Subgroups — C₁₇×#25403 #16883147

Order 4352.

1034 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#470	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₇×#465	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₇×#464	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₇×#435	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#2540	C₂	1	1	yes	maximal, characteristic
6	C₁₇×#2538	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#2035	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₇×#2034	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#2001	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#2000	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#1959	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#1948	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₇×#1895	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₇×#1892	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#1763	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Q₁₆×C₁₇	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₁₇	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₁₇	C₂²	1	1	yes	characteristic
20	C₂×C₁₇×#124	C₂²	1	1	yes	characteristic
21	C₂×C₁₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₇×#121	C₂²	1	1	yes	characteristic
26	C₂×C₁₇×#121	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
29	C₁₇×#470	—	2	4	no	—
30	C₁₇×#465	—	2	4	no	—
31	C₁₇×#464	—	2	4	no	—
32	C₁₇×#435	—	2	4	no	—
33	C₂×C₁₇×#106	C₂²	1	1	yes	characteristic
34	C₂×C₁₇×#106	C₂²	1	1	yes	characteristic
35	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₁₇×#103	C₂²	1	1	yes	characteristic
37	C₂×C₁₇×#103	C₂²	1	1	yes	characteristic
38	C₂×C₁₇×#103	C₂²	1	1	yes	characteristic
39	C₂×C₁₇×#103	C₂²	1	1	yes	characteristic
40	C₂×C₁₇×#103	C₂²	1	1	yes	characteristic
41	C₂×C₁₇×#102	C₂²	1	1	yes	characteristic
42	C₂×C₁₇×#102	C₂²	1	1	yes	characteristic
43	C₂×C₁₇×#102	C₂²	1	1	yes	characteristic
44	C₂×C₁₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
45	C₂×C₁₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
46	C₂×C₁₇×#97	C₂²	1	1	yes	characteristic
47	C₁₇×#399	—	2	1	no	—
48	C₁₇×#396	—	2	1	no	—
49	C₁₇×#396	—	2	1	no	—
50	C₁₇×#392	—	2	1	no	—
51	C₁₇×#390	—	2	1	no	—
52	C₁₇×#390	—	2	1	no	—
53	C₁₇×#390	—	2	1	no	—
54	C₁₇×#389	—	2	1	no	—
55	C₁₇×#384	C₂²	1	1	yes	characteristic
56	C₁₇×#380	C₂²	1	1	yes	characteristic
57	C₁₇×#380	C₂²	1	1	yes	characteristic
58	C₄×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
59	C₁₇×#340	C₂²	1	1	yes	characteristic
60	C₁₇×#340	C₂²	1	1	yes	characteristic
61	C₁₇×#340	C₂²	1	1	yes	characteristic
62	C₁₇×#340	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
64	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₁₇	—	2	1	no	—
66	C₂²×D₄×C₁₇	—	2	1	no	—
67	C₂²×D₄×C₁₇	D₄	1	1	yes	characteristic
68	C₂²×D₄×C₁₇	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
71	C₂×Q₁₆×C₁₇	—	2	2	no	—
72	C₂×Q₁₆×C₁₇	—	2	2	no	—
73	C₂×Q₁₆×C₁₇	—	4	1	no	—
74	C₂×SD₁₆×C₁₇	—	2	2	no	—
75	C₂×SD₁₆×C₁₇	—	2	2	no	—
76	C₂×SD₁₆×C₁₇	—	4	1	no	—
77	C₂×M₁₆×C₁₇	—	2	2	no	—
78	C₂×M₁₆×C₁₇	—	2	2	no	—
79	C₂×M₁₆×C₁₇	—	4	1	no	—
80	C₂²×C₈×C₁₇	—	2	2	no	—
81	C₂²×C₈×C₁₇	—	2	2	no	—
82	C₂²×C₈×C₁₇	—	4	1	no	—
83	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
87	C₁₇×#124	—	2	2	no	—
88	C₁₇×#124	—	2	2	no	—
89	C₁₇×C₂²⋊Q₈	—	2	2	no	—
90	C₁₇×C₂²⋊Q₈	—	2	2	no	—
91	C₁₇×C₂²⋊Q₈	—	2	2	no	—
92	C₁₇×C₂²⋊Q₈	—	2	2	no	—
93	C₁₇×C₂²⋊Q₈	—	4	1	no	—
94	C₁₇×C₂²⋊Q₈	—	4	1	no	—
95	C₁₇×C₂²⋊Q₈	—	4	1	no	—
96	C₁₇×C₂²⋊Q₈	—	4	1	no	—
97	C₁₇×#121	—	2	2	no	—
98	C₁₇×#121	—	2	2	no	—
99	C₁₇×#121	—	4	1	no	—
100	C₁₇×#121	—	4	1	no	—
101	C₄×Q₈×C₁₇	—	2	2	no	—
102	C₄×Q₈×C₁₇	—	2	2	no	—
103	C₄×D₄×C₁₇	—	2	2	no	—
104	C₄×D₄×C₁₇	—	2	2	no	—
105	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
106	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
107	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
108	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
109	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
110	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
111	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
112	C₂×C₄⋊C₄×C₁₇	D₄	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
118	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
119	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
120	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
123	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
127	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
128	C₂×C₂²⋊C₄×C₁₇	D₄	1	1	yes	characteristic
129	C₂×C₂²⋊C₄×C₁₇	D₄	1	1	yes	characteristic
130	C₂×C₄²×C₁₇	—	2	1	no	—
131	C₂×C₄²×C₁₇	—	2	1	no	—
132	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
133	C₁₇×#106	—	2	2	no	—
134	C₁₇×#106	—	2	2	no	—
135	C₁₇×C₄⋊C₈	D₄	1	4	yes	complemented
136	C₁₇×#103	—	2	2	no	—
137	C₁₇×#103	—	2	2	no	—
138	C₁₇×#103	—	2	2	no	—
139	C₁₇×#103	—	4	1	no	—
140	C₁₇×#103	D₄	1	4	yes	complemented
141	C₁₇×#102	—	2	2	no	—
142	C₁₇×#102	—	2	2	no	—
143	C₁₇×#102	—	4	1	no	—
144	C₁₇×C₂²⋊C₈	—	2	2	no	—
145	C₁₇×C₂²⋊C₈	—	2	2	no	—
146	C₁₇×#97	—	2	2	no	—
147	C₁₇×#95	—	2	1	no	—
148	C₁₇×#95	—	2	1	no	—
149	C₁₇×#95	—	2	1	no	—
150	C₂⁴×C₁₇	—	2	1	no	—
151	C₂⁴×C₁₇	C₂×D₄	1	1	yes	characteristic
152	C₂⁴×C₁₇	C₂×D₄	1	1	yes	characteristic
153	C₂×Q₈×C₁₇	—	2	1	no	—
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	—	2	1	no	—
160	C₂×Q₈×C₁₇	—	2	1	no	—
161	C₂×Q₈×C₁₇	—	2	1	no	—
162	C₂×Q₈×C₁₇	—	2	1	no	—
163	C₂×Q₈×C₁₇	—	2	1	no	—
164	C₂×Q₈×C₁₇	C₂×D₄	1	2	yes	—
165	C₂×D₄×C₁₇	—	2	2	no	—
166	C₂×D₄×C₁₇	—	2	2	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	—	2	1	no	—
171	C₂×D₄×C₁₇	—	2	1	no	—
172	C₂×D₄×C₁₇	—	2	1	no	—
173	C₂×D₄×C₁₇	—	4	1	no	—
174	C₂×D₄×C₁₇	—	4	2	no	—
175	C₂×D₄×C₁₇	—	4	2	no	—
176	C₂×D₄×C₁₇	—	4	2	no	—
177	C₂×D₄×C₁₇	—	4	2	no	—
178	C₂×D₄×C₁₇	—	8	1	no	—
179	C₂×D₄×C₁₇	—	8	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	—	2	1	no	—
190	C₂²×C₄×C₁₇	—	2	1	no	—
191	C₂²×C₄×C₁₇	—	2	1	no	—
192	C₂²×C₄×C₁₇	—	2	1	no	—
193	C₂²×C₄×C₁₇	—	2	1	no	—
194	C₂²×C₄×C₁₇	—	2	1	no	—
195	C₂²×C₄×C₁₇	—	2	1	no	—
196	C₂²×C₄×C₁₇	—	2	1	no	—
197	C₂²×C₄×C₁₇	—	2	1	no	—
198	C₂²×C₄×C₁₇	—	2	1	no	—
199	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
204	Q₁₆×C₁₇	—	4	4	no	—
205	SD₁₆×C₁₇	—	4	4	no	—
206	M₁₆×C₁₇	—	4	4	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	—	2	1	no	—
216	C₂×C₈×C₁₇	—	4	4	no	—
217	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
218	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
219	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
220	C₄⋊C₄×C₁₇	—	2	2	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	—	2	1	no	—
228	C₄⋊C₄×C₁₇	—	2	1	no	—
229	C₄⋊C₄×C₁₇	—	4	2	no	—
230	C₄⋊C₄×C₁₇	—	4	2	no	—
231	C₄⋊C₄×C₁₇	—	4	2	no	—
232	C₄⋊C₄×C₁₇	—	4	2	no	—
233	C₄⋊C₄×C₁₇	—	4	2	no	—
234	C₄⋊C₄×C₁₇	—	4	2	no	—
235	C₄⋊C₄×C₁₇	—	8	1	no	—
236	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
237	C₄⋊C₄×C₁₇	#41	1	2	yes	—
238	C₂²⋊C₄×C₁₇	—	2	2	no	—
239	C₂²⋊C₄×C₁₇	—	2	2	no	—
240	C₂²⋊C₄×C₁₇	—	4	2	no	—
241	C₂²⋊C₄×C₁₇	—	4	2	no	—
242	C₂²⋊C₄×C₁₇	—	4	2	no	—
243	C₂²⋊C₄×C₁₇	—	4	2	no	—
244	C₂²⋊C₄×C₁₇	—	4	2	no	—
245	C₂²⋊C₄×C₁₇	—	4	2	no	—
246	C₂²⋊C₄×C₁₇	—	4	2	no	—
247	C₂²⋊C₄×C₁₇	—	4	2	no	—
248	C₂²⋊C₄×C₁₇	—	8	1	no	—
249	C₂²⋊C₄×C₁₇	—	8	1	no	—
250	C₄²×C₁₇	—	4	2	no	—
251	C₄²×C₁₇	—	8	1	no	—
252	C₄²×C₁₇	C₂×D₄	1	2	yes	—
253	C₄²×C₁₇	#41	1	2	yes	—
254	#25403	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	1	no	—
260	C₂³×C₁₇	—	2	1	no	—
261	C₂³×C₁₇	—	2	1	no	—
262	C₂³×C₁₇	—	2	1	no	—
263	C₂³×C₁₇	—	2	1	no	—
264	C₂³×C₁₇	—	2	1	no	—
265	C₂³×C₁₇	—	2	1	no	—
266	C₂³×C₁₇	—	2	1	no	—
267	C₂³×C₁₇	—	2	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	—	4	1	no	—
273	C₂³×C₁₇	—	4	1	no	—
274	C₂³×C₁₇	—	4	1	no	—
275	C₂³×C₁₇	#137	1	2	yes	—
276	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
277	Q₈×C₁₇	—	2	2	no	—
278	Q₈×C₁₇	—	2	2	no	—
279	Q₈×C₁₇	—	4	1	no	—
280	Q₈×C₁₇	—	4	1	no	—
281	Q₈×C₁₇	—	4	1	no	—
282	Q₈×C₁₇	—	4	1	no	—
283	Q₈×C₁₇	—	4	1	no	—
284	Q₈×C₁₇	—	4	1	no	—
285	D₄×C₁₇	—	4	4	no	—
286	D₄×C₁₇	—	4	1	no	—
287	D₄×C₁₇	—	4	1	no	—
288	D₄×C₁₇	—	4	1	no	—
289	D₄×C₁₇	—	4	1	no	—
290	D₄×C₁₇	—	8	4	no	—
291	D₄×C₁₇	—	8	4	no	—
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	1	no	—
297	C₂×C₄×C₁₇	—	2	1	no	—
298	C₂×C₄×C₁₇	—	2	2	no	—
299	C₂×C₄×C₁₇	—	2	1	no	—
300	C₂×C₄×C₁₇	—	2	2	no	—
301	C₂×C₄×C₁₇	—	2	1	no	—
302	C₂×C₄×C₁₇	—	2	2	no	—
303	C₂×C₄×C₁₇	—	2	1	no	—
304	C₂×C₄×C₁₇	—	2	1	no	—
305	C₂×C₄×C₁₇	—	4	1	no	—
306	C₂×C₄×C₁₇	—	4	1	no	—
307	C₂×C₄×C₁₇	—	4	1	no	—
308	C₂×C₄×C₁₇	—	4	1	no	—
309	C₂×C₄×C₁₇	—	4	1	no	—
310	C₂×C₄×C₁₇	—	4	1	no	—
311	C₂×C₄×C₁₇	—	4	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	—	4	1	no	—
328	C₂×C₄×C₁₇	—	4	1	no	—
329	C₂×C₄×C₁₇	—	4	1	no	—
330	C₂×C₄×C₁₇	—	4	1	no	—
331	C₂×C₄×C₁₇	#121	1	2	yes	—
332	C₂×C₄×C₁₇	#121	1	2	yes	—
333	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
334	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
336	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
337	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
338	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
339	C₈×C₁₇	—	2	2	no	—
340	C₈×C₁₇	—	2	2	no	—
341	C₈×C₁₇	—	2	2	no	—
342	C₈×C₁₇	—	4	1	no	—
343	C₂×#470	C₂×C₁₇	1	1	yes	characteristic, complemented
344	C₂×#465	C₂×C₁₇	1	1	yes	characteristic, complemented
345	C₂×#464	C₂×C₁₇	1	1	yes	characteristic, complemented
346	C₂×#435	C₂×C₁₇	1	1	yes	characteristic, complemented
347	#2540	C₂×C₁₇	1	1	yes	characteristic
348	#2538	C₂×C₁₇	1	1	yes	characteristic, complemented
349	#2035	C₂×C₁₇	1	1	yes	characteristic, complemented
350	#2034	C₂×C₁₇	1	1	yes	characteristic, complemented
351	#2001	C₂×C₁₇	1	1	yes	characteristic, complemented
352	#2000	C₂×C₁₇	1	1	yes	characteristic, complemented
353	#1959	C₂×C₁₇	1	1	yes	characteristic, complemented
354	#1948	C₂×C₁₇	1	1	yes	characteristic, complemented
355	#1895	C₂×C₁₇	1	1	yes	characteristic, complemented
356	#1892	C₂×C₁₇	1	1	yes	characteristic, complemented
357	#1763	C₂×C₁₇	1	1	yes	characteristic, complemented
358	C₂²×C₁₇	—	2	2	no	—
359	C₂²×C₁₇	—	2	2	no	—
360	C₂²×C₁₇	—	2	2	no	—
361	C₂²×C₁₇	—	4	1	no	—
362	C₂²×C₁₇	—	4	1	no	—
363	C₂²×C₁₇	—	4	1	no	—
364	C₂²×C₁₇	—	4	1	no	—
365	C₂²×C₁₇	—	4	1	no	—
366	C₂²×C₁₇	—	4	1	no	—
367	C₂²×C₁₇	—	4	1	no	—
368	C₂²×C₁₇	—	4	1	no	—
369	C₂²×C₁₇	—	4	1	no	—
370	C₂²×C₁₇	—	4	1	no	—
371	C₂²×C₁₇	—	4	1	no	—
372	C₂²×C₁₇	—	8	1	no	—
373	C₂²×C₁₇	—	8	1	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	—	8	1	no	—
379	C₂²×C₁₇	C₂×#121	1	1	yes	characteristic
380	C₂²×C₁₇	D₄²	1	1	yes	characteristic
381	C₂²×C₁₇	#546	1	1	yes	characteristic
382	C₂²×C₁₇	C₂×#137	1	1	yes	characteristic
383	C₂²×C₁₇	#575	1	1	yes	characteristic
384	C₂²×C₁₇	#577	1	1	yes	characteristic
385	C₂²×C₁₇	#577	1	1	yes	characteristic
386	C₄×C₁₇	—	2	2	no	—
387	C₄×C₁₇	—	2	2	no	—
388	C₄×C₁₇	—	4	1	no	—
389	C₄×C₁₇	—	4	1	no	—
390	C₄×C₁₇	—	4	2	no	—
391	C₄×C₁₇	—	4	2	no	—
392	C₄×C₁₇	—	4	2	no	—
393	C₄×C₁₇	—	8	1	no	—
394	C₄×C₁₇	—	8	1	no	—
395	C₄×C₁₇	—	8	1	no	—
396	C₄×C₁₇	—	8	1	no	—
397	C₄×C₁₇	#532	1	1	yes	characteristic
398	C₄×C₁₇	#540	1	1	yes	characteristic
399	C₄×C₁₇	D₄²	1	1	yes	characteristic
400	C₄×C₁₇	#550	1	1	yes	characteristic
401	C₂²×Q₁₆	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	C₂³×C₈	C₂²×C₁₇	1	1	yes	characteristic
405	C₂×#124	C₂²×C₁₇	1	1	yes	characteristic
406	C₂×C₂²⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
407	C₂×C₂²⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
408	C₂×C₂²⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
409	C₂×C₂²⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
410	C₂×#121	C₂²×C₁₇	1	1	yes	characteristic
411	C₂×#121	C₂²×C₁₇	1	1	yes	characteristic
412	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
413	C₂×C₄×D₄	C₂²×C₁₇	1	1	yes	characteristic
414	#470	—	2	4	no	—
415	#465	—	2	4	no	—
416	#464	—	2	4	no	—
417	#435	—	2	4	no	—
418	C₂×#106	C₂²×C₁₇	1	1	yes	characteristic
419	C₂×#106	C₂²×C₁₇	1	1	yes	characteristic
420	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
421	C₂×#103	C₂²×C₁₇	1	1	yes	characteristic
422	C₂×#103	C₂²×C₁₇	1	1	yes	characteristic
423	C₂×#103	C₂²×C₁₇	1	1	yes	characteristic
424	C₂×#103	C₂²×C₁₇	1	1	yes	characteristic
425	C₂×#103	C₂²×C₁₇	1	1	yes	characteristic
426	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic
427	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic
428	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic
429	C₂×C₂²⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
430	C₂×C₂²⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
431	C₂×#97	C₂²×C₁₇	1	1	yes	characteristic
432	#399	—	2	1	no	—
433	#396	—	2	1	no	—
434	#396	—	2	1	no	—
435	#392	—	2	1	no	—
436	#390	—	2	1	no	—
437	#390	—	2	1	no	—
438	#390	—	2	1	no	—
439	#389	—	2	1	no	—
440	#384	C₂²×C₁₇	1	1	yes	characteristic
441	#380	C₂²×C₁₇	1	1	yes	characteristic
442	#380	C₂²×C₁₇	1	1	yes	characteristic
443	C₄×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
444	#340	C₂²×C₁₇	1	1	yes	characteristic
445	#340	C₂²×C₁₇	1	1	yes	characteristic
446	#340	C₂²×C₁₇	1	1	yes	characteristic
447	#340	C₂²×C₁₇	1	1	yes	characteristic
448	C₂×C₁₇	—	4	2	no	—
449	C₂×C₁₇	—	8	1	no	—
450	C₂×C₁₇	—	16	1	no	—
451	C₂×C₁₇	#2428	1	1	yes	characteristic
452	C₂×C₁₇	#3056	1	1	yes	characteristic
453	C₂×C₁₇	#3060	1	1	yes	characteristic
454	C₂×C₁₇	#3266	1	1	yes	characteristic
455	C₂×C₁₇	#3271	1	1	yes	characteristic
456	C₂×C₁₇	#3311	1	1	yes	characteristic
457	C₂×C₁₇	#3316	1	1	yes	characteristic
458	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
459	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
460	C₂²×D₄	—	2	1	no	—
461	C₂²×D₄	—	2	1	no	—
462	C₂²×D₄	D₄×C₁₇	1	1	yes	characteristic
463	C₂²×D₄	C₂³×C₁₇	1	1	yes	characteristic
464	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
465	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
466	C₂×Q₁₆	—	2	2	no	—
467	C₂×Q₁₆	—	2	2	no	—
468	C₂×Q₁₆	—	4	1	no	—
469	C₂×SD₁₆	—	2	2	no	—
470	C₂×SD₁₆	—	2	2	no	—
471	C₂×SD₁₆	—	4	1	no	—
472	C₂×M₁₆	—	2	2	no	—
473	C₂×M₁₆	—	2	2	no	—
474	C₂×M₁₆	—	4	1	no	—
475	C₂²×C₈	—	2	2	no	—
476	C₂²×C₈	—	2	2	no	—
477	C₂²×C₈	—	4	1	no	—
478	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
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	#124	—	2	2	no	—
483	#124	—	2	2	no	—
484	C₂²⋊Q₈	—	2	2	no	—
485	C₂²⋊Q₈	—	2	2	no	—
486	C₂²⋊Q₈	—	2	2	no	—
487	C₂²⋊Q₈	—	2	2	no	—
488	C₂²⋊Q₈	—	4	1	no	—
489	C₂²⋊Q₈	—	4	1	no	—
490	C₂²⋊Q₈	—	4	1	no	—
491	C₂²⋊Q₈	—	4	1	no	—
492	#121	—	2	2	no	—
493	#121	—	2	2	no	—
494	#121	—	4	1	no	—
495	#121	—	4	1	no	—
496	C₄×Q₈	—	2	2	no	—
497	C₄×Q₈	—	2	2	no	—
498	C₄×D₄	—	2	2	no	—
499	C₄×D₄	—	2	2	no	—
500	C₂×C₄⋊C₄	—	2	1	no	—
501	C₂×C₄⋊C₄	—	2	1	no	—
502	C₂×C₄⋊C₄	—	2	1	no	—
503	C₂×C₄⋊C₄	—	2	1	no	—
504	C₂×C₄⋊C₄	—	2	1	no	—
505	C₂×C₄⋊C₄	—	2	1	no	—
506	C₂×C₄⋊C₄	—	2	1	no	—
507	C₂×C₄⋊C₄	D₄×C₁₇	1	1	yes	characteristic
508	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
509	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
510	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
511	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
512	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
513	C₂×C₂²⋊C₄	—	2	1	no	—
514	C₂×C₂²⋊C₄	—	2	1	no	—
515	C₂×C₂²⋊C₄	—	2	1	no	—
516	C₂×C₂²⋊C₄	—	2	1	no	—
517	C₂×C₂²⋊C₄	—	2	1	no	—
518	C₂×C₂²⋊C₄	—	2	1	no	—
519	C₂×C₂²⋊C₄	—	2	1	no	—
520	C₂×C₂²⋊C₄	—	2	1	no	—
521	C₂×C₂²⋊C₄	—	2	1	no	—
522	C₂×C₂²⋊C₄	—	2	1	no	—
523	C₂×C₂²⋊C₄	D₄×C₁₇	1	1	yes	characteristic
524	C₂×C₂²⋊C₄	D₄×C₁₇	1	1	yes	characteristic
525	C₂×C₄²	—	2	1	no	—
526	C₂×C₄²	—	2	1	no	—
527	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
528	#106	—	2	2	no	—
529	#106	—	2	2	no	—
530	C₄⋊C₈	D₄×C₁₇	1	4	yes	complemented
531	#103	—	2	2	no	—
532	#103	—	2	2	no	—
533	#103	—	2	2	no	—
534	#103	—	4	1	no	—
535	#103	D₄×C₁₇	1	4	yes	complemented
536	#102	—	2	2	no	—
537	#102	—	2	2	no	—
538	#102	—	4	1	no	—
539	C₂²⋊C₈	—	2	2	no	—
540	C₂²⋊C₈	—	2	2	no	—
541	#97	—	2	2	no	—
542	#95	—	2	1	no	—
543	#95	—	2	1	no	—
544	#95	—	2	1	no	—
545	C₁₇	#25403	1	1	yes	characteristic, direct product factor, Sylow
546	C₂⁴	—	2	1	no	—
547	C₂⁴	C₂×D₄×C₁₇	1	1	yes	characteristic
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	—	2	1	no	—
555	C₂×Q₈	—	2	1	no	—
556	C₂×Q₈	—	2	1	no	—
557	C₂×Q₈	—	2	1	no	—
558	C₂×Q₈	—	2	1	no	—
559	C₂×Q₈	—	2	1	no	—
560	C₂×Q₈	C₂×D₄×C₁₇	1	2	yes	—
561	C₂×D₄	—	2	2	no	—
562	C₂×D₄	—	2	1	no	—
563	C₂×D₄	—	2	1	no	—
564	C₂×D₄	—	2	1	no	—
565	C₂×D₄	—	2	1	no	—
566	C₂×D₄	—	2	1	no	—
567	C₂×D₄	—	2	1	no	—
568	C₂×D₄	—	2	2	no	—
569	C₂×D₄	—	4	1	no	—
570	C₂×D₄	—	4	2	no	—
571	C₂×D₄	—	4	2	no	—
572	C₂×D₄	—	4	2	no	—
573	C₂×D₄	—	4	2	no	—
574	C₂×D₄	—	8	1	no	—
575	C₂×D₄	—	8	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	—	2	1	no	—
585	C₂²×C₄	—	2	1	no	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	—	2	1	no	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	2	1	no	—
591	C₂²×C₄	—	2	1	no	—
592	C₂²×C₄	—	2	1	no	—
593	C₂²×C₄	—	2	1	no	—
594	C₂²×C₄	—	2	1	no	—
595	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
596	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
597	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
598	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
599	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
600	Q₁₆	—	4	4	no	—
601	SD₁₆	—	4	4	no	—
602	M₁₆	—	4	4	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	—	2	1	no	—
611	C₂×C₈	—	2	1	no	—
612	C₂×C₈	—	4	4	no	—
613	C₂×C₈	C₂×D₄×C₁₇	1	2	yes	—
614	C₂×C₈	C₂×D₄×C₁₇	1	2	yes	—
615	C₂×C₈	C₂×D₄×C₁₇	1	2	yes	—
616	C₄⋊C₄	—	2	1	no	—
617	C₄⋊C₄	—	2	1	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	1	no	—
620	C₄⋊C₄	—	2	1	no	—
621	C₄⋊C₄	—	2	1	no	—
622	C₄⋊C₄	—	2	1	no	—
623	C₄⋊C₄	—	2	1	no	—
624	C₄⋊C₄	—	2	1	no	—
625	C₄⋊C₄	—	4	2	no	—
626	C₄⋊C₄	—	4	2	no	—
627	C₄⋊C₄	—	4	2	no	—
628	C₄⋊C₄	—	4	2	no	—
629	C₄⋊C₄	—	4	2	no	—
630	C₄⋊C₄	—	4	2	no	—
631	C₄⋊C₄	—	8	1	no	—
632	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
633	C₄⋊C₄	#41×C₁₇	1	2	yes	—
634	C₂²⋊C₄	—	2	2	no	—
635	C₂²⋊C₄	—	2	2	no	—
636	C₂²⋊C₄	—	4	2	no	—
637	C₂²⋊C₄	—	4	2	no	—
638	C₂²⋊C₄	—	4	2	no	—
639	C₂²⋊C₄	—	4	2	no	—
640	C₂²⋊C₄	—	4	2	no	—
641	C₂²⋊C₄	—	4	2	no	—
642	C₂²⋊C₄	—	4	2	no	—
643	C₂²⋊C₄	—	4	2	no	—
644	C₂²⋊C₄	—	8	1	no	—
645	C₂²⋊C₄	—	8	1	no	—
646	C₄²	—	4	2	no	—
647	C₄²	—	8	1	no	—
648	C₄²	C₂×D₄×C₁₇	1	2	yes	—
649	C₄²	#41×C₁₇	1	2	yes	—
650	C₂³	—	2	1	no	—
651	C₂³	—	2	1	no	—
652	C₂³	—	2	1	no	—
653	C₂³	—	2	1	no	—
654	C₂³	—	2	1	no	—
655	C₂³	—	2	1	no	—
656	C₂³	—	2	1	no	—
657	C₂³	—	2	1	no	—
658	C₂³	—	2	1	no	—
659	C₂³	—	2	1	no	—
660	C₂³	—	2	1	no	—
661	C₂³	—	2	1	no	—
662	C₂³	—	2	1	no	—
663	C₂³	—	4	1	no	—
664	C₂³	—	4	1	no	—
665	C₂³	—	4	1	no	—
666	C₂³	—	4	1	no	—
667	C₂³	—	4	1	no	—
668	C₂³	—	4	1	no	—
669	C₂³	—	4	1	no	—
670	C₂³	C₁₇×#137	1	2	yes	—
671	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
672	Q₈	—	2	2	no	—
673	Q₈	—	2	2	no	—
674	Q₈	—	4	1	no	—
675	Q₈	—	4	1	no	—
676	Q₈	—	4	1	no	—
677	Q₈	—	4	1	no	—
678	Q₈	—	4	1	no	—
679	Q₈	—	4	1	no	—
680	D₄	—	4	4	no	—
681	D₄	—	4	1	no	—
682	D₄	—	4	1	no	—
683	D₄	—	4	1	no	—
684	D₄	—	4	1	no	—
685	D₄	—	8	4	no	—
686	D₄	—	8	4	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	4	1	no	—
701	C₂×C₄	—	4	1	no	—
702	C₂×C₄	—	4	1	no	—
703	C₂×C₄	—	4	1	no	—
704	C₂×C₄	—	4	1	no	—
705	C₂×C₄	—	4	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	—	4	1	no	—
722	C₂×C₄	—	4	1	no	—
723	C₂×C₄	—	4	1	no	—
724	C₂×C₄	—	4	1	no	—
725	C₂×C₄	—	4	1	no	—
726	C₂×C₄	C₁₇×#121	1	2	yes	—
727	C₂×C₄	C₁₇×#121	1	2	yes	—
728	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
729	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
730	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
731	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
732	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
733	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
734	C₈	—	2	2	no	—
735	C₈	—	2	2	no	—
736	C₈	—	2	2	no	—
737	C₈	—	4	1	no	—
738	C₂²	—	2	2	no	—
739	C₂²	—	2	2	no	—
740	C₂²	—	2	2	no	—
741	C₂²	—	4	1	no	—
742	C₂²	—	4	1	no	—
743	C₂²	—	4	1	no	—
744	C₂²	—	4	1	no	—
745	C₂²	—	4	1	no	—
746	C₂²	—	4	1	no	—
747	C₂²	—	4	1	no	—
748	C₂²	—	4	1	no	—
749	C₂²	—	4	1	no	—
750	C₂²	—	4	1	no	—
751	C₂²	—	4	1	no	—
752	C₂²	—	8	1	no	—
753	C₂²	—	8	1	no	—
754	C₂²	—	8	1	no	—
755	C₂²	—	8	1	no	—
756	C₂²	—	8	1	no	—
757	C₂²	—	8	1	no	—
758	C₂²	—	8	1	no	—
759	C₂²	C₂×C₁₇×#121	1	1	yes	characteristic
760	C₂²	D₄²×C₁₇	1	1	yes	characteristic
761	C₂²	C₁₇×#546	1	1	yes	characteristic
762	C₂²	C₂×C₁₇×#137	1	1	yes	characteristic
763	C₂²	C₁₇×#575	1	1	yes	characteristic
764	C₂²	C₁₇×#577	1	1	yes	characteristic
765	C₂²	C₁₇×#577	1	1	yes	characteristic
766	C₄	—	2	2	no	—
767	C₄	—	2	2	no	—
768	C₄	—	4	2	no	—
769	C₄	—	4	2	no	—
770	C₄	—	4	1	no	—
771	C₄	—	4	1	no	—
772	C₄	—	4	2	no	—
773	C₄	—	8	1	no	—
774	C₄	—	8	1	no	—
775	C₄	—	8	1	no	—
776	C₄	—	8	1	no	—
777	C₄	C₁₇×#532	1	1	yes	characteristic
778	C₄	C₁₇×#540	1	1	yes	characteristic
779	C₄	D₄²×C₁₇	1	1	yes	characteristic
780	C₄	C₁₇×#550	1	1	yes	characteristic
781	C₂	—	4	2	no	—
782	C₂	—	8	1	no	—
783	C₂	—	16	1	no	—
784	C₂	C₁₇×#2428	1	1	yes	characteristic
785	C₂	C₁₇×#3056	1	1	yes	characteristic
786	C₂	C₁₇×#3060	1	1	yes	characteristic
787	C₂	C₁₇×#3266	1	1	yes	characteristic
788	C₂	C₁₇×#3271	1	1	yes	characteristic
789	C₂	C₁₇×#3311	1	1	yes	characteristic
790	C₂	C₁₇×#3316	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₇
prime radical	C₁₇×#2540	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₂×C₄×D₄×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₇×#470	C₂	semidirect
2. C₂×C₁₇×#465	C₂	semidirect
3. C₂×C₁₇×#464	C₂	semidirect
4. C₂×C₁₇×#435	C₂	semidirect
6. C₁₇×#2538	C₂	semidirect
7. C₁₇×#2035	C₂	semidirect
8. C₁₇×#2034	C₂	semidirect
9. C₁₇×#2001	C₂	semidirect
10. C₁₇×#2000	C₂	semidirect
11. C₁₇×#1959	C₂	semidirect
12. C₁₇×#1948	C₂	semidirect
13. C₁₇×#1895	C₂	semidirect
14. C₁₇×#1892	C₂	semidirect
15. C₁₇×#1763	C₂	semidirect
135. C₁₇×C₄⋊C₈	D₄	semidirect
140. C₁₇×#103	D₄	semidirect
254. #25403	C₁₇	direct (N × H)
343. C₂×#470	C₂×C₁₇	semidirect
344. C₂×#465	C₂×C₁₇	semidirect
345. C₂×#464	C₂×C₁₇	semidirect
346. C₂×#435	C₂×C₁₇	semidirect
348. #2538	C₂×C₁₇	semidirect
349. #2035	C₂×C₁₇	semidirect
350. #2034	C₂×C₁₇	semidirect
351. #2001	C₂×C₁₇	semidirect
352. #2000	C₂×C₁₇	semidirect
353. #1959	C₂×C₁₇	semidirect
354. #1948	C₂×C₁₇	semidirect
355. #1895	C₂×C₁₇	semidirect
356. #1892	C₂×C₁₇	semidirect
357. #1763	C₂×C₁₇	semidirect
530. C₄⋊C₈	D₄×C₁₇	semidirect
535. #103	D₄×C₁₇	semidirect
545. C₁₇	#25403	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×#470	2
C₂×C₁₇×#465	2
C₂×C₁₇×#464	2
C₂×C₁₇×#435	2
C₁₇×#2540	2
C₁₇×#2538	2
C₁₇×#2035	2
C₁₇×#2034	2
C₁₇×#2001	2
C₁₇×#2000	2
C₁₇×#1959	2
C₁₇×#1948	2
C₁₇×#1895	2
C₁₇×#1892	2
C₁₇×#1763	2
#25403	17

Subgroups — C17×#25403 #16883147

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#25403 #16883147