Subgroups — C₁₇×#34264 #16892008

Order 4352.

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×C₁₇×#534	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₇×#518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×D₄×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#2364	C₂	1	4	yes	maximal, complemented
5	C₁₇×#2361	C₂	1	4	yes	maximal, complemented
6	C₁₇×#2359	C₂	1	4	yes	maximal, complemented
7	C₁₇×#2358	C₂	1	4	yes	maximal, complemented
8	C₁₇×#2322	C₂	1	2	yes	maximal, complemented
9	C₁₇×#2321	C₂	1	2	yes	maximal, complemented
10	C₁₇×#2308	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₇×#123	C₂	1	2	yes	maximal, complemented
12	C₄×C₁₇×#120	C₂	1	2	yes	maximal, complemented
13	C₂×C₁₇×#386	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₇×#385	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#2273	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₁₇	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₁₇	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₁₇	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
20	C₁₇×#534	C₄	1	16	yes	complemented
21	C₂×C₁₇×#123	C₂²	1	2	yes	—
22	C₂×C₁₇×#123	C₂²	1	2	yes	—
23	C₂×C₁₇×#121	C₂²	1	4	yes	—
24	C₂×C₁₇×#120	C₂²	1	2	yes	—
25	C₂×C₁₇×#120	C₂²	1	2	yes	—
26	C₁₇×#518	—	2	8	no	—
27	C₂×C₄×D₄×C₁₇	—	2	8	no	—
28	C₂×C₄×D₄×C₁₇	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₁₇	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₁₇	C₂²	1	4	yes	—
31	C₂×C₄×D₄×C₁₇	C₂²	1	2	yes	complemented
32	C₂×C₄×D₄×C₁₇	C₂²	1	4	yes	complemented
33	C₂×C₄×D₄×C₁₇	C₂²	1	2	yes	complemented
34	C₂×C₄×D₄×C₁₇	C₂²	1	4	yes	complemented
35	C₂×C₁₇×#117	C₂²	1	2	yes	complemented
36	C₂²×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₄⋊C₄×C₁₇	C₂²	1	2	yes	complemented
38	C₂²×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
39	C₂²×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
40	C₂²×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
41	C₂²×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
42	C₂²×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
43	C₂²×C₂²⋊C₄×C₁₇	C₂²	1	2	yes	complemented
44	C₂²×C₂²⋊C₄×C₁₇	C₂²	1	2	yes	complemented
45	C₂²×C₄²×C₁₇	C₂²	1	1	yes	characteristic, complemented
46	C₁₇×#390	C₂²	1	4	yes	complemented
47	C₁₇×#389	C₂²	1	4	yes	complemented
48	C₁₇×#388	C₂²	1	4	yes	complemented
49	C₁₇×#388	C₂²	1	4	yes	complemented
50	C₁₇×#388	C₂²	1	4	yes	complemented
51	C₁₇×#388	C₂²	1	4	yes	complemented
52	C₁₇×#387	C₂²	1	4	yes	complemented
53	C₁₇×#387	C₂²	1	4	yes	complemented
54	C₁₇×#386	C₂²	1	2	yes	—
55	C₁₇×#386	C₂²	1	2	yes	—
56	C₁₇×#386	C₂²	1	4	yes	—
57	C₁₇×#386	C₂²	1	4	yes	complemented
58	C₁₇×#386	C₂²	1	4	yes	complemented
59	C₁₇×#386	C₂²	1	2	yes	complemented
60	C₁₇×#386	C₂²	1	2	yes	complemented
61	C₁₇×#386	C₂²	1	4	yes	complemented
62	C₁₇×#385	C₂²	1	2	yes	complemented
63	C₁₇×#385	C₂²	1	2	yes	complemented
64	C₁₇×#385	C₂²	1	4	yes	complemented
65	C₁₇×#385	C₂²	1	4	yes	complemented
66	C₁₇×#385	C₂²	1	4	yes	complemented
67	C₁₇×#381	C₂²	1	2	yes	complemented
68	C₁₇×#379	C₂²	1	2	yes	complemented
69	C₄×C₄⋊C₄×C₁₇	C₂²	1	4	yes	complemented
70	C₄×C₂²⋊C₄×C₁₇	C₂²	1	2	yes	complemented
71	C₄×C₂²⋊C₄×C₁₇	C₂²	1	2	yes	complemented
72	C₄×C₂²⋊C₄×C₁₇	C₂²	1	4	yes	complemented
73	C₄×C₂²⋊C₄×C₁₇	C₂²	1	4	yes	complemented
74	C₄×C₂²⋊C₄×C₁₇	C₂²	1	4	yes	complemented
75	C₄×C₂²⋊C₄×C₁₇	C₂²	1	4	yes	complemented
76	C₂×C₁₇×#95	C₂²	1	2	yes	complemented
77	C₂×C₁₇×#95	C₂²	1	2	yes	complemented
78	C₂⁵×C₁₇	C₂³	1	1	yes	characteristic
79	C₂⁵×C₁₇	C₂³	1	1	yes	characteristic
80	C₂⁵×C₁₇	C₂³	1	1	yes	characteristic
81	C₂²×D₄×C₁₇	—	2	4	no	—
82	C₂²×D₄×C₁₇	—	2	4	no	—
83	C₂²×D₄×C₁₇	—	2	4	no	—
84	C₂²×D₄×C₁₇	—	2	4	no	—
85	C₂²×D₄×C₁₇	C₂×C₄	1	8	yes	complemented
86	C₂²×D₄×C₁₇	C₂×C₄	1	8	yes	complemented
87	C₂²×D₄×C₁₇	C₂³	1	2	yes	—
88	C₂²×D₄×C₁₇	C₂³	1	2	yes	—
89	C₂²×D₄×C₁₇	C₂³	1	2	yes	—
90	C₂²×D₄×C₁₇	C₂³	1	2	yes	—
91	C₂²×D₄×C₁₇	C₂³	1	4	yes	—
92	C₂³×C₄×C₁₇	—	2	4	no	—
93	C₂³×C₄×C₁₇	—	2	4	no	—
94	C₂³×C₄×C₁₇	—	4	4	no	—
95	C₂³×C₄×C₁₇	—	4	4	no	—
96	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
98	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
99	C₂³×C₄×C₁₇	C₂³	1	4	yes	—
100	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
103	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
107	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
108	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
109	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
111	C₁₇×#123	C₂×C₄	1	16	yes	complemented
112	C₁₇×#123	C₂×C₄	1	16	yes	complemented
113	C₁₇×#121	C₂×C₄	1	32	yes	complemented
114	C₁₇×#120	C₂×C₄	1	16	yes	complemented
115	C₁₇×#120	C₂×C₄	1	16	yes	complemented
116	C₄×D₄×C₁₇	—	2	8	no	—
117	C₄×D₄×C₁₇	—	2	8	no	—
118	C₄×D₄×C₁₇	—	2	16	no	—
119	C₄×D₄×C₁₇	—	2	16	no	—
120	C₄×D₄×C₁₇	—	2	8	no	—
121	C₄×D₄×C₁₇	—	2	8	no	—
122	C₄×D₄×C₁₇	—	4	8	no	—
123	C₁₇×#117	—	2	8	no	—
124	C₂×C₄⋊C₄×C₁₇	—	2	4	no	—
125	C₂×C₄⋊C₄×C₁₇	—	4	4	no	—
126	C₂×C₄⋊C₄×C₁₇	C₂³	1	4	yes	—
127	C₂×C₄⋊C₄×C₁₇	C₂³	1	4	yes	—
128	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₁₇	C₂³	1	4	yes	—
131	C₂×C₄⋊C₄×C₁₇	C₂³	1	4	yes	—
132	C₂×C₂²⋊C₄×C₁₇	—	2	4	no	—
133	C₂×C₂²⋊C₄×C₁₇	—	2	4	no	—
134	C₂×C₂²⋊C₄×C₁₇	—	2	4	no	—
135	C₂×C₂²⋊C₄×C₁₇	—	2	8	no	—
136	C₂×C₂²⋊C₄×C₁₇	—	4	4	no	—
137	C₂×C₂²⋊C₄×C₁₇	C₂×C₄	1	8	yes	complemented
138	C₂×C₂²⋊C₄×C₁₇	D₄	1	8	yes	complemented
139	C₂×C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₁₇	C₂³	1	4	yes	—
145	C₂×C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₁₇	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₁₇	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₁₇	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₁₇	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₁₇	C₂³	1	4	yes	—
153	C₂×C₂²⋊C₄×C₁₇	C₂³	1	4	yes	—
154	C₂×C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
156	C₂×C₄²×C₁₇	—	2	4	no	—
157	C₂×C₄²×C₁₇	C₂³	1	4	yes	—
158	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
159	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
160	C₂×C₄²×C₁₇	C₂³	1	4	yes	—
161	C₂×C₄²×C₁₇	C₂³	1	4	yes	—
162	C₁₇×#95	C₂³	1	4	yes	—
163	C₁₇×#95	C₂³	1	4	yes	—
164	C₁₇×#95	C₂³	1	4	yes	—
165	C₁₇×#95	C₂³	1	4	yes	—
166	C₁₇×#95	C₂³	1	4	yes	—
167	C₁₇×#95	C₂³	1	4	yes	—
168	C₁₇×#95	C₂³	1	4	yes	—
169	C₁₇×#95	C₂³	1	4	yes	—
170	C₂⁴×C₁₇	—	2	2	no	—
171	C₂⁴×C₁₇	—	2	2	no	—
172	C₂⁴×C₁₇	—	2	2	no	—
173	C₂⁴×C₁₇	—	2	2	no	—
174	C₂⁴×C₁₇	—	4	2	no	—
175	C₂⁴×C₁₇	—	4	2	no	—
176	C₂⁴×C₁₇	—	4	2	no	—
177	C₂⁴×C₁₇	—	4	2	no	—
178	C₂⁴×C₁₇	—	4	2	no	—
179	C₂⁴×C₁₇	—	4	2	no	—
180	C₂⁴×C₁₇	C₂²×C₄	1	4	yes	—
181	C₂⁴×C₁₇	C₂²×C₄	1	4	yes	—
182	C₂⁴×C₁₇	C₂²×C₄	1	4	yes	complemented
183	C₂⁴×C₁₇	C₂×D₄	1	4	yes	—
184	C₂⁴×C₁₇	#41	1	4	yes	—
185	C₂⁴×C₁₇	C₂⁴	1	2	yes	—
186	C₂⁴×C₁₇	C₂⁴	1	2	yes	—
187	C₂⁴×C₁₇	C₂⁴	1	1	yes	characteristic
188	C₂⁴×C₁₇	C₂⁴	1	1	yes	characteristic
189	C₂⁴×C₁₇	C₂⁴	1	1	yes	characteristic
190	C₂×D₄×C₁₇	—	2	32	no	—
191	C₂×D₄×C₁₇	—	2	32	no	—
192	C₂×D₄×C₁₇	—	2	4	no	—
193	C₂×D₄×C₁₇	—	2	4	no	—
194	C₂×D₄×C₁₇	—	2	4	no	—
195	C₂×D₄×C₁₇	—	2	4	no	—
196	C₂×D₄×C₁₇	—	2	4	no	—
197	C₂×D₄×C₁₇	—	2	4	no	—
198	C₂×D₄×C₁₇	—	2	4	no	—
199	C₂×D₄×C₁₇	—	2	4	no	—
200	C₂×D₄×C₁₇	—	4	4	no	—
201	C₂×D₄×C₁₇	—	4	4	no	—
202	C₂×D₄×C₁₇	C₂²×C₄	1	8	yes	—
203	C₂×D₄×C₁₇	C₂²×C₄	1	8	yes	—
204	C₂×D₄×C₁₇	C₂²×C₄	1	8	yes	—
205	C₂×D₄×C₁₇	C₂²×C₄	1	8	yes	complemented
206	C₂×D₄×C₁₇	C₂²×C₄	1	16	yes	complemented
207	C₂²×C₄×C₁₇	—	2	2	no	—
208	C₂²×C₄×C₁₇	—	2	2	no	—
209	C₂²×C₄×C₁₇	—	2	2	no	—
210	C₂²×C₄×C₁₇	—	2	2	no	—
211	C₂²×C₄×C₁₇	—	2	2	no	—
212	C₂²×C₄×C₁₇	—	2	4	no	—
213	C₂²×C₄×C₁₇	—	2	2	no	—
214	C₂²×C₄×C₁₇	—	2	4	no	—
215	C₂²×C₄×C₁₇	—	2	4	no	—
216	C₂²×C₄×C₁₇	—	2	2	no	—
217	C₂²×C₄×C₁₇	—	2	2	no	—
218	C₂²×C₄×C₁₇	—	2	4	no	—
219	C₂²×C₄×C₁₇	—	2	8	no	—
220	C₂²×C₄×C₁₇	—	2	4	no	—
221	C₂²×C₄×C₁₇	—	2	4	no	—
222	C₂²×C₄×C₁₇	—	2	8	no	—
223	C₂²×C₄×C₁₇	—	2	4	no	—
224	C₂²×C₄×C₁₇	—	2	4	no	—
225	C₂²×C₄×C₁₇	—	4	2	no	—
226	C₂²×C₄×C₁₇	—	4	4	no	—
227	C₂²×C₄×C₁₇	—	4	2	no	—
228	C₂²×C₄×C₁₇	—	4	2	no	—
229	C₂²×C₄×C₁₇	—	4	2	no	—
230	C₂²×C₄×C₁₇	—	4	2	no	—
231	C₂²×C₄×C₁₇	—	4	2	no	—
232	C₂²×C₄×C₁₇	—	4	2	no	—
233	C₂²×C₄×C₁₇	—	4	4	no	—
234	C₂²×C₄×C₁₇	—	4	2	no	—
235	C₂²×C₄×C₁₇	—	4	2	no	—
236	C₂²×C₄×C₁₇	—	4	2	no	—
237	C₂²×C₄×C₁₇	—	4	2	no	—
238	C₂²×C₄×C₁₇	—	4	4	no	—
239	C₂²×C₄×C₁₇	—	4	16	no	—
240	C₂²×C₄×C₁₇	—	4	16	no	—
241	C₂²×C₄×C₁₇	C₂²×C₄	1	4	yes	—
242	C₂²×C₄×C₁₇	C₂²×C₄	1	4	yes	complemented
243	C₂²×C₄×C₁₇	C₂²×C₄	1	8	yes	complemented
244	C₂²×C₄×C₁₇	C₂×D₄	1	4	yes	—
245	C₂²×C₄×C₁₇	C₂×D₄	1	4	yes	—
246	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₁₇	C₂⁴	1	4	yes	—
250	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₁₇	C₂⁴	1	4	yes	—
253	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
256	C₄⋊C₄×C₁₇	—	2	8	no	—
257	C₄⋊C₄×C₁₇	—	2	4	no	—
258	C₄⋊C₄×C₁₇	—	2	4	no	—
259	C₄⋊C₄×C₁₇	—	2	8	no	—
260	C₄⋊C₄×C₁₇	—	4	4	no	—
261	C₄⋊C₄×C₁₇	C₂²×C₄	1	16	yes	complemented
262	C₂²⋊C₄×C₁₇	—	2	4	no	—
263	C₂²⋊C₄×C₁₇	—	2	4	no	—
264	C₂²⋊C₄×C₁₇	—	2	4	no	—
265	C₂²⋊C₄×C₁₇	—	2	4	no	—
266	C₂²⋊C₄×C₁₇	—	2	4	no	—
267	C₂²⋊C₄×C₁₇	—	2	4	no	—
268	C₂²⋊C₄×C₁₇	—	2	8	no	—
269	C₂²⋊C₄×C₁₇	—	2	8	no	—
270	C₂²⋊C₄×C₁₇	—	4	4	no	—
271	C₂²⋊C₄×C₁₇	—	4	4	no	—
272	C₂²⋊C₄×C₁₇	—	4	4	no	—
273	C₂²⋊C₄×C₁₇	C₂²×C₄	1	8	yes	—
274	C₂²⋊C₄×C₁₇	C₂²×C₄	1	8	yes	complemented
275	C₂²⋊C₄×C₁₇	C₂²×C₄	1	16	yes	complemented
276	C₂²⋊C₄×C₁₇	C₂²×C₄	1	16	yes	complemented
277	C₂²⋊C₄×C₁₇	C₂×D₄	1	8	yes	—
278	C₂²⋊C₄×C₁₇	C₂×D₄	1	8	yes	—
279	C₄²×C₁₇	—	2	8	no	—
280	C₄²×C₁₇	—	2	4	no	—
281	C₄²×C₁₇	—	2	4	no	—
282	C₄²×C₁₇	—	4	4	no	—
283	C₄²×C₁₇	—	4	4	no	—
284	#34264	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
285	C₂³×C₁₇	—	2	2	no	—
286	C₂³×C₁₇	—	2	2	no	—
287	C₂³×C₁₇	—	2	2	no	—
288	C₂³×C₁₇	—	2	2	no	—
289	C₂³×C₁₇	—	2	2	no	—
290	C₂³×C₁₇	—	2	2	no	—
291	C₂³×C₁₇	—	2	8	no	—
292	C₂³×C₁₇	—	2	2	no	—
293	C₂³×C₁₇	—	2	2	no	—
294	C₂³×C₁₇	—	2	2	no	—
295	C₂³×C₁₇	—	2	2	no	—
296	C₂³×C₁₇	—	2	4	no	—
297	C₂³×C₁₇	—	2	4	no	—
298	C₂³×C₁₇	—	2	4	no	—
299	C₂³×C₁₇	—	2	4	no	—
300	C₂³×C₁₇	—	2	8	no	—
301	C₂³×C₁₇	—	4	4	no	—
302	C₂³×C₁₇	—	4	8	no	—
303	C₂³×C₁₇	—	4	8	no	—
304	C₂³×C₁₇	—	4	4	no	—
305	C₂³×C₁₇	—	4	8	no	—
306	C₂³×C₁₇	—	4	8	no	—
307	C₂³×C₁₇	—	4	4	no	—
308	C₂³×C₁₇	—	4	4	no	—
309	C₂³×C₁₇	—	4	8	no	—
310	C₂³×C₁₇	—	8	2	no	—
311	C₂³×C₁₇	—	8	2	no	—
312	C₂³×C₁₇	—	8	4	no	—
313	C₂³×C₁₇	C₄×D₄	1	16	yes	complemented
314	C₂³×C₁₇	C₂³×C₄	1	4	yes	—
315	C₂³×C₁₇	C₂³×C₄	1	4	yes	—
316	C₂³×C₁₇	C₂³×C₄	1	2	yes	—
317	C₂³×C₁₇	C₂³×C₄	1	2	yes	—
318	C₂³×C₁₇	C₂³×C₄	1	2	yes	—
319	C₂³×C₁₇	C₂²×D₄	1	2	yes	—
320	C₂³×C₁₇	C₂²×D₄	1	2	yes	—
321	C₂³×C₁₇	C₂²×D₄	1	2	yes	—
322	C₂³×C₁₇	C₂×#41	1	2	yes	—
323	C₂³×C₁₇	C₂×#41	1	2	yes	—
324	C₂³×C₁₇	C₂×#41	1	2	yes	—
325	C₂³×C₁₇	C₂⁵	1	1	yes	characteristic
326	D₄×C₁₇	—	2	16	no	—
327	D₄×C₁₇	—	2	16	no	—
328	D₄×C₁₇	—	2	16	no	—
329	D₄×C₁₇	—	2	16	no	—
330	D₄×C₁₇	—	4	16	no	—
331	C₂×C₄×C₁₇	—	2	8	no	—
332	C₂×C₄×C₁₇	—	2	8	no	—
333	C₂×C₄×C₁₇	—	2	8	no	—
334	C₂×C₄×C₁₇	—	2	2	no	—
335	C₂×C₄×C₁₇	—	2	2	no	—
336	C₂×C₄×C₁₇	—	2	2	no	—
337	C₂×C₄×C₁₇	—	2	2	no	—
338	C₂×C₄×C₁₇	—	2	2	no	—
339	C₂×C₄×C₁₇	—	2	4	no	—
340	C₂×C₄×C₁₇	—	2	4	no	—
341	C₂×C₄×C₁₇	—	2	2	no	—
342	C₂×C₄×C₁₇	—	2	4	no	—
343	C₂×C₄×C₁₇	—	2	4	no	—
344	C₂×C₄×C₁₇	—	2	2	no	—
345	C₂×C₄×C₁₇	—	2	2	no	—
346	C₂×C₄×C₁₇	—	2	2	no	—
347	C₂×C₄×C₁₇	—	2	4	no	—
348	C₂×C₄×C₁₇	—	2	4	no	—
349	C₂×C₄×C₁₇	—	2	2	no	—
350	C₂×C₄×C₁₇	—	2	4	no	—
351	C₂×C₄×C₁₇	—	2	2	no	—
352	C₂×C₄×C₁₇	—	2	4	no	—
353	C₂×C₄×C₁₇	—	2	4	no	—
354	C₂×C₄×C₁₇	—	4	4	no	—
355	C₂×C₄×C₁₇	—	4	8	no	—
356	C₂×C₄×C₁₇	—	4	4	no	—
357	C₂×C₄×C₁₇	—	4	16	no	—
358	C₂×C₄×C₁₇	—	4	8	no	—
359	C₂×C₄×C₁₇	—	4	8	no	—
360	C₂×C₄×C₁₇	—	4	4	no	—
361	C₂×C₄×C₁₇	—	8	4	no	—
362	C₂×C₄×C₁₇	—	8	4	no	—
363	C₂×C₄×C₁₇	—	8	2	no	—
364	C₂×C₄×C₁₇	—	8	2	no	—
365	C₂×C₄×C₁₇	—	8	4	no	—
366	C₂×C₄×C₁₇	C₂³×C₄	1	8	yes	—
367	C₂×C₄×C₁₇	C₂³×C₄	1	4	yes	—
368	C₂×C₄×C₁₇	C₂³×C₄	1	4	yes	—
369	C₂×C₄×C₁₇	C₂²×D₄	1	4	yes	—
370	C₂×C₄×C₁₇	C₂²×D₄	1	4	yes	—
371	C₂×C₄×C₁₇	H(5,𝔽₂)	1	4	yes	—
372	C₂×#534	C₂×C₁₇	1	1	yes	characteristic
373	C₂×#518	C₂×C₁₇	1	1	yes	characteristic, complemented
374	C₂²×C₄×D₄	C₂×C₁₇	1	1	yes	characteristic, complemented
375	#2364	C₂×C₁₇	1	4	yes	complemented
376	#2361	C₂×C₁₇	1	4	yes	complemented
377	#2359	C₂×C₁₇	1	4	yes	complemented
378	#2358	C₂×C₁₇	1	4	yes	complemented
379	#2322	C₂×C₁₇	1	2	yes	complemented
380	#2321	C₂×C₁₇	1	2	yes	complemented
381	#2308	C₂×C₁₇	1	1	yes	characteristic, complemented
382	C₄×#123	C₂×C₁₇	1	2	yes	complemented
383	C₄×#120	C₂×C₁₇	1	2	yes	complemented
384	C₂×#386	C₂×C₁₇	1	1	yes	characteristic, complemented
385	C₂×#385	C₂×C₁₇	1	1	yes	characteristic, complemented
386	#2273	C₂×C₁₇	1	1	yes	characteristic, complemented
387	C₂²×C₁₇	—	2	4	no	—
388	C₂²×C₁₇	—	2	4	no	—
389	C₂²×C₁₇	—	2	4	no	—
390	C₂²×C₁₇	—	2	2	no	—
391	C₂²×C₁₇	—	2	2	no	—
392	C₂²×C₁₇	—	2	2	no	—
393	C₂²×C₁₇	—	2	2	no	—
394	C₂²×C₁₇	—	2	2	no	—
395	C₂²×C₁₇	—	2	2	no	—
396	C₂²×C₁₇	—	2	4	no	—
397	C₂²×C₁₇	—	2	4	no	—
398	C₂²×C₁₇	—	2	4	no	—
399	C₂²×C₁₇	—	2	4	no	—
400	C₂²×C₁₇	—	2	4	no	—
401	C₂²×C₁₇	—	2	8	no	—
402	C₂²×C₁₇	—	2	8	no	—
403	C₂²×C₁₇	—	4	16	no	—
404	C₂²×C₁₇	—	4	16	no	—
405	C₂²×C₁₇	—	4	2	no	—
406	C₂²×C₁₇	—	4	2	no	—
407	C₂²×C₁₇	—	4	2	no	—
408	C₂²×C₁₇	—	4	2	no	—
409	C₂²×C₁₇	—	4	4	no	—
410	C₂²×C₁₇	—	4	4	no	—
411	C₂²×C₁₇	—	8	8	no	—
412	C₂²×C₁₇	C₂×C₄×D₄	1	4	yes	—
413	C₂²×C₁₇	C₂×C₄×D₄	1	4	yes	—
414	C₂²×C₁₇	C₂×C₄×D₄	1	4	yes	—
415	C₂²×C₁₇	C₂⁴×C₄	1	1	yes	characteristic
416	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
417	C₂²×C₁₇	C₂²×#41	1	1	yes	characteristic
418	C₂²×C₁₇	C₂×H(5,𝔽₂)	1	2	yes	—
419	C₂²×C₁₇	#585	1	2	yes	—
420	C₄×C₁₇	—	2	4	no	—
421	C₄×C₁₇	—	2	4	no	—
422	C₄×C₁₇	—	2	8	no	—
423	C₄×C₁₇	—	2	4	no	—
424	C₄×C₁₇	—	2	4	no	—
425	C₄×C₁₇	—	2	4	no	—
426	C₄×C₁₇	—	4	2	no	—
427	C₄×C₁₇	—	4	2	no	—
428	C₄×C₁₇	—	4	2	no	—
429	C₄×C₁₇	—	4	4	no	—
430	C₂³×D₄	C₂²×C₁₇	1	1	yes	characteristic
431	C₂³×D₄	C₂²×C₁₇	1	1	yes	characteristic
432	C₂⁴×C₄	C₂²×C₁₇	1	1	yes	characteristic
433	C₂⁴×C₄	C₂²×C₁₇	1	1	yes	characteristic, complemented
434	#534	C₄×C₁₇	1	16	yes	complemented
435	C₂×#123	C₂²×C₁₇	1	2	yes	—
436	C₂×#123	C₂²×C₁₇	1	2	yes	—
437	C₂×#121	C₂²×C₁₇	1	4	yes	—
438	C₂×#120	C₂²×C₁₇	1	2	yes	—
439	C₂×#120	C₂²×C₁₇	1	2	yes	—
440	#518	—	2	8	no	—
441	C₂×C₄×D₄	—	2	8	no	—
442	C₂×C₄×D₄	C₂²×C₁₇	1	2	yes	—
443	C₂×C₄×D₄	C₂²×C₁₇	1	2	yes	—
444	C₂×C₄×D₄	C₂²×C₁₇	1	4	yes	—
445	C₂×C₄×D₄	C₂²×C₁₇	1	2	yes	complemented
446	C₂×C₄×D₄	C₂²×C₁₇	1	4	yes	complemented
447	C₂×C₄×D₄	C₂²×C₁₇	1	2	yes	complemented
448	C₂×C₄×D₄	C₂²×C₁₇	1	4	yes	complemented
449	C₂×#117	C₂²×C₁₇	1	2	yes	complemented
450	C₂²×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic, complemented
451	C₂²×C₄⋊C₄	C₂²×C₁₇	1	2	yes	complemented
452	C₂²×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
453	C₂²×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
454	C₂²×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
455	C₂²×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
456	C₂²×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic, complemented
457	C₂²×C₂²⋊C₄	C₂²×C₁₇	1	2	yes	complemented
458	C₂²×C₂²⋊C₄	C₂²×C₁₇	1	2	yes	complemented
459	C₂²×C₄²	C₂²×C₁₇	1	1	yes	characteristic, complemented
460	#390	C₂²×C₁₇	1	4	yes	complemented
461	#389	C₂²×C₁₇	1	4	yes	complemented
462	#388	C₂²×C₁₇	1	4	yes	complemented
463	#388	C₂²×C₁₇	1	4	yes	complemented
464	#388	C₂²×C₁₇	1	4	yes	complemented
465	#388	C₂²×C₁₇	1	4	yes	complemented
466	#387	C₂²×C₁₇	1	4	yes	complemented
467	#387	C₂²×C₁₇	1	4	yes	complemented
468	#386	C₂²×C₁₇	1	4	yes	—
469	#386	C₂²×C₁₇	1	2	yes	—
470	#386	C₂²×C₁₇	1	2	yes	—
471	#386	C₂²×C₁₇	1	2	yes	complemented
472	#386	C₂²×C₁₇	1	2	yes	complemented
473	#386	C₂²×C₁₇	1	4	yes	complemented
474	#386	C₂²×C₁₇	1	4	yes	complemented
475	#386	C₂²×C₁₇	1	4	yes	complemented
476	#385	C₂²×C₁₇	1	2	yes	complemented
477	#385	C₂²×C₁₇	1	4	yes	complemented
478	#385	C₂²×C₁₇	1	4	yes	complemented
479	#385	C₂²×C₁₇	1	4	yes	complemented
480	#385	C₂²×C₁₇	1	2	yes	complemented
481	#381	C₂²×C₁₇	1	2	yes	complemented
482	#379	C₂²×C₁₇	1	2	yes	complemented
483	C₄×C₄⋊C₄	C₂²×C₁₇	1	4	yes	complemented
484	C₄×C₂²⋊C₄	C₂²×C₁₇	1	2	yes	complemented
485	C₄×C₂²⋊C₄	C₂²×C₁₇	1	2	yes	complemented
486	C₄×C₂²⋊C₄	C₂²×C₁₇	1	4	yes	complemented
487	C₄×C₂²⋊C₄	C₂²×C₁₇	1	4	yes	complemented
488	C₄×C₂²⋊C₄	C₂²×C₁₇	1	4	yes	complemented
489	C₄×C₂²⋊C₄	C₂²×C₁₇	1	4	yes	complemented
490	C₂×#95	C₂²×C₁₇	1	2	yes	complemented
491	C₂×#95	C₂²×C₁₇	1	2	yes	complemented
492	C₂×C₁₇	—	2	4	no	—
493	C₂×C₁₇	—	2	4	no	—
494	C₂×C₁₇	—	2	4	no	—
495	C₂×C₁₇	—	4	4	no	—
496	C₂×C₁₇	—	4	4	no	—
497	C₂×C₁₇	C₂²×C₄×D₄	1	1	yes	characteristic
498	C₂×C₁₇	C₄×H(5,𝔽₂)	1	2	yes	—
499	C₂×C₁₇	#3484	1	1	yes	characteristic
500	C₂×C₁₇	#3485	1	1	yes	characteristic
501	C₂×C₁₇	#3505	1	2	yes	—
502	C₂⁵	C₂³×C₁₇	1	1	yes	characteristic
503	C₂⁵	C₂³×C₁₇	1	1	yes	characteristic
504	C₂⁵	C₂³×C₁₇	1	1	yes	characteristic
505	C₂²×D₄	—	2	4	no	—
506	C₂²×D₄	—	2	4	no	—
507	C₂²×D₄	—	2	4	no	—
508	C₂²×D₄	—	2	4	no	—
509	C₂²×D₄	C₂×C₄×C₁₇	1	8	yes	complemented
510	C₂²×D₄	C₂×C₄×C₁₇	1	8	yes	complemented
511	C₂²×D₄	C₂³×C₁₇	1	2	yes	—
512	C₂²×D₄	C₂³×C₁₇	1	2	yes	—
513	C₂²×D₄	C₂³×C₁₇	1	2	yes	—
514	C₂²×D₄	C₂³×C₁₇	1	2	yes	—
515	C₂²×D₄	C₂³×C₁₇	1	4	yes	—
516	C₂³×C₄	—	2	4	no	—
517	C₂³×C₄	—	2	4	no	—
518	C₂³×C₄	—	4	4	no	—
519	C₂³×C₄	—	4	4	no	—
520	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
521	C₂³×C₄	C₂³×C₁₇	1	2	yes	—
522	C₂³×C₄	C₂³×C₁₇	1	2	yes	—
523	C₂³×C₄	C₂³×C₁₇	1	4	yes	—
524	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
525	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
526	C₂³×C₄	C₂³×C₁₇	1	2	yes	—
527	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
528	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
529	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
530	C₂³×C₄	C₂³×C₁₇	1	2	yes	—
531	C₂³×C₄	C₂³×C₁₇	1	2	yes	—
532	C₂³×C₄	C₂³×C₁₇	1	2	yes	—
533	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
534	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
535	#123	C₂×C₄×C₁₇	1	16	yes	complemented
536	#123	C₂×C₄×C₁₇	1	16	yes	complemented
537	#121	C₂×C₄×C₁₇	1	32	yes	complemented
538	#120	C₂×C₄×C₁₇	1	16	yes	complemented
539	#120	C₂×C₄×C₁₇	1	16	yes	complemented
540	C₄×D₄	—	2	8	no	—
541	C₄×D₄	—	2	8	no	—
542	C₄×D₄	—	2	16	no	—
543	C₄×D₄	—	2	16	no	—
544	C₄×D₄	—	2	8	no	—
545	C₄×D₄	—	2	8	no	—
546	C₄×D₄	—	4	8	no	—
547	#117	—	2	8	no	—
548	C₂×C₄⋊C₄	—	2	4	no	—
549	C₂×C₄⋊C₄	—	4	4	no	—
550	C₂×C₄⋊C₄	C₂³×C₁₇	1	4	yes	—
551	C₂×C₄⋊C₄	C₂³×C₁₇	1	4	yes	—
552	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
553	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
554	C₂×C₄⋊C₄	C₂³×C₁₇	1	4	yes	—
555	C₂×C₄⋊C₄	C₂³×C₁₇	1	4	yes	—
556	C₂×C₂²⋊C₄	—	2	4	no	—
557	C₂×C₂²⋊C₄	—	2	4	no	—
558	C₂×C₂²⋊C₄	—	2	4	no	—
559	C₂×C₂²⋊C₄	—	2	8	no	—
560	C₂×C₂²⋊C₄	—	4	4	no	—
561	C₂×C₂²⋊C₄	C₂×C₄×C₁₇	1	8	yes	complemented
562	C₂×C₂²⋊C₄	D₄×C₁₇	1	8	yes	complemented
563	C₂×C₂²⋊C₄	C₂³×C₁₇	1	2	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₁₇	1	2	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₁₇	1	2	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₁₇	1	2	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₁₇	1	2	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₁₇	1	4	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₁₇	1	2	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₁₇	1	4	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₁₇	1	4	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₁₇	1	4	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₁₇	1	4	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₁₇	1	2	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₁₇	1	2	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₁₇	1	4	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₁₇	1	4	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₁₇	1	2	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₁₇	1	2	yes	—
580	C₂×C₄²	—	2	4	no	—
581	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
582	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
583	C₂×C₄²	C₂³×C₁₇	1	4	yes	—
584	C₂×C₄²	C₂³×C₁₇	1	4	yes	—
585	C₂×C₄²	C₂³×C₁₇	1	4	yes	—
586	#95	C₂³×C₁₇	1	4	yes	—
587	#95	C₂³×C₁₇	1	4	yes	—
588	#95	C₂³×C₁₇	1	4	yes	—
589	#95	C₂³×C₁₇	1	4	yes	—
590	#95	C₂³×C₁₇	1	4	yes	—
591	#95	C₂³×C₁₇	1	4	yes	—
592	#95	C₂³×C₁₇	1	4	yes	—
593	#95	C₂³×C₁₇	1	4	yes	—
594	C₁₇	#34264	1	1	yes	characteristic, direct product factor, Sylow
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×C₁₇	1	4	yes	—
606	C₂⁴	C₂²×C₄×C₁₇	1	4	yes	—
607	C₂⁴	C₂²×C₄×C₁₇	1	4	yes	complemented
608	C₂⁴	C₂×D₄×C₁₇	1	4	yes	—
609	C₂⁴	#41×C₁₇	1	4	yes	—
610	C₂⁴	C₂⁴×C₁₇	1	2	yes	—
611	C₂⁴	C₂⁴×C₁₇	1	2	yes	—
612	C₂⁴	C₂⁴×C₁₇	1	1	yes	characteristic
613	C₂⁴	C₂⁴×C₁₇	1	1	yes	characteristic
614	C₂⁴	C₂⁴×C₁₇	1	1	yes	characteristic
615	C₂×D₄	—	2	4	no	—
616	C₂×D₄	—	2	4	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	32	no	—
624	C₂×D₄	—	2	32	no	—
625	C₂×D₄	—	4	4	no	—
626	C₂×D₄	—	4	4	no	—
627	C₂×D₄	C₂²×C₄×C₁₇	1	8	yes	—
628	C₂×D₄	C₂²×C₄×C₁₇	1	8	yes	—
629	C₂×D₄	C₂²×C₄×C₁₇	1	8	yes	—
630	C₂×D₄	C₂²×C₄×C₁₇	1	8	yes	complemented
631	C₂×D₄	C₂²×C₄×C₁₇	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×C₁₇	1	4	yes	—
667	C₂²×C₄	C₂²×C₄×C₁₇	1	4	yes	complemented
668	C₂²×C₄	C₂²×C₄×C₁₇	1	8	yes	complemented
669	C₂²×C₄	C₂×D₄×C₁₇	1	4	yes	—
670	C₂²×C₄	C₂×D₄×C₁₇	1	4	yes	—
671	C₂²×C₄	C₂⁴×C₁₇	1	4	yes	—
672	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
673	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
674	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
675	C₂²×C₄	C₂⁴×C₁₇	1	4	yes	—
676	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
677	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
678	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
680	C₂²×C₄	C₂⁴×C₁₇	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×C₁₇	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×C₁₇	1	8	yes	—
699	C₂²⋊C₄	C₂²×C₄×C₁₇	1	8	yes	complemented
700	C₂²⋊C₄	C₂²×C₄×C₁₇	1	16	yes	complemented
701	C₂²⋊C₄	C₂²×C₄×C₁₇	1	16	yes	complemented
702	C₂²⋊C₄	C₂×D₄×C₁₇	1	8	yes	—
703	C₂²⋊C₄	C₂×D₄×C₁₇	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×C₁₇	1	16	yes	complemented
738	C₂³	C₂³×C₄×C₁₇	1	4	yes	—
739	C₂³	C₂³×C₄×C₁₇	1	4	yes	—
740	C₂³	C₂³×C₄×C₁₇	1	2	yes	—
741	C₂³	C₂³×C₄×C₁₇	1	2	yes	—
742	C₂³	C₂³×C₄×C₁₇	1	2	yes	—
743	C₂³	C₂²×D₄×C₁₇	1	2	yes	—
744	C₂³	C₂²×D₄×C₁₇	1	2	yes	—
745	C₂³	C₂²×D₄×C₁₇	1	2	yes	—
746	C₂³	C₂×#41×C₁₇	1	2	yes	—
747	C₂³	C₂×#41×C₁₇	1	2	yes	—
748	C₂³	C₂×#41×C₁₇	1	2	yes	—
749	C₂³	C₂⁵×C₁₇	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×C₁₇	1	8	yes	—
791	C₂×C₄	C₂³×C₄×C₁₇	1	4	yes	—
792	C₂×C₄	C₂³×C₄×C₁₇	1	4	yes	—
793	C₂×C₄	C₂²×D₄×C₁₇	1	4	yes	—
794	C₂×C₄	C₂²×D₄×C₁₇	1	4	yes	—
795	C₂×C₄	C₁₇×H(5,𝔽₂)	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×C₁₇	1	4	yes	—
822	C₂²	C₂×C₄×D₄×C₁₇	1	4	yes	—
823	C₂²	C₂×C₄×D₄×C₁₇	1	4	yes	—
824	C₂²	C₂⁴×C₄×C₁₇	1	1	yes	characteristic
825	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
826	C₂²	C₂²×#41×C₁₇	1	1	yes	characteristic
827	C₂²	C₂×C₁₇×H(5,𝔽₂)	1	2	yes	—
828	C₂²	C₁₇×#585	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×C₁₇	1	1	yes	characteristic
845	C₂	C₄×C₁₇×H(5,𝔽₂)	1	2	yes	—
846	C₂	C₁₇×#3484	1	1	yes	characteristic
847	C₂	C₁₇×#3485	1	1	yes	characteristic
848	C₂	C₁₇×#3505	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₇
Frattini, cosocle	C₂³	C₂⁵×C₁₇
prime radical	C₂×C₁₇×#534	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₇×#518	C₂	semidirect
3. C₂²×C₄×D₄×C₁₇	C₂	semidirect
4. C₁₇×#2364	C₂	semidirect
5. C₁₇×#2361	C₂	semidirect
6. C₁₇×#2359	C₂	semidirect
7. C₁₇×#2358	C₂	semidirect
8. C₁₇×#2322	C₂	semidirect
9. C₁₇×#2321	C₂	semidirect
10. C₁₇×#2308	C₂	semidirect
11. C₄×C₁₇×#123	C₂	semidirect
12. C₄×C₁₇×#120	C₂	semidirect
13. C₂×C₁₇×#386	C₂	semidirect
14. C₂×C₁₇×#385	C₂	semidirect
15. C₁₇×#2273	C₂	semidirect
19. C₂⁴×C₄×C₁₇	C₂²	semidirect
20. C₁₇×#534	C₄	semidirect
31. C₂×C₄×D₄×C₁₇	C₂²	semidirect
32. C₂×C₄×D₄×C₁₇	C₂²	semidirect
33. C₂×C₄×D₄×C₁₇	C₂²	semidirect
34. C₂×C₄×D₄×C₁₇	C₂²	semidirect
35. C₂×C₁₇×#117	C₂²	semidirect
36. C₂²×C₄⋊C₄×C₁₇	C₂²	semidirect
37. C₂²×C₄⋊C₄×C₁₇	C₂²	semidirect
42. C₂²×C₂²⋊C₄×C₁₇	C₂²	semidirect
43. C₂²×C₂²⋊C₄×C₁₇	C₂²	semidirect
44. C₂²×C₂²⋊C₄×C₁₇	C₂²	semidirect
45. C₂²×C₄²×C₁₇	C₂²	semidirect
46. C₁₇×#390	C₂²	semidirect
47. C₁₇×#389	C₂²	semidirect
48. C₁₇×#388	C₂²	semidirect
49. C₁₇×#388	C₂²	semidirect
50. C₁₇×#388	C₂²	semidirect
51. C₁₇×#388	C₂²	semidirect
52. C₁₇×#387	C₂²	semidirect
53. C₁₇×#387	C₂²	semidirect
57. C₁₇×#386	C₂²	semidirect
58. C₁₇×#386	C₂²	semidirect
59. C₁₇×#386	C₂²	semidirect
60. C₁₇×#386	C₂²	semidirect
61. C₁₇×#386	C₂²	semidirect
62. C₁₇×#385	C₂²	semidirect
63. C₁₇×#385	C₂²	semidirect
64. C₁₇×#385	C₂²	semidirect
65. C₁₇×#385	C₂²	semidirect
66. C₁₇×#385	C₂²	semidirect
67. C₁₇×#381	C₂²	semidirect
68. C₁₇×#379	C₂²	semidirect
69. C₄×C₄⋊C₄×C₁₇	C₂²	semidirect
70. C₄×C₂²⋊C₄×C₁₇	C₂²	semidirect
71. C₄×C₂²⋊C₄×C₁₇	C₂²	semidirect
72. C₄×C₂²⋊C₄×C₁₇	C₂²	semidirect
73. C₄×C₂²⋊C₄×C₁₇	C₂²	semidirect
74. C₄×C₂²⋊C₄×C₁₇	C₂²	semidirect
75. C₄×C₂²⋊C₄×C₁₇	C₂²	semidirect
76. C₂×C₁₇×#95	C₂²	semidirect
77. C₂×C₁₇×#95	C₂²	semidirect
85. C₂²×D₄×C₁₇	C₂×C₄	semidirect
86. C₂²×D₄×C₁₇	C₂×C₄	semidirect
111. C₁₇×#123	C₂×C₄	semidirect
112. C₁₇×#123	C₂×C₄	semidirect
113. C₁₇×#121	C₂×C₄	semidirect
114. C₁₇×#120	C₂×C₄	semidirect
115. C₁₇×#120	C₂×C₄	semidirect
137. C₂×C₂²⋊C₄×C₁₇	C₂×C₄	semidirect
138. C₂×C₂²⋊C₄×C₁₇	D₄	semidirect
182. C₂⁴×C₁₇	C₂²×C₄	semidirect
205. C₂×D₄×C₁₇	C₂²×C₄	semidirect
206. C₂×D₄×C₁₇	C₂²×C₄	semidirect
242. C₂²×C₄×C₁₇	C₂²×C₄	semidirect
243. C₂²×C₄×C₁₇	C₂²×C₄	semidirect
261. C₄⋊C₄×C₁₇	C₂²×C₄	semidirect
274. C₂²⋊C₄×C₁₇	C₂²×C₄	semidirect
275. C₂²⋊C₄×C₁₇	C₂²×C₄	semidirect
276. C₂²⋊C₄×C₁₇	C₂²×C₄	semidirect
284. #34264	C₁₇	direct (N × H)
313. C₂³×C₁₇	C₄×D₄	semidirect
373. C₂×#518	C₂×C₁₇	semidirect
374. C₂²×C₄×D₄	C₂×C₁₇	semidirect
375. #2364	C₂×C₁₇	semidirect
376. #2361	C₂×C₁₇	semidirect
377. #2359	C₂×C₁₇	semidirect
378. #2358	C₂×C₁₇	semidirect
379. #2322	C₂×C₁₇	semidirect
380. #2321	C₂×C₁₇	semidirect
381. #2308	C₂×C₁₇	semidirect
382. C₄×#123	C₂×C₁₇	semidirect
383. C₄×#120	C₂×C₁₇	semidirect
384. C₂×#386	C₂×C₁₇	semidirect
385. C₂×#385	C₂×C₁₇	semidirect
386. #2273	C₂×C₁₇	semidirect
433. C₂⁴×C₄	C₂²×C₁₇	semidirect
434. #534	C₄×C₁₇	semidirect
445. C₂×C₄×D₄	C₂²×C₁₇	semidirect
446. C₂×C₄×D₄	C₂²×C₁₇	semidirect
447. C₂×C₄×D₄	C₂²×C₁₇	semidirect
448. C₂×C₄×D₄	C₂²×C₁₇	semidirect
449. C₂×#117	C₂²×C₁₇	semidirect
450. C₂²×C₄⋊C₄	C₂²×C₁₇	semidirect
451. C₂²×C₄⋊C₄	C₂²×C₁₇	semidirect
456. C₂²×C₂²⋊C₄	C₂²×C₁₇	semidirect
457. C₂²×C₂²⋊C₄	C₂²×C₁₇	semidirect
458. C₂²×C₂²⋊C₄	C₂²×C₁₇	semidirect
459. C₂²×C₄²	C₂²×C₁₇	semidirect
460. #390	C₂²×C₁₇	semidirect
461. #389	C₂²×C₁₇	semidirect
462. #388	C₂²×C₁₇	semidirect
463. #388	C₂²×C₁₇	semidirect
464. #388	C₂²×C₁₇	semidirect
465. #388	C₂²×C₁₇	semidirect
466. #387	C₂²×C₁₇	semidirect
467. #387	C₂²×C₁₇	semidirect
471. #386	C₂²×C₁₇	semidirect
472. #386	C₂²×C₁₇	semidirect
473. #386	C₂²×C₁₇	semidirect
474. #386	C₂²×C₁₇	semidirect
475. #386	C₂²×C₁₇	semidirect
476. #385	C₂²×C₁₇	semidirect
477. #385	C₂²×C₁₇	semidirect
478. #385	C₂²×C₁₇	semidirect
479. #385	C₂²×C₁₇	semidirect
480. #385	C₂²×C₁₇	semidirect
481. #381	C₂²×C₁₇	semidirect
482. #379	C₂²×C₁₇	semidirect
483. C₄×C₄⋊C₄	C₂²×C₁₇	semidirect
484. C₄×C₂²⋊C₄	C₂²×C₁₇	semidirect
485. C₄×C₂²⋊C₄	C₂²×C₁₇	semidirect
486. C₄×C₂²⋊C₄	C₂²×C₁₇	semidirect
487. C₄×C₂²⋊C₄	C₂²×C₁₇	semidirect
488. C₄×C₂²⋊C₄	C₂²×C₁₇	semidirect
489. C₄×C₂²⋊C₄	C₂²×C₁₇	semidirect
490. C₂×#95	C₂²×C₁₇	semidirect
491. C₂×#95	C₂²×C₁₇	semidirect
509. C₂²×D₄	C₂×C₄×C₁₇	semidirect
510. C₂²×D₄	C₂×C₄×C₁₇	semidirect
535. #123	C₂×C₄×C₁₇	semidirect
536. #123	C₂×C₄×C₁₇	semidirect
537. #121	C₂×C₄×C₁₇	semidirect
538. #120	C₂×C₄×C₁₇	semidirect
539. #120	C₂×C₄×C₁₇	semidirect
561. C₂×C₂²⋊C₄	C₂×C₄×C₁₇	semidirect
562. C₂×C₂²⋊C₄	D₄×C₁₇	semidirect
594. C₁₇	#34264	direct (N × H)
607. C₂⁴	C₂²×C₄×C₁₇	semidirect
630. C₂×D₄	C₂²×C₄×C₁₇	semidirect
631. C₂×D₄	C₂²×C₄×C₁₇	semidirect
667. C₂²×C₄	C₂²×C₄×C₁₇	semidirect
668. C₂²×C₄	C₂²×C₄×C₁₇	semidirect
686. C₄⋊C₄	C₂²×C₄×C₁₇	semidirect
699. C₂²⋊C₄	C₂²×C₄×C₁₇	semidirect
700. C₂²⋊C₄	C₂²×C₄×C₁₇	semidirect
701. C₂²⋊C₄	C₂²×C₄×C₁₇	semidirect
737. C₂³	C₄×D₄×C₁₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₇×#534	2
C₂×C₁₇×#518	2
C₂²×C₄×D₄×C₁₇	2
C₁₇×#2364	2
C₁₇×#2361	2
C₁₇×#2359	2
C₁₇×#2358	2
C₁₇×#2322	2
C₁₇×#2321	2
C₁₇×#2308	2
C₄×C₁₇×#123	2
C₄×C₁₇×#120	2
C₂×C₁₇×#386	2
C₂×C₁₇×#385	2
C₁₇×#2273	2
#34264	17

Subgroups — C17×#34264 #16892008

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#34264 #16892008