Subgroups — C₁₇×#20995 #16878739

Order 4352.

1664 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#575	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₇×#568	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₇×#421	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#2896	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₇×#413	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#1903	C₂	1	4	yes	maximal, complemented
7	C₁₇×#1902	C₂	1	4	yes	maximal, complemented
8	C₂×C₁₇×#344	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₇×#338	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₁₇	C₂²	1	1	yes	characteristic
11	C₂²×#41×C₁₇	C₂²	1	1	yes	characteristic
12	C₁₇×#575	—	2	2	no	—
13	C₁₇×#575	—	2	2	no	—
14	C₁₇×#575	—	2	2	no	—
15	C₁₇×#575	—	2	2	no	—
16	C₂×C₁₇×#137	C₄	1	2	yes	complemented
17	C₂×C₁₇×#137	C₂²	1	2	yes	—
18	C₂×C₁₇×AGL(1,ℤ/8)	C₄	1	2	yes	complemented
19	C₂×C₁₇×AGL(1,ℤ/8)	C₂²	1	2	yes	—
20	C₂×C₁₇×#135	C₄	1	4	yes	complemented
21	C₁₇×#568	—	2	2	no	—
22	C₁₇×#568	—	2	2	no	—
23	C₁₇×#568	—	2	2	no	—
24	C₁₇×#568	C₂²	1	4	yes	—
25	C₂×C₁₇×#131	—	2	2	no	—
26	C₂×C₁₇×#131	—	2	2	no	—
27	C₂²×M₁₆×C₁₇	—	2	2	no	—
28	C₂²×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
29	C₂²×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
30	C₂²×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
31	C₂²×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
32	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
33	C₁₇×#421	—	2	2	no	—
34	C₁₇×#421	C₂²	1	4	yes	—
35	C₂×C₁₇×#104	—	2	2	no	—
36	C₁₇×#419	C₂²	1	2	yes	complemented
37	C₁₇×#418	C₂²	1	2	yes	complemented
38	C₁₇×#417	—	2	2	no	—
39	C₁₇×#416	—	2	2	no	—
40	C₁₇×#413	—	2	2	no	—
41	C₁₇×#413	—	2	2	no	—
42	C₂×C₁₇×#101	C₂²	1	2	yes	complemented
43	C₂×C₁₇×#100	C₂²	1	2	yes	complemented
44	C₁₇×#344	C₂²	1	4	yes	complemented
45	C₁₇×#338	C₂²	1	4	yes	complemented
46	C₂×#41×C₁₇	—	2	1	no	—
47	C₂×#41×C₁₇	—	2	1	no	—
48	C₂×#41×C₁₇	—	2	1	no	—
49	C₂×#41×C₁₇	—	2	1	no	—
50	C₂×#41×C₁₇	—	2	1	no	—
51	C₂×#41×C₁₇	—	2	1	no	—
52	C₂×#41×C₁₇	—	2	1	no	—
53	C₂×#41×C₁₇	—	2	1	no	—
54	C₂×#41×C₁₇	—	2	1	no	—
55	C₂×#41×C₁₇	—	2	1	no	—
56	C₂×#41×C₁₇	—	2	1	no	—
57	C₂×#41×C₁₇	—	2	1	no	—
58	C₂×#41×C₁₇	—	2	1	no	—
59	C₂×#41×C₁₇	—	2	1	no	—
60	C₂×#41×C₁₇	—	2	1	no	—
61	C₂×#41×C₁₇	—	2	1	no	—
62	C₂×#41×C₁₇	C₂×C₄	1	2	yes	—
63	C₂×#41×C₁₇	C₂×C₄	1	2	yes	—
64	C₂×#41×C₁₇	C₂×C₄	1	2	yes	—
65	C₂×#41×C₁₇	D₄	1	2	yes	—
66	C₂×#41×C₁₇	D₄	1	2	yes	—
67	C₂×#41×C₁₇	D₄	1	2	yes	—
68	C₂×#41×C₁₇	D₄	1	2	yes	—
69	C₂×#41×C₁₇	C₂³	1	2	yes	—
70	C₂²×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
71	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₁₇	—	2	1	no	—
73	C₂²×D₄×C₁₇	—	2	1	no	—
74	C₂²×D₄×C₁₇	C₂×C₄	1	1	yes	characteristic
75	C₂²×D₄×C₁₇	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₁₇	—	2	1	no	—
77	C₂³×C₄×C₁₇	—	2	1	no	—
78	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
79	C₁₇×#137	—	2	4	no	—
80	C₁₇×#137	—	2	4	no	—
81	C₁₇×#137	—	2	4	no	—
82	C₁₇×#137	—	2	4	no	—
83	C₁₇×AGL(1,ℤ/8)	—	2	4	no	—
84	C₁₇×AGL(1,ℤ/8)	—	2	4	no	—
85	C₁₇×AGL(1,ℤ/8)	—	2	4	no	—
86	C₁₇×AGL(1,ℤ/8)	—	2	4	no	—
87	C₁₇×#135	—	2	8	no	—
88	C₁₇×#135	—	2	8	no	—
89	C₂×Q₁₆×C₁₇	C₂×C₄	1	4	yes	complemented
90	C₂×SD₁₆×C₁₇	C₂×C₄	1	4	yes	complemented
91	C₂×SD₁₆×C₁₇	C₂×C₄	1	4	yes	complemented
92	C₂×D₈×C₁₇	C₂×C₄	1	4	yes	complemented
93	C₁₇×#131	—	2	8	no	—
94	C₁₇×#131	—	2	8	no	—
95	C₁₇×#131	—	2	8	no	—
96	C₁₇×#131	—	2	8	no	—
97	C₂×M₁₆×C₁₇	—	2	4	no	—
98	C₂×M₁₆×C₁₇	—	2	8	no	—
99	C₂×M₁₆×C₁₇	—	2	1	no	—
100	C₂×M₁₆×C₁₇	—	2	1	no	—
101	C₂×M₁₆×C₁₇	—	2	1	no	—
102	C₂×M₁₆×C₁₇	—	2	1	no	—
103	C₂×M₁₆×C₁₇	—	2	1	no	—
104	C₂×M₁₆×C₁₇	—	2	1	no	—
105	C₂×M₁₆×C₁₇	—	2	1	no	—
106	C₂×M₁₆×C₁₇	—	2	1	no	—
107	C₂×M₁₆×C₁₇	—	2	1	no	—
108	C₂×M₁₆×C₁₇	—	2	1	no	—
109	C₂×M₁₆×C₁₇	—	2	1	no	—
110	C₂×M₁₆×C₁₇	—	2	8	no	—
111	C₂×M₁₆×C₁₇	—	2	1	no	—
112	C₂×M₁₆×C₁₇	—	2	1	no	—
113	C₂×M₁₆×C₁₇	—	2	1	no	—
114	C₂×M₁₆×C₁₇	—	2	1	no	—
115	C₂×M₁₆×C₁₇	—	2	1	no	—
116	C₂×M₁₆×C₁₇	C₂×C₄	1	2	yes	—
117	C₂×M₁₆×C₁₇	D₄	1	2	yes	—
118	C₂×M₁₆×C₁₇	D₄	1	2	yes	—
119	C₂×M₁₆×C₁₇	D₄	1	2	yes	—
120	C₂×M₁₆×C₁₇	C₂³	1	2	yes	—
121	C₂×M₁₆×C₁₇	C₂³	1	2	yes	—
122	C₂×M₁₆×C₁₇	C₂³	1	2	yes	—
123	C₂×M₁₆×C₁₇	C₂³	1	2	yes	—
124	C₂²×C₈×C₁₇	—	2	4	no	—
125	C₂²×C₈×C₁₇	—	2	1	no	—
126	C₂²×C₈×C₁₇	—	2	1	no	—
127	C₂²×C₈×C₁₇	C₂×C₄	1	2	yes	—
128	C₂²×C₈×C₁₇	D₄	1	2	yes	—
129	C₁₇×#117	—	2	1	no	—
130	C₁₇×#117	—	2	1	no	—
131	C₁₇×#117	—	2	1	no	—
132	C₁₇×#117	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
134	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
135	C₂×C₄²×C₁₇	—	2	1	no	—
136	C₁₇×#104	—	2	8	no	—
137	C₁₇×#103	—	2	4	no	—
138	C₁₇×#102	—	2	4	no	—
139	C₁₇×#101	—	2	4	no	—
140	C₁₇×#100	—	2	4	no	—
141	C₂⁴×C₁₇	—	2	1	no	—
142	C₂⁴×C₁₇	—	2	1	no	—
143	C₂⁴×C₁₇	#41	1	1	yes	characteristic
144	#41×C₁₇	—	2	2	no	—
145	#41×C₁₇	—	2	2	no	—
146	#41×C₁₇	—	2	2	no	—
147	#41×C₁₇	—	2	2	no	—
148	#41×C₁₇	—	2	2	no	—
149	#41×C₁₇	—	2	2	no	—
150	#41×C₁₇	—	2	2	no	—
151	#41×C₁₇	—	2	2	no	—
152	#41×C₁₇	—	2	2	no	—
153	#41×C₁₇	—	2	2	no	—
154	#41×C₁₇	—	2	2	no	—
155	#41×C₁₇	—	2	2	no	—
156	#41×C₁₇	—	2	2	no	—
157	#41×C₁₇	—	2	2	no	—
158	#41×C₁₇	—	2	2	no	—
159	#41×C₁₇	—	2	2	no	—
160	#41×C₁₇	—	2	2	no	—
161	#41×C₁₇	—	2	2	no	—
162	#41×C₁₇	—	2	2	no	—
163	#41×C₁₇	—	2	2	no	—
164	#41×C₁₇	—	4	1	no	—
165	#41×C₁₇	—	4	1	no	—
166	#41×C₁₇	—	4	1	no	—
167	#41×C₁₇	—	4	1	no	—
168	#41×C₁₇	—	4	1	no	—
169	#41×C₁₇	—	4	1	no	—
170	#41×C₁₇	—	4	1	no	—
171	#41×C₁₇	—	4	1	no	—
172	#41×C₁₇	C₂²⋊C₄	1	4	yes	—
173	#41×C₁₇	C₂²⋊C₄	1	4	yes	—
174	#41×C₁₇	C₂×D₄	1	4	yes	—
175	#41×C₁₇	C₂×D₄	1	4	yes	—
176	C₂×Q₈×C₁₇	—	2	1	no	—
177	C₂×Q₈×C₁₇	—	2	1	no	—
178	C₂×Q₈×C₁₇	—	2	1	no	—
179	C₂×Q₈×C₁₇	—	2	1	no	—
180	C₂×Q₈×C₁₇	—	2	1	no	—
181	C₂×Q₈×C₁₇	—	2	1	no	—
182	C₂×Q₈×C₁₇	—	2	1	no	—
183	C₂×Q₈×C₁₇	—	2	1	no	—
184	C₂×Q₈×C₁₇	C₂²⋊C₄	1	2	yes	—
185	C₂×Q₈×C₁₇	C₂²⋊C₄	1	2	yes	—
186	C₂×Q₈×C₁₇	C₂²×C₄	1	2	yes	—
187	C₂×Q₈×C₁₇	C₂²×C₄	1	2	yes	—
188	C₂×D₄×C₁₇	—	2	2	no	—
189	C₂×D₄×C₁₇	—	2	2	no	—
190	C₂×D₄×C₁₇	—	2	2	no	—
191	C₂×D₄×C₁₇	—	2	2	no	—
192	C₂×D₄×C₁₇	—	2	2	no	—
193	C₂×D₄×C₁₇	—	2	2	no	—
194	C₂×D₄×C₁₇	—	2	2	no	—
195	C₂×D₄×C₁₇	—	2	2	no	—
196	C₂×D₄×C₁₇	—	2	1	no	—
197	C₂×D₄×C₁₇	—	2	1	no	—
198	C₂×D₄×C₁₇	—	2	1	no	—
199	C₂×D₄×C₁₇	—	2	1	no	—
200	C₂×D₄×C₁₇	—	2	1	no	—
201	C₂×D₄×C₁₇	—	2	1	no	—
202	C₂×D₄×C₁₇	—	2	1	no	—
203	C₂×D₄×C₁₇	—	2	1	no	—
204	C₂×D₄×C₁₇	—	4	1	no	—
205	C₂×D₄×C₁₇	—	4	1	no	—
206	C₂×D₄×C₁₇	—	4	1	no	—
207	C₂×D₄×C₁₇	—	4	1	no	—
208	C₂×D₄×C₁₇	C₂²⋊C₄	1	2	yes	—
209	C₂×D₄×C₁₇	C₂²⋊C₄	1	2	yes	—
210	C₂×D₄×C₁₇	C₂²×C₄	1	2	yes	—
211	C₂×D₄×C₁₇	C₂²×C₄	1	2	yes	—
212	C₂²×C₄×C₁₇	—	2	1	no	—
213	C₂²×C₄×C₁₇	—	2	2	no	—
214	C₂²×C₄×C₁₇	—	2	2	no	—
215	C₂²×C₄×C₁₇	—	2	2	no	—
216	C₂²×C₄×C₁₇	—	2	2	no	—
217	C₂²×C₄×C₁₇	—	2	2	no	—
218	C₂²×C₄×C₁₇	—	2	2	no	—
219	C₂²×C₄×C₁₇	—	2	1	no	—
220	C₂²×C₄×C₁₇	—	2	2	no	—
221	C₂²×C₄×C₁₇	—	2	2	no	—
222	C₂²×C₄×C₁₇	—	4	1	no	—
223	C₂²×C₄×C₁₇	—	4	1	no	—
224	C₂²×C₄×C₁₇	—	4	1	no	—
225	C₂²×C₄×C₁₇	—	4	1	no	—
226	C₂²×C₄×C₁₇	—	4	1	no	—
227	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
228	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
229	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
238	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
239	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
240	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
241	Q₁₆×C₁₇	—	2	8	no	—
242	SD₁₆×C₁₇	—	2	8	no	—
243	SD₁₆×C₁₇	—	2	8	no	—
244	D₈×C₁₇	—	2	8	no	—
245	M₁₆×C₁₇	—	2	16	no	—
246	M₁₆×C₁₇	—	2	2	no	—
247	M₁₆×C₁₇	—	2	2	no	—
248	M₁₆×C₁₇	—	2	2	no	—
249	M₁₆×C₁₇	—	2	2	no	—
250	M₁₆×C₁₇	—	2	2	no	—
251	M₁₆×C₁₇	—	2	2	no	—
252	M₁₆×C₁₇	—	2	2	no	—
253	M₁₆×C₁₇	—	2	2	no	—
254	M₁₆×C₁₇	—	2	2	no	—
255	M₁₆×C₁₇	—	2	2	no	—
256	M₁₆×C₁₇	—	2	2	no	—
257	M₁₆×C₁₇	—	2	2	no	—
258	M₁₆×C₁₇	—	2	2	no	—
259	M₁₆×C₁₇	—	4	1	no	—
260	M₁₆×C₁₇	—	4	1	no	—
261	M₁₆×C₁₇	C₂×D₄	1	4	yes	—
262	C₂×C₈×C₁₇	—	2	16	no	—
263	C₂×C₈×C₁₇	—	2	2	no	—
264	C₂×C₈×C₁₇	—	2	2	no	—
265	C₂×C₈×C₁₇	—	2	2	no	—
266	C₂×C₈×C₁₇	—	2	2	no	—
267	C₂×C₈×C₁₇	—	2	2	no	—
268	C₂×C₈×C₁₇	—	2	2	no	—
269	C₂×C₈×C₁₇	—	2	2	no	—
270	C₂×C₈×C₁₇	—	2	2	no	—
271	C₂×C₈×C₁₇	—	4	1	no	—
272	C₂×C₈×C₁₇	—	4	1	no	—
273	C₂×C₈×C₁₇	C₂²×C₄	1	4	yes	—
274	C₂×C₈×C₁₇	C₂×D₄	1	4	yes	—
275	C₄⋊C₄×C₁₇	—	2	2	no	—
276	C₄⋊C₄×C₁₇	—	4	1	no	—
277	C₂²⋊C₄×C₁₇	—	2	2	no	—
278	C₂²⋊C₄×C₁₇	—	4	1	no	—
279	C₄²×C₁₇	—	2	2	no	—
280	C₄²×C₁₇	—	4	1	no	—
281	#20995	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
282	C₂³×C₁₇	—	2	2	no	—
283	C₂³×C₁₇	—	2	2	no	—
284	C₂³×C₁₇	—	2	2	no	—
285	C₂³×C₁₇	—	2	2	no	—
286	C₂³×C₁₇	—	4	1	no	—
287	C₂³×C₁₇	—	4	1	no	—
288	C₂³×C₁₇	—	8	1	no	—
289	C₂³×C₁₇	—	8	2	no	—
290	C₂³×C₁₇	—	8	2	no	—
291	C₂³×C₁₇	C₄×D₄	1	1	yes	characteristic
292	C₂³×C₁₇	C₄×D₄	1	1	yes	characteristic
293	C₂³×C₁₇	#121	1	1	yes	characteristic
294	C₂³×C₁₇	#121	1	1	yes	characteristic
295	C₂³×C₁₇	#123	1	1	yes	characteristic
296	C₂³×C₁₇	#123	1	1	yes	characteristic
297	C₂³×C₁₇	C₂×#41	1	1	yes	characteristic
298	Q₈×C₁₇	—	2	2	no	—
299	Q₈×C₁₇	—	2	2	no	—
300	Q₈×C₁₇	—	2	2	no	—
301	Q₈×C₁₇	—	2	2	no	—
302	Q₈×C₁₇	—	2	2	no	—
303	Q₈×C₁₇	—	4	1	no	—
304	Q₈×C₁₇	—	4	1	no	—
305	Q₈×C₁₇	C₂×C₂²⋊C₄	1	4	yes	—
306	D₄×C₁₇	—	2	4	no	—
307	D₄×C₁₇	—	2	4	no	—
308	D₄×C₁₇	—	2	4	no	—
309	D₄×C₁₇	—	2	4	no	—
310	D₄×C₁₇	—	2	2	no	—
311	D₄×C₁₇	—	2	2	no	—
312	D₄×C₁₇	—	2	2	no	—
313	D₄×C₁₇	—	2	2	no	—
314	D₄×C₁₇	—	2	2	no	—
315	D₄×C₁₇	—	4	2	no	—
316	D₄×C₁₇	—	4	2	no	—
317	D₄×C₁₇	—	4	2	no	—
318	D₄×C₁₇	—	4	2	no	—
319	D₄×C₁₇	—	4	1	no	—
320	D₄×C₁₇	—	4	1	no	—
321	D₄×C₁₇	C₂×C₂²⋊C₄	1	4	yes	—
322	C₂×C₄×C₁₇	—	2	2	no	—
323	C₂×C₄×C₁₇	—	2	2	no	—
324	C₂×C₄×C₁₇	—	2	2	no	—
325	C₂×C₄×C₁₇	—	2	4	no	—
326	C₂×C₄×C₁₇	—	2	4	no	—
327	C₂×C₄×C₁₇	—	2	4	no	—
328	C₂×C₄×C₁₇	—	2	4	no	—
329	C₂×C₄×C₁₇	—	2	2	no	—
330	C₂×C₄×C₁₇	—	4	1	no	—
331	C₂×C₄×C₁₇	—	4	1	no	—
332	C₂×C₄×C₁₇	—	4	2	no	—
333	C₂×C₄×C₁₇	—	4	2	no	—
334	C₂×C₄×C₁₇	—	4	2	no	—
335	C₂×C₄×C₁₇	—	4	2	no	—
336	C₂×C₄×C₁₇	—	4	2	no	—
337	C₂×C₄×C₁₇	—	8	2	no	—
338	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
339	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
340	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
341	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
342	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
343	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
344	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
345	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
346	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
347	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
348	C₂×C₄×C₁₇	#120	1	1	yes	characteristic
349	C₂×C₄×C₁₇	#120	1	1	yes	characteristic
350	C₂×C₄×C₁₇	#120	1	1	yes	characteristic
351	C₂×C₄×C₁₇	#120	1	1	yes	characteristic
352	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
353	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
354	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
355	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
356	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
357	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
358	C₂×C₄×C₁₇	#123	1	1	yes	characteristic
359	C₂×C₄×C₁₇	#123	1	1	yes	characteristic
360	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
361	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
362	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
363	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
364	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
365	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
366	C₈×C₁₇	—	2	4	no	—
367	C₈×C₁₇	—	2	4	no	—
368	C₈×C₁₇	—	2	4	no	—
369	C₈×C₁₇	—	4	2	no	—
370	C₂×#575	C₂×C₁₇	1	1	yes	characteristic
371	C₂×#568	C₂×C₁₇	1	1	yes	characteristic, complemented
372	C₂×#421	C₂×C₁₇	1	1	yes	characteristic, complemented
373	#2896	C₂×C₁₇	1	1	yes	characteristic, complemented
374	C₂×#413	C₂×C₁₇	1	1	yes	characteristic, complemented
375	#1903	C₂×C₁₇	1	4	yes	complemented
376	#1902	C₂×C₁₇	1	4	yes	complemented
377	C₂×#344	C₂×C₁₇	1	1	yes	characteristic, complemented
378	C₂×#338	C₂×C₁₇	1	1	yes	characteristic, complemented
379	C₂²×C₁₇	—	2	4	no	—
380	C₂²×C₁₇	—	4	1	no	—
381	C₂²×C₁₇	—	4	1	no	—
382	C₂²×C₁₇	—	4	1	no	—
383	C₂²×C₁₇	—	4	1	no	—
384	C₂²×C₁₇	—	4	1	no	—
385	C₂²×C₁₇	—	4	1	no	—
386	C₂²×C₁₇	—	4	1	no	—
387	C₂²×C₁₇	—	4	4	no	—
388	C₂²×C₁₇	—	4	2	no	—
389	C₂²×C₁₇	—	8	2	no	—
390	C₂²×C₁₇	—	8	2	no	—
391	C₂²×C₁₇	—	8	2	no	—
392	C₂²×C₁₇	—	8	2	no	—
393	C₂²×C₁₇	—	8	2	no	—
394	C₂²×C₁₇	#386	1	1	yes	characteristic
395	C₂²×C₁₇	#386	1	1	yes	characteristic
396	C₂²×C₁₇	#386	1	1	yes	characteristic
397	C₂²×C₁₇	#386	1	1	yes	characteristic
398	C₂²×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
399	C₂²×C₁₇	C₂×#121	1	1	yes	characteristic
400	C₂²×C₁₇	C₂×#123	1	1	yes	characteristic
401	C₄×C₁₇	—	2	4	no	—
402	C₄×C₁₇	—	4	2	no	—
403	C₄×C₁₇	—	8	2	no	—
404	C₄×C₁₇	#386	1	1	yes	characteristic
405	C₄×C₁₇	#386	1	1	yes	characteristic
406	C₄×C₁₇	#386	1	1	yes	characteristic
407	C₄×C₁₇	#386	1	1	yes	characteristic
408	C₄×C₁₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
409	C₄×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
410	C₄×C₁₇	C₂×#120	1	1	yes	characteristic
411	C₄×C₁₇	C₂×#121	1	1	yes	characteristic
412	C₂²×#41	C₂²×C₁₇	1	1	yes	characteristic
413	C₂²×#41	C₂²×C₁₇	1	1	yes	characteristic
414	#575	—	2	2	no	—
415	#575	—	2	2	no	—
416	#575	—	2	2	no	—
417	#575	—	2	2	no	—
418	C₂×#137	C₄×C₁₇	1	2	yes	complemented
419	C₂×#137	C₂²×C₁₇	1	2	yes	—
420	C₂×AGL(1,ℤ/8)	C₄×C₁₇	1	2	yes	complemented
421	C₂×AGL(1,ℤ/8)	C₂²×C₁₇	1	2	yes	—
422	C₂×#135	C₄×C₁₇	1	4	yes	complemented
423	#568	—	2	2	no	—
424	#568	—	2	2	no	—
425	#568	—	2	2	no	—
426	#568	C₂²×C₁₇	1	4	yes	—
427	C₂×#131	—	2	2	no	—
428	C₂×#131	—	2	2	no	—
429	C₂²×M₁₆	—	2	2	no	—
430	C₂²×M₁₆	C₂²×C₁₇	1	1	yes	characteristic
431	C₂²×M₁₆	C₂²×C₁₇	1	1	yes	characteristic
432	C₂²×M₁₆	C₂²×C₁₇	1	1	yes	characteristic
433	C₂²×M₁₆	C₂²×C₁₇	1	1	yes	characteristic
434	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
435	#421	—	2	2	no	—
436	#421	C₂²×C₁₇	1	4	yes	—
437	C₂×#104	—	2	2	no	—
438	#419	C₂²×C₁₇	1	2	yes	complemented
439	#418	C₂²×C₁₇	1	2	yes	complemented
440	#417	—	2	2	no	—
441	#416	—	2	2	no	—
442	#413	—	2	2	no	—
443	#413	—	2	2	no	—
444	C₂×#101	C₂²×C₁₇	1	2	yes	complemented
445	C₂×#100	C₂²×C₁₇	1	2	yes	complemented
446	#344	C₂²×C₁₇	1	4	yes	complemented
447	#338	C₂²×C₁₇	1	4	yes	complemented
448	C₂×C₁₇	—	2	1	no	—
449	C₂×C₁₇	—	2	1	no	—
450	C₂×C₁₇	—	2	1	no	—
451	C₂×C₁₇	—	2	1	no	—
452	C₂×C₁₇	—	2	1	no	—
453	C₂×C₁₇	—	2	1	no	—
454	C₂×C₁₇	—	2	1	no	—
455	C₂×C₁₇	—	4	4	no	—
456	C₂×C₁₇	—	8	2	no	—
457	C₂×C₁₇	C₂×#386	1	1	yes	characteristic
458	C₂×#41	—	2	1	no	—
459	C₂×#41	—	2	1	no	—
460	C₂×#41	—	2	1	no	—
461	C₂×#41	—	2	1	no	—
462	C₂×#41	—	2	1	no	—
463	C₂×#41	—	2	1	no	—
464	C₂×#41	—	2	1	no	—
465	C₂×#41	—	2	1	no	—
466	C₂×#41	—	2	1	no	—
467	C₂×#41	—	2	1	no	—
468	C₂×#41	—	2	1	no	—
469	C₂×#41	—	2	1	no	—
470	C₂×#41	—	2	1	no	—
471	C₂×#41	—	2	1	no	—
472	C₂×#41	—	2	1	no	—
473	C₂×#41	—	2	1	no	—
474	C₂×#41	C₂×C₄×C₁₇	1	2	yes	—
475	C₂×#41	C₂×C₄×C₁₇	1	2	yes	—
476	C₂×#41	C₂×C₄×C₁₇	1	2	yes	—
477	C₂×#41	D₄×C₁₇	1	2	yes	—
478	C₂×#41	D₄×C₁₇	1	2	yes	—
479	C₂×#41	D₄×C₁₇	1	2	yes	—
480	C₂×#41	D₄×C₁₇	1	2	yes	—
481	C₂×#41	C₂³×C₁₇	1	2	yes	—
482	C₂²×Q₈	C₂×C₄×C₁₇	1	1	yes	characteristic
483	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
484	C₂²×D₄	—	2	1	no	—
485	C₂²×D₄	—	2	1	no	—
486	C₂²×D₄	C₂×C₄×C₁₇	1	1	yes	characteristic
487	C₂²×D₄	C₂³×C₁₇	1	1	yes	characteristic
488	C₂³×C₄	—	2	1	no	—
489	C₂³×C₄	—	2	1	no	—
490	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
491	#137	—	2	4	no	—
492	#137	—	2	4	no	—
493	#137	—	2	4	no	—
494	#137	—	2	4	no	—
495	AGL(1,ℤ/8)	—	2	4	no	—
496	AGL(1,ℤ/8)	—	2	4	no	—
497	AGL(1,ℤ/8)	—	2	4	no	—
498	AGL(1,ℤ/8)	—	2	4	no	—
499	#135	—	2	8	no	—
500	#135	—	2	8	no	—
501	C₂×Q₁₆	C₂×C₄×C₁₇	1	4	yes	complemented
502	C₂×SD₁₆	C₂×C₄×C₁₇	1	4	yes	complemented
503	C₂×SD₁₆	C₂×C₄×C₁₇	1	4	yes	complemented
504	C₂×D₈	C₂×C₄×C₁₇	1	4	yes	complemented
505	#131	—	2	8	no	—
506	#131	—	2	8	no	—
507	#131	—	2	8	no	—
508	#131	—	2	8	no	—
509	C₂×M₁₆	—	2	4	no	—
510	C₂×M₁₆	—	2	8	no	—
511	C₂×M₁₆	—	2	1	no	—
512	C₂×M₁₆	—	2	1	no	—
513	C₂×M₁₆	—	2	1	no	—
514	C₂×M₁₆	—	2	1	no	—
515	C₂×M₁₆	—	2	1	no	—
516	C₂×M₁₆	—	2	1	no	—
517	C₂×M₁₆	—	2	1	no	—
518	C₂×M₁₆	—	2	1	no	—
519	C₂×M₁₆	—	2	1	no	—
520	C₂×M₁₆	—	2	1	no	—
521	C₂×M₁₆	—	2	1	no	—
522	C₂×M₁₆	—	2	8	no	—
523	C₂×M₁₆	—	2	1	no	—
524	C₂×M₁₆	—	2	1	no	—
525	C₂×M₁₆	—	2	1	no	—
526	C₂×M₁₆	—	2	1	no	—
527	C₂×M₁₆	—	2	1	no	—
528	C₂×M₁₆	C₂×C₄×C₁₇	1	2	yes	—
529	C₂×M₁₆	D₄×C₁₇	1	2	yes	—
530	C₂×M₁₆	D₄×C₁₇	1	2	yes	—
531	C₂×M₁₆	D₄×C₁₇	1	2	yes	—
532	C₂×M₁₆	C₂³×C₁₇	1	2	yes	—
533	C₂×M₁₆	C₂³×C₁₇	1	2	yes	—
534	C₂×M₁₆	C₂³×C₁₇	1	2	yes	—
535	C₂×M₁₆	C₂³×C₁₇	1	2	yes	—
536	C₂²×C₈	—	2	4	no	—
537	C₂²×C₈	—	2	1	no	—
538	C₂²×C₈	—	2	1	no	—
539	C₂²×C₈	C₂×C₄×C₁₇	1	2	yes	—
540	C₂²×C₈	D₄×C₁₇	1	2	yes	—
541	#117	—	2	1	no	—
542	#117	—	2	1	no	—
543	#117	—	2	1	no	—
544	#117	C₂³×C₁₇	1	2	yes	—
545	C₂×C₄⋊C₄	—	2	1	no	—
546	C₂×C₂²⋊C₄	—	2	1	no	—
547	C₂×C₄²	—	2	1	no	—
548	#104	—	2	8	no	—
549	#103	—	2	4	no	—
550	#102	—	2	4	no	—
551	#101	—	2	4	no	—
552	#100	—	2	4	no	—
553	C₁₇	#20995	1	1	yes	characteristic, direct product factor, Sylow
554	C₂⁴	—	2	1	no	—
555	C₂⁴	—	2	1	no	—
556	C₂⁴	#41×C₁₇	1	1	yes	characteristic
557	#41	—	2	2	no	—
558	#41	—	2	2	no	—
559	#41	—	2	2	no	—
560	#41	—	2	2	no	—
561	#41	—	2	2	no	—
562	#41	—	2	2	no	—
563	#41	—	2	2	no	—
564	#41	—	2	2	no	—
565	#41	—	2	2	no	—
566	#41	—	2	2	no	—
567	#41	—	2	2	no	—
568	#41	—	2	2	no	—
569	#41	—	2	2	no	—
570	#41	—	2	2	no	—
571	#41	—	2	2	no	—
572	#41	—	2	2	no	—
573	#41	—	2	2	no	—
574	#41	—	2	2	no	—
575	#41	—	2	2	no	—
576	#41	—	2	2	no	—
577	#41	—	4	1	no	—
578	#41	—	4	1	no	—
579	#41	—	4	1	no	—
580	#41	—	4	1	no	—
581	#41	—	4	1	no	—
582	#41	—	4	1	no	—
583	#41	—	4	1	no	—
584	#41	—	4	1	no	—
585	#41	C₂²⋊C₄×C₁₇	1	4	yes	—
586	#41	C₂²⋊C₄×C₁₇	1	4	yes	—
587	#41	C₂×D₄×C₁₇	1	4	yes	—
588	#41	C₂×D₄×C₁₇	1	4	yes	—
589	C₂×Q₈	—	2	1	no	—
590	C₂×Q₈	—	2	1	no	—
591	C₂×Q₈	—	2	1	no	—
592	C₂×Q₈	—	2	1	no	—
593	C₂×Q₈	—	2	1	no	—
594	C₂×Q₈	—	2	1	no	—
595	C₂×Q₈	—	2	1	no	—
596	C₂×Q₈	—	2	1	no	—
597	C₂×Q₈	C₂²⋊C₄×C₁₇	1	2	yes	—
598	C₂×Q₈	C₂²⋊C₄×C₁₇	1	2	yes	—
599	C₂×Q₈	C₂²×C₄×C₁₇	1	2	yes	—
600	C₂×Q₈	C₂²×C₄×C₁₇	1	2	yes	—
601	C₂×D₄	—	2	2	no	—
602	C₂×D₄	—	2	2	no	—
603	C₂×D₄	—	2	2	no	—
604	C₂×D₄	—	2	2	no	—
605	C₂×D₄	—	2	2	no	—
606	C₂×D₄	—	2	2	no	—
607	C₂×D₄	—	2	2	no	—
608	C₂×D₄	—	2	2	no	—
609	C₂×D₄	—	2	1	no	—
610	C₂×D₄	—	2	1	no	—
611	C₂×D₄	—	2	1	no	—
612	C₂×D₄	—	2	1	no	—
613	C₂×D₄	—	2	1	no	—
614	C₂×D₄	—	2	1	no	—
615	C₂×D₄	—	2	1	no	—
616	C₂×D₄	—	2	1	no	—
617	C₂×D₄	—	4	1	no	—
618	C₂×D₄	—	4	1	no	—
619	C₂×D₄	—	4	1	no	—
620	C₂×D₄	—	4	1	no	—
621	C₂×D₄	C₂²⋊C₄×C₁₇	1	2	yes	—
622	C₂×D₄	C₂²⋊C₄×C₁₇	1	2	yes	—
623	C₂×D₄	C₂²×C₄×C₁₇	1	2	yes	—
624	C₂×D₄	C₂²×C₄×C₁₇	1	2	yes	—
625	C₂²×C₄	—	2	1	no	—
626	C₂²×C₄	—	2	2	no	—
627	C₂²×C₄	—	2	2	no	—
628	C₂²×C₄	—	2	2	no	—
629	C₂²×C₄	—	2	2	no	—
630	C₂²×C₄	—	2	2	no	—
631	C₂²×C₄	—	2	2	no	—
632	C₂²×C₄	—	2	1	no	—
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	4	1	no	—
636	C₂²×C₄	—	4	1	no	—
637	C₂²×C₄	—	4	1	no	—
638	C₂²×C₄	—	4	1	no	—
639	C₂²×C₄	—	4	1	no	—
640	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
641	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
642	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
643	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
644	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
645	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
646	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
647	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
648	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
649	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
650	C₂²×C₄	#41×C₁₇	1	1	yes	characteristic
651	C₂²×C₄	#41×C₁₇	1	1	yes	characteristic
652	C₂²×C₄	#41×C₁₇	1	1	yes	characteristic
653	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
654	Q₁₆	—	2	8	no	—
655	SD₁₆	—	2	8	no	—
656	SD₁₆	—	2	8	no	—
657	D₈	—	2	8	no	—
658	M₁₆	—	2	16	no	—
659	M₁₆	—	2	2	no	—
660	M₁₆	—	2	2	no	—
661	M₁₆	—	2	2	no	—
662	M₁₆	—	2	2	no	—
663	M₁₆	—	2	2	no	—
664	M₁₆	—	2	2	no	—
665	M₁₆	—	2	2	no	—
666	M₁₆	—	2	2	no	—
667	M₁₆	—	2	2	no	—
668	M₁₆	—	2	2	no	—
669	M₁₆	—	2	2	no	—
670	M₁₆	—	2	2	no	—
671	M₁₆	—	2	2	no	—
672	M₁₆	—	4	1	no	—
673	M₁₆	—	4	1	no	—
674	M₁₆	C₂×D₄×C₁₇	1	4	yes	—
675	C₂×C₈	—	2	16	no	—
676	C₂×C₈	—	2	2	no	—
677	C₂×C₈	—	2	2	no	—
678	C₂×C₈	—	2	2	no	—
679	C₂×C₈	—	2	2	no	—
680	C₂×C₈	—	2	2	no	—
681	C₂×C₈	—	2	2	no	—
682	C₂×C₈	—	2	2	no	—
683	C₂×C₈	—	2	2	no	—
684	C₂×C₈	—	4	1	no	—
685	C₂×C₈	—	4	1	no	—
686	C₂×C₈	C₂²×C₄×C₁₇	1	4	yes	—
687	C₂×C₈	C₂×D₄×C₁₇	1	4	yes	—
688	C₄⋊C₄	—	2	2	no	—
689	C₄⋊C₄	—	4	1	no	—
690	C₂²⋊C₄	—	2	2	no	—
691	C₂²⋊C₄	—	4	1	no	—
692	C₄²	—	2	2	no	—
693	C₄²	—	4	1	no	—
694	C₂³	—	2	2	no	—
695	C₂³	—	2	2	no	—
696	C₂³	—	2	2	no	—
697	C₂³	—	2	2	no	—
698	C₂³	—	4	1	no	—
699	C₂³	—	4	1	no	—
700	C₂³	—	8	1	no	—
701	C₂³	—	8	2	no	—
702	C₂³	—	8	2	no	—
703	C₂³	C₄×D₄×C₁₇	1	1	yes	characteristic
704	C₂³	C₄×D₄×C₁₇	1	1	yes	characteristic
705	C₂³	C₁₇×#121	1	1	yes	characteristic
706	C₂³	C₁₇×#121	1	1	yes	characteristic
707	C₂³	C₁₇×#123	1	1	yes	characteristic
708	C₂³	C₁₇×#123	1	1	yes	characteristic
709	C₂³	C₂×#41×C₁₇	1	1	yes	characteristic
710	Q₈	—	2	2	no	—
711	Q₈	—	2	2	no	—
712	Q₈	—	2	2	no	—
713	Q₈	—	2	2	no	—
714	Q₈	—	2	2	no	—
715	Q₈	—	4	1	no	—
716	Q₈	—	4	1	no	—
717	Q₈	C₂×C₂²⋊C₄×C₁₇	1	4	yes	—
718	D₄	—	2	4	no	—
719	D₄	—	2	4	no	—
720	D₄	—	2	4	no	—
721	D₄	—	2	4	no	—
722	D₄	—	2	2	no	—
723	D₄	—	2	2	no	—
724	D₄	—	2	2	no	—
725	D₄	—	2	2	no	—
726	D₄	—	2	2	no	—
727	D₄	—	4	2	no	—
728	D₄	—	4	2	no	—
729	D₄	—	4	2	no	—
730	D₄	—	4	2	no	—
731	D₄	—	4	1	no	—
732	D₄	—	4	1	no	—
733	D₄	C₂×C₂²⋊C₄×C₁₇	1	4	yes	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	4	no	—
738	C₂×C₄	—	2	4	no	—
739	C₂×C₄	—	2	4	no	—
740	C₂×C₄	—	2	4	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	4	1	no	—
743	C₂×C₄	—	4	1	no	—
744	C₂×C₄	—	4	2	no	—
745	C₂×C₄	—	4	2	no	—
746	C₂×C₄	—	4	2	no	—
747	C₂×C₄	—	4	2	no	—
748	C₂×C₄	—	4	2	no	—
749	C₂×C₄	—	8	2	no	—
750	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
751	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
752	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
753	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
754	C₂×C₄	C₄×D₄×C₁₇	1	1	yes	characteristic
755	C₂×C₄	C₄×D₄×C₁₇	1	1	yes	characteristic
756	C₂×C₄	C₄×D₄×C₁₇	1	1	yes	characteristic
757	C₂×C₄	C₄×D₄×C₁₇	1	1	yes	characteristic
758	C₂×C₄	C₄×D₄×C₁₇	1	1	yes	characteristic
759	C₂×C₄	C₄×D₄×C₁₇	1	1	yes	characteristic
760	C₂×C₄	C₁₇×#120	1	1	yes	characteristic
761	C₂×C₄	C₁₇×#120	1	1	yes	characteristic
762	C₂×C₄	C₁₇×#120	1	1	yes	characteristic
763	C₂×C₄	C₁₇×#120	1	1	yes	characteristic
764	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
765	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
766	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
767	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
768	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
769	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
770	C₂×C₄	C₁₇×#123	1	1	yes	characteristic
771	C₂×C₄	C₁₇×#123	1	1	yes	characteristic
772	C₂×C₄	C₂³×C₄×C₁₇	1	1	yes	characteristic
773	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
774	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
775	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
776	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
777	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
778	C₈	—	2	4	no	—
779	C₈	—	2	4	no	—
780	C₈	—	2	4	no	—
781	C₈	—	4	2	no	—
782	C₂²	—	2	4	no	—
783	C₂²	—	4	1	no	—
784	C₂²	—	4	1	no	—
785	C₂²	—	4	1	no	—
786	C₂²	—	4	1	no	—
787	C₂²	—	4	1	no	—
788	C₂²	—	4	1	no	—
789	C₂²	—	4	1	no	—
790	C₂²	—	4	4	no	—
791	C₂²	—	4	2	no	—
792	C₂²	—	8	2	no	—
793	C₂²	—	8	2	no	—
794	C₂²	—	8	2	no	—
795	C₂²	—	8	2	no	—
796	C₂²	—	8	2	no	—
797	C₂²	C₁₇×#386	1	1	yes	characteristic
798	C₂²	C₁₇×#386	1	1	yes	characteristic
799	C₂²	C₁₇×#386	1	1	yes	characteristic
800	C₂²	C₁₇×#386	1	1	yes	characteristic
801	C₂²	C₂×C₄×D₄×C₁₇	1	1	yes	characteristic
802	C₂²	C₂×C₁₇×#121	1	1	yes	characteristic
803	C₂²	C₂×C₁₇×#123	1	1	yes	characteristic
804	C₄	—	2	4	no	—
805	C₄	—	4	2	no	—
806	C₄	—	8	2	no	—
807	C₄	C₁₇×#386	1	1	yes	characteristic
808	C₄	C₁₇×#386	1	1	yes	characteristic
809	C₄	C₁₇×#386	1	1	yes	characteristic
810	C₄	C₁₇×#386	1	1	yes	characteristic
811	C₄	C₂²×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
812	C₄	C₂×C₄×D₄×C₁₇	1	1	yes	characteristic
813	C₄	C₂×C₁₇×#120	1	1	yes	characteristic
814	C₄	C₂×C₁₇×#121	1	1	yes	characteristic
815	C₂	—	2	1	no	—
816	C₂	—	2	1	no	—
817	C₂	—	2	1	no	—
818	C₂	—	2	1	no	—
819	C₂	—	2	1	no	—
820	C₂	—	2	1	no	—
821	C₂	—	2	1	no	—
822	C₂	—	4	4	no	—
823	C₂	—	8	2	no	—
824	C₂	C₂×C₁₇×#386	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₇	#386
commutator	C₂×C₄	C₂³×C₄×C₁₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₇
socle	C₂×C₁₇	C₂×#386
prime radical	C₂×C₁₇×#575	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂³×C₄×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₇×#568	C₂	semidirect
3. C₂×C₁₇×#421	C₂	semidirect
4. C₁₇×#2896	C₂	semidirect
5. C₂×C₁₇×#413	C₂	semidirect
6. C₁₇×#1903	C₂	semidirect
7. C₁₇×#1902	C₂	semidirect
8. C₂×C₁₇×#344	C₂	semidirect
9. C₂×C₁₇×#338	C₂	semidirect
16. C₂×C₁₇×#137	C₄	semidirect
18. C₂×C₁₇×AGL(1,ℤ/8)	C₄	semidirect
20. C₂×C₁₇×#135	C₄	semidirect
36. C₁₇×#419	C₂²	semidirect
37. C₁₇×#418	C₂²	semidirect
42. C₂×C₁₇×#101	C₂²	semidirect
43. C₂×C₁₇×#100	C₂²	semidirect
44. C₁₇×#344	C₂²	semidirect
45. C₁₇×#338	C₂²	semidirect
89. C₂×Q₁₆×C₁₇	C₂×C₄	semidirect
90. C₂×SD₁₆×C₁₇	C₂×C₄	semidirect
91. C₂×SD₁₆×C₁₇	C₂×C₄	semidirect
92. C₂×D₈×C₁₇	C₂×C₄	semidirect
281. #20995	C₁₇	direct (N × H)
371. C₂×#568	C₂×C₁₇	semidirect
372. C₂×#421	C₂×C₁₇	semidirect
373. #2896	C₂×C₁₇	semidirect
374. C₂×#413	C₂×C₁₇	semidirect
375. #1903	C₂×C₁₇	semidirect
376. #1902	C₂×C₁₇	semidirect
377. C₂×#344	C₂×C₁₇	semidirect
378. C₂×#338	C₂×C₁₇	semidirect
418. C₂×#137	C₄×C₁₇	semidirect
420. C₂×AGL(1,ℤ/8)	C₄×C₁₇	semidirect
422. C₂×#135	C₄×C₁₇	semidirect
438. #419	C₂²×C₁₇	semidirect
439. #418	C₂²×C₁₇	semidirect
444. C₂×#101	C₂²×C₁₇	semidirect
445. C₂×#100	C₂²×C₁₇	semidirect
446. #344	C₂²×C₁₇	semidirect
447. #338	C₂²×C₁₇	semidirect
501. C₂×Q₁₆	C₂×C₄×C₁₇	semidirect
502. C₂×SD₁₆	C₂×C₄×C₁₇	semidirect
503. C₂×SD₁₆	C₂×C₄×C₁₇	semidirect
504. C₂×D₈	C₂×C₄×C₁₇	semidirect
553. C₁₇	#20995	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×#575	2
C₂×C₁₇×#568	2
C₂×C₁₇×#421	2
C₁₇×#2896	2
C₂×C₁₇×#413	2
C₁₇×#1903	2
C₁₇×#1902	2
C₂×C₁₇×#344	2
C₂×C₁₇×#338	2
#20995	17

Subgroups — C17×#20995 #16878739

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#20995 #16878739