Subgroups — C₂×C₁₀₉×#2472 #42152652

Order 27904.

4946 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#124×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂²⋊Q₈×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#120×C₁₀₉	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₂²⋊C₄×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₉×#2472	C₂	1	16	yes	maximal, direct product factor
6	C₂×#397×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#394×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#394×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#393×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#390×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#388×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#388×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#386×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#386×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#379×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×C₂²⋊C₄×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂⁶×C₁₀₉	C₂²	1	1	yes	characteristic
18	C₂³×Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
19	C₂³×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
20	C₂³×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
21	C₂³×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
22	C₂⁴×C₄×C₁₀₉	C₂²	1	1	yes	characteristic
23	C₂⁴×C₄×C₁₀₉	C₂²	1	1	yes	characteristic
24	C₂×#124×C₁₀₉	—	2	8	no	—
25	C₂×#124×C₁₀₉	C₂²	1	8	yes	complemented
26	C₂×C₂²⋊Q₈×C₁₀₉	—	2	8	no	—
27	C₂×C₂²⋊Q₈×C₁₀₉	C₂²	1	8	yes	complemented
28	C₂×#120×C₁₀₉	—	2	8	no	—
29	C₂×#120×C₁₀₉	C₂²	1	8	yes	—
30	C₂²×C₄⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₄⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₄⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₂²⋊C₄×C₁₀₉	—	2	8	no	—
34	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
35	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
36	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
37	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
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
43	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
44	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
45	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
46	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
47	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	8	yes	complemented
48	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
49	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
50	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
51	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
52	C₂²×C₄²×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
53	C₂²×C₄²×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
54	#397×C₁₀₉	C₂²	1	8	yes	complemented
55	#394×C₁₀₉	C₂²	1	8	yes	complemented
56	#394×C₁₀₉	C₂²	1	8	yes	complemented
57	#393×C₁₀₉	C₂²	1	8	yes	complemented
58	#390×C₁₀₉	C₂²	1	8	yes	complemented
59	#388×C₁₀₉	C₂²	1	8	yes	complemented
60	#388×C₁₀₉	C₂²	1	8	yes	complemented
61	#386×C₁₀₉	C₂²	1	8	yes	complemented
62	#386×C₁₀₉	C₂²	1	8	yes	complemented
63	#379×C₁₀₉	C₂²	1	8	yes	complemented
64	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	8	yes	complemented
65	C₂×#95×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
66	C₂×#95×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
67	C₂×#95×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
68	C₂×#95×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
69	C₂×#95×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
70	C₂×#95×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
71	C₂⁵×C₁₀₉	—	2	4	no	—
72	C₂⁵×C₁₀₉	—	2	4	no	—
73	C₂⁵×C₁₀₉	—	2	4	no	—
74	C₂⁵×C₁₀₉	—	2	4	no	—
75	C₂⁵×C₁₀₉	—	2	4	no	—
76	C₂⁵×C₁₀₉	—	4	2	no	—
77	C₂⁵×C₁₀₉	—	4	2	no	—
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	C₂⁵×C₁₀₉	C₂³	1	4	yes	—
82	C₂⁵×C₁₀₉	C₂³	1	1	yes	characteristic
83	C₂²×Q₈×C₁₀₉	—	2	4	no	—
84	C₂²×Q₈×C₁₀₉	—	2	4	no	—
85	C₂²×Q₈×C₁₀₉	—	4	2	no	—
86	C₂²×Q₈×C₁₀₉	C₂³	1	4	yes	complemented
87	C₂²×D₄×C₁₀₉	—	2	4	no	—
88	C₂²×D₄×C₁₀₉	—	2	4	no	—
89	C₂²×D₄×C₁₀₉	—	2	4	no	—
90	C₂²×D₄×C₁₀₉	—	2	4	no	—
91	C₂²×D₄×C₁₀₉	—	2	4	no	—
92	C₂²×D₄×C₁₀₉	—	2	4	no	—
93	C₂²×D₄×C₁₀₉	—	2	4	no	—
94	C₂²×D₄×C₁₀₉	—	4	2	no	—
95	C₂²×D₄×C₁₀₉	—	4	2	no	—
96	C₂²×D₄×C₁₀₉	C₂³	1	4	yes	—
97	C₂²×D₄×C₁₀₉	C₂³	1	4	yes	—
98	C₂²×D₄×C₁₀₉	C₂³	1	4	yes	—
99	C₂³×C₄×C₁₀₉	—	2	4	no	—
100	C₂³×C₄×C₁₀₉	—	2	4	no	—
101	C₂³×C₄×C₁₀₉	—	2	4	no	—
102	C₂³×C₄×C₁₀₉	—	2	4	no	—
103	C₂³×C₄×C₁₀₉	—	4	2	no	—
104	C₂³×C₄×C₁₀₉	—	4	2	no	—
105	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₁₀₉	C₂³	1	4	yes	—
113	C₂³×C₄×C₁₀₉	C₂³	1	4	yes	—
114	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
118	#124×C₁₀₉	—	2	32	no	—
119	C₂²⋊Q₈×C₁₀₉	—	2	32	no	—
120	#120×C₁₀₉	—	2	32	no	—
121	C₂×C₄⋊C₄×C₁₀₉	—	2	4	no	—
122	C₂×C₄⋊C₄×C₁₀₉	—	2	4	no	—
123	C₂×C₄⋊C₄×C₁₀₉	—	2	4	no	—
124	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	4	yes	complemented
125	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	4	yes	complemented
126	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	4	yes	complemented
127	C₂×C₂²⋊C₄×C₁₀₉	—	2	4	no	—
128	C₂×C₂²⋊C₄×C₁₀₉	—	2	4	no	—
129	C₂×C₂²⋊C₄×C₁₀₉	—	2	4	no	—
130	C₂×C₂²⋊C₄×C₁₀₉	—	2	4	no	—
131	C₂×C₂²⋊C₄×C₁₀₉	—	2	4	no	—
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	4	no	—
136	C₂×C₂²⋊C₄×C₁₀₉	—	2	4	no	—
137	C₂×C₂²⋊C₄×C₁₀₉	—	2	4	no	—
138	C₂×C₂²⋊C₄×C₁₀₉	—	2	32	no	—
139	C₂×C₂²⋊C₄×C₁₀₉	—	4	2	no	—
140	C₂×C₂²⋊C₄×C₁₀₉	—	4	2	no	—
141	C₂×C₂²⋊C₄×C₁₀₉	—	4	2	no	—
142	C₂×C₂²⋊C₄×C₁₀₉	—	4	2	no	—
143	C₂×C₂²⋊C₄×C₁₀₉	D₄	1	8	yes	—
144	C₂×C₂²⋊C₄×C₁₀₉	D₄	1	8	yes	complemented
145	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	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	4	yes	—
151	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	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	4	yes	—
155	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
156	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
157	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
158	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	complemented
159	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	complemented
160	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	complemented
161	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	complemented
162	C₂×C₄²×C₁₀₉	—	2	4	no	—
163	C₂×C₄²×C₁₀₉	—	4	2	no	—
164	C₂×C₄²×C₁₀₉	C₂³	1	4	yes	complemented
165	C₂×C₄²×C₁₀₉	C₂³	1	4	yes	complemented
166	#95×C₁₀₉	C₂³	1	4	yes	complemented
167	#95×C₁₀₉	C₂³	1	4	yes	complemented
168	#95×C₁₀₉	C₂³	1	4	yes	complemented
169	#95×C₁₀₉	C₂³	1	4	yes	complemented
170	#95×C₁₀₉	C₂³	1	4	yes	complemented
171	#95×C₁₀₉	C₂³	1	4	yes	complemented
172	C₂⁴×C₁₀₉	—	2	2	no	—
173	C₂⁴×C₁₀₉	—	2	2	no	—
174	C₂⁴×C₁₀₉	—	2	2	no	—
175	C₂⁴×C₁₀₉	—	2	2	no	—
176	C₂⁴×C₁₀₉	—	2	32	no	—
177	C₂⁴×C₁₀₉	—	2	8	no	—
178	C₂⁴×C₁₀₉	—	2	2	no	—
179	C₂⁴×C₁₀₉	—	2	2	no	—
180	C₂⁴×C₁₀₉	—	2	2	no	—
181	C₂⁴×C₁₀₉	—	2	8	no	—
182	C₂⁴×C₁₀₉	—	2	8	no	—
183	C₂⁴×C₁₀₉	—	2	2	no	—
184	C₂⁴×C₁₀₉	—	2	2	no	—
185	C₂⁴×C₁₀₉	—	2	2	no	—
186	C₂⁴×C₁₀₉	—	2	2	no	—
187	C₂⁴×C₁₀₉	—	2	2	no	—
188	C₂⁴×C₁₀₉	—	2	2	no	—
189	C₂⁴×C₁₀₉	—	2	2	no	—
190	C₂⁴×C₁₀₉	—	2	2	no	—
191	C₂⁴×C₁₀₉	—	2	2	no	—
192	C₂⁴×C₁₀₉	—	2	2	no	—
193	C₂⁴×C₁₀₉	—	2	8	no	—
194	C₂⁴×C₁₀₉	—	2	2	no	—
195	C₂⁴×C₁₀₉	—	2	2	no	—
196	C₂⁴×C₁₀₉	—	2	2	no	—
197	C₂⁴×C₁₀₉	—	2	2	no	—
198	C₂⁴×C₁₀₉	—	2	8	no	—
199	C₂⁴×C₁₀₉	—	2	2	no	—
200	C₂⁴×C₁₀₉	—	2	2	no	—
201	C₂⁴×C₁₀₉	—	4	4	no	—
202	C₂⁴×C₁₀₉	—	4	4	no	—
203	C₂⁴×C₁₀₉	—	4	16	no	—
204	C₂⁴×C₁₀₉	—	4	16	no	—
205	C₂⁴×C₁₀₉	—	4	16	no	—
206	C₂⁴×C₁₀₉	—	4	16	no	—
207	C₂⁴×C₁₀₉	—	4	16	no	—
208	C₂⁴×C₁₀₉	—	4	16	no	—
209	C₂⁴×C₁₀₉	C₂×D₄	1	4	yes	—
210	C₂⁴×C₁₀₉	C₂×D₄	1	4	yes	—
211	C₂⁴×C₁₀₉	#41	1	4	yes	—
212	C₂⁴×C₁₀₉	#41	1	4	yes	—
213	C₂⁴×C₁₀₉	#41	1	4	yes	—
214	C₂⁴×C₁₀₉	C₂⁴	1	2	yes	—
215	C₂⁴×C₁₀₉	C₂⁴	1	2	yes	—
216	C₂⁴×C₁₀₉	C₂⁴	1	2	yes	—
217	C₂⁴×C₁₀₉	C₂⁴	1	2	yes	—
218	C₂⁴×C₁₀₉	C₂⁴	1	1	yes	characteristic
219	C₂×Q₈×C₁₀₉	—	2	8	no	—
220	C₂×Q₈×C₁₀₉	—	2	8	no	—
221	C₂×Q₈×C₁₀₉	—	4	4	no	—
222	C₂×Q₈×C₁₀₉	—	4	16	no	—
223	C₂×D₄×C₁₀₉	—	2	8	no	—
224	C₂×D₄×C₁₀₉	—	2	8	no	—
225	C₂×D₄×C₁₀₉	—	2	8	no	—
226	C₂×D₄×C₁₀₉	—	2	8	no	—
227	C₂×D₄×C₁₀₉	—	2	8	no	—
228	C₂×D₄×C₁₀₉	—	2	8	no	—
229	C₂×D₄×C₁₀₉	—	2	8	no	—
230	C₂×D₄×C₁₀₉	—	4	4	no	—
231	C₂×D₄×C₁₀₉	—	4	4	no	—
232	C₂×D₄×C₁₀₉	—	4	16	no	—
233	C₂×D₄×C₁₀₉	—	4	16	no	—
234	C₂×D₄×C₁₀₉	—	4	16	no	—
235	C₂²×C₄×C₁₀₉	—	2	2	no	—
236	C₂²×C₄×C₁₀₉	—	2	2	no	—
237	C₂²×C₄×C₁₀₉	—	2	2	no	—
238	C₂²×C₄×C₁₀₉	—	2	2	no	—
239	C₂²×C₄×C₁₀₉	—	2	2	no	—
240	C₂²×C₄×C₁₀₉	—	2	2	no	—
241	C₂²×C₄×C₁₀₉	—	2	2	no	—
242	C₂²×C₄×C₁₀₉	—	2	2	no	—
243	C₂²×C₄×C₁₀₉	—	2	2	no	—
244	C₂²×C₄×C₁₀₉	—	2	2	no	—
245	C₂²×C₄×C₁₀₉	—	2	2	no	—
246	C₂²×C₄×C₁₀₉	—	2	2	no	—
247	C₂²×C₄×C₁₀₉	—	2	2	no	—
248	C₂²×C₄×C₁₀₉	—	2	2	no	—
249	C₂²×C₄×C₁₀₉	—	2	2	no	—
250	C₂²×C₄×C₁₀₉	—	2	2	no	—
251	C₂²×C₄×C₁₀₉	—	2	8	no	—
252	C₂²×C₄×C₁₀₉	—	2	2	no	—
253	C₂²×C₄×C₁₀₉	—	2	2	no	—
254	C₂²×C₄×C₁₀₉	—	2	2	no	—
255	C₂²×C₄×C₁₀₉	—	2	2	no	—
256	C₂²×C₄×C₁₀₉	—	2	8	no	—
257	C₂²×C₄×C₁₀₉	—	2	2	no	—
258	C₂²×C₄×C₁₀₉	—	2	2	no	—
259	C₂²×C₄×C₁₀₉	—	2	2	no	—
260	C₂²×C₄×C₁₀₉	—	2	2	no	—
261	C₂²×C₄×C₁₀₉	—	2	2	no	—
262	C₂²×C₄×C₁₀₉	—	2	2	no	—
263	C₂²×C₄×C₁₀₉	—	2	2	no	—
264	C₂²×C₄×C₁₀₉	—	2	2	no	—
265	C₂²×C₄×C₁₀₉	—	2	2	no	—
266	C₂²×C₄×C₁₀₉	—	2	8	no	—
267	C₂²×C₄×C₁₀₉	—	2	8	no	—
268	C₂²×C₄×C₁₀₉	—	4	4	no	—
269	C₂²×C₄×C₁₀₉	—	4	4	no	—
270	C₂²×C₄×C₁₀₉	—	4	16	no	—
271	C₂²×C₄×C₁₀₉	—	4	16	no	—
272	C₂²×C₄×C₁₀₉	C₂×D₄	1	4	yes	—
273	C₂²×C₄×C₁₀₉	C₂×D₄	1	4	yes	—
274	C₂²×C₄×C₁₀₉	C₂×D₄	1	4	yes	—
275	C₂²×C₄×C₁₀₉	C₂×D₄	1	4	yes	—
276	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
287	C₄⋊C₄×C₁₀₉	—	2	8	no	—
288	C₄⋊C₄×C₁₀₉	—	2	8	no	—
289	C₄⋊C₄×C₁₀₉	—	2	8	no	—
290	C₂²⋊C₄×C₁₀₉	—	2	8	no	—
291	C₂²⋊C₄×C₁₀₉	—	2	8	no	—
292	C₂²⋊C₄×C₁₀₉	—	2	8	no	—
293	C₂²⋊C₄×C₁₀₉	—	2	8	no	—
294	C₂²⋊C₄×C₁₀₉	—	2	8	no	—
295	C₂²⋊C₄×C₁₀₉	—	2	8	no	—
296	C₂²⋊C₄×C₁₀₉	—	2	8	no	—
297	C₂²⋊C₄×C₁₀₉	—	2	8	no	—
298	C₂²⋊C₄×C₁₀₉	—	2	8	no	—
299	C₂²⋊C₄×C₁₀₉	—	2	8	no	—
300	C₂²⋊C₄×C₁₀₉	—	2	8	no	—
301	C₂²⋊C₄×C₁₀₉	—	4	4	no	—
302	C₂²⋊C₄×C₁₀₉	—	4	4	no	—
303	C₂²⋊C₄×C₁₀₉	—	4	4	no	—
304	C₂²⋊C₄×C₁₀₉	—	4	4	no	—
305	C₂²⋊C₄×C₁₀₉	C₂×D₄	1	16	yes	—
306	C₂²⋊C₄×C₁₀₉	C₂×D₄	1	16	yes	complemented
307	C₄²×C₁₀₉	—	2	8	no	—
308	C₄²×C₁₀₉	—	4	4	no	—
309	C₂³×C₁₀₉	—	2	8	no	—
310	C₂³×C₁₀₉	—	2	8	no	—
311	C₂³×C₁₀₉	—	2	8	no	—
312	C₂³×C₁₀₉	—	2	8	no	—
313	C₂³×C₁₀₉	—	2	8	no	—
314	C₂³×C₁₀₉	—	2	8	no	—
315	C₂³×C₁₀₉	—	2	2	no	—
316	C₂³×C₁₀₉	—	2	2	no	—
317	C₂³×C₁₀₉	—	2	2	no	—
318	C₂³×C₁₀₉	—	2	2	no	—
319	C₂³×C₁₀₉	—	2	32	no	—
320	C₂³×C₁₀₉	—	2	8	no	—
321	C₂³×C₁₀₉	—	2	8	no	—
322	C₂³×C₁₀₉	—	2	8	no	—
323	C₂³×C₁₀₉	—	2	8	no	—
324	C₂³×C₁₀₉	—	2	8	no	—
325	C₂³×C₁₀₉	—	2	8	no	—
326	C₂³×C₁₀₉	—	2	2	no	—
327	C₂³×C₁₀₉	—	2	2	no	—
328	C₂³×C₁₀₉	—	2	2	no	—
329	C₂³×C₁₀₉	—	2	2	no	—
330	C₂³×C₁₀₉	—	2	2	no	—
331	C₂³×C₁₀₉	—	2	2	no	—
332	C₂³×C₁₀₉	—	2	2	no	—
333	C₂³×C₁₀₉	—	2	2	no	—
334	C₂³×C₁₀₉	—	2	2	no	—
335	C₂³×C₁₀₉	—	2	2	no	—
336	C₂³×C₁₀₉	—	2	2	no	—
337	C₂³×C₁₀₉	—	2	2	no	—
338	C₂³×C₁₀₉	—	2	2	no	—
339	C₂³×C₁₀₉	—	2	2	no	—
340	C₂³×C₁₀₉	—	2	2	no	—
341	C₂³×C₁₀₉	—	2	2	no	—
342	C₂³×C₁₀₉	—	2	2	no	—
343	C₂³×C₁₀₉	—	2	2	no	—
344	C₂³×C₁₀₉	—	2	2	no	—
345	C₂³×C₁₀₉	—	4	16	no	—
346	C₂³×C₁₀₉	—	4	16	no	—
347	C₂³×C₁₀₉	—	4	16	no	—
348	C₂³×C₁₀₉	—	4	16	no	—
349	C₂³×C₁₀₉	—	4	16	no	—
350	C₂³×C₁₀₉	—	4	128	no	—
351	C₂³×C₁₀₉	—	4	4	no	—
352	C₂³×C₁₀₉	—	4	4	no	—
353	C₂³×C₁₀₉	—	4	16	no	—
354	C₂³×C₁₀₉	—	4	4	no	—
355	C₂³×C₁₀₉	—	4	4	no	—
356	C₂³×C₁₀₉	—	4	4	no	—
357	C₂³×C₁₀₉	—	4	4	no	—
358	C₂³×C₁₀₉	—	4	4	no	—
359	C₂³×C₁₀₉	—	4	4	no	—
360	C₂³×C₁₀₉	—	4	4	no	—
361	C₂³×C₁₀₉	—	4	4	no	—
362	C₂³×C₁₀₉	—	4	4	no	—
363	C₂³×C₁₀₉	—	4	4	no	—
364	C₂³×C₁₀₉	—	4	4	no	—
365	C₂³×C₁₀₉	—	4	4	no	—
366	C₂³×C₁₀₉	—	4	4	no	—
367	C₂³×C₁₀₉	#124	1	16	yes	complemented
368	C₂³×C₁₀₉	C₂²×D₄	1	4	yes	—
369	C₂³×C₁₀₉	C₂²×D₄	1	4	yes	—
370	C₂³×C₁₀₉	C₂²×D₄	1	2	yes	—
371	C₂³×C₁₀₉	C₂²×D₄	1	2	yes	—
372	C₂³×C₁₀₉	C₂×#41	1	4	yes	—
373	C₂³×C₁₀₉	C₂×#41	1	4	yes	—
374	C₂³×C₁₀₉	C₂×#41	1	4	yes	—
375	C₂³×C₁₀₉	C₂×#41	1	2	yes	—
376	C₂³×C₁₀₉	C₂×#41	1	2	yes	—
377	C₂³×C₁₀₉	C₂×#41	1	2	yes	—
378	C₂³×C₁₀₉	H(5,𝔽₂)	1	2	yes	—
379	C₂³×C₁₀₉	H(5,𝔽₂)	1	2	yes	—
380	C₂³×C₁₀₉	C₂⁵	1	1	yes	characteristic
381	Q₈×C₁₀₉	—	4	16	no	—
382	D₄×C₁₀₉	—	4	16	no	—
383	D₄×C₁₀₉	—	4	16	no	—
384	D₄×C₁₀₉	—	4	16	no	—
385	C₂×C₄×C₁₀₉	—	2	8	no	—
386	C₂×C₄×C₁₀₉	—	2	8	no	—
387	C₂×C₄×C₁₀₉	—	2	8	no	—
388	C₂×C₄×C₁₀₉	—	2	8	no	—
389	C₂×C₄×C₁₀₉	—	2	2	no	—
390	C₂×C₄×C₁₀₉	—	2	2	no	—
391	C₂×C₄×C₁₀₉	—	2	2	no	—
392	C₂×C₄×C₁₀₉	—	2	2	no	—
393	C₂×C₄×C₁₀₉	—	2	2	no	—
394	C₂×C₄×C₁₀₉	—	2	2	no	—
395	C₂×C₄×C₁₀₉	—	2	2	no	—
396	C₂×C₄×C₁₀₉	—	2	2	no	—
397	C₂×C₄×C₁₀₉	—	2	2	no	—
398	C₂×C₄×C₁₀₉	—	2	2	no	—
399	C₂×C₄×C₁₀₉	—	2	2	no	—
400	C₂×C₄×C₁₀₉	—	2	2	no	—
401	C₂×C₄×C₁₀₉	—	2	2	no	—
402	C₂×C₄×C₁₀₉	—	2	2	no	—
403	C₂×C₄×C₁₀₉	—	2	2	no	—
404	C₂×C₄×C₁₀₉	—	2	2	no	—
405	C₂×C₄×C₁₀₉	—	2	2	no	—
406	C₂×C₄×C₁₀₉	—	2	2	no	—
407	C₂×C₄×C₁₀₉	—	2	2	no	—
408	C₂×C₄×C₁₀₉	—	2	2	no	—
409	C₂×C₄×C₁₀₉	—	2	2	no	—
410	C₂×C₄×C₁₀₉	—	2	2	no	—
411	C₂×C₄×C₁₀₉	—	2	2	no	—
412	C₂×C₄×C₁₀₉	—	2	2	no	—
413	C₂×C₄×C₁₀₉	—	2	2	no	—
414	C₂×C₄×C₁₀₉	—	2	2	no	—
415	C₂×C₄×C₁₀₉	—	2	2	no	—
416	C₂×C₄×C₁₀₉	—	2	2	no	—
417	C₂×C₄×C₁₀₉	—	2	2	no	—
418	C₂×C₄×C₁₀₉	—	4	16	no	—
419	C₂×C₄×C₁₀₉	—	4	16	no	—
420	C₂×C₄×C₁₀₉	—	4	4	no	—
421	C₂×C₄×C₁₀₉	—	4	4	no	—
422	C₂×C₄×C₁₀₉	—	4	4	no	—
423	C₂×C₄×C₁₀₉	—	4	4	no	—
424	C₂×C₄×C₁₀₉	—	4	4	no	—
425	C₂×C₄×C₁₀₉	—	4	4	no	—
426	C₂×C₄×C₁₀₉	—	4	4	no	—
427	C₂×C₄×C₁₀₉	C₂²×D₄	1	4	yes	—
428	C₂×C₄×C₁₀₉	C₂²×D₄	1	4	yes	—
429	C₂×C₄×C₁₀₉	C₂²×D₄	1	4	yes	—
430	C₂×C₄×C₁₀₉	C₂²×D₄	1	4	yes	—
431	C₂²×C₁₀₉	—	2	4	no	—
432	C₂²×C₁₀₉	—	2	4	no	—
433	C₂²×C₁₀₉	—	2	4	no	—
434	C₂²×C₁₀₉	—	2	4	no	—
435	C₂²×C₁₀₉	—	2	4	no	—
436	C₂²×C₁₀₉	—	2	4	no	—
437	C₂²×C₁₀₉	—	2	32	no	—
438	C₂²×C₁₀₉	—	2	4	no	—
439	C₂²×C₁₀₉	—	2	4	no	—
440	C₂²×C₁₀₉	—	2	4	no	—
441	C₂²×C₁₀₉	—	2	4	no	—
442	C₂²×C₁₀₉	—	2	4	no	—
443	C₂²×C₁₀₉	—	2	4	no	—
444	C₂²×C₁₀₉	—	4	64	no	—
445	C₂²×C₁₀₉	—	4	2	no	—
446	C₂²×C₁₀₉	—	4	2	no	—
447	C₂²×C₁₀₉	—	4	2	no	—
448	C₂²×C₁₀₉	—	4	2	no	—
449	C₂²×C₁₀₉	—	4	2	no	—
450	C₂²×C₁₀₉	—	4	2	no	—
451	C₂²×C₁₀₉	—	4	2	no	—
452	C₂²×C₁₀₉	—	4	2	no	—
453	C₂²×C₁₀₉	—	4	16	no	—
454	C₂²×C₁₀₉	—	4	16	no	—
455	C₂²×C₁₀₉	—	4	2	no	—
456	C₂²×C₁₀₉	—	4	2	no	—
457	C₂²×C₁₀₉	—	4	2	no	—
458	C₂²×C₁₀₉	—	4	2	no	—
459	C₂²×C₁₀₉	—	4	2	no	—
460	C₂²×C₁₀₉	—	4	2	no	—
461	C₂²×C₁₀₉	—	4	2	no	—
462	C₂²×C₁₀₉	—	8	8	no	—
463	C₂²×C₁₀₉	#525	1	4	yes	—
464	C₂²×C₁₀₉	C₂×#124	1	4	yes	—
465	C₂²×C₁₀₉	C₂×#124	1	8	yes	complemented
466	C₂²×C₁₀₉	#538	1	4	yes	—
467	C₂²×C₁₀₉	D₄²	1	4	yes	—
468	C₂²×C₁₀₉	#546	1	4	yes	—
469	C₂²×C₁₀₉	#546	1	4	yes	—
470	C₂²×C₁₀₉	#551	1	4	yes	—
471	C₂²×C₁₀₉	C₂³×D₄	1	1	yes	characteristic
472	C₂²×C₁₀₉	C₂³×D₄	1	1	yes	characteristic
473	C₂²×C₁₀₉	C₂²×#41	1	1	yes	characteristic
474	C₂²×C₁₀₉	C₂²×#41	1	1	yes	characteristic
475	C₂²×C₁₀₉	C₂²×#41	1	1	yes	characteristic
476	C₂²×C₁₀₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
477	C₂²×C₁₀₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
478	C₄×C₁₀₉	—	2	4	no	—
479	C₄×C₁₀₉	—	2	4	no	—
480	C₄×C₁₀₉	—	2	4	no	—
481	C₄×C₁₀₉	—	2	4	no	—
482	C₄×C₁₀₉	—	4	2	no	—
483	C₄×C₁₀₉	—	4	2	no	—
484	C₄×C₁₀₉	—	4	2	no	—
485	C₄×C₁₀₉	—	4	2	no	—
486	C₄×C₁₀₉	—	4	2	no	—
487	C₄×C₁₀₉	—	4	2	no	—
488	C₄×C₁₀₉	—	4	2	no	—
489	C₂×#2472	C₁₀₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
490	C₂×C₁₀₉	—	2	8	no	—
491	C₂×C₁₀₉	—	4	4	no	—
492	C₂×C₁₀₉	—	4	4	no	—
493	C₂×C₁₀₉	—	8	2	no	—
494	C₂×C₁₀₉	#2472	1	8	yes	direct product factor
495	C₂×C₁₀₉	C₂×#525	1	1	yes	characteristic
496	C₂×C₁₀₉	C₂²×#124	1	1	yes	characteristic
497	C₂×C₁₀₉	C₂×#538	1	1	yes	characteristic
498	C₂×C₁₀₉	C₂×D₄²	1	1	yes	characteristic
499	C₂×C₁₀₉	C₂×#546	1	1	yes	characteristic
500	C₂×C₁₀₉	C₂×#546	1	1	yes	characteristic
501	C₂×C₁₀₉	C₂×#551	1	1	yes	characteristic
502	C₂²×#124	C₂×C₁₀₉	1	1	yes	characteristic, complemented
503	C₂²×C₂²⋊Q₈	C₂×C₁₀₉	1	1	yes	characteristic, complemented
504	C₂²×#120	C₂×C₁₀₉	1	1	yes	characteristic
505	C₂³×C₂²⋊C₄	C₂×C₁₀₉	1	1	yes	characteristic, complemented
506	#2472	C₂×C₁₀₉	1	16	yes	direct product factor
507	C₂×#397	C₂×C₁₀₉	1	1	yes	characteristic, complemented
508	C₂×#394	C₂×C₁₀₉	1	1	yes	characteristic, complemented
509	C₂×#394	C₂×C₁₀₉	1	1	yes	characteristic, complemented
510	C₂×#393	C₂×C₁₀₉	1	1	yes	characteristic, complemented
511	C₂×#390	C₂×C₁₀₉	1	1	yes	characteristic, complemented
512	C₂×#388	C₂×C₁₀₉	1	1	yes	characteristic, complemented
513	C₂×#388	C₂×C₁₀₉	1	1	yes	characteristic, complemented
514	C₂×#386	C₂×C₁₀₉	1	1	yes	characteristic, complemented
515	C₂×#386	C₂×C₁₀₉	1	1	yes	characteristic, complemented
516	C₂×#379	C₂×C₁₀₉	1	1	yes	characteristic, complemented
517	C₂×C₄×C₂²⋊C₄	C₂×C₁₀₉	1	1	yes	characteristic, complemented
518	C₁₀₉	C₂×#2472	1	1	yes	characteristic, direct product factor, Sylow
519	C₂⁶	C₂²×C₁₀₉	1	1	yes	characteristic
520	C₂³×Q₈	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
521	C₂³×D₄	C₂²×C₁₀₉	1	1	yes	characteristic
522	C₂³×D₄	C₂²×C₁₀₉	1	1	yes	characteristic
523	C₂³×D₄	C₂²×C₁₀₉	1	1	yes	characteristic
524	C₂⁴×C₄	C₂²×C₁₀₉	1	1	yes	characteristic
525	C₂⁴×C₄	C₂²×C₁₀₉	1	1	yes	characteristic
526	C₂×#124	—	2	8	no	—
527	C₂×#124	C₂²×C₁₀₉	1	8	yes	complemented
528	C₂×C₂²⋊Q₈	—	2	8	no	—
529	C₂×C₂²⋊Q₈	C₂²×C₁₀₉	1	8	yes	complemented
530	C₂×#120	—	2	8	no	—
531	C₂×#120	C₂²×C₁₀₉	1	8	yes	—
532	C₂²×C₄⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
533	C₂²×C₄⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
534	C₂²×C₄⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
535	C₂²×C₂²⋊C₄	—	2	8	no	—
536	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
537	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
538	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
539	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
540	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
541	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
542	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
543	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
544	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
545	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
546	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
547	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
548	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
549	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	8	yes	complemented
550	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
551	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
552	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
553	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
554	C₂²×C₄²	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
555	C₂²×C₄²	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
556	#397	C₂²×C₁₀₉	1	8	yes	complemented
557	#394	C₂²×C₁₀₉	1	8	yes	complemented
558	#394	C₂²×C₁₀₉	1	8	yes	complemented
559	#393	C₂²×C₁₀₉	1	8	yes	complemented
560	#390	C₂²×C₁₀₉	1	8	yes	complemented
561	#388	C₂²×C₁₀₉	1	8	yes	complemented
562	#388	C₂²×C₁₀₉	1	8	yes	complemented
563	#386	C₂²×C₁₀₉	1	8	yes	complemented
564	#386	C₂²×C₁₀₉	1	8	yes	complemented
565	#379	C₂²×C₁₀₉	1	8	yes	complemented
566	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	8	yes	complemented
567	C₂×#95	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
568	C₂×#95	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
569	C₂×#95	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
570	C₂×#95	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
571	C₂×#95	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
572	C₂×#95	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
573	C₂⁵	—	2	4	no	—
574	C₂⁵	—	2	4	no	—
575	C₂⁵	—	2	4	no	—
576	C₂⁵	—	2	4	no	—
577	C₂⁵	—	2	4	no	—
578	C₂⁵	—	4	2	no	—
579	C₂⁵	—	4	2	no	—
580	C₂⁵	C₂³×C₁₀₉	1	1	yes	characteristic
581	C₂⁵	C₂³×C₁₀₉	1	1	yes	characteristic
582	C₂⁵	C₂³×C₁₀₉	1	1	yes	characteristic
583	C₂⁵	C₂³×C₁₀₉	1	4	yes	—
584	C₂⁵	C₂³×C₁₀₉	1	1	yes	characteristic
585	C₂²×Q₈	—	2	4	no	—
586	C₂²×Q₈	—	2	4	no	—
587	C₂²×Q₈	—	4	2	no	—
588	C₂²×Q₈	C₂³×C₁₀₉	1	4	yes	complemented
589	C₂²×D₄	—	2	4	no	—
590	C₂²×D₄	—	2	4	no	—
591	C₂²×D₄	—	2	4	no	—
592	C₂²×D₄	—	2	4	no	—
593	C₂²×D₄	—	2	4	no	—
594	C₂²×D₄	—	2	4	no	—
595	C₂²×D₄	—	2	4	no	—
596	C₂²×D₄	—	4	2	no	—
597	C₂²×D₄	—	4	2	no	—
598	C₂²×D₄	C₂³×C₁₀₉	1	4	yes	—
599	C₂²×D₄	C₂³×C₁₀₉	1	4	yes	—
600	C₂²×D₄	C₂³×C₁₀₉	1	4	yes	—
601	C₂³×C₄	—	2	4	no	—
602	C₂³×C₄	—	2	4	no	—
603	C₂³×C₄	—	2	4	no	—
604	C₂³×C₄	—	2	4	no	—
605	C₂³×C₄	—	4	2	no	—
606	C₂³×C₄	—	4	2	no	—
607	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
608	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
609	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
610	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
611	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
612	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
613	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
614	C₂³×C₄	C₂³×C₁₀₉	1	4	yes	—
615	C₂³×C₄	C₂³×C₁₀₉	1	4	yes	—
616	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
617	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
618	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
619	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
620	#124	—	2	32	no	—
621	C₂²⋊Q₈	—	2	32	no	—
622	#120	—	2	32	no	—
623	C₂×C₄⋊C₄	—	2	4	no	—
624	C₂×C₄⋊C₄	—	2	4	no	—
625	C₂×C₄⋊C₄	—	2	4	no	—
626	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	4	yes	complemented
627	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	4	yes	complemented
628	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	4	yes	complemented
629	C₂×C₂²⋊C₄	—	2	4	no	—
630	C₂×C₂²⋊C₄	—	2	4	no	—
631	C₂×C₂²⋊C₄	—	2	4	no	—
632	C₂×C₂²⋊C₄	—	2	4	no	—
633	C₂×C₂²⋊C₄	—	2	4	no	—
634	C₂×C₂²⋊C₄	—	2	4	no	—
635	C₂×C₂²⋊C₄	—	2	4	no	—
636	C₂×C₂²⋊C₄	—	2	4	no	—
637	C₂×C₂²⋊C₄	—	2	4	no	—
638	C₂×C₂²⋊C₄	—	2	4	no	—
639	C₂×C₂²⋊C₄	—	2	4	no	—
640	C₂×C₂²⋊C₄	—	2	32	no	—
641	C₂×C₂²⋊C₄	—	4	2	no	—
642	C₂×C₂²⋊C₄	—	4	2	no	—
643	C₂×C₂²⋊C₄	—	4	2	no	—
644	C₂×C₂²⋊C₄	—	4	2	no	—
645	C₂×C₂²⋊C₄	D₄×C₁₀₉	1	8	yes	—
646	C₂×C₂²⋊C₄	D₄×C₁₀₉	1	8	yes	complemented
647	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
648	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	complemented
661	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	complemented
662	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	complemented
663	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	complemented
664	C₂×C₄²	—	2	4	no	—
665	C₂×C₄²	—	4	2	no	—
666	C₂×C₄²	C₂³×C₁₀₉	1	4	yes	complemented
667	C₂×C₄²	C₂³×C₁₀₉	1	4	yes	complemented
668	#95	C₂³×C₁₀₉	1	4	yes	complemented
669	#95	C₂³×C₁₀₉	1	4	yes	complemented
670	#95	C₂³×C₁₀₉	1	4	yes	complemented
671	#95	C₂³×C₁₀₉	1	4	yes	complemented
672	#95	C₂³×C₁₀₉	1	4	yes	complemented
673	#95	C₂³×C₁₀₉	1	4	yes	complemented
674	C₂⁴	—	2	2	no	—
675	C₂⁴	—	2	2	no	—
676	C₂⁴	—	2	2	no	—
677	C₂⁴	—	2	2	no	—
678	C₂⁴	—	2	32	no	—
679	C₂⁴	—	2	8	no	—
680	C₂⁴	—	2	2	no	—
681	C₂⁴	—	2	2	no	—
682	C₂⁴	—	2	2	no	—
683	C₂⁴	—	2	8	no	—
684	C₂⁴	—	2	8	no	—
685	C₂⁴	—	2	2	no	—
686	C₂⁴	—	2	2	no	—
687	C₂⁴	—	2	2	no	—
688	C₂⁴	—	2	2	no	—
689	C₂⁴	—	2	2	no	—
690	C₂⁴	—	2	2	no	—
691	C₂⁴	—	2	2	no	—
692	C₂⁴	—	2	2	no	—
693	C₂⁴	—	2	2	no	—
694	C₂⁴	—	2	2	no	—
695	C₂⁴	—	2	8	no	—
696	C₂⁴	—	2	2	no	—
697	C₂⁴	—	2	2	no	—
698	C₂⁴	—	2	2	no	—
699	C₂⁴	—	2	2	no	—
700	C₂⁴	—	2	8	no	—
701	C₂⁴	—	2	2	no	—
702	C₂⁴	—	2	2	no	—
703	C₂⁴	—	4	4	no	—
704	C₂⁴	—	4	4	no	—
705	C₂⁴	—	4	16	no	—
706	C₂⁴	—	4	16	no	—
707	C₂⁴	—	4	16	no	—
708	C₂⁴	—	4	16	no	—
709	C₂⁴	—	4	16	no	—
710	C₂⁴	—	4	16	no	—
711	C₂⁴	C₂×D₄×C₁₀₉	1	4	yes	—
712	C₂⁴	C₂×D₄×C₁₀₉	1	4	yes	—
713	C₂⁴	#41×C₁₀₉	1	4	yes	—
714	C₂⁴	#41×C₁₀₉	1	4	yes	—
715	C₂⁴	#41×C₁₀₉	1	4	yes	—
716	C₂⁴	C₂⁴×C₁₀₉	1	2	yes	—
717	C₂⁴	C₂⁴×C₁₀₉	1	2	yes	—
718	C₂⁴	C₂⁴×C₁₀₉	1	2	yes	—
719	C₂⁴	C₂⁴×C₁₀₉	1	2	yes	—
720	C₂⁴	C₂⁴×C₁₀₉	1	1	yes	characteristic
721	C₂×Q₈	—	2	8	no	—
722	C₂×Q₈	—	2	8	no	—
723	C₂×Q₈	—	4	4	no	—
724	C₂×Q₈	—	4	16	no	—
725	C₂×D₄	—	2	8	no	—
726	C₂×D₄	—	2	8	no	—
727	C₂×D₄	—	2	8	no	—
728	C₂×D₄	—	2	8	no	—
729	C₂×D₄	—	2	8	no	—
730	C₂×D₄	—	2	8	no	—
731	C₂×D₄	—	2	8	no	—
732	C₂×D₄	—	4	4	no	—
733	C₂×D₄	—	4	4	no	—
734	C₂×D₄	—	4	16	no	—
735	C₂×D₄	—	4	16	no	—
736	C₂×D₄	—	4	16	no	—
737	C₂²×C₄	—	2	2	no	—
738	C₂²×C₄	—	2	2	no	—
739	C₂²×C₄	—	2	2	no	—
740	C₂²×C₄	—	2	2	no	—
741	C₂²×C₄	—	2	2	no	—
742	C₂²×C₄	—	2	2	no	—
743	C₂²×C₄	—	2	2	no	—
744	C₂²×C₄	—	2	2	no	—
745	C₂²×C₄	—	2	2	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	2	no	—
748	C₂²×C₄	—	2	2	no	—
749	C₂²×C₄	—	2	2	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	2	no	—
752	C₂²×C₄	—	2	2	no	—
753	C₂²×C₄	—	2	8	no	—
754	C₂²×C₄	—	2	2	no	—
755	C₂²×C₄	—	2	2	no	—
756	C₂²×C₄	—	2	2	no	—
757	C₂²×C₄	—	2	2	no	—
758	C₂²×C₄	—	2	8	no	—
759	C₂²×C₄	—	2	2	no	—
760	C₂²×C₄	—	2	2	no	—
761	C₂²×C₄	—	2	2	no	—
762	C₂²×C₄	—	2	2	no	—
763	C₂²×C₄	—	2	2	no	—
764	C₂²×C₄	—	2	2	no	—
765	C₂²×C₄	—	2	2	no	—
766	C₂²×C₄	—	2	2	no	—
767	C₂²×C₄	—	2	2	no	—
768	C₂²×C₄	—	2	8	no	—
769	C₂²×C₄	—	2	8	no	—
770	C₂²×C₄	—	4	4	no	—
771	C₂²×C₄	—	4	4	no	—
772	C₂²×C₄	—	4	16	no	—
773	C₂²×C₄	—	4	16	no	—
774	C₂²×C₄	C₂×D₄×C₁₀₉	1	4	yes	—
775	C₂²×C₄	C₂×D₄×C₁₀₉	1	4	yes	—
776	C₂²×C₄	C₂×D₄×C₁₀₉	1	4	yes	—
777	C₂²×C₄	C₂×D₄×C₁₀₉	1	4	yes	—
778	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
779	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
780	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
781	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
782	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
783	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
784	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
785	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
786	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
787	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
788	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
789	C₄⋊C₄	—	2	8	no	—
790	C₄⋊C₄	—	2	8	no	—
791	C₄⋊C₄	—	2	8	no	—
792	C₂²⋊C₄	—	2	8	no	—
793	C₂²⋊C₄	—	2	8	no	—
794	C₂²⋊C₄	—	2	8	no	—
795	C₂²⋊C₄	—	2	8	no	—
796	C₂²⋊C₄	—	2	8	no	—
797	C₂²⋊C₄	—	2	8	no	—
798	C₂²⋊C₄	—	2	8	no	—
799	C₂²⋊C₄	—	2	8	no	—
800	C₂²⋊C₄	—	2	8	no	—
801	C₂²⋊C₄	—	2	8	no	—
802	C₂²⋊C₄	—	2	8	no	—
803	C₂²⋊C₄	—	4	4	no	—
804	C₂²⋊C₄	—	4	4	no	—
805	C₂²⋊C₄	—	4	4	no	—
806	C₂²⋊C₄	—	4	4	no	—
807	C₂²⋊C₄	C₂×D₄×C₁₀₉	1	16	yes	—
808	C₂²⋊C₄	C₂×D₄×C₁₀₉	1	16	yes	complemented
809	C₄²	—	2	8	no	—
810	C₄²	—	4	4	no	—
811	C₂³	—	2	8	no	—
812	C₂³	—	2	8	no	—
813	C₂³	—	2	8	no	—
814	C₂³	—	2	8	no	—
815	C₂³	—	2	8	no	—
816	C₂³	—	2	8	no	—
817	C₂³	—	2	2	no	—
818	C₂³	—	2	2	no	—
819	C₂³	—	2	2	no	—
820	C₂³	—	2	2	no	—
821	C₂³	—	2	32	no	—
822	C₂³	—	2	8	no	—
823	C₂³	—	2	8	no	—
824	C₂³	—	2	8	no	—
825	C₂³	—	2	8	no	—
826	C₂³	—	2	8	no	—
827	C₂³	—	2	8	no	—
828	C₂³	—	2	2	no	—
829	C₂³	—	2	2	no	—
830	C₂³	—	2	2	no	—
831	C₂³	—	2	2	no	—
832	C₂³	—	2	2	no	—
833	C₂³	—	2	2	no	—
834	C₂³	—	2	2	no	—
835	C₂³	—	2	2	no	—
836	C₂³	—	2	2	no	—
837	C₂³	—	2	2	no	—
838	C₂³	—	2	2	no	—
839	C₂³	—	2	2	no	—
840	C₂³	—	2	2	no	—
841	C₂³	—	2	2	no	—
842	C₂³	—	2	2	no	—
843	C₂³	—	2	2	no	—
844	C₂³	—	2	2	no	—
845	C₂³	—	2	2	no	—
846	C₂³	—	2	2	no	—
847	C₂³	—	4	16	no	—
848	C₂³	—	4	16	no	—
849	C₂³	—	4	16	no	—
850	C₂³	—	4	16	no	—
851	C₂³	—	4	16	no	—
852	C₂³	—	4	128	no	—
853	C₂³	—	4	4	no	—
854	C₂³	—	4	4	no	—
855	C₂³	—	4	16	no	—
856	C₂³	—	4	4	no	—
857	C₂³	—	4	4	no	—
858	C₂³	—	4	4	no	—
859	C₂³	—	4	4	no	—
860	C₂³	—	4	4	no	—
861	C₂³	—	4	4	no	—
862	C₂³	—	4	4	no	—
863	C₂³	—	4	4	no	—
864	C₂³	—	4	4	no	—
865	C₂³	—	4	4	no	—
866	C₂³	—	4	4	no	—
867	C₂³	—	4	4	no	—
868	C₂³	—	4	4	no	—
869	C₂³	#124×C₁₀₉	1	16	yes	complemented
870	C₂³	C₂²×D₄×C₁₀₉	1	4	yes	—
871	C₂³	C₂²×D₄×C₁₀₉	1	4	yes	—
872	C₂³	C₂²×D₄×C₁₀₉	1	2	yes	—
873	C₂³	C₂²×D₄×C₁₀₉	1	2	yes	—
874	C₂³	C₂×#41×C₁₀₉	1	4	yes	—
875	C₂³	C₂×#41×C₁₀₉	1	4	yes	—
876	C₂³	C₂×#41×C₁₀₉	1	4	yes	—
877	C₂³	C₂×#41×C₁₀₉	1	2	yes	—
878	C₂³	C₂×#41×C₁₀₉	1	2	yes	—
879	C₂³	C₂×#41×C₁₀₉	1	2	yes	—
880	C₂³	H(5,𝔽₂)×C₁₀₉	1	2	yes	—
881	C₂³	H(5,𝔽₂)×C₁₀₉	1	2	yes	—
882	C₂³	C₂⁵×C₁₀₉	1	1	yes	characteristic
883	Q₈	—	4	16	no	—
884	D₄	—	4	16	no	—
885	D₄	—	4	16	no	—
886	D₄	—	4	16	no	—
887	C₂×C₄	—	2	8	no	—
888	C₂×C₄	—	2	8	no	—
889	C₂×C₄	—	2	8	no	—
890	C₂×C₄	—	2	8	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	4	16	no	—
921	C₂×C₄	—	4	16	no	—
922	C₂×C₄	—	4	4	no	—
923	C₂×C₄	—	4	4	no	—
924	C₂×C₄	—	4	4	no	—
925	C₂×C₄	—	4	4	no	—
926	C₂×C₄	—	4	4	no	—
927	C₂×C₄	—	4	4	no	—
928	C₂×C₄	—	4	4	no	—
929	C₂×C₄	C₂²×D₄×C₁₀₉	1	4	yes	—
930	C₂×C₄	C₂²×D₄×C₁₀₉	1	4	yes	—
931	C₂×C₄	C₂²×D₄×C₁₀₉	1	4	yes	—
932	C₂×C₄	C₂²×D₄×C₁₀₉	1	4	yes	—
933	C₂²	—	2	4	no	—
934	C₂²	—	2	4	no	—
935	C₂²	—	2	4	no	—
936	C₂²	—	2	4	no	—
937	C₂²	—	2	4	no	—
938	C₂²	—	2	32	no	—
939	C₂²	—	2	4	no	—
940	C₂²	—	2	4	no	—
941	C₂²	—	2	4	no	—
942	C₂²	—	2	4	no	—
943	C₂²	—	2	4	no	—
944	C₂²	—	2	4	no	—
945	C₂²	—	2	4	no	—
946	C₂²	—	4	64	no	—
947	C₂²	—	4	2	no	—
948	C₂²	—	4	2	no	—
949	C₂²	—	4	2	no	—
950	C₂²	—	4	2	no	—
951	C₂²	—	4	2	no	—
952	C₂²	—	4	2	no	—
953	C₂²	—	4	16	no	—
954	C₂²	—	4	16	no	—
955	C₂²	—	4	2	no	—
956	C₂²	—	4	2	no	—
957	C₂²	—	4	2	no	—
958	C₂²	—	4	2	no	—
959	C₂²	—	4	2	no	—
960	C₂²	—	4	2	no	—
961	C₂²	—	4	2	no	—
962	C₂²	—	4	2	no	—
963	C₂²	—	4	2	no	—
964	C₂²	—	8	8	no	—
965	C₂²	#525×C₁₀₉	1	4	yes	—
966	C₂²	C₂×#124×C₁₀₉	1	4	yes	—
967	C₂²	C₂×#124×C₁₀₉	1	8	yes	complemented
968	C₂²	#538×C₁₀₉	1	4	yes	—
969	C₂²	D₄²×C₁₀₉	1	4	yes	—
970	C₂²	#546×C₁₀₉	1	4	yes	—
971	C₂²	#546×C₁₀₉	1	4	yes	—
972	C₂²	#551×C₁₀₉	1	4	yes	—
973	C₂²	C₂³×D₄×C₁₀₉	1	1	yes	characteristic
974	C₂²	C₂³×D₄×C₁₀₉	1	1	yes	characteristic
975	C₂²	C₂²×#41×C₁₀₉	1	1	yes	characteristic
976	C₂²	C₂²×#41×C₁₀₉	1	1	yes	characteristic
977	C₂²	C₂²×#41×C₁₀₉	1	1	yes	characteristic
978	C₂²	C₂×H(5,𝔽₂)×C₁₀₉	1	1	yes	characteristic
979	C₂²	C₂×H(5,𝔽₂)×C₁₀₉	1	1	yes	characteristic
980	C₄	—	2	4	no	—
981	C₄	—	2	4	no	—
982	C₄	—	2	4	no	—
983	C₄	—	2	4	no	—
984	C₄	—	4	2	no	—
985	C₄	—	4	2	no	—
986	C₄	—	4	2	no	—
987	C₄	—	4	2	no	—
988	C₄	—	4	2	no	—
989	C₄	—	4	2	no	—
990	C₄	—	4	2	no	—
991	C₂	—	2	8	no	—
992	C₂	—	4	4	no	—
993	C₂	—	4	4	no	—
994	C₂	—	8	2	no	—
995	C₂	C₁₀₉×#2472	1	8	yes	direct product factor
996	C₂	C₂×#525×C₁₀₉	1	1	yes	characteristic
997	C₂	C₂²×#124×C₁₀₉	1	1	yes	characteristic
998	C₂	C₂×#538×C₁₀₉	1	1	yes	characteristic
999	C₂	C₂×D₄²×C₁₀₉	1	1	yes	characteristic
1000	C₂	C₂×#546×C₁₀₉	1	1	yes	characteristic
1001	C₂	C₂×#546×C₁₀₉	1	1	yes	characteristic
1002	C₂	C₂×#551×C₁₀₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₀₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₀₉
prime radical	C₂²×#120×C₁₀₉	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₀₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#124×C₁₀₉	C₂	semidirect
2. C₂²×C₂²⋊Q₈×C₁₀₉	C₂	semidirect
4. C₂³×C₂²⋊C₄×C₁₀₉	C₂	semidirect
5. C₁₀₉×#2472	C₂	direct (N × H)
6. C₂×#397×C₁₀₉	C₂	semidirect
7. C₂×#394×C₁₀₉	C₂	semidirect
8. C₂×#394×C₁₀₉	C₂	semidirect
9. C₂×#393×C₁₀₉	C₂	semidirect
10. C₂×#390×C₁₀₉	C₂	semidirect
11. C₂×#388×C₁₀₉	C₂	semidirect
12. C₂×#388×C₁₀₉	C₂	semidirect
13. C₂×#386×C₁₀₉	C₂	semidirect
14. C₂×#386×C₁₀₉	C₂	semidirect
15. C₂×#379×C₁₀₉	C₂	semidirect
16. C₂×C₄×C₂²⋊C₄×C₁₀₉	C₂	semidirect
18. C₂³×Q₈×C₁₀₉	C₂²	semidirect
25. C₂×#124×C₁₀₉	C₂²	semidirect
27. C₂×C₂²⋊Q₈×C₁₀₉	C₂²	semidirect
30. C₂²×C₄⋊C₄×C₁₀₉	C₂²	semidirect
31. C₂²×C₄⋊C₄×C₁₀₉	C₂²	semidirect
32. C₂²×C₄⋊C₄×C₁₀₉	C₂²	semidirect
47. C₂²×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
48. C₂²×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
49. C₂²×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
50. C₂²×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
51. C₂²×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
52. C₂²×C₄²×C₁₀₉	C₂²	semidirect
53. C₂²×C₄²×C₁₀₉	C₂²	semidirect
54. #397×C₁₀₉	C₂²	semidirect
55. #394×C₁₀₉	C₂²	semidirect
56. #394×C₁₀₉	C₂²	semidirect
57. #393×C₁₀₉	C₂²	semidirect
58. #390×C₁₀₉	C₂²	semidirect
59. #388×C₁₀₉	C₂²	semidirect
60. #388×C₁₀₉	C₂²	semidirect
61. #386×C₁₀₉	C₂²	semidirect
62. #386×C₁₀₉	C₂²	semidirect
63. #379×C₁₀₉	C₂²	semidirect
64. C₄×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
65. C₂×#95×C₁₀₉	C₂²	semidirect
66. C₂×#95×C₁₀₉	C₂²	semidirect
67. C₂×#95×C₁₀₉	C₂²	semidirect
68. C₂×#95×C₁₀₉	C₂²	semidirect
69. C₂×#95×C₁₀₉	C₂²	semidirect
70. C₂×#95×C₁₀₉	C₂²	semidirect
86. C₂²×Q₈×C₁₀₉	C₂³	semidirect
124. C₂×C₄⋊C₄×C₁₀₉	C₂³	semidirect
125. C₂×C₄⋊C₄×C₁₀₉	C₂³	semidirect
126. C₂×C₄⋊C₄×C₁₀₉	C₂³	semidirect
144. C₂×C₂²⋊C₄×C₁₀₉	D₄	semidirect
158. C₂×C₂²⋊C₄×C₁₀₉	C₂³	semidirect
159. C₂×C₂²⋊C₄×C₁₀₉	C₂³	semidirect
160. C₂×C₂²⋊C₄×C₁₀₉	C₂³	semidirect
161. C₂×C₂²⋊C₄×C₁₀₉	C₂³	semidirect
164. C₂×C₄²×C₁₀₉	C₂³	semidirect
165. C₂×C₄²×C₁₀₉	C₂³	semidirect
166. #95×C₁₀₉	C₂³	semidirect
167. #95×C₁₀₉	C₂³	semidirect
168. #95×C₁₀₉	C₂³	semidirect
169. #95×C₁₀₉	C₂³	semidirect
170. #95×C₁₀₉	C₂³	semidirect
171. #95×C₁₀₉	C₂³	semidirect
306. C₂²⋊C₄×C₁₀₉	C₂×D₄	semidirect
367. C₂³×C₁₀₉	#124	semidirect
465. C₂²×C₁₀₉	C₂×#124	semidirect
489. C₂×#2472	C₁₀₉	direct (N × H)
494. C₂×C₁₀₉	#2472	direct (N × H)
502. C₂²×#124	C₂×C₁₀₉	semidirect
503. C₂²×C₂²⋊Q₈	C₂×C₁₀₉	semidirect
505. C₂³×C₂²⋊C₄	C₂×C₁₀₉	semidirect
506. #2472	C₂×C₁₀₉	direct (N × H)
507. C₂×#397	C₂×C₁₀₉	semidirect
508. C₂×#394	C₂×C₁₀₉	semidirect
509. C₂×#394	C₂×C₁₀₉	semidirect
510. C₂×#393	C₂×C₁₀₉	semidirect
511. C₂×#390	C₂×C₁₀₉	semidirect
512. C₂×#388	C₂×C₁₀₉	semidirect
513. C₂×#388	C₂×C₁₀₉	semidirect
514. C₂×#386	C₂×C₁₀₉	semidirect
515. C₂×#386	C₂×C₁₀₉	semidirect
516. C₂×#379	C₂×C₁₀₉	semidirect
517. C₂×C₄×C₂²⋊C₄	C₂×C₁₀₉	semidirect
518. C₁₀₉	C₂×#2472	direct (N × H)
520. C₂³×Q₈	C₂²×C₁₀₉	semidirect
527. C₂×#124	C₂²×C₁₀₉	semidirect
529. C₂×C₂²⋊Q₈	C₂²×C₁₀₉	semidirect
532. C₂²×C₄⋊C₄	C₂²×C₁₀₉	semidirect
533. C₂²×C₄⋊C₄	C₂²×C₁₀₉	semidirect
534. C₂²×C₄⋊C₄	C₂²×C₁₀₉	semidirect
549. C₂²×C₂²⋊C₄	C₂²×C₁₀₉	semidirect
550. C₂²×C₂²⋊C₄	C₂²×C₁₀₉	semidirect
551. C₂²×C₂²⋊C₄	C₂²×C₁₀₉	semidirect
552. C₂²×C₂²⋊C₄	C₂²×C₁₀₉	semidirect
553. C₂²×C₂²⋊C₄	C₂²×C₁₀₉	semidirect
554. C₂²×C₄²	C₂²×C₁₀₉	semidirect
555. C₂²×C₄²	C₂²×C₁₀₉	semidirect
556. #397	C₂²×C₁₀₉	semidirect
557. #394	C₂²×C₁₀₉	semidirect
558. #394	C₂²×C₁₀₉	semidirect
559. #393	C₂²×C₁₀₉	semidirect
560. #390	C₂²×C₁₀₉	semidirect
561. #388	C₂²×C₁₀₉	semidirect
562. #388	C₂²×C₁₀₉	semidirect
563. #386	C₂²×C₁₀₉	semidirect
564. #386	C₂²×C₁₀₉	semidirect
565. #379	C₂²×C₁₀₉	semidirect
566. C₄×C₂²⋊C₄	C₂²×C₁₀₉	semidirect
567. C₂×#95	C₂²×C₁₀₉	semidirect
568. C₂×#95	C₂²×C₁₀₉	semidirect
569. C₂×#95	C₂²×C₁₀₉	semidirect
570. C₂×#95	C₂²×C₁₀₉	semidirect
571. C₂×#95	C₂²×C₁₀₉	semidirect
572. C₂×#95	C₂²×C₁₀₉	semidirect
588. C₂²×Q₈	C₂³×C₁₀₉	semidirect
626. C₂×C₄⋊C₄	C₂³×C₁₀₉	semidirect
627. C₂×C₄⋊C₄	C₂³×C₁₀₉	semidirect
628. C₂×C₄⋊C₄	C₂³×C₁₀₉	semidirect
646. C₂×C₂²⋊C₄	D₄×C₁₀₉	semidirect
660. C₂×C₂²⋊C₄	C₂³×C₁₀₉	semidirect
661. C₂×C₂²⋊C₄	C₂³×C₁₀₉	semidirect
662. C₂×C₂²⋊C₄	C₂³×C₁₀₉	semidirect
663. C₂×C₂²⋊C₄	C₂³×C₁₀₉	semidirect
666. C₂×C₄²	C₂³×C₁₀₉	semidirect
667. C₂×C₄²	C₂³×C₁₀₉	semidirect
668. #95	C₂³×C₁₀₉	semidirect
669. #95	C₂³×C₁₀₉	semidirect
670. #95	C₂³×C₁₀₉	semidirect
671. #95	C₂³×C₁₀₉	semidirect
672. #95	C₂³×C₁₀₉	semidirect
673. #95	C₂³×C₁₀₉	semidirect
808. C₂²⋊C₄	C₂×D₄×C₁₀₉	semidirect
869. C₂³	#124×C₁₀₉	semidirect
967. C₂²	C₂×#124×C₁₀₉	semidirect
995. C₂	C₁₀₉×#2472	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#124×C₁₀₉	2
C₂²×C₂²⋊Q₈×C₁₀₉	2
C₂²×#120×C₁₀₉	2
C₂³×C₂²⋊C₄×C₁₀₉	2
C₁₀₉×#2472	2
C₂×#397×C₁₀₉	2
C₂×#394×C₁₀₉	2
C₂×#393×C₁₀₉	2
C₂×#390×C₁₀₉	2
C₂×#388×C₁₀₉	2
C₂×#386×C₁₀₉	2
C₂×#379×C₁₀₉	2
C₂×C₄×C₂²⋊C₄×C₁₀₉	2
C₂×#2472	109

Subgroups — C2×C109×#2472 #42152652

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₀₉×#2472 #42152652