Subgroups — C₁₀₉×#34264 #42152258

Order 27904.

3658 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#534×C₁₀₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#518×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×D₄×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₉×#2364	C₂	1	4	yes	maximal, complemented
5	C₁₀₉×#2361	C₂	1	4	yes	maximal, complemented
6	C₁₀₉×#2359	C₂	1	4	yes	maximal, complemented
7	C₁₀₉×#2358	C₂	1	4	yes	maximal, complemented
8	C₁₀₉×#2322	C₂	1	2	yes	maximal, complemented
9	C₁₀₉×#2321	C₂	1	2	yes	maximal, complemented
10	C₁₀₉×#2308	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#123×C₁₀₉	C₂	1	2	yes	maximal, complemented
12	C₄×#120×C₁₀₉	C₂	1	2	yes	maximal, complemented
13	C₂×#386×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#385×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₀₉×#2273	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₁₀₉	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
20	#534×C₁₀₉	C₄	1	16	yes	complemented
21	C₂×#123×C₁₀₉	C₂²	1	2	yes	—
22	C₂×#123×C₁₀₉	C₂²	1	2	yes	—
23	C₂×#121×C₁₀₉	C₂²	1	4	yes	—
24	C₂×#120×C₁₀₉	C₂²	1	2	yes	—
25	C₂×#120×C₁₀₉	C₂²	1	2	yes	—
26	#518×C₁₀₉	—	2	8	no	—
27	C₂×C₄×D₄×C₁₀₉	—	2	8	no	—
28	C₂×C₄×D₄×C₁₀₉	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₁₀₉	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₁₀₉	C₂²	1	4	yes	—
31	C₂×C₄×D₄×C₁₀₉	C₂²	1	2	yes	complemented
32	C₂×C₄×D₄×C₁₀₉	C₂²	1	4	yes	complemented
33	C₂×C₄×D₄×C₁₀₉	C₂²	1	2	yes	complemented
34	C₂×C₄×D₄×C₁₀₉	C₂²	1	4	yes	complemented
35	C₂×#117×C₁₀₉	C₂²	1	2	yes	complemented
36	C₂²×C₄⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₄⋊C₄×C₁₀₉	C₂²	1	2	yes	complemented
38	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
39	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
40	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
41	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
42	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
43	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	2	yes	complemented
44	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	2	yes	complemented
45	C₂²×C₄²×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
46	#390×C₁₀₉	C₂²	1	4	yes	complemented
47	#389×C₁₀₉	C₂²	1	4	yes	complemented
48	#388×C₁₀₉	C₂²	1	4	yes	complemented
49	#388×C₁₀₉	C₂²	1	4	yes	complemented
50	#388×C₁₀₉	C₂²	1	4	yes	complemented
51	#388×C₁₀₉	C₂²	1	4	yes	complemented
52	#387×C₁₀₉	C₂²	1	4	yes	complemented
53	#387×C₁₀₉	C₂²	1	4	yes	complemented
54	#386×C₁₀₉	C₂²	1	2	yes	—
55	#386×C₁₀₉	C₂²	1	2	yes	—
56	#386×C₁₀₉	C₂²	1	4	yes	—
57	#386×C₁₀₉	C₂²	1	4	yes	complemented
58	#386×C₁₀₉	C₂²	1	4	yes	complemented
59	#386×C₁₀₉	C₂²	1	2	yes	complemented
60	#386×C₁₀₉	C₂²	1	2	yes	complemented
61	#386×C₁₀₉	C₂²	1	4	yes	complemented
62	#385×C₁₀₉	C₂²	1	2	yes	complemented
63	#385×C₁₀₉	C₂²	1	2	yes	complemented
64	#385×C₁₀₉	C₂²	1	4	yes	complemented
65	#385×C₁₀₉	C₂²	1	4	yes	complemented
66	#385×C₁₀₉	C₂²	1	4	yes	complemented
67	#381×C₁₀₉	C₂²	1	2	yes	complemented
68	#379×C₁₀₉	C₂²	1	2	yes	complemented
69	C₄×C₄⋊C₄×C₁₀₉	C₂²	1	4	yes	complemented
70	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	2	yes	complemented
71	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	2	yes	complemented
72	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	4	yes	complemented
73	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	4	yes	complemented
74	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	4	yes	complemented
75	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	4	yes	complemented
76	C₂×#95×C₁₀₉	C₂²	1	2	yes	complemented
77	C₂×#95×C₁₀₉	C₂²	1	2	yes	complemented
78	C₂⁵×C₁₀₉	C₂³	1	1	yes	characteristic
79	C₂⁵×C₁₀₉	C₂³	1	1	yes	characteristic
80	C₂⁵×C₁₀₉	C₂³	1	1	yes	characteristic
81	C₂²×D₄×C₁₀₉	—	2	4	no	—
82	C₂²×D₄×C₁₀₉	—	2	4	no	—
83	C₂²×D₄×C₁₀₉	—	2	4	no	—
84	C₂²×D₄×C₁₀₉	—	2	4	no	—
85	C₂²×D₄×C₁₀₉	C₂×C₄	1	8	yes	complemented
86	C₂²×D₄×C₁₀₉	C₂×C₄	1	8	yes	complemented
87	C₂²×D₄×C₁₀₉	C₂³	1	2	yes	—
88	C₂²×D₄×C₁₀₉	C₂³	1	2	yes	—
89	C₂²×D₄×C₁₀₉	C₂³	1	2	yes	—
90	C₂²×D₄×C₁₀₉	C₂³	1	2	yes	—
91	C₂²×D₄×C₁₀₉	C₂³	1	4	yes	—
92	C₂³×C₄×C₁₀₉	—	2	4	no	—
93	C₂³×C₄×C₁₀₉	—	2	4	no	—
94	C₂³×C₄×C₁₀₉	—	4	4	no	—
95	C₂³×C₄×C₁₀₉	—	4	4	no	—
96	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₁₀₉	C₂³	1	2	yes	—
98	C₂³×C₄×C₁₀₉	C₂³	1	2	yes	—
99	C₂³×C₄×C₁₀₉	C₂³	1	4	yes	—
100	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₁₀₉	C₂³	1	2	yes	—
103	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₁₀₉	C₂³	1	2	yes	—
107	C₂³×C₄×C₁₀₉	C₂³	1	2	yes	—
108	C₂³×C₄×C₁₀₉	C₂³	1	2	yes	—
109	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
111	#123×C₁₀₉	C₂×C₄	1	16	yes	complemented
112	#123×C₁₀₉	C₂×C₄	1	16	yes	complemented
113	#121×C₁₀₉	C₂×C₄	1	32	yes	complemented
114	#120×C₁₀₉	C₂×C₄	1	16	yes	complemented
115	#120×C₁₀₉	C₂×C₄	1	16	yes	complemented
116	C₄×D₄×C₁₀₉	—	2	8	no	—
117	C₄×D₄×C₁₀₉	—	2	8	no	—
118	C₄×D₄×C₁₀₉	—	2	16	no	—
119	C₄×D₄×C₁₀₉	—	2	16	no	—
120	C₄×D₄×C₁₀₉	—	2	8	no	—
121	C₄×D₄×C₁₀₉	—	2	8	no	—
122	C₄×D₄×C₁₀₉	—	4	8	no	—
123	#117×C₁₀₉	—	2	8	no	—
124	C₂×C₄⋊C₄×C₁₀₉	—	2	4	no	—
125	C₂×C₄⋊C₄×C₁₀₉	—	4	4	no	—
126	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	4	yes	—
127	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	4	yes	—
128	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	4	yes	—
131	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	4	yes	—
132	C₂×C₂²⋊C₄×C₁₀₉	—	2	4	no	—
133	C₂×C₂²⋊C₄×C₁₀₉	—	2	4	no	—
134	C₂×C₂²⋊C₄×C₁₀₉	—	2	4	no	—
135	C₂×C₂²⋊C₄×C₁₀₉	—	2	8	no	—
136	C₂×C₂²⋊C₄×C₁₀₉	—	4	4	no	—
137	C₂×C₂²⋊C₄×C₁₀₉	C₂×C₄	1	8	yes	complemented
138	C₂×C₂²⋊C₄×C₁₀₉	D₄	1	8	yes	complemented
139	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
145	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
153	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
154	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
156	C₂×C₄²×C₁₀₉	—	2	4	no	—
157	C₂×C₄²×C₁₀₉	C₂³	1	4	yes	—
158	C₂×C₄²×C₁₀₉	C₂³	1	2	yes	—
159	C₂×C₄²×C₁₀₉	C₂³	1	2	yes	—
160	C₂×C₄²×C₁₀₉	C₂³	1	4	yes	—
161	C₂×C₄²×C₁₀₉	C₂³	1	4	yes	—
162	#95×C₁₀₉	C₂³	1	4	yes	—
163	#95×C₁₀₉	C₂³	1	4	yes	—
164	#95×C₁₀₉	C₂³	1	4	yes	—
165	#95×C₁₀₉	C₂³	1	4	yes	—
166	#95×C₁₀₉	C₂³	1	4	yes	—
167	#95×C₁₀₉	C₂³	1	4	yes	—
168	#95×C₁₀₉	C₂³	1	4	yes	—
169	#95×C₁₀₉	C₂³	1	4	yes	—
170	C₂⁴×C₁₀₉	—	2	2	no	—
171	C₂⁴×C₁₀₉	—	2	2	no	—
172	C₂⁴×C₁₀₉	—	2	2	no	—
173	C₂⁴×C₁₀₉	—	2	2	no	—
174	C₂⁴×C₁₀₉	—	4	2	no	—
175	C₂⁴×C₁₀₉	—	4	2	no	—
176	C₂⁴×C₁₀₉	—	4	2	no	—
177	C₂⁴×C₁₀₉	—	4	2	no	—
178	C₂⁴×C₁₀₉	—	4	2	no	—
179	C₂⁴×C₁₀₉	—	4	2	no	—
180	C₂⁴×C₁₀₉	C₂²×C₄	1	4	yes	—
181	C₂⁴×C₁₀₉	C₂²×C₄	1	4	yes	—
182	C₂⁴×C₁₀₉	C₂²×C₄	1	4	yes	complemented
183	C₂⁴×C₁₀₉	C₂×D₄	1	4	yes	—
184	C₂⁴×C₁₀₉	#41	1	4	yes	—
185	C₂⁴×C₁₀₉	C₂⁴	1	2	yes	—
186	C₂⁴×C₁₀₉	C₂⁴	1	2	yes	—
187	C₂⁴×C₁₀₉	C₂⁴	1	1	yes	characteristic
188	C₂⁴×C₁₀₉	C₂⁴	1	1	yes	characteristic
189	C₂⁴×C₁₀₉	C₂⁴	1	1	yes	characteristic
190	C₂×D₄×C₁₀₉	—	2	32	no	—
191	C₂×D₄×C₁₀₉	—	2	32	no	—
192	C₂×D₄×C₁₀₉	—	2	4	no	—
193	C₂×D₄×C₁₀₉	—	2	4	no	—
194	C₂×D₄×C₁₀₉	—	2	4	no	—
195	C₂×D₄×C₁₀₉	—	2	4	no	—
196	C₂×D₄×C₁₀₉	—	2	4	no	—
197	C₂×D₄×C₁₀₉	—	2	4	no	—
198	C₂×D₄×C₁₀₉	—	2	4	no	—
199	C₂×D₄×C₁₀₉	—	2	4	no	—
200	C₂×D₄×C₁₀₉	—	4	4	no	—
201	C₂×D₄×C₁₀₉	—	4	4	no	—
202	C₂×D₄×C₁₀₉	C₂²×C₄	1	8	yes	—
203	C₂×D₄×C₁₀₉	C₂²×C₄	1	8	yes	—
204	C₂×D₄×C₁₀₉	C₂²×C₄	1	8	yes	—
205	C₂×D₄×C₁₀₉	C₂²×C₄	1	8	yes	complemented
206	C₂×D₄×C₁₀₉	C₂²×C₄	1	16	yes	complemented
207	C₂²×C₄×C₁₀₉	—	2	2	no	—
208	C₂²×C₄×C₁₀₉	—	2	2	no	—
209	C₂²×C₄×C₁₀₉	—	2	2	no	—
210	C₂²×C₄×C₁₀₉	—	2	2	no	—
211	C₂²×C₄×C₁₀₉	—	2	2	no	—
212	C₂²×C₄×C₁₀₉	—	2	4	no	—
213	C₂²×C₄×C₁₀₉	—	2	2	no	—
214	C₂²×C₄×C₁₀₉	—	2	4	no	—
215	C₂²×C₄×C₁₀₉	—	2	4	no	—
216	C₂²×C₄×C₁₀₉	—	2	2	no	—
217	C₂²×C₄×C₁₀₉	—	2	2	no	—
218	C₂²×C₄×C₁₀₉	—	2	4	no	—
219	C₂²×C₄×C₁₀₉	—	2	8	no	—
220	C₂²×C₄×C₁₀₉	—	2	4	no	—
221	C₂²×C₄×C₁₀₉	—	2	4	no	—
222	C₂²×C₄×C₁₀₉	—	2	8	no	—
223	C₂²×C₄×C₁₀₉	—	2	4	no	—
224	C₂²×C₄×C₁₀₉	—	2	4	no	—
225	C₂²×C₄×C₁₀₉	—	4	2	no	—
226	C₂²×C₄×C₁₀₉	—	4	2	no	—
227	C₂²×C₄×C₁₀₉	—	4	4	no	—
228	C₂²×C₄×C₁₀₉	—	4	2	no	—
229	C₂²×C₄×C₁₀₉	—	4	2	no	—
230	C₂²×C₄×C₁₀₉	—	4	2	no	—
231	C₂²×C₄×C₁₀₉	—	4	2	no	—
232	C₂²×C₄×C₁₀₉	—	4	2	no	—
233	C₂²×C₄×C₁₀₉	—	4	2	no	—
234	C₂²×C₄×C₁₀₉	—	4	2	no	—
235	C₂²×C₄×C₁₀₉	—	4	4	no	—
236	C₂²×C₄×C₁₀₉	—	4	4	no	—
237	C₂²×C₄×C₁₀₉	—	4	2	no	—
238	C₂²×C₄×C₁₀₉	—	4	2	no	—
239	C₂²×C₄×C₁₀₉	—	4	16	no	—
240	C₂²×C₄×C₁₀₉	—	4	16	no	—
241	C₂²×C₄×C₁₀₉	C₂²×C₄	1	4	yes	—
242	C₂²×C₄×C₁₀₉	C₂²×C₄	1	4	yes	complemented
243	C₂²×C₄×C₁₀₉	C₂²×C₄	1	8	yes	complemented
244	C₂²×C₄×C₁₀₉	C₂×D₄	1	4	yes	—
245	C₂²×C₄×C₁₀₉	C₂×D₄	1	4	yes	—
246	C₂²×C₄×C₁₀₉	C₂⁴	1	4	yes	—
247	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₁₀₉	C₂⁴	1	4	yes	—
251	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
256	C₄⋊C₄×C₁₀₉	—	2	8	no	—
257	C₄⋊C₄×C₁₀₉	—	2	4	no	—
258	C₄⋊C₄×C₁₀₉	—	2	4	no	—
259	C₄⋊C₄×C₁₀₉	—	2	8	no	—
260	C₄⋊C₄×C₁₀₉	—	4	4	no	—
261	C₄⋊C₄×C₁₀₉	C₂²×C₄	1	16	yes	complemented
262	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
263	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
264	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
265	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
266	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
267	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
268	C₂²⋊C₄×C₁₀₉	—	2	8	no	—
269	C₂²⋊C₄×C₁₀₉	—	2	8	no	—
270	C₂²⋊C₄×C₁₀₉	—	4	4	no	—
271	C₂²⋊C₄×C₁₀₉	—	4	4	no	—
272	C₂²⋊C₄×C₁₀₉	—	4	4	no	—
273	C₂²⋊C₄×C₁₀₉	C₂²×C₄	1	8	yes	—
274	C₂²⋊C₄×C₁₀₉	C₂²×C₄	1	8	yes	complemented
275	C₂²⋊C₄×C₁₀₉	C₂²×C₄	1	16	yes	complemented
276	C₂²⋊C₄×C₁₀₉	C₂²×C₄	1	16	yes	complemented
277	C₂²⋊C₄×C₁₀₉	C₂×D₄	1	8	yes	—
278	C₂²⋊C₄×C₁₀₉	C₂×D₄	1	8	yes	—
279	C₄²×C₁₀₉	—	2	8	no	—
280	C₄²×C₁₀₉	—	2	4	no	—
281	C₄²×C₁₀₉	—	2	4	no	—
282	C₄²×C₁₀₉	—	4	4	no	—
283	C₄²×C₁₀₉	—	4	4	no	—
284	C₂³×C₁₀₉	—	2	2	no	—
285	C₂³×C₁₀₉	—	2	2	no	—
286	C₂³×C₁₀₉	—	2	2	no	—
287	C₂³×C₁₀₉	—	2	2	no	—
288	C₂³×C₁₀₉	—	2	2	no	—
289	C₂³×C₁₀₉	—	2	2	no	—
290	C₂³×C₁₀₉	—	2	8	no	—
291	C₂³×C₁₀₉	—	2	2	no	—
292	C₂³×C₁₀₉	—	2	2	no	—
293	C₂³×C₁₀₉	—	2	2	no	—
294	C₂³×C₁₀₉	—	2	2	no	—
295	C₂³×C₁₀₉	—	2	4	no	—
296	C₂³×C₁₀₉	—	2	4	no	—
297	C₂³×C₁₀₉	—	2	4	no	—
298	C₂³×C₁₀₉	—	2	4	no	—
299	C₂³×C₁₀₉	—	2	8	no	—
300	C₂³×C₁₀₉	—	4	4	no	—
301	C₂³×C₁₀₉	—	4	8	no	—
302	C₂³×C₁₀₉	—	4	8	no	—
303	C₂³×C₁₀₉	—	4	4	no	—
304	C₂³×C₁₀₉	—	4	8	no	—
305	C₂³×C₁₀₉	—	4	8	no	—
306	C₂³×C₁₀₉	—	4	4	no	—
307	C₂³×C₁₀₉	—	4	4	no	—
308	C₂³×C₁₀₉	—	4	8	no	—
309	C₂³×C₁₀₉	—	8	2	no	—
310	C₂³×C₁₀₉	—	8	2	no	—
311	C₂³×C₁₀₉	—	8	4	no	—
312	C₂³×C₁₀₉	C₄×D₄	1	16	yes	complemented
313	C₂³×C₁₀₉	C₂³×C₄	1	4	yes	—
314	C₂³×C₁₀₉	C₂³×C₄	1	4	yes	—
315	C₂³×C₁₀₉	C₂³×C₄	1	2	yes	—
316	C₂³×C₁₀₉	C₂³×C₄	1	2	yes	—
317	C₂³×C₁₀₉	C₂³×C₄	1	2	yes	—
318	C₂³×C₁₀₉	C₂²×D₄	1	2	yes	—
319	C₂³×C₁₀₉	C₂²×D₄	1	2	yes	—
320	C₂³×C₁₀₉	C₂²×D₄	1	2	yes	—
321	C₂³×C₁₀₉	C₂×#41	1	2	yes	—
322	C₂³×C₁₀₉	C₂×#41	1	2	yes	—
323	C₂³×C₁₀₉	C₂×#41	1	2	yes	—
324	C₂³×C₁₀₉	C₂⁵	1	1	yes	characteristic
325	D₄×C₁₀₉	—	2	16	no	—
326	D₄×C₁₀₉	—	2	16	no	—
327	D₄×C₁₀₉	—	2	16	no	—
328	D₄×C₁₀₉	—	2	16	no	—
329	D₄×C₁₀₉	—	4	16	no	—
330	C₂×C₄×C₁₀₉	—	2	8	no	—
331	C₂×C₄×C₁₀₉	—	2	8	no	—
332	C₂×C₄×C₁₀₉	—	2	8	no	—
333	C₂×C₄×C₁₀₉	—	2	2	no	—
334	C₂×C₄×C₁₀₉	—	2	2	no	—
335	C₂×C₄×C₁₀₉	—	2	2	no	—
336	C₂×C₄×C₁₀₉	—	2	2	no	—
337	C₂×C₄×C₁₀₉	—	2	2	no	—
338	C₂×C₄×C₁₀₉	—	2	4	no	—
339	C₂×C₄×C₁₀₉	—	2	4	no	—
340	C₂×C₄×C₁₀₉	—	2	2	no	—
341	C₂×C₄×C₁₀₉	—	2	4	no	—
342	C₂×C₄×C₁₀₉	—	2	4	no	—
343	C₂×C₄×C₁₀₉	—	2	2	no	—
344	C₂×C₄×C₁₀₉	—	2	2	no	—
345	C₂×C₄×C₁₀₉	—	2	2	no	—
346	C₂×C₄×C₁₀₉	—	2	4	no	—
347	C₂×C₄×C₁₀₉	—	2	4	no	—
348	C₂×C₄×C₁₀₉	—	2	2	no	—
349	C₂×C₄×C₁₀₉	—	2	4	no	—
350	C₂×C₄×C₁₀₉	—	2	2	no	—
351	C₂×C₄×C₁₀₉	—	2	4	no	—
352	C₂×C₄×C₁₀₉	—	2	4	no	—
353	C₂×C₄×C₁₀₉	—	4	4	no	—
354	C₂×C₄×C₁₀₉	—	4	8	no	—
355	C₂×C₄×C₁₀₉	—	4	4	no	—
356	C₂×C₄×C₁₀₉	—	4	16	no	—
357	C₂×C₄×C₁₀₉	—	4	8	no	—
358	C₂×C₄×C₁₀₉	—	4	8	no	—
359	C₂×C₄×C₁₀₉	—	4	4	no	—
360	C₂×C₄×C₁₀₉	—	8	4	no	—
361	C₂×C₄×C₁₀₉	—	8	4	no	—
362	C₂×C₄×C₁₀₉	—	8	2	no	—
363	C₂×C₄×C₁₀₉	—	8	2	no	—
364	C₂×C₄×C₁₀₉	—	8	4	no	—
365	C₂×C₄×C₁₀₉	C₂³×C₄	1	8	yes	—
366	C₂×C₄×C₁₀₉	C₂³×C₄	1	4	yes	—
367	C₂×C₄×C₁₀₉	C₂³×C₄	1	4	yes	—
368	C₂×C₄×C₁₀₉	C₂²×D₄	1	4	yes	—
369	C₂×C₄×C₁₀₉	C₂²×D₄	1	4	yes	—
370	C₂×C₄×C₁₀₉	H(5,𝔽₂)	1	4	yes	—
371	C₂²×C₁₀₉	—	2	4	no	—
372	C₂²×C₁₀₉	—	2	4	no	—
373	C₂²×C₁₀₉	—	2	4	no	—
374	C₂²×C₁₀₉	—	2	2	no	—
375	C₂²×C₁₀₉	—	2	2	no	—
376	C₂²×C₁₀₉	—	2	2	no	—
377	C₂²×C₁₀₉	—	2	2	no	—
378	C₂²×C₁₀₉	—	2	2	no	—
379	C₂²×C₁₀₉	—	2	2	no	—
380	C₂²×C₁₀₉	—	2	4	no	—
381	C₂²×C₁₀₉	—	2	4	no	—
382	C₂²×C₁₀₉	—	2	4	no	—
383	C₂²×C₁₀₉	—	2	4	no	—
384	C₂²×C₁₀₉	—	2	4	no	—
385	C₂²×C₁₀₉	—	2	8	no	—
386	C₂²×C₁₀₉	—	2	8	no	—
387	C₂²×C₁₀₉	—	4	16	no	—
388	C₂²×C₁₀₉	—	4	16	no	—
389	C₂²×C₁₀₉	—	4	2	no	—
390	C₂²×C₁₀₉	—	4	2	no	—
391	C₂²×C₁₀₉	—	4	2	no	—
392	C₂²×C₁₀₉	—	4	2	no	—
393	C₂²×C₁₀₉	—	4	4	no	—
394	C₂²×C₁₀₉	—	4	4	no	—
395	C₂²×C₁₀₉	—	8	8	no	—
396	C₂²×C₁₀₉	C₂×C₄×D₄	1	4	yes	—
397	C₂²×C₁₀₉	C₂×C₄×D₄	1	4	yes	—
398	C₂²×C₁₀₉	C₂×C₄×D₄	1	4	yes	—
399	C₂²×C₁₀₉	C₂⁴×C₄	1	1	yes	characteristic
400	C₂²×C₁₀₉	C₂³×D₄	1	1	yes	characteristic
401	C₂²×C₁₀₉	C₂²×#41	1	1	yes	characteristic
402	C₂²×C₁₀₉	C₂×H(5,𝔽₂)	1	2	yes	—
403	C₂²×C₁₀₉	#585	1	2	yes	—
404	C₄×C₁₀₉	—	2	4	no	—
405	C₄×C₁₀₉	—	2	4	no	—
406	C₄×C₁₀₉	—	2	8	no	—
407	C₄×C₁₀₉	—	2	4	no	—
408	C₄×C₁₀₉	—	2	4	no	—
409	C₄×C₁₀₉	—	2	4	no	—
410	C₄×C₁₀₉	—	4	2	no	—
411	C₄×C₁₀₉	—	4	2	no	—
412	C₄×C₁₀₉	—	4	2	no	—
413	C₄×C₁₀₉	—	4	4	no	—
414	#34264	C₁₀₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
415	C₂×C₁₀₉	—	2	4	no	—
416	C₂×C₁₀₉	—	2	4	no	—
417	C₂×C₁₀₉	—	2	4	no	—
418	C₂×C₁₀₉	—	4	4	no	—
419	C₂×C₁₀₉	—	4	4	no	—
420	C₂×C₁₀₉	C₂²×C₄×D₄	1	1	yes	characteristic
421	C₂×C₁₀₉	C₄×H(5,𝔽₂)	1	2	yes	—
422	C₂×C₁₀₉	#3484	1	1	yes	characteristic
423	C₂×C₁₀₉	#3485	1	1	yes	characteristic
424	C₂×C₁₀₉	#3505	1	2	yes	—
425	C₂×#534	C₂×C₁₀₉	1	1	yes	characteristic
426	C₂×#518	C₂×C₁₀₉	1	1	yes	characteristic, complemented
427	C₂²×C₄×D₄	C₂×C₁₀₉	1	1	yes	characteristic, complemented
428	#2364	C₂×C₁₀₉	1	4	yes	complemented
429	#2361	C₂×C₁₀₉	1	4	yes	complemented
430	#2359	C₂×C₁₀₉	1	4	yes	complemented
431	#2358	C₂×C₁₀₉	1	4	yes	complemented
432	#2322	C₂×C₁₀₉	1	2	yes	complemented
433	#2321	C₂×C₁₀₉	1	2	yes	complemented
434	#2308	C₂×C₁₀₉	1	1	yes	characteristic, complemented
435	C₄×#123	C₂×C₁₀₉	1	2	yes	complemented
436	C₄×#120	C₂×C₁₀₉	1	2	yes	complemented
437	C₂×#386	C₂×C₁₀₉	1	1	yes	characteristic, complemented
438	C₂×#385	C₂×C₁₀₉	1	1	yes	characteristic, complemented
439	#2273	C₂×C₁₀₉	1	1	yes	characteristic, complemented
440	C₁₀₉	#34264	1	1	yes	characteristic, direct product factor, Sylow
441	C₂³×D₄	C₂²×C₁₀₉	1	1	yes	characteristic
442	C₂³×D₄	C₂²×C₁₀₉	1	1	yes	characteristic
443	C₂⁴×C₄	C₂²×C₁₀₉	1	1	yes	characteristic
444	C₂⁴×C₄	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
445	#534	C₄×C₁₀₉	1	16	yes	complemented
446	C₂×#123	C₂²×C₁₀₉	1	2	yes	—
447	C₂×#123	C₂²×C₁₀₉	1	2	yes	—
448	C₂×#121	C₂²×C₁₀₉	1	4	yes	—
449	C₂×#120	C₂²×C₁₀₉	1	2	yes	—
450	C₂×#120	C₂²×C₁₀₉	1	2	yes	—
451	#518	—	2	8	no	—
452	C₂×C₄×D₄	—	2	8	no	—
453	C₂×C₄×D₄	C₂²×C₁₀₉	1	2	yes	—
454	C₂×C₄×D₄	C₂²×C₁₀₉	1	2	yes	—
455	C₂×C₄×D₄	C₂²×C₁₀₉	1	4	yes	—
456	C₂×C₄×D₄	C₂²×C₁₀₉	1	2	yes	complemented
457	C₂×C₄×D₄	C₂²×C₁₀₉	1	4	yes	complemented
458	C₂×C₄×D₄	C₂²×C₁₀₉	1	2	yes	complemented
459	C₂×C₄×D₄	C₂²×C₁₀₉	1	4	yes	complemented
460	C₂×#117	C₂²×C₁₀₉	1	2	yes	complemented
461	C₂²×C₄⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
462	C₂²×C₄⋊C₄	C₂²×C₁₀₉	1	2	yes	complemented
463	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
464	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
465	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
466	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
467	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
468	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	2	yes	complemented
469	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	2	yes	complemented
470	C₂²×C₄²	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
471	#390	C₂²×C₁₀₉	1	4	yes	complemented
472	#389	C₂²×C₁₀₉	1	4	yes	complemented
473	#388	C₂²×C₁₀₉	1	4	yes	complemented
474	#388	C₂²×C₁₀₉	1	4	yes	complemented
475	#388	C₂²×C₁₀₉	1	4	yes	complemented
476	#388	C₂²×C₁₀₉	1	4	yes	complemented
477	#387	C₂²×C₁₀₉	1	4	yes	complemented
478	#387	C₂²×C₁₀₉	1	4	yes	complemented
479	#386	C₂²×C₁₀₉	1	4	yes	—
480	#386	C₂²×C₁₀₉	1	2	yes	—
481	#386	C₂²×C₁₀₉	1	2	yes	—
482	#386	C₂²×C₁₀₉	1	2	yes	complemented
483	#386	C₂²×C₁₀₉	1	2	yes	complemented
484	#386	C₂²×C₁₀₉	1	4	yes	complemented
485	#386	C₂²×C₁₀₉	1	4	yes	complemented
486	#386	C₂²×C₁₀₉	1	4	yes	complemented
487	#385	C₂²×C₁₀₉	1	2	yes	complemented
488	#385	C₂²×C₁₀₉	1	4	yes	complemented
489	#385	C₂²×C₁₀₉	1	4	yes	complemented
490	#385	C₂²×C₁₀₉	1	4	yes	complemented
491	#385	C₂²×C₁₀₉	1	2	yes	complemented
492	#381	C₂²×C₁₀₉	1	2	yes	complemented
493	#379	C₂²×C₁₀₉	1	2	yes	complemented
494	C₄×C₄⋊C₄	C₂²×C₁₀₉	1	4	yes	complemented
495	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	2	yes	complemented
496	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	2	yes	complemented
497	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	4	yes	complemented
498	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	4	yes	complemented
499	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	4	yes	complemented
500	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	4	yes	complemented
501	C₂×#95	C₂²×C₁₀₉	1	2	yes	complemented
502	C₂×#95	C₂²×C₁₀₉	1	2	yes	complemented
503	C₂⁵	C₂³×C₁₀₉	1	1	yes	characteristic
504	C₂⁵	C₂³×C₁₀₉	1	1	yes	characteristic
505	C₂⁵	C₂³×C₁₀₉	1	1	yes	characteristic
506	C₂²×D₄	—	2	4	no	—
507	C₂²×D₄	—	2	4	no	—
508	C₂²×D₄	—	2	4	no	—
509	C₂²×D₄	—	2	4	no	—
510	C₂²×D₄	C₂×C₄×C₁₀₉	1	8	yes	complemented
511	C₂²×D₄	C₂×C₄×C₁₀₉	1	8	yes	complemented
512	C₂²×D₄	C₂³×C₁₀₉	1	2	yes	—
513	C₂²×D₄	C₂³×C₁₀₉	1	2	yes	—
514	C₂²×D₄	C₂³×C₁₀₉	1	2	yes	—
515	C₂²×D₄	C₂³×C₁₀₉	1	2	yes	—
516	C₂²×D₄	C₂³×C₁₀₉	1	4	yes	—
517	C₂³×C₄	—	2	4	no	—
518	C₂³×C₄	—	2	4	no	—
519	C₂³×C₄	—	4	4	no	—
520	C₂³×C₄	—	4	4	no	—
521	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
522	C₂³×C₄	C₂³×C₁₀₉	1	2	yes	—
523	C₂³×C₄	C₂³×C₁₀₉	1	2	yes	—
524	C₂³×C₄	C₂³×C₁₀₉	1	4	yes	—
525	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
526	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
527	C₂³×C₄	C₂³×C₁₀₉	1	2	yes	—
528	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
529	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
530	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
531	C₂³×C₄	C₂³×C₁₀₉	1	2	yes	—
532	C₂³×C₄	C₂³×C₁₀₉	1	2	yes	—
533	C₂³×C₄	C₂³×C₁₀₉	1	2	yes	—
534	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
535	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
536	#123	C₂×C₄×C₁₀₉	1	16	yes	complemented
537	#123	C₂×C₄×C₁₀₉	1	16	yes	complemented
538	#121	C₂×C₄×C₁₀₉	1	32	yes	complemented
539	#120	C₂×C₄×C₁₀₉	1	16	yes	complemented
540	#120	C₂×C₄×C₁₀₉	1	16	yes	complemented
541	C₄×D₄	—	2	8	no	—
542	C₄×D₄	—	2	8	no	—
543	C₄×D₄	—	2	16	no	—
544	C₄×D₄	—	2	16	no	—
545	C₄×D₄	—	2	8	no	—
546	C₄×D₄	—	2	8	no	—
547	C₄×D₄	—	4	8	no	—
548	#117	—	2	8	no	—
549	C₂×C₄⋊C₄	—	2	4	no	—
550	C₂×C₄⋊C₄	—	4	4	no	—
551	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	4	yes	—
552	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	4	yes	—
553	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
554	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	4	yes	—
556	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	4	yes	—
557	C₂×C₂²⋊C₄	—	2	4	no	—
558	C₂×C₂²⋊C₄	—	2	4	no	—
559	C₂×C₂²⋊C₄	—	2	4	no	—
560	C₂×C₂²⋊C₄	—	2	8	no	—
561	C₂×C₂²⋊C₄	—	4	4	no	—
562	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₉	1	8	yes	complemented
563	C₂×C₂²⋊C₄	D₄×C₁₀₉	1	8	yes	complemented
564	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
581	C₂×C₄²	—	2	4	no	—
582	C₂×C₄²	C₂³×C₁₀₉	1	2	yes	—
583	C₂×C₄²	C₂³×C₁₀₉	1	2	yes	—
584	C₂×C₄²	C₂³×C₁₀₉	1	4	yes	—
585	C₂×C₄²	C₂³×C₁₀₉	1	4	yes	—
586	C₂×C₄²	C₂³×C₁₀₉	1	4	yes	—
587	#95	C₂³×C₁₀₉	1	4	yes	—
588	#95	C₂³×C₁₀₉	1	4	yes	—
589	#95	C₂³×C₁₀₉	1	4	yes	—
590	#95	C₂³×C₁₀₉	1	4	yes	—
591	#95	C₂³×C₁₀₉	1	4	yes	—
592	#95	C₂³×C₁₀₉	1	4	yes	—
593	#95	C₂³×C₁₀₉	1	4	yes	—
594	#95	C₂³×C₁₀₉	1	4	yes	—
595	C₂⁴	—	2	2	no	—
596	C₂⁴	—	2	2	no	—
597	C₂⁴	—	2	2	no	—
598	C₂⁴	—	2	2	no	—
599	C₂⁴	—	4	2	no	—
600	C₂⁴	—	4	2	no	—
601	C₂⁴	—	4	2	no	—
602	C₂⁴	—	4	2	no	—
603	C₂⁴	—	4	2	no	—
604	C₂⁴	—	4	2	no	—
605	C₂⁴	C₂²×C₄×C₁₀₉	1	4	yes	—
606	C₂⁴	C₂²×C₄×C₁₀₉	1	4	yes	—
607	C₂⁴	C₂²×C₄×C₁₀₉	1	4	yes	complemented
608	C₂⁴	C₂×D₄×C₁₀₉	1	4	yes	—
609	C₂⁴	#41×C₁₀₉	1	4	yes	—
610	C₂⁴	C₂⁴×C₁₀₉	1	2	yes	—
611	C₂⁴	C₂⁴×C₁₀₉	1	2	yes	—
612	C₂⁴	C₂⁴×C₁₀₉	1	1	yes	characteristic
613	C₂⁴	C₂⁴×C₁₀₉	1	1	yes	characteristic
614	C₂⁴	C₂⁴×C₁₀₉	1	1	yes	characteristic
615	C₂×D₄	—	2	32	no	—
616	C₂×D₄	—	2	32	no	—
617	C₂×D₄	—	2	4	no	—
618	C₂×D₄	—	2	4	no	—
619	C₂×D₄	—	2	4	no	—
620	C₂×D₄	—	2	4	no	—
621	C₂×D₄	—	2	4	no	—
622	C₂×D₄	—	2	4	no	—
623	C₂×D₄	—	2	4	no	—
624	C₂×D₄	—	2	4	no	—
625	C₂×D₄	—	4	4	no	—
626	C₂×D₄	—	4	4	no	—
627	C₂×D₄	C₂²×C₄×C₁₀₉	1	8	yes	—
628	C₂×D₄	C₂²×C₄×C₁₀₉	1	8	yes	—
629	C₂×D₄	C₂²×C₄×C₁₀₉	1	8	yes	—
630	C₂×D₄	C₂²×C₄×C₁₀₉	1	8	yes	complemented
631	C₂×D₄	C₂²×C₄×C₁₀₉	1	16	yes	complemented
632	C₂²×C₄	—	2	2	no	—
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	2	2	no	—
636	C₂²×C₄	—	2	2	no	—
637	C₂²×C₄	—	2	4	no	—
638	C₂²×C₄	—	2	2	no	—
639	C₂²×C₄	—	2	4	no	—
640	C₂²×C₄	—	2	4	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	2	4	no	—
644	C₂²×C₄	—	2	8	no	—
645	C₂²×C₄	—	2	4	no	—
646	C₂²×C₄	—	2	4	no	—
647	C₂²×C₄	—	2	8	no	—
648	C₂²×C₄	—	2	4	no	—
649	C₂²×C₄	—	2	4	no	—
650	C₂²×C₄	—	4	2	no	—
651	C₂²×C₄	—	4	2	no	—
652	C₂²×C₄	—	4	4	no	—
653	C₂²×C₄	—	4	2	no	—
654	C₂²×C₄	—	4	2	no	—
655	C₂²×C₄	—	4	2	no	—
656	C₂²×C₄	—	4	2	no	—
657	C₂²×C₄	—	4	2	no	—
658	C₂²×C₄	—	4	2	no	—
659	C₂²×C₄	—	4	2	no	—
660	C₂²×C₄	—	4	4	no	—
661	C₂²×C₄	—	4	4	no	—
662	C₂²×C₄	—	4	2	no	—
663	C₂²×C₄	—	4	2	no	—
664	C₂²×C₄	—	4	16	no	—
665	C₂²×C₄	—	4	16	no	—
666	C₂²×C₄	C₂²×C₄×C₁₀₉	1	4	yes	—
667	C₂²×C₄	C₂²×C₄×C₁₀₉	1	4	yes	complemented
668	C₂²×C₄	C₂²×C₄×C₁₀₉	1	8	yes	complemented
669	C₂²×C₄	C₂×D₄×C₁₀₉	1	4	yes	—
670	C₂²×C₄	C₂×D₄×C₁₀₉	1	4	yes	—
671	C₂²×C₄	C₂⁴×C₁₀₉	1	4	yes	—
672	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
673	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
674	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
675	C₂²×C₄	C₂⁴×C₁₀₉	1	4	yes	—
676	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
677	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
678	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
680	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
681	C₄⋊C₄	—	2	8	no	—
682	C₄⋊C₄	—	2	4	no	—
683	C₄⋊C₄	—	2	4	no	—
684	C₄⋊C₄	—	2	8	no	—
685	C₄⋊C₄	—	4	4	no	—
686	C₄⋊C₄	C₂²×C₄×C₁₀₉	1	16	yes	complemented
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	4	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	4	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	—	2	8	no	—
694	C₂²⋊C₄	—	2	8	no	—
695	C₂²⋊C₄	—	4	4	no	—
696	C₂²⋊C₄	—	4	4	no	—
697	C₂²⋊C₄	—	4	4	no	—
698	C₂²⋊C₄	C₂²×C₄×C₁₀₉	1	8	yes	—
699	C₂²⋊C₄	C₂²×C₄×C₁₀₉	1	8	yes	complemented
700	C₂²⋊C₄	C₂²×C₄×C₁₀₉	1	16	yes	complemented
701	C₂²⋊C₄	C₂²×C₄×C₁₀₉	1	16	yes	complemented
702	C₂²⋊C₄	C₂×D₄×C₁₀₉	1	8	yes	—
703	C₂²⋊C₄	C₂×D₄×C₁₀₉	1	8	yes	—
704	C₄²	—	2	8	no	—
705	C₄²	—	2	4	no	—
706	C₄²	—	2	4	no	—
707	C₄²	—	4	4	no	—
708	C₄²	—	4	4	no	—
709	C₂³	—	2	2	no	—
710	C₂³	—	2	2	no	—
711	C₂³	—	2	2	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	2	2	no	—
714	C₂³	—	2	2	no	—
715	C₂³	—	2	8	no	—
716	C₂³	—	2	2	no	—
717	C₂³	—	2	2	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	2	2	no	—
720	C₂³	—	2	4	no	—
721	C₂³	—	2	4	no	—
722	C₂³	—	2	4	no	—
723	C₂³	—	2	4	no	—
724	C₂³	—	2	8	no	—
725	C₂³	—	4	4	no	—
726	C₂³	—	4	8	no	—
727	C₂³	—	4	8	no	—
728	C₂³	—	4	4	no	—
729	C₂³	—	4	8	no	—
730	C₂³	—	4	8	no	—
731	C₂³	—	4	4	no	—
732	C₂³	—	4	4	no	—
733	C₂³	—	4	8	no	—
734	C₂³	—	8	2	no	—
735	C₂³	—	8	2	no	—
736	C₂³	—	8	4	no	—
737	C₂³	C₄×D₄×C₁₀₉	1	16	yes	complemented
738	C₂³	C₂³×C₄×C₁₀₉	1	4	yes	—
739	C₂³	C₂³×C₄×C₁₀₉	1	4	yes	—
740	C₂³	C₂³×C₄×C₁₀₉	1	2	yes	—
741	C₂³	C₂³×C₄×C₁₀₉	1	2	yes	—
742	C₂³	C₂³×C₄×C₁₀₉	1	2	yes	—
743	C₂³	C₂²×D₄×C₁₀₉	1	2	yes	—
744	C₂³	C₂²×D₄×C₁₀₉	1	2	yes	—
745	C₂³	C₂²×D₄×C₁₀₉	1	2	yes	—
746	C₂³	C₂×#41×C₁₀₉	1	2	yes	—
747	C₂³	C₂×#41×C₁₀₉	1	2	yes	—
748	C₂³	C₂×#41×C₁₀₉	1	2	yes	—
749	C₂³	C₂⁵×C₁₀₉	1	1	yes	characteristic
750	D₄	—	2	16	no	—
751	D₄	—	2	16	no	—
752	D₄	—	2	16	no	—
753	D₄	—	2	16	no	—
754	D₄	—	4	16	no	—
755	C₂×C₄	—	2	8	no	—
756	C₂×C₄	—	2	8	no	—
757	C₂×C₄	—	2	8	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	4	no	—
764	C₂×C₄	—	2	4	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	4	no	—
767	C₂×C₄	—	2	4	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	4	no	—
772	C₂×C₄	—	2	4	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	4	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	4	no	—
777	C₂×C₄	—	2	4	no	—
778	C₂×C₄	—	4	4	no	—
779	C₂×C₄	—	4	8	no	—
780	C₂×C₄	—	4	4	no	—
781	C₂×C₄	—	4	16	no	—
782	C₂×C₄	—	4	8	no	—
783	C₂×C₄	—	4	8	no	—
784	C₂×C₄	—	4	4	no	—
785	C₂×C₄	—	8	4	no	—
786	C₂×C₄	—	8	4	no	—
787	C₂×C₄	—	8	2	no	—
788	C₂×C₄	—	8	2	no	—
789	C₂×C₄	—	8	4	no	—
790	C₂×C₄	C₂³×C₄×C₁₀₉	1	8	yes	—
791	C₂×C₄	C₂³×C₄×C₁₀₉	1	4	yes	—
792	C₂×C₄	C₂³×C₄×C₁₀₉	1	4	yes	—
793	C₂×C₄	C₂²×D₄×C₁₀₉	1	4	yes	—
794	C₂×C₄	C₂²×D₄×C₁₀₉	1	4	yes	—
795	C₂×C₄	H(5,𝔽₂)×C₁₀₉	1	4	yes	—
796	C₂²	—	2	2	no	—
797	C₂²	—	2	2	no	—
798	C₂²	—	2	2	no	—
799	C₂²	—	2	2	no	—
800	C₂²	—	2	2	no	—
801	C₂²	—	2	2	no	—
802	C₂²	—	2	4	no	—
803	C₂²	—	2	4	no	—
804	C₂²	—	2	4	no	—
805	C₂²	—	2	4	no	—
806	C₂²	—	2	4	no	—
807	C₂²	—	2	4	no	—
808	C₂²	—	2	4	no	—
809	C₂²	—	2	4	no	—
810	C₂²	—	2	8	no	—
811	C₂²	—	2	8	no	—
812	C₂²	—	4	16	no	—
813	C₂²	—	4	16	no	—
814	C₂²	—	4	2	no	—
815	C₂²	—	4	2	no	—
816	C₂²	—	4	2	no	—
817	C₂²	—	4	2	no	—
818	C₂²	—	4	4	no	—
819	C₂²	—	4	4	no	—
820	C₂²	—	8	8	no	—
821	C₂²	C₂×C₄×D₄×C₁₀₉	1	4	yes	—
822	C₂²	C₂×C₄×D₄×C₁₀₉	1	4	yes	—
823	C₂²	C₂×C₄×D₄×C₁₀₉	1	4	yes	—
824	C₂²	C₂⁴×C₄×C₁₀₉	1	1	yes	characteristic
825	C₂²	C₂³×D₄×C₁₀₉	1	1	yes	characteristic
826	C₂²	C₂²×#41×C₁₀₉	1	1	yes	characteristic
827	C₂²	C₂×H(5,𝔽₂)×C₁₀₉	1	2	yes	—
828	C₂²	#585×C₁₀₉	1	2	yes	—
829	C₄	—	2	4	no	—
830	C₄	—	2	4	no	—
831	C₄	—	2	4	no	—
832	C₄	—	2	4	no	—
833	C₄	—	2	4	no	—
834	C₄	—	2	8	no	—
835	C₄	—	4	2	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	4	no	—
839	C₂	—	2	4	no	—
840	C₂	—	2	4	no	—
841	C₂	—	2	4	no	—
842	C₂	—	4	4	no	—
843	C₂	—	4	4	no	—
844	C₂	C₂²×C₄×D₄×C₁₀₉	1	1	yes	characteristic
845	C₂	C₄×H(5,𝔽₂)×C₁₀₉	1	2	yes	—
846	C₂	C₁₀₉×#3484	1	1	yes	characteristic
847	C₂	C₁₀₉×#3485	1	1	yes	characteristic
848	C₂	C₁₀₉×#3505	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₀₉	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₀₉
Frattini, cosocle	C₂³	C₂⁵×C₁₀₉
prime radical	C₂×#534×C₁₀₉	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#518×C₁₀₉	C₂	semidirect
3. C₂²×C₄×D₄×C₁₀₉	C₂	semidirect
4. C₁₀₉×#2364	C₂	semidirect
5. C₁₀₉×#2361	C₂	semidirect
6. C₁₀₉×#2359	C₂	semidirect
7. C₁₀₉×#2358	C₂	semidirect
8. C₁₀₉×#2322	C₂	semidirect
9. C₁₀₉×#2321	C₂	semidirect
10. C₁₀₉×#2308	C₂	semidirect
11. C₄×#123×C₁₀₉	C₂	semidirect
12. C₄×#120×C₁₀₉	C₂	semidirect
13. C₂×#386×C₁₀₉	C₂	semidirect
14. C₂×#385×C₁₀₉	C₂	semidirect
15. C₁₀₉×#2273	C₂	semidirect
19. C₂⁴×C₄×C₁₀₉	C₂²	semidirect
20. #534×C₁₀₉	C₄	semidirect
31. C₂×C₄×D₄×C₁₀₉	C₂²	semidirect
32. C₂×C₄×D₄×C₁₀₉	C₂²	semidirect
33. C₂×C₄×D₄×C₁₀₉	C₂²	semidirect
34. C₂×C₄×D₄×C₁₀₉	C₂²	semidirect
35. C₂×#117×C₁₀₉	C₂²	semidirect
36. C₂²×C₄⋊C₄×C₁₀₉	C₂²	semidirect
37. C₂²×C₄⋊C₄×C₁₀₉	C₂²	semidirect
42. C₂²×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
43. C₂²×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
44. C₂²×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
45. C₂²×C₄²×C₁₀₉	C₂²	semidirect
46. #390×C₁₀₉	C₂²	semidirect
47. #389×C₁₀₉	C₂²	semidirect
48. #388×C₁₀₉	C₂²	semidirect
49. #388×C₁₀₉	C₂²	semidirect
50. #388×C₁₀₉	C₂²	semidirect
51. #388×C₁₀₉	C₂²	semidirect
52. #387×C₁₀₉	C₂²	semidirect
53. #387×C₁₀₉	C₂²	semidirect
57. #386×C₁₀₉	C₂²	semidirect
58. #386×C₁₀₉	C₂²	semidirect
59. #386×C₁₀₉	C₂²	semidirect
60. #386×C₁₀₉	C₂²	semidirect
61. #386×C₁₀₉	C₂²	semidirect
62. #385×C₁₀₉	C₂²	semidirect
63. #385×C₁₀₉	C₂²	semidirect
64. #385×C₁₀₉	C₂²	semidirect
65. #385×C₁₀₉	C₂²	semidirect
66. #385×C₁₀₉	C₂²	semidirect
67. #381×C₁₀₉	C₂²	semidirect
68. #379×C₁₀₉	C₂²	semidirect
69. C₄×C₄⋊C₄×C₁₀₉	C₂²	semidirect
70. C₄×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
71. C₄×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
72. C₄×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
73. C₄×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
74. C₄×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
75. C₄×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
76. C₂×#95×C₁₀₉	C₂²	semidirect
77. C₂×#95×C₁₀₉	C₂²	semidirect
85. C₂²×D₄×C₁₀₉	C₂×C₄	semidirect
86. C₂²×D₄×C₁₀₉	C₂×C₄	semidirect
111. #123×C₁₀₉	C₂×C₄	semidirect
112. #123×C₁₀₉	C₂×C₄	semidirect
113. #121×C₁₀₉	C₂×C₄	semidirect
114. #120×C₁₀₉	C₂×C₄	semidirect
115. #120×C₁₀₉	C₂×C₄	semidirect
137. C₂×C₂²⋊C₄×C₁₀₉	C₂×C₄	semidirect
138. C₂×C₂²⋊C₄×C₁₀₉	D₄	semidirect
182. C₂⁴×C₁₀₉	C₂²×C₄	semidirect
205. C₂×D₄×C₁₀₉	C₂²×C₄	semidirect
206. C₂×D₄×C₁₀₉	C₂²×C₄	semidirect
242. C₂²×C₄×C₁₀₉	C₂²×C₄	semidirect
243. C₂²×C₄×C₁₀₉	C₂²×C₄	semidirect
261. C₄⋊C₄×C₁₀₉	C₂²×C₄	semidirect
274. C₂²⋊C₄×C₁₀₉	C₂²×C₄	semidirect
275. C₂²⋊C₄×C₁₀₉	C₂²×C₄	semidirect
276. C₂²⋊C₄×C₁₀₉	C₂²×C₄	semidirect
312. C₂³×C₁₀₉	C₄×D₄	semidirect
414. #34264	C₁₀₉	direct (N × H)
426. C₂×#518	C₂×C₁₀₉	semidirect
427. C₂²×C₄×D₄	C₂×C₁₀₉	semidirect
428. #2364	C₂×C₁₀₉	semidirect
429. #2361	C₂×C₁₀₉	semidirect
430. #2359	C₂×C₁₀₉	semidirect
431. #2358	C₂×C₁₀₉	semidirect
432. #2322	C₂×C₁₀₉	semidirect
433. #2321	C₂×C₁₀₉	semidirect
434. #2308	C₂×C₁₀₉	semidirect
435. C₄×#123	C₂×C₁₀₉	semidirect
436. C₄×#120	C₂×C₁₀₉	semidirect
437. C₂×#386	C₂×C₁₀₉	semidirect
438. C₂×#385	C₂×C₁₀₉	semidirect
439. #2273	C₂×C₁₀₉	semidirect
440. C₁₀₉	#34264	direct (N × H)
444. C₂⁴×C₄	C₂²×C₁₀₉	semidirect
445. #534	C₄×C₁₀₉	semidirect
456. C₂×C₄×D₄	C₂²×C₁₀₉	semidirect
457. C₂×C₄×D₄	C₂²×C₁₀₉	semidirect
458. C₂×C₄×D₄	C₂²×C₁₀₉	semidirect
459. C₂×C₄×D₄	C₂²×C₁₀₉	semidirect
460. C₂×#117	C₂²×C₁₀₉	semidirect
461. C₂²×C₄⋊C₄	C₂²×C₁₀₉	semidirect
462. C₂²×C₄⋊C₄	C₂²×C₁₀₉	semidirect
467. C₂²×C₂²⋊C₄	C₂²×C₁₀₉	semidirect
468. C₂²×C₂²⋊C₄	C₂²×C₁₀₉	semidirect
469. C₂²×C₂²⋊C₄	C₂²×C₁₀₉	semidirect
470. C₂²×C₄²	C₂²×C₁₀₉	semidirect
471. #390	C₂²×C₁₀₉	semidirect
472. #389	C₂²×C₁₀₉	semidirect
473. #388	C₂²×C₁₀₉	semidirect
474. #388	C₂²×C₁₀₉	semidirect
475. #388	C₂²×C₁₀₉	semidirect
476. #388	C₂²×C₁₀₉	semidirect
477. #387	C₂²×C₁₀₉	semidirect
478. #387	C₂²×C₁₀₉	semidirect
482. #386	C₂²×C₁₀₉	semidirect
483. #386	C₂²×C₁₀₉	semidirect
484. #386	C₂²×C₁₀₉	semidirect
485. #386	C₂²×C₁₀₉	semidirect
486. #386	C₂²×C₁₀₉	semidirect
487. #385	C₂²×C₁₀₉	semidirect
488. #385	C₂²×C₁₀₉	semidirect
489. #385	C₂²×C₁₀₉	semidirect
490. #385	C₂²×C₁₀₉	semidirect
491. #385	C₂²×C₁₀₉	semidirect
492. #381	C₂²×C₁₀₉	semidirect
493. #379	C₂²×C₁₀₉	semidirect
494. C₄×C₄⋊C₄	C₂²×C₁₀₉	semidirect
495. C₄×C₂²⋊C₄	C₂²×C₁₀₉	semidirect
496. C₄×C₂²⋊C₄	C₂²×C₁₀₉	semidirect
497. C₄×C₂²⋊C₄	C₂²×C₁₀₉	semidirect
498. C₄×C₂²⋊C₄	C₂²×C₁₀₉	semidirect
499. C₄×C₂²⋊C₄	C₂²×C₁₀₉	semidirect
500. C₄×C₂²⋊C₄	C₂²×C₁₀₉	semidirect
501. C₂×#95	C₂²×C₁₀₉	semidirect
502. C₂×#95	C₂²×C₁₀₉	semidirect
510. C₂²×D₄	C₂×C₄×C₁₀₉	semidirect
511. C₂²×D₄	C₂×C₄×C₁₀₉	semidirect
536. #123	C₂×C₄×C₁₀₉	semidirect
537. #123	C₂×C₄×C₁₀₉	semidirect
538. #121	C₂×C₄×C₁₀₉	semidirect
539. #120	C₂×C₄×C₁₀₉	semidirect
540. #120	C₂×C₄×C₁₀₉	semidirect
562. C₂×C₂²⋊C₄	C₂×C₄×C₁₀₉	semidirect
563. C₂×C₂²⋊C₄	D₄×C₁₀₉	semidirect
607. C₂⁴	C₂²×C₄×C₁₀₉	semidirect
630. C₂×D₄	C₂²×C₄×C₁₀₉	semidirect
631. C₂×D₄	C₂²×C₄×C₁₀₉	semidirect
667. C₂²×C₄	C₂²×C₄×C₁₀₉	semidirect
668. C₂²×C₄	C₂²×C₄×C₁₀₉	semidirect
686. C₄⋊C₄	C₂²×C₄×C₁₀₉	semidirect
699. C₂²⋊C₄	C₂²×C₄×C₁₀₉	semidirect
700. C₂²⋊C₄	C₂²×C₄×C₁₀₉	semidirect
701. C₂²⋊C₄	C₂²×C₄×C₁₀₉	semidirect
737. C₂³	C₄×D₄×C₁₀₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#534×C₁₀₉	2
C₂×#518×C₁₀₉	2
C₂²×C₄×D₄×C₁₀₉	2
C₁₀₉×#2364	2
C₁₀₉×#2361	2
C₁₀₉×#2359	2
C₁₀₉×#2358	2
C₁₀₉×#2322	2
C₁₀₉×#2321	2
C₁₀₉×#2308	2
C₄×#123×C₁₀₉	2
C₄×#120×C₁₀₉	2
C₂×#386×C₁₀₉	2
C₂×#385×C₁₀₉	2
C₁₀₉×#2273	2
#34264	109

Subgroups — C109×#34264 #42152258

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₉×#34264 #42152258