Subgroups — C₁₇×#34327 #16892071

Order 4352.

2584 conjugacy classes of subgroups.

The subgroup lattice has 1084 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#548	C₂	1	1	yes	maximal, characteristic
2	C₁₇×#2372	C₂	1	2	yes	maximal, complemented
3	C₁₇×#2368	C₂	1	2	yes	maximal, complemented
4	C₁₇×#2367	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#2364	C₂	1	2	yes	maximal, complemented
6	C₁₇×#2362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#2361	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₇×#2356	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#2353	C₂	1	2	yes	maximal, complemented
10	C₁₇×#2352	C₂	1	1	yes	maximal, characteristic, complemented
11	Q₈×C₂²⋊C₄×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#2339	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₇×#2337	C₂	1	2	yes	maximal, complemented
14	C₁₇×#2332	C₂	1	2	yes	maximal, complemented
15	C₁₇×#2325	C₂	1	2	yes	maximal, complemented
16	C₄×C₁₇×#124	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₁₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₁₇×#121	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₇×#2297	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₇×#2295	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×C₁₇×#391	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₇×#2275	C₂	1	2	yes	maximal, complemented
23	C₄²×D₄×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₁₇	C₂²	1	1	yes	characteristic
25	C₂³×Q₈×C₁₇	C₂²	1	1	yes	characteristic
26	C₁₇×#548	C₄	1	16	yes	complemented
27	C₂×C₁₇×#124	C₂²	1	1	yes	characteristic
28	C₂×C₁₇×#124	C₂²	1	2	yes	—
29	C₂×C₁₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₇×C₂²⋊Q₈	C₂²	1	2	yes	—
31	C₂×C₁₇×#121	C₂²	1	1	yes	characteristic
32	C₂×C₁₇×#121	C₂²	1	2	yes	—
33	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
35	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₁₇	C₂²	1	2	yes	—
39	C₂×C₄×D₄×C₁₇	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₁₇	C₂²	1	2	yes	—
44	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
45	C₂²×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
46	C₂²×C₄²×C₁₇	C₂²	1	1	yes	characteristic
47	C₂²×C₄²×C₁₇	C₂²	1	1	yes	characteristic
48	C₁₇×#391	C₂²	1	1	yes	characteristic
49	C₁₇×#391	C₂²	1	1	yes	characteristic
50	C₁₇×#391	C₂²	1	2	yes	—
51	C₁₇×#391	C₂²	1	1	yes	characteristic
52	C₁₇×#391	C₂²	1	1	yes	characteristic
53	C₁₇×#391	C₂²	1	2	yes	—
54	C₁₇×#391	C₂²	1	1	yes	characteristic
55	C₁₇×#391	C₂²	1	1	yes	characteristic
56	C₁₇×#391	C₂²	1	2	yes	—
57	C₁₇×#391	C₂²	1	2	yes	—
58	C₁₇×#390	C₂²	1	1	yes	characteristic
59	C₁₇×#390	C₂²	1	1	yes	characteristic
60	C₁₇×#389	C₂²	1	1	yes	characteristic
61	C₁₇×#389	C₂²	1	1	yes	characteristic
62	C₁₇×#388	C₂²	1	2	yes	—
63	C₁₇×#388	C₂²	1	2	yes	—
64	C₁₇×#388	C₂²	1	2	yes	—
65	C₁₇×#388	C₂²	1	2	yes	—
66	C₁₇×#388	C₂²	1	2	yes	—
67	C₁₇×#388	C₂²	1	2	yes	—
68	C₁₇×#388	C₂²	1	2	yes	—
69	C₁₇×#388	C₂²	1	2	yes	—
70	C₁₇×#388	C₂²	1	2	yes	—
71	C₁₇×#387	C₂²	1	2	yes	—
72	C₁₇×#387	C₂²	1	2	yes	—
73	C₁₇×#387	C₂²	1	2	yes	—
74	C₁₇×#387	C₂²	1	2	yes	—
75	C₁₇×#387	C₂²	1	2	yes	—
76	C₁₇×#387	C₂²	1	2	yes	—
77	C₁₇×#387	C₂²	1	2	yes	—
78	C₁₇×#386	C₂²	1	2	yes	—
79	C₁₇×#386	C₂²	1	2	yes	—
80	C₁₇×#386	C₂²	1	2	yes	—
81	C₁₇×#386	C₂²	1	2	yes	—
82	C₁₇×#386	C₂²	1	2	yes	—
83	C₁₇×#386	C₂²	1	2	yes	—
84	C₁₇×#386	C₂²	1	2	yes	—
85	C₁₇×#385	C₂²	1	2	yes	—
86	C₁₇×#385	C₂²	1	2	yes	—
87	C₁₇×#385	C₂²	1	2	yes	—
88	C₁₇×#383	C₂²	1	2	yes	—
89	C₁₇×#382	C₂²	1	1	yes	characteristic
90	C₁₇×#381	C₂²	1	2	yes	—
91	C₁₇×#380	C₂²	1	1	yes	characteristic
92	C₁₇×#380	C₂²	1	1	yes	characteristic
93	C₁₇×#380	C₂²	1	2	yes	—
94	C₄×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
95	C₄×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
96	C₄×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
97	C₄×C₄⋊C₄×C₁₇	C₂²	1	2	yes	—
98	C₄×C₄⋊C₄×C₁₇	C₂²	1	2	yes	—
99	C₄×C₄⋊C₄×C₁₇	C₂²	1	2	yes	—
100	C₄×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
101	C₄×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
102	C₄×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
103	C₄×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
104	C₄×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
105	C₄×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
106	C₄×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
107	C₄×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
108	C₄×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
109	C₄×C₂²⋊C₄×C₁₇	C₂²	1	2	yes	—
110	C₄×C₂²⋊C₄×C₁₇	C₂²	1	2	yes	—
111	C₄×C₂²⋊C₄×C₁₇	C₂²	1	2	yes	—
112	C₄×C₂²⋊C₄×C₁₇	C₂²	1	2	yes	—
113	C₄×C₂²⋊C₄×C₁₇	C₂²	1	2	yes	—
114	C₄×C₂²⋊C₄×C₁₇	C₂²	1	2	yes	—
115	C₄×C₂²⋊C₄×C₁₇	C₂²	1	2	yes	—
116	C₄×C₂²⋊C₄×C₁₇	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₁₇	C₂²	1	2	yes	—
118	C₁₇×#376	C₂²	1	2	yes	—
119	C₁₇×#376	C₂²	1	2	yes	—
120	C₂×C₁₇×#95	C₂²	1	2	yes	—
121	C₂×C₁₇×#95	C₂²	1	2	yes	—
122	C₂×C₁₇×#95	C₂²	1	2	yes	—
123	C₄³×C₁₇	C₂²	1	1	yes	characteristic
124	C₂×#41×C₁₇	—	4	2	no	—
125	C₂×#41×C₁₇	—	4	2	no	—
126	C₂×#41×C₁₇	C₂×C₄	1	8	yes	complemented
127	C₂²×Q₈×C₁₇	—	4	2	no	—
128	C₂²×Q₈×C₁₇	—	4	2	no	—
129	C₂²×Q₈×C₁₇	C₂×C₄	1	8	yes	complemented
130	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
131	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
132	C₂²×Q₈×C₁₇	C₂³	1	2	yes	—
133	C₂²×D₄×C₁₇	C₂³	1	1	yes	characteristic
134	C₂²×D₄×C₁₇	C₂³	1	2	yes	—
135	C₂²×D₄×C₁₇	C₂³	1	1	yes	characteristic
136	C₂²×D₄×C₁₇	C₂³	1	2	yes	—
137	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
143	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
144	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
145	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
146	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
147	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
148	C₁₇×#124	C₂×C₄	1	8	yes	complemented
149	C₁₇×#124	C₂×C₄	1	16	yes	complemented
150	C₁₇×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
151	C₁₇×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
152	C₁₇×#121	C₂×C₄	1	8	yes	complemented
153	C₁₇×#121	C₂×C₄	1	16	yes	complemented
154	C₄×Q₈×C₁₇	—	4	2	no	—
155	C₄×Q₈×C₁₇	—	4	2	no	—
156	C₄×Q₈×C₁₇	C₂×C₄	1	8	yes	complemented
157	C₄×D₄×C₁₇	—	2	4	no	—
158	C₄×D₄×C₁₇	—	2	8	no	—
159	C₄×D₄×C₁₇	—	2	4	no	—
160	C₄×D₄×C₁₇	—	2	8	no	—
161	C₄×D₄×C₁₇	—	4	2	no	—
162	C₄×D₄×C₁₇	—	4	2	no	—
163	C₄×D₄×C₁₇	C₂×C₄	1	8	yes	complemented
164	C₄×D₄×C₁₇	C₂×C₄	1	16	yes	complemented
165	C₁₇×#117	—	4	2	no	—
166	C₂×C₄⋊C₄×C₁₇	—	4	2	no	—
167	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
170	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
172	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
183	C₂×C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
185	C₂×C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
186	C₂×C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
195	C₂×C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
196	C₂×C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₁₇	—	4	2	no	—
202	C₂×C₄²×C₁₇	—	4	2	no	—
203	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
210	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
211	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
217	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
218	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
219	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
220	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
221	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
222	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
223	C₁₇×#95	C₂³	1	2	yes	—
224	C₁₇×#95	C₂³	1	1	yes	characteristic
225	C₁₇×#95	C₂³	1	2	yes	—
226	C₁₇×#95	C₂³	1	2	yes	—
227	C₁₇×#95	C₂³	1	2	yes	—
228	C₁₇×#95	C₂³	1	2	yes	—
229	C₁₇×#95	C₂³	1	2	yes	—
230	C₁₇×#95	C₂³	1	2	yes	—
231	C₁₇×#95	C₂³	1	2	yes	—
232	C₁₇×#95	C₂³	1	2	yes	—
233	C₁₇×#95	C₂³	1	2	yes	—
234	C₁₇×#95	C₂³	1	1	yes	characteristic
235	C₁₇×#95	C₂³	1	2	yes	—
236	C₁₇×#95	C₂³	1	2	yes	—
237	C₁₇×#95	C₂³	1	2	yes	—
238	C₁₇×#95	C₂³	1	2	yes	—
239	C₁₇×#95	C₂³	1	2	yes	—
240	C₁₇×#95	C₂³	1	1	yes	characteristic
241	C₁₇×#95	C₂³	1	1	yes	characteristic
242	C₁₇×#95	C₂³	1	1	yes	characteristic
243	C₁₇×#95	C₂³	1	1	yes	characteristic
244	C₁₇×#95	C₂³	1	2	yes	—
245	C₁₇×#95	C₂³	1	2	yes	—
246	C₁₇×#95	C₂³	1	2	yes	—
247	C₁₇×#95	C₂³	1	2	yes	—
248	C₁₇×#95	C₂³	1	2	yes	—
249	C₁₇×#95	C₂³	1	2	yes	—
250	C₂⁴×C₁₇	C₂⁴	1	1	yes	characteristic
251	C₂⁴×C₁₇	C₂⁴	1	2	yes	—
252	C₂⁴×C₁₇	C₂⁴	1	1	yes	characteristic
253	#41×C₁₇	—	4	16	no	—
254	C₂×Q₈×C₁₇	—	2	2	no	—
255	C₂×Q₈×C₁₇	—	2	2	no	—
256	C₂×Q₈×C₁₇	—	2	2	no	—
257	C₂×Q₈×C₁₇	—	2	2	no	—
258	C₂×Q₈×C₁₇	—	4	2	no	—
259	C₂×Q₈×C₁₇	—	4	2	no	—
260	C₂×Q₈×C₁₇	—	4	16	no	—
261	C₂×Q₈×C₁₇	C₂²×C₄	1	4	yes	—
262	C₂×Q₈×C₁₇	C₂²×C₄	1	4	yes	—
263	C₂×Q₈×C₁₇	C₂²×C₄	1	8	yes	—
264	C₂×D₄×C₁₇	—	2	2	no	—
265	C₂×D₄×C₁₇	—	2	4	no	—
266	C₂×D₄×C₁₇	—	2	4	no	—
267	C₂×D₄×C₁₇	—	2	2	no	—
268	C₂×D₄×C₁₇	—	2	2	no	—
269	C₂×D₄×C₁₇	—	2	2	no	—
270	C₂×D₄×C₁₇	—	4	2	no	—
271	C₂×D₄×C₁₇	—	4	2	no	—
272	C₂×D₄×C₁₇	C₂²×C₄	1	4	yes	—
273	C₂×D₄×C₁₇	C₂²×C₄	1	4	yes	—
274	C₂×D₄×C₁₇	C₂²×C₄	1	8	yes	—
275	C₂×D₄×C₁₇	C₂²×C₄	1	8	yes	—
276	C₂²×C₄×C₁₇	—	2	2	no	—
277	C₂²×C₄×C₁₇	—	2	2	no	—
278	C₂²×C₄×C₁₇	—	2	2	no	—
279	C₂²×C₄×C₁₇	—	2	2	no	—
280	C₂²×C₄×C₁₇	—	2	2	no	—
281	C₂²×C₄×C₁₇	—	2	4	no	—
282	C₂²×C₄×C₁₇	—	2	2	no	—
283	C₂²×C₄×C₁₇	—	2	2	no	—
284	C₂²×C₄×C₁₇	—	2	2	no	—
285	C₂²×C₄×C₁₇	—	2	2	no	—
286	C₂²×C₄×C₁₇	—	2	4	no	—
287	C₂²×C₄×C₁₇	—	2	4	no	—
288	C₂²×C₄×C₁₇	—	4	1	no	—
289	C₂²×C₄×C₁₇	—	4	1	no	—
290	C₂²×C₄×C₁₇	—	4	2	no	—
291	C₂²×C₄×C₁₇	—	4	2	no	—
292	C₂²×C₄×C₁₇	—	4	2	no	—
293	C₂²×C₄×C₁₇	—	4	2	no	—
294	C₂²×C₄×C₁₇	—	4	1	no	—
295	C₂²×C₄×C₁₇	—	4	1	no	—
296	C₂²×C₄×C₁₇	—	4	1	no	—
297	C₂²×C₄×C₁₇	—	4	1	no	—
298	C₂²×C₄×C₁₇	—	4	2	no	—
299	C₂²×C₄×C₁₇	—	4	2	no	—
300	C₂²×C₄×C₁₇	—	4	2	no	—
301	C₂²×C₄×C₁₇	—	4	2	no	—
302	C₂²×C₄×C₁₇	—	4	2	no	—
303	C₂²×C₄×C₁₇	—	4	2	no	—
304	C₂²×C₄×C₁₇	C₂²×C₄	1	4	yes	—
305	C₂²×C₄×C₁₇	C₂²×C₄	1	4	yes	—
306	C₂²×C₄×C₁₇	C₂²×C₄	1	8	yes	—
307	C₂²×C₄×C₁₇	C₂²×C₄	1	8	yes	—
308	C₂²×C₄×C₁₇	#41	1	4	yes	complemented
309	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
314	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
321	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
329	C₄⋊C₄×C₁₇	—	2	2	no	—
330	C₄⋊C₄×C₁₇	—	2	2	no	—
331	C₄⋊C₄×C₁₇	—	2	4	no	—
332	C₄⋊C₄×C₁₇	—	2	4	no	—
333	C₄⋊C₄×C₁₇	—	2	2	no	—
334	C₄⋊C₄×C₁₇	—	2	2	no	—
335	C₄⋊C₄×C₁₇	—	2	2	no	—
336	C₄⋊C₄×C₁₇	—	2	2	no	—
337	C₄⋊C₄×C₁₇	—	4	2	no	—
338	C₄⋊C₄×C₁₇	—	4	2	no	—
339	C₄⋊C₄×C₁₇	—	4	2	no	—
340	C₄⋊C₄×C₁₇	C₂²×C₄	1	4	yes	—
341	C₄⋊C₄×C₁₇	C₂²×C₄	1	8	yes	—
342	C₄⋊C₄×C₁₇	C₂²×C₄	1	8	yes	—
343	C₄⋊C₄×C₁₇	C₂²×C₄	1	4	yes	—
344	C₂²⋊C₄×C₁₇	—	2	2	no	—
345	C₂²⋊C₄×C₁₇	—	2	4	no	—
346	C₂²⋊C₄×C₁₇	—	2	2	no	—
347	C₂²⋊C₄×C₁₇	—	2	4	no	—
348	C₂²⋊C₄×C₁₇	—	2	4	no	—
349	C₂²⋊C₄×C₁₇	—	2	2	no	—
350	C₂²⋊C₄×C₁₇	—	2	4	no	—
351	C₂²⋊C₄×C₁₇	—	4	2	no	—
352	C₂²⋊C₄×C₁₇	—	4	2	no	—
353	C₂²⋊C₄×C₁₇	—	4	2	no	—
354	C₂²⋊C₄×C₁₇	—	4	2	no	—
355	C₂²⋊C₄×C₁₇	—	4	2	no	—
356	C₂²⋊C₄×C₁₇	C₂²×C₄	1	8	yes	—
357	C₂²⋊C₄×C₁₇	C₂²×C₄	1	8	yes	—
358	C₂²⋊C₄×C₁₇	C₂²×C₄	1	8	yes	—
359	C₂²⋊C₄×C₁₇	C₂²×C₄	1	4	yes	—
360	C₂²⋊C₄×C₁₇	C₂²×C₄	1	8	yes	—
361	C₂²⋊C₄×C₁₇	C₂²×C₄	1	4	yes	—
362	C₂²⋊C₄×C₁₇	#41	1	4	yes	complemented
363	C₄²×C₁₇	—	2	2	no	—
364	C₄²×C₁₇	—	2	4	no	—
365	C₄²×C₁₇	—	2	2	no	—
366	C₄²×C₁₇	—	2	4	no	—
367	C₄²×C₁₇	—	2	2	no	—
368	C₄²×C₁₇	—	2	2	no	—
369	C₄²×C₁₇	—	2	2	no	—
370	C₄²×C₁₇	—	2	2	no	—
371	C₄²×C₁₇	—	2	2	no	—
372	C₄²×C₁₇	—	4	1	no	—
373	C₄²×C₁₇	—	4	1	no	—
374	C₄²×C₁₇	—	4	1	no	—
375	C₄²×C₁₇	—	4	1	no	—
376	C₄²×C₁₇	—	4	1	no	—
377	C₄²×C₁₇	—	4	2	no	—
378	C₄²×C₁₇	—	4	2	no	—
379	C₄²×C₁₇	—	4	2	no	—
380	C₄²×C₁₇	—	4	2	no	—
381	C₄²×C₁₇	C₂²×C₄	1	8	yes	—
382	C₄²×C₁₇	C₂²×C₄	1	4	yes	—
383	#34327	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
384	C₂³×C₁₇	—	2	1	no	—
385	C₂³×C₁₇	—	2	1	no	—
386	C₂³×C₁₇	—	2	1	no	—
387	C₂³×C₁₇	—	2	1	no	—
388	C₂³×C₁₇	—	2	1	no	—
389	C₂³×C₁₇	—	2	2	no	—
390	C₂³×C₁₇	—	2	2	no	—
391	C₂³×C₁₇	—	2	1	no	—
392	C₂³×C₁₇	—	2	1	no	—
393	C₂³×C₁₇	—	2	2	no	—
394	C₂³×C₁₇	—	2	2	no	—
395	C₂³×C₁₇	—	2	1	no	—
396	C₂³×C₁₇	—	2	2	no	—
397	C₂³×C₁₇	—	2	1	no	—
398	C₂³×C₁₇	—	2	1	no	—
399	C₂³×C₁₇	—	2	2	no	—
400	C₂³×C₁₇	C₂³×C₄	1	2	yes	—
401	C₂³×C₁₇	C₂³×C₄	1	4	yes	—
402	C₂³×C₁₇	C₂³×C₄	1	2	yes	—
403	C₂³×C₁₇	C₂×#41	1	2	yes	—
404	C₂³×C₁₇	C₂×#41	1	2	yes	—
405	C₂³×C₁₇	C₂⁵	1	1	yes	characteristic
406	Q₈×C₁₇	—	2	8	no	—
407	Q₈×C₁₇	—	2	8	no	—
408	Q₈×C₁₇	—	4	8	no	—
409	D₄×C₁₇	—	2	8	no	—
410	D₄×C₁₇	—	2	16	no	—
411	D₄×C₁₇	—	2	8	no	—
412	D₄×C₁₇	—	4	8	no	—
413	C₂×C₄×C₁₇	—	2	2	no	—
414	C₂×C₄×C₁₇	—	2	1	no	—
415	C₂×C₄×C₁₇	—	2	1	no	—
416	C₂×C₄×C₁₇	—	2	2	no	—
417	C₂×C₄×C₁₇	—	2	1	no	—
418	C₂×C₄×C₁₇	—	2	1	no	—
419	C₂×C₄×C₁₇	—	2	1	no	—
420	C₂×C₄×C₁₇	—	2	1	no	—
421	C₂×C₄×C₁₇	—	2	1	no	—
422	C₂×C₄×C₁₇	—	2	1	no	—
423	C₂×C₄×C₁₇	—	2	1	no	—
424	C₂×C₄×C₁₇	—	2	1	no	—
425	C₂×C₄×C₁₇	—	2	1	no	—
426	C₂×C₄×C₁₇	—	2	2	no	—
427	C₂×C₄×C₁₇	—	2	2	no	—
428	C₂×C₄×C₁₇	—	2	1	no	—
429	C₂×C₄×C₁₇	—	2	2	no	—
430	C₂×C₄×C₁₇	—	2	2	no	—
431	C₂×C₄×C₁₇	—	2	1	no	—
432	C₂×C₄×C₁₇	—	2	1	no	—
433	C₂×C₄×C₁₇	—	2	1	no	—
434	C₂×C₄×C₁₇	—	2	1	no	—
435	C₂×C₄×C₁₇	—	2	1	no	—
436	C₂×C₄×C₁₇	—	2	1	no	—
437	C₂×C₄×C₁₇	—	2	8	no	—
438	C₂×C₄×C₁₇	—	2	8	no	—
439	C₂×C₄×C₁₇	—	2	1	no	—
440	C₂×C₄×C₁₇	—	2	2	no	—
441	C₂×C₄×C₁₇	—	2	2	no	—
442	C₂×C₄×C₁₇	—	2	1	no	—
443	C₂×C₄×C₁₇	—	2	2	no	—
444	C₂×C₄×C₁₇	—	2	2	no	—
445	C₂×C₄×C₁₇	—	2	1	no	—
446	C₂×C₄×C₁₇	—	2	1	no	—
447	C₂×C₄×C₁₇	—	2	1	no	—
448	C₂×C₄×C₁₇	—	2	1	no	—
449	C₂×C₄×C₁₇	—	2	2	no	—
450	C₂×C₄×C₁₇	—	2	2	no	—
451	C₂×C₄×C₁₇	—	2	2	no	—
452	C₂×C₄×C₁₇	—	2	2	no	—
453	C₂×C₄×C₁₇	—	2	1	no	—
454	C₂×C₄×C₁₇	—	2	2	no	—
455	C₂×C₄×C₁₇	—	2	1	no	—
456	C₂×C₄×C₁₇	—	2	2	no	—
457	C₂×C₄×C₁₇	—	2	2	no	—
458	C₂×C₄×C₁₇	—	2	1	no	—
459	C₂×C₄×C₁₇	—	2	2	no	—
460	C₂×C₄×C₁₇	—	4	8	no	—
461	C₂×C₄×C₁₇	—	4	8	no	—
462	C₂×C₄×C₁₇	—	4	4	no	—
463	C₂×C₄×C₁₇	—	4	4	no	—
464	C₂×C₄×C₁₇	—	4	4	no	—
465	C₂×C₄×C₁₇	—	4	4	no	—
466	C₂×C₄×C₁₇	—	8	4	no	—
467	C₂×C₄×C₁₇	—	8	4	no	—
468	C₂×C₄×C₁₇	—	8	4	no	—
469	C₂×C₄×C₁₇	C₂³×C₄	1	2	yes	—
470	C₂×C₄×C₁₇	C₂³×C₄	1	4	yes	—
471	C₂×C₄×C₁₇	C₂³×C₄	1	2	yes	—
472	C₂×C₄×C₁₇	C₂³×C₄	1	4	yes	—
473	C₂×C₄×C₁₇	C₂³×C₄	1	2	yes	—
474	C₂×C₄×C₁₇	C₂³×C₄	1	4	yes	—
475	C₂×C₄×C₁₇	C₂³×C₄	1	2	yes	—
476	C₂×C₄×C₁₇	C₂³×C₄	1	2	yes	—
477	C₂×C₄×C₁₇	C₂×#41	1	2	yes	—
478	C₂×C₄×C₁₇	C₂×#41	1	2	yes	—
479	C₂×C₄×C₁₇	C₂×#41	1	2	yes	—
480	C₂×C₄×C₁₇	C₂×#41	1	2	yes	—
481	C₂×C₄×C₁₇	H(5,𝔽₂)	1	2	yes	—
482	C₂×C₄×C₁₇	H(5,𝔽₂)	1	2	yes	—
483	C₂×C₄×C₁₇	2₋¹⁺⁴	1	2	yes	—
484	C₂×#548	C₂×C₁₇	1	1	yes	characteristic
485	#2372	C₂×C₁₇	1	2	yes	complemented
486	#2368	C₂×C₁₇	1	2	yes	complemented
487	#2367	C₂×C₁₇	1	1	yes	characteristic, complemented
488	#2364	C₂×C₁₇	1	2	yes	complemented
489	#2362	C₂×C₁₇	1	1	yes	characteristic, complemented
490	#2361	C₂×C₁₇	1	1	yes	characteristic, complemented
491	#2356	C₂×C₁₇	1	1	yes	characteristic, complemented
492	#2353	C₂×C₁₇	1	2	yes	complemented
493	#2352	C₂×C₁₇	1	1	yes	characteristic, complemented
494	Q₈×C₂²⋊C₄	C₂×C₁₇	1	1	yes	characteristic, complemented
495	#2339	C₂×C₁₇	1	1	yes	characteristic, complemented
496	#2337	C₂×C₁₇	1	2	yes	complemented
497	#2332	C₂×C₁₇	1	2	yes	complemented
498	#2325	C₂×C₁₇	1	2	yes	complemented
499	C₄×#124	C₂×C₁₇	1	1	yes	characteristic, complemented
500	C₄×C₂²⋊Q₈	C₂×C₁₇	1	1	yes	characteristic, complemented
501	C₄×#121	C₂×C₁₇	1	1	yes	characteristic, complemented
502	#2297	C₂×C₁₇	1	1	yes	characteristic, complemented
503	#2295	C₂×C₁₇	1	1	yes	characteristic, complemented
504	C₂×#391	C₂×C₁₇	1	1	yes	characteristic, complemented
505	#2275	C₂×C₁₇	1	2	yes	complemented
506	C₄²×D₄	C₂×C₁₇	1	1	yes	characteristic, complemented
507	C₂²×C₁₇	—	2	2	no	—
508	C₂²×C₁₇	—	2	2	no	—
509	C₂²×C₁₇	—	2	2	no	—
510	C₂²×C₁₇	—	2	2	no	—
511	C₂²×C₁₇	—	2	2	no	—
512	C₂²×C₁₇	—	2	2	no	—
513	C₂²×C₁₇	—	2	2	no	—
514	C₂²×C₁₇	—	2	4	no	—
515	C₂²×C₁₇	—	2	2	no	—
516	C₂²×C₁₇	—	2	4	no	—
517	C₂²×C₁₇	—	2	4	no	—
518	C₂²×C₁₇	—	2	2	no	—
519	C₂²×C₁₇	—	4	1	no	—
520	C₂²×C₁₇	—	4	2	no	—
521	C₂²×C₁₇	—	4	1	no	—
522	C₂²×C₁₇	—	4	2	no	—
523	C₂²×C₁₇	—	4	2	no	—
524	C₂²×C₁₇	—	4	1	no	—
525	C₂²×C₁₇	—	4	1	no	—
526	C₂²×C₁₇	—	4	2	no	—
527	C₂²×C₁₇	C₄×#41	1	4	yes	—
528	C₂²×C₁₇	C₂⁴×C₄	1	1	yes	characteristic
529	C₂²×C₁₇	C₂²×#41	1	1	yes	characteristic
530	C₂²×C₁₇	C₂²×#41	1	1	yes	characteristic
531	C₂²×C₁₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
532	C₂²×C₁₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
533	C₂²×C₁₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
534	C₂²×C₁₇	#585	1	1	yes	characteristic
535	C₄×C₁₇	—	2	4	no	—
536	C₄×C₁₇	—	2	2	no	—
537	C₄×C₁₇	—	2	2	no	—
538	C₄×C₁₇	—	2	2	no	—
539	C₄×C₁₇	—	2	4	no	—
540	C₄×C₁₇	—	2	4	no	—
541	C₄×C₁₇	—	2	2	no	—
542	C₄×C₁₇	—	2	2	no	—
543	C₄×C₁₇	—	2	2	no	—
544	C₄×C₁₇	—	2	2	no	—
545	C₄×C₁₇	—	2	2	no	—
546	C₄×C₁₇	—	2	2	no	—
547	C₄×C₁₇	—	4	1	no	—
548	C₄×C₁₇	—	4	2	no	—
549	C₄×C₁₇	—	4	1	no	—
550	C₄×C₁₇	—	4	2	no	—
551	C₄×C₁₇	—	4	2	no	—
552	C₄×C₁₇	—	4	2	no	—
553	C₄×C₁₇	—	4	1	no	—
554	C₄×C₁₇	#518	1	4	yes	—
555	C₂²×#41	C₂²×C₁₇	1	1	yes	characteristic
556	C₂³×Q₈	C₂²×C₁₇	1	1	yes	characteristic
557	#548	C₄×C₁₇	1	16	yes	complemented
558	C₂×#124	C₂²×C₁₇	1	2	yes	—
559	C₂×#124	C₂²×C₁₇	1	1	yes	characteristic
560	C₂×C₂²⋊Q₈	C₂²×C₁₇	1	2	yes	—
561	C₂×C₂²⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
562	C₂×#121	C₂²×C₁₇	1	2	yes	—
563	C₂×#121	C₂²×C₁₇	1	1	yes	characteristic
564	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
565	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
566	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
567	C₂×C₄×D₄	C₂²×C₁₇	1	1	yes	characteristic
568	C₂×C₄×D₄	C₂²×C₁₇	1	2	yes	—
569	C₂×C₄×D₄	C₂²×C₁₇	1	2	yes	—
570	C₂×C₄×D₄	C₂²×C₁₇	1	1	yes	characteristic
571	C₂×C₄×D₄	C₂²×C₁₇	1	1	yes	characteristic
572	C₂×C₄×D₄	C₂²×C₁₇	1	1	yes	characteristic
573	C₂×C₄×D₄	C₂²×C₁₇	1	1	yes	characteristic
574	C₂×C₄×D₄	C₂²×C₁₇	1	2	yes	—
575	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
576	C₂²×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
577	C₂²×C₄²	C₂²×C₁₇	1	1	yes	characteristic
578	C₂²×C₄²	C₂²×C₁₇	1	1	yes	characteristic
579	#391	C₂²×C₁₇	1	2	yes	—
580	#391	C₂²×C₁₇	1	2	yes	—
581	#391	C₂²×C₁₇	1	2	yes	—
582	#391	C₂²×C₁₇	1	1	yes	characteristic
583	#391	C₂²×C₁₇	1	1	yes	characteristic
584	#391	C₂²×C₁₇	1	1	yes	characteristic
585	#391	C₂²×C₁₇	1	1	yes	characteristic
586	#391	C₂²×C₁₇	1	2	yes	—
587	#391	C₂²×C₁₇	1	1	yes	characteristic
588	#391	C₂²×C₁₇	1	1	yes	characteristic
589	#390	C₂²×C₁₇	1	1	yes	characteristic
590	#390	C₂²×C₁₇	1	1	yes	characteristic
591	#389	C₂²×C₁₇	1	1	yes	characteristic
592	#389	C₂²×C₁₇	1	1	yes	characteristic
593	#388	C₂²×C₁₇	1	2	yes	—
594	#388	C₂²×C₁₇	1	2	yes	—
595	#388	C₂²×C₁₇	1	2	yes	—
596	#388	C₂²×C₁₇	1	2	yes	—
597	#388	C₂²×C₁₇	1	2	yes	—
598	#388	C₂²×C₁₇	1	2	yes	—
599	#388	C₂²×C₁₇	1	2	yes	—
600	#388	C₂²×C₁₇	1	2	yes	—
601	#388	C₂²×C₁₇	1	2	yes	—
602	#387	C₂²×C₁₇	1	2	yes	—
603	#387	C₂²×C₁₇	1	2	yes	—
604	#387	C₂²×C₁₇	1	2	yes	—
605	#387	C₂²×C₁₇	1	2	yes	—
606	#387	C₂²×C₁₇	1	2	yes	—
607	#387	C₂²×C₁₇	1	2	yes	—
608	#387	C₂²×C₁₇	1	2	yes	—
609	#386	C₂²×C₁₇	1	2	yes	—
610	#386	C₂²×C₁₇	1	2	yes	—
611	#386	C₂²×C₁₇	1	2	yes	—
612	#386	C₂²×C₁₇	1	2	yes	—
613	#386	C₂²×C₁₇	1	2	yes	—
614	#386	C₂²×C₁₇	1	2	yes	—
615	#386	C₂²×C₁₇	1	2	yes	—
616	#385	C₂²×C₁₇	1	2	yes	—
617	#385	C₂²×C₁₇	1	2	yes	—
618	#385	C₂²×C₁₇	1	2	yes	—
619	#383	C₂²×C₁₇	1	2	yes	—
620	#382	C₂²×C₁₇	1	1	yes	characteristic
621	#381	C₂²×C₁₇	1	2	yes	—
622	#380	C₂²×C₁₇	1	2	yes	—
623	#380	C₂²×C₁₇	1	1	yes	characteristic
624	#380	C₂²×C₁₇	1	1	yes	characteristic
625	C₄×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
626	C₄×C₄⋊C₄	C₂²×C₁₇	1	2	yes	—
627	C₄×C₄⋊C₄	C₂²×C₁₇	1	2	yes	—
628	C₄×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
629	C₄×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
630	C₄×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
631	C₄×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
632	C₄×C₄⋊C₄	C₂²×C₁₇	1	2	yes	—
633	C₄×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
634	C₄×C₂²⋊C₄	C₂²×C₁₇	1	2	yes	—
635	C₄×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
636	C₄×C₂²⋊C₄	C₂²×C₁₇	1	2	yes	—
637	C₄×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
638	C₄×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
639	C₄×C₂²⋊C₄	C₂²×C₁₇	1	2	yes	—
640	C₄×C₂²⋊C₄	C₂²×C₁₇	1	2	yes	—
641	C₄×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
642	C₄×C₂²⋊C₄	C₂²×C₁₇	1	2	yes	—
643	C₄×C₂²⋊C₄	C₂²×C₁₇	1	2	yes	—
644	C₄×C₂²⋊C₄	C₂²×C₁₇	1	2	yes	—
645	C₄×C₂²⋊C₄	C₂²×C₁₇	1	2	yes	—
646	C₄×C₂²⋊C₄	C₂²×C₁₇	1	2	yes	—
647	C₄×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
648	C₄×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
649	#376	C₂²×C₁₇	1	2	yes	—
650	#376	C₂²×C₁₇	1	2	yes	—
651	C₂×#95	C₂²×C₁₇	1	2	yes	—
652	C₂×#95	C₂²×C₁₇	1	2	yes	—
653	C₂×#95	C₂²×C₁₇	1	2	yes	—
654	C₄³	C₂²×C₁₇	1	1	yes	characteristic
655	C₂×C₁₇	—	2	4	no	—
656	C₂×C₁₇	—	4	2	no	—
657	C₂×C₁₇	—	4	4	no	—
658	C₂×C₁₇	C₂×C₄×#41	1	1	yes	characteristic
659	C₂×C₁₇	C₂×#518	1	1	yes	characteristic
660	C₂×C₁₇	C₄×2₋¹⁺⁴	1	1	yes	characteristic
661	C₂×C₁₇	#3505	1	1	yes	characteristic
662	C₂×C₁₇	#3511	1	1	yes	characteristic
663	C₂×C₁₇	#3514	1	1	yes	characteristic
664	C₂×C₁₇	#3520	1	1	yes	characteristic
665	C₂×#41	—	4	2	no	—
666	C₂×#41	—	4	2	no	—
667	C₂×#41	C₂×C₄×C₁₇	1	8	yes	complemented
668	C₂²×Q₈	—	4	2	no	—
669	C₂²×Q₈	—	4	2	no	—
670	C₂²×Q₈	C₂×C₄×C₁₇	1	8	yes	complemented
671	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
672	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
673	C₂²×Q₈	C₂³×C₁₇	1	2	yes	—
674	C₂²×D₄	C₂³×C₁₇	1	1	yes	characteristic
675	C₂²×D₄	C₂³×C₁₇	1	2	yes	—
676	C₂²×D₄	C₂³×C₁₇	1	1	yes	characteristic
677	C₂²×D₄	C₂³×C₁₇	1	2	yes	—
678	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
679	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
680	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
681	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
682	C₂³×C₄	C₂³×C₁₇	1	2	yes	—
683	C₂³×C₄	C₂³×C₁₇	1	2	yes	—
684	C₂³×C₄	C₂³×C₁₇	1	2	yes	—
685	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
686	C₂³×C₄	C₂³×C₁₇	1	2	yes	—
687	C₂³×C₄	C₂³×C₁₇	1	2	yes	—
688	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
689	#124	C₂×C₄×C₁₇	1	8	yes	complemented
690	#124	C₂×C₄×C₁₇	1	16	yes	complemented
691	C₂²⋊Q₈	C₂×C₄×C₁₇	1	8	yes	complemented
692	C₂²⋊Q₈	C₂×C₄×C₁₇	1	16	yes	complemented
693	#121	C₂×C₄×C₁₇	1	8	yes	complemented
694	#121	C₂×C₄×C₁₇	1	16	yes	complemented
695	C₄×Q₈	—	4	2	no	—
696	C₄×Q₈	—	4	2	no	—
697	C₄×Q₈	C₂×C₄×C₁₇	1	8	yes	complemented
698	C₄×D₄	—	2	4	no	—
699	C₄×D₄	—	2	8	no	—
700	C₄×D₄	—	2	4	no	—
701	C₄×D₄	—	2	8	no	—
702	C₄×D₄	—	4	2	no	—
703	C₄×D₄	—	4	2	no	—
704	C₄×D₄	C₂×C₄×C₁₇	1	8	yes	complemented
705	C₄×D₄	C₂×C₄×C₁₇	1	16	yes	complemented
706	#117	—	4	2	no	—
707	C₂×C₄⋊C₄	—	4	2	no	—
708	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
709	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
710	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
711	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
712	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
713	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
714	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
715	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
716	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
717	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
718	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
719	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
720	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
721	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
722	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
723	C₂×C₂²⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
724	C₂×C₂²⋊C₄	C₂³×C₁₇	1	2	yes	—
725	C₂×C₂²⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
726	C₂×C₂²⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
727	C₂×C₂²⋊C₄	C₂³×C₁₇	1	2	yes	—
728	C₂×C₂²⋊C₄	C₂³×C₁₇	1	2	yes	—
729	C₂×C₂²⋊C₄	C₂³×C₁₇	1	2	yes	—
730	C₂×C₂²⋊C₄	C₂³×C₁₇	1	2	yes	—
731	C₂×C₂²⋊C₄	C₂³×C₁₇	1	2	yes	—
732	C₂×C₂²⋊C₄	C₂³×C₁₇	1	2	yes	—
733	C₂×C₂²⋊C₄	C₂³×C₁₇	1	2	yes	—
734	C₂×C₂²⋊C₄	C₂³×C₁₇	1	2	yes	—
735	C₂×C₂²⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
736	C₂×C₂²⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
737	C₂×C₂²⋊C₄	C₂³×C₁₇	1	2	yes	—
738	C₂×C₂²⋊C₄	C₂³×C₁₇	1	2	yes	—
739	C₂×C₂²⋊C₄	C₂³×C₁₇	1	2	yes	—
740	C₂×C₂²⋊C₄	C₂³×C₁₇	1	2	yes	—
741	C₂×C₂²⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
742	C₂×C₄²	—	4	2	no	—
743	C₂×C₄²	—	4	2	no	—
744	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
745	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
746	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
747	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
748	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
749	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
750	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
751	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
752	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
753	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
754	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
755	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
756	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
757	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
758	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
759	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
760	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
761	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
762	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
763	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
764	#95	C₂³×C₁₇	1	2	yes	—
765	#95	C₂³×C₁₇	1	1	yes	characteristic
766	#95	C₂³×C₁₇	1	2	yes	—
767	#95	C₂³×C₁₇	1	2	yes	—
768	#95	C₂³×C₁₇	1	2	yes	—
769	#95	C₂³×C₁₇	1	2	yes	—
770	#95	C₂³×C₁₇	1	2	yes	—
771	#95	C₂³×C₁₇	1	2	yes	—
772	#95	C₂³×C₁₇	1	2	yes	—
773	#95	C₂³×C₁₇	1	2	yes	—
774	#95	C₂³×C₁₇	1	2	yes	—
775	#95	C₂³×C₁₇	1	1	yes	characteristic
776	#95	C₂³×C₁₇	1	2	yes	—
777	#95	C₂³×C₁₇	1	2	yes	—
778	#95	C₂³×C₁₇	1	2	yes	—
779	#95	C₂³×C₁₇	1	2	yes	—
780	#95	C₂³×C₁₇	1	2	yes	—
781	#95	C₂³×C₁₇	1	1	yes	characteristic
782	#95	C₂³×C₁₇	1	1	yes	characteristic
783	#95	C₂³×C₁₇	1	1	yes	characteristic
784	#95	C₂³×C₁₇	1	1	yes	characteristic
785	#95	C₂³×C₁₇	1	2	yes	—
786	#95	C₂³×C₁₇	1	2	yes	—
787	#95	C₂³×C₁₇	1	2	yes	—
788	#95	C₂³×C₁₇	1	2	yes	—
789	#95	C₂³×C₁₇	1	2	yes	—
790	#95	C₂³×C₁₇	1	2	yes	—
791	C₁₇	#34327	1	1	yes	characteristic, direct product factor, Sylow
792	C₂⁴	C₂⁴×C₁₇	1	1	yes	characteristic
793	C₂⁴	C₂⁴×C₁₇	1	2	yes	—
794	C₂⁴	C₂⁴×C₁₇	1	1	yes	characteristic
795	#41	—	4	16	no	—
796	C₂×Q₈	—	2	2	no	—
797	C₂×Q₈	—	2	2	no	—
798	C₂×Q₈	—	2	2	no	—
799	C₂×Q₈	—	2	2	no	—
800	C₂×Q₈	—	4	2	no	—
801	C₂×Q₈	—	4	2	no	—
802	C₂×Q₈	—	4	16	no	—
803	C₂×Q₈	C₂²×C₄×C₁₇	1	4	yes	—
804	C₂×Q₈	C₂²×C₄×C₁₇	1	4	yes	—
805	C₂×Q₈	C₂²×C₄×C₁₇	1	8	yes	—
806	C₂×D₄	—	2	2	no	—
807	C₂×D₄	—	2	4	no	—
808	C₂×D₄	—	2	4	no	—
809	C₂×D₄	—	2	2	no	—
810	C₂×D₄	—	2	2	no	—
811	C₂×D₄	—	2	2	no	—
812	C₂×D₄	—	4	2	no	—
813	C₂×D₄	—	4	2	no	—
814	C₂×D₄	C₂²×C₄×C₁₇	1	4	yes	—
815	C₂×D₄	C₂²×C₄×C₁₇	1	8	yes	—
816	C₂×D₄	C₂²×C₄×C₁₇	1	4	yes	—
817	C₂×D₄	C₂²×C₄×C₁₇	1	8	yes	—
818	C₂²×C₄	—	2	2	no	—
819	C₂²×C₄	—	2	2	no	—
820	C₂²×C₄	—	2	2	no	—
821	C₂²×C₄	—	2	2	no	—
822	C₂²×C₄	—	2	2	no	—
823	C₂²×C₄	—	2	4	no	—
824	C₂²×C₄	—	2	2	no	—
825	C₂²×C₄	—	2	2	no	—
826	C₂²×C₄	—	2	2	no	—
827	C₂²×C₄	—	2	2	no	—
828	C₂²×C₄	—	2	4	no	—
829	C₂²×C₄	—	2	4	no	—
830	C₂²×C₄	—	4	1	no	—
831	C₂²×C₄	—	4	1	no	—
832	C₂²×C₄	—	4	1	no	—
833	C₂²×C₄	—	4	1	no	—
834	C₂²×C₄	—	4	1	no	—
835	C₂²×C₄	—	4	1	no	—
836	C₂²×C₄	—	4	2	no	—
837	C₂²×C₄	—	4	2	no	—
838	C₂²×C₄	—	4	2	no	—
839	C₂²×C₄	—	4	2	no	—
840	C₂²×C₄	—	4	2	no	—
841	C₂²×C₄	—	4	2	no	—
842	C₂²×C₄	—	4	2	no	—
843	C₂²×C₄	—	4	2	no	—
844	C₂²×C₄	—	4	2	no	—
845	C₂²×C₄	—	4	2	no	—
846	C₂²×C₄	C₂²×C₄×C₁₇	1	4	yes	—
847	C₂²×C₄	C₂²×C₄×C₁₇	1	4	yes	—
848	C₂²×C₄	C₂²×C₄×C₁₇	1	8	yes	—
849	C₂²×C₄	C₂²×C₄×C₁₇	1	8	yes	—
850	C₂²×C₄	#41×C₁₇	1	4	yes	complemented
851	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
852	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
853	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
854	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
855	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
856	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
857	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
858	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
859	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
860	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
861	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
862	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
863	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
864	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
865	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
866	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
867	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
868	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
869	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
870	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
871	C₄⋊C₄	—	2	2	no	—
872	C₄⋊C₄	—	2	2	no	—
873	C₄⋊C₄	—	2	4	no	—
874	C₄⋊C₄	—	2	4	no	—
875	C₄⋊C₄	—	2	2	no	—
876	C₄⋊C₄	—	2	2	no	—
877	C₄⋊C₄	—	2	2	no	—
878	C₄⋊C₄	—	2	2	no	—
879	C₄⋊C₄	—	4	2	no	—
880	C₄⋊C₄	—	4	2	no	—
881	C₄⋊C₄	—	4	2	no	—
882	C₄⋊C₄	C₂²×C₄×C₁₇	1	4	yes	—
883	C₄⋊C₄	C₂²×C₄×C₁₇	1	8	yes	—
884	C₄⋊C₄	C₂²×C₄×C₁₇	1	8	yes	—
885	C₄⋊C₄	C₂²×C₄×C₁₇	1	4	yes	—
886	C₂²⋊C₄	—	2	2	no	—
887	C₂²⋊C₄	—	2	4	no	—
888	C₂²⋊C₄	—	2	2	no	—
889	C₂²⋊C₄	—	2	4	no	—
890	C₂²⋊C₄	—	2	4	no	—
891	C₂²⋊C₄	—	2	2	no	—
892	C₂²⋊C₄	—	2	4	no	—
893	C₂²⋊C₄	—	4	2	no	—
894	C₂²⋊C₄	—	4	2	no	—
895	C₂²⋊C₄	—	4	2	no	—
896	C₂²⋊C₄	—	4	2	no	—
897	C₂²⋊C₄	—	4	2	no	—
898	C₂²⋊C₄	C₂²×C₄×C₁₇	1	4	yes	—
899	C₂²⋊C₄	C₂²×C₄×C₁₇	1	4	yes	—
900	C₂²⋊C₄	C₂²×C₄×C₁₇	1	8	yes	—
901	C₂²⋊C₄	C₂²×C₄×C₁₇	1	8	yes	—
902	C₂²⋊C₄	C₂²×C₄×C₁₇	1	8	yes	—
903	C₂²⋊C₄	C₂²×C₄×C₁₇	1	8	yes	—
904	C₂²⋊C₄	#41×C₁₇	1	4	yes	complemented
905	C₄²	—	2	2	no	—
906	C₄²	—	2	4	no	—
907	C₄²	—	2	2	no	—
908	C₄²	—	2	4	no	—
909	C₄²	—	2	2	no	—
910	C₄²	—	2	2	no	—
911	C₄²	—	2	2	no	—
912	C₄²	—	2	2	no	—
913	C₄²	—	2	2	no	—
914	C₄²	—	4	1	no	—
915	C₄²	—	4	1	no	—
916	C₄²	—	4	1	no	—
917	C₄²	—	4	1	no	—
918	C₄²	—	4	1	no	—
919	C₄²	—	4	2	no	—
920	C₄²	—	4	2	no	—
921	C₄²	—	4	2	no	—
922	C₄²	—	4	2	no	—
923	C₄²	C₂²×C₄×C₁₇	1	8	yes	—
924	C₄²	C₂²×C₄×C₁₇	1	4	yes	—
925	C₂³	—	2	1	no	—
926	C₂³	—	2	1	no	—
927	C₂³	—	2	1	no	—
928	C₂³	—	2	1	no	—
929	C₂³	—	2	1	no	—
930	C₂³	—	2	2	no	—
931	C₂³	—	2	2	no	—
932	C₂³	—	2	1	no	—
933	C₂³	—	2	1	no	—
934	C₂³	—	2	2	no	—
935	C₂³	—	2	2	no	—
936	C₂³	—	2	1	no	—
937	C₂³	—	2	2	no	—
938	C₂³	—	2	1	no	—
939	C₂³	—	2	1	no	—
940	C₂³	—	2	2	no	—
941	C₂³	C₂³×C₄×C₁₇	1	2	yes	—
942	C₂³	C₂³×C₄×C₁₇	1	4	yes	—
943	C₂³	C₂³×C₄×C₁₇	1	2	yes	—
944	C₂³	C₂×#41×C₁₇	1	2	yes	—
945	C₂³	C₂×#41×C₁₇	1	2	yes	—
946	C₂³	C₂⁵×C₁₇	1	1	yes	characteristic
947	Q₈	—	2	8	no	—
948	Q₈	—	2	8	no	—
949	Q₈	—	4	8	no	—
950	D₄	—	2	8	no	—
951	D₄	—	2	16	no	—
952	D₄	—	2	8	no	—
953	D₄	—	4	8	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	1	no	—
956	C₂×C₄	—	2	1	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	1	no	—
960	C₂×C₄	—	2	1	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	2	1	no	—
963	C₂×C₄	—	2	1	no	—
964	C₂×C₄	—	2	1	no	—
965	C₂×C₄	—	2	1	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	2	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	1	no	—
973	C₂×C₄	—	2	1	no	—
974	C₂×C₄	—	2	1	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	2	1	no	—
978	C₂×C₄	—	2	8	no	—
979	C₂×C₄	—	2	8	no	—
980	C₂×C₄	—	2	1	no	—
981	C₂×C₄	—	2	2	no	—
982	C₂×C₄	—	2	2	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	2	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	1	no	—
990	C₂×C₄	—	2	2	no	—
991	C₂×C₄	—	2	2	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	2	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	2	2	no	—
998	C₂×C₄	—	2	2	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	4	8	no	—
1002	C₂×C₄	—	4	8	no	—
1003	C₂×C₄	—	4	4	no	—
1004	C₂×C₄	—	4	4	no	—
1005	C₂×C₄	—	4	4	no	—
1006	C₂×C₄	—	4	4	no	—
1007	C₂×C₄	—	8	4	no	—
1008	C₂×C₄	—	8	4	no	—
1009	C₂×C₄	—	8	4	no	—
1010	C₂×C₄	C₂³×C₄×C₁₇	1	2	yes	—
1011	C₂×C₄	C₂³×C₄×C₁₇	1	4	yes	—
1012	C₂×C₄	C₂³×C₄×C₁₇	1	2	yes	—
1013	C₂×C₄	C₂³×C₄×C₁₇	1	4	yes	—
1014	C₂×C₄	C₂³×C₄×C₁₇	1	2	yes	—
1015	C₂×C₄	C₂³×C₄×C₁₇	1	4	yes	—
1016	C₂×C₄	C₂³×C₄×C₁₇	1	2	yes	—
1017	C₂×C₄	C₂³×C₄×C₁₇	1	2	yes	—
1018	C₂×C₄	C₂×#41×C₁₇	1	2	yes	—
1019	C₂×C₄	C₂×#41×C₁₇	1	2	yes	—
1020	C₂×C₄	C₂×#41×C₁₇	1	2	yes	—
1021	C₂×C₄	C₂×#41×C₁₇	1	2	yes	—
1022	C₂×C₄	C₁₇×H(5,𝔽₂)	1	2	yes	—
1023	C₂×C₄	C₁₇×H(5,𝔽₂)	1	2	yes	—
1024	C₂×C₄	C₁₇×2₋¹⁺⁴	1	2	yes	—
1025	C₂²	—	2	2	no	—
1026	C₂²	—	2	2	no	—
1027	C₂²	—	2	2	no	—
1028	C₂²	—	2	2	no	—
1029	C₂²	—	2	2	no	—
1030	C₂²	—	2	2	no	—
1031	C₂²	—	2	2	no	—
1032	C₂²	—	2	4	no	—
1033	C₂²	—	2	2	no	—
1034	C₂²	—	2	4	no	—
1035	C₂²	—	2	4	no	—
1036	C₂²	—	2	2	no	—
1037	C₂²	—	4	1	no	—
1038	C₂²	—	4	2	no	—
1039	C₂²	—	4	1	no	—
1040	C₂²	—	4	2	no	—
1041	C₂²	—	4	2	no	—
1042	C₂²	—	4	1	no	—
1043	C₂²	—	4	1	no	—
1044	C₂²	—	4	2	no	—
1045	C₂²	C₄×#41×C₁₇	1	4	yes	—
1046	C₂²	C₂⁴×C₄×C₁₇	1	1	yes	characteristic
1047	C₂²	C₂²×#41×C₁₇	1	1	yes	characteristic
1048	C₂²	C₂²×#41×C₁₇	1	1	yes	characteristic
1049	C₂²	C₂×C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
1050	C₂²	C₂×C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
1051	C₂²	C₂×C₁₇×2₋¹⁺⁴	1	1	yes	characteristic
1052	C₂²	C₁₇×#585	1	1	yes	characteristic
1053	C₄	—	2	2	no	—
1054	C₄	—	2	2	no	—
1055	C₄	—	2	2	no	—
1056	C₄	—	2	2	no	—
1057	C₄	—	2	2	no	—
1058	C₄	—	2	4	no	—
1059	C₄	—	2	2	no	—
1060	C₄	—	2	2	no	—
1061	C₄	—	2	2	no	—
1062	C₄	—	2	4	no	—
1063	C₄	—	2	4	no	—
1064	C₄	—	2	2	no	—
1065	C₄	—	4	1	no	—
1066	C₄	—	4	2	no	—
1067	C₄	—	4	1	no	—
1068	C₄	—	4	2	no	—
1069	C₄	—	4	2	no	—
1070	C₄	—	4	2	no	—
1071	C₄	—	4	1	no	—
1072	C₄	C₁₇×#518	1	4	yes	—
1073	C₂	—	2	4	no	—
1074	C₂	—	4	2	no	—
1075	C₂	—	4	4	no	—
1076	C₂	C₂×C₄×#41×C₁₇	1	1	yes	characteristic
1077	C₂	C₂×C₁₇×#518	1	1	yes	characteristic
1078	C₂	C₄×C₁₇×2₋¹⁺⁴	1	1	yes	characteristic
1079	C₂	C₁₇×#3505	1	1	yes	characteristic
1080	C₂	C₁₇×#3511	1	1	yes	characteristic
1081	C₂	C₁₇×#3514	1	1	yes	characteristic
1082	C₂	C₁₇×#3520	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₇
Frattini, cosocle	C₂³	C₂⁵×C₁₇
prime radical	C₂×C₁₇×#548	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₇×#2372	C₂	semidirect
3. C₁₇×#2368	C₂	semidirect
4. C₁₇×#2367	C₂	semidirect
5. C₁₇×#2364	C₂	semidirect
6. C₁₇×#2362	C₂	semidirect
7. C₁₇×#2361	C₂	semidirect
8. C₁₇×#2356	C₂	semidirect
9. C₁₇×#2353	C₂	semidirect
10. C₁₇×#2352	C₂	semidirect
11. Q₈×C₂²⋊C₄×C₁₇	C₂	semidirect
12. C₁₇×#2339	C₂	semidirect
13. C₁₇×#2337	C₂	semidirect
14. C₁₇×#2332	C₂	semidirect
15. C₁₇×#2325	C₂	semidirect
16. C₄×C₁₇×#124	C₂	semidirect
17. C₄×C₁₇×C₂²⋊Q₈	C₂	semidirect
18. C₄×C₁₇×#121	C₂	semidirect
19. C₁₇×#2297	C₂	semidirect
20. C₁₇×#2295	C₂	semidirect
21. C₂×C₁₇×#391	C₂	semidirect
22. C₁₇×#2275	C₂	semidirect
23. C₄²×D₄×C₁₇	C₂	semidirect
26. C₁₇×#548	C₄	semidirect
126. C₂×#41×C₁₇	C₂×C₄	semidirect
129. C₂²×Q₈×C₁₇	C₂×C₄	semidirect
148. C₁₇×#124	C₂×C₄	semidirect
149. C₁₇×#124	C₂×C₄	semidirect
150. C₁₇×C₂²⋊Q₈	C₂×C₄	semidirect
151. C₁₇×C₂²⋊Q₈	C₂×C₄	semidirect
152. C₁₇×#121	C₂×C₄	semidirect
153. C₁₇×#121	C₂×C₄	semidirect
156. C₄×Q₈×C₁₇	C₂×C₄	semidirect
163. C₄×D₄×C₁₇	C₂×C₄	semidirect
164. C₄×D₄×C₁₇	C₂×C₄	semidirect
308. C₂²×C₄×C₁₇	#41	semidirect
362. C₂²⋊C₄×C₁₇	#41	semidirect
383. #34327	C₁₇	direct (N × H)
485. #2372	C₂×C₁₇	semidirect
486. #2368	C₂×C₁₇	semidirect
487. #2367	C₂×C₁₇	semidirect
488. #2364	C₂×C₁₇	semidirect
489. #2362	C₂×C₁₇	semidirect
490. #2361	C₂×C₁₇	semidirect
491. #2356	C₂×C₁₇	semidirect
492. #2353	C₂×C₁₇	semidirect
493. #2352	C₂×C₁₇	semidirect
494. Q₈×C₂²⋊C₄	C₂×C₁₇	semidirect
495. #2339	C₂×C₁₇	semidirect
496. #2337	C₂×C₁₇	semidirect
497. #2332	C₂×C₁₇	semidirect
498. #2325	C₂×C₁₇	semidirect
499. C₄×#124	C₂×C₁₇	semidirect
500. C₄×C₂²⋊Q₈	C₂×C₁₇	semidirect
501. C₄×#121	C₂×C₁₇	semidirect
502. #2297	C₂×C₁₇	semidirect
503. #2295	C₂×C₁₇	semidirect
504. C₂×#391	C₂×C₁₇	semidirect
505. #2275	C₂×C₁₇	semidirect
506. C₄²×D₄	C₂×C₁₇	semidirect
557. #548	C₄×C₁₇	semidirect
667. C₂×#41	C₂×C₄×C₁₇	semidirect
670. C₂²×Q₈	C₂×C₄×C₁₇	semidirect
689. #124	C₂×C₄×C₁₇	semidirect
690. #124	C₂×C₄×C₁₇	semidirect
691. C₂²⋊Q₈	C₂×C₄×C₁₇	semidirect
692. C₂²⋊Q₈	C₂×C₄×C₁₇	semidirect
693. #121	C₂×C₄×C₁₇	semidirect
694. #121	C₂×C₄×C₁₇	semidirect
697. C₄×Q₈	C₂×C₄×C₁₇	semidirect
704. C₄×D₄	C₂×C₄×C₁₇	semidirect
705. C₄×D₄	C₂×C₄×C₁₇	semidirect
791. C₁₇	#34327	direct (N × H)
850. C₂²×C₄	#41×C₁₇	semidirect
904. C₂²⋊C₄	#41×C₁₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₇×#548	2
C₁₇×#2372	2
C₁₇×#2368	2
C₁₇×#2367	2
C₁₇×#2364	2
C₁₇×#2362	2
C₁₇×#2361	2
C₁₇×#2356	2
C₁₇×#2353	2
C₁₇×#2352	2
Q₈×C₂²⋊C₄×C₁₇	2
C₁₇×#2339	2
C₁₇×#2337	2
C₁₇×#2332	2
C₁₇×#2325	2
C₄×C₁₇×#124	2
C₄×C₁₇×C₂²⋊Q₈	2
C₄×C₁₇×#121	2
C₁₇×#2297	2
C₁₇×#2295	2
C₂×C₁₇×#391	2
C₁₇×#2275	2
C₄²×D₄×C₁₇	2
#34327	17

Subgroups — C17×#34327 #16892071

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#34327 #16892071