Subgroups — C₁₇×#61553 #16919297

Order 4352.

1886 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3520	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇×#3514	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#3394	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×D₈×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#3373	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#3367	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#3357	C₂	1	2	yes	maximal, complemented
8	C₁₇×#3353	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#3319	C₂	1	2	yes	maximal, complemented
10	C₁₇×#3314	C₂	1	2	yes	maximal, complemented
11	C₁₇×#3302	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#3294	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₇×#3273	C₂	1	2	yes	maximal, complemented
14	C₁₇×#3272	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#3182	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₇×#3175	C₂	1	2	yes	maximal, complemented
17	C₁₇×#3124	C₂	1	2	yes	maximal, complemented
18	C₁₇×#3118	C₂	1	2	yes	maximal, complemented
19	C₁₇×#3107	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₇×#3100	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₇×#2969	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₇×#2946	C₂	1	2	yes	maximal, complemented
23	C₄×C₁₇×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₇×AGL(1,ℤ/8)	C₂²	1	2	yes	—
25	C₂×C₁₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
26	C₁₇×#559	C₂²	1	1	yes	characteristic, complemented
27	C₁₇×#556	C₂²	1	1	yes	characteristic, complemented
28	C₁₇×#556	C₂²	1	1	yes	characteristic, complemented
29	C₁₇×#555	C₂²	1	2	yes	—
30	C₁₇×#554	C₂²	1	2	yes	complemented
31	C₁₇×#552	—	2	1	no	—
32	C₁₇×#551	—	2	2	no	—
33	C₁₇×#551	—	2	2	no	—
34	D₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
35	D₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
36	C₁₇×#548	—	2	1	no	—
37	C₁₇×#548	—	2	1	no	—
38	C₁₇×#547	C₂²	1	1	yes	characteristic
39	C₁₇×#547	C₂²	1	1	yes	characteristic
40	C₁₇×#546	—	2	1	no	—
41	C₁₇×#546	C₂²	1	2	yes	—
42	C₁₇×#546	C₂²	1	2	yes	complemented
43	D₄²×C₁₇	C₂²	1	1	yes	characteristic, complemented
44	C₁₇×#542	C₂²	1	2	yes	complemented
45	C₁₇×#542	C₂²	1	2	yes	complemented
46	C₁₇×#539	—	2	2	no	—
47	C₁₇×#538	—	2	2	no	—
48	C₁₇×#533	C₂²	1	1	yes	characteristic, complemented
49	C₁₇×#532	C₂²	1	1	yes	characteristic
50	C₁₇×#529	—	2	1	no	—
51	C₁₇×#529	C₂²	1	1	yes	characteristic
52	C₂×C₁₇×#124	—	2	1	no	—
53	C₁₇×#525	—	2	1	no	—
54	C₂×C₁₇×C₂²⋊Q₈	—	2	1	no	—
55	C₁₇×#520	C₂²	1	2	yes	complemented
56	C₁₇×#518	C₂²	1	2	yes	complemented
57	C₄×#41×C₁₇	C₂²	1	1	yes	characteristic
58	C₂×C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
59	C₁₇×#500	C₂²	1	1	yes	characteristic, complemented
60	C₁₇×#500	C₂²	1	2	yes	complemented
61	C₁₇×#495	C₂²	1	2	yes	complemented
62	C₁₇×#492	C₂²	1	1	yes	characteristic, complemented
63	C₁₇×#489	C₂²	1	2	yes	complemented
64	C₁₇×#489	C₂²	1	2	yes	complemented
65	C₁₇×#487	C₂²	1	1	yes	characteristic, complemented
66	C₁₇×#486	C₂²	1	1	yes	characteristic, complemented
67	C₁₇×#485	C₂²	1	2	yes	complemented
68	C₁₇×#485	C₂²	1	2	yes	complemented
69	C₁₇×#484	C₂²	1	2	yes	complemented
70	C₁₇×#482	C₂²	1	2	yes	complemented
71	C₁₇×#480	C₂²	1	2	yes	complemented
72	C₁₇×#480	C₂²	1	2	yes	complemented
73	C₁₇×#477	C₂²	1	2	yes	complemented
74	C₁₇×#476	C₂²	1	2	yes	complemented
75	C₁₇×#475	C₂²	1	1	yes	characteristic, complemented
76	C₁₇×#474	C₂²	1	1	yes	characteristic, complemented
77	C₁₇×#474	C₂²	1	1	yes	characteristic, complemented
78	C₁₇×#474	C₂²	1	2	yes	complemented
79	C₁₇×#474	C₂²	1	2	yes	complemented
80	C₁₇×#474	C₂²	1	1	yes	characteristic, complemented
81	C₁₇×#468	C₂²	1	2	yes	complemented
82	C₁₇×#468	C₂²	1	2	yes	complemented
83	C₁₇×#468	C₂²	1	2	yes	complemented
84	C₁₇×#468	C₂²	1	2	yes	complemented
85	C₁₇×#467	C₂²	1	2	yes	complemented
86	C₁₇×#466	C₂²	1	2	yes	—
87	C₁₇×#464	C₂²	1	2	yes	complemented
88	C₁₇×#463	C₂²	1	2	yes	—
89	C₁₇×#463	C₂²	1	2	yes	complemented
90	C₁₇×#463	C₂²	1	2	yes	complemented
91	C₁₇×#462	C₂²	1	1	yes	characteristic, complemented
92	C₁₇×#461	C₂²	1	1	yes	characteristic, complemented
93	C₁₇×#459	C₂²	1	1	yes	characteristic
94	C₁₇×#459	C₂²	1	1	yes	characteristic
95	C₁₇×#452	C₂²	1	2	yes	—
96	C₁₇×#452	C₂²	1	2	yes	complemented
97	C₁₇×#450	C₂²	1	2	yes	complemented
98	C₁₇×#449	C₂²	1	2	yes	—
99	C₁₇×#447	C₂²	1	2	yes	—
100	C₁₇×#447	C₂²	1	2	yes	complemented
101	C₁₇×#446	C₂²	1	1	yes	characteristic, complemented
102	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
103	C₁₇×#442	C₂²	1	1	yes	characteristic
104	C₁₇×#442	C₂²	1	1	yes	characteristic
105	C₁₇×#442	C₂²	1	2	yes	complemented
106	C₁₇×#440	C₂²	1	2	yes	complemented
107	C₁₇×#440	C₂²	1	2	yes	complemented
108	C₁₇×#440	C₂²	1	2	yes	complemented
109	C₁₇×#440	C₂²	1	1	yes	characteristic, complemented
110	C₁₇×#440	C₂²	1	1	yes	characteristic, complemented
111	C₄×Q₁₆×C₁₇	C₂²	1	2	yes	complemented
112	C₄×SD₁₆×C₁₇	C₂²	1	2	yes	complemented
113	C₄×SD₁₆×C₁₇	C₂²	1	2	yes	complemented
114	C₄×SD₁₆×C₁₇	C₂²	1	1	yes	characteristic, complemented
115	C₄×SD₁₆×C₁₇	C₂²	1	1	yes	characteristic, complemented
116	C₄×D₈×C₁₇	C₂²	1	2	yes	—
117	C₄×D₈×C₁₇	C₂²	1	1	yes	characteristic
118	C₄×D₈×C₁₇	C₂²	1	1	yes	characteristic
119	C₄×D₈×C₁₇	C₂²	1	2	yes	complemented
120	C₄×D₈×C₁₇	C₂²	1	2	yes	complemented
121	C₁₇×#436	C₂²	1	1	yes	characteristic, complemented
122	C₁₇×#436	C₂²	1	2	yes	complemented
123	C₁₇×#435	C₂²	1	2	yes	complemented
124	C₈×D₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
125	C₁₇×#433	C₂²	1	2	yes	complemented
126	C₁₇×#431	C₂²	1	1	yes	characteristic, complemented
127	C₁₇×#428	C₂²	1	2	yes	complemented
128	C₁₇×#428	C₂²	1	1	yes	characteristic, complemented
129	C₁₇×#418	C₂²	1	1	yes	characteristic, complemented
130	C₁₇×#417	C₂²	1	1	yes	characteristic
131	C₁₇×#416	C₂²	1	2	yes	complemented
132	C₂×C₁₇×#102	C₂²	1	2	yes	complemented
133	C₁₇×#405	C₂²	1	2	yes	complemented
134	C₄×M₁₆×C₁₇	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₁₇	—	2	1	no	—
136	C₂×#41×C₁₇	—	2	1	no	—
137	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
138	C₂×#41×C₁₇	C₂³	1	2	yes	—
139	C₂²×Q₈×C₁₇	—	2	1	no	—
140	C₂²×Q₈×C₁₇	—	2	1	no	—
141	C₂²×D₄×C₁₇	—	2	1	no	—
142	C₂²×D₄×C₁₇	C₂³	1	1	yes	characteristic
143	C₂²×D₄×C₁₇	C₂³	1	2	yes	—
144	C₂³×C₄×C₁₇	—	2	1	no	—
145	C₁₇×AGL(1,ℤ/8)	—	2	8	no	—
146	C₁₇×AGL(1,ℤ/8)	—	2	4	no	—
147	C₂×Q₁₆×C₁₇	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₁₇	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₁₇	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₁₇	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₁₇	C₂³	1	1	yes	characteristic
152	C₂×SD₁₆×C₁₇	C₂³	1	2	yes	—
153	C₂×D₈×C₁₇	C₂³	1	1	yes	characteristic
154	C₂×D₈×C₁₇	C₂³	1	2	yes	—
155	C₂×D₈×C₁₇	C₂³	1	2	yes	—
156	C₂×D₈×C₁₇	C₂³	1	1	yes	characteristic
157	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
158	C₂×M₁₆×C₁₇	C₂³	1	2	yes	—
159	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
160	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
161	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
165	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
166	C₁₇×#127	C₂³	1	1	yes	characteristic
167	C₁₇×#126	—	2	2	no	—
168	C₁₇×#126	—	2	2	no	—
169	C₁₇×#126	—	2	2	no	—
170	C₁₇×#126	—	2	2	no	—
171	C₁₇×#126	D₄	1	2	yes	—
172	C₁₇×#125	—	2	2	no	—
173	C₁₇×#125	—	2	1	no	—
174	C₁₇×#125	D₄	1	1	yes	characteristic
175	C₁₇×#124	—	2	1	no	—
176	C₁₇×#124	—	2	1	no	—
177	C₁₇×#124	—	2	2	no	—
178	C₁₇×#124	—	2	2	no	—
179	C₁₇×#124	—	2	2	no	—
180	C₁₇×#124	—	2	2	no	—
181	C₁₇×#124	—	2	1	no	—
182	C₁₇×#124	D₄	1	1	yes	characteristic
183	C₁₇×#124	C₂³	1	2	yes	—
184	C₁₇×#124	C₂³	1	2	yes	—
185	C₁₇×#123	—	2	2	no	—
186	C₁₇×#123	—	2	2	no	—
187	C₁₇×#123	—	2	2	no	—
188	C₁₇×#123	—	2	2	no	—
189	C₁₇×#123	—	2	2	no	—
190	C₁₇×#123	—	2	2	no	—
191	C₁₇×#123	—	2	2	no	—
192	C₁₇×#123	D₄	1	2	yes	—
193	C₁₇×C₂²⋊Q₈	—	2	1	no	—
194	C₁₇×C₂²⋊Q₈	—	2	1	no	—
195	C₁₇×C₂²⋊Q₈	—	2	2	no	—
196	C₁₇×C₂²⋊Q₈	—	2	1	no	—
197	C₁₇×C₂²⋊Q₈	—	2	1	no	—
198	C₁₇×C₂²⋊Q₈	—	2	1	no	—
199	C₁₇×C₂²⋊Q₈	—	2	2	no	—
200	C₁₇×C₂²⋊Q₈	—	2	2	no	—
201	C₁₇×C₂²⋊Q₈	—	2	2	no	—
202	C₁₇×C₂²⋊Q₈	—	2	2	no	—
203	C₁₇×C₂²⋊Q₈	—	2	2	no	—
204	C₁₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
205	C₁₇×C₂²⋊Q₈	C₂³	1	2	yes	—
206	C₁₇×C₂²⋊Q₈	C₂³	1	2	yes	—
207	C₁₇×C₂²⋊Q₈	C₂³	1	2	yes	—
208	C₁₇×#121	—	2	1	no	—
209	C₁₇×#121	—	2	2	no	—
210	C₁₇×#121	—	2	1	no	—
211	C₁₇×#121	—	2	1	no	—
212	C₁₇×#121	—	2	2	no	—
213	C₁₇×#121	—	2	2	no	—
214	C₁₇×#121	D₄	1	1	yes	characteristic
215	C₁₇×#121	C₂³	1	2	yes	—
216	C₁₇×#121	C₂³	1	2	yes	—
217	C₁₇×#121	C₂³	1	2	yes	—
218	C₁₇×#120	—	2	2	no	—
219	C₁₇×#120	—	2	2	no	—
220	C₁₇×#120	—	2	2	no	—
221	C₄×Q₈×C₁₇	—	2	1	no	—
222	C₄×Q₈×C₁₇	—	2	1	no	—
223	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
224	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
226	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
227	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
228	C₄×D₄×C₁₇	—	2	2	no	—
229	C₄×D₄×C₁₇	—	2	1	no	—
230	C₄×D₄×C₁₇	—	2	1	no	—
231	C₄×D₄×C₁₇	—	2	2	no	—
232	C₄×D₄×C₁₇	—	2	2	no	—
233	C₄×D₄×C₁₇	—	2	1	no	—
234	C₄×D₄×C₁₇	—	2	2	no	—
235	C₄×D₄×C₁₇	—	2	2	no	—
236	C₄×D₄×C₁₇	—	2	1	no	—
237	C₄×D₄×C₁₇	—	2	1	no	—
238	C₄×D₄×C₁₇	—	2	1	no	—
239	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₁₇	C₂³	1	2	yes	—
246	C₄×D₄×C₁₇	C₂³	1	2	yes	—
247	C₄×D₄×C₁₇	C₂³	1	2	yes	—
248	C₄×D₄×C₁₇	C₂³	1	2	yes	—
249	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₁₇	C₂³	1	2	yes	—
251	C₁₇×#117	—	2	1	no	—
252	C₁₇×#117	—	2	2	no	—
253	C₁₇×#117	—	2	1	no	—
254	C₁₇×#117	—	2	2	no	—
255	C₁₇×#117	—	2	1	no	—
256	C₁₇×#117	C₂³	1	1	yes	characteristic
257	C₁₇×#117	C₂³	1	2	yes	—
258	C₁₇×#117	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
260	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
261	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
263	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
264	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
265	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
266	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
267	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
268	C₂×C₄²×C₁₇	—	2	1	no	—
269	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
270	C₁₇×#107	C₂³	1	1	yes	characteristic
271	C₁₇×#107	C₂³	1	2	yes	—
272	C₁₇×#107	C₂³	1	2	yes	—
273	C₁₇×#107	C₂³	1	2	yes	—
274	C₁₇×#107	C₂³	1	2	yes	—
275	C₁₇×#107	C₂³	1	1	yes	characteristic
276	C₁₇×#107	C₂³	1	2	yes	—
277	C₁₇×#106	C₂³	1	1	yes	characteristic
278	C₁₇×#106	C₂³	1	1	yes	characteristic
279	C₁₇×#106	C₂³	1	2	yes	—
280	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
283	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
284	C₁₇×#103	C₂³	1	2	yes	—
285	C₁₇×#103	C₂³	1	2	yes	—
286	C₁₇×#103	C₂³	1	1	yes	characteristic
287	C₁₇×#103	C₂³	1	1	yes	characteristic
288	C₁₇×#103	C₂³	1	2	yes	—
289	C₁₇×#103	C₂³	1	2	yes	—
290	C₁₇×#103	C₂³	1	2	yes	—
291	C₁₇×#102	C₂³	1	1	yes	characteristic
292	C₁₇×#102	C₂³	1	2	yes	—
293	C₁₇×#102	C₂³	1	2	yes	—
294	C₁₇×#102	C₂³	1	2	yes	—
295	C₁₇×#102	C₂³	1	1	yes	characteristic
296	C₁₇×#102	C₂³	1	2	yes	—
297	C₁₇×#102	C₂³	1	1	yes	characteristic
298	C₁₇×#102	C₂³	1	1	yes	characteristic
299	C₁₇×#102	C₂³	1	1	yes	characteristic
300	C₁₇×#102	C₂³	1	1	yes	characteristic
301	C₁₇×#102	C₂³	1	2	yes	—
302	C₁₇×#102	C₂³	1	2	yes	—
303	C₁₇×#102	C₂³	1	2	yes	—
304	C₁₇×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₁₇×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₁₇×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₁₇×#97	C₂³	1	1	yes	characteristic
308	C₁₇×#97	C₂³	1	1	yes	characteristic
309	C₁₇×#97	C₂³	1	2	yes	—
310	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₁₇	C₂³	1	2	yes	—
312	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₁₇	C₂³	1	2	yes	—
314	C₂⁴×C₁₇	—	2	1	no	—
315	C₂⁴×C₁₇	—	2	2	no	—
316	#41×C₁₇	—	2	4	no	—
317	#41×C₁₇	—	2	2	no	—
318	#41×C₁₇	—	4	2	no	—
319	#41×C₁₇	—	4	1	no	—
320	#41×C₁₇	—	8	2	no	—
321	#41×C₁₇	—	8	2	no	—
322	C₂×Q₈×C₁₇	—	2	1	no	—
323	C₂×Q₈×C₁₇	—	2	1	no	—
324	C₂×Q₈×C₁₇	—	2	2	no	—
325	C₂×Q₈×C₁₇	—	2	2	no	—
326	C₂×Q₈×C₁₇	—	8	2	no	—
327	C₂×Q₈×C₁₇	—	8	2	no	—
328	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
329	C₂×Q₈×C₁₇	C₂⁴	1	1	yes	characteristic
330	C₂×Q₈×C₁₇	C₂⁴	1	2	yes	—
331	C₂×D₄×C₁₇	—	2	2	no	—
332	C₂×D₄×C₁₇	—	2	4	no	—
333	C₂×D₄×C₁₇	—	2	2	no	—
334	C₂×D₄×C₁₇	—	2	1	no	—
335	C₂×D₄×C₁₇	—	2	2	no	—
336	C₂×D₄×C₁₇	—	2	2	no	—
337	C₂×D₄×C₁₇	—	2	2	no	—
338	C₂×D₄×C₁₇	—	2	1	no	—
339	C₂×D₄×C₁₇	—	2	2	no	—
340	C₂×D₄×C₁₇	—	2	1	no	—
341	C₂×D₄×C₁₇	—	2	1	no	—
342	C₂×D₄×C₁₇	—	4	2	no	—
343	C₂×D₄×C₁₇	—	4	1	no	—
344	C₂×D₄×C₁₇	—	8	2	no	—
345	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
346	C₂×D₄×C₁₇	C₂×D₄	1	2	yes	—
347	C₂×D₄×C₁₇	C₂⁴	1	1	yes	characteristic
348	C₂×D₄×C₁₇	C₂⁴	1	2	yes	—
349	C₂×D₄×C₁₇	C₂⁴	1	1	yes	characteristic
350	C₂×D₄×C₁₇	C₂⁴	1	1	yes	characteristic
351	C₂²×C₄×C₁₇	—	2	1	no	—
352	C₂²×C₄×C₁₇	—	2	2	no	—
353	C₂²×C₄×C₁₇	—	2	1	no	—
354	C₂²×C₄×C₁₇	—	2	1	no	—
355	C₂²×C₄×C₁₇	—	2	1	no	—
356	C₂²×C₄×C₁₇	—	2	1	no	—
357	C₂²×C₄×C₁₇	—	2	2	no	—
358	C₂²×C₄×C₁₇	—	2	1	no	—
359	C₂²×C₄×C₁₇	—	2	2	no	—
360	C₂²×C₄×C₁₇	—	2	2	no	—
361	C₂²×C₄×C₁₇	—	2	2	no	—
362	C₂²×C₄×C₁₇	—	2	2	no	—
363	C₂²×C₄×C₁₇	—	2	1	no	—
364	C₂²×C₄×C₁₇	—	2	1	no	—
365	C₂²×C₄×C₁₇	—	8	2	no	—
366	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
367	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
368	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
369	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
370	Q₁₆×C₁₇	—	4	2	no	—
371	SD₁₆×C₁₇	—	2	2	no	—
372	SD₁₆×C₁₇	—	2	4	no	—
373	SD₁₆×C₁₇	—	2	4	no	—
374	SD₁₆×C₁₇	—	2	2	no	—
375	SD₁₆×C₁₇	—	4	2	no	—
376	D₈×C₁₇	—	2	4	no	—
377	D₈×C₁₇	—	2	2	no	—
378	D₈×C₁₇	—	4	2	no	—
379	D₈×C₁₇	#41	1	4	yes	complemented
380	M₁₆×C₁₇	—	2	2	no	—
381	M₁₆×C₁₇	—	2	4	no	—
382	M₁₆×C₁₇	—	4	1	no	—
383	C₂×C₈×C₁₇	—	4	2	no	—
384	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
386	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
387	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
388	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
389	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
390	C₄⋊C₄×C₁₇	—	2	2	no	—
391	C₄⋊C₄×C₁₇	—	2	2	no	—
392	C₄⋊C₄×C₁₇	—	2	1	no	—
393	C₄⋊C₄×C₁₇	—	2	1	no	—
394	C₄⋊C₄×C₁₇	—	2	2	no	—
395	C₄⋊C₄×C₁₇	—	2	2	no	—
396	C₄⋊C₄×C₁₇	—	2	2	no	—
397	C₄⋊C₄×C₁₇	—	2	2	no	—
398	C₄⋊C₄×C₁₇	—	2	1	no	—
399	C₄⋊C₄×C₁₇	—	2	1	no	—
400	C₄⋊C₄×C₁₇	—	2	1	no	—
401	C₄⋊C₄×C₁₇	—	2	2	no	—
402	C₄⋊C₄×C₁₇	—	2	2	no	—
403	C₄⋊C₄×C₁₇	—	2	1	no	—
404	C₄⋊C₄×C₁₇	—	2	1	no	—
405	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
406	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
407	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
408	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
409	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
411	C₄⋊C₄×C₁₇	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
413	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
414	C₄⋊C₄×C₁₇	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄×C₁₇	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄×C₁₇	C₂⁴	1	1	yes	characteristic
417	C₂²⋊C₄×C₁₇	—	2	2	no	—
418	C₂²⋊C₄×C₁₇	—	2	2	no	—
419	C₂²⋊C₄×C₁₇	—	2	2	no	—
420	C₂²⋊C₄×C₁₇	—	2	2	no	—
421	C₂²⋊C₄×C₁₇	—	2	1	no	—
422	C₂²⋊C₄×C₁₇	—	2	2	no	—
423	C₂²⋊C₄×C₁₇	—	2	1	no	—
424	C₂²⋊C₄×C₁₇	—	2	2	no	—
425	C₂²⋊C₄×C₁₇	—	2	2	no	—
426	C₂²⋊C₄×C₁₇	—	2	2	no	—
427	C₂²⋊C₄×C₁₇	—	2	1	no	—
428	C₂²⋊C₄×C₁₇	—	2	2	no	—
429	C₂²⋊C₄×C₁₇	—	2	2	no	—
430	C₂²⋊C₄×C₁₇	—	2	2	no	—
431	C₂²⋊C₄×C₁₇	—	2	2	no	—
432	C₂²⋊C₄×C₁₇	—	2	1	no	—
433	C₂²⋊C₄×C₁₇	—	2	2	no	—
434	C₂²⋊C₄×C₁₇	—	2	2	no	—
435	C₂²⋊C₄×C₁₇	—	2	1	no	—
436	C₂²⋊C₄×C₁₇	—	2	2	no	—
437	C₂²⋊C₄×C₁₇	—	2	1	no	—
438	C₂²⋊C₄×C₁₇	—	2	1	no	—
439	C₂²⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
440	C₂²⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
441	C₂²⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
442	C₂²⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
443	C₂²⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
444	C₄²×C₁₇	—	2	1	no	—
445	C₄²×C₁₇	—	2	1	no	—
446	C₄²×C₁₇	—	2	1	no	—
447	C₄²×C₁₇	—	2	2	no	—
448	C₄²×C₁₇	—	2	2	no	—
449	C₄²×C₁₇	—	2	2	no	—
450	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
451	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
452	C₄²×C₁₇	C₂⁴	1	2	yes	—
453	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
454	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
455	#61553	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
456	C₂³×C₁₇	—	2	1	no	—
457	C₂³×C₁₇	—	2	1	no	—
458	C₂³×C₁₇	—	2	1	no	—
459	C₂³×C₁₇	—	2	2	no	—
460	C₂³×C₁₇	—	4	2	no	—
461	C₂³×C₁₇	—	4	4	no	—
462	C₂³×C₁₇	—	4	2	no	—
463	C₂³×C₁₇	—	8	1	no	—
464	C₂³×C₁₇	—	8	2	no	—
465	C₂³×C₁₇	—	8	2	no	—
466	C₂³×C₁₇	C₂²×D₄	1	2	yes	—
467	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
468	Q₈×C₁₇	—	2	2	no	—
469	Q₈×C₁₇	—	2	1	no	—
470	Q₈×C₁₇	—	2	2	no	—
471	Q₈×C₁₇	—	2	2	no	—
472	Q₈×C₁₇	—	2	1	no	—
473	Q₈×C₁₇	—	4	2	no	—
474	Q₈×C₁₇	—	4	2	no	—
475	Q₈×C₁₇	—	8	2	no	—
476	Q₈×C₁₇	—	8	2	no	—
477	D₄×C₁₇	—	2	2	no	—
478	D₄×C₁₇	—	2	1	no	—
479	D₄×C₁₇	—	2	2	no	—
480	D₄×C₁₇	—	2	1	no	—
481	D₄×C₁₇	—	2	1	no	—
482	D₄×C₁₇	—	2	1	no	—
483	D₄×C₁₇	—	2	2	no	—
484	D₄×C₁₇	—	4	2	no	—
485	D₄×C₁₇	—	4	2	no	—
486	D₄×C₁₇	—	4	4	no	—
487	D₄×C₁₇	—	4	4	no	—
488	D₄×C₁₇	—	4	2	no	—
489	D₄×C₁₇	—	4	2	no	—
490	D₄×C₁₇	—	8	1	no	—
491	D₄×C₁₇	—	8	2	no	—
492	D₄×C₁₇	—	8	2	no	—
493	D₄×C₁₇	—	8	2	no	—
494	D₄×C₁₇	C₂×#41	1	2	yes	—
495	D₄×C₁₇	C₂×#41	1	2	yes	—
496	C₂×C₄×C₁₇	—	2	2	no	—
497	C₂×C₄×C₁₇	—	2	2	no	—
498	C₂×C₄×C₁₇	—	2	1	no	—
499	C₂×C₄×C₁₇	—	2	2	no	—
500	C₂×C₄×C₁₇	—	2	1	no	—
501	C₂×C₄×C₁₇	—	2	1	no	—
502	C₂×C₄×C₁₇	—	2	1	no	—
503	C₂×C₄×C₁₇	—	2	2	no	—
504	C₂×C₄×C₁₇	—	2	1	no	—
505	C₂×C₄×C₁₇	—	2	1	no	—
506	C₂×C₄×C₁₇	—	2	2	no	—
507	C₂×C₄×C₁₇	—	2	2	no	—
508	C₂×C₄×C₁₇	—	2	1	no	—
509	C₂×C₄×C₁₇	—	4	1	no	—
510	C₂×C₄×C₁₇	—	4	4	no	—
511	C₂×C₄×C₁₇	—	4	2	no	—
512	C₂×C₄×C₁₇	—	4	2	no	—
513	C₂×C₄×C₁₇	—	4	2	no	—
514	C₂×C₄×C₁₇	—	4	2	no	—
515	C₂×C₄×C₁₇	—	8	1	no	—
516	C₂×C₄×C₁₇	—	8	2	no	—
517	C₂×C₄×C₁₇	—	8	1	no	—
518	C₂×C₄×C₁₇	—	8	1	no	—
519	C₂×C₄×C₁₇	—	8	2	no	—
520	C₂×C₄×C₁₇	—	8	2	no	—
521	C₂×C₄×C₁₇	—	8	2	no	—
522	C₂×C₄×C₁₇	—	8	1	no	—
523	C₂×C₄×C₁₇	—	8	2	no	—
524	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
527	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
528	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
531	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
532	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
533	C₈×C₁₇	—	2	1	no	—
534	C₈×C₁₇	—	2	2	no	—
535	C₈×C₁₇	—	2	1	no	—
536	C₈×C₁₇	—	2	2	no	—
537	C₈×C₁₇	—	2	1	no	—
538	C₈×C₁₇	C₂×#41	1	2	yes	—
539	#3520	C₂×C₁₇	1	1	yes	characteristic, complemented
540	#3514	C₂×C₁₇	1	1	yes	characteristic, complemented
541	#3394	C₂×C₁₇	1	1	yes	characteristic, complemented
542	Q₈×D₈	C₂×C₁₇	1	1	yes	characteristic, complemented
543	#3373	C₂×C₁₇	1	1	yes	characteristic, complemented
544	#3367	C₂×C₁₇	1	1	yes	characteristic, complemented
545	#3357	C₂×C₁₇	1	2	yes	complemented
546	#3353	C₂×C₁₇	1	1	yes	characteristic, complemented
547	#3319	C₂×C₁₇	1	2	yes	complemented
548	#3314	C₂×C₁₇	1	2	yes	complemented
549	#3302	C₂×C₁₇	1	1	yes	characteristic, complemented
550	#3294	C₂×C₁₇	1	1	yes	characteristic, complemented
551	#3273	C₂×C₁₇	1	2	yes	complemented
552	#3272	C₂×C₁₇	1	1	yes	characteristic, complemented
553	#3182	C₂×C₁₇	1	1	yes	characteristic, complemented
554	#3175	C₂×C₁₇	1	2	yes	complemented
555	#3124	C₂×C₁₇	1	2	yes	complemented
556	#3118	C₂×C₁₇	1	2	yes	complemented
557	#3107	C₂×C₁₇	1	1	yes	characteristic, complemented
558	#3100	C₂×C₁₇	1	1	yes	characteristic, complemented
559	#2969	C₂×C₁₇	1	1	yes	characteristic, complemented
560	#2946	C₂×C₁₇	1	2	yes	complemented
561	C₄×AGL(1,ℤ/8)	C₂×C₁₇	1	1	yes	characteristic, complemented
562	C₂²×C₁₇	—	2	1	no	—
563	C₂²×C₁₇	—	2	2	no	—
564	C₂²×C₁₇	—	2	1	no	—
565	C₂²×C₁₇	—	2	2	no	—
566	C₂²×C₁₇	—	2	2	no	—
567	C₂²×C₁₇	—	2	2	no	—
568	C₂²×C₁₇	—	2	1	no	—
569	C₂²×C₁₇	—	2	2	no	—
570	C₂²×C₁₇	—	4	1	no	—
571	C₂²×C₁₇	—	4	1	no	—
572	C₂²×C₁₇	—	4	1	no	—
573	C₂²×C₁₇	—	4	1	no	—
574	C₂²×C₁₇	—	4	2	no	—
575	C₂²×C₁₇	—	4	1	no	—
576	C₂²×C₁₇	—	4	1	no	—
577	C₂²×C₁₇	—	4	2	no	—
578	C₂²×C₁₇	—	4	1	no	—
579	C₂²×C₁₇	—	4	2	no	—
580	C₂²×C₁₇	—	8	4	no	—
581	C₂²×C₁₇	—	16	4	no	—
582	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
583	C₄×C₁₇	—	2	1	no	—
584	C₄×C₁₇	—	2	1	no	—
585	C₄×C₁₇	—	2	2	no	—
586	C₄×C₁₇	—	2	2	no	—
587	C₄×C₁₇	—	2	1	no	—
588	C₄×C₁₇	—	2	1	no	—
589	C₄×C₁₇	—	2	2	no	—
590	C₄×C₁₇	—	4	1	no	—
591	C₄×C₁₇	—	4	1	no	—
592	C₄×C₁₇	—	4	2	no	—
593	C₄×C₁₇	—	4	1	no	—
594	C₄×C₁₇	—	4	1	no	—
595	C₄×C₁₇	—	4	1	no	—
596	C₄×C₁₇	—	4	2	no	—
597	C₄×C₁₇	—	4	2	no	—
598	C₄×C₁₇	#576	1	2	yes	—
599	C₄×C₁₇	C₂²×#41	1	1	yes	characteristic
600	C₄×C₁₇	#585	1	1	yes	characteristic
601	C₂×AGL(1,ℤ/8)	C₂²×C₁₇	1	1	yes	characteristic
602	C₂×AGL(1,ℤ/8)	C₂²×C₁₇	1	2	yes	—
603	#559	C₂²×C₁₇	1	1	yes	characteristic, complemented
604	#556	C₂²×C₁₇	1	1	yes	characteristic, complemented
605	#556	C₂²×C₁₇	1	1	yes	characteristic, complemented
606	#555	C₂²×C₁₇	1	2	yes	—
607	#554	C₂²×C₁₇	1	2	yes	complemented
608	#552	—	2	1	no	—
609	#551	—	2	2	no	—
610	#551	—	2	2	no	—
611	D₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic, complemented
612	D₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic, complemented
613	#548	—	2	1	no	—
614	#548	—	2	1	no	—
615	#547	C₂²×C₁₇	1	1	yes	characteristic
616	#547	C₂²×C₁₇	1	1	yes	characteristic
617	#546	—	2	1	no	—
618	#546	C₂²×C₁₇	1	2	yes	—
619	#546	C₂²×C₁₇	1	2	yes	complemented
620	D₄²	C₂²×C₁₇	1	1	yes	characteristic, complemented
621	#542	C₂²×C₁₇	1	2	yes	complemented
622	#542	C₂²×C₁₇	1	2	yes	complemented
623	#539	—	2	2	no	—
624	#538	—	2	2	no	—
625	#533	C₂²×C₁₇	1	1	yes	characteristic, complemented
626	#532	C₂²×C₁₇	1	1	yes	characteristic
627	#529	—	2	1	no	—
628	#529	C₂²×C₁₇	1	1	yes	characteristic
629	C₂×#124	—	2	1	no	—
630	#525	—	2	1	no	—
631	C₂×C₂²⋊Q₈	—	2	1	no	—
632	#520	C₂²×C₁₇	1	2	yes	complemented
633	#518	C₂²×C₁₇	1	2	yes	complemented
634	C₄×#41	C₂²×C₁₇	1	1	yes	characteristic
635	C₂×C₄×D₄	C₂²×C₁₇	1	1	yes	characteristic, complemented
636	#500	C₂²×C₁₇	1	1	yes	characteristic, complemented
637	#500	C₂²×C₁₇	1	2	yes	complemented
638	#495	C₂²×C₁₇	1	2	yes	complemented
639	#492	C₂²×C₁₇	1	1	yes	characteristic, complemented
640	#489	C₂²×C₁₇	1	2	yes	complemented
641	#489	C₂²×C₁₇	1	2	yes	complemented
642	#487	C₂²×C₁₇	1	1	yes	characteristic, complemented
643	#486	C₂²×C₁₇	1	1	yes	characteristic, complemented
644	#485	C₂²×C₁₇	1	2	yes	complemented
645	#485	C₂²×C₁₇	1	2	yes	complemented
646	#484	C₂²×C₁₇	1	2	yes	complemented
647	#482	C₂²×C₁₇	1	2	yes	complemented
648	#480	C₂²×C₁₇	1	2	yes	complemented
649	#480	C₂²×C₁₇	1	2	yes	complemented
650	#477	C₂²×C₁₇	1	2	yes	complemented
651	#476	C₂²×C₁₇	1	2	yes	complemented
652	#475	C₂²×C₁₇	1	1	yes	characteristic, complemented
653	#474	C₂²×C₁₇	1	1	yes	characteristic, complemented
654	#474	C₂²×C₁₇	1	1	yes	characteristic, complemented
655	#474	C₂²×C₁₇	1	1	yes	characteristic, complemented
656	#474	C₂²×C₁₇	1	2	yes	complemented
657	#474	C₂²×C₁₇	1	2	yes	complemented
658	#468	C₂²×C₁₇	1	2	yes	complemented
659	#468	C₂²×C₁₇	1	2	yes	complemented
660	#468	C₂²×C₁₇	1	2	yes	complemented
661	#468	C₂²×C₁₇	1	2	yes	complemented
662	#467	C₂²×C₁₇	1	2	yes	complemented
663	#466	C₂²×C₁₇	1	2	yes	—
664	#464	C₂²×C₁₇	1	2	yes	complemented
665	#463	C₂²×C₁₇	1	2	yes	—
666	#463	C₂²×C₁₇	1	2	yes	complemented
667	#463	C₂²×C₁₇	1	2	yes	complemented
668	#462	C₂²×C₁₇	1	1	yes	characteristic, complemented
669	#461	C₂²×C₁₇	1	1	yes	characteristic, complemented
670	#459	C₂²×C₁₇	1	1	yes	characteristic
671	#459	C₂²×C₁₇	1	1	yes	characteristic
672	#452	C₂²×C₁₇	1	2	yes	—
673	#452	C₂²×C₁₇	1	2	yes	complemented
674	#450	C₂²×C₁₇	1	2	yes	complemented
675	#449	C₂²×C₁₇	1	2	yes	—
676	#447	C₂²×C₁₇	1	2	yes	—
677	#447	C₂²×C₁₇	1	2	yes	complemented
678	#446	C₂²×C₁₇	1	1	yes	characteristic, complemented
679	C₈×Q₈	C₂²×C₁₇	1	1	yes	characteristic, complemented
680	#442	C₂²×C₁₇	1	1	yes	characteristic
681	#442	C₂²×C₁₇	1	1	yes	characteristic
682	#442	C₂²×C₁₇	1	2	yes	complemented
683	#440	C₂²×C₁₇	1	2	yes	complemented
684	#440	C₂²×C₁₇	1	2	yes	complemented
685	#440	C₂²×C₁₇	1	1	yes	characteristic, complemented
686	#440	C₂²×C₁₇	1	1	yes	characteristic, complemented
687	#440	C₂²×C₁₇	1	2	yes	complemented
688	C₄×Q₁₆	C₂²×C₁₇	1	2	yes	complemented
689	C₄×SD₁₆	C₂²×C₁₇	1	1	yes	characteristic, complemented
690	C₄×SD₁₆	C₂²×C₁₇	1	2	yes	complemented
691	C₄×SD₁₆	C₂²×C₁₇	1	2	yes	complemented
692	C₄×SD₁₆	C₂²×C₁₇	1	1	yes	characteristic, complemented
693	C₄×D₈	C₂²×C₁₇	1	1	yes	characteristic
694	C₄×D₈	C₂²×C₁₇	1	1	yes	characteristic
695	C₄×D₈	C₂²×C₁₇	1	2	yes	—
696	C₄×D₈	C₂²×C₁₇	1	2	yes	complemented
697	C₄×D₈	C₂²×C₁₇	1	2	yes	complemented
698	#436	C₂²×C₁₇	1	1	yes	characteristic, complemented
699	#436	C₂²×C₁₇	1	2	yes	complemented
700	#435	C₂²×C₁₇	1	2	yes	complemented
701	C₈×D₄	C₂²×C₁₇	1	1	yes	characteristic, complemented
702	#433	C₂²×C₁₇	1	2	yes	complemented
703	#431	C₂²×C₁₇	1	1	yes	characteristic, complemented
704	#428	C₂²×C₁₇	1	2	yes	complemented
705	#428	C₂²×C₁₇	1	1	yes	characteristic, complemented
706	#418	C₂²×C₁₇	1	1	yes	characteristic, complemented
707	#417	C₂²×C₁₇	1	1	yes	characteristic
708	#416	C₂²×C₁₇	1	2	yes	complemented
709	C₂×#102	C₂²×C₁₇	1	2	yes	complemented
710	#405	C₂²×C₁₇	1	2	yes	complemented
711	C₄×M₁₆	C₂²×C₁₇	1	1	yes	characteristic, complemented
712	C₂×C₁₇	—	4	1	no	—
713	C₂×C₁₇	—	4	2	no	—
714	C₂×C₁₇	—	4	2	no	—
715	C₂×C₁₇	—	4	2	no	—
716	C₂×C₁₇	—	8	1	no	—
717	C₂×C₁₇	—	8	2	no	—
718	C₂×C₁₇	D₄×#41	1	1	yes	characteristic
719	C₂×C₁₇	C₂×#576	1	1	yes	characteristic
720	C₂×C₁₇	#3586	1	1	yes	characteristic
721	C₂×#41	—	2	1	no	—
722	C₂×#41	—	2	1	no	—
723	C₂×#41	C₂³×C₁₇	1	1	yes	characteristic
724	C₂×#41	C₂³×C₁₇	1	2	yes	—
725	C₂²×Q₈	—	2	1	no	—
726	C₂²×Q₈	—	2	1	no	—
727	C₂²×D₄	—	2	1	no	—
728	C₂²×D₄	C₂³×C₁₇	1	1	yes	characteristic
729	C₂²×D₄	C₂³×C₁₇	1	2	yes	—
730	C₂³×C₄	—	2	1	no	—
731	AGL(1,ℤ/8)	—	2	4	no	—
732	AGL(1,ℤ/8)	—	2	8	no	—
733	C₂×Q₁₆	C₂³×C₁₇	1	2	yes	—
734	C₂×SD₁₆	C₂³×C₁₇	1	2	yes	—
735	C₂×SD₁₆	C₂³×C₁₇	1	1	yes	characteristic
736	C₂×SD₁₆	C₂³×C₁₇	1	2	yes	—
737	C₂×SD₁₆	C₂³×C₁₇	1	1	yes	characteristic
738	C₂×SD₁₆	C₂³×C₁₇	1	2	yes	—
739	C₂×D₈	C₂³×C₁₇	1	1	yes	characteristic
740	C₂×D₈	C₂³×C₁₇	1	2	yes	—
741	C₂×D₈	C₂³×C₁₇	1	2	yes	—
742	C₂×D₈	C₂³×C₁₇	1	1	yes	characteristic
743	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
744	C₂×M₁₆	C₂³×C₁₇	1	2	yes	—
745	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
746	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
747	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
748	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
749	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
750	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
751	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
752	#127	C₂³×C₁₇	1	1	yes	characteristic
753	#126	—	2	2	no	—
754	#126	—	2	2	no	—
755	#126	—	2	2	no	—
756	#126	—	2	2	no	—
757	#126	D₄×C₁₇	1	2	yes	—
758	#125	—	2	2	no	—
759	#125	—	2	1	no	—
760	#125	D₄×C₁₇	1	1	yes	characteristic
761	#124	—	2	1	no	—
762	#124	—	2	1	no	—
763	#124	—	2	2	no	—
764	#124	—	2	2	no	—
765	#124	—	2	2	no	—
766	#124	—	2	2	no	—
767	#124	—	2	1	no	—
768	#124	D₄×C₁₇	1	1	yes	characteristic
769	#124	C₂³×C₁₇	1	2	yes	—
770	#124	C₂³×C₁₇	1	2	yes	—
771	#123	—	2	2	no	—
772	#123	—	2	2	no	—
773	#123	—	2	2	no	—
774	#123	—	2	2	no	—
775	#123	—	2	2	no	—
776	#123	—	2	2	no	—
777	#123	—	2	2	no	—
778	#123	D₄×C₁₇	1	2	yes	—
779	C₂²⋊Q₈	—	2	1	no	—
780	C₂²⋊Q₈	—	2	1	no	—
781	C₂²⋊Q₈	—	2	2	no	—
782	C₂²⋊Q₈	—	2	1	no	—
783	C₂²⋊Q₈	—	2	1	no	—
784	C₂²⋊Q₈	—	2	1	no	—
785	C₂²⋊Q₈	—	2	2	no	—
786	C₂²⋊Q₈	—	2	2	no	—
787	C₂²⋊Q₈	—	2	2	no	—
788	C₂²⋊Q₈	—	2	2	no	—
789	C₂²⋊Q₈	—	2	2	no	—
790	C₂²⋊Q₈	D₄×C₁₇	1	1	yes	characteristic
791	C₂²⋊Q₈	C₂³×C₁₇	1	2	yes	—
792	C₂²⋊Q₈	C₂³×C₁₇	1	2	yes	—
793	C₂²⋊Q₈	C₂³×C₁₇	1	2	yes	—
794	#121	—	2	1	no	—
795	#121	—	2	2	no	—
796	#121	—	2	1	no	—
797	#121	—	2	1	no	—
798	#121	—	2	2	no	—
799	#121	—	2	2	no	—
800	#121	D₄×C₁₇	1	1	yes	characteristic
801	#121	C₂³×C₁₇	1	2	yes	—
802	#121	C₂³×C₁₇	1	2	yes	—
803	#121	C₂³×C₁₇	1	2	yes	—
804	#120	—	2	2	no	—
805	#120	—	2	2	no	—
806	#120	—	2	2	no	—
807	C₄×Q₈	—	2	1	no	—
808	C₄×Q₈	—	2	1	no	—
809	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
810	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
811	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
812	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
813	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
814	C₄×D₄	—	2	2	no	—
815	C₄×D₄	—	2	1	no	—
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	—	2	2	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	1	no	—
820	C₄×D₄	—	2	2	no	—
821	C₄×D₄	—	2	2	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	1	no	—
825	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
826	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
827	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
828	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
829	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
830	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
831	C₄×D₄	C₂³×C₁₇	1	2	yes	—
832	C₄×D₄	C₂³×C₁₇	1	2	yes	—
833	C₄×D₄	C₂³×C₁₇	1	2	yes	—
834	C₄×D₄	C₂³×C₁₇	1	2	yes	—
835	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
836	C₄×D₄	C₂³×C₁₇	1	2	yes	—
837	#117	—	2	1	no	—
838	#117	—	2	2	no	—
839	#117	—	2	1	no	—
840	#117	—	2	2	no	—
841	#117	—	2	1	no	—
842	#117	C₂³×C₁₇	1	1	yes	characteristic
843	#117	C₂³×C₁₇	1	2	yes	—
844	#117	C₂³×C₁₇	1	2	yes	—
845	C₂×C₄⋊C₄	—	2	2	no	—
846	C₂×C₄⋊C₄	—	2	1	no	—
847	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
848	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
849	C₂×C₂²⋊C₄	—	2	1	no	—
850	C₂×C₂²⋊C₄	—	2	2	no	—
851	C₂×C₂²⋊C₄	—	2	2	no	—
852	C₂×C₂²⋊C₄	—	2	2	no	—
853	C₂×C₂²⋊C₄	—	2	2	no	—
854	C₂×C₄²	—	2	1	no	—
855	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
856	#107	C₂³×C₁₇	1	1	yes	characteristic
857	#107	C₂³×C₁₇	1	2	yes	—
858	#107	C₂³×C₁₇	1	1	yes	characteristic
859	#107	C₂³×C₁₇	1	2	yes	—
860	#107	C₂³×C₁₇	1	2	yes	—
861	#107	C₂³×C₁₇	1	2	yes	—
862	#107	C₂³×C₁₇	1	2	yes	—
863	#106	C₂³×C₁₇	1	1	yes	characteristic
864	#106	C₂³×C₁₇	1	1	yes	characteristic
865	#106	C₂³×C₁₇	1	2	yes	—
866	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
867	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
868	C₄⋊C₈	C₂³×C₁₇	1	2	yes	—
869	C₄⋊C₈	C₂³×C₁₇	1	2	yes	—
870	#103	C₂³×C₁₇	1	2	yes	—
871	#103	C₂³×C₁₇	1	2	yes	—
872	#103	C₂³×C₁₇	1	1	yes	characteristic
873	#103	C₂³×C₁₇	1	1	yes	characteristic
874	#103	C₂³×C₁₇	1	2	yes	—
875	#103	C₂³×C₁₇	1	2	yes	—
876	#103	C₂³×C₁₇	1	2	yes	—
877	#102	C₂³×C₁₇	1	1	yes	characteristic
878	#102	C₂³×C₁₇	1	2	yes	—
879	#102	C₂³×C₁₇	1	2	yes	—
880	#102	C₂³×C₁₇	1	2	yes	—
881	#102	C₂³×C₁₇	1	1	yes	characteristic
882	#102	C₂³×C₁₇	1	2	yes	—
883	#102	C₂³×C₁₇	1	1	yes	characteristic
884	#102	C₂³×C₁₇	1	1	yes	characteristic
885	#102	C₂³×C₁₇	1	1	yes	characteristic
886	#102	C₂³×C₁₇	1	1	yes	characteristic
887	#102	C₂³×C₁₇	1	2	yes	—
888	#102	C₂³×C₁₇	1	2	yes	—
889	#102	C₂³×C₁₇	1	2	yes	—
890	C₂²⋊C₈	C₂³×C₁₇	1	2	yes	—
891	C₂²⋊C₈	C₂³×C₁₇	1	2	yes	—
892	C₂²⋊C₈	C₂³×C₁₇	1	2	yes	—
893	#97	C₂³×C₁₇	1	1	yes	characteristic
894	#97	C₂³×C₁₇	1	1	yes	characteristic
895	#97	C₂³×C₁₇	1	2	yes	—
896	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
897	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
898	C₄×C₈	C₂³×C₁₇	1	2	yes	—
899	C₄×C₈	C₂³×C₁₇	1	2	yes	—
900	C₁₇	#61553	1	1	yes	characteristic, direct product factor, Sylow
901	C₂⁴	—	2	1	no	—
902	C₂⁴	—	2	2	no	—
903	#41	—	2	4	no	—
904	#41	—	2	2	no	—
905	#41	—	4	2	no	—
906	#41	—	4	1	no	—
907	#41	—	8	2	no	—
908	#41	—	8	2	no	—
909	C₂×Q₈	—	2	1	no	—
910	C₂×Q₈	—	2	1	no	—
911	C₂×Q₈	—	2	2	no	—
912	C₂×Q₈	—	2	2	no	—
913	C₂×Q₈	—	8	2	no	—
914	C₂×Q₈	—	8	2	no	—
915	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
916	C₂×Q₈	C₂⁴×C₁₇	1	1	yes	characteristic
917	C₂×Q₈	C₂⁴×C₁₇	1	2	yes	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	4	no	—
920	C₂×D₄	—	2	1	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	1	no	—
927	C₂×D₄	—	2	1	no	—
928	C₂×D₄	—	2	1	no	—
929	C₂×D₄	—	4	2	no	—
930	C₂×D₄	—	4	1	no	—
931	C₂×D₄	—	8	2	no	—
932	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
933	C₂×D₄	C₂×D₄×C₁₇	1	2	yes	—
934	C₂×D₄	C₂⁴×C₁₇	1	1	yes	characteristic
935	C₂×D₄	C₂⁴×C₁₇	1	2	yes	—
936	C₂×D₄	C₂⁴×C₁₇	1	1	yes	characteristic
937	C₂×D₄	C₂⁴×C₁₇	1	1	yes	characteristic
938	C₂²×C₄	—	2	1	no	—
939	C₂²×C₄	—	2	2	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	1	no	—
942	C₂²×C₄	—	2	2	no	—
943	C₂²×C₄	—	2	1	no	—
944	C₂²×C₄	—	2	1	no	—
945	C₂²×C₄	—	2	1	no	—
946	C₂²×C₄	—	2	2	no	—
947	C₂²×C₄	—	2	2	no	—
948	C₂²×C₄	—	2	2	no	—
949	C₂²×C₄	—	2	2	no	—
950	C₂²×C₄	—	2	1	no	—
951	C₂²×C₄	—	2	1	no	—
952	C₂²×C₄	—	8	2	no	—
953	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
954	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
955	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
956	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
957	Q₁₆	—	4	2	no	—
958	SD₁₆	—	2	2	no	—
959	SD₁₆	—	2	4	no	—
960	SD₁₆	—	2	4	no	—
961	SD₁₆	—	2	2	no	—
962	SD₁₆	—	4	2	no	—
963	D₈	—	2	4	no	—
964	D₈	—	2	2	no	—
965	D₈	—	4	2	no	—
966	D₈	#41×C₁₇	1	4	yes	complemented
967	M₁₆	—	2	2	no	—
968	M₁₆	—	2	4	no	—
969	M₁₆	—	4	1	no	—
970	C₂×C₈	—	4	2	no	—
971	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
972	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
973	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
974	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
975	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
976	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	1	no	—
987	C₄⋊C₄	—	2	1	no	—
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	2	no	—
991	C₄⋊C₄	—	2	2	no	—
992	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
993	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
994	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
995	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
996	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
997	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
998	C₄⋊C₄	C₂⁴×C₁₇	1	1	yes	characteristic
999	C₄⋊C₄	C₂⁴×C₁₇	1	1	yes	characteristic
1000	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
1001	C₄⋊C₄	C₂⁴×C₁₇	1	1	yes	characteristic
1002	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
1003	C₄⋊C₄	C₂⁴×C₁₇	1	1	yes	characteristic
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	1	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	1	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
1027	C₂²⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
1028	C₂²⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
1029	C₂²⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
1030	C₂²⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
1031	C₄²	—	2	1	no	—
1032	C₄²	—	2	1	no	—
1033	C₄²	—	2	1	no	—
1034	C₄²	—	2	2	no	—
1035	C₄²	—	2	2	no	—
1036	C₄²	—	2	2	no	—
1037	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
1038	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
1039	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
1040	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
1041	C₄²	C₂⁴×C₁₇	1	2	yes	—
1042	C₂³	—	2	1	no	—
1043	C₂³	—	2	1	no	—
1044	C₂³	—	2	1	no	—
1045	C₂³	—	2	2	no	—
1046	C₂³	—	4	2	no	—
1047	C₂³	—	4	4	no	—
1048	C₂³	—	4	2	no	—
1049	C₂³	—	8	1	no	—
1050	C₂³	—	8	2	no	—
1051	C₂³	—	8	2	no	—
1052	C₂³	C₂²×D₄×C₁₇	1	2	yes	—
1053	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
1054	Q₈	—	2	2	no	—
1055	Q₈	—	2	1	no	—
1056	Q₈	—	2	2	no	—
1057	Q₈	—	2	2	no	—
1058	Q₈	—	2	1	no	—
1059	Q₈	—	4	2	no	—
1060	Q₈	—	4	2	no	—
1061	Q₈	—	8	2	no	—
1062	Q₈	—	8	2	no	—
1063	D₄	—	2	2	no	—
1064	D₄	—	2	1	no	—
1065	D₄	—	2	2	no	—
1066	D₄	—	2	1	no	—
1067	D₄	—	2	1	no	—
1068	D₄	—	2	1	no	—
1069	D₄	—	2	2	no	—
1070	D₄	—	4	2	no	—
1071	D₄	—	4	2	no	—
1072	D₄	—	4	4	no	—
1073	D₄	—	4	4	no	—
1074	D₄	—	4	2	no	—
1075	D₄	—	4	2	no	—
1076	D₄	—	8	1	no	—
1077	D₄	—	8	2	no	—
1078	D₄	—	8	2	no	—
1079	D₄	—	8	2	no	—
1080	D₄	C₂×#41×C₁₇	1	2	yes	—
1081	D₄	C₂×#41×C₁₇	1	2	yes	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	2	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	4	1	no	—
1096	C₂×C₄	—	4	4	no	—
1097	C₂×C₄	—	4	2	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	2	no	—
1100	C₂×C₄	—	4	2	no	—
1101	C₂×C₄	—	8	1	no	—
1102	C₂×C₄	—	8	1	no	—
1103	C₂×C₄	—	8	2	no	—
1104	C₂×C₄	—	8	2	no	—
1105	C₂×C₄	—	8	2	no	—
1106	C₂×C₄	—	8	1	no	—
1107	C₂×C₄	—	8	2	no	—
1108	C₂×C₄	—	8	1	no	—
1109	C₂×C₄	—	8	2	no	—
1110	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
1111	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
1112	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
1113	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
1114	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
1115	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
1116	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
1117	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
1118	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
1119	C₈	—	2	1	no	—
1120	C₈	—	2	2	no	—
1121	C₈	—	2	1	no	—
1122	C₈	—	2	2	no	—
1123	C₈	—	2	1	no	—
1124	C₈	C₂×#41×C₁₇	1	2	yes	—
1125	C₂²	—	2	1	no	—
1126	C₂²	—	2	2	no	—
1127	C₂²	—	2	2	no	—
1128	C₂²	—	2	2	no	—
1129	C₂²	—	2	1	no	—
1130	C₂²	—	2	2	no	—
1131	C₂²	—	2	1	no	—
1132	C₂²	—	2	2	no	—
1133	C₂²	—	4	1	no	—
1134	C₂²	—	4	1	no	—
1135	C₂²	—	4	1	no	—
1136	C₂²	—	4	1	no	—
1137	C₂²	—	4	1	no	—
1138	C₂²	—	4	2	no	—
1139	C₂²	—	4	1	no	—
1140	C₂²	—	4	2	no	—
1141	C₂²	—	4	2	no	—
1142	C₂²	—	4	1	no	—
1143	C₂²	—	8	4	no	—
1144	C₂²	—	16	4	no	—
1145	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
1146	C₄	—	2	2	no	—
1147	C₄	—	2	1	no	—
1148	C₄	—	2	1	no	—
1149	C₄	—	2	2	no	—
1150	C₄	—	2	1	no	—
1151	C₄	—	2	1	no	—
1152	C₄	—	2	2	no	—
1153	C₄	—	4	1	no	—
1154	C₄	—	4	2	no	—
1155	C₄	—	4	1	no	—
1156	C₄	—	4	1	no	—
1157	C₄	—	4	1	no	—
1158	C₄	—	4	2	no	—
1159	C₄	—	4	2	no	—
1160	C₄	—	4	1	no	—
1161	C₄	C₁₇×#576	1	2	yes	—
1162	C₄	C₂²×#41×C₁₇	1	1	yes	characteristic
1163	C₄	C₁₇×#585	1	1	yes	characteristic
1164	C₂	—	4	1	no	—
1165	C₂	—	4	2	no	—
1166	C₂	—	4	2	no	—
1167	C₂	—	4	2	no	—
1168	C₂	—	8	1	no	—
1169	C₂	—	8	2	no	—
1170	C₂	D₄×#41×C₁₇	1	1	yes	characteristic
1171	C₂	C₂×C₁₇×#576	1	1	yes	characteristic
1172	C₂	C₁₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₁₇×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₇×#3520	C₂	semidirect
2. C₁₇×#3514	C₂	semidirect
3. C₁₇×#3394	C₂	semidirect
4. Q₈×D₈×C₁₇	C₂	semidirect
5. C₁₇×#3373	C₂	semidirect
6. C₁₇×#3367	C₂	semidirect
7. C₁₇×#3357	C₂	semidirect
8. C₁₇×#3353	C₂	semidirect
9. C₁₇×#3319	C₂	semidirect
10. C₁₇×#3314	C₂	semidirect
11. C₁₇×#3302	C₂	semidirect
12. C₁₇×#3294	C₂	semidirect
13. C₁₇×#3273	C₂	semidirect
14. C₁₇×#3272	C₂	semidirect
15. C₁₇×#3182	C₂	semidirect
16. C₁₇×#3175	C₂	semidirect
17. C₁₇×#3124	C₂	semidirect
18. C₁₇×#3118	C₂	semidirect
19. C₁₇×#3107	C₂	semidirect
20. C₁₇×#3100	C₂	semidirect
21. C₁₇×#2969	C₂	semidirect
22. C₁₇×#2946	C₂	semidirect
23. C₄×C₁₇×AGL(1,ℤ/8)	C₂	semidirect
26. C₁₇×#559	C₂²	semidirect
27. C₁₇×#556	C₂²	semidirect
28. C₁₇×#556	C₂²	semidirect
30. C₁₇×#554	C₂²	semidirect
34. D₄×Q₈×C₁₇	C₂²	semidirect
35. D₄×Q₈×C₁₇	C₂²	semidirect
42. C₁₇×#546	C₂²	semidirect
43. D₄²×C₁₇	C₂²	semidirect
44. C₁₇×#542	C₂²	semidirect
45. C₁₇×#542	C₂²	semidirect
48. C₁₇×#533	C₂²	semidirect
55. C₁₇×#520	C₂²	semidirect
56. C₁₇×#518	C₂²	semidirect
58. C₂×C₄×D₄×C₁₇	C₂²	semidirect
59. C₁₇×#500	C₂²	semidirect
60. C₁₇×#500	C₂²	semidirect
61. C₁₇×#495	C₂²	semidirect
62. C₁₇×#492	C₂²	semidirect
63. C₁₇×#489	C₂²	semidirect
64. C₁₇×#489	C₂²	semidirect
65. C₁₇×#487	C₂²	semidirect
66. C₁₇×#486	C₂²	semidirect
67. C₁₇×#485	C₂²	semidirect
68. C₁₇×#485	C₂²	semidirect
69. C₁₇×#484	C₂²	semidirect
70. C₁₇×#482	C₂²	semidirect
71. C₁₇×#480	C₂²	semidirect
72. C₁₇×#480	C₂²	semidirect
73. C₁₇×#477	C₂²	semidirect
74. C₁₇×#476	C₂²	semidirect
75. C₁₇×#475	C₂²	semidirect
76. C₁₇×#474	C₂²	semidirect
77. C₁₇×#474	C₂²	semidirect
78. C₁₇×#474	C₂²	semidirect
79. C₁₇×#474	C₂²	semidirect
80. C₁₇×#474	C₂²	semidirect
81. C₁₇×#468	C₂²	semidirect
82. C₁₇×#468	C₂²	semidirect
83. C₁₇×#468	C₂²	semidirect
84. C₁₇×#468	C₂²	semidirect
85. C₁₇×#467	C₂²	semidirect
87. C₁₇×#464	C₂²	semidirect
89. C₁₇×#463	C₂²	semidirect
90. C₁₇×#463	C₂²	semidirect
91. C₁₇×#462	C₂²	semidirect
92. C₁₇×#461	C₂²	semidirect
96. C₁₇×#452	C₂²	semidirect
97. C₁₇×#450	C₂²	semidirect
100. C₁₇×#447	C₂²	semidirect
101. C₁₇×#446	C₂²	semidirect
102. C₈×Q₈×C₁₇	C₂²	semidirect
105. C₁₇×#442	C₂²	semidirect
106. C₁₇×#440	C₂²	semidirect
107. C₁₇×#440	C₂²	semidirect
108. C₁₇×#440	C₂²	semidirect
109. C₁₇×#440	C₂²	semidirect
110. C₁₇×#440	C₂²	semidirect
111. C₄×Q₁₆×C₁₇	C₂²	semidirect
112. C₄×SD₁₆×C₁₇	C₂²	semidirect
113. C₄×SD₁₆×C₁₇	C₂²	semidirect
114. C₄×SD₁₆×C₁₇	C₂²	semidirect
115. C₄×SD₁₆×C₁₇	C₂²	semidirect
119. C₄×D₈×C₁₇	C₂²	semidirect
120. C₄×D₈×C₁₇	C₂²	semidirect
121. C₁₇×#436	C₂²	semidirect
122. C₁₇×#436	C₂²	semidirect
123. C₁₇×#435	C₂²	semidirect
124. C₈×D₄×C₁₇	C₂²	semidirect
125. C₁₇×#433	C₂²	semidirect
126. C₁₇×#431	C₂²	semidirect
127. C₁₇×#428	C₂²	semidirect
128. C₁₇×#428	C₂²	semidirect
129. C₁₇×#418	C₂²	semidirect
131. C₁₇×#416	C₂²	semidirect
132. C₂×C₁₇×#102	C₂²	semidirect
133. C₁₇×#405	C₂²	semidirect
134. C₄×M₁₆×C₁₇	C₂²	semidirect
379. D₈×C₁₇	#41	semidirect
455. #61553	C₁₇	direct (N × H)
539. #3520	C₂×C₁₇	semidirect
540. #3514	C₂×C₁₇	semidirect
541. #3394	C₂×C₁₇	semidirect
542. Q₈×D₈	C₂×C₁₇	semidirect
543. #3373	C₂×C₁₇	semidirect
544. #3367	C₂×C₁₇	semidirect
545. #3357	C₂×C₁₇	semidirect
546. #3353	C₂×C₁₇	semidirect
547. #3319	C₂×C₁₇	semidirect
548. #3314	C₂×C₁₇	semidirect
549. #3302	C₂×C₁₇	semidirect
550. #3294	C₂×C₁₇	semidirect
551. #3273	C₂×C₁₇	semidirect
552. #3272	C₂×C₁₇	semidirect
553. #3182	C₂×C₁₇	semidirect
554. #3175	C₂×C₁₇	semidirect
555. #3124	C₂×C₁₇	semidirect
556. #3118	C₂×C₁₇	semidirect
557. #3107	C₂×C₁₇	semidirect
558. #3100	C₂×C₁₇	semidirect
559. #2969	C₂×C₁₇	semidirect
560. #2946	C₂×C₁₇	semidirect
561. C₄×AGL(1,ℤ/8)	C₂×C₁₇	semidirect
603. #559	C₂²×C₁₇	semidirect
604. #556	C₂²×C₁₇	semidirect
605. #556	C₂²×C₁₇	semidirect
607. #554	C₂²×C₁₇	semidirect
611. D₄×Q₈	C₂²×C₁₇	semidirect
612. D₄×Q₈	C₂²×C₁₇	semidirect
619. #546	C₂²×C₁₇	semidirect
620. D₄²	C₂²×C₁₇	semidirect
621. #542	C₂²×C₁₇	semidirect
622. #542	C₂²×C₁₇	semidirect
625. #533	C₂²×C₁₇	semidirect
632. #520	C₂²×C₁₇	semidirect
633. #518	C₂²×C₁₇	semidirect
635. C₂×C₄×D₄	C₂²×C₁₇	semidirect
636. #500	C₂²×C₁₇	semidirect
637. #500	C₂²×C₁₇	semidirect
638. #495	C₂²×C₁₇	semidirect
639. #492	C₂²×C₁₇	semidirect
640. #489	C₂²×C₁₇	semidirect
641. #489	C₂²×C₁₇	semidirect
642. #487	C₂²×C₁₇	semidirect
643. #486	C₂²×C₁₇	semidirect
644. #485	C₂²×C₁₇	semidirect
645. #485	C₂²×C₁₇	semidirect
646. #484	C₂²×C₁₇	semidirect
647. #482	C₂²×C₁₇	semidirect
648. #480	C₂²×C₁₇	semidirect
649. #480	C₂²×C₁₇	semidirect
650. #477	C₂²×C₁₇	semidirect
651. #476	C₂²×C₁₇	semidirect
652. #475	C₂²×C₁₇	semidirect
653. #474	C₂²×C₁₇	semidirect
654. #474	C₂²×C₁₇	semidirect
655. #474	C₂²×C₁₇	semidirect
656. #474	C₂²×C₁₇	semidirect
657. #474	C₂²×C₁₇	semidirect
658. #468	C₂²×C₁₇	semidirect
659. #468	C₂²×C₁₇	semidirect
660. #468	C₂²×C₁₇	semidirect
661. #468	C₂²×C₁₇	semidirect
662. #467	C₂²×C₁₇	semidirect
664. #464	C₂²×C₁₇	semidirect
666. #463	C₂²×C₁₇	semidirect
667. #463	C₂²×C₁₇	semidirect
668. #462	C₂²×C₁₇	semidirect
669. #461	C₂²×C₁₇	semidirect
673. #452	C₂²×C₁₇	semidirect
674. #450	C₂²×C₁₇	semidirect
677. #447	C₂²×C₁₇	semidirect
678. #446	C₂²×C₁₇	semidirect
679. C₈×Q₈	C₂²×C₁₇	semidirect
682. #442	C₂²×C₁₇	semidirect
683. #440	C₂²×C₁₇	semidirect
684. #440	C₂²×C₁₇	semidirect
685. #440	C₂²×C₁₇	semidirect
686. #440	C₂²×C₁₇	semidirect
687. #440	C₂²×C₁₇	semidirect
688. C₄×Q₁₆	C₂²×C₁₇	semidirect
689. C₄×SD₁₆	C₂²×C₁₇	semidirect
690. C₄×SD₁₆	C₂²×C₁₇	semidirect
691. C₄×SD₁₆	C₂²×C₁₇	semidirect
692. C₄×SD₁₆	C₂²×C₁₇	semidirect
696. C₄×D₈	C₂²×C₁₇	semidirect
697. C₄×D₈	C₂²×C₁₇	semidirect
698. #436	C₂²×C₁₇	semidirect
699. #436	C₂²×C₁₇	semidirect
700. #435	C₂²×C₁₇	semidirect
701. C₈×D₄	C₂²×C₁₇	semidirect
702. #433	C₂²×C₁₇	semidirect
703. #431	C₂²×C₁₇	semidirect
704. #428	C₂²×C₁₇	semidirect
705. #428	C₂²×C₁₇	semidirect
706. #418	C₂²×C₁₇	semidirect
708. #416	C₂²×C₁₇	semidirect
709. C₂×#102	C₂²×C₁₇	semidirect
710. #405	C₂²×C₁₇	semidirect
711. C₄×M₁₆	C₂²×C₁₇	semidirect
900. C₁₇	#61553	direct (N × H)
966. D₈	#41×C₁₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₇×#3520	2
C₁₇×#3514	2
C₁₇×#3394	2
Q₈×D₈×C₁₇	2
C₁₇×#3373	2
C₁₇×#3367	2
C₁₇×#3357	2
C₁₇×#3353	2
C₁₇×#3319	2
C₁₇×#3314	2
C₁₇×#3302	2
C₁₇×#3294	2
C₁₇×#3273	2
C₁₇×#3272	2
C₁₇×#3182	2
C₁₇×#3175	2
C₁₇×#3124	2
C₁₇×#3118	2
C₁₇×#3107	2
C₁₇×#3100	2
C₁₇×#2969	2
C₁₇×#2946	2
C₄×C₁₇×AGL(1,ℤ/8)	2
#61553	17

Subgroups — C17×#61553 #16919297

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#61553 #16919297