352	C₂×#41	—	2	2	no	—
353	C₂×#41	—	2	2	no	—
354	C₂×#41	—	2	2	no	—
355	C₂×#41	C₂×Dic₁₃	1	4	yes	—
356	C₂×#41	C₂²×D₁₃	1	4	yes	—
357	C₂²×Q₈	C₂×Dic₁₃	1	2	yes	—
358	C₂²×D₄	—	2	2	no	—
359	C₂²×D₄	C₂×Dic₁₃	1	2	yes	—
360	C₂³×C₄	—	2	2	no	—
361	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
362	#135	—	2	4	no	—
363	#135	—	2	4	no	—
364	#135	—	2	4	no	—
365	#135	—	2	4	no	—
366	#135	—	2	4	no	—
367	#135	—	2	4	no	—
368	#135	—	2	4	no	—
369	#135	—	2	4	no	—
370	C₂×Q₁₆	—	2	1	no	—
371	C₂×Q₁₆	—	2	1	no	—
372	C₂×Q₁₆	—	2	2	no	—
373	C₂×Q₁₆	C₂×Dic₁₃	1	4	yes	complemented
374	C₂×SD₁₆	—	2	2	no	—
375	C₂×SD₁₆	—	2	2	no	—
376	C₂×SD₁₆	—	2	4	no	—
377	C₂×SD₁₆	C₂×Dic₁₃	1	8	yes	complemented
378	C₂×D₈	—	2	1	no	—
379	C₂×D₈	—	2	1	no	—
380	C₂×D₈	—	2	2	no	—
381	C₂×D₈	C₂×Dic₁₃	1	4	yes	complemented
382	C₂×M₁₆	—	13	2	no	—
383	C₂×M₁₆	—	13	2	no	—
384	C₂×M₁₆	—	13	2	no	—
385	C₂×M₁₆	—	26	1	no	—
386	C₂×M₁₆	—	26	1	no	—
387	C₂×M₁₆	—	26	1	no	—
388	C₂²×C₈	—	26	1	no	—
389	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
390	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
391	C₂²×C₈	C₂×Dic₁₃	1	2	yes	—
392	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
393	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
394	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
395	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
396	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
397	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
398	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
399	#117	—	13	2	no	—
400	#117	—	13	2	no	—
401	#117	—	13	4	no	—
402	#117	—	26	1	no	—
403	#117	—	26	1	no	—
404	#117	—	26	2	no	—
405	#117	—	26	2	no	—
406	#117	—	26	2	no	—
407	C₂×C₄⋊C₄	—	26	1	no	—
408	C₂×C₄⋊C₄	—	26	2	no	—
409	C₂×C₂²⋊C₄	—	13	2	no	—
410	C₂×C₂²⋊C₄	—	26	2	no	—
411	C₂×C₄²	—	26	1	no	—
412	C₂×C₄²	—	26	2	no	—
413	#107	—	26	4	no	—
414	#106	—	26	4	no	—
415	#104	—	26	16	no	—
416	#99	—	26	16	no	—
417	#97	—	26	4	no	—
418	C₄×C₈	—	26	4	no	—
419	C₂×C₁₃	—	2	1	no	—
420	C₂×C₁₃	—	2	1	no	—
421	C₂×C₁₃	—	2	1	no	—
422	C₂×C₁₃	—	2	1	no	—
423	C₂×C₁₃	—	2	1	no	—
424	C₂×C₁₃	—	2	1	no	—
425	C₂×C₁₃	—	8	4	no	—
426	C₂×C₁₃	#1976	1	2	yes	complemented
427	C₂×C₁₃	C₂×#390	1	1	yes	characteristic
428	C₂⁴	—	2	2	no	—
429	C₂⁴	D₄×D₁₃	1	1	yes	characteristic
430	#41	—	2	4	no	—
431	#41	—	2	4	no	—
432	#41	—	2	4	no	—
433	#41	—	2	4	no	—
434	#41	—	2	4	no	—
435	#41	—	2	4	no	—
436	#41	—	2	4	no	—
437	#41	—	2	4	no	—
438	#41	—	4	2	no	—
439	#41	—	4	2	no	—
440	#41	—	4	2	no	—
441	#41	—	4	2	no	—
442	#41	—	4	2	no	—
443	#41	—	4	2	no	—
444	#41	—	4	2	no	—
445	#41	—	4	2	no	—
446	C₂×Q₈	—	2	2	no	—
447	C₂×Q₈	—	2	2	no	—
448	C₂×Q₈	—	2	2	no	—
449	C₂×Q₈	—	2	2	no	—
450	C₂×Q₈	—	2	2	no	—
451	C₂×Q₈	C₂²×Dic₁₃	1	4	yes	—
452	C₂×D₄	—	2	4	no	—
453	C₂×D₄	—	2	4	no	—
454	C₂×D₄	—	2	2	no	—
455	C₂×D₄	—	2	2	no	—
456	C₂×D₄	—	2	2	no	—
457	C₂×D₄	—	2	2	no	—
458	C₂×D₄	—	2	2	no	—
459	C₂×D₄	—	4	2	no	—
460	C₂×D₄	—	4	2	no	—
461	C₂×D₄	—	4	2	no	—
462	C₂×D₄	—	4	2	no	—
463	C₂×D₄	C₂²×Dic₁₃	1	4	yes	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	2	4	no	—
466	C₂²×C₄	—	2	4	no	—
467	C₂²×C₄	—	4	2	no	—
468	C₂²×C₄	—	4	2	no	—
469	C₂²×C₄	—	4	2	no	—
470	C₂²×C₄	—	4	2	no	—
471	C₂²×C₄	—	26	2	no	—
472	C₂²×C₄	—	52	2	no	—
473	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
474	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
475	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
476	C₂²×C₄	#6129	1	1	yes	characteristic
477	C₂²×C₄	#6129	1	1	yes	characteristic
478	C₂²×C₄	#6129	1	1	yes	characteristic
479	C₂²×C₄	#6129	1	1	yes	characteristic
480	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
481	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
482	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
483	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
484	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
485	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
486	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
487	Q₁₆	—	2	4	no	—
488	Q₁₆	—	2	4	no	—
489	SD₁₆	—	2	8	no	—
490	SD₁₆	—	2	8	no	—
491	D₈	—	2	4	no	—
492	D₈	—	2	4	no	—
493	M₁₆	—	13	4	no	—
494	M₁₆	—	26	2	no	—
495	M₁₆	—	26	2	no	—
496	M₁₆	—	26	2	no	—
497	C₂×C₈	—	26	2	no	—
498	C₂×C₈	—	26	2	no	—
499	C₂×C₈	—	26	2	no	—
500	C₂×C₈	C₂²⋊Dic₁₃	1	1	yes	characteristic
501	C₂×C₈	C₂²⋊Dic₁₃	1	1	yes	characteristic
502	C₂×C₈	C₂²⋊Dic₁₃	1	2	yes	—
503	C₂×C₈	C₂²⋊Dic₁₃	1	1	yes	characteristic
504	C₂×C₈	C₂²⋊Dic₁₃	1	1	yes	characteristic
505	C₂×C₈	C₂²⋊Dic₁₃	1	2	yes	—
506	C₂×C₈	C₂²⋊Dic₁₃	1	2	yes	—
507	C₂×C₈	C₂²⋊Dic₁₃	1	2	yes	—
508	C₂×C₈	C₂²⋊Dic₁₃	1	2	yes	—
509	C₂×C₈	C₂²⋊Dic₁₃	1	2	yes	—
510	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
511	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
512	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
513	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
514	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
515	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
516	C₄⋊C₄	—	26	2	no	—
517	C₄⋊C₄	—	26	2	no	—
518	C₄⋊C₄	—	26	4	no	—
519	C₄⋊C₄	—	52	2	no	—
520	C₂²⋊C₄	—	13	4	no	—
521	C₂²⋊C₄	—	26	2	no	—
522	C₂²⋊C₄	—	26	4	no	—
523	C₂²⋊C₄	—	52	2	no	—
524	C₄²	—	26	2	no	—
525	C₄²	—	26	2	no	—
526	C₄²	—	26	4	no	—
527	C₄²	—	52	2	no	—
528	C₁₃	C₂×#1976	1	1	yes	characteristic, complemented, Sylow
529	C₂³	—	2	4	no	—
530	C₂³	—	4	2	no	—
531	C₂³	—	4	2	no	—
532	C₂³	—	4	2	no	—
533	C₂³	—	8	4	no	—
534	C₂³	D₄×Dic₁₃	1	1	yes	characteristic
535	C₂³	D₄×Dic₁₃	1	1	yes	characteristic
536	C₂³	#88192	1	1	yes	characteristic
537	C₂³	#88192	1	1	yes	characteristic
538	C₂³	#88194	1	1	yes	characteristic
539	C₂³	#88194	1	1	yes	characteristic
540	C₂³	C₂×D₄×D₁₃	1	1	yes	characteristic
541	Q₈	—	2	4	no	—
542	Q₈	—	2	4	no	—
543	Q₈	—	4	2	no	—
544	Q₈	—	4	2	no	—
545	D₄	—	2	4	no	—
546	D₄	—	2	4	no	—
547	D₄	—	4	4	no	—
548	D₄	—	4	4	no	—
549	D₄	—	4	4	no	—
550	D₄	—	4	4	no	—
551	D₄	—	4	2	no	—
552	D₄	—	4	2	no	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	4	no	—
557	C₂×C₄	—	4	4	no	—
558	C₂×C₄	—	4	4	no	—
559	C₂×C₄	—	4	4	no	—
560	C₂×C₄	—	26	4	no	—
561	C₂×C₄	—	52	4	no	—
562	C₂×C₄	—	52	4	no	—
563	C₂×C₄	—	104	4	no	—
564	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
565	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
566	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
567	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
568	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
569	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
570	C₂×C₄	#88190	1	1	yes	characteristic
571	C₂×C₄	#88190	1	1	yes	characteristic
572	C₂×C₄	#88190	1	1	yes	characteristic
573	C₂×C₄	#88190	1	1	yes	characteristic
574	C₂×C₄	#88192	1	1	yes	characteristic
575	C₂×C₄	#88192	1	1	yes	characteristic
576	C₂×C₄	#88192	1	1	yes	characteristic
577	C₂×C₄	#88192	1	1	yes	characteristic
578	C₂×C₄	#88192	1	1	yes	characteristic
579	C₂×C₄	#88192	1	1	yes	characteristic
580	C₂×C₄	#88194	1	1	yes	characteristic
581	C₂×C₄	#88194	1	1	yes	characteristic
582	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
583	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
584	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
585	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
586	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
587	C₂×C₄	C₂×#6129	1	1	yes	characteristic
588	C₂×C₄	C₂×#6129	1	1	yes	characteristic
589	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
590	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
591	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
592	C₈	—	26	4	no	—
593	C₈	C₂×C₂²⋊Dic₁₃	1	2	yes	—
594	C₈	C₂×C₂²⋊Dic₁₃	1	2	yes	—
595	C₈	C₂×C₂²⋊Dic₁₃	1	2	yes	—
596	C₈	C₂×C₂²⋊Dic₁₃	1	2	yes	—
597	C₂²	—	2	2	no	—
598	C₂²	—	2	2	no	—
599	C₂²	—	2	2	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	4	4	no	—
605	C₂²	—	8	4	no	—
606	C₂²	—	8	4	no	—
607	C₂²	—	8	4	no	—
608	C₂²	#11718882	1	1	yes	characteristic
609	C₂²	#11718882	1	1	yes	characteristic
610	C₂²	#11718882	1	1	yes	characteristic
611	C₂²	#11718882	1	1	yes	characteristic
612	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
613	C₂²	C₂×#88192	1	1	yes	characteristic
614	C₂²	C₂×#88194	1	1	yes	characteristic
615	C₄	—	4	4	no	—
616	C₄	—	52	4	no	—
617	C₄	—	104	4	no	—
618	C₄	#11718882	1	1	yes	characteristic
619	C₄	#11718882	1	1	yes	characteristic
620	C₄	#11718882	1	1	yes	characteristic
621	C₄	#11718882	1	1	yes	characteristic
622	C₄	C₂×D₄×Dic₁₃	1	1	yes	characteristic
623	C₄	C₂×#88190	1	1	yes	characteristic
624	C₄	C₂×#88192	1	1	yes	characteristic
625	C₄	C₂²×C₂²⋊Dic₁₃	1	1	yes	characteristic
626	C₂	—	2	1	no	—
627	C₂	—	2	1	no	—
628	C₂	—	2	1	no	—
629	C₂	—	2	1	no	—
630	C₂	—	2	1	no	—
631	C₂	—	2	1	no	—
632	C₂	—	8	4	no	—
633	C₂	#13115735	1	2	yes	direct product factor
634	C₂	C₂×#11718882	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#88192
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting, prime radical	C₂²×C₁₃×#135	C₂
socle	C₂²×C₁₃	#390
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂²×#135	D₁₃
hypocenter	C₁₃	C₂×#1976
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×#135

Complements

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

N	H ≅ G/N	type
1. C₂×#11718767	C₂	semidirect
2. C₂×#11718897	C₂	semidirect
3. C₂×#11718901	C₂	semidirect
4. C₂×#11718762	C₂	semidirect
5. #13115735	C₂	direct (N × H)
14. C₂×C₁₃×#135	C₄	semidirect
16. C₂²×C₁₃×Q₁₆	C₄	semidirect
17. C₂²×C₁₃×SD₁₆	C₄	semidirect
18. C₂²×C₁₃×D₈	C₄	semidirect
24. #11718901	C₂²	semidirect
26. #11718897	C₂²	semidirect
30. #11718767	C₂²	semidirect
34. #11718762	C₂²	semidirect
65. C₂×C₁₃×Q₁₆	C₂×C₄	semidirect
69. C₂×C₁₃×SD₁₆	C₂×C₄	semidirect
73. C₂×C₁₃×D₈	C₂×C₄	semidirect
293. C₂×#135	Dic₁₃	semidirect
295. C₂²×Q₁₆	Dic₁₃	semidirect
296. C₂²×SD₁₆	Dic₁₃	semidirect
297. C₂²×D₈	Dic₁₃	semidirect
373. C₂×Q₁₆	C₂×Dic₁₃	semidirect
377. C₂×SD₁₆	C₂×Dic₁₃	semidirect
381. C₂×D₈	C₂×Dic₁₃	semidirect
426. C₂×C₁₃	#1976	semidirect
528. C₁₃	C₂×#1976	semidirect
633. C₂	#13115735	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×#11718767	2
C₂×#11718897	2
C₂×#11718901	2
C₂×#11718762	2
#13115735	2
C₂²×C₁₃×#135	2
C₂×#1976	13

Subgroups — C2×#13115735 #15866894

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13115735 #15866894