Subgroups — C₁₇×#22864 #16880608

Order 4352.

1274 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#450	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₇×#440	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₇×#418	C₂	1	1	yes	maximal, characteristic
4	C₁₇×#2362	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄×C₂²⋊C₄×C₁₇	C₂	1	1	yes	maximal, characteristic
6	C₁₇×#1968	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#1936	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₇×#1925	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#1894	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#1880	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#1877	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#1864	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₇×#1854	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₁₇×#102	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#1753	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₁₇	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₁₇	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₁₇	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
20	C₂×C₁₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
24	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
25	C₂²×C₂²⋊C₄×C₁₇	—	2	1	no	—
26	C₁₇×#450	C₄	1	8	yes	complemented
27	C₁₇×#440	—	2	4	no	—
28	C₂×C₁₇×#107	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₁₇×#106	C₂²	1	1	yes	characteristic, complemented
30	C₁₇×#418	—	2	4	no	—
31	C₂×C₁₇×#103	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₁₇×#103	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₁₇×#102	C₂²	1	1	yes	characteristic
34	C₂×C₁₇×#102	C₂²	1	1	yes	characteristic
35	C₂×C₁₇×#102	C₂²	1	1	yes	characteristic
36	C₂×C₁₇×#102	C₂²	1	1	yes	characteristic
37	C₂×C₁₇×#102	C₂²	1	1	yes	characteristic
38	C₂×C₁₇×#102	C₂²	1	1	yes	characteristic
39	C₂×C₁₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₁₇×#97	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
42	C₁₇×#391	C₂²	1	1	yes	characteristic, complemented
43	C₁₇×#390	C₂²	1	1	yes	characteristic
44	C₁₇×#390	C₂²	1	1	yes	characteristic
45	C₁₇×#389	C₂²	1	1	yes	characteristic, complemented
46	C₁₇×#388	—	2	1	no	—
47	C₁₇×#388	—	2	1	no	—
48	C₁₇×#387	—	2	1	no	—
49	C₁₇×#386	—	2	1	no	—
50	C₁₇×#386	—	2	1	no	—
51	C₁₇×#380	C₂²	1	1	yes	characteristic
52	C₁₇×#379	—	2	1	no	—
53	C₄×C₄⋊C₄×C₁₇	—	2	1	no	—
54	C₄×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
55	C₄×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
56	C₁₇×#340	C₂²	1	1	yes	characteristic, complemented
57	C₁₇×#340	C₂²	1	1	yes	characteristic, complemented
58	C₁₇×#340	C₂²	1	1	yes	characteristic, complemented
59	C₁₇×#340	C₂²	1	1	yes	characteristic, complemented
60	C₁₇×#336	C₂²	1	1	yes	characteristic, complemented
61	C₁₇×#336	C₂²	1	1	yes	characteristic, complemented
62	C₂⁵×C₁₇	—	2	1	no	—
63	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₁₇	—	2	2	no	—
65	C₂²×D₄×C₁₇	—	2	2	no	—
66	C₂²×D₄×C₁₇	—	2	1	no	—
67	C₂²×D₄×C₁₇	—	2	2	no	—
68	C₂²×D₄×C₁₇	—	4	1	no	—
69	C₂²×D₄×C₁₇	—	4	1	no	—
70	C₂²×D₄×C₁₇	C₂×C₄	1	4	yes	—
71	C₂²×D₄×C₁₇	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₁₇	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₁₇	—	2	1	no	—
74	C₂³×C₄×C₁₇	—	2	1	no	—
75	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
76	C₂×SD₁₆×C₁₇	—	2	2	no	—
77	C₂×SD₁₆×C₁₇	—	2	2	no	—
78	C₂×SD₁₆×C₁₇	—	4	1	no	—
79	C₂×SD₁₆×C₁₇	—	4	1	no	—
80	C₂×SD₁₆×C₁₇	C₂×C₄	1	4	yes	—
81	C₂×SD₁₆×C₁₇	C₂×C₄	1	4	yes	complemented
82	C₂×M₁₆×C₁₇	—	2	2	no	—
83	C₂×M₁₆×C₁₇	—	2	2	no	—
84	C₂×M₁₆×C₁₇	—	4	1	no	—
85	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
89	C₁₇×C₂²⋊Q₈	—	2	2	no	—
90	C₁₇×C₂²⋊Q₈	C₂×C₄	1	4	yes	complemented
91	C₄×Q₈×C₁₇	—	2	2	no	—
92	C₄×Q₈×C₁₇	—	4	1	no	—
93	C₄×D₄×C₁₇	—	2	2	no	—
94	C₄×D₄×C₁₇	—	2	2	no	—
95	C₄×D₄×C₁₇	—	4	1	no	—
96	C₄×D₄×C₁₇	—	4	1	no	—
97	C₁₇×#117	—	2	2	no	—
98	C₁₇×#117	—	4	1	no	—
99	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
100	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
101	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
102	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
107	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
111	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
112	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
114	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₁₇	—	4	4	no	—
117	C₂×C₂²⋊C₄×C₁₇	D₄	1	1	yes	characteristic
118	C₂×C₂²⋊C₄×C₁₇	D₄	1	1	yes	characteristic
119	C₂×C₄²×C₁₇	—	2	1	no	—
120	C₂×C₄²×C₁₇	—	2	1	no	—
121	C₂×C₄²×C₁₇	—	2	1	no	—
122	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
124	C₁₇×#107	—	2	2	no	—
125	C₁₇×#106	—	4	1	no	—
126	C₁₇×#103	—	2	2	no	—
127	C₁₇×#103	—	4	1	no	—
128	C₁₇×#102	—	2	2	no	—
129	C₁₇×#102	—	2	2	no	—
130	C₁₇×#102	—	2	2	no	—
131	C₁₇×#102	C₂×C₄	1	4	yes	—
132	C₁₇×#102	C₂×C₄	1	4	yes	complemented
133	C₁₇×#102	D₄	1	4	yes	—
134	C₁₇×C₂²⋊C₈	C₂×C₄	1	4	yes	complemented
135	C₁₇×#97	—	2	2	no	—
136	C₄×C₈×C₁₇	—	4	1	no	—
137	C₁₇×#95	—	2	1	no	—
138	C₁₇×#95	—	2	1	no	—
139	C₁₇×#95	—	2	1	no	—
140	C₁₇×#95	—	2	1	no	—
141	C₁₇×#95	—	2	1	no	—
142	C₁₇×#95	D₄	1	1	yes	characteristic
143	C₁₇×#95	D₄	1	1	yes	characteristic
144	C₂⁴×C₁₇	—	2	1	no	—
145	C₂⁴×C₁₇	—	2	1	no	—
146	C₂⁴×C₁₇	—	2	4	no	—
147	C₂⁴×C₁₇	—	4	2	no	—
148	C₂⁴×C₁₇	—	4	2	no	—
149	C₂⁴×C₁₇	—	4	2	no	—
150	C₂⁴×C₁₇	—	4	2	no	—
151	C₂⁴×C₁₇	—	8	1	no	—
152	C₂⁴×C₁₇	—	8	1	no	—
153	C₂⁴×C₁₇	C₂×D₄	1	1	yes	characteristic
154	C₂×Q₈×C₁₇	—	2	1	no	—
155	C₂×Q₈×C₁₇	—	2	1	no	—
156	C₂×Q₈×C₁₇	—	2	1	no	—
157	C₂×Q₈×C₁₇	—	2	1	no	—
158	C₂×Q₈×C₁₇	—	2	1	no	—
159	C₂×Q₈×C₁₇	C₂²×C₄	1	2	yes	—
160	C₂×D₄×C₁₇	—	2	8	no	—
161	C₂×D₄×C₁₇	—	2	4	no	—
162	C₂×D₄×C₁₇	—	2	1	no	—
163	C₂×D₄×C₁₇	—	2	1	no	—
164	C₂×D₄×C₁₇	—	2	1	no	—
165	C₂×D₄×C₁₇	—	2	1	no	—
166	C₂×D₄×C₁₇	—	2	1	no	—
167	C₂×D₄×C₁₇	—	2	1	no	—
168	C₂×D₄×C₁₇	—	2	1	no	—
169	C₂×D₄×C₁₇	—	2	1	no	—
170	C₂×D₄×C₁₇	—	4	4	no	—
171	C₂×D₄×C₁₇	—	4	4	no	—
172	C₂×D₄×C₁₇	—	4	4	no	—
173	C₂×D₄×C₁₇	—	4	2	no	—
174	C₂×D₄×C₁₇	—	4	2	no	—
175	C₂×D₄×C₁₇	C₂²×C₄	1	2	yes	—
176	C₂×D₄×C₁₇	C₂²×C₄	1	2	yes	—
177	C₂×D₄×C₁₇	C₂×D₄	1	2	yes	—
178	C₂×D₄×C₁₇	#41	1	2	yes	—
179	C₂²×C₄×C₁₇	—	2	1	no	—
180	C₂²×C₄×C₁₇	—	2	1	no	—
181	C₂²×C₄×C₁₇	—	2	1	no	—
182	C₂²×C₄×C₁₇	—	2	1	no	—
183	C₂²×C₄×C₁₇	—	2	1	no	—
184	C₂²×C₄×C₁₇	—	2	1	no	—
185	C₂²×C₄×C₁₇	—	2	1	no	—
186	C₂²×C₄×C₁₇	—	2	1	no	—
187	C₂²×C₄×C₁₇	—	2	1	no	—
188	C₂²×C₄×C₁₇	—	2	1	no	—
189	C₂²×C₄×C₁₇	—	4	2	no	—
190	C₂²×C₄×C₁₇	—	4	2	no	—
191	C₂²×C₄×C₁₇	—	4	2	no	—
192	C₂²×C₄×C₁₇	—	4	2	no	—
193	C₂²×C₄×C₁₇	—	8	1	no	—
194	C₂²×C₄×C₁₇	—	8	1	no	—
195	C₂²×C₄×C₁₇	C₂²×C₄	1	2	yes	—
196	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₁₇	#41	1	2	yes	—
202	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
203	SD₁₆×C₁₇	—	2	8	no	—
204	SD₁₆×C₁₇	—	4	4	no	—
205	M₁₆×C₁₇	—	4	4	no	—
206	C₂×C₈×C₁₇	—	2	1	no	—
207	C₂×C₈×C₁₇	—	2	1	no	—
208	C₂×C₈×C₁₇	—	2	1	no	—
209	C₂×C₈×C₁₇	—	2	1	no	—
210	C₂×C₈×C₁₇	—	2	1	no	—
211	C₂×C₈×C₁₇	—	2	1	no	—
212	C₂×C₈×C₁₇	—	2	1	no	—
213	C₂×C₈×C₁₇	—	2	1	no	—
214	C₂×C₈×C₁₇	—	2	1	no	—
215	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
216	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
217	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
218	C₄⋊C₄×C₁₇	—	2	4	no	—
219	C₄⋊C₄×C₁₇	—	2	1	no	—
220	C₄⋊C₄×C₁₇	—	2	1	no	—
221	C₄⋊C₄×C₁₇	—	2	1	no	—
222	C₄⋊C₄×C₁₇	—	2	1	no	—
223	C₄⋊C₄×C₁₇	—	2	1	no	—
224	C₄⋊C₄×C₁₇	—	2	1	no	—
225	C₄⋊C₄×C₁₇	—	2	1	no	—
226	C₄⋊C₄×C₁₇	—	2	1	no	—
227	C₄⋊C₄×C₁₇	—	4	2	no	—
228	C₄⋊C₄×C₁₇	—	4	2	no	—
229	C₄⋊C₄×C₁₇	C₂²×C₄	1	2	yes	—
230	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
231	C₂²⋊C₄×C₁₇	—	2	4	no	—
232	C₂²⋊C₄×C₁₇	—	2	2	no	—
233	C₂²⋊C₄×C₁₇	—	4	1	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	2	no	—
239	C₂²⋊C₄×C₁₇	—	4	2	no	—
240	C₂²⋊C₄×C₁₇	—	8	1	no	—
241	C₂²⋊C₄×C₁₇	—	8	1	no	—
242	C₄²×C₁₇	—	2	1	no	—
243	C₄²×C₁₇	—	2	1	no	—
244	C₄²×C₁₇	—	2	1	no	—
245	C₄²×C₁₇	—	2	1	no	—
246	C₄²×C₁₇	—	4	2	no	—
247	C₄²×C₁₇	—	4	2	no	—
248	C₄²×C₁₇	—	4	2	no	—
249	#22864	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
250	C₂³×C₁₇	—	2	2	no	—
251	C₂³×C₁₇	—	2	1	no	—
252	C₂³×C₁₇	—	2	2	no	—
253	C₂³×C₁₇	—	2	2	no	—
254	C₂³×C₁₇	—	2	1	no	—
255	C₂³×C₁₇	—	2	1	no	—
256	C₂³×C₁₇	—	2	1	no	—
257	C₂³×C₁₇	—	2	1	no	—
258	C₂³×C₁₇	—	2	1	no	—
259	C₂³×C₁₇	—	2	2	no	—
260	C₂³×C₁₇	—	4	8	no	—
261	C₂³×C₁₇	—	4	8	no	—
262	C₂³×C₁₇	—	4	1	no	—
263	C₂³×C₁₇	—	4	1	no	—
264	C₂³×C₁₇	—	4	1	no	—
265	C₂³×C₁₇	—	4	1	no	—
266	C₂³×C₁₇	—	4	1	no	—
267	C₂³×C₁₇	—	4	1	no	—
268	C₂³×C₁₇	—	4	1	no	—
269	C₂³×C₁₇	—	4	1	no	—
270	C₂³×C₁₇	—	4	1	no	—
271	C₂³×C₁₇	—	4	1	no	—
272	C₂³×C₁₇	—	8	4	no	—
273	C₂³×C₁₇	—	8	4	no	—
274	C₂³×C₁₇	—	8	4	no	—
275	C₂³×C₁₇	—	8	4	no	—
276	C₂³×C₁₇	—	8	4	no	—
277	C₂³×C₁₇	C₄×D₄	1	2	yes	—
278	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
279	Q₈×C₁₇	—	2	2	no	—
280	Q₈×C₁₇	—	2	2	no	—
281	Q₈×C₁₇	—	4	1	no	—
282	Q₈×C₁₇	—	4	1	no	—
283	D₄×C₁₇	—	2	2	no	—
284	D₄×C₁₇	—	2	2	no	—
285	D₄×C₁₇	—	2	2	no	—
286	D₄×C₁₇	—	2	2	no	—
287	D₄×C₁₇	—	2	2	no	—
288	D₄×C₁₇	—	4	8	no	—
289	D₄×C₁₇	—	4	1	no	—
290	D₄×C₁₇	—	4	1	no	—
291	D₄×C₁₇	C₄×D₄	1	4	yes	—
292	C₂×C₄×C₁₇	—	2	1	no	—
293	C₂×C₄×C₁₇	—	2	1	no	—
294	C₂×C₄×C₁₇	—	2	1	no	—
295	C₂×C₄×C₁₇	—	2	1	no	—
296	C₂×C₄×C₁₇	—	2	2	no	—
297	C₂×C₄×C₁₇	—	2	2	no	—
298	C₂×C₄×C₁₇	—	2	2	no	—
299	C₂×C₄×C₁₇	—	2	2	no	—
300	C₂×C₄×C₁₇	—	2	2	no	—
301	C₂×C₄×C₁₇	—	2	2	no	—
302	C₂×C₄×C₁₇	—	2	1	no	—
303	C₂×C₄×C₁₇	—	2	1	no	—
304	C₂×C₄×C₁₇	—	2	2	no	—
305	C₂×C₄×C₁₇	—	2	1	no	—
306	C₂×C₄×C₁₇	—	2	1	no	—
307	C₂×C₄×C₁₇	—	2	1	no	—
308	C₂×C₄×C₁₇	—	2	1	no	—
309	C₂×C₄×C₁₇	—	2	1	no	—
310	C₂×C₄×C₁₇	—	2	1	no	—
311	C₂×C₄×C₁₇	—	2	1	no	—
312	C₂×C₄×C₁₇	—	4	1	no	—
313	C₂×C₄×C₁₇	—	4	1	no	—
314	C₂×C₄×C₁₇	—	4	1	no	—
315	C₂×C₄×C₁₇	—	4	1	no	—
316	C₂×C₄×C₁₇	—	4	1	no	—
317	C₂×C₄×C₁₇	—	4	1	no	—
318	C₂×C₄×C₁₇	—	4	1	no	—
319	C₂×C₄×C₁₇	—	4	1	no	—
320	C₂×C₄×C₁₇	—	4	1	no	—
321	C₂×C₄×C₁₇	—	4	1	no	—
322	C₂×C₄×C₁₇	—	4	1	no	—
323	C₂×C₄×C₁₇	—	4	1	no	—
324	C₂×C₄×C₁₇	—	4	1	no	—
325	C₂×C₄×C₁₇	—	4	1	no	—
326	C₂×C₄×C₁₇	—	4	1	no	—
327	C₂×C₄×C₁₇	—	8	4	no	—
328	C₂×C₄×C₁₇	—	8	4	no	—
329	C₂×C₄×C₁₇	C₄×D₄	1	2	yes	—
330	C₂×C₄×C₁₇	AGL(1,ℤ/8)	1	2	yes	—
331	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
332	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
333	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
334	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
335	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
336	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
337	C₈×C₁₇	—	2	2	no	—
338	C₈×C₁₇	—	2	2	no	—
339	C₈×C₁₇	—	2	2	no	—
340	C₈×C₁₇	—	4	1	no	—
341	C₂×#450	C₂×C₁₇	1	1	yes	characteristic
342	C₂×#440	C₂×C₁₇	1	1	yes	characteristic, complemented
343	C₂×#418	C₂×C₁₇	1	1	yes	characteristic
344	#2362	C₂×C₁₇	1	1	yes	characteristic, complemented
345	D₄×C₂²⋊C₄	C₂×C₁₇	1	1	yes	characteristic
346	#1968	C₂×C₁₇	1	1	yes	characteristic, complemented
347	#1936	C₂×C₁₇	1	1	yes	characteristic, complemented
348	#1925	C₂×C₁₇	1	1	yes	characteristic, complemented
349	#1894	C₂×C₁₇	1	1	yes	characteristic, complemented
350	#1880	C₂×C₁₇	1	1	yes	characteristic, complemented
351	#1877	C₂×C₁₇	1	1	yes	characteristic, complemented
352	#1864	C₂×C₁₇	1	1	yes	characteristic, complemented
353	#1854	C₂×C₁₇	1	1	yes	characteristic, complemented
354	C₄×#102	C₂×C₁₇	1	1	yes	characteristic, complemented
355	#1753	C₂×C₁₇	1	1	yes	characteristic, complemented
356	C₂²×C₁₇	—	2	2	no	—
357	C₂²×C₁₇	—	2	4	no	—
358	C₂²×C₁₇	—	2	2	no	—
359	C₂²×C₁₇	—	2	2	no	—
360	C₂²×C₁₇	—	4	2	no	—
361	C₂²×C₁₇	—	4	2	no	—
362	C₂²×C₁₇	—	4	2	no	—
363	C₂²×C₁₇	—	4	1	no	—
364	C₂²×C₁₇	—	4	1	no	—
365	C₂²×C₁₇	—	4	2	no	—
366	C₂²×C₁₇	—	4	2	no	—
367	C₂²×C₁₇	—	4	1	no	—
368	C₂²×C₁₇	—	4	1	no	—
369	C₂²×C₁₇	—	4	2	no	—
370	C₂²×C₁₇	—	4	2	no	—
371	C₂²×C₁₇	—	4	2	no	—
372	C₂²×C₁₇	—	4	2	no	—
373	C₂²×C₁₇	—	8	16	no	—
374	C₂²×C₁₇	—	8	1	no	—
375	C₂²×C₁₇	—	8	1	no	—
376	C₂²×C₁₇	—	8	1	no	—
377	C₂²×C₁₇	—	8	1	no	—
378	C₂²×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
379	C₂²×C₁₇	D₄²	1	1	yes	characteristic
380	C₂²×C₁₇	#546	1	1	yes	characteristic
381	C₂²×C₁₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
382	C₂²×C₁₇	#575	1	1	yes	characteristic
383	C₂²×C₁₇	#577	1	1	yes	characteristic
384	C₂²×C₁₇	#577	1	1	yes	characteristic
385	C₄×C₁₇	—	2	2	no	—
386	C₄×C₁₇	—	2	2	no	—
387	C₄×C₁₇	—	4	2	no	—
388	C₄×C₁₇	—	4	2	no	—
389	C₄×C₁₇	—	4	1	no	—
390	C₄×C₁₇	—	4	2	no	—
391	C₄×C₁₇	—	4	1	no	—
392	C₄×C₁₇	—	4	1	no	—
393	C₄×C₁₇	—	8	1	no	—
394	C₄×C₁₇	—	8	1	no	—
395	C₄×C₁₇	—	8	1	no	—
396	C₄×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
397	C₄×C₁₇	#518	1	1	yes	characteristic
398	C₄×C₁₇	#546	1	1	yes	characteristic
399	C₄×C₁₇	#551	1	1	yes	characteristic
400	C₂³×D₄	C₂²×C₁₇	1	1	yes	characteristic
401	C₂²×SD₁₆	C₂²×C₁₇	1	1	yes	characteristic
402	C₂²×SD₁₆	C₂²×C₁₇	1	1	yes	characteristic
403	C₂²×M₁₆	C₂²×C₁₇	1	1	yes	characteristic
404	C₂×C₂²⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
405	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic, complemented
406	C₂×C₄×D₄	C₂²×C₁₇	1	1	yes	characteristic
407	C₂×C₄×D₄	C₂²×C₁₇	1	1	yes	characteristic
408	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
409	C₂²×C₂²⋊C₄	—	2	1	no	—
410	#450	C₄×C₁₇	1	8	yes	complemented
411	#440	—	2	4	no	—
412	C₂×#107	C₂²×C₁₇	1	1	yes	characteristic, complemented
413	C₂×#106	C₂²×C₁₇	1	1	yes	characteristic, complemented
414	#418	—	2	4	no	—
415	C₂×#103	C₂²×C₁₇	1	1	yes	characteristic, complemented
416	C₂×#103	C₂²×C₁₇	1	1	yes	characteristic, complemented
417	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic
418	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic
419	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic
420	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic
421	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic
422	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic
423	C₂×C₂²⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
424	C₂×#97	C₂²×C₁₇	1	1	yes	characteristic, complemented
425	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic, complemented
426	#391	C₂²×C₁₇	1	1	yes	characteristic, complemented
427	#390	C₂²×C₁₇	1	1	yes	characteristic
428	#390	C₂²×C₁₇	1	1	yes	characteristic
429	#389	C₂²×C₁₇	1	1	yes	characteristic, complemented
430	#388	—	2	1	no	—
431	#388	—	2	1	no	—
432	#387	—	2	1	no	—
433	#386	—	2	1	no	—
434	#386	—	2	1	no	—
435	#380	C₂²×C₁₇	1	1	yes	characteristic
436	#379	—	2	1	no	—
437	C₄×C₄⋊C₄	—	2	1	no	—
438	C₄×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic, complemented
439	C₄×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
440	#340	C₂²×C₁₇	1	1	yes	characteristic, complemented
441	#340	C₂²×C₁₇	1	1	yes	characteristic, complemented
442	#340	C₂²×C₁₇	1	1	yes	characteristic, complemented
443	#340	C₂²×C₁₇	1	1	yes	characteristic, complemented
444	#336	C₂²×C₁₇	1	1	yes	characteristic, complemented
445	#336	C₂²×C₁₇	1	1	yes	characteristic, complemented
446	C₂×C₁₇	—	4	2	no	—
447	C₂×C₁₇	—	4	4	no	—
448	C₂×C₁₇	—	8	2	no	—
449	C₂×C₁₇	#2358	1	1	yes	characteristic
450	C₂×C₁₇	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
451	C₂×C₁₇	#2949	1	1	yes	characteristic
452	C₂×C₁₇	#3272	1	1	yes	characteristic
453	C₂×C₁₇	#3275	1	1	yes	characteristic
454	C₂×C₁₇	#3310	1	1	yes	characteristic
455	C₂×C₁₇	#3311	1	1	yes	characteristic
456	C₂⁵	—	2	1	no	—
457	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
458	C₂²×D₄	—	2	2	no	—
459	C₂²×D₄	—	2	2	no	—
460	C₂²×D₄	—	2	1	no	—
461	C₂²×D₄	—	2	2	no	—
462	C₂²×D₄	—	4	1	no	—
463	C₂²×D₄	—	4	1	no	—
464	C₂²×D₄	C₂×C₄×C₁₇	1	4	yes	—
465	C₂²×D₄	C₂³×C₁₇	1	1	yes	characteristic
466	C₂²×D₄	C₂³×C₁₇	1	1	yes	characteristic
467	C₂³×C₄	—	2	1	no	—
468	C₂³×C₄	—	2	1	no	—
469	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
470	C₂×SD₁₆	—	2	2	no	—
471	C₂×SD₁₆	—	2	2	no	—
472	C₂×SD₁₆	—	4	1	no	—
473	C₂×SD₁₆	—	4	1	no	—
474	C₂×SD₁₆	C₂×C₄×C₁₇	1	4	yes	—
475	C₂×SD₁₆	C₂×C₄×C₁₇	1	4	yes	complemented
476	C₂×M₁₆	—	2	2	no	—
477	C₂×M₁₆	—	2	2	no	—
478	C₂×M₁₆	—	4	1	no	—
479	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
480	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
481	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
482	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
483	C₂²⋊Q₈	—	2	2	no	—
484	C₂²⋊Q₈	C₂×C₄×C₁₇	1	4	yes	complemented
485	C₄×Q₈	—	2	2	no	—
486	C₄×Q₈	—	4	1	no	—
487	C₄×D₄	—	2	2	no	—
488	C₄×D₄	—	2	2	no	—
489	C₄×D₄	—	4	1	no	—
490	C₄×D₄	—	4	1	no	—
491	#117	—	2	2	no	—
492	#117	—	4	1	no	—
493	C₂×C₄⋊C₄	—	2	1	no	—
494	C₂×C₄⋊C₄	—	2	1	no	—
495	C₂×C₄⋊C₄	—	2	1	no	—
496	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
497	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
498	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
499	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
500	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
501	C₂×C₂²⋊C₄	—	2	1	no	—
502	C₂×C₂²⋊C₄	—	2	1	no	—
503	C₂×C₂²⋊C₄	—	2	1	no	—
504	C₂×C₂²⋊C₄	—	2	1	no	—
505	C₂×C₂²⋊C₄	—	2	1	no	—
506	C₂×C₂²⋊C₄	—	2	1	no	—
507	C₂×C₂²⋊C₄	—	2	1	no	—
508	C₂×C₂²⋊C₄	—	2	1	no	—
509	C₂×C₂²⋊C₄	—	2	1	no	—
510	C₂×C₂²⋊C₄	—	4	4	no	—
511	C₂×C₂²⋊C₄	D₄×C₁₇	1	1	yes	characteristic
512	C₂×C₂²⋊C₄	D₄×C₁₇	1	1	yes	characteristic
513	C₂×C₄²	—	2	1	no	—
514	C₂×C₄²	—	2	1	no	—
515	C₂×C₄²	—	2	1	no	—
516	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
517	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
518	#107	—	2	2	no	—
519	#106	—	4	1	no	—
520	#103	—	2	2	no	—
521	#103	—	4	1	no	—
522	#102	—	2	2	no	—
523	#102	—	2	2	no	—
524	#102	—	2	2	no	—
525	#102	C₂×C₄×C₁₇	1	4	yes	—
526	#102	C₂×C₄×C₁₇	1	4	yes	complemented
527	#102	D₄×C₁₇	1	4	yes	—
528	C₂²⋊C₈	C₂×C₄×C₁₇	1	4	yes	complemented
529	#97	—	2	2	no	—
530	C₄×C₈	—	4	1	no	—
531	#95	—	2	1	no	—
532	#95	—	2	1	no	—
533	#95	—	2	1	no	—
534	#95	—	2	1	no	—
535	#95	—	2	1	no	—
536	#95	D₄×C₁₇	1	1	yes	characteristic
537	#95	D₄×C₁₇	1	1	yes	characteristic
538	C₁₇	#22864	1	1	yes	characteristic, direct product factor, Sylow
539	C₂⁴	—	2	1	no	—
540	C₂⁴	—	2	1	no	—
541	C₂⁴	—	2	4	no	—
542	C₂⁴	—	4	2	no	—
543	C₂⁴	—	4	2	no	—
544	C₂⁴	—	4	2	no	—
545	C₂⁴	—	4	2	no	—
546	C₂⁴	—	8	1	no	—
547	C₂⁴	—	8	1	no	—
548	C₂⁴	C₂×D₄×C₁₇	1	1	yes	characteristic
549	C₂×Q₈	—	2	1	no	—
550	C₂×Q₈	—	2	1	no	—
551	C₂×Q₈	—	2	1	no	—
552	C₂×Q₈	—	2	1	no	—
553	C₂×Q₈	—	2	1	no	—
554	C₂×Q₈	C₂²×C₄×C₁₇	1	2	yes	—
555	C₂×D₄	—	2	8	no	—
556	C₂×D₄	—	2	1	no	—
557	C₂×D₄	—	2	1	no	—
558	C₂×D₄	—	2	1	no	—
559	C₂×D₄	—	2	1	no	—
560	C₂×D₄	—	2	1	no	—
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	—	2	1	no	—
563	C₂×D₄	—	2	1	no	—
564	C₂×D₄	—	2	4	no	—
565	C₂×D₄	—	4	4	no	—
566	C₂×D₄	—	4	4	no	—
567	C₂×D₄	—	4	4	no	—
568	C₂×D₄	—	4	2	no	—
569	C₂×D₄	—	4	2	no	—
570	C₂×D₄	C₂²×C₄×C₁₇	1	2	yes	—
571	C₂×D₄	C₂²×C₄×C₁₇	1	2	yes	—
572	C₂×D₄	C₂×D₄×C₁₇	1	2	yes	—
573	C₂×D₄	#41×C₁₇	1	2	yes	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	4	2	no	—
585	C₂²×C₄	—	4	2	no	—
586	C₂²×C₄	—	4	2	no	—
587	C₂²×C₄	—	4	2	no	—
588	C₂²×C₄	—	8	1	no	—
589	C₂²×C₄	—	8	1	no	—
590	C₂²×C₄	C₂²×C₄×C₁₇	1	2	yes	—
591	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
592	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
593	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
594	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
595	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
596	C₂²×C₄	#41×C₁₇	1	2	yes	—
597	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
598	SD₁₆	—	2	8	no	—
599	SD₁₆	—	4	4	no	—
600	M₁₆	—	4	4	no	—
601	C₂×C₈	—	2	1	no	—
602	C₂×C₈	—	2	1	no	—
603	C₂×C₈	—	2	1	no	—
604	C₂×C₈	—	2	1	no	—
605	C₂×C₈	—	2	1	no	—
606	C₂×C₈	—	2	1	no	—
607	C₂×C₈	—	2	1	no	—
608	C₂×C₈	—	2	1	no	—
609	C₂×C₈	—	2	1	no	—
610	C₂×C₈	C₂²×C₄×C₁₇	1	2	yes	—
611	C₂×C₈	C₂²×C₄×C₁₇	1	2	yes	—
612	C₂×C₈	C₂×D₄×C₁₇	1	2	yes	—
613	C₄⋊C₄	—	2	1	no	—
614	C₄⋊C₄	—	2	1	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	1	no	—
617	C₄⋊C₄	—	2	1	no	—
618	C₄⋊C₄	—	2	1	no	—
619	C₄⋊C₄	—	2	1	no	—
620	C₄⋊C₄	—	2	1	no	—
621	C₄⋊C₄	—	2	1	no	—
622	C₄⋊C₄	—	4	2	no	—
623	C₄⋊C₄	—	4	2	no	—
624	C₄⋊C₄	C₂²×C₄×C₁₇	1	2	yes	—
625	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
626	C₂²⋊C₄	—	2	4	no	—
627	C₂²⋊C₄	—	2	2	no	—
628	C₂²⋊C₄	—	4	1	no	—
629	C₂²⋊C₄	—	4	2	no	—
630	C₂²⋊C₄	—	4	2	no	—
631	C₂²⋊C₄	—	4	2	no	—
632	C₂²⋊C₄	—	4	2	no	—
633	C₂²⋊C₄	—	4	2	no	—
634	C₂²⋊C₄	—	4	2	no	—
635	C₂²⋊C₄	—	8	1	no	—
636	C₂²⋊C₄	—	8	1	no	—
637	C₄²	—	2	1	no	—
638	C₄²	—	2	1	no	—
639	C₄²	—	2	1	no	—
640	C₄²	—	2	1	no	—
641	C₄²	—	4	2	no	—
642	C₄²	—	4	2	no	—
643	C₄²	—	4	2	no	—
644	C₂³	—	2	2	no	—
645	C₂³	—	2	1	no	—
646	C₂³	—	2	2	no	—
647	C₂³	—	2	2	no	—
648	C₂³	—	2	1	no	—
649	C₂³	—	2	1	no	—
650	C₂³	—	2	1	no	—
651	C₂³	—	2	1	no	—
652	C₂³	—	2	1	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	4	8	no	—
655	C₂³	—	4	8	no	—
656	C₂³	—	4	1	no	—
657	C₂³	—	4	1	no	—
658	C₂³	—	4	1	no	—
659	C₂³	—	4	1	no	—
660	C₂³	—	4	1	no	—
661	C₂³	—	4	1	no	—
662	C₂³	—	4	1	no	—
663	C₂³	—	4	1	no	—
664	C₂³	—	4	1	no	—
665	C₂³	—	4	1	no	—
666	C₂³	—	8	4	no	—
667	C₂³	—	8	4	no	—
668	C₂³	—	8	4	no	—
669	C₂³	—	8	4	no	—
670	C₂³	—	8	4	no	—
671	C₂³	C₄×D₄×C₁₇	1	2	yes	—
672	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
673	Q₈	—	2	2	no	—
674	Q₈	—	2	2	no	—
675	Q₈	—	4	1	no	—
676	Q₈	—	4	1	no	—
677	D₄	—	2	2	no	—
678	D₄	—	2	2	no	—
679	D₄	—	2	2	no	—
680	D₄	—	2	2	no	—
681	D₄	—	2	2	no	—
682	D₄	—	4	8	no	—
683	D₄	—	4	1	no	—
684	D₄	—	4	1	no	—
685	D₄	C₄×D₄×C₁₇	1	4	yes	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	4	1	no	—
707	C₂×C₄	—	4	1	no	—
708	C₂×C₄	—	4	1	no	—
709	C₂×C₄	—	4	1	no	—
710	C₂×C₄	—	4	1	no	—
711	C₂×C₄	—	4	1	no	—
712	C₂×C₄	—	4	1	no	—
713	C₂×C₄	—	4	1	no	—
714	C₂×C₄	—	4	1	no	—
715	C₂×C₄	—	4	1	no	—
716	C₂×C₄	—	4	1	no	—
717	C₂×C₄	—	4	1	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	4	1	no	—
721	C₂×C₄	—	8	4	no	—
722	C₂×C₄	—	8	4	no	—
723	C₂×C₄	C₄×D₄×C₁₇	1	2	yes	—
724	C₂×C₄	C₁₇×AGL(1,ℤ/8)	1	2	yes	—
725	C₂×C₄	C₂³×C₄×C₁₇	1	1	yes	characteristic
726	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
727	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
728	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
729	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
730	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
731	C₈	—	2	2	no	—
732	C₈	—	2	2	no	—
733	C₈	—	2	2	no	—
734	C₈	—	4	1	no	—
735	C₂²	—	2	2	no	—
736	C₂²	—	2	2	no	—
737	C₂²	—	2	4	no	—
738	C₂²	—	2	2	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	2	no	—
741	C₂²	—	4	1	no	—
742	C₂²	—	4	1	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	4	1	no	—
746	C₂²	—	4	1	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	2	no	—
751	C₂²	—	4	2	no	—
752	C₂²	—	8	16	no	—
753	C₂²	—	8	1	no	—
754	C₂²	—	8	1	no	—
755	C₂²	—	8	1	no	—
756	C₂²	—	8	1	no	—
757	C₂²	C₂×C₄×D₄×C₁₇	1	1	yes	characteristic
758	C₂²	D₄²×C₁₇	1	1	yes	characteristic
759	C₂²	C₁₇×#546	1	1	yes	characteristic
760	C₂²	C₂×C₁₇×AGL(1,ℤ/8)	1	1	yes	characteristic
761	C₂²	C₁₇×#575	1	1	yes	characteristic
762	C₂²	C₁₇×#577	1	1	yes	characteristic
763	C₂²	C₁₇×#577	1	1	yes	characteristic
764	C₄	—	2	2	no	—
765	C₄	—	2	2	no	—
766	C₄	—	4	1	no	—
767	C₄	—	4	2	no	—
768	C₄	—	4	1	no	—
769	C₄	—	4	1	no	—
770	C₄	—	4	2	no	—
771	C₄	—	4	2	no	—
772	C₄	—	8	1	no	—
773	C₄	—	8	1	no	—
774	C₄	—	8	1	no	—
775	C₄	C₂×C₄×D₄×C₁₇	1	1	yes	characteristic
776	C₄	C₁₇×#518	1	1	yes	characteristic
777	C₄	C₁₇×#546	1	1	yes	characteristic
778	C₄	C₁₇×#551	1	1	yes	characteristic
779	C₂	—	4	2	no	—
780	C₂	—	4	4	no	—
781	C₂	—	8	2	no	—
782	C₂	C₁₇×#2358	1	1	yes	characteristic
783	C₂	C₄×C₁₇×AGL(1,ℤ/8)	1	1	yes	characteristic
784	C₂	C₁₇×#2949	1	1	yes	characteristic
785	C₂	C₁₇×#3272	1	1	yes	characteristic
786	C₂	C₁₇×#3275	1	1	yes	characteristic
787	C₂	C₁₇×#3310	1	1	yes	characteristic
788	C₂	C₁₇×#3311	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₇
prime radical	C₂³×D₄×C₁₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₄×C₂²⋊C₄×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₇×#440	C₂	semidirect
4. C₁₇×#2362	C₂	semidirect
6. C₁₇×#1968	C₂	semidirect
7. C₁₇×#1936	C₂	semidirect
8. C₁₇×#1925	C₂	semidirect
9. C₁₇×#1894	C₂	semidirect
10. C₁₇×#1880	C₂	semidirect
11. C₁₇×#1877	C₂	semidirect
12. C₁₇×#1864	C₂	semidirect
13. C₁₇×#1854	C₂	semidirect
14. C₄×C₁₇×#102	C₂	semidirect
15. C₁₇×#1753	C₂	semidirect
21. C₂×C₄×Q₈×C₁₇	C₂²	semidirect
26. C₁₇×#450	C₄	semidirect
28. C₂×C₁₇×#107	C₂²	semidirect
29. C₂×C₁₇×#106	C₂²	semidirect
31. C₂×C₁₇×#103	C₂²	semidirect
32. C₂×C₁₇×#103	C₂²	semidirect
40. C₂×C₁₇×#97	C₂²	semidirect
41. C₂×C₄×C₈×C₁₇	C₂²	semidirect
42. C₁₇×#391	C₂²	semidirect
45. C₁₇×#389	C₂²	semidirect
54. C₄×C₄⋊C₄×C₁₇	C₂²	semidirect
56. C₁₇×#340	C₂²	semidirect
57. C₁₇×#340	C₂²	semidirect
58. C₁₇×#340	C₂²	semidirect
59. C₁₇×#340	C₂²	semidirect
60. C₁₇×#336	C₂²	semidirect
61. C₁₇×#336	C₂²	semidirect
81. C₂×SD₁₆×C₁₇	C₂×C₄	semidirect
90. C₁₇×C₂²⋊Q₈	C₂×C₄	semidirect
132. C₁₇×#102	C₂×C₄	semidirect
134. C₁₇×C₂²⋊C₈	C₂×C₄	semidirect
249. #22864	C₁₇	direct (N × H)
342. C₂×#440	C₂×C₁₇	semidirect
344. #2362	C₂×C₁₇	semidirect
346. #1968	C₂×C₁₇	semidirect
347. #1936	C₂×C₁₇	semidirect
348. #1925	C₂×C₁₇	semidirect
349. #1894	C₂×C₁₇	semidirect
350. #1880	C₂×C₁₇	semidirect
351. #1877	C₂×C₁₇	semidirect
352. #1864	C₂×C₁₇	semidirect
353. #1854	C₂×C₁₇	semidirect
354. C₄×#102	C₂×C₁₇	semidirect
355. #1753	C₂×C₁₇	semidirect
405. C₂×C₄×Q₈	C₂²×C₁₇	semidirect
410. #450	C₄×C₁₇	semidirect
412. C₂×#107	C₂²×C₁₇	semidirect
413. C₂×#106	C₂²×C₁₇	semidirect
415. C₂×#103	C₂²×C₁₇	semidirect
416. C₂×#103	C₂²×C₁₇	semidirect
424. C₂×#97	C₂²×C₁₇	semidirect
425. C₂×C₄×C₈	C₂²×C₁₇	semidirect
426. #391	C₂²×C₁₇	semidirect
429. #389	C₂²×C₁₇	semidirect
438. C₄×C₄⋊C₄	C₂²×C₁₇	semidirect
440. #340	C₂²×C₁₇	semidirect
441. #340	C₂²×C₁₇	semidirect
442. #340	C₂²×C₁₇	semidirect
443. #340	C₂²×C₁₇	semidirect
444. #336	C₂²×C₁₇	semidirect
445. #336	C₂²×C₁₇	semidirect
475. C₂×SD₁₆	C₂×C₄×C₁₇	semidirect
484. C₂²⋊Q₈	C₂×C₄×C₁₇	semidirect
526. #102	C₂×C₄×C₁₇	semidirect
528. C₂²⋊C₈	C₂×C₄×C₁₇	semidirect
538. C₁₇	#22864	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₇×#450	2
C₂×C₁₇×#440	2
C₂×C₁₇×#418	2
C₁₇×#2362	2
D₄×C₂²⋊C₄×C₁₇	2
C₁₇×#1968	2
C₁₇×#1936	2
C₁₇×#1925	2
C₁₇×#1894	2
C₁₇×#1880	2
C₁₇×#1877	2
C₁₇×#1864	2
C₁₇×#1854	2
C₄×C₁₇×#102	2
C₁₇×#1753	2
#22864	17

Subgroups — C17×#22864 #16880608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#22864 #16880608