Subgroups — #28376452

Order 13952.

1140 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20295653	C₂	1	1	yes	maximal, characteristic, complemented
2	#20295648	C₂	1	1	yes	maximal, characteristic, complemented
3	#20295646	C₂	1	2	yes	maximal, complemented
4	#20295631	C₂	1	1	yes	maximal, characteristic, complemented
5	#20295628	C₂	1	2	yes	maximal, complemented
6	#20295627	C₂	1	1	yes	maximal, characteristic, complemented
7	#20295615	C₂	1	2	yes	maximal, complemented
8	#20295610	C₂	1	2	yes	maximal, complemented
9	#20295606	C₂	1	1	yes	maximal, characteristic, complemented
10	#20295594	C₂	1	1	yes	maximal, characteristic, complemented
11	#20295592	C₂	1	1	yes	maximal, characteristic, complemented
12	#20295577	C₂	1	1	yes	maximal, characteristic, complemented
13	#20295575	C₂	1	2	yes	maximal, complemented
14	#20295571	C₂	1	1	yes	maximal, characteristic, complemented
15	#20295562	C₂	1	1	yes	maximal, characteristic, complemented
16	#20295559	C₂	1	2	yes	maximal, complemented
17	#20295555	C₂	1	1	yes	maximal, characteristic, complemented
18	#20295539	C₂	1	2	yes	maximal, complemented
19	#20295534	C₂	1	2	yes	maximal, complemented
20	C₄×#13182030	C₂	1	1	yes	maximal, characteristic, complemented
21	#20295494	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×D₄×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
23	#542×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13182030	C₂²	1	1	yes	characteristic
25	C₂×#13182030	C₂²	1	2	yes	complemented
26	C₂×#13182029	C₂²	1	1	yes	characteristic
27	C₂×#13182028	C₂²	1	2	yes	complemented
28	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₁₀₉	C₂²	1	2	yes	—
30	#16812698	C₂²	1	1	yes	characteristic, complemented
31	#16812697	C₂²	1	2	yes	complemented
32	#16812696	C₂²	1	1	yes	characteristic
33	#16812695	C₂²	1	1	yes	characteristic
34	#16812695	C₂²	1	2	yes	—
35	#16812694	C₂²	1	2	yes	complemented
36	#16812693	C₂²	1	2	yes	complemented
37	#16812692	C₂²	1	2	yes	complemented
38	#16812691	C₂²	1	1	yes	characteristic, complemented
39	#16812690	C₂²	1	1	yes	characteristic, complemented
40	#16812689	C₂²	1	2	yes	complemented
41	#16812688	C₂²	1	1	yes	characteristic
42	#16812688	C₂²	1	2	yes	complemented
43	#16812687	C₂²	1	2	yes	complemented
44	#16812685	C₂²	1	2	yes	—
45	#16812685	C₂²	1	2	yes	complemented
46	#16812684	C₂²	1	2	yes	complemented
47	#16812684	C₂²	1	2	yes	complemented
48	#16812684	C₂²	1	2	yes	complemented
49	#16812683	C₂²	1	2	yes	complemented
50	#16812682	C₂²	1	2	yes	complemented
51	#16812681	C₂²	1	2	yes	complemented
52	#16812681	C₂²	1	2	yes	complemented
53	#16812677	C₂²	1	2	yes	—
54	#16812677	C₂²	1	2	yes	complemented
55	#16812677	C₂²	1	2	yes	complemented
56	#16812675	C₂²	1	2	yes	—
57	#16812675	C₂²	1	1	yes	characteristic, complemented
58	#16812674	C₂²	1	2	yes	—
59	#16812674	C₂²	1	1	yes	characteristic
60	#16812674	C₂²	1	1	yes	characteristic, complemented
61	#16812674	C₂²	1	2	yes	complemented
62	#16812673	C₂²	1	1	yes	characteristic
63	#16812673	C₂²	1	2	yes	complemented
64	#16812673	C₂²	1	1	yes	characteristic, complemented
65	#16812672	C₂²	1	2	yes	—
66	#16812672	C₂²	1	2	yes	—
67	#16812672	C₂²	1	2	yes	—
68	#16812672	C₂²	1	2	yes	complemented
69	#16812672	C₂²	1	2	yes	complemented
70	#16812672	C₂²	1	2	yes	complemented
71	#16812672	C₂²	1	2	yes	complemented
72	#16812671	C₂²	1	2	yes	complemented
73	#16812670	C₂²	1	1	yes	characteristic
74	#16812669	C₂²	1	2	yes	—
75	#16812669	C₂²	1	2	yes	—
76	#16812669	C₂²	1	2	yes	—
77	#16812667	C₂²	1	2	yes	—
78	Q₈×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
79	#16812664	C₂²	1	1	yes	characteristic, complemented
80	#16812664	C₂²	1	1	yes	characteristic, complemented
81	C₄×D₄₃₆	C₂²	1	1	yes	characteristic
82	C₄×D₄₃₆	C₂²	1	2	yes	—
83	C₄×D₄₃₆	C₂²	1	1	yes	characteristic, complemented
84	D₄×Dic₁₀₉	C₂²	1	1	yes	characteristic
85	#16812661	C₂²	1	1	yes	characteristic
86	#16812661	C₂²	1	1	yes	characteristic
87	#16812661	C₂²	1	1	yes	characteristic
88	#16812661	C₂²	1	2	yes	—
89	#16812661	C₂²	1	1	yes	characteristic, complemented
90	#16812661	C₂²	1	2	yes	complemented
91	C₄×C₂²⋊D₁₀₉	C₂²	1	2	yes	—
92	#16812659	C₂²	1	2	yes	—
93	#16812659	C₂²	1	1	yes	characteristic
94	#16812659	C₂²	1	1	yes	characteristic
95	#16812659	C₂²	1	1	yes	characteristic, complemented
96	#16812659	C₂²	1	1	yes	characteristic, complemented
97	#16812659	C₂²	1	2	yes	complemented
98	#16812659	C₂²	1	2	yes	complemented
99	#16812659	C₂²	1	2	yes	complemented
100	#16812657	C₂²	1	1	yes	characteristic
101	#16812657	C₂²	1	2	yes	complemented
102	#16812657	C₂²	1	2	yes	complemented
103	#16812656	C₂²	1	1	yes	characteristic
104	#16812656	C₂²	1	1	yes	characteristic, complemented
105	#16812655	C₂²	1	2	yes	complemented
106	C₄⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic
107	C₂²⋊C₄×D₁₀₉	C₂²	1	2	yes	—
108	C₂×C₄×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
109	C₄²×D₁₀₉	C₂²	1	1	yes	characteristic
110	C₄²×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
111	C₄²×D₁₀₉	C₂²	1	2	yes	complemented
112	C₄⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
113	#126×C₁₀₉	C₂²	1	2	yes	complemented
114	#124×C₁₀₉	C₂²	1	1	yes	characteristic
115	#124×C₁₀₉	C₂²	1	2	yes	complemented
116	#123×C₁₀₉	C₂²	1	2	yes	complemented
117	C₂²⋊Q₈×C₁₀₉	C₂²	1	2	yes	complemented
118	C₂²⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
119	#121×C₁₀₉	C₂²	1	1	yes	characteristic
120	C₄×Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
122	#117×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₀₉	C₂³	1	2	yes	—
124	#13182030	—	2	4	no	—
125	#13182030	—	4	4	no	—
126	#13182029	—	2	4	no	—
127	#13182028	—	4	4	no	—
128	C₂×Dic₂₁₈	C₂³	1	1	yes	characteristic
129	C₂×Dic₂₁₈	C₂³	1	2	yes	—
130	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
131	C₂×D₄₃₆	C₂³	1	2	yes	—
132	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
133	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
134	C₂×D₄₃₆	C₂³	1	2	yes	—
135	C₂×D₄₃₆	C₂³	1	2	yes	—
136	C₂×D₄₃₆	C₂³	1	2	yes	—
137	C₂×D₄₃₆	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₁₀₉	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₁₀₉	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
146	D₄×D₁₀₉	—	2	4	no	—
147	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
148	C₂²×Dic₁₀₉	C₂³	1	2	yes	—
149	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₁₀₉	—	4	4	no	—
151	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
154	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
156	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
157	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
160	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
161	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
162	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
163	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
164	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
165	C₄⋊Dic₁₀₉	C₂³	1	2	yes	—
166	C₄⋊Dic₁₀₉	C₂³	1	2	yes	—
167	#13182008	C₂³	1	2	yes	—
168	#13182008	C₂³	1	2	yes	—
169	#13182008	C₂³	1	2	yes	—
170	#13182008	C₂³	1	1	yes	characteristic
171	#13182008	C₂³	1	1	yes	characteristic
172	#13182008	C₂³	1	1	yes	characteristic
173	#13182008	C₂³	1	1	yes	characteristic
174	#13182008	C₂³	1	2	yes	—
175	#13182008	C₂³	1	2	yes	—
176	#13182008	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₀₉	C₂³	1	2	yes	—
178	C₂²⋊Dic₁₀₉	C₂³	1	2	yes	—
179	#13182006	C₂³	1	2	yes	—
180	#13182006	C₂³	1	2	yes	—
181	#13182006	C₂³	1	1	yes	characteristic
182	#13182006	C₂³	1	1	yes	characteristic
183	#13182006	C₂³	1	1	yes	characteristic
184	#13182006	C₂³	1	1	yes	characteristic
185	#13182006	C₂³	1	2	yes	—
186	#13182006	C₂³	1	2	yes	—
187	#13182006	C₂³	1	2	yes	—
188	#13182006	C₂³	1	2	yes	—
189	#13182006	C₂³	1	2	yes	—
190	#13182006	C₂³	1	2	yes	—
191	#13182006	C₂³	1	2	yes	—
192	#13182006	C₂³	1	2	yes	—
193	#13182006	C₂³	1	2	yes	—
194	#13182006	C₂³	1	2	yes	—
195	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
196	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
197	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
198	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
199	C₄×Dic₁₀₉	C₂³	1	2	yes	—
200	C₄×Dic₁₀₉	C₂³	1	2	yes	—
201	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
202	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
203	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
204	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
205	C₂×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
206	C₂×Q₈×C₁₀₉	C₂³	1	2	yes	—
207	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
208	C₂×D₄×C₁₀₉	C₂³	1	2	yes	—
209	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
210	C₂²×C₄×C₁₀₉	C₂³	1	2	yes	—
211	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
212	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
213	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
214	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
215	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
216	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
217	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
218	C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
219	C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
220	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
224	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
225	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
226	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
227	C₄²×C₁₀₉	C₂³	1	2	yes	—
228	C₂³×C₁₀₉	C₂⁴	1	2	yes	—
229	C₂³×C₁₀₉	C₂⁴	1	1	yes	characteristic
230	C₂²×D₁₀₉	—	2	4	no	—
231	C₂²×D₁₀₉	—	4	2	no	—
232	C₂²×D₁₀₉	—	4	2	no	—
233	C₂²×D₁₀₉	C₂⁴	1	2	yes	—
234	C₂²×D₁₀₉	C₂⁴	1	2	yes	—
235	C₂²×D₁₀₉	C₂⁴	1	1	yes	characteristic
236	C₂²×D₁₀₉	C₂⁴	1	1	yes	characteristic
237	Q₈×C₁₀₉	—	2	2	no	—
238	Q₈×C₁₀₉	—	4	2	no	—
239	D₄×C₁₀₉	—	2	2	no	—
240	D₄×C₁₀₉	—	4	2	no	—
241	C₂×C₄×C₁₀₉	—	2	2	no	—
242	C₂×C₄×C₁₀₉	—	4	2	no	—
243	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
246	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
249	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
251	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
252	C₂²⋊D₁₀₉	—	2	2	no	—
253	C₂²⋊D₁₀₉	—	2	4	no	—
254	C₂²⋊D₁₀₉	—	2	2	no	—
255	C₂²⋊D₁₀₉	—	4	2	no	—
256	C₂²⋊D₁₀₉	—	4	2	no	—
257	C₂²⋊D₁₀₉	—	4	2	no	—
258	C₂²⋊D₁₀₉	—	4	2	no	—
259	C₂²⋊D₁₀₉	—	4	2	no	—
260	C₂×Dic₁₀₉	—	2	4	no	—
261	C₂×Dic₁₀₉	—	2	2	no	—
262	C₂×Dic₁₀₉	—	4	1	no	—
263	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
266	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
268	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
269	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
271	D₄₃₆	—	2	2	no	—
272	D₄₃₆	—	2	4	no	—
273	D₄₃₆	—	2	2	no	—
274	D₄₃₆	—	2	2	no	—
275	D₄₃₆	—	4	2	no	—
276	D₄₃₆	—	4	2	no	—
277	D₄₃₆	—	4	2	no	—
278	D₄₃₆	—	4	2	no	—
279	C₄×D₁₀₉	—	2	2	no	—
280	C₄×D₁₀₉	—	2	4	no	—
281	C₄×D₁₀₉	—	2	2	no	—
282	C₄×D₁₀₉	—	2	4	no	—
283	C₄×D₁₀₉	—	2	4	no	—
284	C₄×D₁₀₉	—	2	2	no	—
285	C₄×D₁₀₉	—	4	2	no	—
286	C₄×D₁₀₉	—	4	2	no	—
287	C₄×D₁₀₉	—	4	1	no	—
288	C₄×D₁₀₉	—	4	1	no	—
289	C₄×D₁₀₉	—	4	2	no	—
290	C₄×D₁₀₉	#41	1	4	yes	complemented
291	Dic₂₁₈	—	2	2	no	—
292	Dic₂₁₈	—	4	2	no	—
293	C₂²×C₁₀₉	—	2	1	no	—
294	C₂²×C₁₀₉	—	2	2	no	—
295	C₂²×C₁₀₉	—	2	1	no	—
296	C₂²×C₁₀₉	—	2	2	no	—
297	C₂²×C₁₀₉	—	2	1	no	—
298	C₂²×C₁₀₉	—	2	2	no	—
299	C₂²×C₁₀₉	C₂⁵	1	1	yes	characteristic
300	C₂×D₁₀₉	—	2	1	no	—
301	C₂×D₁₀₉	—	2	1	no	—
302	C₂×D₁₀₉	—	2	2	no	—
303	C₂×D₁₀₉	—	2	1	no	—
304	C₂×D₁₀₉	—	2	2	no	—
305	C₂×D₁₀₉	—	2	2	no	—
306	C₂×D₁₀₉	—	2	1	no	—
307	C₂×D₁₀₉	—	2	2	no	—
308	C₂×D₁₀₉	—	2	2	no	—
309	C₂×D₁₀₉	—	2	1	no	—
310	C₂×D₁₀₉	—	2	2	no	—
311	C₂×D₁₀₉	—	4	8	no	—
312	C₂×D₁₀₉	C₂×#41	1	2	yes	—
313	C₄×C₁₀₉	—	2	1	no	—
314	C₄×C₁₀₉	—	2	2	no	—
315	C₄×C₁₀₉	—	2	2	no	—
316	C₄×C₁₀₉	—	2	1	no	—
317	C₄×C₁₀₉	—	2	2	no	—
318	C₄×C₁₀₉	—	2	1	no	—
319	C₄×C₁₀₉	—	2	1	no	—
320	C₄×C₁₀₉	—	2	1	no	—
321	C₄×C₁₀₉	C₂×#41	1	2	yes	—
322	Dic₁₀₉	—	2	1	no	—
323	Dic₁₀₉	—	2	1	no	—
324	Dic₁₀₉	—	2	2	no	—
325	Dic₁₀₉	—	2	1	no	—
326	Dic₁₀₉	—	2	2	no	—
327	Dic₁₀₉	—	2	1	no	—
328	Dic₁₀₉	C₂×#41	1	2	yes	—
329	Dic₁₀₉	H(5,𝔽₂)	1	2	yes	—
330	C₂×C₁₀₉	—	4	2	no	—
331	C₂×C₁₀₉	—	4	1	no	—
332	C₂×C₁₀₉	C₂²×#41	1	1	yes	characteristic
333	C₂×C₁₀₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
334	C₂×C₁₀₉	#585	1	1	yes	characteristic
335	D₁₀₉	—	2	2	no	—
336	D₁₀₉	—	4	2	no	—
337	D₁₀₉	—	4	1	no	—
338	D₁₀₉	—	4	2	no	—
339	#3460	—	109	1	no	maximal, Sylow
340	C₁₀₉	#3460	1	1	yes	characteristic, complemented, Sylow
341	#544	—	109	1	no	—
342	#542	—	109	2	no	—
343	#542	—	109	1	no	—
344	#542	D₁₀₉	1	1	yes	characteristic, complemented
345	#540	—	109	2	no	—
346	#540	—	109	1	no	—
347	#540	—	109	1	no	—
348	#538	—	109	2	no	—
349	#538	—	109	2	no	—
350	#537	—	109	1	no	—
351	#535	—	109	1	no	—
352	#535	—	109	1	no	—
353	#532	—	109	1	no	—
354	#532	—	109	2	no	—
355	#532	—	109	1	no	—
356	#529	—	109	2	no	—
357	#529	—	109	1	no	—
358	#529	—	109	1	no	—
359	#525	—	109	2	no	—
360	#525	—	109	2	no	—
361	C₄×#41	—	109	1	no	—
362	C₄×#41	—	109	1	no	—
363	C₂×C₄×D₄	—	109	1	no	—
364	C₂×#41	—	109	2	no	—
365	C₂×#41	—	109	1	no	—
366	C₂×#41	—	109	2	no	—
367	C₂×#41	—	109	1	no	—
368	C₂²×D₄	—	109	1	no	—
369	C₂³×C₄	—	109	2	no	—
370	C₄⋊Q₈	—	109	2	no	—
371	C₄⋊Q₈	—	109	1	no	—
372	C₄⋊Q₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
373	#127	—	109	1	no	—
374	#127	—	109	2	no	—
375	#127	—	109	1	no	—
376	#126	—	109	2	no	—
377	#126	—	109	2	no	—
378	#126	—	109	2	no	—
379	#126	C₂×D₁₀₉	1	2	yes	complemented
380	#125	—	109	2	no	—
381	#125	—	109	1	no	—
382	#125	—	109	1	no	—
383	#124	—	109	1	no	—
384	#124	—	109	2	no	—
385	#124	—	109	2	no	—
386	#124	—	109	2	no	—
387	#124	—	109	2	no	—
388	#124	C₂×D₁₀₉	1	1	yes	characteristic
389	#124	C₂×D₁₀₉	1	2	yes	complemented
390	#123	—	109	2	no	—
391	#123	—	109	2	no	—
392	#123	—	109	2	no	—
393	#123	—	109	2	no	—
394	#123	—	109	2	no	—
395	#123	—	109	2	no	—
396	#123	—	109	2	no	—
397	#123	C₂×D₁₀₉	1	2	yes	complemented
398	C₂²⋊Q₈	—	109	2	no	—
399	C₂²⋊Q₈	—	109	1	no	—
400	C₂²⋊Q₈	—	109	2	no	—
401	C₂²⋊Q₈	—	109	2	no	—
402	C₂²⋊Q₈	—	109	2	no	—
403	C₂²⋊Q₈	C₂×D₁₀₉	1	2	yes	complemented
404	C₂²⋊Q₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
405	#121	—	109	1	no	—
406	#121	—	109	2	no	—
407	#121	—	109	2	no	—
408	#121	—	109	1	no	—
409	#121	—	109	1	no	—
410	#121	—	109	2	no	—
411	#121	—	109	1	no	—
412	#121	—	109	1	no	—
413	#121	—	109	2	no	—
414	#121	—	109	2	no	—
415	#121	—	109	2	no	—
416	#121	—	109	2	no	—
417	#121	—	109	2	no	—
418	#121	—	109	2	no	—
419	#121	—	109	2	no	—
420	#121	—	109	2	no	—
421	#121	C₂×D₁₀₉	1	1	yes	characteristic
422	#120	—	109	2	no	—
423	#120	—	109	2	no	—
424	#120	—	109	2	no	—
425	#120	—	109	2	no	—
426	C₄×Q₈	—	109	1	no	—
427	C₄×Q₈	—	109	1	no	—
428	C₄×Q₈	—	109	1	no	—
429	C₄×Q₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
430	C₄×D₄	—	109	1	no	—
431	C₄×D₄	—	109	2	no	—
432	C₄×D₄	—	109	1	no	—
433	C₄×D₄	—	109	2	no	—
434	C₄×D₄	—	109	1	no	—
435	C₄×D₄	—	109	1	no	—
436	C₄×D₄	—	109	1	no	—
437	C₄×D₄	—	109	2	no	—
438	C₄×D₄	—	109	2	no	—
439	C₄×D₄	—	109	1	no	—
440	C₄×D₄	—	109	1	no	—
441	C₄×D₄	—	109	1	no	—
442	C₄×D₄	—	109	1	no	—
443	C₄×D₄	—	109	2	no	—
444	C₄×D₄	—	109	2	no	—
445	C₄×D₄	—	109	2	no	—
446	C₄×D₄	—	109	1	no	—
447	C₄×D₄	—	109	2	no	—
448	C₄×D₄	—	109	1	no	—
449	C₄×D₄	C₂×D₁₀₉	1	1	yes	characteristic
450	#117	—	109	1	no	—
451	#117	—	109	2	no	—
452	#117	—	109	2	no	—
453	#117	—	109	2	no	—
454	#117	—	109	1	no	—
455	#117	—	109	1	no	—
456	#117	C₂×D₁₀₉	1	1	yes	characteristic, complemented
457	C₂×C₄⋊C₄	—	109	1	no	—
458	C₂×C₂²⋊C₄	—	109	2	no	—
459	C₂×C₄²	—	109	1	no	—
460	C₂×C₄²	—	109	1	no	—
461	C₂×C₄²	—	109	2	no	—
462	C₂×C₄²	—	109	1	no	—
463	C₂⁴	—	109	2	no	—
464	#41	—	436	4	no	—
465	#41	—	436	4	no	—
466	#41	—	218	4	no	—
467	#41	—	218	4	no	—
468	C₂×Q₈	—	109	2	no	—
469	C₂×Q₈	—	109	1	no	—
470	C₂×Q₈	C₂²×D₁₀₉	1	1	yes	characteristic
471	C₂×Q₈	C₂²×D₁₀₉	1	2	yes	—
472	C₂×D₄	—	109	2	no	—
473	C₂×D₄	—	109	2	no	—
474	C₂×D₄	—	109	2	no	—
475	C₂×D₄	—	109	2	no	—
476	C₂×D₄	—	109	2	no	—
477	C₂×D₄	—	109	1	no	—
478	C₂×D₄	—	109	2	no	—
479	C₂×D₄	—	109	1	no	—
480	C₂×D₄	—	109	2	no	—
481	C₂×D₄	—	109	2	no	—
482	C₂×D₄	—	109	2	no	—
483	C₂×D₄	—	109	2	no	—
484	C₂×D₄	—	109	1	no	—
485	C₂×D₄	—	109	2	no	—
486	C₂×D₄	—	109	1	no	—
487	C₂×D₄	—	109	1	no	—
488	C₂×D₄	—	218	4	no	—
489	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
490	C₂×D₄	C₂²×D₁₀₉	1	2	yes	—
491	C₂²×C₄	—	109	1	no	—
492	C₂²×C₄	—	109	1	no	—
493	C₂²×C₄	—	109	1	no	—
494	C₂²×C₄	—	109	2	no	—
495	C₂²×C₄	—	109	1	no	—
496	C₂²×C₄	—	109	1	no	—
497	C₂²×C₄	—	109	2	no	—
498	C₂²×C₄	—	109	2	no	—
499	C₂²×C₄	—	109	2	no	—
500	C₂²×C₄	—	109	2	no	—
501	C₂²×C₄	—	109	1	no	—
502	C₂²×C₄	—	109	1	no	—
503	C₂²×C₄	—	109	2	no	—
504	C₂²×C₄	—	109	1	no	—
505	C₂²×C₄	—	109	2	no	—
506	C₂²×C₄	—	436	4	no	—
507	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
508	C₂²×C₄	C₂²×D₁₀₉	1	2	yes	—
509	C₄⋊C₄	—	109	2	no	—
510	C₄⋊C₄	—	109	1	no	—
511	C₄⋊C₄	—	109	1	no	—
512	C₄⋊C₄	—	109	1	no	—
513	C₄⋊C₄	—	109	1	no	—
514	C₄⋊C₄	—	109	2	no	—
515	C₄⋊C₄	—	109	2	no	—
516	C₄⋊C₄	—	109	2	no	—
517	C₄⋊C₄	—	109	2	no	—
518	C₄⋊C₄	—	109	2	no	—
519	C₄⋊C₄	—	109	1	no	—
520	C₄⋊C₄	—	109	1	no	—
521	C₄⋊C₄	—	109	2	no	—
522	C₄⋊C₄	—	109	2	no	—
523	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
524	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
525	C₄⋊C₄	C₂²×D₁₀₉	1	2	yes	—
526	C₄⋊C₄	C₂²×D₁₀₉	1	2	yes	—
527	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
528	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
529	C₄⋊C₄	C₂²×D₁₀₉	1	2	yes	—
530	C₂²⋊C₄	—	109	2	no	—
531	C₂²⋊C₄	—	109	2	no	—
532	C₂²⋊C₄	—	109	2	no	—
533	C₂²⋊C₄	—	109	2	no	—
534	C₂²⋊C₄	—	109	2	no	—
535	C₂²⋊C₄	—	109	1	no	—
536	C₂²⋊C₄	—	109	1	no	—
537	C₂²⋊C₄	—	109	1	no	—
538	C₂²⋊C₄	—	109	2	no	—
539	C₂²⋊C₄	—	109	2	no	—
540	C₂²⋊C₄	—	109	1	no	—
541	C₂²⋊C₄	—	109	2	no	—
542	C₂²⋊C₄	—	109	2	no	—
543	C₂²⋊C₄	—	109	2	no	—
544	C₂²⋊C₄	—	109	2	no	—
545	C₂²⋊C₄	—	109	2	no	—
546	C₂²⋊C₄	—	109	2	no	—
547	C₂²⋊C₄	—	109	2	no	—
548	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	—
549	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	—
550	C₂²⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
551	C₂²⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
552	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	—
553	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	—
554	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	—
555	C₄²	—	109	1	no	—
556	C₄²	—	109	1	no	—
557	C₄²	—	109	1	no	—
558	C₄²	—	109	1	no	—
559	C₄²	—	109	2	no	—
560	C₄²	—	109	1	no	—
561	C₄²	—	109	2	no	—
562	C₄²	—	109	1	no	—
563	C₄²	—	109	1	no	—
564	C₄²	—	109	1	no	—
565	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
566	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
567	C₄²	C₂²×D₁₀₉	1	2	yes	—
568	C₂³	—	109	1	no	—
569	C₂³	—	109	2	no	—
570	C₂³	—	109	1	no	—
571	C₂³	—	109	2	no	—
572	C₂³	—	436	2	no	—
573	C₂³	—	436	2	no	—
574	C₂³	—	218	4	no	—
575	C₂³	C₂³×D₁₀₉	1	2	yes	—
576	C₂³	C₂³×D₁₀₉	1	1	yes	characteristic
577	Q₈	—	2	2	no	—
578	Q₈	—	4	2	no	—
579	Q₈	—	436	2	no	—
580	Q₈	—	218	2	no	—
581	D₄	—	2	2	no	—
582	D₄	—	4	2	no	—
583	D₄	—	436	2	no	—
584	D₄	—	436	2	no	—
585	D₄	—	436	2	no	—
586	D₄	—	436	2	no	—
587	D₄	—	436	2	no	—
588	D₄	—	436	2	no	—
589	D₄	—	436	2	no	—
590	D₄	—	436	2	no	—
591	D₄	—	436	2	no	—
592	D₄	—	218	2	no	—
593	D₄	—	218	4	no	—
594	D₄	—	218	4	no	—
595	D₄	—	218	2	no	—
596	D₄	—	218	2	no	—
597	D₄	—	218	2	no	—
598	D₄	—	218	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	109	1	no	—
602	C₂×C₄	—	109	1	no	—
603	C₂×C₄	—	109	4	no	—
604	C₂×C₄	—	109	1	no	—
605	C₂×C₄	—	109	1	no	—
606	C₂×C₄	—	109	2	no	—
607	C₂×C₄	—	109	1	no	—
608	C₂×C₄	—	109	1	no	—
609	C₂×C₄	—	109	2	no	—
610	C₂×C₄	—	436	2	no	—
611	C₂×C₄	—	436	2	no	—
612	C₂×C₄	—	436	1	no	—
613	C₂×C₄	—	436	2	no	—
614	C₂×C₄	—	436	1	no	—
615	C₂×C₄	—	436	1	no	—
616	C₂×C₄	—	218	2	no	—
617	C₂×C₄	—	218	4	no	—
618	C₂×C₄	—	218	4	no	—
619	C₂×C₄	—	218	2	no	—
620	C₂×C₄	—	218	4	no	—
621	C₂×C₄	—	218	4	no	—
622	C₂×C₄	—	218	2	no	—
623	C₂×C₄	—	218	2	no	—
624	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
626	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
627	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
628	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
629	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
630	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
631	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
632	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
633	C₂²	—	2	1	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	1	no	—
637	C₂²	—	2	1	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	109	2	no	—
640	C₂²	—	436	8	no	—
641	C₂²	—	218	2	no	—
642	C₂²	—	218	1	no	—
643	C₂²	—	218	2	no	—
644	C₂²	—	218	2	no	—
645	C₂²	—	218	1	no	—
646	C₂²	—	218	2	no	—
647	C₂²	—	218	2	no	—
648	C₂²	—	218	1	no	—
649	C₂²	—	218	2	no	—
650	C₂²	—	218	1	no	—
651	C₂²	—	218	1	no	—
652	C₂²	C₂⁴×D₁₀₉	1	1	yes	characteristic
653	C₄	—	2	1	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	1	no	—
656	C₄	—	2	2	no	—
657	C₄	—	2	2	no	—
658	C₄	—	2	1	no	—
659	C₄	—	2	1	no	—
660	C₄	—	2	1	no	—
661	C₄	—	109	2	no	—
662	C₄	—	109	2	no	—
663	C₄	—	218	1	no	—
664	C₄	—	218	2	no	—
665	C₄	—	218	1	no	—
666	C₄	—	218	1	no	—
667	C₄	—	218	2	no	—
668	C₄	—	218	1	no	—
669	C₄	#41×D₁₀₉	1	2	yes	—
670	C₂	—	4	2	no	—
671	C₂	—	4	1	no	—
672	C₂	—	436	2	no	—
673	C₂	—	436	2	no	—
674	C₂	—	436	1	no	—
675	C₂	—	218	2	no	—
676	C₂	C₂×#41×D₁₀₉	1	1	yes	characteristic
677	C₂	H(5,𝔽₂)×D₁₀₉	1	1	yes	characteristic
678	C₂	#20295863	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₀₉
commutator, socle, cosocle	C₂²×C₁₀₉	C₂⁵
Fitting	#542×C₁₀₉	C₂
hypercenter	#542	D₁₀₉
hypocenter	C₁₀₉	#3460
LCS	G ▷ C₂²×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. #20295653	C₂	semidirect
2. #20295648	C₂	semidirect
3. #20295646	C₂	semidirect
4. #20295631	C₂	semidirect
5. #20295628	C₂	semidirect
6. #20295627	C₂	semidirect
7. #20295615	C₂	semidirect
8. #20295610	C₂	semidirect
9. #20295606	C₂	semidirect
10. #20295594	C₂	semidirect
11. #20295592	C₂	semidirect
12. #20295577	C₂	semidirect
13. #20295575	C₂	semidirect
14. #20295571	C₂	semidirect
15. #20295562	C₂	semidirect
16. #20295559	C₂	semidirect
17. #20295555	C₂	semidirect
18. #20295539	C₂	semidirect
19. #20295534	C₂	semidirect
20. C₄×#13182030	C₂	semidirect
21. #20295494	C₂	semidirect
22. C₄×D₄×D₁₀₉	C₂	semidirect
23. #542×C₁₀₉	C₂	semidirect
25. C₂×#13182030	C₂²	semidirect
27. C₂×#13182028	C₂²	semidirect
30. #16812698	C₂²	semidirect
31. #16812697	C₂²	semidirect
35. #16812694	C₂²	semidirect
36. #16812693	C₂²	semidirect
37. #16812692	C₂²	semidirect
38. #16812691	C₂²	semidirect
39. #16812690	C₂²	semidirect
40. #16812689	C₂²	semidirect
42. #16812688	C₂²	semidirect
43. #16812687	C₂²	semidirect
45. #16812685	C₂²	semidirect
46. #16812684	C₂²	semidirect
47. #16812684	C₂²	semidirect
48. #16812684	C₂²	semidirect
49. #16812683	C₂²	semidirect
50. #16812682	C₂²	semidirect
51. #16812681	C₂²	semidirect
52. #16812681	C₂²	semidirect
54. #16812677	C₂²	semidirect
55. #16812677	C₂²	semidirect
57. #16812675	C₂²	semidirect
60. #16812674	C₂²	semidirect
61. #16812674	C₂²	semidirect
63. #16812673	C₂²	semidirect
64. #16812673	C₂²	semidirect
68. #16812672	C₂²	semidirect
69. #16812672	C₂²	semidirect
70. #16812672	C₂²	semidirect
71. #16812672	C₂²	semidirect
72. #16812671	C₂²	semidirect
78. Q₈×Dic₁₀₉	C₂²	semidirect
79. #16812664	C₂²	semidirect
80. #16812664	C₂²	semidirect
83. C₄×D₄₃₆	C₂²	semidirect
89. #16812661	C₂²	semidirect
90. #16812661	C₂²	semidirect
95. #16812659	C₂²	semidirect
96. #16812659	C₂²	semidirect
97. #16812659	C₂²	semidirect
98. #16812659	C₂²	semidirect
99. #16812659	C₂²	semidirect
101. #16812657	C₂²	semidirect
102. #16812657	C₂²	semidirect
104. #16812656	C₂²	semidirect
105. #16812655	C₂²	semidirect
108. C₂×C₄×Dic₁₀₉	C₂²	semidirect
110. C₄²×D₁₀₉	C₂²	semidirect
111. C₄²×D₁₀₉	C₂²	semidirect
112. C₄⋊Q₈×C₁₀₉	C₂²	semidirect
113. #126×C₁₀₉	C₂²	semidirect
115. #124×C₁₀₉	C₂²	semidirect
116. #123×C₁₀₉	C₂²	semidirect
117. C₂²⋊Q₈×C₁₀₉	C₂²	semidirect
118. C₂²⋊Q₈×C₁₀₉	C₂²	semidirect
120. C₄×Q₈×C₁₀₉	C₂²	semidirect
122. #117×C₁₀₉	C₂²	semidirect
290. C₄×D₁₀₉	#41	semidirect
340. C₁₀₉	#3460	semidirect
344. #542	D₁₀₉	semidirect
372. C₄⋊Q₈	C₂×D₁₀₉	semidirect
379. #126	C₂×D₁₀₉	semidirect
389. #124	C₂×D₁₀₉	semidirect
397. #123	C₂×D₁₀₉	semidirect
403. C₂²⋊Q₈	C₂×D₁₀₉	semidirect
404. C₂²⋊Q₈	C₂×D₁₀₉	semidirect
429. C₄×Q₈	C₂×D₁₀₉	semidirect
456. #117	C₂×D₁₀₉	semidirect

Maximal subgroups

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

subgroup	index
#20295653	2
#20295648	2
#20295646	2
#20295631	2
#20295628	2
#20295627	2
#20295615	2
#20295610	2
#20295606	2
#20295594	2
#20295592	2
#20295577	2
#20295575	2
#20295571	2
#20295562	2
#20295559	2
#20295555	2
#20295539	2
#20295534	2
C₄×#13182030	2
#20295494	2
C₄×D₄×D₁₀₉	2
#542×C₁₀₉	2
#3460	109