Subgroups — #529×D₁₀₉ #28376290

Order 13952.

1232 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20295563	C₂	1	1	yes	maximal, characteristic, complemented
2	#20295562	C₂	1	1	yes	maximal, characteristic, complemented
3	#20295561	C₂	1	1	yes	maximal, characteristic, complemented
4	#20295560	C₂	1	1	yes	maximal, characteristic, complemented
5	#20295559	C₂	1	2	yes	maximal, complemented
6	#20295558	C₂	1	1	yes	maximal, characteristic, complemented
7	#20295557	C₂	1	1	yes	maximal, characteristic, complemented
8	#20295556	C₂	1	2	yes	maximal, complemented
9	#20295555	C₂	1	1	yes	maximal, characteristic, complemented
10	#20295554	C₂	1	2	yes	maximal, complemented
11	#20295553	C₂	1	2	yes	maximal, complemented
12	#126×D₁₀₉	C₂	1	2	yes	maximal, complemented
13	#125×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#124×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#123×D₁₀₉	C₂	1	2	yes	maximal, complemented
16	C₂²⋊Q₈×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#121×D₁₀₉	C₂	1	1	yes	maximal, characteristic
18	C₄×Q₈×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×D₄×D₁₀₉	C₂	1	2	yes	maximal, complemented
20	C₄×D₄×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
21	#117×D₁₀₉	C₂	1	2	yes	maximal, complemented
22	C₂×C₄²×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
23	#529×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₈×D₁₀₉	C₂²	1	1	yes	characteristic
25	C₂×D₄×D₁₀₉	C₂²	1	2	yes	—
26	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic
27	C₂²×C₄×D₁₀₉	C₂²	1	1	yes	characteristic
28	C₂²×C₄×D₁₀₉	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₁₀₉	C₂²	1	1	yes	characteristic
30	C₂²×C₄×D₁₀₉	C₂²	1	2	yes	—
31	#16812694	C₂²	1	2	yes	complemented
32	#16812694	C₂²	1	2	yes	complemented
33	#16812694	C₂²	1	2	yes	complemented
34	#16812693	C₂²	1	2	yes	complemented
35	#16812692	C₂²	1	2	yes	complemented
36	#16812692	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	#16812690	C₂²	1	1	yes	characteristic, complemented
41	#16812689	C₂²	1	2	yes	complemented
42	#16812689	C₂²	1	2	yes	complemented
43	#16812688	C₂²	1	1	yes	characteristic, complemented
44	#16812687	C₂²	1	1	yes	characteristic, complemented
45	#16812686	C₂²	1	1	yes	characteristic, complemented
46	#16812685	C₂²	1	2	yes	complemented
47	#16812685	C₂²	1	2	yes	complemented
48	#16812684	C₂²	1	2	yes	complemented
49	#16812684	C₂²	1	2	yes	complemented
50	#16812683	C₂²	1	2	yes	complemented
51	#16812682	C₂²	1	2	yes	complemented
52	#16812681	C₂²	1	2	yes	complemented
53	#16812681	C₂²	1	2	yes	complemented
54	#16812680	C₂²	1	2	yes	complemented
55	#16812679	C₂²	1	1	yes	characteristic, complemented
56	#16812678	C₂²	1	1	yes	characteristic, complemented
57	#16812677	C₂²	1	2	yes	complemented
58	#16812676	C₂²	1	2	yes	complemented
59	#16812675	C₂²	1	1	yes	characteristic, complemented
60	#16812674	C₂²	1	1	yes	characteristic
61	#16812673	C₂²	1	1	yes	characteristic
62	#16812672	C₂²	1	2	yes	—
63	#16812671	C₂²	1	2	yes	—
64	#16812670	C₂²	1	1	yes	characteristic
65	Q₈×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
66	C₄×Dic₂₁₈	C₂²	1	2	yes	complemented
67	C₄×Dic₂₁₈	C₂²	1	1	yes	characteristic, complemented
68	#16812664	C₂²	1	2	yes	complemented
69	#16812664	C₂²	1	1	yes	characteristic, complemented
70	C₄×D₄₃₆	C₂²	1	2	yes	complemented
71	C₄×D₄₃₆	C₂²	1	1	yes	characteristic, complemented
72	D₄×Dic₁₀₉	C₂²	1	2	yes	complemented
73	D₄×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
74	#16812661	C₂²	1	2	yes	complemented
75	#16812661	C₂²	1	1	yes	characteristic, complemented
76	C₄×C₂²⋊D₁₀₉	C₂²	1	2	yes	complemented
77	C₄×C₂²⋊D₁₀₉	C₂²	1	2	yes	complemented
78	C₄×C₂²⋊D₁₀₉	C₂²	1	2	yes	complemented
79	#16812659	C₂²	1	2	yes	complemented
80	#16812659	C₂²	1	2	yes	complemented
81	#16812659	C₂²	1	2	yes	complemented
82	#16812658	C₂²	1	2	yes	complemented
83	#16812657	C₂²	1	2	yes	complemented
84	#16812657	C₂²	1	2	yes	complemented
85	#16812656	C₂²	1	2	yes	complemented
86	#16812656	C₂²	1	2	yes	complemented
87	#16812655	C₂²	1	2	yes	complemented
88	#16812655	C₂²	1	2	yes	complemented
89	C₄⋊C₄×D₁₀₉	C₂²	1	2	yes	—
90	C₄⋊C₄×D₁₀₉	C₂²	1	2	yes	—
91	C₄⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic
92	C₄⋊C₄×D₁₀₉	C₂²	1	2	yes	—
93	C₄⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic
94	C₄⋊C₄×D₁₀₉	C₂²	1	2	yes	—
95	C₂²⋊C₄×D₁₀₉	C₂²	1	2	yes	—
96	C₂²⋊C₄×D₁₀₉	C₂²	1	2	yes	—
97	C₂²⋊C₄×D₁₀₉	C₂²	1	2	yes	—
98	C₂²⋊C₄×D₁₀₉	C₂²	1	2	yes	—
99	C₂²⋊C₄×D₁₀₉	C₂²	1	2	yes	—
100	C₂×C₄×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
101	C₂×C₄×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
102	C₂×C₄×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
103	C₄²×D₁₀₉	C₂²	1	1	yes	characteristic
104	C₄²×D₁₀₉	C₂²	1	1	yes	characteristic
105	C₄²×D₁₀₉	C₂²	1	1	yes	characteristic
106	C₄²×D₁₀₉	C₂²	1	1	yes	characteristic
107	C₄²×D₁₀₉	C₂²	1	2	yes	—
108	C₄²×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
109	C₄²×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
110	C₄²×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
111	C₄²×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
112	#126×C₁₀₉	C₂²	1	2	yes	complemented
113	#125×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
114	#124×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
115	#123×C₁₀₉	C₂²	1	2	yes	complemented
116	C₂²⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
117	#121×C₁₀₉	C₂²	1	1	yes	characteristic
118	C₄×Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₁₀₉	C₂²	1	2	yes	complemented
120	C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
121	#117×C₁₀₉	C₂²	1	2	yes	complemented
122	C₂×C₄²×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₀₉	C₂³	1	2	yes	—
124	C₂³×D₁₀₉	C₂³	1	1	yes	characteristic
125	C₂×Dic₂₁₈	C₂³	1	2	yes	—
126	C₂×Dic₂₁₈	C₂³	1	1	yes	characteristic
127	Q₈×D₁₀₉	—	2	4	no	—
128	C₂×D₄₃₆	C₂³	1	2	yes	—
129	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
130	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
133	D₄×D₁₀₉	—	2	8	no	—
134	D₄×D₁₀₉	—	2	4	no	—
135	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
136	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
137	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
138	C₂²×Dic₁₀₉	C₂³	1	2	yes	—
139	C₂×C₄×D₁₀₉	—	2	4	no	—
140	C₂×C₄×D₁₀₉	—	2	4	no	—
141	C₂×C₄×D₁₀₉	—	2	8	no	—
142	C₂×C₄×D₁₀₉	—	2	4	no	—
143	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
148	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
149	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
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	2	yes	—
158	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
160	C₄⋊Dic₁₀₉	C₂³	1	2	yes	—
161	C₄⋊Dic₁₀₉	C₂³	1	2	yes	—
162	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
163	C₄⋊Dic₁₀₉	C₂³	1	2	yes	—
164	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
165	C₄⋊Dic₁₀₉	C₂³	1	2	yes	—
166	#13182008	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	2	yes	—
171	#13182008	C₂³	1	2	yes	—
172	#13182008	C₂³	1	2	yes	—
173	#13182008	C₂³	1	2	yes	—
174	#13182008	C₂³	1	2	yes	—
175	#13182008	C₂³	1	2	yes	—
176	C₂²⋊Dic₁₀₉	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₀₉	C₂³	1	2	yes	—
178	C₂²⋊Dic₁₀₉	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₀₉	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₀₉	C₂³	1	2	yes	—
181	#13182006	C₂³	1	2	yes	—
182	#13182006	C₂³	1	2	yes	—
183	#13182006	C₂³	1	2	yes	—
184	#13182006	C₂³	1	2	yes	—
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	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
192	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
193	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
194	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
200	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
201	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
202	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
203	C₄×Dic₁₀₉	C₂³	1	2	yes	—
204	C₄×Dic₁₀₉	C₂³	1	2	yes	—
205	C₄×Dic₁₀₉	C₂³	1	2	yes	—
206	C₂×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
207	C₂×D₄×C₁₀₉	C₂³	1	2	yes	—
208	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
209	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
210	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
211	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
212	C₂²×C₄×C₁₀₉	C₂³	1	2	yes	—
213	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
214	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
215	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
216	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
217	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
218	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
219	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
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	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
225	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
226	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
227	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
228	C₄²×C₁₀₉	C₂³	1	2	yes	—
229	C₂³×C₁₀₉	C₂⁴	1	2	yes	—
230	C₂³×C₁₀₉	C₂⁴	1	1	yes	characteristic
231	C₂²×D₁₀₉	—	2	2	no	—
232	C₂²×D₁₀₉	—	2	2	no	—
233	C₂²×D₁₀₉	—	2	4	no	—
234	C₂²×D₁₀₉	—	2	4	no	—
235	C₂²×D₁₀₉	—	2	4	no	—
236	C₂²×D₁₀₉	#41	1	4	yes	—
237	C₂²×D₁₀₉	C₂⁴	1	2	yes	—
238	C₂²×D₁₀₉	C₂⁴	1	1	yes	characteristic
239	C₂²×D₁₀₉	C₂⁴	1	1	yes	characteristic
240	Q₈×C₁₀₉	—	2	2	no	—
241	D₄×C₁₀₉	—	2	4	no	—
242	D₄×C₁₀₉	—	2	2	no	—
243	C₂×C₄×C₁₀₉	—	2	2	no	—
244	C₂×C₄×C₁₀₉	—	2	2	no	—
245	C₂×C₄×C₁₀₉	—	2	2	no	—
246	C₂×C₄×C₁₀₉	—	2	4	no	—
247	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
252	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
253	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
254	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
256	C₂²⋊D₁₀₉	—	2	4	no	—
257	C₂²⋊D₁₀₉	—	2	4	no	—
258	C₂²⋊D₁₀₉	—	2	4	no	—
259	C₂×Dic₁₀₉	—	2	2	no	—
260	C₂×Dic₁₀₉	—	2	2	no	—
261	C₂×Dic₁₀₉	—	2	2	no	—
262	C₂×Dic₁₀₉	—	2	4	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	2	yes	—
270	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
272	D₄₃₆	—	2	4	no	—
273	D₄₃₆	—	2	2	no	—
274	C₄×D₁₀₉	—	2	2	no	—
275	C₄×D₁₀₉	—	2	2	no	—
276	C₄×D₁₀₉	—	2	2	no	—
277	C₄×D₁₀₉	—	2	2	no	—
278	C₄×D₁₀₉	—	2	2	no	—
279	C₄×D₁₀₉	—	2	2	no	—
280	C₄×D₁₀₉	—	2	4	no	—
281	C₄×D₁₀₉	—	2	4	no	—
282	C₄×D₁₀₉	—	2	4	no	—
283	C₄×D₁₀₉	—	2	2	no	—
284	C₄×D₁₀₉	—	2	2	no	—
285	C₄×D₁₀₉	—	2	4	no	—
286	C₄×D₁₀₉	—	2	2	no	—
287	C₄×D₁₀₉	—	2	2	no	—
288	C₄×D₁₀₉	—	2	4	no	—
289	C₄×D₁₀₉	#41	1	4	yes	—
290	C₄×D₁₀₉	#41	1	4	yes	—
291	Dic₂₁₈	—	2	2	no	—
292	Dic₂₁₈	—	2	4	no	—
293	C₂²×C₁₀₉	—	2	1	no	—
294	C₂²×C₁₀₉	—	2	1	no	—
295	C₂²×C₁₀₉	—	2	2	no	—
296	C₂²×C₁₀₉	—	2	2	no	—
297	C₂²×C₁₀₉	—	2	2	no	—
298	C₂²×C₁₀₉	C₂×#41	1	2	yes	—
299	C₂²×C₁₀₉	C₂⁵	1	1	yes	characteristic
300	C₂×D₁₀₉	—	2	1	no	—
301	C₂×D₁₀₉	—	2	1	no	—
302	C₂×D₁₀₉	—	2	8	no	—
303	C₂×D₁₀₉	—	2	2	no	—
304	C₂×D₁₀₉	—	2	2	no	—
305	C₂×D₁₀₉	—	2	2	no	—
306	C₂×D₁₀₉	—	4	8	no	—
307	C₂×D₁₀₉	C₂×#41	1	2	yes	—
308	C₂×D₁₀₉	C₂×#41	1	2	yes	—
309	C₂×D₁₀₉	C₂×#41	1	2	yes	—
310	C₂×D₁₀₉	C₂×#41	1	2	yes	—
311	C₄×C₁₀₉	—	2	2	no	—
312	C₄×C₁₀₉	—	2	1	no	—
313	C₄×C₁₀₉	—	2	1	no	—
314	C₄×C₁₀₉	—	2	1	no	—
315	C₄×C₁₀₉	—	2	1	no	—
316	C₄×C₁₀₉	—	2	2	no	—
317	C₄×C₁₀₉	—	2	2	no	—
318	C₄×C₁₀₉	C₂×#41	1	2	yes	—
319	C₄×C₁₀₉	C₂×#41	1	2	yes	—
320	Dic₁₀₉	—	2	2	no	—
321	Dic₁₀₉	—	2	1	no	—
322	Dic₁₀₉	—	2	1	no	—
323	Dic₁₀₉	—	2	1	no	—
324	Dic₁₀₉	—	2	1	no	—
325	Dic₁₀₉	—	2	2	no	—
326	Dic₁₀₉	—	2	2	no	—
327	Dic₁₀₉	C₂×#41	1	2	yes	—
328	Dic₁₀₉	C₂×#41	1	2	yes	—
329	C₂×C₁₀₉	—	2	2	no	—
330	C₂×C₁₀₉	—	4	2	no	—
331	C₂×C₁₀₉	C₂²×#41	1	1	yes	characteristic
332	C₂×C₁₀₉	C₂²×#41	1	1	yes	characteristic
333	C₂×C₁₀₉	C₂²×#41	1	1	yes	characteristic
334	D₁₀₉	—	2	2	no	—
335	D₁₀₉	—	4	2	no	—
336	D₁₀₉	#529	1	4	yes	direct product factor
337	C₂×#529	—	109	1	no	maximal, Sylow
338	C₁₀₉	C₂×#529	1	1	yes	characteristic, complemented, Sylow
339	#529	—	109	2	no	—
340	#529	—	109	1	no	—
341	#529	—	109	1	no	—
342	#529	—	109	2	no	—
343	#529	—	109	1	no	—
344	#529	—	109	1	no	—
345	#529	—	109	1	no	—
346	#529	—	109	2	no	—
347	#529	—	109	1	no	—
348	#529	—	109	2	no	—
349	#529	—	109	1	no	—
350	#529	D₁₀₉	1	1	yes	characteristic, direct product factor
351	C₂×#126	—	109	2	no	—
352	C₂×#125	—	109	1	no	—
353	C₂×#124	—	109	1	no	—
354	C₂×#123	—	109	2	no	—
355	C₂×C₂²⋊Q₈	—	109	1	no	—
356	C₂×#121	—	109	1	no	—
357	C₂×C₄×Q₈	—	109	1	no	—
358	C₂×C₄×D₄	—	109	2	no	—
359	C₂×C₄×D₄	—	109	1	no	—
360	C₂×#117	—	109	2	no	—
361	C₂²×C₄²	—	109	1	no	—
362	C₂²×Q₈	—	109	1	no	—
363	C₂²×D₄	—	109	2	no	—
364	C₂²×D₄	—	109	1	no	—
365	C₂³×C₄	—	109	2	no	—
366	C₂³×C₄	—	109	1	no	—
367	C₂³×C₄	—	109	1	no	—
368	C₂³×C₄	—	109	1	no	—
369	#126	—	109	2	no	—
370	#126	—	109	2	no	—
371	#126	—	109	2	no	—
372	#126	—	109	2	no	—
373	#126	—	109	2	no	—
374	#126	—	109	2	no	—
375	#126	—	109	2	no	—
376	#126	C₂×D₁₀₉	1	2	yes	complemented
377	#125	—	109	2	no	—
378	#125	—	109	2	no	—
379	#125	—	109	1	no	—
380	#125	—	109	1	no	—
381	#125	—	109	1	no	—
382	#125	C₂×D₁₀₉	1	1	yes	characteristic, complemented
383	#124	—	109	1	no	—
384	#124	—	109	1	no	—
385	#124	—	109	2	no	—
386	#124	—	109	2	no	—
387	#124	—	109	1	no	—
388	#124	C₂×D₁₀₉	1	1	yes	characteristic, complemented
389	#123	—	109	2	no	—
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	C₂×D₁₀₉	1	2	yes	complemented
397	C₂²⋊Q₈	—	109	1	no	—
398	C₂²⋊Q₈	—	109	1	no	—
399	C₂²⋊Q₈	—	109	2	no	—
400	C₂²⋊Q₈	—	109	1	no	—
401	C₂²⋊Q₈	—	109	2	no	—
402	C₂²⋊Q₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
403	#121	—	109	1	no	—
404	#121	—	109	2	no	—
405	#121	—	109	1	no	—
406	#121	—	109	1	no	—
407	#121	—	109	2	no	—
408	#121	C₂×D₁₀₉	1	1	yes	characteristic
409	C₄×Q₈	—	109	1	no	—
410	C₄×Q₈	—	109	2	no	—
411	C₄×Q₈	—	109	1	no	—
412	C₄×Q₈	—	109	2	no	—
413	C₄×Q₈	—	109	1	no	—
414	C₄×Q₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
415	C₄×D₄	—	109	1	no	—
416	C₄×D₄	—	109	2	no	—
417	C₄×D₄	—	109	2	no	—
418	C₄×D₄	—	109	2	no	—
419	C₄×D₄	—	109	2	no	—
420	C₄×D₄	—	109	1	no	—
421	C₄×D₄	—	109	2	no	—
422	C₄×D₄	—	109	2	no	—
423	C₄×D₄	—	109	2	no	—
424	C₄×D₄	—	109	2	no	—
425	C₄×D₄	—	109	1	no	—
426	C₄×D₄	—	109	2	no	—
427	C₄×D₄	C₂×D₁₀₉	1	1	yes	characteristic, complemented
428	C₄×D₄	C₂×D₁₀₉	1	2	yes	complemented
429	#117	—	109	2	no	—
430	#117	—	109	2	no	—
431	#117	—	109	2	no	—
432	#117	—	109	2	no	—
433	#117	—	109	2	no	—
434	#117	—	109	2	no	—
435	#117	—	109	2	no	—
436	#117	C₂×D₁₀₉	1	2	yes	complemented
437	C₂×C₄⋊C₄	—	109	2	no	—
438	C₂×C₄⋊C₄	—	109	2	no	—
439	C₂×C₄⋊C₄	—	109	1	no	—
440	C₂×C₄⋊C₄	—	109	2	no	—
441	C₂×C₄⋊C₄	—	109	1	no	—
442	C₂×C₄⋊C₄	—	109	2	no	—
443	C₂×C₂²⋊C₄	—	109	2	no	—
444	C₂×C₂²⋊C₄	—	109	2	no	—
445	C₂×C₂²⋊C₄	—	109	2	no	—
446	C₂×C₂²⋊C₄	—	109	2	no	—
447	C₂×C₂²⋊C₄	—	109	2	no	—
448	C₂×C₄²	—	109	1	no	—
449	C₂×C₄²	—	109	1	no	—
450	C₂×C₄²	—	109	1	no	—
451	C₂×C₄²	—	109	1	no	—
452	C₂×C₄²	—	109	2	no	—
453	C₂×C₄²	—	109	1	no	—
454	C₂×C₄²	—	109	1	no	—
455	C₂×C₄²	—	109	1	no	—
456	C₂×C₄²	—	109	1	no	—
457	C₂×C₄²	—	109	1	no	—
458	C₂×C₄²	—	109	1	no	—
459	C₂×C₄²	—	109	1	no	—
460	C₂×C₄²	C₂×D₁₀₉	1	1	yes	characteristic, complemented
461	C₂⁴	—	109	1	no	—
462	C₂⁴	—	109	2	no	—
463	C₂×Q₈	—	109	2	no	—
464	C₂×Q₈	—	109	1	no	—
465	C₂×Q₈	—	218	4	no	—
466	C₂×Q₈	C₂²×D₁₀₉	1	1	yes	characteristic
467	C₂×D₄	—	109	2	no	—
468	C₂×D₄	—	109	2	no	—
469	C₂×D₄	—	109	2	no	—
470	C₂×D₄	—	109	2	no	—
471	C₂×D₄	—	109	1	no	—
472	C₂×D₄	—	218	4	no	—
473	C₂×D₄	—	218	8	no	—
474	C₂×D₄	C₂²×D₁₀₉	1	2	yes	—
475	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
476	C₂²×C₄	—	109	1	no	—
477	C₂²×C₄	—	109	1	no	—
478	C₂²×C₄	—	109	1	no	—
479	C₂²×C₄	—	109	1	no	—
480	C₂²×C₄	—	109	1	no	—
481	C₂²×C₄	—	109	2	no	—
482	C₂²×C₄	—	109	1	no	—
483	C₂²×C₄	—	109	1	no	—
484	C₂²×C₄	—	109	1	no	—
485	C₂²×C₄	—	109	1	no	—
486	C₂²×C₄	—	109	1	no	—
487	C₂²×C₄	—	109	1	no	—
488	C₂²×C₄	—	109	1	no	—
489	C₂²×C₄	—	109	1	no	—
490	C₂²×C₄	—	109	1	no	—
491	C₂²×C₄	—	109	2	no	—
492	C₂²×C₄	—	109	2	no	—
493	C₂²×C₄	—	109	2	no	—
494	C₂²×C₄	—	109	2	no	—
495	C₂²×C₄	—	109	1	no	—
496	C₂²×C₄	—	109	2	no	—
497	C₂²×C₄	—	218	8	no	—
498	C₂²×C₄	—	218	4	no	—
499	C₂²×C₄	—	218	4	no	—
500	C₂²×C₄	—	218	4	no	—
501	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
502	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
503	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
504	C₂²×C₄	C₂²×D₁₀₉	1	2	yes	—
505	C₄⋊C₄	—	109	2	no	—
506	C₄⋊C₄	—	109	2	no	—
507	C₄⋊C₄	—	109	2	no	—
508	C₄⋊C₄	—	109	2	no	—
509	C₄⋊C₄	—	109	2	no	—
510	C₄⋊C₄	—	109	2	no	—
511	C₄⋊C₄	—	109	2	no	—
512	C₄⋊C₄	—	109	2	no	—
513	C₄⋊C₄	—	109	2	no	—
514	C₄⋊C₄	—	109	2	no	—
515	C₄⋊C₄	—	109	2	no	—
516	C₄⋊C₄	—	109	2	no	—
517	C₄⋊C₄	—	109	1	no	—
518	C₄⋊C₄	—	109	2	no	—
519	C₄⋊C₄	—	109	1	no	—
520	C₄⋊C₄	—	109	2	no	—
521	C₄⋊C₄	C₂²×D₁₀₉	1	2	yes	—
522	C₄⋊C₄	C₂²×D₁₀₉	1	2	yes	—
523	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
524	C₄⋊C₄	C₂²×D₁₀₉	1	2	yes	—
525	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
526	C₄⋊C₄	C₂²×D₁₀₉	1	2	yes	—
527	C₂²⋊C₄	—	109	2	no	—
528	C₂²⋊C₄	—	109	2	no	—
529	C₂²⋊C₄	—	109	2	no	—
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	2	no	—
536	C₂²⋊C₄	—	109	2	no	—
537	C₂²⋊C₄	—	109	2	no	—
538	C₂²⋊C₄	—	109	2	no	—
539	C₂²⋊C₄	—	109	2	no	—
540	C₂²⋊C₄	—	109	2	no	—
541	C₂²⋊C₄	—	109	2	no	—
542	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	—
543	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	—
544	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	—
545	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	—
546	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	—
547	C₄²	—	109	1	no	—
548	C₄²	—	109	1	no	—
549	C₄²	—	109	1	no	—
550	C₄²	—	109	1	no	—
551	C₄²	—	109	1	no	—
552	C₄²	—	109	1	no	—
553	C₄²	—	109	1	no	—
554	C₄²	—	109	1	no	—
555	C₄²	—	109	1	no	—
556	C₄²	—	109	1	no	—
557	C₄²	—	109	2	no	—
558	C₄²	—	109	2	no	—
559	C₄²	—	109	1	no	—
560	C₄²	—	109	1	no	—
561	C₄²	—	109	2	no	—
562	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
563	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
564	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
565	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
566	C₄²	C₂²×D₁₀₉	1	2	yes	—
567	C₂³	—	109	1	no	—
568	C₂³	—	109	4	no	—
569	C₂³	—	109	1	no	—
570	C₂³	—	109	2	no	—
571	C₂³	—	218	4	no	—
572	C₂³	—	218	4	no	—
573	C₂³	—	218	4	no	—
574	C₂³	—	218	2	no	—
575	C₂³	—	218	2	no	—
576	C₂³	C₂³×D₁₀₉	1	2	yes	—
577	C₂³	C₂³×D₁₀₉	1	1	yes	characteristic
578	Q₈	—	2	2	no	—
579	Q₈	—	218	4	no	—
580	Q₈	—	218	2	no	—
581	D₄	—	2	4	no	—
582	D₄	—	2	2	no	—
583	D₄	—	218	4	no	—
584	D₄	—	218	4	no	—
585	D₄	—	218	4	no	—
586	D₄	—	218	4	no	—
587	D₄	—	218	2	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	4	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	109	1	no	—
593	C₂×C₄	—	109	1	no	—
594	C₂×C₄	—	109	4	no	—
595	C₂×C₄	—	109	4	no	—
596	C₂×C₄	—	109	1	no	—
597	C₂×C₄	—	109	1	no	—
598	C₂×C₄	—	109	1	no	—
599	C₂×C₄	—	109	1	no	—
600	C₂×C₄	—	109	2	no	—
601	C₂×C₄	—	109	2	no	—
602	C₂×C₄	—	109	2	no	—
603	C₂×C₄	—	218	4	no	—
604	C₂×C₄	—	218	2	no	—
605	C₂×C₄	—	218	2	no	—
606	C₂×C₄	—	218	2	no	—
607	C₂×C₄	—	218	2	no	—
608	C₂×C₄	—	218	4	no	—
609	C₂×C₄	—	218	2	no	—
610	C₂×C₄	—	218	2	no	—
611	C₂×C₄	—	218	2	no	—
612	C₂×C₄	—	218	2	no	—
613	C₂×C₄	—	218	4	no	—
614	C₂×C₄	—	218	4	no	—
615	C₂×C₄	—	218	2	no	—
616	C₂×C₄	—	218	4	no	—
617	C₂×C₄	—	218	2	no	—
618	C₂×C₄	—	218	2	no	—
619	C₂×C₄	—	218	4	no	—
620	C₂×C₄	—	218	2	no	—
621	C₂×C₄	—	218	2	no	—
622	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
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	2	yes	—
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	C₂²	—	2	1	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	109	2	no	—
637	C₂²	—	109	2	no	—
638	C₂²	—	109	2	no	—
639	C₂²	—	109	2	no	—
640	C₂²	—	436	8	no	—
641	C₂²	—	218	8	no	—
642	C₂²	—	218	2	no	—
643	C₂²	—	218	2	no	—
644	C₂²	—	218	2	no	—
645	C₂²	—	218	1	no	—
646	C₂²	—	218	1	no	—
647	C₂²	#41×D₁₀₉	1	2	yes	—
648	C₂²	C₂⁴×D₁₀₉	1	1	yes	characteristic
649	C₄	—	2	1	no	—
650	C₄	—	2	1	no	—
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	2	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	2	no	—
656	C₄	—	109	2	no	—
657	C₄	—	109	2	no	—
658	C₄	—	218	1	no	—
659	C₄	—	218	1	no	—
660	C₄	—	218	1	no	—
661	C₄	—	218	1	no	—
662	C₄	—	218	2	no	—
663	C₄	—	218	2	no	—
664	C₄	—	218	2	no	—
665	C₄	#41×D₁₀₉	1	2	yes	—
666	C₄	#41×D₁₀₉	1	2	yes	—
667	C₂	—	2	2	no	—
668	C₂	—	4	2	no	—
669	C₂	—	109	4	no	—
670	C₂	—	436	2	no	—
671	C₂	—	218	2	no	—
672	C₂	C₂×#41×D₁₀₉	1	1	yes	characteristic
673	C₂	C₂×#41×D₁₀₉	1	1	yes	characteristic
674	C₂	C₂×#41×D₁₀₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₀₉
commutator, socle, cosocle	C₂²×C₁₀₉	C₂⁵
Frattini	C₂²	C₂⁴×D₁₀₉
Fitting	#529×C₁₀₉	C₂
prime radical	#121×D₁₀₉	C₂
hypercenter	#529	D₁₀₉
hypocenter	C₁₀₉	C₂×#529
LCS	G ▷ C₂²×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂×C₄ ◁ #529

Complements

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

N	H ≅ G/N	type
1. #20295563	C₂	semidirect
2. #20295562	C₂	semidirect
3. #20295561	C₂	semidirect
4. #20295560	C₂	semidirect
5. #20295559	C₂	semidirect
6. #20295558	C₂	semidirect
7. #20295557	C₂	semidirect
8. #20295556	C₂	semidirect
9. #20295555	C₂	semidirect
10. #20295554	C₂	semidirect
11. #20295553	C₂	semidirect
12. #126×D₁₀₉	C₂	semidirect
13. #125×D₁₀₉	C₂	semidirect
14. #124×D₁₀₉	C₂	semidirect
15. #123×D₁₀₉	C₂	semidirect
16. C₂²⋊Q₈×D₁₀₉	C₂	semidirect
18. C₄×Q₈×D₁₀₉	C₂	semidirect
19. C₄×D₄×D₁₀₉	C₂	semidirect
20. C₄×D₄×D₁₀₉	C₂	semidirect
21. #117×D₁₀₉	C₂	semidirect
22. C₂×C₄²×D₁₀₉	C₂	semidirect
23. #529×C₁₀₉	C₂	semidirect
31. #16812694	C₂²	semidirect
32. #16812694	C₂²	semidirect
33. #16812694	C₂²	semidirect
34. #16812693	C₂²	semidirect
35. #16812692	C₂²	semidirect
36. #16812692	C₂²	semidirect
37. #16812692	C₂²	semidirect
38. #16812691	C₂²	semidirect
39. #16812690	C₂²	semidirect
40. #16812690	C₂²	semidirect
41. #16812689	C₂²	semidirect
42. #16812689	C₂²	semidirect
43. #16812688	C₂²	semidirect
44. #16812687	C₂²	semidirect
45. #16812686	C₂²	semidirect
46. #16812685	C₂²	semidirect
47. #16812685	C₂²	semidirect
48. #16812684	C₂²	semidirect
49. #16812684	C₂²	semidirect
50. #16812683	C₂²	semidirect
51. #16812682	C₂²	semidirect
52. #16812681	C₂²	semidirect
53. #16812681	C₂²	semidirect
54. #16812680	C₂²	semidirect
55. #16812679	C₂²	semidirect
56. #16812678	C₂²	semidirect
57. #16812677	C₂²	semidirect
58. #16812676	C₂²	semidirect
59. #16812675	C₂²	semidirect
65. Q₈×Dic₁₀₉	C₂²	semidirect
66. C₄×Dic₂₁₈	C₂²	semidirect
67. C₄×Dic₂₁₈	C₂²	semidirect
68. #16812664	C₂²	semidirect
69. #16812664	C₂²	semidirect
70. C₄×D₄₃₆	C₂²	semidirect
71. C₄×D₄₃₆	C₂²	semidirect
72. D₄×Dic₁₀₉	C₂²	semidirect
73. D₄×Dic₁₀₉	C₂²	semidirect
74. #16812661	C₂²	semidirect
75. #16812661	C₂²	semidirect
76. C₄×C₂²⋊D₁₀₉	C₂²	semidirect
77. C₄×C₂²⋊D₁₀₉	C₂²	semidirect
78. C₄×C₂²⋊D₁₀₉	C₂²	semidirect
79. #16812659	C₂²	semidirect
80. #16812659	C₂²	semidirect
81. #16812659	C₂²	semidirect
82. #16812658	C₂²	semidirect
83. #16812657	C₂²	semidirect
84. #16812657	C₂²	semidirect
85. #16812656	C₂²	semidirect
86. #16812656	C₂²	semidirect
87. #16812655	C₂²	semidirect
88. #16812655	C₂²	semidirect
100. C₂×C₄×Dic₁₀₉	C₂²	semidirect
101. C₂×C₄×Dic₁₀₉	C₂²	semidirect
102. C₂×C₄×Dic₁₀₉	C₂²	semidirect
108. C₄²×D₁₀₉	C₂²	semidirect
109. C₄²×D₁₀₉	C₂²	semidirect
110. C₄²×D₁₀₉	C₂²	semidirect
111. C₄²×D₁₀₉	C₂²	semidirect
112. #126×C₁₀₉	C₂²	semidirect
113. #125×C₁₀₉	C₂²	semidirect
114. #124×C₁₀₉	C₂²	semidirect
115. #123×C₁₀₉	C₂²	semidirect
116. C₂²⋊Q₈×C₁₀₉	C₂²	semidirect
118. C₄×Q₈×C₁₀₉	C₂²	semidirect
119. C₄×D₄×C₁₀₉	C₂²	semidirect
120. C₄×D₄×C₁₀₉	C₂²	semidirect
121. #117×C₁₀₉	C₂²	semidirect
122. C₂×C₄²×C₁₀₉	C₂²	semidirect
336. D₁₀₉	#529	direct (N × H)
338. C₁₀₉	C₂×#529	semidirect
350. #529	D₁₀₉	direct (N × H)
376. #126	C₂×D₁₀₉	semidirect
382. #125	C₂×D₁₀₉	semidirect
388. #124	C₂×D₁₀₉	semidirect
396. #123	C₂×D₁₀₉	semidirect
402. C₂²⋊Q₈	C₂×D₁₀₉	semidirect
414. C₄×Q₈	C₂×D₁₀₉	semidirect
427. C₄×D₄	C₂×D₁₀₉	semidirect
428. C₄×D₄	C₂×D₁₀₉	semidirect
436. #117	C₂×D₁₀₉	semidirect
460. C₂×C₄²	C₂×D₁₀₉	semidirect

Maximal subgroups

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

subgroup	index
#20295563	2
#20295562	2
#20295561	2
#20295560	2
#20295559	2
#20295558	2
#20295557	2
#20295556	2
#20295555	2
#20295554	2
#20295553	2
#126×D₁₀₉	2
#125×D₁₀₉	2
#124×D₁₀₉	2
#123×D₁₀₉	2
C₂²⋊Q₈×D₁₀₉	2
#121×D₁₀₉	2
C₄×Q₈×D₁₀₉	2
C₄×D₄×D₁₀₉	2
#117×D₁₀₉	2
C₂×C₄²×D₁₀₉	2
#529×C₁₀₉	2
C₂×#529	109

Subgroups — #529×D109 #28376290

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #529×D₁₀₉ #28376290