Subgroups — C₁₇×#24403 #16882147

Order 4352.

1332 conjugacy classes of subgroups.

The subgroup lattice has 948 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×#473	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₇×#471	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#3007	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₇×#452	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#2880	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#2052	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₇×#2051	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#2020	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#2019	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#1908	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#1907	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₇×#1901	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₇×#1855	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#1785	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₁₇	C₂²	1	1	yes	characteristic
17	C₂²×#41×C₁₇	C₂²	1	1	yes	characteristic
18	C₁₇×#575	—	2	4	no	—
19	C₁₇×#575	—	2	4	no	—
20	C₂×C₁₇×#137	—	2	1	no	—
21	C₂×C₁₇×#137	C₂²	1	1	yes	characteristic
22	C₂×C₁₇×#137	C₂²	1	1	yes	characteristic
23	C₂×C₁₇×#137	C₂²	1	1	yes	characteristic
24	C₂×C₁₇×#137	C₂²	1	1	yes	characteristic
25	C₂×C₁₇×AGL(1,ℤ/8)	—	2	1	no	—
26	C₂×C₁₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
27	C₂×C₁₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
28	C₂×C₁₇×#135	—	2	1	no	—
29	C₂×C₁₇×#135	—	2	1	no	—
30	C₂²×Q₁₆×C₁₇	C₂²	1	1	yes	characteristic, complemented
31	C₂²×SD₁₆×C₁₇	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₁₇×#131	C₂²	1	1	yes	characteristic
33	C₂×C₁₇×#131	C₂²	1	1	yes	characteristic
34	C₂²×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
35	C₂×C₁₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
36	C₁₇×#473	—	2	4	no	—
37	C₁₇×#471	—	2	4	no	—
38	C₁₇×#452	—	2	1	no	—
39	C₁₇×#452	—	2	1	no	—
40	C₁₇×#452	—	2	1	no	—
41	C₁₇×#452	—	2	1	no	—
42	C₁₇×#452	—	2	1	no	—
43	C₁₇×#452	—	2	1	no	—
44	C₁₇×#451	—	2	1	no	—
45	C₁₇×#450	—	2	1	no	—
46	C₂×C₁₇×#108	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₁₇×#108	C₂²	1	1	yes	characteristic, complemented
48	C₁₇×#417	C₂²	1	1	yes	characteristic
49	C₁₇×#417	C₂²	1	1	yes	characteristic
50	C₂×C₁₇×#103	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₁₇×#102	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₁₇×#101	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₁₇×#101	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₁₇×#101	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₁₇×#101	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₁₇×#100	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₁₇×#100	C₂²	1	1	yes	characteristic, complemented
58	C₁₇×#408	—	2	1	no	—
59	C₁₇×#408	—	2	1	no	—
60	C₁₇×#408	C₂²	1	1	yes	characteristic
61	C₁₇×#408	C₂²	1	1	yes	characteristic
62	C₁₇×#407	—	2	1	no	—
63	C₁₇×#407	C₂²	1	1	yes	characteristic
64	C₁₇×#407	C₂²	1	1	yes	characteristic
65	C₂×C₁₇×C₂²⋊C₈	—	2	1	no	—
66	C₂×C₁₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
67	C₁₇×#343	C₂²	1	1	yes	characteristic, complemented
68	C₁₇×#343	C₂²	1	1	yes	characteristic, complemented
69	C₁₇×#341	C₂²	1	1	yes	characteristic, complemented
70	C₁₇×#341	C₂²	1	1	yes	characteristic, complemented
71	C₂×#41×C₁₇	—	2	1	no	—
72	C₂×#41×C₁₇	—	2	1	no	—
73	C₂×#41×C₁₇	—	2	2	no	—
74	C₂×#41×C₁₇	—	2	2	no	—
75	C₂×#41×C₁₇	—	2	2	no	—
76	C₂×#41×C₁₇	—	2	2	no	—
77	C₂×#41×C₁₇	—	2	1	no	—
78	C₂×#41×C₁₇	—	2	1	no	—
79	C₂×#41×C₁₇	—	2	1	no	—
80	C₂×#41×C₁₇	—	2	1	no	—
81	C₂×#41×C₁₇	—	4	1	no	—
82	C₂×#41×C₁₇	—	4	1	no	—
83	C₂×#41×C₁₇	—	4	1	no	—
84	C₂×#41×C₁₇	—	4	1	no	—
85	C₂×#41×C₁₇	D₄	1	1	yes	characteristic
86	C₂×#41×C₁₇	D₄	1	1	yes	characteristic
87	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
88	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
89	C₂²×Q₈×C₁₇	D₄	1	1	yes	characteristic
90	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
91	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
92	C₂²×D₄×C₁₇	—	2	1	no	—
93	C₂²×D₄×C₁₇	—	2	1	no	—
94	C₂²×D₄×C₁₇	D₄	1	1	yes	characteristic
95	C₂²×D₄×C₁₇	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₁₇	—	2	1	no	—
97	C₂³×C₄×C₁₇	—	2	1	no	—
98	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
99	C₁₇×#137	—	2	8	no	—
100	C₁₇×#137	—	2	2	no	—
101	C₁₇×#137	—	2	2	no	—
102	C₁₇×#137	—	2	2	no	—
103	C₁₇×#137	—	2	2	no	—
104	C₁₇×#137	—	2	2	no	—
105	C₁₇×#137	—	4	1	no	—
106	C₁₇×#137	—	4	1	no	—
107	C₁₇×#137	D₄	1	4	yes	—
108	C₁₇×AGL(1,ℤ/8)	—	2	8	no	—
109	C₁₇×AGL(1,ℤ/8)	—	2	2	no	—
110	C₁₇×AGL(1,ℤ/8)	—	2	2	no	—
111	C₁₇×AGL(1,ℤ/8)	—	2	2	no	—
112	C₁₇×AGL(1,ℤ/8)	D₄	1	4	yes	—
113	C₁₇×#135	—	2	8	no	—
114	C₁₇×#135	—	2	8	no	—
115	C₂×Q₁₆×C₁₇	—	2	1	no	—
116	C₂×Q₁₆×C₁₇	—	2	1	no	—
117	C₂×Q₁₆×C₁₇	—	2	2	no	—
118	C₂×Q₁₆×C₁₇	—	2	1	no	—
119	C₂×Q₁₆×C₁₇	—	2	1	no	—
120	C₂×Q₁₆×C₁₇	—	2	1	no	—
121	C₂×Q₁₆×C₁₇	—	2	1	no	—
122	C₂×Q₁₆×C₁₇	—	4	1	no	—
123	C₂×SD₁₆×C₁₇	—	2	1	no	—
124	C₂×SD₁₆×C₁₇	—	2	1	no	—
125	C₂×SD₁₆×C₁₇	—	2	1	no	—
126	C₂×SD₁₆×C₁₇	—	2	1	no	—
127	C₂×SD₁₆×C₁₇	—	2	2	no	—
128	C₂×SD₁₆×C₁₇	—	2	1	no	—
129	C₂×SD₁₆×C₁₇	—	2	1	no	—
130	C₂×SD₁₆×C₁₇	—	2	1	no	—
131	C₂×SD₁₆×C₁₇	—	2	1	no	—
132	C₂×SD₁₆×C₁₇	—	4	1	no	—
133	C₂×D₈×C₁₇	—	2	1	no	—
134	C₂×D₈×C₁₇	—	2	1	no	—
135	C₁₇×#131	—	2	2	no	—
136	C₁₇×#131	—	2	2	no	—
137	C₁₇×#131	—	4	1	no	—
138	C₁₇×#131	—	4	1	no	—
139	C₂×M₁₆×C₁₇	—	2	1	no	—
140	C₂×M₁₆×C₁₇	—	2	2	no	—
141	C₂×M₁₆×C₁₇	—	2	2	no	—
142	C₂×M₁₆×C₁₇	—	2	1	no	—
143	C₂×M₁₆×C₁₇	—	2	1	no	—
144	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
145	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
146	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
147	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
148	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
149	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
150	C₂²×C₈×C₁₇	—	2	1	no	—
151	C₂²×C₈×C₁₇	—	2	1	no	—
152	C₂²×C₈×C₁₇	—	2	1	no	—
153	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
154	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
155	C₁₇×C₂²⋊Q₈	—	2	1	no	—
156	C₁₇×C₂²⋊Q₈	—	2	1	no	—
157	C₁₇×C₂²⋊Q₈	—	2	1	no	—
158	C₁₇×C₂²⋊Q₈	—	2	1	no	—
159	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
160	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
161	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
162	C₁₇×#108	—	2	2	no	—
163	C₁₇×#108	—	2	2	no	—
164	C₁₇×#103	—	2	1	no	—
165	C₁₇×#103	—	2	1	no	—
166	C₁₇×#103	—	2	1	no	—
167	C₁₇×#103	—	2	1	no	—
168	C₁₇×#102	—	2	1	no	—
169	C₁₇×#102	—	2	1	no	—
170	C₁₇×#102	—	2	1	no	—
171	C₁₇×#102	—	2	1	no	—
172	C₁₇×#101	—	2	2	no	—
173	C₁₇×#101	—	2	2	no	—
174	C₁₇×#101	—	2	2	no	—
175	C₁₇×#101	—	4	1	no	—
176	C₁₇×#100	—	2	2	no	—
177	C₁₇×#100	—	4	1	no	—
178	C₁₇×C₂²⋊C₈	—	2	1	no	—
179	C₁₇×C₂²⋊C₈	—	2	1	no	—
180	C₁₇×C₂²⋊C₈	—	2	1	no	—
181	C₁₇×C₂²⋊C₈	—	2	1	no	—
182	C₁₇×C₂²⋊C₈	—	2	1	no	—
183	C₁₇×C₂²⋊C₈	—	2	1	no	—
184	C₁₇×C₂²⋊C₈	—	2	1	no	—
185	C₁₇×C₂²⋊C₈	—	2	1	no	—
186	C₁₇×C₂²⋊C₈	D₄	1	1	yes	characteristic
187	C₁₇×C₂²⋊C₈	D₄	1	1	yes	characteristic
188	C₁₇×C₂²⋊C₈	D₄	1	1	yes	characteristic
189	C₁₇×C₂²⋊C₈	D₄	1	1	yes	characteristic
190	C₂⁴×C₁₇	—	2	1	no	—
191	C₂⁴×C₁₇	—	2	1	no	—
192	C₂⁴×C₁₇	#41	1	1	yes	characteristic
193	#41×C₁₇	—	2	1	no	—
194	#41×C₁₇	—	2	1	no	—
195	#41×C₁₇	—	2	4	no	—
196	#41×C₁₇	—	2	4	no	—
197	#41×C₁₇	—	2	2	no	—
198	#41×C₁₇	—	2	2	no	—
199	#41×C₁₇	—	2	1	no	—
200	#41×C₁₇	—	2	1	no	—
201	#41×C₁₇	—	2	1	no	—
202	#41×C₁₇	—	2	1	no	—
203	#41×C₁₇	—	4	2	no	—
204	#41×C₁₇	—	4	2	no	—
205	#41×C₁₇	—	4	1	no	—
206	#41×C₁₇	—	4	1	no	—
207	#41×C₁₇	—	4	2	no	—
208	#41×C₁₇	—	4	2	no	—
209	#41×C₁₇	—	4	2	no	—
210	#41×C₁₇	—	4	2	no	—
211	#41×C₁₇	—	4	2	no	—
212	#41×C₁₇	—	4	2	no	—
213	#41×C₁₇	—	4	2	no	—
214	#41×C₁₇	—	4	2	no	—
215	#41×C₁₇	C₂×D₄	1	2	yes	—
216	#41×C₁₇	C₂×D₄	1	2	yes	—
217	C₂×Q₈×C₁₇	—	2	1	no	—
218	C₂×Q₈×C₁₇	—	2	1	no	—
219	C₂×Q₈×C₁₇	—	2	2	no	—
220	C₂×Q₈×C₁₇	—	2	1	no	—
221	C₂×Q₈×C₁₇	—	2	1	no	—
222	C₂×Q₈×C₁₇	—	2	1	no	—
223	C₂×Q₈×C₁₇	—	2	1	no	—
224	C₂×Q₈×C₁₇	—	2	1	no	—
225	C₂×Q₈×C₁₇	—	2	1	no	—
226	C₂×Q₈×C₁₇	—	2	1	no	—
227	C₂×Q₈×C₁₇	—	2	1	no	—
228	C₂×Q₈×C₁₇	—	2	1	no	—
229	C₂×Q₈×C₁₇	—	2	1	no	—
230	C₂×Q₈×C₁₇	—	4	1	no	—
231	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
232	C₂×Q₈×C₁₇	C₂×D₄	1	2	yes	—
233	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
234	C₂×D₄×C₁₇	—	2	1	no	—
235	C₂×D₄×C₁₇	—	2	2	no	—
236	C₂×D₄×C₁₇	—	2	1	no	—
237	C₂×D₄×C₁₇	—	2	1	no	—
238	C₂×D₄×C₁₇	—	2	1	no	—
239	C₂×D₄×C₁₇	—	2	1	no	—
240	C₂×D₄×C₁₇	—	2	1	no	—
241	C₂×D₄×C₁₇	—	2	1	no	—
242	C₂×D₄×C₁₇	—	2	1	no	—
243	C₂×D₄×C₁₇	—	2	1	no	—
244	C₂×D₄×C₁₇	—	2	1	no	—
245	C₂×D₄×C₁₇	—	4	1	no	—
246	C₂×D₄×C₁₇	—	4	2	no	—
247	C₂×D₄×C₁₇	—	4	2	no	—
248	C₂×D₄×C₁₇	—	4	2	no	—
249	C₂×D₄×C₁₇	—	4	2	no	—
250	C₂×D₄×C₁₇	—	4	1	no	—
251	C₂×D₄×C₁₇	—	4	1	no	—
252	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
253	C₂×D₄×C₁₇	C₂×D₄	1	2	yes	—
254	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₁₇	—	2	1	no	—
256	C₂²×C₄×C₁₇	—	2	1	no	—
257	C₂²×C₄×C₁₇	—	2	1	no	—
258	C₂²×C₄×C₁₇	—	2	1	no	—
259	C₂²×C₄×C₁₇	—	2	1	no	—
260	C₂²×C₄×C₁₇	—	2	1	no	—
261	C₂²×C₄×C₁₇	—	2	1	no	—
262	C₂²×C₄×C₁₇	—	2	1	no	—
263	C₂²×C₄×C₁₇	—	2	1	no	—
264	C₂²×C₄×C₁₇	—	2	1	no	—
265	C₂²×C₄×C₁₇	—	2	1	no	—
266	C₂²×C₄×C₁₇	—	2	1	no	—
267	C₂²×C₄×C₁₇	—	4	2	no	—
268	C₂²×C₄×C₁₇	—	4	2	no	—
269	C₂²×C₄×C₁₇	—	4	2	no	—
270	C₂²×C₄×C₁₇	—	4	2	no	—
271	C₂²×C₄×C₁₇	—	4	1	no	—
272	C₂²×C₄×C₁₇	—	4	1	no	—
273	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
277	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
278	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
279	Q₁₆×C₁₇	—	2	4	no	—
280	Q₁₆×C₁₇	—	2	4	no	—
281	Q₁₆×C₁₇	—	4	2	no	—
282	Q₁₆×C₁₇	—	4	2	no	—
283	Q₁₆×C₁₇	—	4	2	no	—
284	Q₁₆×C₁₇	—	4	2	no	—
285	SD₁₆×C₁₇	—	2	4	no	—
286	SD₁₆×C₁₇	—	2	4	no	—
287	SD₁₆×C₁₇	—	2	4	no	—
288	SD₁₆×C₁₇	—	2	4	no	—
289	SD₁₆×C₁₇	—	4	2	no	—
290	SD₁₆×C₁₇	—	4	2	no	—
291	SD₁₆×C₁₇	—	4	2	no	—
292	SD₁₆×C₁₇	—	4	2	no	—
293	D₈×C₁₇	—	2	4	no	—
294	D₈×C₁₇	—	2	4	no	—
295	M₁₆×C₁₇	—	2	4	no	—
296	M₁₆×C₁₇	—	2	1	no	—
297	M₁₆×C₁₇	—	2	1	no	—
298	M₁₆×C₁₇	—	2	1	no	—
299	M₁₆×C₁₇	—	2	1	no	—
300	M₁₆×C₁₇	—	2	1	no	—
301	M₁₆×C₁₇	—	2	1	no	—
302	M₁₆×C₁₇	—	2	1	no	—
303	M₁₆×C₁₇	—	2	1	no	—
304	M₁₆×C₁₇	—	2	1	no	—
305	M₁₆×C₁₇	—	2	1	no	—
306	M₁₆×C₁₇	—	4	2	no	—
307	M₁₆×C₁₇	—	4	2	no	—
308	M₁₆×C₁₇	C₂×D₄	1	2	yes	—
309	M₁₆×C₁₇	C₂×D₄	1	2	yes	—
310	C₂×C₈×C₁₇	—	2	4	no	—
311	C₂×C₈×C₁₇	—	2	1	no	—
312	C₂×C₈×C₁₇	—	2	1	no	—
313	C₂×C₈×C₁₇	—	2	1	no	—
314	C₂×C₈×C₁₇	—	2	1	no	—
315	C₂×C₈×C₁₇	—	2	1	no	—
316	C₂×C₈×C₁₇	—	2	1	no	—
317	C₂×C₈×C₁₇	—	2	1	no	—
318	C₂×C₈×C₁₇	—	2	1	no	—
319	C₂×C₈×C₁₇	—	2	1	no	—
320	C₂×C₈×C₁₇	—	2	1	no	—
321	C₂×C₈×C₁₇	—	4	2	no	—
322	C₂×C₈×C₁₇	—	4	2	no	—
323	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
324	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
325	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
326	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
327	C₄⋊C₄×C₁₇	—	2	1	no	—
328	C₄⋊C₄×C₁₇	—	2	1	no	—
329	C₄⋊C₄×C₁₇	—	4	1	no	—
330	C₄⋊C₄×C₁₇	—	4	1	no	—
331	C₂²⋊C₄×C₁₇	—	4	1	no	—
332	C₂²⋊C₄×C₁₇	—	4	1	no	—
333	#24403	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
334	C₂³×C₁₇	—	2	1	no	—
335	C₂³×C₁₇	—	2	1	no	—
336	C₂³×C₁₇	—	2	1	no	—
337	C₂³×C₁₇	—	2	1	no	—
338	C₂³×C₁₇	—	2	2	no	—
339	C₂³×C₁₇	—	4	1	no	—
340	C₂³×C₁₇	—	4	1	no	—
341	C₂³×C₁₇	—	4	2	no	—
342	C₂³×C₁₇	—	4	2	no	—
343	C₂³×C₁₇	—	4	1	no	—
344	C₂³×C₁₇	—	4	1	no	—
345	C₂³×C₁₇	—	8	1	no	—
346	C₂³×C₁₇	—	8	1	no	—
347	C₂³×C₁₇	—	8	1	no	—
348	C₂³×C₁₇	#121	1	1	yes	characteristic
349	C₂³×C₁₇	#121	1	1	yes	characteristic
350	C₂³×C₁₇	C₂×#41	1	1	yes	characteristic
351	Q₈×C₁₇	—	2	1	no	—
352	Q₈×C₁₇	—	2	1	no	—
353	Q₈×C₁₇	—	2	2	no	—
354	Q₈×C₁₇	—	2	1	no	—
355	Q₈×C₁₇	—	2	2	no	—
356	Q₈×C₁₇	—	4	2	no	—
357	Q₈×C₁₇	—	4	1	no	—
358	Q₈×C₁₇	—	4	1	no	—
359	Q₈×C₁₇	—	4	1	no	—
360	Q₈×C₁₇	—	4	1	no	—
361	Q₈×C₁₇	—	4	1	no	—
362	Q₈×C₁₇	—	4	1	no	—
363	Q₈×C₁₇	#120	1	2	yes	—
364	D₄×C₁₇	—	2	2	no	—
365	D₄×C₁₇	—	2	2	no	—
366	D₄×C₁₇	—	2	1	no	—
367	D₄×C₁₇	—	2	2	no	—
368	D₄×C₁₇	—	2	1	no	—
369	D₄×C₁₇	—	2	1	no	—
370	D₄×C₁₇	—	2	2	no	—
371	D₄×C₁₇	—	4	2	no	—
372	D₄×C₁₇	—	4	2	no	—
373	D₄×C₁₇	—	4	2	no	—
374	D₄×C₁₇	—	4	4	no	—
375	D₄×C₁₇	—	4	4	no	—
376	D₄×C₁₇	—	4	1	no	—
377	D₄×C₁₇	—	4	1	no	—
378	D₄×C₁₇	—	4	1	no	—
379	D₄×C₁₇	—	4	1	no	—
380	D₄×C₁₇	#120	1	2	yes	—
381	C₂×C₄×C₁₇	—	2	1	no	—
382	C₂×C₄×C₁₇	—	2	1	no	—
383	C₂×C₄×C₁₇	—	2	1	no	—
384	C₂×C₄×C₁₇	—	2	1	no	—
385	C₂×C₄×C₁₇	—	2	1	no	—
386	C₂×C₄×C₁₇	—	2	1	no	—
387	C₂×C₄×C₁₇	—	2	1	no	—
388	C₂×C₄×C₁₇	—	2	2	no	—
389	C₂×C₄×C₁₇	—	2	2	no	—
390	C₂×C₄×C₁₇	—	2	1	no	—
391	C₂×C₄×C₁₇	—	2	1	no	—
392	C₂×C₄×C₁₇	—	2	1	no	—
393	C₂×C₄×C₁₇	—	2	1	no	—
394	C₂×C₄×C₁₇	—	2	1	no	—
395	C₂×C₄×C₁₇	—	2	2	no	—
396	C₂×C₄×C₁₇	—	4	2	no	—
397	C₂×C₄×C₁₇	—	4	2	no	—
398	C₂×C₄×C₁₇	—	4	2	no	—
399	C₂×C₄×C₁₇	—	4	4	no	—
400	C₂×C₄×C₁₇	—	4	4	no	—
401	C₂×C₄×C₁₇	—	4	1	no	—
402	C₂×C₄×C₁₇	—	4	1	no	—
403	C₂×C₄×C₁₇	—	4	1	no	—
404	C₂×C₄×C₁₇	—	4	1	no	—
405	C₂×C₄×C₁₇	—	4	1	no	—
406	C₂×C₄×C₁₇	—	4	1	no	—
407	C₂×C₄×C₁₇	—	4	1	no	—
408	C₂×C₄×C₁₇	—	4	1	no	—
409	C₂×C₄×C₁₇	—	8	1	no	—
410	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
411	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
412	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
413	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
414	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
415	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
416	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
417	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
418	C₈×C₁₇	—	2	2	no	—
419	C₈×C₁₇	—	2	2	no	—
420	C₈×C₁₇	—	2	1	no	—
421	C₈×C₁₇	—	2	1	no	—
422	C₈×C₁₇	—	2	1	no	—
423	C₈×C₁₇	—	2	1	no	—
424	C₈×C₁₇	—	4	1	no	—
425	C₈×C₁₇	—	4	1	no	—
426	C₈×C₁₇	—	4	1	no	—
427	C₈×C₁₇	—	4	1	no	—
428	C₂×#575	C₂×C₁₇	1	1	yes	characteristic
429	C₂×#473	C₂×C₁₇	1	1	yes	characteristic, complemented
430	C₂×#471	C₂×C₁₇	1	1	yes	characteristic, complemented
431	#3007	C₂×C₁₇	1	1	yes	characteristic, complemented
432	C₂×#452	C₂×C₁₇	1	1	yes	characteristic, complemented
433	#2880	C₂×C₁₇	1	1	yes	characteristic, complemented
434	#2052	C₂×C₁₇	1	1	yes	characteristic, complemented
435	#2051	C₂×C₁₇	1	1	yes	characteristic, complemented
436	#2020	C₂×C₁₇	1	1	yes	characteristic, complemented
437	#2019	C₂×C₁₇	1	1	yes	characteristic, complemented
438	#1908	C₂×C₁₇	1	1	yes	characteristic, complemented
439	#1907	C₂×C₁₇	1	1	yes	characteristic, complemented
440	#1901	C₂×C₁₇	1	1	yes	characteristic, complemented
441	#1855	C₂×C₁₇	1	1	yes	characteristic, complemented
442	#1785	C₂×C₁₇	1	1	yes	characteristic, complemented
443	C₂²×C₁₇	—	2	1	no	—
444	C₂²×C₁₇	—	2	1	no	—
445	C₂²×C₁₇	—	2	1	no	—
446	C₂²×C₁₇	—	2	1	no	—
447	C₂²×C₁₇	—	2	2	no	—
448	C₂²×C₁₇	—	2	1	no	—
449	C₂²×C₁₇	—	2	1	no	—
450	C₂²×C₁₇	—	2	1	no	—
451	C₂²×C₁₇	—	2	1	no	—
452	C₂²×C₁₇	—	4	1	no	—
453	C₂²×C₁₇	—	4	1	no	—
454	C₂²×C₁₇	—	4	1	no	—
455	C₂²×C₁₇	—	4	2	no	—
456	C₂²×C₁₇	—	4	1	no	—
457	C₂²×C₁₇	—	4	1	no	—
458	C₂²×C₁₇	—	8	1	no	—
459	C₂²×C₁₇	—	8	1	no	—
460	C₂²×C₁₇	—	8	2	no	—
461	C₂²×C₁₇	—	8	2	no	—
462	C₂²×C₁₇	—	8	4	no	—
463	C₂²×C₁₇	—	8	1	no	—
464	C₂²×C₁₇	—	8	1	no	—
465	C₂²×C₁₇	C₂×#121	1	1	yes	characteristic
466	C₂²×C₁₇	#546	1	1	yes	characteristic
467	C₂²×C₁₇	#546	1	1	yes	characteristic
468	C₄×C₁₇	—	2	1	no	—
469	C₄×C₁₇	—	2	1	no	—
470	C₄×C₁₇	—	2	2	no	—
471	C₄×C₁₇	—	4	1	no	—
472	C₄×C₁₇	—	4	2	no	—
473	C₄×C₁₇	—	8	1	no	—
474	C₄×C₁₇	—	8	1	no	—
475	C₄×C₁₇	C₂×#120	1	1	yes	characteristic
476	C₄×C₁₇	#534	1	1	yes	characteristic
477	C₄×C₁₇	D₄²	1	1	yes	characteristic
478	C₄×C₁₇	D₄²	1	1	yes	characteristic
479	C₂²×#41	C₂²×C₁₇	1	1	yes	characteristic
480	C₂²×#41	C₂²×C₁₇	1	1	yes	characteristic
481	#575	—	2	4	no	—
482	#575	—	2	4	no	—
483	C₂×#137	—	2	1	no	—
484	C₂×#137	C₂²×C₁₇	1	1	yes	characteristic
485	C₂×#137	C₂²×C₁₇	1	1	yes	characteristic
486	C₂×#137	C₂²×C₁₇	1	1	yes	characteristic
487	C₂×#137	C₂²×C₁₇	1	1	yes	characteristic
488	C₂×AGL(1,ℤ/8)	—	2	1	no	—
489	C₂×AGL(1,ℤ/8)	C₂²×C₁₇	1	1	yes	characteristic
490	C₂×AGL(1,ℤ/8)	C₂²×C₁₇	1	1	yes	characteristic
491	C₂×#135	—	2	1	no	—
492	C₂×#135	—	2	1	no	—
493	C₂²×Q₁₆	C₂²×C₁₇	1	1	yes	characteristic, complemented
494	C₂²×SD₁₆	C₂²×C₁₇	1	1	yes	characteristic, complemented
495	C₂×#131	C₂²×C₁₇	1	1	yes	characteristic
496	C₂×#131	C₂²×C₁₇	1	1	yes	characteristic
497	C₂²×M₁₆	C₂²×C₁₇	1	1	yes	characteristic
498	C₂×C₂²⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
499	#473	—	2	4	no	—
500	#471	—	2	4	no	—
501	#452	—	2	1	no	—
502	#452	—	2	1	no	—
503	#452	—	2	1	no	—
504	#452	—	2	1	no	—
505	#452	—	2	1	no	—
506	#452	—	2	1	no	—
507	#451	—	2	1	no	—
508	#450	—	2	1	no	—
509	C₂×#108	C₂²×C₁₇	1	1	yes	characteristic, complemented
510	C₂×#108	C₂²×C₁₇	1	1	yes	characteristic, complemented
511	#417	C₂²×C₁₇	1	1	yes	characteristic
512	#417	C₂²×C₁₇	1	1	yes	characteristic
513	C₂×#103	C₂²×C₁₇	1	1	yes	characteristic, complemented
514	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic, complemented
515	C₂×#101	C₂²×C₁₇	1	1	yes	characteristic, complemented
516	C₂×#101	C₂²×C₁₇	1	1	yes	characteristic, complemented
517	C₂×#101	C₂²×C₁₇	1	1	yes	characteristic, complemented
518	C₂×#101	C₂²×C₁₇	1	1	yes	characteristic, complemented
519	C₂×#100	C₂²×C₁₇	1	1	yes	characteristic, complemented
520	C₂×#100	C₂²×C₁₇	1	1	yes	characteristic, complemented
521	#408	—	2	1	no	—
522	#408	—	2	1	no	—
523	#408	C₂²×C₁₇	1	1	yes	characteristic
524	#408	C₂²×C₁₇	1	1	yes	characteristic
525	#407	—	2	1	no	—
526	#407	C₂²×C₁₇	1	1	yes	characteristic
527	#407	C₂²×C₁₇	1	1	yes	characteristic
528	C₂×C₂²⋊C₈	—	2	1	no	—
529	C₂×C₂²⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
530	#343	C₂²×C₁₇	1	1	yes	characteristic, complemented
531	#343	C₂²×C₁₇	1	1	yes	characteristic, complemented
532	#341	C₂²×C₁₇	1	1	yes	characteristic, complemented
533	#341	C₂²×C₁₇	1	1	yes	characteristic, complemented
534	C₂×C₁₇	—	2	1	no	—
535	C₂×C₁₇	—	2	1	no	—
536	C₂×C₁₇	—	4	1	no	—
537	C₂×C₁₇	—	4	1	no	—
538	C₂×C₁₇	—	4	2	no	—
539	C₂×C₁₇	—	8	1	no	—
540	C₂×C₁₇	—	8	2	no	—
541	C₂×C₁₇	#2410	1	1	yes	characteristic
542	C₂×C₁₇	#3067	1	1	yes	characteristic
543	C₂×C₁₇	#3069	1	1	yes	characteristic
544	C₂×#41	—	2	1	no	—
545	C₂×#41	—	2	1	no	—
546	C₂×#41	—	2	2	no	—
547	C₂×#41	—	2	2	no	—
548	C₂×#41	—	2	2	no	—
549	C₂×#41	—	2	2	no	—
550	C₂×#41	—	2	1	no	—
551	C₂×#41	—	2	1	no	—
552	C₂×#41	—	2	1	no	—
553	C₂×#41	—	2	1	no	—
554	C₂×#41	—	4	1	no	—
555	C₂×#41	—	4	1	no	—
556	C₂×#41	—	4	1	no	—
557	C₂×#41	—	4	1	no	—
558	C₂×#41	D₄×C₁₇	1	1	yes	characteristic
559	C₂×#41	D₄×C₁₇	1	1	yes	characteristic
560	C₂×#41	C₂³×C₁₇	1	1	yes	characteristic
561	C₂×#41	C₂³×C₁₇	1	1	yes	characteristic
562	C₂²×Q₈	D₄×C₁₇	1	1	yes	characteristic
563	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
564	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
565	C₂²×D₄	—	2	1	no	—
566	C₂²×D₄	—	2	1	no	—
567	C₂²×D₄	D₄×C₁₇	1	1	yes	characteristic
568	C₂²×D₄	C₂³×C₁₇	1	1	yes	characteristic
569	C₂³×C₄	—	2	1	no	—
570	C₂³×C₄	—	2	1	no	—
571	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
572	#137	—	2	8	no	—
573	#137	—	2	2	no	—
574	#137	—	2	2	no	—
575	#137	—	2	2	no	—
576	#137	—	2	2	no	—
577	#137	—	2	2	no	—
578	#137	—	4	1	no	—
579	#137	—	4	1	no	—
580	#137	D₄×C₁₇	1	4	yes	—
581	AGL(1,ℤ/8)	—	2	8	no	—
582	AGL(1,ℤ/8)	—	2	2	no	—
583	AGL(1,ℤ/8)	—	2	2	no	—
584	AGL(1,ℤ/8)	—	2	2	no	—
585	AGL(1,ℤ/8)	D₄×C₁₇	1	4	yes	—
586	#135	—	2	8	no	—
587	#135	—	2	8	no	—
588	C₂×Q₁₆	—	2	1	no	—
589	C₂×Q₁₆	—	2	1	no	—
590	C₂×Q₁₆	—	2	2	no	—
591	C₂×Q₁₆	—	2	1	no	—
592	C₂×Q₁₆	—	2	1	no	—
593	C₂×Q₁₆	—	2	1	no	—
594	C₂×Q₁₆	—	2	1	no	—
595	C₂×Q₁₆	—	4	1	no	—
596	C₂×SD₁₆	—	2	1	no	—
597	C₂×SD₁₆	—	2	1	no	—
598	C₂×SD₁₆	—	2	1	no	—
599	C₂×SD₁₆	—	2	1	no	—
600	C₂×SD₁₆	—	2	2	no	—
601	C₂×SD₁₆	—	2	1	no	—
602	C₂×SD₁₆	—	2	1	no	—
603	C₂×SD₁₆	—	2	1	no	—
604	C₂×SD₁₆	—	2	1	no	—
605	C₂×SD₁₆	—	4	1	no	—
606	C₂×D₈	—	2	1	no	—
607	C₂×D₈	—	2	1	no	—
608	#131	—	2	2	no	—
609	#131	—	2	2	no	—
610	#131	—	4	1	no	—
611	#131	—	4	1	no	—
612	C₂×M₁₆	—	2	1	no	—
613	C₂×M₁₆	—	2	2	no	—
614	C₂×M₁₆	—	2	2	no	—
615	C₂×M₁₆	—	2	1	no	—
616	C₂×M₁₆	—	2	1	no	—
617	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
618	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
619	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
620	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
621	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
622	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
623	C₂²×C₈	—	2	1	no	—
624	C₂²×C₈	—	2	1	no	—
625	C₂²×C₈	—	2	1	no	—
626	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
627	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
628	C₂²⋊Q₈	—	2	1	no	—
629	C₂²⋊Q₈	—	2	1	no	—
630	C₂²⋊Q₈	—	2	1	no	—
631	C₂²⋊Q₈	—	2	1	no	—
632	C₂×C₄⋊C₄	—	2	1	no	—
633	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
634	C₂×C₂²⋊C₄	—	2	1	no	—
635	#108	—	2	2	no	—
636	#108	—	2	2	no	—
637	#103	—	2	1	no	—
638	#103	—	2	1	no	—
639	#103	—	2	1	no	—
640	#103	—	2	1	no	—
641	#102	—	2	1	no	—
642	#102	—	2	1	no	—
643	#102	—	2	1	no	—
644	#102	—	2	1	no	—
645	#101	—	2	2	no	—
646	#101	—	2	2	no	—
647	#101	—	2	2	no	—
648	#101	—	4	1	no	—
649	#100	—	2	2	no	—
650	#100	—	4	1	no	—
651	C₂²⋊C₈	—	2	1	no	—
652	C₂²⋊C₈	—	2	1	no	—
653	C₂²⋊C₈	—	2	1	no	—
654	C₂²⋊C₈	—	2	1	no	—
655	C₂²⋊C₈	—	2	1	no	—
656	C₂²⋊C₈	—	2	1	no	—
657	C₂²⋊C₈	—	2	1	no	—
658	C₂²⋊C₈	—	2	1	no	—
659	C₂²⋊C₈	D₄×C₁₇	1	1	yes	characteristic
660	C₂²⋊C₈	D₄×C₁₇	1	1	yes	characteristic
661	C₂²⋊C₈	D₄×C₁₇	1	1	yes	characteristic
662	C₂²⋊C₈	D₄×C₁₇	1	1	yes	characteristic
663	C₁₇	#24403	1	1	yes	characteristic, direct product factor, Sylow
664	C₂⁴	—	2	1	no	—
665	C₂⁴	—	2	1	no	—
666	C₂⁴	#41×C₁₇	1	1	yes	characteristic
667	#41	—	2	1	no	—
668	#41	—	2	1	no	—
669	#41	—	2	4	no	—
670	#41	—	2	4	no	—
671	#41	—	2	2	no	—
672	#41	—	2	2	no	—
673	#41	—	2	1	no	—
674	#41	—	2	1	no	—
675	#41	—	2	1	no	—
676	#41	—	2	1	no	—
677	#41	—	4	2	no	—
678	#41	—	4	2	no	—
679	#41	—	4	1	no	—
680	#41	—	4	1	no	—
681	#41	—	4	2	no	—
682	#41	—	4	2	no	—
683	#41	—	4	2	no	—
684	#41	—	4	2	no	—
685	#41	—	4	2	no	—
686	#41	—	4	2	no	—
687	#41	—	4	2	no	—
688	#41	—	4	2	no	—
689	#41	C₂×D₄×C₁₇	1	2	yes	—
690	#41	C₂×D₄×C₁₇	1	2	yes	—
691	C₂×Q₈	—	2	1	no	—
692	C₂×Q₈	—	2	1	no	—
693	C₂×Q₈	—	2	2	no	—
694	C₂×Q₈	—	2	1	no	—
695	C₂×Q₈	—	2	1	no	—
696	C₂×Q₈	—	2	1	no	—
697	C₂×Q₈	—	2	1	no	—
698	C₂×Q₈	—	2	1	no	—
699	C₂×Q₈	—	2	1	no	—
700	C₂×Q₈	—	2	1	no	—
701	C₂×Q₈	—	2	1	no	—
702	C₂×Q₈	—	2	1	no	—
703	C₂×Q₈	—	2	1	no	—
704	C₂×Q₈	—	4	1	no	—
705	C₂×Q₈	C₂×D₄×C₁₇	1	2	yes	—
706	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
707	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
708	C₂×D₄	—	2	1	no	—
709	C₂×D₄	—	2	2	no	—
710	C₂×D₄	—	2	1	no	—
711	C₂×D₄	—	2	1	no	—
712	C₂×D₄	—	2	1	no	—
713	C₂×D₄	—	2	1	no	—
714	C₂×D₄	—	2	1	no	—
715	C₂×D₄	—	2	1	no	—
716	C₂×D₄	—	2	1	no	—
717	C₂×D₄	—	2	1	no	—
718	C₂×D₄	—	2	1	no	—
719	C₂×D₄	—	4	1	no	—
720	C₂×D₄	—	4	2	no	—
721	C₂×D₄	—	4	2	no	—
722	C₂×D₄	—	4	2	no	—
723	C₂×D₄	—	4	2	no	—
724	C₂×D₄	—	4	1	no	—
725	C₂×D₄	—	4	1	no	—
726	C₂×D₄	C₂×D₄×C₁₇	1	2	yes	—
727	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
728	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
729	C₂²×C₄	—	2	1	no	—
730	C₂²×C₄	—	2	1	no	—
731	C₂²×C₄	—	2	1	no	—
732	C₂²×C₄	—	2	1	no	—
733	C₂²×C₄	—	2	1	no	—
734	C₂²×C₄	—	2	1	no	—
735	C₂²×C₄	—	2	1	no	—
736	C₂²×C₄	—	2	1	no	—
737	C₂²×C₄	—	2	1	no	—
738	C₂²×C₄	—	2	1	no	—
739	C₂²×C₄	—	2	1	no	—
740	C₂²×C₄	—	2	1	no	—
741	C₂²×C₄	—	4	2	no	—
742	C₂²×C₄	—	4	2	no	—
743	C₂²×C₄	—	4	2	no	—
744	C₂²×C₄	—	4	2	no	—
745	C₂²×C₄	—	4	1	no	—
746	C₂²×C₄	—	4	1	no	—
747	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
748	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
749	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
750	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
751	C₂²×C₄	#41×C₁₇	1	1	yes	characteristic
752	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
753	Q₁₆	—	2	4	no	—
754	Q₁₆	—	2	4	no	—
755	Q₁₆	—	4	2	no	—
756	Q₁₆	—	4	2	no	—
757	Q₁₆	—	4	2	no	—
758	Q₁₆	—	4	2	no	—
759	SD₁₆	—	2	4	no	—
760	SD₁₆	—	2	4	no	—
761	SD₁₆	—	2	4	no	—
762	SD₁₆	—	2	4	no	—
763	SD₁₆	—	4	2	no	—
764	SD₁₆	—	4	2	no	—
765	SD₁₆	—	4	2	no	—
766	SD₁₆	—	4	2	no	—
767	D₈	—	2	4	no	—
768	D₈	—	2	4	no	—
769	M₁₆	—	2	4	no	—
770	M₁₆	—	2	1	no	—
771	M₁₆	—	2	1	no	—
772	M₁₆	—	2	1	no	—
773	M₁₆	—	2	1	no	—
774	M₁₆	—	2	1	no	—
775	M₁₆	—	2	1	no	—
776	M₁₆	—	2	1	no	—
777	M₁₆	—	2	1	no	—
778	M₁₆	—	2	1	no	—
779	M₁₆	—	2	1	no	—
780	M₁₆	—	4	2	no	—
781	M₁₆	—	4	2	no	—
782	M₁₆	C₂×D₄×C₁₇	1	2	yes	—
783	M₁₆	C₂×D₄×C₁₇	1	2	yes	—
784	C₂×C₈	—	2	4	no	—
785	C₂×C₈	—	2	1	no	—
786	C₂×C₈	—	2	1	no	—
787	C₂×C₈	—	2	1	no	—
788	C₂×C₈	—	2	1	no	—
789	C₂×C₈	—	2	1	no	—
790	C₂×C₈	—	2	1	no	—
791	C₂×C₈	—	2	1	no	—
792	C₂×C₈	—	2	1	no	—
793	C₂×C₈	—	2	1	no	—
794	C₂×C₈	—	2	1	no	—
795	C₂×C₈	—	4	2	no	—
796	C₂×C₈	—	4	2	no	—
797	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
798	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
799	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
800	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
801	C₄⋊C₄	—	2	1	no	—
802	C₄⋊C₄	—	2	1	no	—
803	C₄⋊C₄	—	4	1	no	—
804	C₄⋊C₄	—	4	1	no	—
805	C₂²⋊C₄	—	4	1	no	—
806	C₂²⋊C₄	—	4	1	no	—
807	C₂³	—	2	1	no	—
808	C₂³	—	2	1	no	—
809	C₂³	—	2	1	no	—
810	C₂³	—	2	1	no	—
811	C₂³	—	2	2	no	—
812	C₂³	—	4	1	no	—
813	C₂³	—	4	1	no	—
814	C₂³	—	4	2	no	—
815	C₂³	—	4	2	no	—
816	C₂³	—	4	1	no	—
817	C₂³	—	4	1	no	—
818	C₂³	—	8	1	no	—
819	C₂³	—	8	1	no	—
820	C₂³	—	8	1	no	—
821	C₂³	C₁₇×#121	1	1	yes	characteristic
822	C₂³	C₁₇×#121	1	1	yes	characteristic
823	C₂³	C₂×#41×C₁₇	1	1	yes	characteristic
824	Q₈	—	2	1	no	—
825	Q₈	—	2	1	no	—
826	Q₈	—	2	2	no	—
827	Q₈	—	2	1	no	—
828	Q₈	—	2	2	no	—
829	Q₈	—	4	2	no	—
830	Q₈	—	4	1	no	—
831	Q₈	—	4	1	no	—
832	Q₈	—	4	1	no	—
833	Q₈	—	4	1	no	—
834	Q₈	—	4	1	no	—
835	Q₈	—	4	1	no	—
836	Q₈	C₁₇×#120	1	2	yes	—
837	D₄	—	2	2	no	—
838	D₄	—	2	2	no	—
839	D₄	—	2	1	no	—
840	D₄	—	2	2	no	—
841	D₄	—	2	1	no	—
842	D₄	—	2	1	no	—
843	D₄	—	2	2	no	—
844	D₄	—	4	2	no	—
845	D₄	—	4	2	no	—
846	D₄	—	4	2	no	—
847	D₄	—	4	4	no	—
848	D₄	—	4	4	no	—
849	D₄	—	4	1	no	—
850	D₄	—	4	1	no	—
851	D₄	—	4	1	no	—
852	D₄	—	4	1	no	—
853	D₄	C₁₇×#120	1	2	yes	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	4	2	no	—
870	C₂×C₄	—	4	2	no	—
871	C₂×C₄	—	4	2	no	—
872	C₂×C₄	—	4	4	no	—
873	C₂×C₄	—	4	4	no	—
874	C₂×C₄	—	4	1	no	—
875	C₂×C₄	—	4	1	no	—
876	C₂×C₄	—	4	1	no	—
877	C₂×C₄	—	4	1	no	—
878	C₂×C₄	—	4	1	no	—
879	C₂×C₄	—	4	1	no	—
880	C₂×C₄	—	4	1	no	—
881	C₂×C₄	—	4	1	no	—
882	C₂×C₄	—	8	1	no	—
883	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
884	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
885	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
886	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
887	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
888	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
889	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
890	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
891	C₈	—	2	2	no	—
892	C₈	—	2	2	no	—
893	C₈	—	2	1	no	—
894	C₈	—	2	1	no	—
895	C₈	—	2	1	no	—
896	C₈	—	2	1	no	—
897	C₈	—	4	1	no	—
898	C₈	—	4	1	no	—
899	C₈	—	4	1	no	—
900	C₈	—	4	1	no	—
901	C₂²	—	2	1	no	—
902	C₂²	—	2	1	no	—
903	C₂²	—	2	1	no	—
904	C₂²	—	2	1	no	—
905	C₂²	—	2	1	no	—
906	C₂²	—	2	1	no	—
907	C₂²	—	2	1	no	—
908	C₂²	—	2	1	no	—
909	C₂²	—	2	2	no	—
910	C₂²	—	4	1	no	—
911	C₂²	—	4	1	no	—
912	C₂²	—	4	1	no	—
913	C₂²	—	4	1	no	—
914	C₂²	—	4	1	no	—
915	C₂²	—	4	2	no	—
916	C₂²	—	8	1	no	—
917	C₂²	—	8	1	no	—
918	C₂²	—	8	2	no	—
919	C₂²	—	8	2	no	—
920	C₂²	—	8	4	no	—
921	C₂²	—	8	1	no	—
922	C₂²	—	8	1	no	—
923	C₂²	C₂×C₁₇×#121	1	1	yes	characteristic
924	C₂²	C₁₇×#546	1	1	yes	characteristic
925	C₂²	C₁₇×#546	1	1	yes	characteristic
926	C₄	—	2	1	no	—
927	C₄	—	2	1	no	—
928	C₄	—	2	2	no	—
929	C₄	—	4	1	no	—
930	C₄	—	4	2	no	—
931	C₄	—	8	1	no	—
932	C₄	—	8	1	no	—
933	C₄	C₂×C₁₇×#120	1	1	yes	characteristic
934	C₄	C₁₇×#534	1	1	yes	characteristic
935	C₄	D₄²×C₁₇	1	1	yes	characteristic
936	C₄	D₄²×C₁₇	1	1	yes	characteristic
937	C₂	—	2	1	no	—
938	C₂	—	2	1	no	—
939	C₂	—	4	1	no	—
940	C₂	—	4	1	no	—
941	C₂	—	4	2	no	—
942	C₂	—	8	1	no	—
943	C₂	—	8	2	no	—
944	C₂	C₁₇×#2410	1	1	yes	characteristic
945	C₂	C₁₇×#3067	1	1	yes	characteristic
946	C₂	C₁₇×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₇
prime radical	C₂×C₁₇×#575	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₄×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₇×#473	C₂	semidirect
3. C₂×C₁₇×#471	C₂	semidirect
4. C₁₇×#3007	C₂	semidirect
5. C₂×C₁₇×#452	C₂	semidirect
6. C₁₇×#2880	C₂	semidirect
7. C₁₇×#2052	C₂	semidirect
8. C₁₇×#2051	C₂	semidirect
9. C₁₇×#2020	C₂	semidirect
10. C₁₇×#2019	C₂	semidirect
11. C₁₇×#1908	C₂	semidirect
12. C₁₇×#1907	C₂	semidirect
13. C₁₇×#1901	C₂	semidirect
14. C₁₇×#1855	C₂	semidirect
15. C₁₇×#1785	C₂	semidirect
30. C₂²×Q₁₆×C₁₇	C₂²	semidirect
31. C₂²×SD₁₆×C₁₇	C₂²	semidirect
46. C₂×C₁₇×#108	C₂²	semidirect
47. C₂×C₁₇×#108	C₂²	semidirect
50. C₂×C₁₇×#103	C₂²	semidirect
51. C₂×C₁₇×#102	C₂²	semidirect
52. C₂×C₁₇×#101	C₂²	semidirect
53. C₂×C₁₇×#101	C₂²	semidirect
54. C₂×C₁₇×#101	C₂²	semidirect
55. C₂×C₁₇×#101	C₂²	semidirect
56. C₂×C₁₇×#100	C₂²	semidirect
57. C₂×C₁₇×#100	C₂²	semidirect
67. C₁₇×#343	C₂²	semidirect
68. C₁₇×#343	C₂²	semidirect
69. C₁₇×#341	C₂²	semidirect
70. C₁₇×#341	C₂²	semidirect
333. #24403	C₁₇	direct (N × H)
429. C₂×#473	C₂×C₁₇	semidirect
430. C₂×#471	C₂×C₁₇	semidirect
431. #3007	C₂×C₁₇	semidirect
432. C₂×#452	C₂×C₁₇	semidirect
433. #2880	C₂×C₁₇	semidirect
434. #2052	C₂×C₁₇	semidirect
435. #2051	C₂×C₁₇	semidirect
436. #2020	C₂×C₁₇	semidirect
437. #2019	C₂×C₁₇	semidirect
438. #1908	C₂×C₁₇	semidirect
439. #1907	C₂×C₁₇	semidirect
440. #1901	C₂×C₁₇	semidirect
441. #1855	C₂×C₁₇	semidirect
442. #1785	C₂×C₁₇	semidirect
493. C₂²×Q₁₆	C₂²×C₁₇	semidirect
494. C₂²×SD₁₆	C₂²×C₁₇	semidirect
509. C₂×#108	C₂²×C₁₇	semidirect
510. C₂×#108	C₂²×C₁₇	semidirect
513. C₂×#103	C₂²×C₁₇	semidirect
514. C₂×#102	C₂²×C₁₇	semidirect
515. C₂×#101	C₂²×C₁₇	semidirect
516. C₂×#101	C₂²×C₁₇	semidirect
517. C₂×#101	C₂²×C₁₇	semidirect
518. C₂×#101	C₂²×C₁₇	semidirect
519. C₂×#100	C₂²×C₁₇	semidirect
520. C₂×#100	C₂²×C₁₇	semidirect
530. #343	C₂²×C₁₇	semidirect
531. #343	C₂²×C₁₇	semidirect
532. #341	C₂²×C₁₇	semidirect
533. #341	C₂²×C₁₇	semidirect
663. C₁₇	#24403	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×#473	2
C₂×C₁₇×#471	2
C₁₇×#3007	2
C₂×C₁₇×#452	2
C₁₇×#2880	2
C₁₇×#2052	2
C₁₇×#2051	2
C₁₇×#2020	2
C₁₇×#2019	2
C₁₇×#1908	2
C₁₇×#1907	2
C₁₇×#1901	2
C₁₇×#1855	2
C₁₇×#1785	2
#24403	17

Subgroups — C17×#24403 #16882147

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#24403 #16882147