Subgroups — #28376594

Order 13952.

1132 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20295748	C₂	1	1	yes	maximal, characteristic, complemented
2	#20295739	C₂	1	1	yes	maximal, characteristic, complemented
3	#20295735	C₂	1	1	yes	maximal, characteristic, complemented
4	#20295725	C₂	1	2	yes	maximal, complemented
5	#20295717	C₂	1	1	yes	maximal, characteristic, complemented
6	#20295715	C₂	1	1	yes	maximal, characteristic, complemented
7	#20295709	C₂	1	2	yes	maximal, complemented
8	#20295705	C₂	1	2	yes	maximal, complemented
9	#20295700	C₂	1	2	yes	maximal, complemented
10	#20295675	C₂	1	1	yes	maximal, characteristic, complemented
11	#20295671	C₂	1	1	yes	maximal, characteristic, complemented
12	#20295664	C₂	1	1	yes	maximal, characteristic, complemented
13	#20295580	C₂	1	1	yes	maximal, characteristic, complemented
14	#20295563	C₂	1	1	yes	maximal, characteristic, complemented
15	#20295560	C₂	1	2	yes	maximal, complemented
16	#20295560	C₂	1	1	yes	maximal, characteristic, complemented
17	#20295556	C₂	1	2	yes	maximal, complemented
18	#20295535	C₂	1	2	yes	maximal, complemented
19	C₄×#13182029	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#13182028	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×D₄×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#16812656	C₂	1	2	yes	maximal, complemented
23	C₄×#41×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13182029	C₂²	1	1	yes	characteristic
25	C₂×#13182028	C₂²	1	1	yes	characteristic
26	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic
27	C₂²×C₄×D₁₀₉	C₂²	1	2	yes	—
28	#16812698	C₂²	1	1	yes	characteristic, complemented
29	#16812697	C₂²	1	1	yes	characteristic, complemented
30	#16812694	C₂²	1	2	yes	complemented
31	#16812694	C₂²	1	2	yes	complemented
32	#16812693	C₂²	1	2	yes	complemented
33	#16812693	C₂²	1	2	yes	complemented
34	#16812693	C₂²	1	2	yes	complemented
35	#16812692	C₂²	1	2	yes	complemented
36	#16812691	C₂²	1	2	yes	complemented
37	#16812691	C₂²	1	1	yes	characteristic, complemented
38	#16812690	C₂²	1	1	yes	characteristic, complemented
39	#16812689	C₂²	1	2	yes	complemented
40	#16812689	C₂²	1	2	yes	complemented
41	#16812688	C₂²	1	1	yes	characteristic
42	#16812687	C₂²	1	1	yes	characteristic
43	#16812687	C₂²	1	2	yes	complemented
44	#16812685	C₂²	1	2	yes	complemented
45	#16812684	C₂²	1	2	yes	—
46	#16812684	C₂²	1	2	yes	complemented
47	#16812683	C₂²	1	2	yes	—
48	#16812682	C₂²	1	2	yes	—
49	#16812682	C₂²	1	2	yes	complemented
50	#16812682	C₂²	1	2	yes	complemented
51	#16812681	C₂²	1	2	yes	—
52	#16812680	C₂²	1	2	yes	complemented
53	#16812679	C₂²	1	1	yes	characteristic
54	#16812678	C₂²	1	2	yes	complemented
55	#16812678	C₂²	1	1	yes	characteristic, complemented
56	#16812677	C₂²	1	2	yes	—
57	#16812677	C₂²	1	2	yes	complemented
58	#16812676	C₂²	1	2	yes	complemented
59	#16812676	C₂²	1	2	yes	complemented
60	#16812675	C₂²	1	1	yes	characteristic
61	#16812675	C₂²	1	1	yes	characteristic, complemented
62	#16812674	C₂²	1	1	yes	characteristic
63	#16812673	C₂²	1	2	yes	—
64	#16812673	C₂²	1	1	yes	characteristic
65	#16812672	C₂²	1	2	yes	complemented
66	#16812671	C₂²	1	2	yes	—
67	#16812671	C₂²	1	2	yes	complemented
68	#16812669	C₂²	1	2	yes	—
69	#16812667	C₂²	1	2	yes	—
70	C₄×Dic₂₁₈	C₂²	1	1	yes	characteristic, complemented
71	C₄×Dic₂₁₈	C₂²	1	1	yes	characteristic, complemented
72	C₄×Dic₂₁₈	C₂²	1	1	yes	characteristic, complemented
73	C₄×Dic₂₁₈	C₂²	1	2	yes	complemented
74	#16812664	C₂²	1	1	yes	characteristic, complemented
75	C₄×D₄₃₆	C₂²	1	1	yes	characteristic
76	C₄×D₄₃₆	C₂²	1	1	yes	characteristic
77	C₄×D₄₃₆	C₂²	1	1	yes	characteristic
78	C₄×D₄₃₆	C₂²	1	2	yes	complemented
79	D₄×Dic₁₀₉	C₂²	1	1	yes	characteristic
80	D₄×Dic₁₀₉	C₂²	1	1	yes	characteristic
81	#16812661	C₂²	1	1	yes	characteristic
82	C₄×C₂²⋊D₁₀₉	C₂²	1	1	yes	characteristic
83	C₄×C₂²⋊D₁₀₉	C₂²	1	1	yes	characteristic
84	C₄×C₂²⋊D₁₀₉	C₂²	1	2	yes	—
85	C₄×C₂²⋊D₁₀₉	C₂²	1	1	yes	characteristic, complemented
86	C₄×C₂²⋊D₁₀₉	C₂²	1	1	yes	characteristic, complemented
87	C₄×C₂²⋊D₁₀₉	C₂²	1	2	yes	complemented
88	C₄×C₂²⋊D₁₀₉	C₂²	1	2	yes	complemented
89	#16812659	C₂²	1	2	yes	—
90	#16812659	C₂²	1	2	yes	complemented
91	#16812658	C₂²	1	1	yes	characteristic, complemented
92	#16812657	C₂²	1	1	yes	characteristic, complemented
93	#16812656	C₂²	1	2	yes	—
94	#16812656	C₂²	1	2	yes	—
95	#16812656	C₂²	1	1	yes	characteristic
96	#16812656	C₂²	1	2	yes	—
97	#16812656	C₂²	1	2	yes	complemented
98	#16812656	C₂²	1	2	yes	complemented
99	#16812656	C₂²	1	2	yes	complemented
100	#16812656	C₂²	1	2	yes	complemented
101	#16812656	C₂²	1	1	yes	characteristic, complemented
102	#16812655	C₂²	1	2	yes	complemented
103	C₂×#13182008	C₂²	1	2	yes	complemented
104	C₂×#13182008	C₂²	1	2	yes	complemented
105	C₄⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic
106	C₂×#13182006	C₂²	1	2	yes	—
107	C₂×#13182006	C₂²	1	2	yes	—
108	C₂²⋊C₄×D₁₀₉	C₂²	1	2	yes	—
109	C₂×C₄×Dic₁₀₉	C₂²	1	2	yes	complemented
110	C₄²×D₁₀₉	C₂²	1	1	yes	characteristic
111	C₄²×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
112	C₂×#41×C₁₀₉	C₂²	1	1	yes	characteristic
113	C₄×Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
114	C₄×Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
115	C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
116	C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
117	C₄×D₄×C₁₀₉	C₂²	1	2	yes	complemented
118	C₄×D₄×C₁₀₉	C₂²	1	2	yes	complemented
119	#117×C₁₀₉	C₂²	1	2	yes	complemented
120	#117×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
121	C₂×C₄²×C₁₀₉	C₂²	1	2	yes	complemented
122	C₂×C₄²×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₀₉	C₂³	1	2	yes	—
124	#13182029	—	2	4	no	—
125	#13182028	—	2	4	no	—
126	C₂×Dic₂₁₈	C₂³	1	1	yes	characteristic
127	C₂×Dic₂₁₈	C₂³	1	1	yes	characteristic
128	C₂×Dic₂₁₈	C₂³	1	2	yes	—
129	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
130	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
131	C₂×D₄₃₆	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₀₉	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₁₀₉	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
137	D₄×D₁₀₉	—	2	4	no	—
138	C₂²×Dic₁₀₉	C₂³	1	2	yes	—
139	C₂²×Dic₁₀₉	C₂³	1	2	yes	—
140	C₂²×Dic₁₀₉	C₂³	1	2	yes	—
141	C₂×C₄×D₁₀₉	—	2	8	no	—
142	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
146	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
147	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
148	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
151	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
152	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
153	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
154	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
155	C₄⋊Dic₁₀₉	C₂³	1	2	yes	—
156	C₄⋊Dic₁₀₉	C₂³	1	2	yes	—
157	#13182008	C₂³	1	2	yes	—
158	#13182008	C₂³	1	1	yes	characteristic
159	#13182008	C₂³	1	1	yes	characteristic
160	#13182008	C₂³	1	2	yes	—
161	#13182008	C₂³	1	2	yes	—
162	#13182008	C₂³	1	2	yes	—
163	#13182008	C₂³	1	2	yes	—
164	#13182008	C₂³	1	2	yes	—
165	#13182008	C₂³	1	2	yes	—
166	#13182008	C₂³	1	2	yes	—
167	#13182008	C₂³	1	2	yes	—
168	#13182008	C₂³	1	1	yes	characteristic
169	#13182008	C₂³	1	1	yes	characteristic
170	#13182008	C₂³	1	2	yes	—
171	#13182008	C₂³	1	2	yes	—
172	#13182008	C₂³	1	2	yes	—
173	C₂²⋊Dic₁₀₉	C₂³	1	2	yes	—
174	C₂²⋊Dic₁₀₉	C₂³	1	2	yes	—
175	C₂²⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₁₀₉	C₂³	1	2	yes	—
178	#13182006	C₂³	1	2	yes	—
179	#13182006	C₂³	1	2	yes	—
180	#13182006	C₂³	1	1	yes	characteristic
181	#13182006	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
189	#13182006	C₂³	1	1	yes	characteristic
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	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	2	yes	—
201	C₄×Dic₁₀₉	C₂³	1	2	yes	—
202	C₄×Dic₁₀₉	C₂³	1	2	yes	—
203	#41×C₁₀₉	—	2	4	no	—
204	C₂×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
205	C₂×D₄×C₁₀₉	C₂³	1	2	yes	—
206	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
207	C₂²×C₄×C₁₀₉	C₂³	1	2	yes	—
208	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
209	C₂²×C₄×C₁₀₉	C₂³	1	2	yes	—
210	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
211	C₂²×C₄×C₁₀₉	C₂³	1	2	yes	—
212	C₂²×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	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
218	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
219	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
220	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
221	C₄²×C₁₀₉	C₂³	1	2	yes	—
222	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
223	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
224	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
225	C₄²×C₁₀₉	C₂³	1	2	yes	—
226	C₄²×C₁₀₉	C₂³	1	2	yes	—
227	C₂³×C₁₀₉	C₂⁴	1	1	yes	characteristic
228	C₂³×C₁₀₉	C₂⁴	1	2	yes	—
229	C₂²×D₁₀₉	—	2	4	no	—
230	C₂²×D₁₀₉	—	2	4	no	—
231	C₂²×D₁₀₉	—	4	2	no	—
232	C₂²×D₁₀₉	C₂⁴	1	2	yes	—
233	C₂²×D₁₀₉	C₂⁴	1	1	yes	characteristic
234	C₂²×D₁₀₉	C₂⁴	1	1	yes	characteristic
235	Q₈×C₁₀₉	—	2	2	no	—
236	D₄×C₁₀₉	—	2	4	no	—
237	D₄×C₁₀₉	#41	1	4	yes	complemented
238	C₂×C₄×C₁₀₉	—	2	4	no	—
239	C₂×C₄×C₁₀₉	—	2	2	no	—
240	C₂×C₄×C₁₀₉	—	2	4	no	—
241	C₂×C₄×C₁₀₉	—	2	2	no	—
242	C₂×C₄×C₁₀₉	—	4	2	no	—
243	C₂×C₄×C₁₀₉	—	4	1	no	—
244	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
247	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
250	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
251	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
253	C₂²⋊D₁₀₉	—	2	4	no	—
254	C₂²⋊D₁₀₉	—	2	4	no	—
255	C₂²⋊D₁₀₉	—	2	2	no	—
256	C₂²⋊D₁₀₉	—	2	2	no	—
257	C₂²⋊D₁₀₉	—	4	2	no	—
258	C₂×Dic₁₀₉	—	2	4	no	—
259	C₂×Dic₁₀₉	—	2	4	no	—
260	C₂×Dic₁₀₉	—	4	2	no	—
261	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
262	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
265	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
266	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
268	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
269	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
270	D₄₃₆	—	2	2	no	—
271	D₄₃₆	—	2	2	no	—
272	D₄₃₆	—	4	2	no	—
273	C₄×D₁₀₉	—	2	4	no	—
274	C₄×D₁₀₉	—	2	4	no	—
275	C₄×D₁₀₉	—	2	2	no	—
276	C₄×D₁₀₉	—	2	2	no	—
277	C₄×D₁₀₉	—	2	2	no	—
278	C₄×D₁₀₉	—	2	4	no	—
279	C₄×D₁₀₉	—	4	1	no	—
280	C₄×D₁₀₉	—	4	1	no	—
281	C₄×D₁₀₉	#41	1	4	yes	complemented
282	Dic₂₁₈	—	2	2	no	—
283	Dic₂₁₈	—	2	2	no	—
284	Dic₂₁₈	—	4	2	no	—
285	C₂²×C₁₀₉	—	2	2	no	—
286	C₂²×C₁₀₉	—	2	2	no	—
287	C₂²×C₁₀₉	—	2	1	no	—
288	C₂²×C₁₀₉	—	2	1	no	—
289	C₂²×C₁₀₉	—	2	1	no	—
290	C₂²×C₁₀₉	C₂×#41	1	4	yes	—
291	C₂²×C₁₀₉	C₂⁵	1	1	yes	characteristic
292	C₂×D₁₀₉	—	2	1	no	—
293	C₂×D₁₀₉	—	2	1	no	—
294	C₂×D₁₀₉	—	2	2	no	—
295	C₂×D₁₀₉	—	2	1	no	—
296	C₂×D₁₀₉	—	2	1	no	—
297	C₂×D₁₀₉	—	2	2	no	—
298	C₂×D₁₀₉	—	2	1	no	—
299	C₂×D₁₀₉	—	2	2	no	—
300	C₂×D₁₀₉	—	4	8	no	—
301	C₂×D₁₀₉	C₂×#41	1	2	yes	—
302	C₄×C₁₀₉	—	2	1	no	—
303	C₄×C₁₀₉	—	2	2	no	—
304	C₄×C₁₀₉	—	2	1	no	—
305	C₄×C₁₀₉	—	2	2	no	—
306	C₄×C₁₀₉	—	2	2	no	—
307	C₄×C₁₀₉	—	2	1	no	—
308	C₄×C₁₀₉	—	2	1	no	—
309	C₄×C₁₀₉	C₂×#41	1	2	yes	—
310	C₄×C₁₀₉	C₂×#41	1	2	yes	—
311	Dic₁₀₉	—	2	1	no	—
312	Dic₁₀₉	—	2	2	no	—
313	Dic₁₀₉	—	2	2	no	—
314	Dic₁₀₉	—	2	1	no	—
315	Dic₁₀₉	—	2	1	no	—
316	Dic₁₀₉	—	2	1	no	—
317	Dic₁₀₉	—	2	2	no	—
318	Dic₁₀₉	—	2	1	no	—
319	Dic₁₀₉	C₂×#41	1	2	yes	—
320	C₂×C₁₀₉	—	2	4	no	—
321	C₂×C₁₀₉	—	4	1	no	—
322	C₂×C₁₀₉	C₂²×#41	1	1	yes	characteristic
323	C₂×C₁₀₉	C₂²×#41	1	1	yes	characteristic
324	C₂×C₁₀₉	#585	1	1	yes	characteristic
325	D₁₀₉	—	2	2	no	—
326	D₁₀₉	—	4	1	no	—
327	D₁₀₉	—	4	2	no	—
328	#3475	—	109	1	no	maximal, Sylow
329	C₁₀₉	#3475	1	1	yes	characteristic, complemented, Sylow
330	#556	—	109	1	no	—
331	#555	—	109	1	no	—
332	#554	—	109	1	no	—
333	#553	—	109	2	no	—
334	#552	—	109	1	no	—
335	#552	—	109	2	no	—
336	#552	—	109	1	no	—
337	#551	—	109	2	no	—
338	#551	—	109	2	no	—
339	#547	—	109	1	no	—
340	#546	—	109	1	no	—
341	#546	—	109	1	no	—
342	#533	—	109	1	no	—
343	#529	—	109	1	no	—
344	#529	—	109	2	no	—
345	#529	—	109	2	no	—
346	#529	—	109	1	no	—
347	#525	—	109	2	no	—
348	C₄×#41	—	109	1	no	—
349	C₄×#41	—	109	1	no	—
350	C₄×#41	D₁₀₉	1	1	yes	characteristic, complemented
351	C₂×C₄×D₄	—	109	1	no	—
352	C₂×#117	—	109	2	no	—
353	C₂×#41	—	109	1	no	—
354	C₂×#41	—	109	1	no	—
355	C₂×#41	C₂×D₁₀₉	1	1	yes	characteristic
356	C₂²×D₄	—	109	1	no	—
357	C₂³×C₄	—	109	2	no	—
358	C₄⋊Q₈	—	109	1	no	—
359	C₄⋊Q₈	—	109	1	no	—
360	#126	—	109	2	no	—
361	#126	—	109	2	no	—
362	#126	—	109	2	no	—
363	#126	—	109	2	no	—
364	#126	—	109	2	no	—
365	#126	—	109	2	no	—
366	#125	—	109	2	no	—
367	#125	—	109	1	no	—
368	#125	—	109	2	no	—
369	#125	—	109	2	no	—
370	#125	—	109	1	no	—
371	#124	—	109	1	no	—
372	#124	—	109	2	no	—
373	#124	—	109	1	no	—
374	#124	—	109	2	no	—
375	#123	—	109	2	no	—
376	#123	—	109	2	no	—
377	#123	—	109	2	no	—
378	#123	—	109	2	no	—
379	#123	—	109	2	no	—
380	#123	—	109	2	no	—
381	#123	—	109	2	no	—
382	#123	—	109	2	no	—
383	C₂²⋊Q₈	—	109	1	no	—
384	C₂²⋊Q₈	—	109	1	no	—
385	C₂²⋊Q₈	—	109	1	no	—
386	C₂²⋊Q₈	—	109	2	no	—
387	C₂²⋊Q₈	—	109	2	no	—
388	C₂²⋊Q₈	—	109	1	no	—
389	C₂²⋊Q₈	—	109	2	no	—
390	C₂²⋊Q₈	—	109	2	no	—
391	C₂²⋊Q₈	—	109	2	no	—
392	#121	—	109	2	no	—
393	#121	—	109	2	no	—
394	#121	—	109	2	no	—
395	#121	—	109	1	no	—
396	#121	—	109	1	no	—
397	#121	—	109	2	no	—
398	#120	—	109	2	no	—
399	#120	—	109	2	no	—
400	C₄×Q₈	—	109	1	no	—
401	C₄×Q₈	—	109	1	no	—
402	C₄×Q₈	—	109	1	no	—
403	C₄×Q₈	—	109	1	no	—
404	C₄×Q₈	—	109	2	no	—
405	C₄×Q₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
406	C₄×Q₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
407	C₄×D₄	—	109	1	no	—
408	C₄×D₄	—	109	1	no	—
409	C₄×D₄	—	109	2	no	—
410	C₄×D₄	—	109	2	no	—
411	C₄×D₄	—	109	1	no	—
412	C₄×D₄	—	109	1	no	—
413	C₄×D₄	—	109	1	no	—
414	C₄×D₄	—	109	1	no	—
415	C₄×D₄	—	109	2	no	—
416	C₄×D₄	—	109	1	no	—
417	C₄×D₄	—	109	2	no	—
418	C₄×D₄	—	109	2	no	—
419	C₄×D₄	—	109	1	no	—
420	C₄×D₄	—	109	1	no	—
421	C₄×D₄	—	109	1	no	—
422	C₄×D₄	—	109	2	no	—
423	C₄×D₄	C₂×D₁₀₉	1	1	yes	characteristic
424	C₄×D₄	C₂×D₁₀₉	1	1	yes	characteristic
425	C₄×D₄	C₂×D₁₀₉	1	2	yes	complemented
426	C₄×D₄	C₂×D₁₀₉	1	2	yes	complemented
427	#117	—	109	1	no	—
428	#117	—	109	1	no	—
429	#117	—	109	2	no	—
430	#117	—	109	1	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	—	109	2	no	—
437	#117	—	109	2	no	—
438	#117	—	109	1	no	—
439	#117	C₂×D₁₀₉	1	2	yes	complemented
440	#117	C₂×D₁₀₉	1	1	yes	characteristic, complemented
441	C₂×C₄⋊C₄	—	109	2	no	—
442	C₂×C₄⋊C₄	—	109	2	no	—
443	C₂×C₄⋊C₄	—	109	1	no	—
444	C₂×C₂²⋊C₄	—	109	2	no	—
445	C₂×C₂²⋊C₄	—	109	2	no	—
446	C₂×C₂²⋊C₄	—	109	2	no	—
447	C₂×C₄²	—	109	2	no	—
448	C₂×C₄²	—	109	1	no	—
449	C₂×C₄²	—	109	1	no	—
450	C₂×C₄²	C₂×D₁₀₉	1	2	yes	complemented
451	C₂×C₄²	C₂×D₁₀₉	1	1	yes	characteristic, complemented
452	C₂⁴	—	109	2	no	—
453	#41	—	2	4	no	—
454	#41	—	218	4	no	—
455	#41	—	218	4	no	—
456	C₂×Q₈	—	109	2	no	—
457	C₂×Q₈	—	109	1	no	—
458	C₂×Q₈	—	109	1	no	—
459	C₂×Q₈	C₂²×D₁₀₉	1	1	yes	characteristic
460	C₂×D₄	—	109	2	no	—
461	C₂×D₄	—	109	1	no	—
462	C₂×D₄	—	109	2	no	—
463	C₂×D₄	—	109	1	no	—
464	C₂×D₄	—	109	2	no	—
465	C₂×D₄	—	109	2	no	—
466	C₂×D₄	—	109	1	no	—
467	C₂×D₄	—	109	1	no	—
468	C₂×D₄	—	218	4	no	—
469	C₂×D₄	C₂²×D₁₀₉	1	2	yes	—
470	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
471	C₂²×C₄	—	109	1	no	—
472	C₂²×C₄	—	109	2	no	—
473	C₂²×C₄	—	109	2	no	—
474	C₂²×C₄	—	109	2	no	—
475	C₂²×C₄	—	109	1	no	—
476	C₂²×C₄	—	109	1	no	—
477	C₂²×C₄	—	109	1	no	—
478	C₂²×C₄	—	109	1	no	—
479	C₂²×C₄	—	109	2	no	—
480	C₂²×C₄	—	109	2	no	—
481	C₂²×C₄	—	109	1	no	—
482	C₂²×C₄	—	109	2	no	—
483	C₂²×C₄	—	218	8	no	—
484	C₂²×C₄	C₂²×D₁₀₉	1	2	yes	—
485	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
486	C₂²×C₄	C₂²×D₁₀₉	1	2	yes	—
487	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
488	C₂²×C₄	C₂²×D₁₀₉	1	2	yes	—
489	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
490	C₄⋊C₄	—	109	1	no	—
491	C₄⋊C₄	—	109	1	no	—
492	C₄⋊C₄	—	109	2	no	—
493	C₄⋊C₄	—	109	2	no	—
494	C₄⋊C₄	—	109	2	no	—
495	C₄⋊C₄	—	109	2	no	—
496	C₄⋊C₄	—	109	2	no	—
497	C₄⋊C₄	—	109	2	no	—
498	C₄⋊C₄	—	109	2	no	—
499	C₄⋊C₄	—	109	1	no	—
500	C₄⋊C₄	—	109	2	no	—
501	C₄⋊C₄	—	109	2	no	—
502	C₄⋊C₄	—	109	1	no	—
503	C₄⋊C₄	—	109	2	no	—
504	C₄⋊C₄	—	109	2	no	—
505	C₄⋊C₄	—	109	2	no	—
506	C₄⋊C₄	—	109	1	no	—
507	C₄⋊C₄	—	109	1	no	—
508	C₄⋊C₄	—	109	1	no	—
509	C₄⋊C₄	—	109	1	no	—
510	C₄⋊C₄	—	109	2	no	—
511	C₄⋊C₄	—	109	2	no	—
512	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
513	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
514	C₄⋊C₄	C₂²×D₁₀₉	1	2	yes	—
515	C₄⋊C₄	C₂²×D₁₀₉	1	2	yes	—
516	C₂²⋊C₄	—	109	2	no	—
517	C₂²⋊C₄	—	109	2	no	—
518	C₂²⋊C₄	—	109	1	no	—
519	C₂²⋊C₄	—	109	1	no	—
520	C₂²⋊C₄	—	109	2	no	—
521	C₂²⋊C₄	—	109	1	no	—
522	C₂²⋊C₄	—	109	1	no	—
523	C₂²⋊C₄	—	109	2	no	—
524	C₂²⋊C₄	—	109	2	no	—
525	C₂²⋊C₄	—	109	2	no	—
526	C₂²⋊C₄	—	109	2	no	—
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	1	no	—
532	C₂²⋊C₄	—	109	2	no	—
533	C₂²⋊C₄	—	109	1	no	—
534	C₂²⋊C₄	—	109	2	no	—
535	C₂²⋊C₄	—	109	2	no	—
536	C₂²⋊C₄	—	109	2	no	—
537	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	—
538	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	—
539	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	—
540	C₄²	—	109	2	no	—
541	C₄²	—	109	1	no	—
542	C₄²	—	109	2	no	—
543	C₄²	—	109	1	no	—
544	C₄²	—	109	1	no	—
545	C₄²	—	109	1	no	—
546	C₄²	—	109	1	no	—
547	C₄²	—	109	1	no	—
548	C₄²	—	109	2	no	—
549	C₄²	C₂²×D₁₀₉	1	2	yes	—
550	C₄²	C₂²×D₁₀₉	1	2	yes	—
551	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
552	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
553	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
554	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
555	C₄²	C₂²×D₁₀₉	1	2	yes	—
556	C₂³	—	109	1	no	—
557	C₂³	—	109	2	no	—
558	C₂³	—	109	1	no	—
559	C₂³	—	436	2	no	—
560	C₂³	—	218	4	no	—
561	C₂³	—	218	4	no	—
562	C₂³	C₂³×D₁₀₉	1	1	yes	characteristic
563	C₂³	C₂³×D₁₀₉	1	2	yes	—
564	Q₈	—	2	2	no	—
565	Q₈	—	436	2	no	—
566	Q₈	—	218	2	no	—
567	Q₈	—	218	2	no	—
568	D₄	—	2	4	no	—
569	D₄	—	436	2	no	—
570	D₄	—	436	2	no	—
571	D₄	—	218	2	no	—
572	D₄	—	218	2	no	—
573	D₄	—	218	2	no	—
574	D₄	—	218	4	no	—
575	D₄	—	218	4	no	—
576	D₄	—	218	2	no	—
577	D₄	#13182029	1	4	yes	complemented
578	C₂×C₄	—	2	4	no	—
579	C₂×C₄	—	2	4	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	—	109	1	no	—
585	C₂×C₄	—	109	4	no	—
586	C₂×C₄	—	109	1	no	—
587	C₂×C₄	—	109	1	no	—
588	C₂×C₄	—	109	1	no	—
589	C₂×C₄	—	109	1	no	—
590	C₂×C₄	—	109	2	no	—
591	C₂×C₄	—	109	2	no	—
592	C₂×C₄	—	109	1	no	—
593	C₂×C₄	—	109	2	no	—
594	C₂×C₄	—	436	1	no	—
595	C₂×C₄	—	436	1	no	—
596	C₂×C₄	—	436	2	no	—
597	C₂×C₄	—	218	4	no	—
598	C₂×C₄	—	218	4	no	—
599	C₂×C₄	—	218	4	no	—
600	C₂×C₄	—	218	4	no	—
601	C₂×C₄	—	218	4	no	—
602	C₂×C₄	—	218	2	no	—
603	C₂×C₄	—	218	2	no	—
604	C₂×C₄	—	218	2	no	—
605	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
606	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
607	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
608	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
609	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
610	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
611	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
612	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
613	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
614	C₂²	—	2	2	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	109	2	no	—
620	C₂²	—	436	8	no	—
621	C₂²	—	218	2	no	—
622	C₂²	—	218	1	no	—
623	C₂²	—	218	1	no	—
624	C₂²	—	218	2	no	—
625	C₂²	—	218	1	no	—
626	C₂²	—	218	2	no	—
627	C₂²	—	218	1	no	—
628	C₂²	—	218	1	no	—
629	C₂²	C₂×#13182029	1	4	yes	—
630	C₂²	C₂⁴×D₁₀₉	1	1	yes	characteristic
631	C₄	—	2	2	no	—
632	C₄	—	2	1	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	2	no	—
635	C₄	—	2	1	no	—
636	C₄	—	2	1	no	—
637	C₄	—	2	2	no	—
638	C₄	—	109	2	no	—
639	C₄	—	218	2	no	—
640	C₄	—	218	1	no	—
641	C₄	—	218	1	no	—
642	C₄	—	218	1	no	—
643	C₄	—	218	2	no	—
644	C₄	—	218	1	no	—
645	C₄	—	218	2	no	—
646	C₄	—	218	1	no	—
647	C₄	#41×D₁₀₉	1	2	yes	—
648	C₄	C₂×#13182029	1	2	yes	—
649	C₂	—	2	4	no	—
650	C₂	—	4	1	no	—
651	C₂	—	436	2	no	—
652	C₂	—	436	1	no	—
653	C₂	—	218	2	no	—
654	C₂	C₂×#41×D₁₀₉	1	1	yes	characteristic
655	C₂	C₂²×#13182029	1	1	yes	characteristic
656	C₂	#20295862	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₀₉
commutator, socle, cosocle	C₂²×C₁₀₉	C₂⁵
Frattini	C₂²	C₂⁴×D₁₀₉
Fitting	C₄×#41×C₁₀₉	C₂
hypercenter	C₄×#41	D₁₀₉
hypocenter	C₁₀₉	#3475
LCS	G ▷ C₂²×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41

Complements

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

N	H ≅ G/N	type
1. #20295748	C₂	semidirect
2. #20295739	C₂	semidirect
3. #20295735	C₂	semidirect
4. #20295725	C₂	semidirect
5. #20295717	C₂	semidirect
6. #20295715	C₂	semidirect
7. #20295709	C₂	semidirect
8. #20295705	C₂	semidirect
9. #20295700	C₂	semidirect
10. #20295675	C₂	semidirect
11. #20295671	C₂	semidirect
12. #20295664	C₂	semidirect
13. #20295580	C₂	semidirect
14. #20295563	C₂	semidirect
15. #20295560	C₂	semidirect
16. #20295560	C₂	semidirect
17. #20295556	C₂	semidirect
18. #20295535	C₂	semidirect
19. C₄×#13182029	C₂	semidirect
20. C₄×#13182028	C₂	semidirect
21. C₄×D₄×D₁₀₉	C₂	semidirect
22. C₂×#16812656	C₂	semidirect
23. C₄×#41×C₁₀₉	C₂	semidirect
28. #16812698	C₂²	semidirect
29. #16812697	C₂²	semidirect
30. #16812694	C₂²	semidirect
31. #16812694	C₂²	semidirect
32. #16812693	C₂²	semidirect
33. #16812693	C₂²	semidirect
34. #16812693	C₂²	semidirect
35. #16812692	C₂²	semidirect
36. #16812691	C₂²	semidirect
37. #16812691	C₂²	semidirect
38. #16812690	C₂²	semidirect
39. #16812689	C₂²	semidirect
40. #16812689	C₂²	semidirect
43. #16812687	C₂²	semidirect
44. #16812685	C₂²	semidirect
46. #16812684	C₂²	semidirect
49. #16812682	C₂²	semidirect
50. #16812682	C₂²	semidirect
52. #16812680	C₂²	semidirect
54. #16812678	C₂²	semidirect
55. #16812678	C₂²	semidirect
57. #16812677	C₂²	semidirect
58. #16812676	C₂²	semidirect
59. #16812676	C₂²	semidirect
61. #16812675	C₂²	semidirect
65. #16812672	C₂²	semidirect
67. #16812671	C₂²	semidirect
70. C₄×Dic₂₁₈	C₂²	semidirect
71. C₄×Dic₂₁₈	C₂²	semidirect
72. C₄×Dic₂₁₈	C₂²	semidirect
73. C₄×Dic₂₁₈	C₂²	semidirect
74. #16812664	C₂²	semidirect
78. C₄×D₄₃₆	C₂²	semidirect
85. C₄×C₂²⋊D₁₀₉	C₂²	semidirect
86. C₄×C₂²⋊D₁₀₉	C₂²	semidirect
87. C₄×C₂²⋊D₁₀₉	C₂²	semidirect
88. C₄×C₂²⋊D₁₀₉	C₂²	semidirect
90. #16812659	C₂²	semidirect
91. #16812658	C₂²	semidirect
92. #16812657	C₂²	semidirect
97. #16812656	C₂²	semidirect
98. #16812656	C₂²	semidirect
99. #16812656	C₂²	semidirect
100. #16812656	C₂²	semidirect
101. #16812656	C₂²	semidirect
102. #16812655	C₂²	semidirect
103. C₂×#13182008	C₂²	semidirect
104. C₂×#13182008	C₂²	semidirect
109. C₂×C₄×Dic₁₀₉	C₂²	semidirect
111. C₄²×D₁₀₉	C₂²	semidirect
113. C₄×Q₈×C₁₀₉	C₂²	semidirect
114. C₄×Q₈×C₁₀₉	C₂²	semidirect
117. C₄×D₄×C₁₀₉	C₂²	semidirect
118. C₄×D₄×C₁₀₉	C₂²	semidirect
119. #117×C₁₀₉	C₂²	semidirect
120. #117×C₁₀₉	C₂²	semidirect
121. C₂×C₄²×C₁₀₉	C₂²	semidirect
122. C₂×C₄²×C₁₀₉	C₂²	semidirect
237. D₄×C₁₀₉	#41	semidirect
281. C₄×D₁₀₉	#41	semidirect
329. C₁₀₉	#3475	semidirect
350. C₄×#41	D₁₀₉	semidirect
405. C₄×Q₈	C₂×D₁₀₉	semidirect
406. C₄×Q₈	C₂×D₁₀₉	semidirect
425. C₄×D₄	C₂×D₁₀₉	semidirect
426. C₄×D₄	C₂×D₁₀₉	semidirect
439. #117	C₂×D₁₀₉	semidirect
440. #117	C₂×D₁₀₉	semidirect
450. C₂×C₄²	C₂×D₁₀₉	semidirect
451. C₂×C₄²	C₂×D₁₀₉	semidirect
577. D₄	#13182029	semidirect

Maximal subgroups

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

subgroup	index
#20295748	2
#20295739	2
#20295735	2
#20295725	2
#20295717	2
#20295715	2
#20295709	2
#20295705	2
#20295700	2
#20295675	2
#20295671	2
#20295664	2
#20295580	2
#20295563	2
#20295560	2
#20295556	2
#20295535	2
C₄×#13182029	2
C₄×#13182028	2
C₄×D₄×D₁₀₉	2
C₂×#16812656	2
C₄×#41×C₁₀₉	2
#3475	109