Subgroups — C₁₇×#24295 #16882039

Order 4352.

1302 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#577	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇×#3067	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#3057	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#3020	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#3019	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#2955	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#2049	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₇×#2048	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#2009	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#2008	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#1977	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#1976	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₇×#1814	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₇×#1796	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#1795	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₇×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
17	C₂×C₁₇×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
18	C₁₇×#577	—	2	2	no	—
19	C₁₇×#577	—	2	2	no	—
20	C₁₇×#577	—	2	2	no	—
21	C₁₇×#577	—	2	2	no	—
22	C₁₇×#575	C₂²	1	1	yes	characteristic
23	C₁₇×#575	C₂²	1	1	yes	characteristic
24	C₁₇×#575	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₁₇×#137	—	2	1	no	—
26	C₂×C₁₇×#137	C₂²	1	1	yes	characteristic
27	C₂×C₁₇×AGL(1,ℤ/8)	—	2	1	no	—
28	C₂×C₁₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
29	C₂×C₁₇×#135	—	2	1	no	—
30	C₂×C₁₇×#135	C₂²	1	1	yes	characteristic
31	C₂²×SD₁₆×C₁₇	—	2	1	no	—
32	C₂²×SD₁₆×C₁₇	C₂²	1	1	yes	characteristic
33	C₂×C₁₇×#131	C₂²	1	1	yes	characteristic
34	C₂×C₁₇×#131	C₂²	1	1	yes	characteristic, complemented
35	C₁₇×#536	C₂²	1	1	yes	characteristic, complemented
36	C₁₇×#535	C₂²	1	1	yes	characteristic
37	C₁₇×#473	—	2	1	no	—
38	C₁₇×#472	—	2	1	no	—
39	C₁₇×#471	—	2	1	no	—
40	C₁₇×#471	—	2	1	no	—
41	C₁₇×#468	—	2	2	no	—
42	C₁₇×#465	—	2	2	no	—
43	C₁₇×#456	—	2	2	no	—
44	C₁₇×#455	—	2	2	no	—
45	C₁₇×#454	—	2	2	no	—
46	C₁₇×#453	—	2	2	no	—
47	C₁₇×#444	—	2	2	no	—
48	C₁₇×#443	—	2	2	no	—
49	C₁₇×#430	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₁₇×#108	C₂²	1	1	yes	characteristic, complemented
51	C₁₇×#427	C₂²	1	1	yes	characteristic, complemented
52	C₁₇×#421	C₂²	1	1	yes	characteristic
53	C₁₇×#421	C₂²	1	1	yes	characteristic
54	C₁₇×#421	C₂²	1	1	yes	characteristic
55	C₁₇×#421	C₂²	1	1	yes	characteristic
56	C₁₇×#421	C₂²	1	1	yes	characteristic, complemented
57	C₁₇×#421	C₂²	1	1	yes	characteristic, complemented
58	C₁₇×#419	C₂²	1	1	yes	characteristic, complemented
59	C₁₇×#419	C₂²	1	1	yes	characteristic, complemented
60	C₁₇×#418	C₂²	1	1	yes	characteristic
61	C₁₇×#418	C₂²	1	1	yes	characteristic
62	C₁₇×#413	C₂²	1	1	yes	characteristic
63	C₁₇×#413	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₁₇×#101	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₁₇×#100	C₂²	1	1	yes	characteristic
66	C₁₇×#410	C₂²	1	1	yes	characteristic
67	C₁₇×#410	C₂²	1	1	yes	characteristic, complemented
68	C₁₇×#405	C₂²	1	1	yes	characteristic, complemented
69	C₁₇×#344	C₂²	1	1	yes	characteristic, complemented
70	C₁₇×#344	C₂²	1	1	yes	characteristic, complemented
71	C₁₇×2₋¹⁺⁴	—	2	2	no	—
72	C₁₇×2₋¹⁺⁴	—	2	2	no	—
73	C₁₇×2₋¹⁺⁴	—	2	2	no	—
74	C₁₇×2₋¹⁺⁴	—	4	1	no	—
75	C₁₇×H(5,𝔽₂)	—	2	2	no	—
76	C₁₇×H(5,𝔽₂)	—	2	2	no	—
77	C₁₇×H(5,𝔽₂)	—	2	2	no	—
78	C₁₇×H(5,𝔽₂)	—	4	1	no	—
79	C₂×#41×C₁₇	—	2	1	no	—
80	C₂×#41×C₁₇	—	2	1	no	—
81	C₂×#41×C₁₇	—	2	1	no	—
82	C₂×#41×C₁₇	—	2	1	no	—
83	C₂×#41×C₁₇	—	4	1	no	—
84	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
85	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
86	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
87	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
88	C₂²×Q₈×C₁₇	—	2	1	no	—
89	C₂²×Q₈×C₁₇	—	2	1	no	—
90	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₁₇	—	2	1	no	—
92	C₂²×D₄×C₁₇	—	2	1	no	—
93	C₂²×D₄×C₁₇	—	4	1	no	—
94	C₂²×D₄×C₁₇	C₂³	1	1	yes	characteristic
95	C₁₇×#137	—	2	4	no	—
96	C₁₇×#137	—	2	4	no	—
97	C₁₇×#137	—	2	2	no	—
98	C₁₇×#137	—	2	1	no	—
99	C₁₇×#137	—	2	1	no	—
100	C₁₇×#137	—	2	1	no	—
101	C₁₇×#137	—	2	1	no	—
102	C₁₇×#137	—	2	1	no	—
103	C₁₇×#137	—	2	2	no	—
104	C₁₇×#137	D₄	1	2	yes	—
105	C₁₇×AGL(1,ℤ/8)	—	2	4	no	—
106	C₁₇×AGL(1,ℤ/8)	—	2	4	no	—
107	C₁₇×AGL(1,ℤ/8)	—	2	2	no	—
108	C₁₇×AGL(1,ℤ/8)	—	2	1	no	—
109	C₁₇×AGL(1,ℤ/8)	—	2	1	no	—
110	C₁₇×AGL(1,ℤ/8)	—	2	1	no	—
111	C₁₇×AGL(1,ℤ/8)	—	2	1	no	—
112	C₁₇×AGL(1,ℤ/8)	—	2	1	no	—
113	C₁₇×AGL(1,ℤ/8)	—	2	2	no	—
114	C₁₇×AGL(1,ℤ/8)	D₄	1	2	yes	—
115	C₁₇×#135	—	2	4	no	—
116	C₁₇×#135	—	2	4	no	—
117	C₁₇×#135	—	2	2	no	—
118	C₁₇×#135	—	2	1	no	—
119	C₁₇×#135	—	2	1	no	—
120	C₁₇×#135	—	2	1	no	—
121	C₁₇×#135	—	2	1	no	—
122	C₁₇×#135	—	4	1	no	—
123	C₁₇×#135	—	4	1	no	—
124	C₂×Q₁₆×C₁₇	—	2	1	no	—
125	C₂×Q₁₆×C₁₇	D₄	1	1	yes	characteristic, complemented
126	C₂×SD₁₆×C₁₇	—	2	4	no	—
127	C₂×SD₁₆×C₁₇	—	2	4	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	—	2	1	no	—
133	C₂×SD₁₆×C₁₇	—	2	1	no	—
134	C₂×SD₁₆×C₁₇	D₄	1	2	yes	—
135	C₂×SD₁₆×C₁₇	D₄	1	2	yes	—
136	C₂×SD₁₆×C₁₇	D₄	1	1	yes	characteristic, complemented
137	C₂×SD₁₆×C₁₇	D₄	1	1	yes	characteristic, complemented
138	C₂×D₈×C₁₇	—	2	1	no	—
139	C₂×D₈×C₁₇	D₄	1	1	yes	characteristic, complemented
140	C₁₇×#131	—	2	1	no	—
141	C₁₇×#131	—	2	1	no	—
142	C₁₇×#131	—	2	1	no	—
143	C₁₇×#131	—	2	1	no	—
144	C₁₇×#131	—	2	1	no	—
145	C₁₇×#131	—	2	1	no	—
146	C₁₇×#131	D₄	1	2	yes	complemented
147	C₁₇×#131	D₄	1	2	yes	complemented
148	C₂×M₁₆×C₁₇	—	2	1	no	—
149	C₂×M₁₆×C₁₇	—	2	1	no	—
150	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
151	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
152	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
153	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
154	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
155	C₂²×C₈×C₁₇	—	2	1	no	—
156	C₂²×C₈×C₁₇	—	2	1	no	—
157	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
158	C₁₇×C₄⋊Q₈	—	2	1	no	—
159	C₁₇×#127	—	2	1	no	—
160	C₁₇×#124	—	2	1	no	—
161	C₁₇×#124	—	2	1	no	—
162	C₁₇×#123	—	4	1	no	—
163	C₁₇×C₂²⋊Q₈	—	2	2	no	—
164	C₁₇×#121	—	2	2	no	—
165	C₁₇×#120	—	4	1	no	—
166	C₁₇×#117	C₂³	1	1	yes	characteristic
167	C₁₇×#117	C₂³	1	1	yes	characteristic
168	C₁₇×#117	C₂³	1	1	yes	characteristic
169	C₁₇×#108	—	2	2	no	—
170	C₁₇×#108	—	2	1	no	—
171	C₁₇×#108	—	2	1	no	—
172	C₁₇×#107	—	2	1	no	—
173	C₁₇×#106	—	2	1	no	—
174	C₁₇×#104	—	2	2	no	—
175	C₁₇×#104	—	2	2	no	—
176	C₁₇×#104	—	2	2	no	—
177	C₁₇×#104	—	2	2	no	—
178	C₁₇×#104	—	2	2	no	—
179	C₁₇×#104	—	2	2	no	—
180	C₁₇×#103	—	2	2	no	—
181	C₁₇×#103	—	4	1	no	—
182	C₁₇×#102	—	2	2	no	—
183	C₁₇×#102	—	4	1	no	—
184	C₁₇×#101	—	2	1	no	—
185	C₁₇×#101	—	2	1	no	—
186	C₁₇×#101	—	2	2	no	—
187	C₁₇×#100	—	2	1	no	—
188	C₁₇×#100	—	2	1	no	—
189	C₁₇×#100	—	2	2	no	—
190	C₁₇×#99	—	4	1	no	—
191	C₁₇×#99	—	4	1	no	—
192	C₁₇×#97	—	2	1	no	—
193	C₄×C₈×C₁₇	—	2	1	no	—
194	C₂⁴×C₁₇	—	2	1	no	—
195	C₂⁴×C₁₇	—	4	1	no	—
196	#41×C₁₇	—	2	1	no	—
197	#41×C₁₇	—	2	1	no	—
198	#41×C₁₇	—	2	4	no	—
199	#41×C₁₇	—	2	4	no	—
200	#41×C₁₇	—	2	1	no	—
201	#41×C₁₇	—	2	1	no	—
202	#41×C₁₇	—	2	1	no	—
203	#41×C₁₇	—	2	1	no	—
204	#41×C₁₇	—	2	1	no	—
205	#41×C₁₇	—	2	1	no	—
206	#41×C₁₇	—	2	1	no	—
207	#41×C₁₇	—	2	1	no	—
208	#41×C₁₇	—	2	1	no	—
209	#41×C₁₇	—	2	1	no	—
210	#41×C₁₇	—	2	1	no	—
211	#41×C₁₇	—	2	1	no	—
212	#41×C₁₇	—	4	2	no	—
213	#41×C₁₇	—	4	4	no	—
214	#41×C₁₇	—	4	2	no	—
215	#41×C₁₇	—	4	2	no	—
216	#41×C₁₇	—	4	2	no	—
217	#41×C₁₇	—	4	4	no	—
218	#41×C₁₇	—	4	2	no	—
219	#41×C₁₇	—	4	2	no	—
220	#41×C₁₇	C₂×D₄	1	2	yes	—
221	#41×C₁₇	C₂×D₄	1	2	yes	—
222	C₂×Q₈×C₁₇	—	2	1	no	—
223	C₂×Q₈×C₁₇	—	2	4	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	—	4	1	no	—
229	C₂×Q₈×C₁₇	—	4	2	no	—
230	C₂×Q₈×C₁₇	—	4	2	no	—
231	C₂×Q₈×C₁₇	—	4	2	no	—
232	C₂×Q₈×C₁₇	C₂×D₄	1	2	yes	—
233	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
234	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
235	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
236	C₂×Q₈×C₁₇	#41	1	1	yes	characteristic
237	C₂×D₄×C₁₇	—	2	1	no	—
238	C₂×D₄×C₁₇	—	2	4	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	—	2	1	no	—
246	C₂×D₄×C₁₇	—	2	1	no	—
247	C₂×D₄×C₁₇	—	4	2	no	—
248	C₂×D₄×C₁₇	—	4	1	no	—
249	C₂×D₄×C₁₇	—	4	1	no	—
250	C₂×D₄×C₁₇	—	4	2	no	—
251	C₂×D₄×C₁₇	—	4	4	no	—
252	C₂×D₄×C₁₇	—	4	4	no	—
253	C₂×D₄×C₁₇	—	4	1	no	—
254	C₂×D₄×C₁₇	—	4	2	no	—
255	C₂×D₄×C₁₇	—	4	2	no	—
256	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
257	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
258	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
259	C₂×D₄×C₁₇	C₂×D₄	1	2	yes	—
260	C₂×D₄×C₁₇	#41	1	1	yes	characteristic
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	—	4	1	no	—
267	C₂²×C₄×C₁₇	—	4	1	no	—
268	C₂²×C₄×C₁₇	—	4	1	no	—
269	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
270	Q₁₆×C₁₇	—	2	4	no	—
271	Q₁₆×C₁₇	—	2	2	no	—
272	Q₁₆×C₁₇	—	2	1	no	—
273	Q₁₆×C₁₇	—	2	1	no	—
274	Q₁₆×C₁₇	—	4	1	no	—
275	Q₁₆×C₁₇	—	4	1	no	—
276	SD₁₆×C₁₇	—	2	4	no	—
277	SD₁₆×C₁₇	—	2	4	no	—
278	SD₁₆×C₁₇	—	2	2	no	—
279	SD₁₆×C₁₇	—	2	2	no	—
280	SD₁₆×C₁₇	—	2	2	no	—
281	SD₁₆×C₁₇	—	2	2	no	—
282	SD₁₆×C₁₇	—	2	1	no	—
283	SD₁₆×C₁₇	—	2	1	no	—
284	SD₁₆×C₁₇	—	2	2	no	—
285	SD₁₆×C₁₇	—	2	2	no	—
286	SD₁₆×C₁₇	—	2	1	no	—
287	SD₁₆×C₁₇	—	2	1	no	—
288	SD₁₆×C₁₇	—	4	1	no	—
289	SD₁₆×C₁₇	—	4	1	no	—
290	SD₁₆×C₁₇	—	4	1	no	—
291	SD₁₆×C₁₇	—	4	1	no	—
292	D₈×C₁₇	—	2	4	no	—
293	D₈×C₁₇	—	2	2	no	—
294	D₈×C₁₇	—	2	1	no	—
295	D₈×C₁₇	—	2	1	no	—
296	D₈×C₁₇	—	4	1	no	—
297	D₈×C₁₇	—	4	1	no	—
298	M₁₆×C₁₇	—	2	1	no	—
299	M₁₆×C₁₇	—	2	1	no	—
300	M₁₆×C₁₇	—	2	2	no	—
301	M₁₆×C₁₇	—	2	2	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	—	2	1	no	—
307	M₁₆×C₁₇	—	2	1	no	—
308	M₁₆×C₁₇	—	4	1	no	—
309	M₁₆×C₁₇	—	4	1	no	—
310	M₁₆×C₁₇	C₂×D₄	1	2	yes	—
311	M₁₆×C₁₇	C₂×D₄	1	2	yes	—
312	C₂×C₈×C₁₇	—	2	1	no	—
313	C₂×C₈×C₁₇	—	2	1	no	—
314	C₂×C₈×C₁₇	—	2	2	no	—
315	C₂×C₈×C₁₇	—	2	2	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	—	4	1	no	—
320	C₂×C₈×C₁₇	—	4	1	no	—
321	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
322	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
330	C₄⋊C₄×C₁₇	—	4	2	no	—
331	C₂²⋊C₄×C₁₇	—	2	1	no	—
332	C₂²⋊C₄×C₁₇	—	2	1	no	—
333	C₂²⋊C₄×C₁₇	—	2	1	no	—
334	C₂²⋊C₄×C₁₇	—	4	2	no	—
335	C₂²⋊C₄×C₁₇	—	4	2	no	—
336	C₄²×C₁₇	—	2	1	no	—
337	C₄²×C₁₇	—	2	1	no	—
338	C₄²×C₁₇	—	2	1	no	—
339	#24295	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
340	C₂³×C₁₇	—	2	1	no	—
341	C₂³×C₁₇	—	2	1	no	—
342	C₂³×C₁₇	—	2	2	no	—
343	C₂³×C₁₇	—	2	1	no	—
344	C₂³×C₁₇	—	2	1	no	—
345	C₂³×C₁₇	—	4	4	no	—
346	C₂³×C₁₇	—	4	1	no	—
347	C₂³×C₁₇	—	4	1	no	—
348	C₂³×C₁₇	—	16	1	no	—
349	C₂³×C₁₇	—	16	2	no	—
350	C₂³×C₁₇	H(5,𝔽₂)	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	1	no	—
356	Q₈×C₁₇	—	2	1	no	—
357	Q₈×C₁₇	—	2	1	no	—
358	Q₈×C₁₇	—	2	1	no	—
359	Q₈×C₁₇	—	2	2	no	—
360	Q₈×C₁₇	—	4	4	no	—
361	Q₈×C₁₇	—	4	1	no	—
362	Q₈×C₁₇	—	4	1	no	—
363	Q₈×C₁₇	#121	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	1	no	—
371	D₄×C₁₇	—	2	1	no	—
372	D₄×C₁₇	—	2	1	no	—
373	D₄×C₁₇	—	2	1	no	—
374	D₄×C₁₇	—	2	2	no	—
375	D₄×C₁₇	—	4	4	no	—
376	D₄×C₁₇	—	4	4	no	—
377	D₄×C₁₇	—	4	4	no	—
378	D₄×C₁₇	—	4	1	no	—
379	D₄×C₁₇	—	4	1	no	—
380	D₄×C₁₇	—	4	1	no	—
381	D₄×C₁₇	—	4	1	no	—
382	D₄×C₁₇	—	4	1	no	—
383	D₄×C₁₇	—	4	1	no	—
384	D₄×C₁₇	—	4	1	no	—
385	D₄×C₁₇	—	4	1	no	—
386	D₄×C₁₇	—	16	2	no	—
387	D₄×C₁₇	#121	1	2	yes	—
388	C₂×C₄×C₁₇	—	2	1	no	—
389	C₂×C₄×C₁₇	—	2	2	no	—
390	C₂×C₄×C₁₇	—	2	2	no	—
391	C₂×C₄×C₁₇	—	2	1	no	—
392	C₂×C₄×C₁₇	—	2	2	no	—
393	C₂×C₄×C₁₇	—	2	1	no	—
394	C₂×C₄×C₁₇	—	2	1	no	—
395	C₂×C₄×C₁₇	—	4	4	no	—
396	C₂×C₄×C₁₇	—	4	4	no	—
397	C₂×C₄×C₁₇	—	4	4	no	—
398	C₂×C₄×C₁₇	—	4	1	no	—
399	C₂×C₄×C₁₇	—	4	1	no	—
400	C₂×C₄×C₁₇	—	4	1	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	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
411	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
412	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
413	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
414	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
415	C₈×C₁₇	—	2	2	no	—
416	C₈×C₁₇	—	2	2	no	—
417	C₈×C₁₇	—	4	1	no	—
418	C₈×C₁₇	—	4	1	no	—
419	C₈×C₁₇	—	4	1	no	—
420	C₈×C₁₇	#120	1	1	yes	characteristic
421	C₈×C₁₇	#120	1	1	yes	characteristic
422	C₈×C₁₇	#120	1	1	yes	characteristic
423	C₈×C₁₇	#120	1	1	yes	characteristic
424	C₂×#577	C₂×C₁₇	1	1	yes	characteristic, complemented
425	#3067	C₂×C₁₇	1	1	yes	characteristic, complemented
426	#3057	C₂×C₁₇	1	1	yes	characteristic, complemented
427	#3020	C₂×C₁₇	1	1	yes	characteristic, complemented
428	#3019	C₂×C₁₇	1	1	yes	characteristic, complemented
429	#2955	C₂×C₁₇	1	1	yes	characteristic, complemented
430	#2049	C₂×C₁₇	1	1	yes	characteristic, complemented
431	#2048	C₂×C₁₇	1	1	yes	characteristic, complemented
432	#2009	C₂×C₁₇	1	1	yes	characteristic, complemented
433	#2008	C₂×C₁₇	1	1	yes	characteristic, complemented
434	#1977	C₂×C₁₇	1	1	yes	characteristic, complemented
435	#1976	C₂×C₁₇	1	1	yes	characteristic, complemented
436	#1814	C₂×C₁₇	1	1	yes	characteristic, complemented
437	#1796	C₂×C₁₇	1	1	yes	characteristic, complemented
438	#1795	C₂×C₁₇	1	1	yes	characteristic, complemented
439	C₂²×C₁₇	—	2	2	no	—
440	C₂²×C₁₇	—	4	1	no	—
441	C₂²×C₁₇	—	4	2	no	—
442	C₂²×C₁₇	—	4	2	no	—
443	C₂²×C₁₇	—	4	1	no	—
444	C₂²×C₁₇	—	4	2	no	—
445	C₂²×C₁₇	—	4	1	no	—
446	C₂²×C₁₇	—	4	1	no	—
447	C₂²×C₁₇	—	8	2	no	—
448	C₂²×C₁₇	—	8	1	no	—
449	C₂²×C₁₇	—	8	1	no	—
450	C₂²×C₁₇	—	8	2	no	—
451	C₂²×C₁₇	—	16	1	no	—
452	C₂²×C₁₇	—	16	4	no	—
453	C₂²×C₁₇	#535	1	1	yes	characteristic
454	C₂²×C₁₇	D₄²	1	1	yes	characteristic
455	C₂²×C₁₇	#546	1	1	yes	characteristic
456	C₄×C₁₇	—	2	2	no	—
457	C₄×C₁₇	—	4	1	no	—
458	C₄×C₁₇	—	4	2	no	—
459	C₄×C₁₇	—	4	1	no	—
460	C₄×C₁₇	—	4	1	no	—
461	C₄×C₁₇	—	8	1	no	—
462	C₄×C₁₇	—	8	1	no	—
463	C₄×C₁₇	—	8	1	no	—
464	C₄×C₁₇	C₂×#120	1	1	yes	characteristic
465	C₄×C₁₇	C₂×#121	1	1	yes	characteristic
466	C₄×C₁₇	D₄²	1	1	yes	characteristic
467	C₄×C₁₇	#546	1	1	yes	characteristic
468	C₂×2₋¹⁺⁴	C₂²×C₁₇	1	1	yes	characteristic
469	C₂×H(5,𝔽₂)	C₂²×C₁₇	1	1	yes	characteristic
470	#577	—	2	2	no	—
471	#577	—	2	2	no	—
472	#577	—	2	2	no	—
473	#577	—	2	2	no	—
474	#575	C₂²×C₁₇	1	1	yes	characteristic
475	#575	C₂²×C₁₇	1	1	yes	characteristic
476	#575	C₂²×C₁₇	1	1	yes	characteristic, complemented
477	C₂×#137	—	2	1	no	—
478	C₂×#137	C₂²×C₁₇	1	1	yes	characteristic
479	C₂×AGL(1,ℤ/8)	—	2	1	no	—
480	C₂×AGL(1,ℤ/8)	C₂²×C₁₇	1	1	yes	characteristic
481	C₂×#135	—	2	1	no	—
482	C₂×#135	C₂²×C₁₇	1	1	yes	characteristic
483	C₂²×SD₁₆	—	2	1	no	—
484	C₂²×SD₁₆	C₂²×C₁₇	1	1	yes	characteristic
485	C₂×#131	C₂²×C₁₇	1	1	yes	characteristic
486	C₂×#131	C₂²×C₁₇	1	1	yes	characteristic, complemented
487	#536	C₂²×C₁₇	1	1	yes	characteristic, complemented
488	#535	C₂²×C₁₇	1	1	yes	characteristic
489	#473	—	2	1	no	—
490	#472	—	2	1	no	—
491	#471	—	2	1	no	—
492	#471	—	2	1	no	—
493	#468	—	2	2	no	—
494	#465	—	2	2	no	—
495	#456	—	2	2	no	—
496	#455	—	2	2	no	—
497	#454	—	2	2	no	—
498	#453	—	2	2	no	—
499	#444	—	2	2	no	—
500	#443	—	2	2	no	—
501	#430	C₂²×C₁₇	1	1	yes	characteristic, complemented
502	C₂×#108	C₂²×C₁₇	1	1	yes	characteristic, complemented
503	#427	C₂²×C₁₇	1	1	yes	characteristic, complemented
504	#421	C₂²×C₁₇	1	1	yes	characteristic
505	#421	C₂²×C₁₇	1	1	yes	characteristic
506	#421	C₂²×C₁₇	1	1	yes	characteristic
507	#421	C₂²×C₁₇	1	1	yes	characteristic
508	#421	C₂²×C₁₇	1	1	yes	characteristic, complemented
509	#421	C₂²×C₁₇	1	1	yes	characteristic, complemented
510	#419	C₂²×C₁₇	1	1	yes	characteristic, complemented
511	#419	C₂²×C₁₇	1	1	yes	characteristic, complemented
512	#418	C₂²×C₁₇	1	1	yes	characteristic
513	#418	C₂²×C₁₇	1	1	yes	characteristic
514	#413	C₂²×C₁₇	1	1	yes	characteristic
515	#413	C₂²×C₁₇	1	1	yes	characteristic, complemented
516	C₂×#101	C₂²×C₁₇	1	1	yes	characteristic, complemented
517	C₂×#100	C₂²×C₁₇	1	1	yes	characteristic
518	#410	C₂²×C₁₇	1	1	yes	characteristic
519	#410	C₂²×C₁₇	1	1	yes	characteristic, complemented
520	#405	C₂²×C₁₇	1	1	yes	characteristic, complemented
521	#344	C₂²×C₁₇	1	1	yes	characteristic, complemented
522	#344	C₂²×C₁₇	1	1	yes	characteristic, complemented
523	C₂×C₁₇	—	2	1	no	—
524	C₂×C₁₇	—	2	1	no	—
525	C₂×C₁₇	—	2	1	no	—
526	C₂×C₁₇	—	4	2	no	—
527	C₂×C₁₇	—	8	1	no	—
528	C₂×C₁₇	—	8	1	no	—
529	C₂×C₁₇	—	8	2	no	—
530	C₂×C₁₇	—	8	1	no	—
531	C₂×C₁₇	#2408	1	1	yes	characteristic
532	2₋¹⁺⁴	—	2	2	no	—
533	2₋¹⁺⁴	—	2	2	no	—
534	2₋¹⁺⁴	—	2	2	no	—
535	2₋¹⁺⁴	—	4	1	no	—
536	H(5,𝔽₂)	—	2	2	no	—
537	H(5,𝔽₂)	—	2	2	no	—
538	H(5,𝔽₂)	—	2	2	no	—
539	H(5,𝔽₂)	—	4	1	no	—
540	C₂×#41	—	2	1	no	—
541	C₂×#41	—	2	1	no	—
542	C₂×#41	—	2	1	no	—
543	C₂×#41	—	2	1	no	—
544	C₂×#41	—	4	1	no	—
545	C₂×#41	C₂³×C₁₇	1	1	yes	characteristic
546	C₂×#41	C₂³×C₁₇	1	1	yes	characteristic
547	C₂×#41	C₂³×C₁₇	1	1	yes	characteristic
548	C₂×#41	C₂³×C₁₇	1	1	yes	characteristic
549	C₂²×Q₈	—	2	1	no	—
550	C₂²×Q₈	—	2	1	no	—
551	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
552	C₂²×D₄	—	2	1	no	—
553	C₂²×D₄	—	2	1	no	—
554	C₂²×D₄	—	4	1	no	—
555	C₂²×D₄	C₂³×C₁₇	1	1	yes	characteristic
556	#137	—	2	4	no	—
557	#137	—	2	4	no	—
558	#137	—	2	2	no	—
559	#137	—	2	1	no	—
560	#137	—	2	1	no	—
561	#137	—	2	1	no	—
562	#137	—	2	1	no	—
563	#137	—	2	1	no	—
564	#137	—	2	2	no	—
565	#137	D₄×C₁₇	1	2	yes	—
566	AGL(1,ℤ/8)	—	2	4	no	—
567	AGL(1,ℤ/8)	—	2	4	no	—
568	AGL(1,ℤ/8)	—	2	2	no	—
569	AGL(1,ℤ/8)	—	2	1	no	—
570	AGL(1,ℤ/8)	—	2	1	no	—
571	AGL(1,ℤ/8)	—	2	1	no	—
572	AGL(1,ℤ/8)	—	2	1	no	—
573	AGL(1,ℤ/8)	—	2	1	no	—
574	AGL(1,ℤ/8)	—	2	2	no	—
575	AGL(1,ℤ/8)	D₄×C₁₇	1	2	yes	—
576	#135	—	2	4	no	—
577	#135	—	2	4	no	—
578	#135	—	2	2	no	—
579	#135	—	2	1	no	—
580	#135	—	2	1	no	—
581	#135	—	2	1	no	—
582	#135	—	2	1	no	—
583	#135	—	4	1	no	—
584	#135	—	4	1	no	—
585	C₂×Q₁₆	—	2	1	no	—
586	C₂×Q₁₆	D₄×C₁₇	1	1	yes	characteristic, complemented
587	C₂×SD₁₆	—	2	4	no	—
588	C₂×SD₁₆	—	2	4	no	—
589	C₂×SD₁₆	—	2	1	no	—
590	C₂×SD₁₆	—	2	1	no	—
591	C₂×SD₁₆	—	2	1	no	—
592	C₂×SD₁₆	—	2	1	no	—
593	C₂×SD₁₆	—	2	1	no	—
594	C₂×SD₁₆	—	2	1	no	—
595	C₂×SD₁₆	D₄×C₁₇	1	2	yes	—
596	C₂×SD₁₆	D₄×C₁₇	1	2	yes	—
597	C₂×SD₁₆	D₄×C₁₇	1	1	yes	characteristic, complemented
598	C₂×SD₁₆	D₄×C₁₇	1	1	yes	characteristic, complemented
599	C₂×D₈	—	2	1	no	—
600	C₂×D₈	D₄×C₁₇	1	1	yes	characteristic, complemented
601	#131	—	2	1	no	—
602	#131	—	2	1	no	—
603	#131	—	2	1	no	—
604	#131	—	2	1	no	—
605	#131	—	2	1	no	—
606	#131	—	2	1	no	—
607	#131	D₄×C₁₇	1	2	yes	complemented
608	#131	D₄×C₁₇	1	2	yes	complemented
609	C₂×M₁₆	—	2	1	no	—
610	C₂×M₁₆	—	2	1	no	—
611	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
612	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
613	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
614	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
615	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
616	C₂²×C₈	—	2	1	no	—
617	C₂²×C₈	—	2	1	no	—
618	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
619	C₄⋊Q₈	—	2	1	no	—
620	#127	—	2	1	no	—
621	#124	—	2	1	no	—
622	#124	—	2	1	no	—
623	#123	—	4	1	no	—
624	C₂²⋊Q₈	—	2	2	no	—
625	#121	—	2	2	no	—
626	#120	—	4	1	no	—
627	#117	C₂³×C₁₇	1	1	yes	characteristic
628	#117	C₂³×C₁₇	1	1	yes	characteristic
629	#117	C₂³×C₁₇	1	1	yes	characteristic
630	#108	—	2	2	no	—
631	#108	—	2	1	no	—
632	#108	—	2	1	no	—
633	#107	—	2	1	no	—
634	#106	—	2	1	no	—
635	#104	—	2	2	no	—
636	#104	—	2	2	no	—
637	#104	—	2	2	no	—
638	#104	—	2	2	no	—
639	#104	—	2	2	no	—
640	#104	—	2	2	no	—
641	#103	—	2	2	no	—
642	#103	—	4	1	no	—
643	#102	—	2	2	no	—
644	#102	—	4	1	no	—
645	#101	—	2	1	no	—
646	#101	—	2	1	no	—
647	#101	—	2	2	no	—
648	#100	—	2	1	no	—
649	#100	—	2	1	no	—
650	#100	—	2	2	no	—
651	#99	—	4	1	no	—
652	#99	—	4	1	no	—
653	#97	—	2	1	no	—
654	C₄×C₈	—	2	1	no	—
655	C₁₇	#24295	1	1	yes	characteristic, direct product factor, Sylow
656	C₂⁴	—	2	1	no	—
657	C₂⁴	—	4	1	no	—
658	#41	—	2	1	no	—
659	#41	—	2	1	no	—
660	#41	—	2	4	no	—
661	#41	—	2	4	no	—
662	#41	—	2	1	no	—
663	#41	—	2	1	no	—
664	#41	—	2	1	no	—
665	#41	—	2	1	no	—
666	#41	—	2	1	no	—
667	#41	—	2	1	no	—
668	#41	—	2	1	no	—
669	#41	—	2	1	no	—
670	#41	—	2	1	no	—
671	#41	—	2	1	no	—
672	#41	—	2	1	no	—
673	#41	—	2	1	no	—
674	#41	—	4	2	no	—
675	#41	—	4	4	no	—
676	#41	—	4	2	no	—
677	#41	—	4	2	no	—
678	#41	—	4	2	no	—
679	#41	—	4	4	no	—
680	#41	—	4	2	no	—
681	#41	—	4	2	no	—
682	#41	C₂×D₄×C₁₇	1	2	yes	—
683	#41	C₂×D₄×C₁₇	1	2	yes	—
684	C₂×Q₈	—	2	1	no	—
685	C₂×Q₈	—	2	4	no	—
686	C₂×Q₈	—	2	1	no	—
687	C₂×Q₈	—	2	1	no	—
688	C₂×Q₈	—	2	1	no	—
689	C₂×Q₈	—	2	1	no	—
690	C₂×Q₈	—	4	1	no	—
691	C₂×Q₈	—	4	2	no	—
692	C₂×Q₈	—	4	2	no	—
693	C₂×Q₈	—	4	2	no	—
694	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
695	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
696	C₂×Q₈	C₂×D₄×C₁₇	1	2	yes	—
697	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
698	C₂×Q₈	#41×C₁₇	1	1	yes	characteristic
699	C₂×D₄	—	2	1	no	—
700	C₂×D₄	—	2	4	no	—
701	C₂×D₄	—	2	1	no	—
702	C₂×D₄	—	2	1	no	—
703	C₂×D₄	—	2	1	no	—
704	C₂×D₄	—	2	1	no	—
705	C₂×D₄	—	2	1	no	—
706	C₂×D₄	—	2	1	no	—
707	C₂×D₄	—	2	1	no	—
708	C₂×D₄	—	2	1	no	—
709	C₂×D₄	—	4	2	no	—
710	C₂×D₄	—	4	1	no	—
711	C₂×D₄	—	4	1	no	—
712	C₂×D₄	—	4	2	no	—
713	C₂×D₄	—	4	4	no	—
714	C₂×D₄	—	4	4	no	—
715	C₂×D₄	—	4	1	no	—
716	C₂×D₄	—	4	2	no	—
717	C₂×D₄	—	4	2	no	—
718	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
719	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
720	C₂×D₄	C₂×D₄×C₁₇	1	2	yes	—
721	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
722	C₂×D₄	#41×C₁₇	1	1	yes	characteristic
723	C₂²×C₄	—	2	1	no	—
724	C₂²×C₄	—	2	1	no	—
725	C₂²×C₄	—	2	1	no	—
726	C₂²×C₄	—	2	1	no	—
727	C₂²×C₄	—	2	1	no	—
728	C₂²×C₄	—	4	1	no	—
729	C₂²×C₄	—	4	1	no	—
730	C₂²×C₄	—	4	1	no	—
731	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
732	Q₁₆	—	2	4	no	—
733	Q₁₆	—	2	2	no	—
734	Q₁₆	—	2	1	no	—
735	Q₁₆	—	2	1	no	—
736	Q₁₆	—	4	1	no	—
737	Q₁₆	—	4	1	no	—
738	SD₁₆	—	2	4	no	—
739	SD₁₆	—	2	4	no	—
740	SD₁₆	—	2	2	no	—
741	SD₁₆	—	2	2	no	—
742	SD₁₆	—	2	2	no	—
743	SD₁₆	—	2	2	no	—
744	SD₁₆	—	2	1	no	—
745	SD₁₆	—	2	1	no	—
746	SD₁₆	—	2	2	no	—
747	SD₁₆	—	2	2	no	—
748	SD₁₆	—	2	1	no	—
749	SD₁₆	—	2	1	no	—
750	SD₁₆	—	4	1	no	—
751	SD₁₆	—	4	1	no	—
752	SD₁₆	—	4	1	no	—
753	SD₁₆	—	4	1	no	—
754	D₈	—	2	4	no	—
755	D₈	—	2	2	no	—
756	D₈	—	2	1	no	—
757	D₈	—	2	1	no	—
758	D₈	—	4	1	no	—
759	D₈	—	4	1	no	—
760	M₁₆	—	2	1	no	—
761	M₁₆	—	2	1	no	—
762	M₁₆	—	2	2	no	—
763	M₁₆	—	2	2	no	—
764	M₁₆	—	2	1	no	—
765	M₁₆	—	2	1	no	—
766	M₁₆	—	2	1	no	—
767	M₁₆	—	2	1	no	—
768	M₁₆	—	2	1	no	—
769	M₁₆	—	2	1	no	—
770	M₁₆	—	4	1	no	—
771	M₁₆	—	4	1	no	—
772	M₁₆	C₂×D₄×C₁₇	1	2	yes	—
773	M₁₆	C₂×D₄×C₁₇	1	2	yes	—
774	C₂×C₈	—	2	1	no	—
775	C₂×C₈	—	2	1	no	—
776	C₂×C₈	—	2	2	no	—
777	C₂×C₈	—	2	2	no	—
778	C₂×C₈	—	2	1	no	—
779	C₂×C₈	—	2	1	no	—
780	C₂×C₈	—	2	1	no	—
781	C₂×C₈	—	4	1	no	—
782	C₂×C₈	—	4	1	no	—
783	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
784	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
785	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
786	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
787	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
788	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
789	C₄⋊C₄	—	2	1	no	—
790	C₄⋊C₄	—	2	1	no	—
791	C₄⋊C₄	—	2	1	no	—
792	C₄⋊C₄	—	4	2	no	—
793	C₂²⋊C₄	—	2	1	no	—
794	C₂²⋊C₄	—	2	1	no	—
795	C₂²⋊C₄	—	2	1	no	—
796	C₂²⋊C₄	—	4	2	no	—
797	C₂²⋊C₄	—	4	2	no	—
798	C₄²	—	2	1	no	—
799	C₄²	—	2	1	no	—
800	C₄²	—	2	1	no	—
801	C₂³	—	2	1	no	—
802	C₂³	—	2	1	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	1	no	—
805	C₂³	—	2	1	no	—
806	C₂³	—	4	4	no	—
807	C₂³	—	4	1	no	—
808	C₂³	—	4	1	no	—
809	C₂³	—	16	1	no	—
810	C₂³	—	16	2	no	—
811	C₂³	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
812	Q₈	—	2	1	no	—
813	Q₈	—	2	1	no	—
814	Q₈	—	2	2	no	—
815	Q₈	—	2	1	no	—
816	Q₈	—	2	1	no	—
817	Q₈	—	2	1	no	—
818	Q₈	—	2	1	no	—
819	Q₈	—	2	1	no	—
820	Q₈	—	2	2	no	—
821	Q₈	—	4	4	no	—
822	Q₈	—	4	1	no	—
823	Q₈	—	4	1	no	—
824	Q₈	C₁₇×#121	1	2	yes	—
825	D₄	—	2	2	no	—
826	D₄	—	2	2	no	—
827	D₄	—	2	1	no	—
828	D₄	—	2	2	no	—
829	D₄	—	2	1	no	—
830	D₄	—	2	1	no	—
831	D₄	—	2	1	no	—
832	D₄	—	2	1	no	—
833	D₄	—	2	1	no	—
834	D₄	—	2	1	no	—
835	D₄	—	2	2	no	—
836	D₄	—	4	4	no	—
837	D₄	—	4	4	no	—
838	D₄	—	4	4	no	—
839	D₄	—	4	1	no	—
840	D₄	—	4	1	no	—
841	D₄	—	4	1	no	—
842	D₄	—	4	1	no	—
843	D₄	—	4	1	no	—
844	D₄	—	4	1	no	—
845	D₄	—	4	1	no	—
846	D₄	—	4	1	no	—
847	D₄	—	16	2	no	—
848	D₄	C₁₇×#121	1	2	yes	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	4	4	no	—
857	C₂×C₄	—	4	4	no	—
858	C₂×C₄	—	4	4	no	—
859	C₂×C₄	—	4	1	no	—
860	C₂×C₄	—	4	1	no	—
861	C₂×C₄	—	4	1	no	—
862	C₂×C₄	—	4	1	no	—
863	C₂×C₄	—	4	1	no	—
864	C₂×C₄	—	4	1	no	—
865	C₂×C₄	—	4	1	no	—
866	C₂×C₄	—	4	1	no	—
867	C₂×C₄	—	4	1	no	—
868	C₂×C₄	—	4	1	no	—
869	C₂×C₄	—	4	1	no	—
870	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
871	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
872	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
873	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
874	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
875	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
876	C₈	—	2	2	no	—
877	C₈	—	2	2	no	—
878	C₈	—	4	1	no	—
879	C₈	—	4	1	no	—
880	C₈	—	4	1	no	—
881	C₈	C₁₇×#120	1	1	yes	characteristic
882	C₈	C₁₇×#120	1	1	yes	characteristic
883	C₈	C₁₇×#120	1	1	yes	characteristic
884	C₈	C₁₇×#120	1	1	yes	characteristic
885	C₂²	—	2	2	no	—
886	C₂²	—	4	1	no	—
887	C₂²	—	4	2	no	—
888	C₂²	—	4	2	no	—
889	C₂²	—	4	1	no	—
890	C₂²	—	4	2	no	—
891	C₂²	—	4	1	no	—
892	C₂²	—	4	1	no	—
893	C₂²	—	8	2	no	—
894	C₂²	—	8	1	no	—
895	C₂²	—	8	1	no	—
896	C₂²	—	8	2	no	—
897	C₂²	—	16	1	no	—
898	C₂²	—	16	4	no	—
899	C₂²	C₁₇×#535	1	1	yes	characteristic
900	C₂²	D₄²×C₁₇	1	1	yes	characteristic
901	C₂²	C₁₇×#546	1	1	yes	characteristic
902	C₄	—	2	2	no	—
903	C₄	—	4	1	no	—
904	C₄	—	4	2	no	—
905	C₄	—	4	1	no	—
906	C₄	—	4	1	no	—
907	C₄	—	8	1	no	—
908	C₄	—	8	1	no	—
909	C₄	—	8	1	no	—
910	C₄	C₂×C₁₇×#120	1	1	yes	characteristic
911	C₄	C₂×C₁₇×#121	1	1	yes	characteristic
912	C₄	D₄²×C₁₇	1	1	yes	characteristic
913	C₄	C₁₇×#546	1	1	yes	characteristic
914	C₂	—	2	1	no	—
915	C₂	—	2	1	no	—
916	C₂	—	2	1	no	—
917	C₂	—	4	2	no	—
918	C₂	—	8	1	no	—
919	C₂	—	8	2	no	—
920	C₂	—	8	1	no	—
921	C₂	—	8	1	no	—
922	C₂	C₁₇×#2408	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₇	#2408
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₇
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₇×#577	C₂	semidirect
2. C₁₇×#3067	C₂	semidirect
3. C₁₇×#3057	C₂	semidirect
4. C₁₇×#3020	C₂	semidirect
5. C₁₇×#3019	C₂	semidirect
6. C₁₇×#2955	C₂	semidirect
7. C₁₇×#2049	C₂	semidirect
8. C₁₇×#2048	C₂	semidirect
9. C₁₇×#2009	C₂	semidirect
10. C₁₇×#2008	C₂	semidirect
11. C₁₇×#1977	C₂	semidirect
12. C₁₇×#1976	C₂	semidirect
13. C₁₇×#1814	C₂	semidirect
14. C₁₇×#1796	C₂	semidirect
15. C₁₇×#1795	C₂	semidirect
24. C₁₇×#575	C₂²	semidirect
34. C₂×C₁₇×#131	C₂²	semidirect
35. C₁₇×#536	C₂²	semidirect
49. C₁₇×#430	C₂²	semidirect
50. C₂×C₁₇×#108	C₂²	semidirect
51. C₁₇×#427	C₂²	semidirect
56. C₁₇×#421	C₂²	semidirect
57. C₁₇×#421	C₂²	semidirect
58. C₁₇×#419	C₂²	semidirect
59. C₁₇×#419	C₂²	semidirect
63. C₁₇×#413	C₂²	semidirect
64. C₂×C₁₇×#101	C₂²	semidirect
67. C₁₇×#410	C₂²	semidirect
68. C₁₇×#405	C₂²	semidirect
69. C₁₇×#344	C₂²	semidirect
70. C₁₇×#344	C₂²	semidirect
125. C₂×Q₁₆×C₁₇	D₄	semidirect
136. C₂×SD₁₆×C₁₇	D₄	semidirect
137. C₂×SD₁₆×C₁₇	D₄	semidirect
139. C₂×D₈×C₁₇	D₄	semidirect
146. C₁₇×#131	D₄	semidirect
147. C₁₇×#131	D₄	semidirect
339. #24295	C₁₇	direct (N × H)
424. C₂×#577	C₂×C₁₇	semidirect
425. #3067	C₂×C₁₇	semidirect
426. #3057	C₂×C₁₇	semidirect
427. #3020	C₂×C₁₇	semidirect
428. #3019	C₂×C₁₇	semidirect
429. #2955	C₂×C₁₇	semidirect
430. #2049	C₂×C₁₇	semidirect
431. #2048	C₂×C₁₇	semidirect
432. #2009	C₂×C₁₇	semidirect
433. #2008	C₂×C₁₇	semidirect
434. #1977	C₂×C₁₇	semidirect
435. #1976	C₂×C₁₇	semidirect
436. #1814	C₂×C₁₇	semidirect
437. #1796	C₂×C₁₇	semidirect
438. #1795	C₂×C₁₇	semidirect
476. #575	C₂²×C₁₇	semidirect
486. C₂×#131	C₂²×C₁₇	semidirect
487. #536	C₂²×C₁₇	semidirect
501. #430	C₂²×C₁₇	semidirect
502. C₂×#108	C₂²×C₁₇	semidirect
503. #427	C₂²×C₁₇	semidirect
508. #421	C₂²×C₁₇	semidirect
509. #421	C₂²×C₁₇	semidirect
510. #419	C₂²×C₁₇	semidirect
511. #419	C₂²×C₁₇	semidirect
515. #413	C₂²×C₁₇	semidirect
516. C₂×#101	C₂²×C₁₇	semidirect
519. #410	C₂²×C₁₇	semidirect
520. #405	C₂²×C₁₇	semidirect
521. #344	C₂²×C₁₇	semidirect
522. #344	C₂²×C₁₇	semidirect
586. C₂×Q₁₆	D₄×C₁₇	semidirect
597. C₂×SD₁₆	D₄×C₁₇	semidirect
598. C₂×SD₁₆	D₄×C₁₇	semidirect
600. C₂×D₈	D₄×C₁₇	semidirect
607. #131	D₄×C₁₇	semidirect
608. #131	D₄×C₁₇	semidirect
655. C₁₇	#24295	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×#577	2
C₁₇×#3067	2
C₁₇×#3057	2
C₁₇×#3020	2
C₁₇×#3019	2
C₁₇×#2955	2
C₁₇×#2049	2
C₁₇×#2048	2
C₁₇×#2009	2
C₁₇×#2008	2
C₁₇×#1977	2
C₁₇×#1976	2
C₁₇×#1814	2
C₁₇×#1796	2
C₁₇×#1795	2
#24295	17

Subgroups — C17×#24295 #16882039

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#24295 #16882039