Subgroups — #28376584

Order 13952.

1132 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20295743	C₂	1	1	yes	maximal, characteristic, complemented
2	#20295738	C₂	1	1	yes	maximal, characteristic, complemented
3	#20295730	C₂	1	1	yes	maximal, characteristic, complemented
4	#20295727	C₂	1	1	yes	maximal, characteristic, complemented
5	#20295719	C₂	1	1	yes	maximal, characteristic, complemented
6	#20295713	C₂	1	1	yes	maximal, characteristic, complemented
7	#20295712	C₂	1	1	yes	maximal, characteristic, complemented
8	#20295708	C₂	1	1	yes	maximal, characteristic, complemented
9	#20295708	C₂	1	1	yes	maximal, characteristic, complemented
10	#20295706	C₂	1	1	yes	maximal, characteristic, complemented
11	#20295703	C₂	1	1	yes	maximal, characteristic, complemented
12	#20295701	C₂	1	1	yes	maximal, characteristic, complemented
13	#20295699	C₂	1	1	yes	maximal, characteristic, complemented
14	#20295674	C₂	1	1	yes	maximal, characteristic, complemented
15	#20295668	C₂	1	1	yes	maximal, characteristic, complemented
16	#20295665	C₂	1	1	yes	maximal, characteristic, complemented
17	#20295580	C₂	1	1	yes	maximal, characteristic, complemented
18	#20295563	C₂	1	1	yes	maximal, characteristic, complemented
19	#20295556	C₂	1	1	yes	maximal, characteristic, complemented
20	#20295556	C₂	1	1	yes	maximal, characteristic, complemented
21	#20295554	C₂	1	1	yes	maximal, characteristic, complemented
22	#20295554	C₂	1	1	yes	maximal, characteristic, complemented
23	#20295535	C₂	1	1	yes	maximal, characteristic, complemented
24	#20295535	C₂	1	1	yes	maximal, characteristic, complemented
25	C₄×#13182029	C₂	1	1	yes	maximal, characteristic, complemented
26	#20295494	C₂	1	1	yes	maximal, characteristic, complemented
27	C₄×#13182028	C₂	1	1	yes	maximal, characteristic, complemented
28	C₄×D₄×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
29	C₂×#16812656	C₂	1	1	yes	maximal, characteristic, complemented
30	#117×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
31	#529×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#13182029	C₂²	1	1	yes	characteristic
33	C₂×#13182029	C₂²	1	1	yes	characteristic
34	C₂×#13182028	C₂²	1	1	yes	characteristic
35	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic
36	C₂²×C₄×D₁₀₉	C₂²	1	1	yes	characteristic
37	C₂²×C₄×D₁₀₉	C₂²	1	1	yes	characteristic
38	#16812698	C₂²	1	1	yes	characteristic, complemented
39	#16812697	C₂²	1	1	yes	characteristic, complemented
40	#16812694	C₂²	1	1	yes	characteristic, complemented
41	#16812694	C₂²	1	1	yes	characteristic, complemented
42	#16812694	C₂²	1	1	yes	characteristic, complemented
43	#16812694	C₂²	1	1	yes	characteristic, complemented
44	#16812694	C₂²	1	1	yes	characteristic, complemented
45	#16812694	C₂²	1	1	yes	characteristic, complemented
46	#16812692	C₂²	1	1	yes	characteristic, complemented
47	#16812692	C₂²	1	1	yes	characteristic, complemented
48	#16812692	C₂²	1	1	yes	characteristic, complemented
49	#16812692	C₂²	1	1	yes	characteristic, complemented
50	#16812690	C₂²	1	1	yes	characteristic, complemented
51	#16812689	C₂²	1	1	yes	characteristic, complemented
52	#16812689	C₂²	1	1	yes	characteristic, complemented
53	#16812689	C₂²	1	1	yes	characteristic, complemented
54	#16812689	C₂²	1	1	yes	characteristic, complemented
55	#16812689	C₂²	1	1	yes	characteristic, complemented
56	#16812689	C₂²	1	1	yes	characteristic, complemented
57	#16812688	C₂²	1	1	yes	characteristic, complemented
58	#16812685	C₂²	1	1	yes	characteristic
59	#16812685	C₂²	1	1	yes	characteristic
60	#16812685	C₂²	1	1	yes	characteristic, complemented
61	#16812685	C₂²	1	1	yes	characteristic, complemented
62	#16812684	C₂²	1	1	yes	characteristic
63	#16812684	C₂²	1	1	yes	characteristic
64	#16812684	C₂²	1	1	yes	characteristic
65	#16812684	C₂²	1	1	yes	characteristic
66	#16812684	C₂²	1	1	yes	characteristic, complemented
67	#16812684	C₂²	1	1	yes	characteristic, complemented
68	#16812683	C₂²	1	1	yes	characteristic, complemented
69	#16812683	C₂²	1	1	yes	characteristic, complemented
70	#16812681	C₂²	1	1	yes	characteristic
71	#16812681	C₂²	1	1	yes	characteristic
72	#16812681	C₂²	1	1	yes	characteristic, complemented
73	#16812681	C₂²	1	1	yes	characteristic, complemented
74	#16812680	C₂²	1	1	yes	characteristic
75	#16812680	C₂²	1	1	yes	characteristic, complemented
76	#16812679	C₂²	1	1	yes	characteristic
77	#16812677	C₂²	1	1	yes	characteristic
78	#16812677	C₂²	1	1	yes	characteristic
79	#16812677	C₂²	1	1	yes	characteristic, complemented
80	#16812677	C₂²	1	1	yes	characteristic, complemented
81	#16812677	C₂²	1	1	yes	characteristic, complemented
82	#16812677	C₂²	1	1	yes	characteristic, complemented
83	#16812676	C₂²	1	1	yes	characteristic, complemented
84	#16812676	C₂²	1	1	yes	characteristic, complemented
85	#16812676	C₂²	1	1	yes	characteristic, complemented
86	#16812676	C₂²	1	1	yes	characteristic, complemented
87	#16812675	C₂²	1	1	yes	characteristic
88	#16812675	C₂²	1	1	yes	characteristic, complemented
89	#16812674	C₂²	1	1	yes	characteristic
90	#16812672	C₂²	1	1	yes	characteristic
91	#16812672	C₂²	1	1	yes	characteristic
92	#16812672	C₂²	1	1	yes	characteristic, complemented
93	#16812672	C₂²	1	1	yes	characteristic, complemented
94	#16812671	C₂²	1	1	yes	characteristic
95	#16812671	C₂²	1	1	yes	characteristic
96	#16812671	C₂²	1	1	yes	characteristic, complemented
97	#16812671	C₂²	1	1	yes	characteristic, complemented
98	#16812669	C₂²	1	1	yes	characteristic
99	#16812669	C₂²	1	1	yes	characteristic
100	#16812667	C₂²	1	1	yes	characteristic
101	#16812667	C₂²	1	1	yes	characteristic
102	C₄×Dic₂₁₈	C₂²	1	1	yes	characteristic, complemented
103	C₄×Dic₂₁₈	C₂²	1	1	yes	characteristic, complemented
104	C₄×Dic₂₁₈	C₂²	1	1	yes	characteristic, complemented
105	C₄×Dic₂₁₈	C₂²	1	1	yes	characteristic, complemented
106	#16812664	C₂²	1	1	yes	characteristic, complemented
107	#16812664	C₂²	1	1	yes	characteristic, complemented
108	#16812664	C₂²	1	1	yes	characteristic, complemented
109	C₄×D₄₃₆	C₂²	1	1	yes	characteristic
110	C₄×D₄₃₆	C₂²	1	1	yes	characteristic, complemented
111	C₄×D₄₃₆	C₂²	1	1	yes	characteristic, complemented
112	C₄×D₄₃₆	C₂²	1	1	yes	characteristic, complemented
113	D₄×Dic₁₀₉	C₂²	1	1	yes	characteristic
114	D₄×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
115	#16812661	C₂²	1	1	yes	characteristic
116	#16812661	C₂²	1	1	yes	characteristic
117	#16812661	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊D₁₀₉	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊D₁₀₉	C₂²	1	1	yes	characteristic
120	C₄×C₂²⋊D₁₀₉	C₂²	1	1	yes	characteristic
121	C₄×C₂²⋊D₁₀₉	C₂²	1	1	yes	characteristic, complemented
122	C₄×C₂²⋊D₁₀₉	C₂²	1	1	yes	characteristic, complemented
123	C₄×C₂²⋊D₁₀₉	C₂²	1	1	yes	characteristic, complemented
124	C₄×C₂²⋊D₁₀₉	C₂²	1	1	yes	characteristic, complemented
125	C₄×C₂²⋊D₁₀₉	C₂²	1	1	yes	characteristic, complemented
126	#16812659	C₂²	1	1	yes	characteristic
127	#16812659	C₂²	1	1	yes	characteristic
128	#16812659	C₂²	1	1	yes	characteristic
129	#16812659	C₂²	1	1	yes	characteristic
130	#16812659	C₂²	1	1	yes	characteristic
131	#16812659	C₂²	1	1	yes	characteristic, complemented
132	#16812659	C₂²	1	1	yes	characteristic, complemented
133	#16812659	C₂²	1	1	yes	characteristic, complemented
134	#16812658	C₂²	1	1	yes	characteristic, complemented
135	#16812658	C₂²	1	1	yes	characteristic, complemented
136	#16812657	C₂²	1	1	yes	characteristic
137	#16812657	C₂²	1	1	yes	characteristic
138	#16812657	C₂²	1	1	yes	characteristic, complemented
139	#16812656	C₂²	1	1	yes	characteristic
140	#16812656	C₂²	1	1	yes	characteristic
141	#16812656	C₂²	1	1	yes	characteristic
142	#16812656	C₂²	1	1	yes	characteristic
143	#16812656	C₂²	1	1	yes	characteristic
144	#16812656	C₂²	1	1	yes	characteristic, complemented
145	#16812656	C₂²	1	1	yes	characteristic, complemented
146	#16812656	C₂²	1	1	yes	characteristic, complemented
147	#16812656	C₂²	1	1	yes	characteristic, complemented
148	#16812656	C₂²	1	1	yes	characteristic, complemented
149	#16812656	C₂²	1	1	yes	characteristic, complemented
150	#16812656	C₂²	1	1	yes	characteristic, complemented
151	#16812655	C₂²	1	1	yes	characteristic, complemented
152	#16812655	C₂²	1	1	yes	characteristic, complemented
153	#16812655	C₂²	1	1	yes	characteristic, complemented
154	#16812655	C₂²	1	1	yes	characteristic, complemented
155	C₂×#13182008	C₂²	1	1	yes	characteristic, complemented
156	C₂×#13182008	C₂²	1	1	yes	characteristic, complemented
157	C₄⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic
158	C₄⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
159	C₄⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
160	C₂×#13182006	C₂²	1	1	yes	characteristic
161	C₂×#13182006	C₂²	1	1	yes	characteristic
162	C₂²⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic
163	C₂²⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic
164	C₂²⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic
165	C₂²⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic
166	C₂×C₄×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
167	C₂×C₄×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
168	C₄²×D₁₀₉	C₂²	1	1	yes	characteristic
169	C₄²×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
170	C₄²×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
171	C₄²×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
172	#126×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
173	#126×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
174	#125×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
175	#124×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
176	#123×C₁₀₉	C₂²	1	1	yes	characteristic
177	#123×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
178	C₂²⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
179	#121×C₁₀₉	C₂²	1	1	yes	characteristic
180	C₄×Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
181	C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
182	C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
183	C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
184	#117×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
185	#117×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
186	C₂×C₄²×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
187	C₂³×D₁₀₉	C₂³	1	1	yes	characteristic
188	C₂³×D₁₀₉	C₂³	1	1	yes	characteristic
189	#13182029	—	2	4	no	—
190	#13182029	—	2	4	no	—
191	#13182028	—	2	4	no	—
192	C₂×Dic₂₁₈	C₂³	1	1	yes	characteristic
193	C₂×Dic₂₁₈	C₂³	1	1	yes	characteristic
194	C₂×Dic₂₁₈	C₂³	1	1	yes	characteristic
195	C₂×Dic₂₁₈	C₂³	1	1	yes	characteristic
196	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
197	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
198	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
199	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
200	C₂×C₂²⋊D₁₀₉	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊D₁₀₉	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊D₁₀₉	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊D₁₀₉	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊D₁₀₉	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊D₁₀₉	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊D₁₀₉	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊D₁₀₉	C₂³	1	1	yes	characteristic
208	D₄×D₁₀₉	—	2	4	no	—
209	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
210	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
211	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
212	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
213	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
214	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
215	C₂×C₄×D₁₀₉	—	2	4	no	—
216	C₂×C₄×D₁₀₉	—	2	4	no	—
217	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
218	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
219	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
220	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
221	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
222	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
223	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
224	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
225	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
226	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
227	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
228	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
229	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
230	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
231	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
232	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
233	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
234	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
235	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
236	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
237	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
238	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
239	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
240	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
241	#13182008	C₂³	1	1	yes	characteristic
242	#13182008	C₂³	1	1	yes	characteristic
243	#13182008	C₂³	1	1	yes	characteristic
244	#13182008	C₂³	1	1	yes	characteristic
245	#13182008	C₂³	1	1	yes	characteristic
246	#13182008	C₂³	1	1	yes	characteristic
247	#13182008	C₂³	1	1	yes	characteristic
248	#13182008	C₂³	1	1	yes	characteristic
249	#13182008	C₂³	1	1	yes	characteristic
250	#13182008	C₂³	1	1	yes	characteristic
251	#13182008	C₂³	1	1	yes	characteristic
252	#13182008	C₂³	1	1	yes	characteristic
253	#13182008	C₂³	1	1	yes	characteristic
254	#13182008	C₂³	1	1	yes	characteristic
255	#13182008	C₂³	1	1	yes	characteristic
256	#13182008	C₂³	1	1	yes	characteristic
257	#13182008	C₂³	1	1	yes	characteristic
258	#13182008	C₂³	1	1	yes	characteristic
259	#13182008	C₂³	1	1	yes	characteristic
260	#13182008	C₂³	1	1	yes	characteristic
261	#13182008	C₂³	1	1	yes	characteristic
262	#13182008	C₂³	1	1	yes	characteristic
263	#13182008	C₂³	1	1	yes	characteristic
264	#13182008	C₂³	1	1	yes	characteristic
265	C₂²⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
266	C₂²⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
267	C₂²⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
268	C₂²⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
269	C₂²⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
270	C₂²⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
271	C₂²⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
272	C₂²⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
273	#13182006	C₂³	1	1	yes	characteristic
274	#13182006	C₂³	1	1	yes	characteristic
275	#13182006	C₂³	1	1	yes	characteristic
276	#13182006	C₂³	1	1	yes	characteristic
277	#13182006	C₂³	1	1	yes	characteristic
278	#13182006	C₂³	1	1	yes	characteristic
279	#13182006	C₂³	1	1	yes	characteristic
280	#13182006	C₂³	1	1	yes	characteristic
281	#13182006	C₂³	1	1	yes	characteristic
282	#13182006	C₂³	1	1	yes	characteristic
283	#13182006	C₂³	1	1	yes	characteristic
284	#13182006	C₂³	1	1	yes	characteristic
285	#13182006	C₂³	1	1	yes	characteristic
286	#13182006	C₂³	1	1	yes	characteristic
287	#13182006	C₂³	1	1	yes	characteristic
288	#13182006	C₂³	1	1	yes	characteristic
289	#13182006	C₂³	1	1	yes	characteristic
290	#13182006	C₂³	1	1	yes	characteristic
291	#13182006	C₂³	1	1	yes	characteristic
292	#13182006	C₂³	1	1	yes	characteristic
293	#13182006	C₂³	1	1	yes	characteristic
294	#13182006	C₂³	1	1	yes	characteristic
295	#13182006	C₂³	1	1	yes	characteristic
296	#13182006	C₂³	1	1	yes	characteristic
297	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
298	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
299	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
300	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
301	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
302	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
303	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
304	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
305	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
306	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
307	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
308	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
309	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
310	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
311	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
312	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
313	C₂×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
314	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
315	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
316	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
317	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
318	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
319	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
320	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
321	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
322	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
323	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
324	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
325	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
326	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
327	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
328	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
329	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
330	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
331	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
332	C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
333	C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
334	C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
335	C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
336	C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
337	C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
338	C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
339	C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
340	C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
341	C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
342	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
343	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
344	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
345	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
346	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
347	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
348	C₂³×C₁₀₉	C₂⁴	1	1	yes	characteristic
349	C₂³×C₁₀₉	C₂⁴	1	1	yes	characteristic
350	C₂³×C₁₀₉	C₂⁴	1	1	yes	characteristic
351	C₂²×D₁₀₉	—	2	2	no	—
352	C₂²×D₁₀₉	—	2	2	no	—
353	C₂²×D₁₀₉	—	2	2	no	—
354	C₂²×D₁₀₉	—	2	2	no	—
355	C₂²×D₁₀₉	—	4	1	no	—
356	C₂²×D₁₀₉	—	4	1	no	—
357	C₂²×D₁₀₉	C₂⁴	1	1	yes	characteristic
358	C₂²×D₁₀₉	C₂⁴	1	1	yes	characteristic
359	C₂²×D₁₀₉	C₂⁴	1	1	yes	characteristic
360	C₂²×D₁₀₉	C₂⁴	1	1	yes	characteristic
361	Q₈×C₁₀₉	—	4	1	no	—
362	D₄×C₁₀₉	—	2	2	no	—
363	D₄×C₁₀₉	—	2	2	no	—
364	D₄×C₁₀₉	—	4	1	no	—
365	C₂×C₄×C₁₀₉	—	2	2	no	—
366	C₂×C₄×C₁₀₉	—	2	2	no	—
367	C₂×C₄×C₁₀₉	—	2	2	no	—
368	C₂×C₄×C₁₀₉	—	2	2	no	—
369	C₂×C₄×C₁₀₉	—	4	1	no	—
370	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
371	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
372	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
373	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
374	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
375	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
376	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
377	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
378	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
379	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
380	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
381	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
382	C₂²⋊D₁₀₉	—	2	2	no	—
383	C₂²⋊D₁₀₉	—	2	2	no	—
384	C₂²⋊D₁₀₉	—	2	2	no	—
385	C₂²⋊D₁₀₉	—	2	2	no	—
386	C₂²⋊D₁₀₉	—	2	2	no	—
387	C₂²⋊D₁₀₉	—	4	1	no	—
388	C₂²⋊D₁₀₉	—	4	1	no	—
389	C₂²⋊D₁₀₉	#41	1	4	yes	complemented
390	C₂×Dic₁₀₉	—	2	2	no	—
391	C₂×Dic₁₀₉	—	2	2	no	—
392	C₂×Dic₁₀₉	—	2	2	no	—
393	C₂×Dic₁₀₉	—	2	2	no	—
394	C₂×Dic₁₀₉	—	4	1	no	—
395	C₂×Dic₁₀₉	—	4	1	no	—
396	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
397	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
398	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
399	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
400	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
401	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
402	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
403	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
404	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
405	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
406	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
407	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
408	D₄₃₆	—	2	2	no	—
409	D₄₃₆	—	2	2	no	—
410	D₄₃₆	—	2	2	no	—
411	D₄₃₆	—	4	1	no	—
412	C₄×D₁₀₉	—	2	2	no	—
413	C₄×D₁₀₉	—	2	2	no	—
414	C₄×D₁₀₉	—	2	2	no	—
415	C₄×D₁₀₉	—	2	2	no	—
416	C₄×D₁₀₉	—	2	2	no	—
417	C₄×D₁₀₉	—	2	2	no	—
418	C₄×D₁₀₉	—	2	2	no	—
419	C₄×D₁₀₉	—	2	2	no	—
420	C₄×D₁₀₉	—	2	2	no	—
421	C₄×D₁₀₉	—	2	2	no	—
422	C₄×D₁₀₉	—	2	2	no	—
423	C₄×D₁₀₉	—	4	1	no	—
424	C₄×D₁₀₉	—	4	1	no	—
425	C₄×D₁₀₉	—	4	1	no	—
426	C₄×D₁₀₉	—	4	1	no	—
427	C₄×D₁₀₉	#41	1	4	yes	complemented
428	Dic₂₁₈	—	2	2	no	—
429	Dic₂₁₈	—	2	2	no	—
430	Dic₂₁₈	—	2	2	no	—
431	Dic₂₁₈	—	4	1	no	—
432	C₂²×C₁₀₉	—	2	1	no	—
433	C₂²×C₁₀₉	—	2	1	no	—
434	C₂²×C₁₀₉	—	2	1	no	—
435	C₂²×C₁₀₉	—	2	1	no	—
436	C₂²×C₁₀₉	—	2	1	no	—
437	C₂²×C₁₀₉	—	2	1	no	—
438	C₂²×C₁₀₉	—	2	1	no	—
439	C₂²×C₁₀₉	—	2	1	no	—
440	C₂²×C₁₀₉	C₂×#41	1	2	yes	—
441	C₂²×C₁₀₉	C₂⁵	1	1	yes	characteristic
442	C₂×D₁₀₉	—	2	1	no	—
443	C₂×D₁₀₉	—	2	1	no	—
444	C₂×D₁₀₉	—	2	1	no	—
445	C₂×D₁₀₉	—	2	1	no	—
446	C₂×D₁₀₉	—	2	1	no	—
447	C₂×D₁₀₉	—	2	1	no	—
448	C₂×D₁₀₉	—	2	1	no	—
449	C₂×D₁₀₉	—	2	1	no	—
450	C₂×D₁₀₉	—	2	1	no	—
451	C₂×D₁₀₉	—	2	1	no	—
452	C₂×D₁₀₉	—	4	4	no	—
453	C₂×D₁₀₉	—	4	4	no	—
454	C₂×D₁₀₉	C₂×#41	1	2	yes	—
455	C₂×D₁₀₉	C₂×#41	1	2	yes	—
456	C₄×C₁₀₉	—	2	1	no	—
457	C₄×C₁₀₉	—	2	1	no	—
458	C₄×C₁₀₉	—	2	1	no	—
459	C₄×C₁₀₉	—	2	1	no	—
460	C₄×C₁₀₉	—	2	1	no	—
461	C₄×C₁₀₉	—	2	1	no	—
462	C₄×C₁₀₉	—	2	1	no	—
463	C₄×C₁₀₉	—	2	1	no	—
464	C₄×C₁₀₉	—	2	1	no	—
465	C₄×C₁₀₉	—	2	1	no	—
466	C₄×C₁₀₉	—	2	1	no	—
467	C₄×C₁₀₉	C₂×#41	1	2	yes	—
468	Dic₁₀₉	—	2	1	no	—
469	Dic₁₀₉	—	2	1	no	—
470	Dic₁₀₉	—	2	1	no	—
471	Dic₁₀₉	—	2	1	no	—
472	Dic₁₀₉	—	2	1	no	—
473	Dic₁₀₉	—	2	1	no	—
474	Dic₁₀₉	—	2	1	no	—
475	Dic₁₀₉	—	2	1	no	—
476	Dic₁₀₉	—	2	1	no	—
477	Dic₁₀₉	—	2	1	no	—
478	Dic₁₀₉	C₂×#41	1	2	yes	—
479	Dic₁₀₉	C₂×#41	1	2	yes	—
480	C₂×C₁₀₉	—	2	2	no	—
481	C₂×C₁₀₉	—	4	1	no	—
482	C₂×C₁₀₉	—	4	1	no	—
483	C₂×C₁₀₉	C₂²×#41	1	1	yes	characteristic
484	C₂×C₁₀₉	C₂²×#41	1	1	yes	characteristic
485	C₂×C₁₀₉	#585	1	1	yes	characteristic
486	D₁₀₉	—	2	2	no	—
487	D₁₀₉	—	2	2	no	—
488	D₁₀₉	—	4	1	no	—
489	D₁₀₉	—	4	1	no	—
490	#3475	—	109	1	no	maximal, Sylow
491	C₁₀₉	#3475	1	1	yes	characteristic, complemented, Sylow
492	#556	—	109	1	no	—
493	#555	—	109	1	no	—
494	#554	—	109	1	no	—
495	#553	—	109	1	no	—
496	#553	—	109	1	no	—
497	#552	—	109	1	no	—
498	#552	—	109	1	no	—
499	#552	—	109	1	no	—
500	#552	—	109	1	no	—
501	#551	—	109	1	no	—
502	#551	—	109	1	no	—
503	#551	—	109	1	no	—
504	#551	—	109	1	no	—
505	#547	—	109	1	no	—
506	#546	—	109	1	no	—
507	#546	—	109	1	no	—
508	#533	—	109	1	no	—
509	#529	—	109	1	no	—
510	#529	—	109	1	no	—
511	#529	—	109	1	no	—
512	#529	—	109	1	no	—
513	#529	—	109	1	no	—
514	#529	D₁₀₉	1	1	yes	characteristic, complemented
515	#525	—	109	1	no	—
516	#525	—	109	1	no	—
517	C₄×#41	—	109	1	no	—
518	C₄×#41	—	109	1	no	—
519	C₄×#41	—	109	1	no	—
520	C₂×C₄×D₄	—	109	1	no	—
521	C₂×#117	—	109	1	no	—
522	C₂×#117	—	109	1	no	—
523	C₂×#41	—	109	1	no	—
524	C₂×#41	—	109	1	no	—
525	C₂×#41	—	109	1	no	—
526	C₂²×D₄	—	109	1	no	—
527	C₂³×C₄	—	109	1	no	—
528	C₂³×C₄	—	109	1	no	—
529	C₄⋊Q₈	—	109	1	no	—
530	C₄⋊Q₈	—	109	1	no	—
531	#126	—	109	1	no	—
532	#126	—	109	1	no	—
533	#126	—	109	1	no	—
534	#126	—	109	1	no	—
535	#126	—	109	1	no	—
536	#126	—	109	1	no	—
537	#126	—	109	1	no	—
538	#126	—	109	1	no	—
539	#126	—	109	1	no	—
540	#126	—	109	1	no	—
541	#126	C₂×D₁₀₉	1	1	yes	characteristic, complemented
542	#126	C₂×D₁₀₉	1	1	yes	characteristic, complemented
543	#125	—	109	1	no	—
544	#125	—	109	1	no	—
545	#125	—	109	1	no	—
546	#125	—	109	1	no	—
547	#125	—	109	1	no	—
548	#125	—	109	1	no	—
549	#125	—	109	1	no	—
550	#125	C₂×D₁₀₉	1	1	yes	characteristic, complemented
551	#124	—	109	1	no	—
552	#124	—	109	1	no	—
553	#124	—	109	1	no	—
554	#124	—	109	1	no	—
555	#124	—	109	1	no	—
556	#124	C₂×D₁₀₉	1	1	yes	characteristic, complemented
557	#123	—	109	1	no	—
558	#123	—	109	1	no	—
559	#123	—	109	1	no	—
560	#123	—	109	1	no	—
561	#123	—	109	1	no	—
562	#123	—	109	1	no	—
563	#123	—	109	1	no	—
564	#123	—	109	1	no	—
565	#123	—	109	1	no	—
566	#123	—	109	1	no	—
567	#123	—	109	1	no	—
568	#123	—	109	1	no	—
569	#123	—	109	1	no	—
570	#123	—	109	1	no	—
571	#123	C₂×D₁₀₉	1	1	yes	characteristic
572	#123	C₂×D₁₀₉	1	1	yes	characteristic, complemented
573	C₂²⋊Q₈	—	109	1	no	—
574	C₂²⋊Q₈	—	109	1	no	—
575	C₂²⋊Q₈	—	109	1	no	—
576	C₂²⋊Q₈	—	109	1	no	—
577	C₂²⋊Q₈	—	109	1	no	—
578	C₂²⋊Q₈	—	109	1	no	—
579	C₂²⋊Q₈	—	109	1	no	—
580	C₂²⋊Q₈	—	109	1	no	—
581	C₂²⋊Q₈	—	109	1	no	—
582	C₂²⋊Q₈	—	109	1	no	—
583	C₂²⋊Q₈	—	109	1	no	—
584	C₂²⋊Q₈	—	109	1	no	—
585	C₂²⋊Q₈	—	109	1	no	—
586	C₂²⋊Q₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
587	#121	—	109	1	no	—
588	#121	—	109	1	no	—
589	#121	—	109	1	no	—
590	#121	—	109	1	no	—
591	#121	—	109	1	no	—
592	#121	—	109	1	no	—
593	#121	—	109	1	no	—
594	#121	—	109	1	no	—
595	#121	—	109	1	no	—
596	#121	C₂×D₁₀₉	1	1	yes	characteristic
597	#120	—	109	1	no	—
598	#120	—	109	1	no	—
599	#120	—	109	1	no	—
600	#120	—	109	1	no	—
601	C₄×Q₈	—	109	1	no	—
602	C₄×Q₈	—	109	1	no	—
603	C₄×Q₈	—	109	1	no	—
604	C₄×Q₈	—	109	1	no	—
605	C₄×Q₈	—	109	1	no	—
606	C₄×Q₈	—	109	1	no	—
607	C₄×Q₈	—	109	1	no	—
608	C₄×Q₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
609	C₄×D₄	—	109	1	no	—
610	C₄×D₄	—	109	1	no	—
611	C₄×D₄	—	109	1	no	—
612	C₄×D₄	—	109	1	no	—
613	C₄×D₄	—	109	1	no	—
614	C₄×D₄	—	109	1	no	—
615	C₄×D₄	—	109	1	no	—
616	C₄×D₄	—	109	1	no	—
617	C₄×D₄	—	109	1	no	—
618	C₄×D₄	—	109	1	no	—
619	C₄×D₄	—	109	1	no	—
620	C₄×D₄	—	109	1	no	—
621	C₄×D₄	—	109	1	no	—
622	C₄×D₄	—	109	1	no	—
623	C₄×D₄	—	109	1	no	—
624	C₄×D₄	—	109	1	no	—
625	C₄×D₄	—	109	1	no	—
626	C₄×D₄	—	109	1	no	—
627	C₄×D₄	—	109	1	no	—
628	C₄×D₄	—	109	1	no	—
629	C₄×D₄	—	109	1	no	—
630	C₄×D₄	—	109	1	no	—
631	C₄×D₄	—	109	1	no	—
632	C₄×D₄	—	109	1	no	—
633	C₄×D₄	—	109	1	no	—
634	C₄×D₄	C₂×D₁₀₉	1	1	yes	characteristic
635	C₄×D₄	C₂×D₁₀₉	1	1	yes	characteristic, complemented
636	C₄×D₄	C₂×D₁₀₉	1	1	yes	characteristic, complemented
637	#117	—	109	1	no	—
638	#117	—	109	1	no	—
639	#117	—	109	1	no	—
640	#117	—	109	1	no	—
641	#117	—	109	1	no	—
642	#117	—	109	1	no	—
643	#117	—	109	1	no	—
644	#117	—	109	1	no	—
645	#117	—	109	1	no	—
646	#117	—	109	1	no	—
647	#117	—	109	1	no	—
648	#117	—	109	1	no	—
649	#117	—	109	1	no	—
650	#117	—	109	1	no	—
651	#117	—	109	1	no	—
652	#117	—	109	1	no	—
653	#117	—	109	1	no	—
654	#117	—	109	1	no	—
655	#117	—	109	1	no	—
656	#117	—	109	1	no	—
657	#117	—	109	1	no	—
658	#117	C₂×D₁₀₉	1	1	yes	characteristic, complemented
659	#117	C₂×D₁₀₉	1	1	yes	characteristic, complemented
660	C₂×C₄⋊C₄	—	109	1	no	—
661	C₂×C₄⋊C₄	—	109	1	no	—
662	C₂×C₄⋊C₄	—	109	1	no	—
663	C₂×C₄⋊C₄	—	109	1	no	—
664	C₂×C₄⋊C₄	—	109	1	no	—
665	C₂×C₂²⋊C₄	—	109	1	no	—
666	C₂×C₂²⋊C₄	—	109	1	no	—
667	C₂×C₂²⋊C₄	—	109	1	no	—
668	C₂×C₂²⋊C₄	—	109	1	no	—
669	C₂×C₂²⋊C₄	—	109	1	no	—
670	C₂×C₂²⋊C₄	—	109	1	no	—
671	C₂×C₄²	—	109	1	no	—
672	C₂×C₄²	—	109	1	no	—
673	C₂×C₄²	—	109	1	no	—
674	C₂×C₄²	—	109	1	no	—
675	C₂×C₄²	—	109	1	no	—
676	C₂×C₄²	—	109	1	no	—
677	C₂×C₄²	C₂×D₁₀₉	1	1	yes	characteristic, complemented
678	C₂⁴	—	109	1	no	—
679	C₂⁴	—	109	1	no	—
680	#41	—	218	4	no	—
681	#41	—	218	4	no	—
682	#41	—	218	4	no	—
683	C₂×Q₈	—	109	1	no	—
684	C₂×Q₈	—	109	1	no	—
685	C₂×Q₈	—	109	1	no	—
686	C₂×Q₈	—	109	1	no	—
687	C₂×Q₈	C₂²×D₁₀₉	1	1	yes	characteristic
688	C₂×D₄	—	109	1	no	—
689	C₂×D₄	—	109	1	no	—
690	C₂×D₄	—	109	1	no	—
691	C₂×D₄	—	109	1	no	—
692	C₂×D₄	—	109	1	no	—
693	C₂×D₄	—	109	1	no	—
694	C₂×D₄	—	109	1	no	—
695	C₂×D₄	—	109	1	no	—
696	C₂×D₄	—	109	1	no	—
697	C₂×D₄	—	109	1	no	—
698	C₂×D₄	—	109	1	no	—
699	C₂×D₄	—	109	1	no	—
700	C₂×D₄	—	218	4	no	—
701	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
702	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
703	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
704	C₂²×C₄	—	109	1	no	—
705	C₂²×C₄	—	109	1	no	—
706	C₂²×C₄	—	109	1	no	—
707	C₂²×C₄	—	109	1	no	—
708	C₂²×C₄	—	109	1	no	—
709	C₂²×C₄	—	109	1	no	—
710	C₂²×C₄	—	109	1	no	—
711	C₂²×C₄	—	109	1	no	—
712	C₂²×C₄	—	109	1	no	—
713	C₂²×C₄	—	109	1	no	—
714	C₂²×C₄	—	109	1	no	—
715	C₂²×C₄	—	109	1	no	—
716	C₂²×C₄	—	109	1	no	—
717	C₂²×C₄	—	109	1	no	—
718	C₂²×C₄	—	109	1	no	—
719	C₂²×C₄	—	109	1	no	—
720	C₂²×C₄	—	109	1	no	—
721	C₂²×C₄	—	109	1	no	—
722	C₂²×C₄	—	109	1	no	—
723	C₂²×C₄	—	109	1	no	—
724	C₂²×C₄	—	109	1	no	—
725	C₂²×C₄	—	109	1	no	—
726	C₂²×C₄	—	218	4	no	—
727	C₂²×C₄	—	218	4	no	—
728	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
729	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
730	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
731	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
732	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
733	C₄⋊C₄	—	109	1	no	—
734	C₄⋊C₄	—	109	1	no	—
735	C₄⋊C₄	—	109	1	no	—
736	C₄⋊C₄	—	109	1	no	—
737	C₄⋊C₄	—	109	1	no	—
738	C₄⋊C₄	—	109	1	no	—
739	C₄⋊C₄	—	109	1	no	—
740	C₄⋊C₄	—	109	1	no	—
741	C₄⋊C₄	—	109	1	no	—
742	C₄⋊C₄	—	109	1	no	—
743	C₄⋊C₄	—	109	1	no	—
744	C₄⋊C₄	—	109	1	no	—
745	C₄⋊C₄	—	109	1	no	—
746	C₄⋊C₄	—	109	1	no	—
747	C₄⋊C₄	—	109	1	no	—
748	C₄⋊C₄	—	109	1	no	—
749	C₄⋊C₄	—	109	1	no	—
750	C₄⋊C₄	—	109	1	no	—
751	C₄⋊C₄	—	109	1	no	—
752	C₄⋊C₄	—	109	1	no	—
753	C₄⋊C₄	—	109	1	no	—
754	C₄⋊C₄	—	109	1	no	—
755	C₄⋊C₄	—	109	1	no	—
756	C₄⋊C₄	—	109	1	no	—
757	C₄⋊C₄	—	109	1	no	—
758	C₄⋊C₄	—	109	1	no	—
759	C₄⋊C₄	—	109	1	no	—
760	C₄⋊C₄	—	109	1	no	—
761	C₄⋊C₄	—	109	1	no	—
762	C₄⋊C₄	—	109	1	no	—
763	C₄⋊C₄	—	109	1	no	—
764	C₄⋊C₄	—	109	1	no	—
765	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
766	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
767	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
768	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
769	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
770	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
771	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
772	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
773	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
774	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
775	C₂²⋊C₄	—	109	1	no	—
776	C₂²⋊C₄	—	109	1	no	—
777	C₂²⋊C₄	—	109	1	no	—
778	C₂²⋊C₄	—	109	1	no	—
779	C₂²⋊C₄	—	109	1	no	—
780	C₂²⋊C₄	—	109	1	no	—
781	C₂²⋊C₄	—	109	1	no	—
782	C₂²⋊C₄	—	109	1	no	—
783	C₂²⋊C₄	—	109	1	no	—
784	C₂²⋊C₄	—	109	1	no	—
785	C₂²⋊C₄	—	109	1	no	—
786	C₂²⋊C₄	—	109	1	no	—
787	C₂²⋊C₄	—	109	1	no	—
788	C₂²⋊C₄	—	109	1	no	—
789	C₂²⋊C₄	—	109	1	no	—
790	C₂²⋊C₄	—	109	1	no	—
791	C₂²⋊C₄	—	109	1	no	—
792	C₂²⋊C₄	—	109	1	no	—
793	C₂²⋊C₄	—	109	1	no	—
794	C₂²⋊C₄	—	109	1	no	—
795	C₂²⋊C₄	—	109	1	no	—
796	C₂²⋊C₄	—	109	1	no	—
797	C₂²⋊C₄	—	109	1	no	—
798	C₂²⋊C₄	—	109	1	no	—
799	C₂²⋊C₄	—	109	1	no	—
800	C₂²⋊C₄	—	109	1	no	—
801	C₂²⋊C₄	—	109	1	no	—
802	C₂²⋊C₄	—	109	1	no	—
803	C₂²⋊C₄	—	109	1	no	—
804	C₂²⋊C₄	—	109	1	no	—
805	C₂²⋊C₄	—	109	1	no	—
806	C₂²⋊C₄	—	109	1	no	—
807	C₂²⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
808	C₂²⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
809	C₂²⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
810	C₂²⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
811	C₂²⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
812	C₂²⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
813	C₂²⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
814	C₂²⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
815	C₂²⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
816	C₂²⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
817	C₄²	—	109	1	no	—
818	C₄²	—	109	1	no	—
819	C₄²	—	109	1	no	—
820	C₄²	—	109	1	no	—
821	C₄²	—	109	1	no	—
822	C₄²	—	109	1	no	—
823	C₄²	—	109	1	no	—
824	C₄²	—	109	1	no	—
825	C₄²	—	109	1	no	—
826	C₄²	—	109	1	no	—
827	C₄²	—	109	1	no	—
828	C₄²	—	109	1	no	—
829	C₄²	—	109	1	no	—
830	C₄²	—	109	1	no	—
831	C₄²	—	109	1	no	—
832	C₄²	—	109	1	no	—
833	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
834	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
835	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
836	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
837	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
838	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
839	C₂³	—	109	1	no	—
840	C₂³	—	109	1	no	—
841	C₂³	—	109	1	no	—
842	C₂³	—	109	1	no	—
843	C₂³	—	436	1	no	—
844	C₂³	—	436	1	no	—
845	C₂³	—	218	2	no	—
846	C₂³	—	218	2	no	—
847	C₂³	—	218	2	no	—
848	C₂³	—	218	2	no	—
849	C₂³	C₂³×D₁₀₉	1	1	yes	characteristic
850	C₂³	C₂³×D₁₀₉	1	1	yes	characteristic
851	C₂³	C₂³×D₁₀₉	1	1	yes	characteristic
852	Q₈	—	4	1	no	—
853	Q₈	—	436	1	no	—
854	Q₈	—	218	2	no	—
855	Q₈	—	218	2	no	—
856	Q₈	—	218	2	no	—
857	D₄	—	2	2	no	—
858	D₄	—	2	2	no	—
859	D₄	—	4	1	no	—
860	D₄	—	109	4	no	—
861	D₄	—	436	1	no	—
862	D₄	—	436	1	no	—
863	D₄	—	436	1	no	—
864	D₄	—	218	2	no	—
865	D₄	—	218	2	no	—
866	D₄	—	218	2	no	—
867	D₄	—	218	2	no	—
868	D₄	—	218	2	no	—
869	D₄	—	218	2	no	—
870	D₄	—	218	2	no	—
871	D₄	—	218	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	4	1	no	—
877	C₂×C₄	—	109	1	no	—
878	C₂×C₄	—	109	1	no	—
879	C₂×C₄	—	109	4	no	—
880	C₂×C₄	—	109	1	no	—
881	C₂×C₄	—	109	1	no	—
882	C₂×C₄	—	109	1	no	—
883	C₂×C₄	—	109	1	no	—
884	C₂×C₄	—	109	1	no	—
885	C₂×C₄	—	109	1	no	—
886	C₂×C₄	—	109	1	no	—
887	C₂×C₄	—	109	1	no	—
888	C₂×C₄	—	109	1	no	—
889	C₂×C₄	—	109	1	no	—
890	C₂×C₄	—	436	1	no	—
891	C₂×C₄	—	436	1	no	—
892	C₂×C₄	—	436	1	no	—
893	C₂×C₄	—	436	1	no	—
894	C₂×C₄	—	436	1	no	—
895	C₂×C₄	—	436	1	no	—
896	C₂×C₄	—	218	2	no	—
897	C₂×C₄	—	218	2	no	—
898	C₂×C₄	—	218	2	no	—
899	C₂×C₄	—	218	2	no	—
900	C₂×C₄	—	218	2	no	—
901	C₂×C₄	—	218	2	no	—
902	C₂×C₄	—	218	2	no	—
903	C₂×C₄	—	218	2	no	—
904	C₂×C₄	—	218	2	no	—
905	C₂×C₄	—	218	2	no	—
906	C₂×C₄	—	218	2	no	—
907	C₂×C₄	—	218	2	no	—
908	C₂×C₄	—	218	2	no	—
909	C₂×C₄	—	218	2	no	—
910	C₂×C₄	—	218	2	no	—
911	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
912	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
913	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
914	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
915	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
916	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
917	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
918	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
919	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
920	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
921	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
922	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
923	C₂²	—	2	1	no	—
924	C₂²	—	2	1	no	—
925	C₂²	—	2	1	no	—
926	C₂²	—	2	1	no	—
927	C₂²	—	2	1	no	—
928	C₂²	—	2	1	no	—
929	C₂²	—	2	1	no	—
930	C₂²	—	2	1	no	—
931	C₂²	—	109	2	no	—
932	C₂²	—	109	2	no	—
933	C₂²	—	436	4	no	—
934	C₂²	—	436	4	no	—
935	C₂²	—	218	1	no	—
936	C₂²	—	218	1	no	—
937	C₂²	—	218	1	no	—
938	C₂²	—	218	1	no	—
939	C₂²	—	218	1	no	—
940	C₂²	—	218	1	no	—
941	C₂²	—	218	1	no	—
942	C₂²	—	218	1	no	—
943	C₂²	—	218	1	no	—
944	C₂²	—	218	1	no	—
945	C₂²	#41×D₁₀₉	1	2	yes	—
946	C₂²	C₂⁴×D₁₀₉	1	1	yes	characteristic
947	C₄	—	2	1	no	—
948	C₄	—	2	1	no	—
949	C₄	—	2	1	no	—
950	C₄	—	2	1	no	—
951	C₄	—	2	1	no	—
952	C₄	—	2	1	no	—
953	C₄	—	2	1	no	—
954	C₄	—	2	1	no	—
955	C₄	—	2	1	no	—
956	C₄	—	2	1	no	—
957	C₄	—	2	1	no	—
958	C₄	—	109	2	no	—
959	C₄	—	109	2	no	—
960	C₄	—	218	1	no	—
961	C₄	—	218	1	no	—
962	C₄	—	218	1	no	—
963	C₄	—	218	1	no	—
964	C₄	—	218	1	no	—
965	C₄	—	218	1	no	—
966	C₄	—	218	1	no	—
967	C₄	—	218	1	no	—
968	C₄	—	218	1	no	—
969	C₄	—	218	1	no	—
970	C₄	#41×D₁₀₉	1	2	yes	—
971	C₂	—	2	2	no	—
972	C₂	—	4	1	no	—
973	C₂	—	4	1	no	—
974	C₂	—	436	1	no	—
975	C₂	—	436	1	no	—
976	C₂	—	218	2	no	—
977	C₂	—	218	2	no	—
978	C₂	C₂×#41×D₁₀₉	1	1	yes	characteristic
979	C₂	C₂×#41×D₁₀₉	1	1	yes	characteristic
980	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	#529×C₁₀₉	C₂
hypercenter	#529	D₁₀₉
hypocenter	C₁₀₉	#3475
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. #20295743	C₂	semidirect
2. #20295738	C₂	semidirect
3. #20295730	C₂	semidirect
4. #20295727	C₂	semidirect
5. #20295719	C₂	semidirect
6. #20295713	C₂	semidirect
7. #20295712	C₂	semidirect
8. #20295708	C₂	semidirect
9. #20295708	C₂	semidirect
10. #20295706	C₂	semidirect
11. #20295703	C₂	semidirect
12. #20295701	C₂	semidirect
13. #20295699	C₂	semidirect
14. #20295674	C₂	semidirect
15. #20295668	C₂	semidirect
16. #20295665	C₂	semidirect
17. #20295580	C₂	semidirect
18. #20295563	C₂	semidirect
19. #20295556	C₂	semidirect
20. #20295556	C₂	semidirect
21. #20295554	C₂	semidirect
22. #20295554	C₂	semidirect
23. #20295535	C₂	semidirect
24. #20295535	C₂	semidirect
25. C₄×#13182029	C₂	semidirect
26. #20295494	C₂	semidirect
27. C₄×#13182028	C₂	semidirect
28. C₄×D₄×D₁₀₉	C₂	semidirect
29. C₂×#16812656	C₂	semidirect
30. #117×D₁₀₉	C₂	semidirect
31. #529×C₁₀₉	C₂	semidirect
38. #16812698	C₂²	semidirect
39. #16812697	C₂²	semidirect
40. #16812694	C₂²	semidirect
41. #16812694	C₂²	semidirect
42. #16812694	C₂²	semidirect
43. #16812694	C₂²	semidirect
44. #16812694	C₂²	semidirect
45. #16812694	C₂²	semidirect
46. #16812692	C₂²	semidirect
47. #16812692	C₂²	semidirect
48. #16812692	C₂²	semidirect
49. #16812692	C₂²	semidirect
50. #16812690	C₂²	semidirect
51. #16812689	C₂²	semidirect
52. #16812689	C₂²	semidirect
53. #16812689	C₂²	semidirect
54. #16812689	C₂²	semidirect
55. #16812689	C₂²	semidirect
56. #16812689	C₂²	semidirect
57. #16812688	C₂²	semidirect
60. #16812685	C₂²	semidirect
61. #16812685	C₂²	semidirect
66. #16812684	C₂²	semidirect
67. #16812684	C₂²	semidirect
68. #16812683	C₂²	semidirect
69. #16812683	C₂²	semidirect
72. #16812681	C₂²	semidirect
73. #16812681	C₂²	semidirect
75. #16812680	C₂²	semidirect
79. #16812677	C₂²	semidirect
80. #16812677	C₂²	semidirect
81. #16812677	C₂²	semidirect
82. #16812677	C₂²	semidirect
83. #16812676	C₂²	semidirect
84. #16812676	C₂²	semidirect
85. #16812676	C₂²	semidirect
86. #16812676	C₂²	semidirect
88. #16812675	C₂²	semidirect
92. #16812672	C₂²	semidirect
93. #16812672	C₂²	semidirect
96. #16812671	C₂²	semidirect
97. #16812671	C₂²	semidirect
102. C₄×Dic₂₁₈	C₂²	semidirect
103. C₄×Dic₂₁₈	C₂²	semidirect
104. C₄×Dic₂₁₈	C₂²	semidirect
105. C₄×Dic₂₁₈	C₂²	semidirect
106. #16812664	C₂²	semidirect
107. #16812664	C₂²	semidirect
108. #16812664	C₂²	semidirect
110. C₄×D₄₃₆	C₂²	semidirect
111. C₄×D₄₃₆	C₂²	semidirect
112. C₄×D₄₃₆	C₂²	semidirect
114. D₄×Dic₁₀₉	C₂²	semidirect
121. C₄×C₂²⋊D₁₀₉	C₂²	semidirect
122. C₄×C₂²⋊D₁₀₉	C₂²	semidirect
123. C₄×C₂²⋊D₁₀₉	C₂²	semidirect
124. C₄×C₂²⋊D₁₀₉	C₂²	semidirect
125. C₄×C₂²⋊D₁₀₉	C₂²	semidirect
131. #16812659	C₂²	semidirect
132. #16812659	C₂²	semidirect
133. #16812659	C₂²	semidirect
134. #16812658	C₂²	semidirect
135. #16812658	C₂²	semidirect
138. #16812657	C₂²	semidirect
144. #16812656	C₂²	semidirect
145. #16812656	C₂²	semidirect
146. #16812656	C₂²	semidirect
147. #16812656	C₂²	semidirect
148. #16812656	C₂²	semidirect
149. #16812656	C₂²	semidirect
150. #16812656	C₂²	semidirect
151. #16812655	C₂²	semidirect
152. #16812655	C₂²	semidirect
153. #16812655	C₂²	semidirect
154. #16812655	C₂²	semidirect
155. C₂×#13182008	C₂²	semidirect
156. C₂×#13182008	C₂²	semidirect
158. C₄⋊C₄×D₁₀₉	C₂²	semidirect
159. C₄⋊C₄×D₁₀₉	C₂²	semidirect
166. C₂×C₄×Dic₁₀₉	C₂²	semidirect
167. C₂×C₄×Dic₁₀₉	C₂²	semidirect
169. C₄²×D₁₀₉	C₂²	semidirect
170. C₄²×D₁₀₉	C₂²	semidirect
171. C₄²×D₁₀₉	C₂²	semidirect
172. #126×C₁₀₉	C₂²	semidirect
173. #126×C₁₀₉	C₂²	semidirect
174. #125×C₁₀₉	C₂²	semidirect
175. #124×C₁₀₉	C₂²	semidirect
177. #123×C₁₀₉	C₂²	semidirect
178. C₂²⋊Q₈×C₁₀₉	C₂²	semidirect
180. C₄×Q₈×C₁₀₉	C₂²	semidirect
182. C₄×D₄×C₁₀₉	C₂²	semidirect
183. C₄×D₄×C₁₀₉	C₂²	semidirect
184. #117×C₁₀₉	C₂²	semidirect
185. #117×C₁₀₉	C₂²	semidirect
186. C₂×C₄²×C₁₀₉	C₂²	semidirect
389. C₂²⋊D₁₀₉	#41	semidirect
427. C₄×D₁₀₉	#41	semidirect
491. C₁₀₉	#3475	semidirect
514. #529	D₁₀₉	semidirect
541. #126	C₂×D₁₀₉	semidirect
542. #126	C₂×D₁₀₉	semidirect
550. #125	C₂×D₁₀₉	semidirect
556. #124	C₂×D₁₀₉	semidirect
572. #123	C₂×D₁₀₉	semidirect
586. C₂²⋊Q₈	C₂×D₁₀₉	semidirect
608. C₄×Q₈	C₂×D₁₀₉	semidirect
635. C₄×D₄	C₂×D₁₀₉	semidirect
636. C₄×D₄	C₂×D₁₀₉	semidirect
658. #117	C₂×D₁₀₉	semidirect
659. #117	C₂×D₁₀₉	semidirect
677. 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
#20295743	2
#20295738	2
#20295730	2
#20295727	2
#20295719	2
#20295713	2
#20295712	2
#20295708	2
#20295706	2
#20295703	2
#20295701	2
#20295699	2
#20295674	2
#20295668	2
#20295665	2
#20295580	2
#20295563	2
#20295556	2
#20295554	2
#20295535	2
C₄×#13182029	2
#20295494	2
C₄×#13182028	2
C₄×D₄×D₁₀₉	2
C₂×#16812656	2
#117×D₁₀₉	2
#529×C₁₀₉	2
#3475	109